Institute of Fundamental Technological Research

In view of the demand for accurate modal identification, and based on the characteristics of free vibration response, this paper introduces a new window function for Fourier Transform called the Power–Exponential window. The Power–Exponential window addresses the characteristics of free vibration response. It significantly enhances the accuracy of modal identification by improving the spectral properties of structural response. The proposed window function consists of exponential and power terms. This study focuses on the additional damping and frequency-domain differentiation introduced by the Power–Exponential window function. The exponential term weakens the boundary effect related to the time-domain truncation and suppresses the spectral leakage. Moreover, it can be interpreted in clear physical terms as providing additional damping to the signal. The power term in the window function corresponds to frequency domain differentiation, and it alleviates the spectral broadening that arises due to the additional damping. Furthermore, the analytical expression for the response spectrum confirms that the Power–Exponential window not only aligns the peak response frequency with the damped natural frequency but also establishes an explicit linear relationship between the actual structural damping ratio and the identification result from the half power bandwidth method. Both contribute to an improved accuracy and usability of certain frequency-domain modal identification methods. The influence of the Power–Exponential window parameters on modal parameter identification is analyzed, and the optimal selection principle and suggested parameter values are proposed. Finally, numerical simulations and an experimental frame model test are conducted to verify the accuracy and validity of modal parameter identification based on the Power–Exponential window.

Modal identification, Window function, Frequency domain, Spectrum leakage, Fourier Transform (FT)

Despite the prevalence of well-established and explored navigation systems, alternative localization methods are currently the focus of intensive research. This interest is driven by geopolitical challenges and increasingly sophisticated applications of mobile robots and uncrewed aerial vehicles. This study investigates the problem of real-time positioning in GPS-denied environments. Based on the mapped magnetic anomaly field and using Bayesian formalism for data fusion, the localization obtained from embedded sensors is corrected to reduce cumulative errors. The proposed method has minimal computational cost and a minimal number of tunable parameters. The paper introduces it and demonstrates its effectiveness in a laboratory study. Experimental tests, using a system equipped with an Inertial Measurement Unit, demonstrated a significant reduction in localization uncertainty. The improvement was especially notable in areas with large, smooth variations in the magnetic field. Finally, the accuracy of the method is analyzed, and its performance is compared to a particle filter.

Sensor fusion, Bayesian inference, Real-time positioning, Magnetic anomaly, Intelligent navigation system

The study investigates the problem of decentralized semi-active control of free vibration. The control scheme is designed for implementation in a modular controller architecture, where a collection of subcontrollers is employed, with each subcontroller being associated with a subsystem that represents a component of the vibrating structure. Each subcontroller uses state feedback from adjacent subsystem sensors to perform vibration suppression and energy harvesting using a switching control law. Furthermore, the assumption is made that neighbouring subcontrollers exchange information collaboratively to estimate the effects of coupling forces, achieving control efficiency comparable to that of a centralized approach. The effectiveness of the proposed approach is demonstrated on a modular suspension platform equipped with semi-active dampers and electromagnetic energy harvesters. The approach is evaluated under various free vibration scenarios, encompassing faulty measurement conditions, and is compared to passive and heuristic state-feedback control strategies. The results confirm that the proposed method attains a superior control performance, independent of the degree of decentralization in the adopted controller architecture, rendering it a viable solution for addressing large-scale semi-active control problems.

Vibration control,Energy harvesting,Adaptive control,Semi-active control,Decentralized controller

Vehicle–road coupled system is inherently time–varying, and its responses are traditionally calculated using time–domain methods which involves significant computational effort. Aiming to improve the efficiency of response calculation for the coupled system, this paper proposes a fast calculation method in frequency domain, based on the newly developed moving frequency response function (FRF). Firstly, considering the vibration characteristics of an infinitely long road, the road response is straightforwardly expressed using the road impulse response function (IRF). Subsequently, the concept of the road moving IRF is proposed and derived with respect to the moving observation points. The moving FRF is then obtained by applying Fourier transform, which allows the responses of the road moving observation points to be established in frequency domain for fast calculation under moving loads. Furthermore, by analyzing the vehicle–road coupled vibrations, based on the vehicle FRF and road moving FRF, a formula for the vehicle–road coupling force is derived in frequency domain, along with an expression for the responses at the vehicle–road contact points. Finally, the approach is illustrated in numerical simulations of vehicle–road coupled systems, and its computational efficiency and accuracy are verified through comparison with currently popular methods.

vehicle-road coupled vibration, frequency domain, frequency response function, impulse response function, numerical simulations

This paper investigates the problem of parametric identification of highly uncertain bolted connections. The unknown parameters representing stiffness of the connections are estimated using two commonly accepted methods: (1) the traditional mode matching approach and (2) a probabilistic Bayesian framework based on the maximum a posteriori (MAP) formulation. Additionally, the uncertainties of the unknown parameters are also estimated and compared for both methods. A numerical example and a real lab-scale frame structure with highly uncertain bolted connections were used in the tests. In the experimental case, the system eigenvalues (squares of the natural frequencies) and the mode shapes measured in a broad frequency range were employed. The measured mode shapes were strongly disturbed by assembly discrepancies of the bolted connections. Finally, both methods were compared in terms of computational efficiency on a large-scale FE model (31,848 degrees of freedom). Despite the sophistication of the Bayesian approach in treating the trade-off between measurement errors and expected modeling errors, the results indicate that the two tested methods yield similar values for the unknown parameters. The Bayesian approach requires numerical regularization to calculate the parameter covariance matrix, which may decrease its reliability. In contrast, the mode matching method avoids such numerical difficulties. Furthermore, the Bayesian approach requires a much larger number of iterations and a careful selection of the weighting parameters.

Mode matching, Bayesian approach, Parametric identification, Uncertain bolted connections, Parameter uncertainty, Convergence

The problem of adaptive semi-active control of transient structural vibration induced by unknown harmonic excitation is studied. The controller adaptation is attained by using a specially designed reinforcement learning algorithm that adjusts the parameters of a switching control policy to guarantee efficient dissipation of the structural energy. This algorithm relies on an efficient gradient-based sequence that accelerates the learning protocol and results in suboptimal control. The performance of this method is examined through numerical experiments for a span structure that is equipped with a semi-active device of controlled stiffness and damping parameters. The experiments cover a selection of control learning scenarios and comparisons to optimal open-loop and heuristic state-feedback control strategies. This study has confirmed that the developed method has high stabilizing performance, and the relatively low computational burden of the incorporated iterative learning algorithm facilitates its application to multi–degree-of-freedom structures.

reinforcement learning,semi-active control,optimisation,vibration suppression,bilinear system

Nowadays, consumer electronics offer computer-vision-based (CV) measurements of dynamic displacements with some trade-offs between sampling frequency, resolution and low cost of the device. This study considers a consumer-grade smartphone camera based on complementary metal-oxide semiconductor (CMOS) technology and investigates the influence of its hardware limitations on the estimation of dynamic displacements, modal parameters and stiffness parameters of bolted connections in a laboratory structure. An algorithm that maximizes the zero-normalized cross-correlation function is employed to extract the dynamic displacements. The modal parameters are identified with the stochastic subspace identification method. The stiffness parameters are identified using a model-updating technique based on modal sensitivities. The results are compared with the corresponding data obtained with accelerometers and a laser distance sensor. The CV measurement allows lower-order vibration modes to be identified with a systematic (bias) error that is nearly proportional to the vibration frequency: from 2% for the first mode (9.4 Hz) to 10% for the third mode (71.4 Hz). However, the measurement errors introduced by the smartphone camera have a significantly lower influence on the values of the identified stiffness parameters than the numbers of modes and parameters taken into account. This is due to the bias–variance trade-off. The results show that consumer-grade electronics can be used as a low-cost and easy-to-use measurement tool if lower-order modes are required.

computer vision,smartphone camera,system identification,model updating,uncertain bolted connections

EACS 2022, structural control, structural health monitoring

Computer vision (CV) methods for measurement of structural vibration are less expensive, and their application is more straightforward than methods based on sensors that measure physical quantities at particular points of a structure. However, CV methods produce significantly more measurement errors. Thus, computer vision-based structural health monitoring (CVSHM) requires appropriate methods of damage assessment that are robust with respect to highly contaminated measurement data. In this paper a complete CVSHM framework is proposed, and three damage assessment methods are tested. The first is the augmented inverse estimate (AIE), proposed by Peng et al. in 2021. This method is designed to work with highly contaminated measurement data, but it fails with a large noise provided by CV measurement. The second method, as proposed in this paper, is based on the AIE, but it introduces a weighting matrix that enhances the conditioning of the problem. The third method, also proposed in this paper, introduces additional constraints in the optimization process; these constraints ensure that the stiff ness of structural elements can only decrease. Both proposed methods perform better than the original AIE. The latter of the two proposed methods gives the best results, and it is robust with respect to the selected coefficients, as required by the algorithm.

computer vision,structural health monitoring,physics-based graphical models,augmented inverse estimate,model updating,non-negative least square method

Structural vibrations have adverse effects and can lead to catastrophic failures. Among various methods for mitigation of vibrations, the semi-active control approaches have the advantage of not requiring a large external power supply. In this paper, we propose and test a sliding mode control method for the semi-active mitigation of vibrations in frame structures. The control forces are generated in a purely dissipative manner by means of on/off type actuators that take the form of controllable structural nodes. These nodes are essentially lockable hinges, modeled as viscous dampers, which are capable of the on/off control of the transmission of bending moments between the adjacent beams. The control aim is formulated in terms of the displacement of a selected degree of freedom. A numerically effective model of such a node is developed, and the proposed control method is verified in a numerical experiment of a four-story shear structure subjected to repeated random seismic excitations. In terms of the root-mean-square displacement, the control reduced the response by 48.4-78.4% on average, depending on the number and placement of the applied actuators. The peak mean amplitude at the first mode of natural vibrations was reduced by as much as 70.6-96.5%. Such efficiency levels confirm that the proposed control method can effectively mitigate vibrations in frame structures.

semi-active control,sliding mode control,structural control,controllable nodes,on/off nodes,damping of vibrations

Accurate information about vehicle parameters and road roughness is of great significance in vehicle dynamic analysis, road driving quality, etc. In this study, a method for estimating vehicle parameters and road roughness was developed using the measured vehicle responses from field tests which is efficient, economical, and accurate. First, the full-vehicle model was introduced. Then, vehicle modal parameters were identified using the consequent free responses of a vehicle passing over bumps. Second, the expression of the vehicle frequency response function (FRF) with respect to the wheel contact point was derived from the vehicle equation of motion, and a road roughness estimation method based on the vehicle FRF was developed. Third, field tests in which the vehicle passes over bumps were performed for vehicle model identification. Finally, field tests for road roughness estimation were carried out using a calibrated vehicle to verify the effectiveness of the proposed methods.

road roughness, vehicle parameters, modal identification, frequency response function (FRF), vehicle response

Accurate vehicle parameter information plays an important role in assessing the conditions of roads and bridges, along with the corresponding maintenance. This study considered a vehicle parameter identification method based on a vehicle frequency response function (FRF). First, the vehicle FRF was deduced with respect to the displacements of the vehicle-road contact points, thereby building the relationships among the FRF, vehicle responses, and road profile in the frequency domain. Next, using the responses of vehicles passing over on-road bumps of known size, a direct estimation of the vehicle FRF was described. Then, a combination of Tikhonov regularization and a shape function method was used to update the estimated vehicle FRF by removing the singular data owing to the direct computation of the vehicle FRF. Subsequently, the modifying factors of the vehicle parameters were iteratively identified based on a sensitivity analysis of the estimated FRF to the vehicle parameters. A numerical simulation for vehicle parameter identification was performed to test the effectiveness of the proposed methods, considering a 5% Gaussian noise pollution and the influences of different driving speeds. At last, field tests of a vehicle passing over bumps were performed for the verification of vehicle parameter identification

vehicle parameter identification, frequency response function, Tikhonov regularization, shape function method

Many mode decomposition methods suffer from aliasing effects and modal distortion. This paper proposes a constrained mode decomposition (CMD) method that directly addresses these problems. The CMD is based on a linear combination of structural-free responses. The decomposed response is thus ensured to have a physical meaning and to satisfy the structural equation of motion, which improves the accuracy of mode decomposition and identification. The decomposition aim is to obtain a single-mode response. The CMD defines the corresponding natural frequency as the target frequency, while other natural frequencies are defined as constrained frequencies. The proposed method combines the measured physical responses in such a way that the constrained frequency components are selectively suppressed, while the amplitude of the target frequency component is selectively retained above a predefined level. The result is the intended single-mode free response, which can be used to clearly extract the corresponding modal parameters. For well-separated modes, the criterion for selective suppression is based on the fast Fourier transform (FFT) peak amplitude. For separation of closely spaced modes, a criterion based on FFT derivative is proposed to avoid modal distortion. The accuracy and applicability of the CMD method is tested in a numerical simulation and using a four-story lab frame structure. The experimental data are used to verify the effectiveness of the proposed CMD method and to compare it with two other widely used mode decomposition methods.

frequency-domain response, linear combination, mode decomposition, peak characteristics, structural health monitoring (SHM)

A novel criterion, based on additional virtual masses estimated in multiple tests and the Bayesian theory, is proposed in this paper to improve the efficiency and precision of damage identification. Initially, a method is proposed that uses the experimentally measured frequency-domain response and a predetermined target frequency to estimate the required additional virtual mass. The proposed mass estimation method is flexible with respect to the frequency band of excitation, which can be thus selected according to practical engineering constraints. Furthermore, a new objective function based on the residual between the theoretical and experimental virtual masses is proposed. The objective function avoids calculating the structural modes through Eigen decomposition of the structural mass and stiffness matrices, and it thus improves the computational efficiency. Thirdly, based on the theoretical frequency response function of the finite element model, explicit formulas are derived for quick calculation of the additional masses and their sensitivities with respect to damage factors. In the next step, randomness and the influence of measurement noise are considered, and the approach is formulated in the probabilistic Bayesian framework. Finally, numerical simulations of a simply supported beam, a 3D truss structure and a 3D building, as well as an experimental 3-story frame, are used to verify the effectiveness of the proposed methods. The results clearly indicate that identified damage factors are close to real values, and thus acceptable in engineering.

structural health monitoring (SHM), damage identification, additional virtual mass, sensitivity analysis, Bayesian theory

This paper investigates the mechanisms that can be used to enhance the absorption performance of poro-elastic materials in the viscous regime. It is shown that by adding small inclusions in a poro-elastic foam layer, a mass–spring effect can be introduced. If the poro-elastic material has relatively high viscous losses in the frequency range of interest, the mass–spring effect can enhance the sound absorption of the foam by introducing an additional mode in the frame and increasing its out-of-phase movement with respect to the fluid part. Moreover, different effects such as the trapped mode effect, the modified-mode effect, and the mass–spring effect are differentiated by decomposing the absorption coefficient in terms of the three energy dissipation mechanisms (viscous, thermal, and structural losses) in poro-elastic materials. The physical and geometrical parameters that can amplify or decrease the mass–spring effect are discussed. Additionally, the influence of the incidence angle on the mass–spring effect is evaluated and a discussion on tuning the inclusion to different target frequencies is given.

meta-poro-elastic material, Biot–Allard poroelastic model, mass–spring effect, viscous regime

This paper proposes and tests a semi-active method for mitigation of random and harmonic forced vibrations of frame structures. The method is based on the Prestress Accumulation-Release (PAR) strategy, and it stimulates the transfer of vibration energy from low-order into high-order natural modes of vibration. Due to their high-frequency, the target high-order modes are efficiently mitigated by standard material damping mechanisms. The control is based on local reconfiguration of nodal ability to transfer moments between adjacent beams, which might be momentarily suppressed for selected nodes: performed at the maximum of the local bending strain, such a suppression stimulates a sudden release of the accumulated strain energy into high-frequency local and global vibrations. The effectiveness of the approach is confirmed numerically and experimentally in mitigation of low-frequency vibrations, including resonance conditions, of a slender planar frame structure subjected to harmonic, sweep and random forced excitations.

damping of vibrations, smart structures, semi-active control, decentralized control, truss–frame nodes

Damage of bridge cables is mainly manifested as the decrease in cable forces. These forces are affected by the boundary conditions, cable length, cable stiffness, and cable appendages, making it hard to identify the cable forces. Based on the substructure isolation method, this study proposes an approach for cable force identification to judge cable damage by adding virtual supports to each cable so that the cables share the same length and boundary conditions. The cable forces can then be identified according to the relationship between the natural frequency and cable forces. The basic concept is that the boundary sensors are transformed into virtual supports by a linear combination of the convolution of measured responses to achieve the zero boundary response. A finite element model of a suspension bridge was used to validate the proposed method in a simulation. When the virtual supports were added to the cables, the relationship between the cable forces and the natural frequency was almost linear, and the cable damage could be successfully identified with 5% noise. Finally, the effectiveness of the proposed method was verified experimentally, and the natural frequency of the isolated cable substructure was confirmed to be a highly sensitive damage indicator.

cable damage, cable forces, natural frequency, structural health monitoring (SHM), substructure isolation method, virtual supports

In this study, a novel modal control strategy by means of semi-actively lockable joints is proposed. The control strategy allows for a directed flow of energy between vibrational modes, which makes it suitable not only for vibration attenuation purposes but also for energy scavenging driven by electromechanical energy harvesters. The proposed control strategy is an extension of the prestress-accumulation release (PAR) technique; however, it introduces also new concepts that increase the efficiency of the overall control system. Contrary to the PAR, the proposed method requires measurement of both strains in the vicinity of the semi-active joints and translational velocities that provide global information about system behavior. The latter aspect requires the control system to be organized within a hierarchical feedback architecture. The benefit from this higher complexity of the control system is its better performance compared to the PAR. The proposed semi-active modal control not only attenuates structural vibration faster, but it also achieves this goal with a smaller number of switches implemented in the joints. The effectiveness of the proposed methodology has been demonstrated on structures equipped with two lockable joints. Two practical examples have been investigated: one employs the concept of vibration-based energy harvesting for a two-story frame structure, while the second one reduces vibration of an eight-story frame structure subjected to kinematic excitation.

energy harvesting, lockable joint, modal coupling, semi-active control, vibration attenuation

Damage identification methods based on structural modal parameters are influenced by the structure form, number of measuring sensors and noise, resulting in insufficient modal data and low damage identification accuracy. The additional virtual mass method introduced in this study is based on the virtual deformation method for deriving the frequency-domain response equation of the virtual structure and identify its mode to expand the modal information of the original structure. Based on the initial condition assumption that the structural damage was sparse, the damage identification method based on sparsity with l1 and l2 norm of the damage-factor variation and the orthogonal matching pursuit (OMP) method based on the l0 norm were introduced. According to the characteristics of the additional virtual mass method, an improved OMP method (IOMP) was developed to improve the localization of optimal solution determined using the OMP method and the damage substructure selection process, analyze the damage in the entire structure globally, and improve damage identification accuracy. The accuracy and robustness of each damage identification method for multi-damage scenario were analyzed and verified through simulation and experiment.

structural health monitoring (SHM), damage identification, virtual mass, sparse constraint, IOMP method

Moving load is a fundamental loading pattern for many civil engineering structures and machines. This paper proposes and experimentally verifies an approach for indirect identification of 2D trajectories of moving loads. In line with the "structure as a sensor" paradigm, the identification is performed indirectly, based on the measured mechanical response of the structure. However, trivial solutions that directly fit the mechanical response tend to be erratic due to measurement and modeling errors. To achieve physically meaningful results, these solutions need to be numerically regularized with respect to expected geometric characteristics of trajectories. This paper proposes a respective multicriterial optimization framework based on two groups of criteria of a very different nature: mechanical (to fit the measured response of the structure) and geometric (to account for the geometric regularity of typical trajectories). The state-of-the-art multiobjective genetic algorithm NSGA-II is used to find the Pareto front. The proposed approach is verified experimentally using a lab setup consisting of a plate instrumented with strain gauges and a line-follower robot. Three trajectories are tested, and in each case the determined Pareto front is found to properly balance between the mechanical response fit and the geometric regularity of the trajectory.

structural health monitoring (SHM), moving load, trajectory identification, geometric regularity, multicriterial optimization, load identification, inverse problems, structural mechanics

This paper presents an experimental approach to assessment of semi-active vibration control systems based on the Prestress-Accumulation Release concept. The objectives are threefold: 1) to introduce an experimental validation method for control algorithms based on switchable transfer of moments, 2) to propose a method to assess experimentally the control effects on structural dynamic response under several types of excitation, and 3) to propose an approach for adequate sensor placement. A laboratory frame demonstrator equipped with dedicated semi-active nodes is used. The proposed approach is based on spectral responses and modal analysis. According to the presented findings, the investigated control is effective in reducing the vibration level while keeping the structural dynamic stiffness at a proper level. The investigation is conducted in the case of free response, as well as responses to impact loading and random excitation. The results confirm the accuracy of the adopted algorithm parameters and reveal the sensor locations that provide the best control effectiveness.

This study presents and tests a method for semi-active control of vibrations in sandwich-type beam structures. This method adapts a strategy called prestress accumulation release. The prestress accumulation release strategy is based on structural reconfiguration: it uses short time, impulsive and localised changes of actuator properties (such as stiffness or damping), which are applied to a part of the system in the moments, when its strain energy attains a local maximum. The method has been earlier applied as a global control scheme to mitigate the fundamental vibration mode of a cantilever beam (by stiffness control) and in the task of mitigating the first four modes of a frame structure (by damping control). This study proposes a prestress accumulation release strategy and tests its effectiveness for the case of a three-layered sandwich structure, with the internal layer fabricated from a material with dissipative characteristic locally controllable through the material damping coefficient. In contrast to the earlier research, the control is applied thus at the level of material characteristics instead of a discrete set of dedicated actuators. Based on the finite element method, a numerical experiment involving a passively damped, as well as prestress accumulation release-controlled, three-layered cantilever beam excited by initial displacements was performed. The effectiveness of the approach was studied for a broad range of internal layer damping parameters. The presented results revealed a high potential of the prestress accumulation release strategy in semi-active damping of vibrations of sandwich-type structures.

vibration control, sandwich structure, semi-active control, decentralised control, smart structures, constrained layer method

This paper proposes an on/off semi-active control approach for mitigation of free structural vibrations, designed for application in 2D smart frame structures. The approach is rooted in the Prestress-Accumulation Release (PAR) control strategies. The feedback signal is the global strain energy of the structure, or its approximation in the experimental setup. The actuators take the form of on/off nodes with a controllable ability to transfer moments (blockable hinges). Effectiveness of the approach is confirmed in a numerical simulation, as well as using a laboratory experimental test stand.

structural reconfiguration, structural control, semi-active control, frame structures, controllable nodes‎

Road roughness is an important factor in road network maintenance and ride quality. This paper proposes a road-roughness estimation method using the frequency response function (FRF) of a vehicle. First, based on the motion equation of the vehicle and the time shift property of the Fourier transform, the vehicle FRF with respect to the displacements of vehicle–road contact points, which describes the relationship between the measured response and road roughness, is deduced and simplified. The key to road roughness estimation is the vehicle FRF, which can be estimated directly using the measured response and the designed shape of the road based on the least-squares method. To eliminate the singular data in the estimated FRF, the shape function method was employed to improve the local curve of the FRF. Moreover, the road roughness can be estimated online by combining the estimated roughness in the overlapping time periods. Finally, a half-car model was used to numerically validate the proposed methods of road roughness estimation. Driving tests of a vehicle passing over a known-sized hump were designed to estimate the vehicle FRF, and the simulated vehicle accelerations were taken as the measured responses considering a 5% Gaussian white noise. Based on the directly estimated vehicle FRF and updated FRF, the road roughness estimation, which considers the influence of the sensors and quantity of measured data at different vehicle speeds, is discussed and compared. The results show that road roughness can be estimated using the proposed method with acceptable accuracy and robustness.

structural health monitoring, road roughness, vehicle response, frequency response function, Fourier transform

This paper proposes a computationally effective framework for load‐dependent optimal sensor placement in large‐scale civil engineering structures subjected to moving loads. Two common problems are addressed: selection of modes to be monitored and computational effectiveness. Typical sensor placement methods assume that the set of modes to be monitored is known. In practice, determination of such modes of interest is not straightforward. A practical approach is proposed that facilitates the selection of modes in a quasi‐automatic way based on the structural response at the candidate sensor locations to typical operational loads. The criterion used to assess sensor placement is based on Kammer's Effective Independence (EFI). However, in contrast to typical implementations of EFI, which treat the problem as a computationally demanding discrete problem and use greedy optimization, an approach based on convex relaxation is proposed. A notion of sensor density is applied, which converts the original combinatorial problem into a computationally tractable continuous optimization problem. The proposed framework is tested in application to a real tied‐arch railway bridge located in central Poland.

optimal sensor placement, effective independence method, Fisher information matrix

A scalable optimal control method for structural vibration mitigation is studied. The method relies on a structure's partitioning that leads to a set of dynamically interconnected subsystems. Each subsystem is operated with an individual subcontroller that collects the local state information and collaborates with the neighboring subcontrollers to estimate a short time prediction of the interconnecting forces defining the subsystem's boundary conditions. Using the extended model that represents the subsystem's dynamics together with the evolution of its boundary conditions, each subcontroller computes the control decision based on the solution to a finite‐time horizon optimal control problem. In order to cope with the changes in the boundary conditions, the optimal solution is computed repetitively according to the receding horizon scheme. The method is validated numerically for a cantilever structure equipped with actively controlled electromagnetic actuators and subjected to a variety of initial condition scenarios. The performance of the designed controller is tested by comparisons to the centralized and isolated decentralized controllers. The introduced system partitioning and distributed controller allow performing parallel computing which makes the method fully scalable and applicable to large‐scale structures. The computational complexity of the designed distributed control is studied for different settings in the modeling of the subsystem's boundary conditions.

active control, distributed control, modular structure, scalable optimization, stabilization

Adding a virtual mass is an effective method for damage identification. It can be used to obtain a large amount of information about structural response and dynamics, thereby improving the sensitivity to local damage. In the current research approaches, the virtual mass is determined first, and then the modal characteristics of the virtually modified structure are identified. This requires a wide frequency band excitation; otherwise the crucial modes of the modified structure might be out of the band, which would negatively influence the modal analysis and damage identification. This paper proposes a method that first determines the target frequency and then estimates the corresponding value of the additional virtual mass. The target frequency refers to the desired value of the natural frequency after the virtual mass has been added to the structure. The virtual masses are estimated by tuning the frequency response peaks to the target frequencies. First, two virtual mass estimation methods are proposed. One is to directly calculate the virtual mass, using the frequency‐domain response at the target frequency point only, whereas the second method estimates the mass using a least‐squares fit based on the frequency‐domain response around the target frequency. Both proposed methods utilize merely a small part of the frequency domain. Therefore, an impulse, a simple harmonic, or a narrow spectral excitation can be used for damage identification. Finally, a numerical simulation of a simply supported beam and experiments of a frame structure and a truss structure are used to verify the effectiveness of the proposed method.

damage identification, frequency response, structural health monitoring (SHM), virtual distortion method (VDM), virtual mass

In practical civil engineering, structural damage identification is difficult to implement due to the shortage of measured modal information and the influence of noise. Furthermore, typical damage identification methods generally rely on a precise Finite Element (FE) model of the monitored structure. Pointwise mass alterations of the structure can effectively improve the quantity and sensitivity of measured data, while the data fusion methods can adequately utilize various kinds of data and identification results. This paper proposes a damage identification method that requires only approximate FE models and combines the advantages of pointwise mass additions and data fusion. First, an additional mass is placed at different positions throughout the structure to collect the dynamic response and obtain the corresponding modal information. The resulting relation between natural frequencies and the position of the added mass is sensitive to local damage, and it is thus utilized to form a new objective function based on the modal assurance criterion (MAC) and l1-based sparsity promotion. The proposed objective function is mostly insensitive to global structural parameters, but remains sensitive to local damage. Several approximate FE models are then established and separately used to identify the damage of the structure, and then the Dempster-Shafer method of data fusion is applied to fuse the results from all the approximate models. Finally, fractional data fusion is proposed to combine the results according to the parametric probability distribution of the approximate FE models, which allows the natural weight of each approximate model to be determined for the fusion process. Such an approach circumvents the need for a precise FE model, which is usually not easy to obtain in real application, and thus enhances the practical applicability of the proposed method, while maintaining the damage identification accuracy. The proposed approach is verified numerically and experimentally. Numerical simulations of a simply supported beam and a long-span bridge confirm that it can be used for damage identification, including a single damage and multiple damages, with a high accuracy. Finally, an experiment of a cantilever beam is successfully performed.

structural health monitoring (SHM), damage identification, adding mass, data fusion, objective function, modal assurance criterion (MAC)

Structural damage identification plays an important role in providing effective evidence for the health monitoring of bridges in service. Due to the limitations of measurement points and lack of valid structural response data, the accurate identification of structural damage, especially for large-scale structures, remains difficult. Based on additional virtual mass, this paper presents a damage identification method for bridges using a vehicle bump as the excitation. First, general equations of virtual modifications, including virtual mass, stiffness, and damping, are derived. A theoretical method for damage identification, which is based on additional virtual mass, is formulated. The vehicle bump is analyzed, and the bump-induced excitation is estimated via a detailed analysis in four periods: separation, free-fall, contact, and coupled vibrations. The precise estimation of bump-induced excitation is then applied to a bridge. This allows the additional virtual mass method to be used, which requires knowledge of the excitations and acceleration responses in order to construct the frequency responses of a virtual structure with an additional virtual mass. Via this method, a virtual mass with substantially more weight than a typical vehicle is added to the bridge, which provides a sufficient amount of modal information for accurate damage identification while avoiding the bridge overloading problem. A numerical example of a two-span continuous beam is used to verify the proposed method, where the damage can be identified even with 15% Gaussian random noise pollution using a 1-degree of freedom (DOF) car model and 4-DOF model.

structural health monitoring, damage identification, vehicle bump, additional virtual mass, bridge

Damage identification for liquid–solid coupling structures remains a challenging topic due to the influence of liquid and the limitation of experimental conditions. Therefore, the adding mass method for damage identification is employed in this study. Adding mass to structures is an effective method for damage identification, as it can increase not only the experimental data but also the sensitivity of experimental modes to local damage. First, the fundamental theory of the adding mass method for damage identification is introduced. After that, the method of equating the liquid to the attached mass is proposed by considering the liquid–solid coupling. Finally, the effectiveness and reliability of damage identification, based on adding mass for liquid–solid coupling structures, are verified through experiments of a submerged cantilever beam and liquid storage tank.

structural health monitoring, damage identification, liquid-solid coupling, adding mass, sensitivity

This paper describes a semi-active control strategy that allows to transfer the vibration energy from an arbitrarily induced to a selected structural mode. The intended aim of the proposed control strategy is energy harvesting from structural vibrations. Another potential application is related to structural safety. In the paper, a mathematical model is first introduced to describe the phenomenon of vibrational energy transfer, and then, based on this model, an efficient semi-active control strategy is proposed. Finally, some problems related to measurement techniques are discussed. The effectiveness of the proposed methodology is demonstrated in an example of energy transfer between vibrational modes of a three-bar planar frame structure.

vibration energy, modal control, lockable joint, modal coupling

This paper proposes an approach for multicriterial optimization of modular structures with respect to their structural and geometrical properties. The approach is tested using the quickly deployable and reconfigurable modular ramp system Truss-Z intended for pedestrian traffic. The focus is on modular structures composed of a moderate number of relatively complex modules, which feature an irregular, noncuboidal geometry. Such modules can be assembled into a variety of geometrically different configurations which do not adhere to any predefined spatial grid; their global geometry can be treated as free-form and determined in situ during construction. The optimization variables represent local-level geometrical and structural properties of a single module. The Pareto front is used to balance between two kinds of objectives. The geometrical objective quantifies the ability of the modules to generate geometrically versatile global structures that are well-suited to comply with spatial constraints of real construction sites. The structural objective is formalized in analogy to the minimum weight problem with upper bound constraints imposed on the von Mises stress and the Euler buckling load ratio. A two-level optimization scheme is employed with NSGA-II at the top level and a simulated annealing with adaptive neighborhood at the lower level.

modular structures, multicriterial optimization, shape optimization, sizing optimization, NSGA-II, simulated annealing with adaptive neighborhood

This paper investigates an application of a ball-screw inerter for mitigation of impact loadings. The problem of impact absorption is to provide a minimum reaction force that optimally decelerates and eventually stops an impacting object within the available absorber stroke. It significantly differs from vibration mitigation problems which are typical application of inerters. The paper demonstrates that the optimum absorption can be achieved by fully passive means. For known values of the object mass and inerter parameters, the obtained solution is independent of the impact velocity. The optimum passive absorption is achieved by employing a variable thread lead. As a result, two force components emerge, the typical inertance-related force and a damping-like term, and sum up to provide the optimum constant deceleration force. This result is relatively unique: conventional absorbers do not provide a constant force even with complex active control systems. Finally, an optimization problem is formulated to reduce the influence of process uncertainties (range of possible mass values, unknown friction). The results are verified and analyzed in a numerical example.

This research proposes a damage identification approach for storage tanks that is based on adding virtual masses. First, the frequency response function of a structure with additional virtual masses is deduced based on the Virtual Distortion Method (VDM). Subsequently, a Finite Element (FE) model of a storage tank is established to verify the proposed method; the relation between the added virtual masses and the sensitivity of the virtual structure is analyzed to determine the optimal mass and the corresponding frequency with the highest sensitivity with respect to potential damages. Thereupon, the damage can be localized and quantified by comparing the damage factors of substructures. Finally, an experimental study is conducted on a storage tank. The results confirm that the proposed method is feasible and practical, and that it can be applied for damage identification of storage tanks.

damage identification, storage tanks, sensitivity analysis, frequency

Adding virtual masses to a structure is an efficient way to generate a large number of natural frequencies for damage identification. The influence of a virtual mass can be expressed by Virtual Distortion Method (VDM) using the response measured by a sensor at the involved point. The proper placement of the virtual masses can improve the accuracy of damage identification, therefore the problem of their optimal placement is studied in this paper. Firstly, the damage sensitivity matrix of the structure with added virtual masses is built. The Volumetric Maximum Criterion of the sensitivity matrix is established to ensure the mutual independence of measurement points for the optimization of mass placement. Secondly, a method of sensitivity analysis and error analysis is proposed to determine the values of the virtual masses, and then an improved version of the Particle Swarm Optimization (PSO) algorithm is proposed for placement optimization of the virtual masses. Finally, the optimized placement is used to identify the damage of structures. The effectiveness of the proposed method is verified by a numerical simulation of a simply supported beam structure and a truss structure.

damage identification, sensor optimization, virtual distortion method (VDM), particle swarm optimization (PSO) algorithm, sensitivity

This paper proposes a quantitative criterion for optimization of actuator placement for the Prestress–Accumulation Release (PAR) strategy of mitigation of vibrations. The PAR strategy is a recently developed semi-active control approach that relies on controlled redistribution of vibration energy into high-order modes, which are high-frequency and thus effectively dissipated by means of the natural mechanisms of material damping. The energy transfer is achieved by a controlled temporary removal of selected structural constraints. This paper considers a short-time decoupling of rotational degrees of freedom in a frame node so that the bending moments temporarily cease to be transferred between the involved beams. We propose and test a quantitative criterion for placement of such actuators. The criterion is based on local modal strain energy that can be released into high-order modes. The numerical time complexity is linear with respect to the number of actuators and potential placements, which facilitates quick analysis in case of large structures.

semi-active control, damping of vibrations, actuator placement, smart structures, prestress-accumulation release (PAR)

Damage identification based on modal parameters is an important approach in structural health monitoring (SHM). Generally, traditional objective functions used for damage identification minimize the mismatch between measured modal parameters and the parameters obtained from the finite element (FE) model. However, during the optimization process, the repetitive calculation of structural modes is usually time-consuming and inefficient, especially for large-scale structures. In this paper, an improved objective function is proposed based on certain characteristics of the peaks of the frequency response function (FRF). Traditional objective functions contain terms that quantify modal shapes and/or natural frequencies. Here, it is proposed to replace them by the FRF of the FE model, which allows the repeated full modal analysis to be avoided and thus increases the computational efficiency. Moreover, the efficiency is further enhanced by employing the substructural virtual distortion method (SVDM), which allows the frequency response of the FE model of the damaged structure to be quickly computed without the costly re-analysis of the entire damaged structure. Finally, the effectiveness of the proposed method is verified using an eight-story frame structure model under several damage cases. The damage location and extent of each substructure can be identified accurately with 5% white Gaussian noise, and the optimization efficiency is greatly improved compared with the method using a traditional objective function.

structural health monitoring (SHM), damage identification, substructure, virtual distortion method (VDM), frequency response

This paper proposes, tests numerically and verifies experimentally a decentralized control algorithm with local feedback for semi-active mitigation of free vibrations in frame structures. The algorithm aims at transferring the vibration energy of low-order, lightly-damped structural modes into high-frequency modes of vibration, where it is quickly damped by natural mechanisms of material damping. Such an approach to mitigation of vibrations, known as the prestress-accumulation release (PAR) strategy, has been earlier applied only in global control schemes to the fundamental vibration mode of a cantilever beam. In contrast, the decentralization and local feedback allows the approach proposed here to be applied to more complex frame structures and vibration patterns, where the global control ceases to be intuitively obvious. The actuators (truss–frame nodes with controllable ability to transmit moments) are essentially unblockable hinges that become unblocked only for very short time periods in order to trigger local modal transfer of energy. The paper proposes a computationally simple model of the controllable nodes, specifies the control performance measure, yields basic characteristics of the optimum control, proposes the control algorithm and then tests it in numerical and experimental examples.

Damping of vibrations, Smart structures, Semi-active control, Decentralized control, Truss-frame nodes

Truss-Z (TZ) is an Extremely Modular System (EMS). Such systems allow for creation of structurally sound free-form structures, are comprised of as few types of modules as possible, and are not constrained by a regular tessellation of space. Their objective is to create spatial structures in given environments connecting given terminals without self-intersections and obstacle-intersections. TZ is a skeletal modular system for creating free-form pedestrian ramps and ramp networks. The previous research on TZ focused on global discrete geometric optimization of the spatial configuration of modules. This paper reports on the first attempts at structural optimization of the module for a single-branch TZ. The internal topology and the sizing of module beams are subject to optimization. An important challenge is that the module is to be universal: it must be designed for the worst case scenario, as defined by the module position within a TZ branch and the geometric configuration of the branch itself. There are four variations of each module, and the number of unique TZ configurations grows exponentially with the branch length. The aim is to obtain minimum-mass modules with the von Mises equivalent stress constrained under certain design load. The resulting modules are further evaluated also in terms of the typical structural criterion of compliance.

Extremely Modular System, Truss-Z, structural optimization, modular structures, minimum mass design, frame structures

In vibration-based damage identification, a common problem is that modal information is not enough and insensitive to local damage. To solve this problem, an effective method is to increase the amount of modal information and enhance the sensitivity of the experimental data to the local damage. In this paper, a damage identification method based on additional virtual masses and Bayesian theory is proposed. First, the virtual structure with optimal additional mass and high sensitivity to local damage is determined through sensitivity analysis, and then a large number of virtual structures can be obtained by adding virtual masses; thus, a lot of modal and statistical information of virtual structures can be obtained. Second, the Bayesian theory is used to obtain the posterior probability distribution of the damage factor when structural a priori information is considered. Third, by finding the extreme value of the probability density function, the damage factor is derived based on the a priori information and the statistical information of virtual structures. Finally, the effectiveness of the proposed method is verified by numerical simulations and experiments of a 3-story frame structure. Experimental and numerical results show that the proposed method can be used to identify the damage severity of each substructure and thus damaged substructures can be localized and quantified; the error in damage factor is basically within 5%, which shows the accuracy of the proposed method. The proposed method can not only provide the structural damage localization and quantification result (i.e., the damage factor), but also the probability distribution of the damage factor; moreover, it has high sensitivity to damage and high accuracy and efficiency.

Structural health monitoring, Damage identification, Bayesian theory, Virtual distortion method (VDM), Virtual mass

A damage identification method based on additional virtual masses was proposed aiming at storage tanks' features of space-symmetry, dense lower-order modes and being insensitive to local damages. Firstly, magnitudes of additional masses were determined through sensitivity analysis of storage tanks' structural modes. Then based on the virtual deflection method (VDM), the tanks' frequency responses after attaching additional virtual masses were constructed and their natural frequencies were identified with the original structures' excitation time histories and the original structures' corresponding positions' acceleration response time histories. Furthermore, using the tanks' features of space-symmetry, their damage positions were preliminarily determined according to the distribution law of their natural frequencies after attaching virtual masses. The sensitivity analysis of the tanks' finite element model was used to solve iteratively damages' level. Finally, the tanks' finite element models were used to perform numerical simulations and correctly predict their damage locations and levels. The effectiveness of this proposed method was verified.

storage tanks, damage identification, sensitivity analysis, frequency

This paper proposes and experimentally verifies a Laplace-domain method for identification of structural modifications, which (1) unlike time-domain formulations, allows the identification to be focused on these parts of the frequency spectrum that have a high signal-to-noise ratio, and (2) unlike frequency-domain formulations, decreases the influence of numerical artifacts related to the particular choice of the FFT exponential window decay. In comparison to the time-domain approach proposed earlier, advantages of the proposed method are smaller computational cost and higher accuracy, which leads to reliable performance in more difficult identification cases. Analytical formulas for the first- and second-order sensitivity analysis are derived. The approach is based on a reduced nonparametric model, which has the form of a set of selected structural impulse responses. Such a model can be collected purely experimentally, which obviates the need for design and laborious updating of a parametric model, such as a finite element model. The approach is verified experimentally using a 26-node lab 3D truss structure and 30 identification cases of a single mass modification or two concurrent mass modifications.

structural health monitoring (SHM), nonparametric model, inverse problem, virtual distortion method (VDM), structural reanalysis, sensitivity analysis, Laplace domain

In this paper, a semi-active damping approach is used for reduction of vibrations in a laboratory drivetrain system. The considered drivetrain system is powered by an electric, asynchronous motor at the one side and loaded with a harmonically varying torque on the other side. Here, an influence of electromechanical interaction, i.e., an electromechanical coupling, between the electric motor and the mechanical system has been taken into consideration. The harmonic load signal induces torsional vibrations in the system, which in the steady-state phase of motion become periodic. The aim of the work is to determine the optimal control function for a semi-active damping element, leading to vibration reduction and considering only the steady-state phase of system motion. The optimal control is derived by using a semi-analytical approach based on the optimal control theory aided with supplementary numerical computations. The proposed methodology is fully general, and it can be directly applied to any type of a periodically oscillating system.

electric motor, electromechanical coupling, optimal control, periodic torsional vibrations, semi-active damping

A damage identification approach is presented using substructure virtual distortion method which takes the advantage of the fast structural reanalysis technique of virtual distortion method. The formulas of substructure virtual distortion method are deduced in frequency domain, and then the frequency response function of the damaged structure is constructed quickly via the superposition of the frequency response function of the intact structure and the frequency responses caused by the damage-coupling virtual distortions of the substructures. The structural damage extents are identified using the measured modal parameters. Two steps are adopted to increase the efficiency of optimization: the modals of finite element model are estimated quickly from the fast constructed frequency response function during the optimization and the primary distortions of the substructures are extracted by contribution analysis to further reduce the computational work. A six-story frame numerical model and an experiment of a cantilever beam are carried out, respectively, to verify the efficiency and accuracy of the proposed method.

damage identification, frequency domain, structural health monitoring, substructure, virtual distortion method

The surging quest for safety is a clearly visible trend in modern societies. One of the related areas of research is the design of systems protecting against heavy dynamic loads such as low and medium velocity traffic-related impacts and environmental loadings. Commonly applied passive systems are typically designed to withstand a specified, well-defined heavy load scenario, which limits their performance over any wider range of loads, including the less heavy loads that are encountered in the lifetime of a typical structure much more often than the maximum limiting loads.

Periodical vibrations are common phenomenon affecting a wide range of mechanical systems. Most frequently it affects machines designed to work in a steady-state conditions like: turbine, pump, rail vehicle, etc. In those kinds of machines it is always possible to decompose the system motion to basic average-speed constant component and oscillatory component. Usually the second term is treated as undesirable and various techniques are applied in order to minimize it as far as it is possible. These techniques refers to both the hardware selection – meaning the type of damping system (active, semi-active, passive) and the control method selection – meaning the damping system control method. Concerning the control methods, there are many algorithms available in literature devoted to transient systems. One of typical application is to use them in systems experiencing sudden, external force excitation. After destabilization of the system, caused by excitation, the role of the control algorithm is to restore the system stable position and additionally to reach the extreme of some additional criterion. Typical criterions are minimization of the time, of restoring the stable position, minimizing the consumed control energy, etc. On the other hand, considering the steady-state systems, especially based on semi-active damping elements, there are not so many control methods available.This paper focuses on developing the proper methodology for deriving the optimal control strategy of semi-active damping element, to be used in periodically vibrating mechanical system. The control strategy is developed on the basis of the Optimal Control Theory. Numerical computations are involved in order to solve the optimal control problem for the considered test system. Problem solution reveals the periodical nature of optimal control function.

Optimal Control Theory, Periodical Vibrations, Vibration Reduction

This paper proposes a frequency-domain method of substructure identification for local health monitoring using substructure isolation method (SIM). The first key step of SIM is the numerical construction of the isolated substructure, which is a virtual and independent structure that has the same physical parameters as the real substructure. Damage identification and local monitoring can be then performed using the responses of the simple isolated substructure and any of the classical methods aimed originally at global structural analysis. This paper extends the SIM to frequency domain, which allows the computational efficiency of the method to be significantly increased in comparison to time domain. The mass-spring numerical model is used to introduce the method. Two aluminum beams with the same substructure are then used in experimental verification. In both cases the method performs efficiently and accurately.

structural health monitoring (SHM), damage identification, substructuring frequency domain, boundary

The responsivity of optical fibers to refractive index can be enhanced using high-order skew rays compared with using meridional rays. Skew rays can have a much higher number of reflections with increased interaction length along the core–cladding interface, which gives rise to stronger interactions with the external medium. Reflection/transmission-type refractometric sensors based on twin-coupled-core and multimode fibers showed one/two orders of magnitude increase in responsivity with skew ray excitation. The responsivity and sensitivity for the two types are ∼2000%/RIU, ∼1400%/RIU, and 4.9×10−5  RIU, 7.0×10−5  RIU, respectively.

Fiber optics sensors, Fiber properties, Remote sensing and sensors, Propagation, Biological sensing and sensors

Structural health monitoring (SHM) has become a hot and intensively researched field in civil engineering. Thereinto, damage identification play an important role in maintaining structural integrity and safety. Many effective methods have been proposed for damage identification. However, accurate global identification of large real-world structures is not easy due to their complex and often unknown boundary conditions, nonlinear components, insensitivity of global response to localized damages, etc. Furthermore, global identification often requires lots of sensors and involves large number of unknowns. This is costly, rarely feasible in practice, and usually yields severely ill-conditioned identification problems. Substructuring approach is a possible solution: substructuring methods can focus on local small substructures; they need only a few sensors placed on the substructure and yield smaller and numerically much more feasible identification problems. This paper proposed an improved substructure method using local free response for substructure damage identification. The virtual supports are constructed by Substructure Isolation Method (SIM) using the linear combination of the substructural responses. The influence of the global errors is isolated by adding the virtual supports on the main degree of freedoms (DOFs) of the substructure. Through the correlation analysis, the substructural modes are selected and used for damage identification of the substructure. A plain model of cable stayed bridge is used for the verification of the proposed method.

structural health monitoring (SHM), damage identification, substructure, cable stayed bridge, free response

This paper presents a parameter estimation method for Structural Health Monitoring based on the combined measured structural global frequencies and structural local frequencies. First, the global test is experimented to obtain the low order modes which can reflect the global information of the structure. Secondly, the mass is added on the member of structure to increase the local dynamic characteristic and to make the member have local primary frequency, which belongs to structural local frequency and is sensitive to local parameters. Then the parameters of the structure can be optimized accurately using the combined structural global frequencies and structural local frequencies. The effectiveness and accuracy of the proposed method are verified by the experiment of a space truss.

This paper proposes a methodology on simultaneous identification of substructure excitation and damage. Structural damages are simulated by virtual distortions which are computed together with unknown excitations using the measured responses through the intact isolated substructure model; the damage extent and type is then recovered by a comparison of the virtual and actual distortions. Unknown factors are reduced greatly which allows the method to be applied on practical complex structure. The computational cost is cutoff sharply. A damaged nonlinearity aluminum beam is used in the experimental verification. Both load and damage are successfully identified.

Damage Identification, Load Identification, Structural Health Monitoring (SHM), Substructure

This paper proposes a substructure isolation method, which uses time series of measured local response for online monitoring of substructures. The proposed monitoring process consists of two key steps: construction of the isolated substructure, and its identification. The isolated substructure is an independent virtual structure, which is numerically isolated from the global structure by placing virtual supports on the interface. First, the isolated substructure is constructed by a specific linear combination of time series of its measured local responses. Then, the isolated substructure is identified using its local natural frequencies extracted from the combined responses. The substructure is assumed to be linear; the outside part of the global structure can have any characteristics. The method has no requirements on the initial state of the structure, and so the process can be carried out repetitively for online monitoring. Online isolation and monitoring is illustrated in a numerical example with a frame model, and then verified in a cantilever beam experiment.

A method for the simultaneous identification of moving vehicles and the damages of the supporting structure from measured responses is presented. A two-axle vehicle model with two degrees of freedom (DOF) is adopted. The extent of the damage and the vehicle parameters were chosen as the optimisation variables, which allow ill conditioning to be avoided and decrease the number of sensors required. The identification is performed by minimising the distance between the measured responses and the computed responses to given optimisation variables. The virtual distortion method (VDM) was used, such that the response of the damaged structure can be computed from comparison with the intact structure subjected to the same vehicle excitation and to the response-coupled virtual distortions. These are related to the optimisation variables by the system impulse response matrix and are expressed by a linear system, which allowed both types of optimisation variables to be treated in a unified way. The numerical cost is reduced by using a moving influence matrix. The adjoint variable method is used for fast sensitivity analysis. A three-span bridge numerical example is presented, where the identification was verified with 5% root mean square (RMS) measurement, and model, error whilst also considering the surface roughness of the road.

This paper presents a method for damage identification by adding virtual masses to the structure in order to increase its sensitivity to local damages. The main concept is based on the Virtual Distortion Method (VDM), which is a fast structural reanalysis method that employs virtual distortions or pseudo loads to simulate structural modifications. In this paper, the structure with an added virtual mass is called the virtual structure. First, the acceleration frequency response of the virtual structure is constructed numerically by the VDM using local dynamic data measured only by a single excitation sensor and a single acceleration sensor. Second, the value of the additional mass is determined via sensitivity analysis of the constructed frequency responses of the virtual structure with respect to damage parameters; only the natural frequencies with high sensitivity are selected. This process is repeated for all the considered placements of the virtual mass. At last, the selected natural frequencies of all the virtual structures are used together for damage identification of the real structure. A finite element (FE) model of a plane frame is used to introduce and verify the proposed method. The damage can be identified precisely and effectively even under simulated 5 % Gaussian noise pollution.

Structural health monitoring (SHM), Damage identification, Virtual distortion method (VDM), Virtual mass, Sensitivity analysis

针对土木工程中实测模态相对较少，很难进行大型结构的损伤识别的困难，提出附加虚拟支座的损伤识别方法。该方法利用约束子结构方法在结构上附加虚拟支座来增加结构形式的方法，增加识别模态的数量，从而实现结构的准确损伤识别。约束子结构方法的基本思想是通过响应的卷积组合为零将传感器转化为虚拟支座。将附加虚拟支座后的结构定义为虚拟结构，每个虚拟支座对应一个虚拟结构，那么在结构上不同位置附加虚拟支座，则可以获得多个虚拟结构的模态；联合所有虚拟结构和对应的频率即可准确快速的识别出整体结构的损伤。最后通过三层空间框架模型验证方法的有效性。

结构健康监测, 损伤识别, 约束子结构方法, 灵敏度分析, 频率

本文仅以损伤因子为优化变量，提出一种结构损伤和荷载同步识别的方法。首先通过时域荷载识别的方法将未知荷载转化为损伤因子的函数，将近似荷载作用下的结构响应和实测响应的平方距离作为目标函数，从而降低了需要识别未知参数的数目；然后在目标函数的计算过程中，利用虚拟变形法（VDM）可进行结构快速重分析的思想，快速构造给定损伤因子下系统的脉冲响应，避免每步迭代重新集装系统矩阵，并通过荷载形函数方法进一步提高荷载识别的效率；最后利用二次多项式插值近似结构每个时刻的响应方法和推导对应目标函数的梯度表达式来提高优化搜索的速度。本文利用刚架模型进行数值模拟，准确识别了结构中柱子单元刚度损伤、附加质量以及梁上的未知移动荷载，并通过一个悬臂梁试验进一步验证所提出方法的准确性和可行性。

结构健康监测, 荷载识别, 损伤识别, 虚拟变形法(VDM)

由于土木工程结构的复杂性、传感器测点的有限性以及局部损伤的不敏感性等问题，大型结构的模型修正存在一定困难。针对空间桁架结构，为克服上述问题，对其进行整体和局部的动力测试试验，然后联合实测的结构整体和局部动态信息进行模型修正：首先进行空间桁架整体的动力测试试验，获得反应整体特性的低阶模态；然后为了提高局部杆件的动态特性，在杆件上附加一定质量，获得附加质量后杆件的局部主频率，并在各类杆件中选取一定数目进行动态测试；最后联合所有实测结构整体的低阶模态和杆件的局部主频率，对空间桁架结构进行模型修正。修正后的模态参数与实测模态吻合良好，验证了方法的有效性。

结构健康监测, 模型修正, 桁架, 频率, 振型

针对大型复杂结构的整体监测常常面临测量信息不足等困难,提出只利用局部动态响应进行子结构损伤识别的约束子结构方法。约束子结构方法是通过子结构响应的卷积组合限制子结构边界的响应为零,来实现施加虚拟支座,从而将子结构分离出整体,然后利用构造的相应子结构内部响应,进行子结构损伤识别。该文利用先分段提取结构响应的子时间序列,再延时排列Toeplitz矩阵的方式,使基于不同响应的构造约束子结构的方程具有相同表达式,统一了约束子结构方法的基本思想。通过测量悬臂梁的局部动力响应,利用局部响应的时间序列实现了子结构的快速准确地分离和识别,验证了方法的实用性和有效性。

结构健康监测, 损伤识别, 子结构, 时间序列, 脉冲响应

针对大型土木结构损伤识别优化效率低的问题，提出了子结构虚拟变形方法。虚拟变形方法是一种结构
快速重分析的方法，该方法利用单元的虚拟变形模拟结构的损伤，可以在不重新建立有限元模型的情况下，快速
计算出结构参数改变后的结构响应。该文基于虚拟变形法的基本思想，对子结构的刚度矩阵进行分解和对损伤后
结构运动方程进行整理，推导出利用子结构的虚拟变形刻画损伤的方法，扩展了虚拟变形方法的适用范围；并且
给出了虚拟变形和结构响应的相关性计算公式，通过相关性分析提取主要的虚拟变形，减少参与计算的子结构虚
拟变形的数目，提高计算效率；最后利用一个五十层框架的数值仿真验证方法的有效性

This paper presents a theoretical derivation and reports on a numerical verification of a model-free method for identification of added masses in truss structures. No parametric numerical model of the monitored structure is required, so that there is no need for initial model updating and fine tuning. This is a continuation and an improvement of a previous research that resulted in a time-domain identification method, which was tested to be accurate but very time-consuming. A general methodology is briefly introduced, including the inverse problem, and a numerical verification is reported. The aim of the numerical study is to test the accuracy of the proposed method and its sensitivity to various parameters (such as simulated measurement noise and decay rate of the exponential FFT window) in a numerically controlled environment. The verification uses a finite element model of the same real structure that was tested with the time-domain version of the approach. A natural further step is a lab verification based on experimental data.

This paper presents and experimentally verifies an effective method for simultaneous identification of excitations and damages, which are two crucial factors in structural health monitoring and which often coexist in practice. The unknowns are identified by minimizing a time-domain square distance between the measured and the computed responses. Even though both damage and excitation are unknown, only damage parameters are treated here as the optimization variables: given the damage, the excitation is uniquely determined from the measured responses. As a result, all unknowns are of the same type, which allows standard optimization algorithms to be used and obviates the need for two-step procedures. The sensitivity analysis is facilitated by interpolating in each iteration the relation between structural responses and damage parameters. The numerical costs are further decreased by the fast reanalysis approach of the virtual distortion method (VDM), which is used to compute exact impulse responses of the damaged structure. The proposed methodology is verified both numerically (using a multi-span frame) and experimentally (using a cantilever beam). Stiffness-related damages and mass-related modifications are identified successfully together with the three tested types of external excitation.

Structural health monitoring, Load identification, Damage identification, Virtual distortion method (VDM)

In this paper, a model-free methodology for off-line identification of modifications of structural mass is proposed and verified experimentally. The methodology of the virtual distortion method is used: the modifications are modeled by the equivalent pseudo-loads that act in the related degrees of freedom of the unmodified structure; their influence on the response is computed using a convolution of the pseudo-loads with the experimentally obtained local impulse responses. As a result, experimentally measured data are directly used to model the response of the modified structure in a non-parametric way. The approach obviates the need for a parametric numerical model of the structure and for laborious initial updating of its parameters. Moreover, no topological information about the structure is required, besides potential locations of the modifications. The identification is stated as a problem of minimization of the discrepancy between the measured and the modeled responses of the modified structure. The formulation allows the adjoint variable method to be used for a quick first- and second-order sensitivity analysis, so that Hessian-based optimization algorithms can be used for fast convergence. The proposed methodology was experimentally verified using a 3D truss structure with 70 elements. Mass modifications in a single node and in two nodes were considered. Given the initially measured local impulse responses, a single sensor and single excitation were sufficient for the identification.

mass identification, structural health monitoring (SHM), virtual distortion method (VDM), model-free, non-parametric modeling, adjoint variable method

This paper extends and studies experimentally the substructure isolation method. Local health monitoring is significant for large and complex structures, since it costs less and can be easily implemented compared with global analysis. In contrast to other substructuring methods, in which the substructure is separated from the global structure, but coupled to it via the interface forces, the substructure isolation method isolates the substructure into an independent structure by placing virtual fixed supports on the interface. Model updating or damage identification can be then performed locally and precisely using the constructed responses of the isolated substructure and any of the existing methods aimed originally at global identification. This paper discusses and further extends the approach to improve its performance in real applications. A new type of virtual interface support (free support) is proposed for isolation. Relaxation of the original requirements concerning the type and placement of the isolating excitations is discussed. Previously, the method relied on the linearity of the global structure; here, only the substructure is required to be linear, the global structure besides the substructure can be non-linear, yielding, changing or unknown. A damaged cantilever beam is used in the experimental study. Up to three modified global structures with the same substructure are used to test the robustness of the isolation with respect to unknown modifications and non-linearities of the outside structure. Two typical global health monitoring methods are applied at the substructural level. A comparison with the results obtained from a generic substructure separation method is offered.

Structural Health Monitoring (SHM), substructure isolation method, substructural identification, virtual distortion method (VDM), local monitoring, virtual supports

针对大型复杂结构的整体监测常常面临测量信息不足等困难,提出只利用局部动态响应进行子结构损伤识别的局部主频率方法.子结构的局部主频率指：如果整体模态中含有以局部子结构位移为主的模态,即等价于在局部激励作用下,整体结构的振动主要体现为子结构的振动,并且主要以这阶局部模态振动为主,那么对应的该阶频率即定义为子结构的局部主频率.局部主频率主要反映子结构的局部特性,对子结构损伤的灵敏度高,所以只利用局部主频率就可以识别子结构.当子结构特征不明显时,提出通过附加质量使子结构具有局部主频率的有效方法.该文进行了大型空间桁架的局部动力测试试验,试验中通过附加质量使杆件子结构具有局部主频率,并能准确地识别出杆件损伤的位置和程度.

结构健康监测, 损伤识别, 子结构, 模态分析, 频率响应

针对结构中同时存在未知损伤和荷载的情况，基于虚拟变形法(VDM)发展一种两者共同识别的时域方法。VDM方法利用虚拟变形模拟结构损伤，可快速计算模型改变后的响应。该文首先结合有限元理论把VDM方法拓展到具有多个单元变形的结构中；然后考虑结构存在未知荷载时，利用未损伤理论模型同时识别荷载和虚拟变形，继而由虚拟变形和单元实际变形的关系来识别判断损伤类型和识别损伤大小；最后通过一个悬臂梁的试验进行方法验证，试验中未知荷载和损伤(包括其类型和大小)均能够被有效识别，并利用提出的移动时间窗和荷载形函数方法实现损伤与荷载的在线识别。

结构健康监测, 虚拟变形法(VDM), 荷载识别, 损伤识别, 荷载形函数

基于虚拟变形(VDM)方法中移动动态影响矩阵的概念,利用双自由度质量-弹簧阻尼模型模拟移动车辆,系统推导和阐述了车-桥耦合系统中粗糙路面上移动体参数的识别方法。以移动体参数的修正因子为优化变量,通过最小化桥体结构实测响应和计算响应的平方距离进行识别,识别精度高,对噪声鲁棒性强,且较少的传感器就能识别多个移动体参数。利用移动动态影响矩阵,每步优化中无需时时重构系统参数矩阵,计算效率高。利用一个三跨连续梁模型验证该方法的有效性,在5%的噪声影响下,利用一个传感器可以准确地识别多个移动体参数和移动荷载。此外,通过比较平坦路面与粗糙路面上的移动体参数的识别方法和结果,结合车体参数的灵敏度分析,说明了路面粗糙度、移动体参数对结构响应的影响及不同情况下参数识别中优化变量的选取原则。

结构健康监测, 移动车辆(荷载)识别, 虚拟变形法(VDM), 影响矩阵, 粗糙路面

This paper describes an effective method of substructure isolation for local structural health monitoring (SHM). In practice, often only a small part of a larger structure is critical and needs monitoring. However, typical low-frequency SHM methods require modeling and analysis of the global structure, which can be costly, time-consuming and error-prone. The proposed approach is based on the virtual distortion method (VDM) and uses force distortions to model fixed supports in the boundary nodes to isolate the considered substructure from influences of the rest of the structure. Therefore, given an excitation of the substructure and the measured response of the global structure, the response of the substructure treated as fixed supported can be computed. Local-only monitoring is then possible using virtually any of the existing methods. However, consistently with the isolation methodology, strain distortions are used here for modeling of damages of the isolated substructure. The discrete adjoint variable method is used for the first time within the framework of the VDM in order to perform fast analytical sensitivity analysis and improve the computational effectiveness of the damage identification by one order of magnitude. A numerical example of a frame-truss with 5 and 10% noise level and an experiment of a cantilever beam are presented to validate the isolation methodology.

substructure isolation, damage identification, virtual distortion method (VDM), structural health monitoring, adjoint variable method

在动态荷载识别中常常由于矩阵的病态性影响识别的精度，利用有限元理论中的形函数逼近荷载曲线，将识别离散的荷载历程转化为计算有限的形函数权重，从而显著改善反卷积法识别荷载中存在的采样时间长或采样频率高时数值求解困难的问题；并能改善反问题的病态性，提高对噪音的鲁棒性。一个连续梁的数值算例比较验证了该方法在5%的高斯噪声影响下能精确地识别未知荷载。悬臂梁试验中，通过实测的结构动态响应，在移动时间窗内利用荷载形函数方法可以实现激励的在线识别。

结构健康监测, 荷载识别, 在线识别, 反卷积法, 形函数

利用双自由度质量-弹簧阻尼模型模拟移动车辆, 并基于虚拟变形(VDM)方法的结构快速重分 析思想, 提出一种车-桥耦合系统的移动质量快速识别的有效方法. 该方法以双自由度车体模 型的质量为变量, 通过最小化桥体结构实测响应和计算响应的平方距离来识别移动质量 (载荷), 避免了识别载荷时常遇到的病态问题, 对噪声鲁棒性强, 且需要传感器信息少. 每步优化 中, 利用在VDM方法基础上提出的移动动态影响矩阵概念, 无需时时重构车-桥耦合系统的时 变系统参数矩阵, 显著提高了计算效率. 利用数值框架梁模型, 通过比较不同车辆简化模型 对移动体质量及等效移动载荷的识别效果, 验证了该方法的可行性和有效性, 即使在5% 的噪声影响下, 利用一个传感器可以准确地识别多个移动体的质量.

结构健康监测, 移动车辆识别, 结构重分析, 虚拟变形法, 影响矩阵

Load reconstruction and damage identification are crucial problems in structural health monitoring. However, it seems there is not much investigation on identification of coexistent load and damage, although in practice they usually exist together. This paper presents a methodology to solve this problem based on the Virtual Distortion Method. A damaged structure is modeled by an equivalent intact structure subjected to the same loads and to virtual distortions which model the damages. The measured structural response is used to identify the loads, the distortions and to recover the stress-strain relationship of the damaged elements. This way both the damage type and extent are identified. The approach can be used off-line and online by repetitive applications in a moving time window. A numerical experiment of a truss with 5% measurement error validates that the two tested damage types (constant stiffness reduction and breathing crack) can be identified along with the loads.

Structural health monitoring, Load identification, Damage identification, Virtual Distortion Method (VDM)

A method for simultaneous identification of moving masses and damages of the supporting structure from measured responses is presented. The interaction forces between the masses and the structure are used as excitation. Masses and damage extents are used as the optimization variables; compared to the approaches based on identification of the interaction forces, it allows ill-conditioning to be avoided and decreases the number of required sensors. The virtual distortion method is used; the damaged structure is modeled by the intact structure subjected to response-coupled virtual distortions and moving forces. These are related to the optimization variables via a linear system, which allows the optimization variables of both kinds to be treated in a unified way. A moving dynamic influence matrix is introduced to reduce the numerical costs. The adjoint variable method is used for fast sensitivity analysis. A numerical experiment of a three-span beam with 10% rms measurement error and three types of model errors is presented.

Moving load identification, Damage identification, Mass identification, Virtual distortion method (VDM), Structural health monitoring (SHM)

在车-桥耦合系统的移动质量（荷载）识别反问题中,识别移动质量会面临重构系统、优化缓慢的问题;而若直接识别移动荷载常常会遇到病态问题且对噪音敏感。针对这些缺陷,根据虚拟变形法（VDM）的结构快速重分析思想,提出移动动态影响矩阵,实现利用较少的传感器即可快速而准确地识别移动质量（荷载）。以移动质量为优化变量,避免了识别荷载常遇到的病态问题,对噪音鲁棒性强;且需要传感器信息少。每步优化中,利用移动动态影响矩阵,无需时时重构车-桥耦合系统的时变系统参数矩阵,优化效率高。VDM方法的思想是将实际结构的响应计算转化为初始结构模型在相同外荷载作用下的响应,与在结构模型发生改变的位置施加相关的虚拟变形或虚拟力引起的响应的线性叠加。通过简支梁模型和框架梁模型验证了该方法的可行性和有效性,即使在5%的噪声影响下,利用一个传感器就可以很好地识别多个移动质量。

结构健康监测, 结构重分析, 影响矩阵

This paper considers off-line identification of spatial and temporal characteristics of a dynamic load, and is focused on the case of a limited number of sensors. Both elastic and elasto-plastic structural behaviours are taken into account. The identification is performed off-line, based on optimisation of modelled local structural responses, and—in the case of limited number of sensors—identifies an observationally equivalent load, which in a given sense optimally approximates the actual load. Compared to previous researches this approach allows to identify general dynamic loads of unknown locations, including multiple impacts and moving loads, and gives more insight into the identification process by distinguishing between the reconstructible and unreconstructible load components. Additionally, the problem of optimum sensor location is discussed.

Load identification, Inverse dynamics, Elasto-plastic structures, Black box, Forensic engineering

An adaptive landing gear is a landing gear (LG) capable of active adaptation to particular landing conditions by means of controlled hydraulic force. The objective of the adaptive control is to mitigate the peak force transferred to the aircraft structure during touch-down, and thus to limit the structural fatigue factor. This paper investigates the ultimate limits for improvement due to various strategies of active control. Five strategies are proposed and investigated numerically using a~validated model of a real, passive landing gear as a reference. Potential for improvement is estimated statistically in terms of the mean and median (significant) peak strut forces as well as in terms of the extended safe sinking velocity range. Three control strategies are verified experimentally using a laboratory test stand.

Adaptive landing gear, adaptive impact absorption, shock absorber, load mitigation

This paper present and validates experimentally a model-less methodology for off-line identification of modifications of nodal masses. The proposed approach is entirely based on experimentally measured data; hence no numerical modeling and tedious fine-tuning of the model are necessary. The influence of the added mass is modeled using virtual distortion forces and experimentally obtained system transfer matrices. The identification amounts to solving an optimization problem of minimizing the mean square distance between measured and modeled structural responses, the latter is based on previously recorded responses of the unaffected structure.

mass identification, model-less SHM, virtual distortion method (VDM), inverse dynamics

In the paper active control of transient torsional vibrations induced by the electric motor during run-ups of the radial compressor drive system is performed by means of couplings with the magneto-rheological fluid. The main purpose of these studies is a minimisation of vibration amplitudes in order to increase the fatigue durability of the most responsible elements. The theoretical investigations are based on a hybrid structural model of the vibrating mechanical system and sensitivity analysis of the response with respect to the damping characteristics of the control couplings.

active control, transient vibrations, drive system, electric motor

The paper presents a novel methodology for robust post-accident reconstruction of spatial and temporal characteristics of the load. The methodology is based on analysis of local structural response, and identifies an observationally equivalent load, which in a given sense optimally approximates the real load. Compared to previous researches this approach allows to use a limited number of sensors to reconstruct general dynamic loads of unknown location including multiple impacts and moving loads. Additionally, the problem of optimum sensor location is studied.

impact identification, inverse dynamics, smart systems, structural health monitoring

This contribution considers the problem of topology optimization of modular structures. A bionic trunk-like robotic “Arm-Z” manipulator is considered. The manipulator is modular, that is, it is composed of a sequence of identical modules. In geometric terms, each module is essentially an obliquely cut section of an elliptical pipe, so in the cutting plane it forms a circle. With respect to the previous module, it has a single degree of freedom: the relative twist. Therefore, the total number of the degrees of freedom of the entire manipulator equals the number of its modules. Such a manipulator belongs to the family of Extremely Modular Systems. The advantages of such systems are the economization (due to the possible mass production of modules) and robustness (replacement of a failed module instead of a complex repair).

Topology optimization, Modular manipulator, Multiple loadings, Geometric transformations, Kinematics, Stress constraints.

This contribution applies the machine learning technique of reinforcement learning for simultaneous damage detection and control of structures. The proposed system consists of two components. The control component is responsible for semi-active mitigation of vibrations. The control law is determined experimentally in a trial-and-error interaction with a simulated environment. The process is data-driven: the control agent iteratively improves its control law based on the observed results of past control actions. The robustness relies on the accuracy of the structural model used for training. The control efficiency can decrease if the physical structure is damaged and diverges from the model, that is, when effective control may be most required. Thus, the second component of the proposed system monitors the structure to detect damages and inform the control component. The approach is tested in a numerical experiment of a shear-building under random seismic-type excitation. A semi-active tuned mass damper (TMD) is used as an actuator, and a classical TMD serves as a reference.

semi-active control, structural control, structural monitoring, reinforcement learning, machine learning

Classical approaches to attenuation of vibrations usually aim at dissipation or absorption of the vibration energy in especially designed devices mounted to the structure. A less common approach but recognised as very effective is to induce mechanisms of transferring the vibration energy associated with low-frequency modes into higher-order vibration modes, where it is quickly dissipated by material damping (in structural volume). In the present work, a novel semi-active modal control methodology is proposed for precise control of mechanical energy transfer between vibration modes by means of lockable joints. Moreover, this control strategy is well-suited also for energy harvesting purposes. Energy of the currently induced vibration modes can be transferred into a preselected structural vibration mode that is tuned with an energy harvester. The proposed control strategy is verified numerically, whereas its experimental validation is shown in the accompanying article within the present proceedings.

In this work an experimental study is presented aiming at demonstration of a controlled modal energy transfer concept in frame structures equipped with semi-active members. The proposed semi-active members – lockable joints – allow for local modification of the frame’s stiffness. The objective of the introduced control approach is to provide mechanical energy transfer between particular eigenmodes. A demonstrator has been fabricated for the purpose of the investigation consisting of a double beam frame structure in a cantilever configuration, which is equipped with the semi-active members. The investigated control algorithm employs two types of input signals: local velocity of the structure and local strain of the frame. As a result, a verification of the system effectiveness has been revealed in a variety of frequency ranges. The excitation bandwidth has been appropriately suited to the particular tested cases. The experimentally obtained results confirmed a possibility of the energy transfers between particular structural eigenmodes.

This contribution presents a semi-active control technique intended for mitigation of structural vibrations. The control law is derived in a repeated trial-and-error interaction between the control agent and a simulated environment. The experience-based training approach is used which is the defining feature of the machine learning techniques of reinforcement learning (RL), implemented here using the framework provided by Deep Q Learning (DQN). The involved artificial neural network not only determines the control action, but additionally identifies structural damages, which is a nontrivial task due to the nonlinearity of the control. This requires a specific multi-head architecture, which allows the network to be damage-aware, and a specific training procedure, where the memory pool preserved for the RL stage of experience replay is populated with not only the observations, control actions, and rewards, but also with the momentary status of structural damage. Such an approach can be used to explicitly promote the damage-awareness of the control agent. The proposed technique is tested and verified in a numerical example of a shear-type building model subjected to a random seismic-type excitation. A tuned mass damper (TMD) with a controllable level of viscous damping is used to implement the semi-active actuation, and the optimally tuned classical TMD provides the reference response.

semi-active control, tuned mass damper (TMD), reinforcement learning, damage identification

This paper considers structural control by reinforcement learning. The aim is to mitigate vibrations of a shear building subjected to an earthquake-like excitation and fitted with a semi-active tuned mass damper (TMD). The control force is coupled with the structural response, making the problem intrinsically nonlinear and challenging to solve using classical methods. Structural control by reinforcement learning has not been extensively explored yet. Here, Deep-Q-Learning is used, which appriximates the Q-function with a neural network and optimizes initially random control sequences through interaction with the controlled system. For safety reasons, training must be performed using an inevitably inexact numerical model instead of the real structure. It is thus crucial to assess the robustness of the control with respect to measurement noise and model errors. It is verified to significantly outperform an optimally tuned conventional TMD, and the key outcome is the high robustness to measurement noise and model error.

structural control, semi-active control, reinforcement learning, tuned mass damper (TMD)

Vibration control is a crucial issue in engineering, necessitating the continuous development and refinement of effective control strategies. In the present study, a semi-active control methodology utilizing lockable joints is investigated. The lockable joints provide a modal coupling effect, resulting in controlled energy transfer between vibration modes. Numerical simulations demonstrate that energy can be transferred to higher-order vibration modes and rapidly dissipated through inherent material damping or transferred to a preselected vibration mode for energy harvesting.

Semi-active modal control, Smart Structures, Lockable joints, Energy transfer, Vibration damping

In this study an experimental program for verification of modal control algorithm for semi-active structures is proposed. The considered control approach assumes redirecting of mechanical energy between vibrational modes. The presented research is focused on development of an investigation method that would allow for demonstrating the control concept. Moreover, a suitable flexible structure equipped with semi-active elements is introduced. The proposed laboratory structure is a flat slender frame equipped with a set of six joints. A deliberate design of the joints provides a feasibility for a controllable transfer of the bending moments between chosen adjacent elements of the frame. Such a structure delivers a possibility of real-time modification of its local bending stiffness and therefore can be categorised as semi-active. The investigation covers identification of the modal parameters of the laboratory model, implementation of the control algorithm on an FPGA processor, providing a testing program that exemplifies the process of energy management between the eigenfrequencies. The results reveal that the response of the semi-active structure reflects the derived control algorithm assumptions. To sum up, the modal control algorithm based on real-time monitoring of the structure's modal parameters is experimentally implemented and verified in a laboratory environment.

vibration control, semi-active, modal control, experimental verification, lockable joints

The methodology for optimal single-type sensor placement has been extensively discussed in the literature. However, little attention has been devoted to the distribution of multi-type sensors. The application to large structures, such as bridges or towers, poses a significant challenge. Some responses, for example, the displacements of a bridge over a river, cannot be easily measured directly. Consequently, indirect techniques can be employed to estimate the deflections of such structures. In this contribution, a Kalman filter-based algorithm is presented to address this sensor placement problem. The effectiveness of the proposed method is numerically demonstrated using the example of an actual tied-arch bridge.

sensors, optimal sensor placement, Kalman filter, reduced order model, arch bridge

This contribution presents a sliding-mode control approach for the mitigation of vibrations in frame-like structures. The control is implemented in a semi-active manner, that is, without significant external control forces and substantial power consumption, which are typical for active control approaches. Here, the control is achieved through dynamic, lowcost modification of properties at selected structural nodes. The employed actuators have the untypical form of two-state hinges, which can switch between two extreme states: no transfer of bending moments (effectively a hinge) and full transfer of bending moments (a locked hinge or a typical frame node). Consequently, the control forces are dissipative and coupled to the response. Previous research in this area focused on purely energetic considerations, aiming for global damping of vibrations. In contrast, this paper formulates the control objective in terms of local displacements of a selected degree of freedom, which can be interpreted as the task of isolating it from external excitations. This formulation is employed to define the target sliding hyperplane. The state of the actuators is chosen such that the effective control forces push the structural state toward the target hyperplane. The approach is verified in a numerical example of a six-story shear-type structure subjected to random seismic excitation.

Structural control, Semi-active control, Sliding mode control, On/off nodes

This contribution presents an approach to structural control based on reinforcement learning. Reinforcement learning, a rapidly developing branch of machine learning, is based on the paradigm of learning through interaction with the environment. Here, it is applied in the context of semi-active structural control, where the considered actuators take the form of viscous dampers with a controllable level of damping. The control forces are thus coupled with the structural response, and the formulation is intrinsically nonlinear. The related optimum control problems are usually more difficult than in the case of active structural control systems, which generate and apply arbitrary external control forces. Analytical derivation of the optimum semi-active control is thus rarely possible, so that many control algorithms applied in practice are suboptimal and/or heuristic in nature. Here, an effective control strategy is developed by means of the Q-learning approach. The control algorithm is determined in interaction with the controlled system, that is, by applying initially random control sequences in order to observe, process, and optimize their effects. Such an approach seems to be new and relatively unexplored in the field of structural control. Verification is performed in a numerical experiment, where the Q-learning procedures interact with an independently simulated finite element model of a structure equipped with a tuned mass damper (TMD) and a controllable viscous damper. The results attest to a performance significantly better than that of an optimally tuned conventional TMD.

Reinforcement Learning, Semi-active control, Structural control, Damping, Vibration

In the present study a comparison of frequently used computer vision (CV)-based methods for structural health monitoring of truss structures is shown. The attention is paid to template matching methods that can be classified into one of two groups: area-based and feature-based methods. Synthetic but realistic video is used in this study. Results of the comparison are reliable due to the fact that the exact displacements are known from the finite element model of the investigated structure. From the variety of tested CV methods, the Kanade–Lucas–Tomasi algorithm with FREAK-based repetitive correction outperforms the remaining tested methods in terms of the computation time with a negligibly greater estimation error.

computer vision, structural health monitoring, physics-based graphics models (PBGM), IC-SHM 2021, benchmark test

In this study we show pros and cons of two frequently used approaches for model updating and parametric identification of structural system assembled by uncertain bolted connections. The comparison between classical mode matching and a recently proposed Bayesian approach is demonstrated. Classical methods for modal updating based on modal sensitivity require matching of modal parameters extracted from measurement data with those obtained numerically. Alternative approach is based on a probabilistic framework with the aid of Bayesian methodology. Such an approach explicitly includes the problem of a trade-off between modeling and measurement errors. These two methods are compared an a laboratory-scale three-story frame with unknown parameters corresponding to bolted connections. A total of 82 degrees of freedom are measured using 4 bidirectional accelerometers and roving sensor technique.

This contribution presents, discusses and illustrates the constrained mode decomposition (CMD) method. The CMD is a recently proposed method that extracts single mode components from measured multimodal free structural responses. These components can be then processed, in time domain or in frequency domain, for identification of modal parameters, and ultimately, for structural health monitoring. The aim of the CMD is thus similar to the aims of other well-known mode decomposition approaches, such as the empirical mode decomposition (EMD) or the variational mode decomposition (VMD). However, in contrast to the EMD, the CMD-processed responses retain the characteristics of the free response (satisfy the equation of motion of the same structure) and they have thus a clear, well-defined physical meaning. In comparison to the VMD, the formulation of the CMD is much simpler: the CMD combines linearly recorded structural responses in a way that simultaneously (1) amplifies the selected modal component and (2) constrains/suppresses other components. The amplification/suppression process is quantified in terms of the FRF peaks or, in case of closely spaced modes, in terms of FRF derivatives.

mode decomposition, frequency domain, linear combination, FRF peak, structural health monitoring, modal identification

Performance of any Structural Health Monitoring (SHM) system strongly depends on a set of sensors which are distributed over the structure under investigation. Optimal deployment of sensors on large scale structures such as tied-arch bridges is quite a challenging problem. Moreover, deployment of a sensor network consisting of different types of sensors (accelerometers, inclinometers or strain gauges) over a large scale bridge renders the task of optimization even more demanding. In the present study, a conventional sensor placement method for distribution of a homogenous sensor network is expanded to the heterogeneous case. First, the basic equations governing the estimation error will be recalled. Then, the Fisher information matrix is assembled using normalized translational and rotational mode shapes. Finally, a computational procedure is proposed which allows optimal sensor positions to be selected among thousands candidate locations. The effectiveness of the proposed strategy is demonstrated using a realistic example of a tied-arch bridge located in Poland.

optimal sensor placement, structural health monitoring, tied-arch bridges, multi-type sensor network

This contribution presents and tests experimentally a nonparametric approach for indirect identification of 2D paths of moving loads, based on the recorded mechanical response of the loaded structure. This is an inverse problem of load identification. The method to be proposed is based on multicriterial optimization with two complementary criteria. The first criterion is purely mechanical, and it quantifies the misfit between the recorded mechanical response of the structure and its predicted response under a given trajectory. The second criterion is geometric: it represents the heuristic knowledge about the expected geometric regularity characteristics of the load paths (such as related to linear and angular velocity), and in fact it can be considered to be a regularizing criterion. A multicriterial genetic search is used to determine and advance the Pareto front, which helps to strike the balance between the response fit and the geometric regularity of the path. The proposed approach is tested in an experimental laboratory setup of a plate loaded by a line-follower robot and instrumented with a limited number of strain gauges.

moving load, trajectory identification, inverse problem, structural health monitoring, multicriterial optimization

This paper discusses the potential of meta-poro-elastic systems with small mass inclusions to create broadband sound absorption performance under the quarter-wavelength limit. A first feasibility study is done to evaluate whether embedding small mass inclusions in specific types of foam can lead to near-perfect absorption at tuned frequencies. This paper includes an optimization routine to find the material properties that maximize the losses due to the mass inclusion such that a near-perfect/perfect absorption coefficient can be achieved at specified frequencies. The near-perfect absorption is due to the mass-spring effect, which leads to an increase in the viscous loss. Therefore, it is efficient in the viscous regime. The well-known critical frequency, which depends on the porosity and flow resistivity of the material, is commonly used as a criteria to distinguish the viscous regime from the inertial regime. However, for the types of foam of interest to this work, the value of critical frequency is below the mass-spring resonance frequency. Hence, the inverse quality factor is used to provides a more accurate estimation on the frequency at which the transition from the viscous regime to the inertial regime.

The success of virtually all structural health monitoring (SHM) methods depends on the information content of the measurements, and thus on the placement of the available sensors. This paper presents an efficient method for finding optimal sensor distribution over structural system with many degrees of freedom (DOFs). The objective function is based on the classical Fisher information matrix. Originally, this yields a computationally hard discrete optimization problem. However, the proposed numerical solution method is based on a concept taken from structural topology optimization, where a discrete optimization problem is replaced with a continuous one. Two numerical examples demonstrate the effectiveness of the proposed methodology. These are a 5-bay truss with 24 DOFs and a two-story frame structure whose finite element model has been condensed to 14 DOFs.

Dielectric Electro-Active Polymers (DEAP) are lighweight materials whose dimensions change significantly when subjected to electric stimulation. One form of DEAP construction consists of a thin layer of dielectric sandwiched between two perforated rigid electrodes. They can be used as an actuator or a sensor and have the potential to be an effective replacement for many conventional transducers. This paper refers to their use as loudspeakers. To date, flat DEAP loudspeakers have been portotyped and tested but no numeric prediction of their acoustic performance has been presented. In this paper an elemental model is presented. The electro-dynamic behaviour of the electrodes and dielectric layers is taken into account. The acoustic impedance is calculated assuming baffled conditions. The impedances of the individual layers are stacked together and preliminary results are shown.

loudspeaker, DEAP, sound power

Damage identification attracted a lot of attention during the last three decades. The reason for that is the fact that large number of existing civil infrastructures reached their service life and growing number of structures is equipped with Structural Health Monitoring (SHM) systems. A successful structural damage identification is determined by three inseparably coupled factors: sensor placement, damage location and its extend, and finally location and time-frequency characteristics of the applied excitation. The purpose of this study is to address the first of the mentioned aspects, namely optimal sensor placement. A vast literature has been devoted to optimal sensor placement methods among which Effective Independence (EI) method proposed by Kammer and Tinker is one of the most successfully applied in practice. However, EI method is dedicated rather to test-analysis correlation and therefore more specific methods for damage identification are still needed. Additionally, in the case of large civil structures, which are intended to be equipped with large amount of sensors of different type, other sensor placement methods can be more efficient. Recently, a promising idea of utilizing a topology optimization approach for the purpose of sensor placement has been proposed by Bruggi and Mariani. The goal of this study is to extend their method, which has been verified on a plate structure, to the case of a FE model of a real arch bridge structure consisting a few thousands degrees of freedom. The main purpose of this work is to find the optimal arrangement of sensors on the structure to detect defects most accurately. The objective function for the problem formulated in this way is the total, weighted difference between the deformation of a damaged and undamaged state. This problem is very similar to the topological optimization, where we search for the optimal material distribution minimizing the mass of the structure while meeting the conditions related to some mechanical properties such as the maximum displacement of the structure, stress intensity or load capacity. This similarity led us to apply topological optimization to the problem of optimal placement of damage sensors. Several numerical examples prove the applicability of topological optimization for optimal sensor placement problem.

Sensor Placement, Damage Identification, Topology Optimization

This contribution presents an approach for indirect identification of the 2D path of a moving load. A multicriterial formulation is proposed, where one objective function quantifies the mismatch between the measured and the simulated structural response. The second objective function expresses the natural expectation that the paths of moving loads are continuous and relatively smooth, and it expresses thus a certain spline-based measure of the geometric regularity of the path. The Pareto front is determined in a local evolutionary search and used to strike the balance between the response fit and the geometric regularity of the path. The approach is tested in a laboratory experimental setup of a plate loaded by a line-follower robot. It is found that the implementation of the smoothness-based objective has a regularizing influence on the identification results: it reveals and emphasizes the actual geometrical character of the identified paths.

Trajectory Identification, Moving Load, Inverse Problem, Structural Health Monitoring, Multicriterial Optimization

Recent progress in sensing technology and measurement techniques allows a growing number of critical infrastructures to be equipped with Structural Health Monitoring (SHM) systems. Sensors in such SHM systems should be placed in a proper way to facilitate extracting valuable information from the structure under investigation. In the case of relatively simple spatial truss structures, sensors can be located with the aid of classical methods such as Effective Independence (EI) method proposed by Kammer. However, in the case of large structures, which are intended to be equipped with hundreds if not thousands of sensors, other sensor placement methods may be needed.
The goal of this study is to extend a topology optimization based approach for sensor placement (proposed originally by Mariani and co-workers) to the case of real bridge structures represented by finite element models with a few thousand degrees of freedom. Structural topology optimization aims to find the optimum material distribution in order to minimize the mass of the structure while maintaining mechanical properties (load capacity, displacements, etc.). A similar concept can be used to determine the optimal placement of sensors in a structure to identify its dynamic characteristics. The sensor positions are determined in such a way that estimation error of modal coordinates is minimized. The effectiveness of the proposed methodology is demonstrated on an example of a detailed FE model of a tied-arch bridge.

Optimal sensor placement, Structural parameter identification, Topology optimization

This contribution presents an experimental analysis of the control system configuration for a semi-active frame structure. The structure is equipped with a system that implements a Prestress Accumulation Release strategy for mitigation of vibration. A proper distribution of the sensors for monitoring the actual state of the structure is the key factor that determines the overall effectiveness of the applied strategy. The results and findings presented here reveal a set of basic rules dedicated to solving this crucial issue.

Prestress Accumulation Release, Vibration control, Sensor placement, Semi-active structures, Piezoelectric actuation

This contribution proposes a semi-active control approach for a directed energy transfer between structural vibrational modes. The motivation is the intended localization of the vibration energy in a selected mode for the purpose of energy harvesting and mitigation of structural vibrations. The proposed control strategy aims at the instantaneous maximization of the energy transfer to the target mode. It is based on an untypical approach of dynamic structural reconfiguration and implemented using a semi-actively controllable node: a lockable joint. Such a joint, depending on the control signal, can act as a hinge or as a typical frame node. Effectively, it provides thus an on/off ability to control the transfer of bending moments between the adjacent structural elements. The effectiveness of the approach is demonstrated in a numerical example of a plane frame structure.

Modal control, Semi-active control, Lockable joints, Energy harvesting

Semi-active control systems are investigated for more than 40 years, and despite the great progress in this research area, they are still considered to be a complex topic in both theoretical and technical terms. However, their advantages ensure that these control systems remain an extremely attractive subject of scientific and technological development.
In this contribution, we present a semi-active strategy for mitigation of vibration, which utilizes an energy management approach called Prestress-Accumulation Release and is based on controllable activation and removal of selected structural constraints. Here, it is implemented by means of controllable structural nodes of a specific design that allow the transmission of moments between adjacent structural elements to be controlled in an on/off manner. The developed control strategy turned out to be very effective in damping of free structural vibrations of planar frame structures. Extension of the research to other types of vibrations has shown that the proposed control algorithm is versatile and stays efficient in a range of applications and different configurations of the investigated structures. This work is focused on mitigation of vibrations excited by a randomly generated force load.
Decentralization, understood here as controlling the employed actuators based on locally measured structural response, results in a decisive reduction of the complexity of the data acquisition and control systems, which is crucial for actual implementations in real structures, and which facilitates an ad hoc reconfiguration and expansion of the control system if necessary. It also provides the possibility of considering selected structural elements as separate energy dissipative devices, which in our approach act effectively as vibration dampers. This feature, provided by the decentralization, enables to take the advantage of two complementary, interrelated mechanisms of material damping: global dissipation of vibration energy by the PAR and local dissipation in single involved elements.
Numerical and experimental analyses indicate a high degree of effectiveness in alleviation of the amplitude of vibrations induced by a random transient force excitation. The proposed control strategy can be thus utilized not only in the case of momentary impulsive loads that result in predominantly free vibrations, but also in the case of transient random force excitation. It significantly extends the range of possible modes of operation of a structure equipped with the proposed damping system.

Semi-active damping, Vibration damping, Random vibration, Forced vibration

For over two decades, inerter-based devices are a subject of research papers, patents and engineering reports. Since 2002, when the inerter was introduced as the missing element of mechanical networks, various applications of the inerter have been proposed. They include solutions for earthquake engineering, suspensions of vehicles, aircraft landing gears and even systems improving walking performance of humanoid robots. In contrast to majority of the inerter-based systems, which are mainly developed for vibration mitigation problems, this paper concerns the inerter as the shock-absorber protecting objects excited by the impact. In particular, adaptive performance of the ball-screw inerter with variable moment of the flywheel inertia is investigated. In order to ensure efficient adaptation of the inerter to various excitation conditions, the single reconfiguration technique, which was successfully applied for pneumatic absorber, is now adjusted and implemented in the proposed inertial system. The contribution consists of the concept introduction, discussion of the mathematical model of the system, theoretical as well as numerical analyses. Results of the presented study show that optimal impact absorption can be obtained in semi-passive manner. The properly adjusted geometry of the surface guides for the inertial elements ensure appropriate variability of the flywheel moment of inertia. Variable moment of the flywheel inertia provides optimal deceleration of the amortized object. The calculated moment of inertia depends on the mass of amortized object and friction but it is independent of the impact velocity.

ball-screw inerter, impact absorption, passive absorber, variable inertance, variable moment of inertia, inertial damping

In this paper the possibility of enhancing the absorption coefficient of a poro-elastic material using small, elastic mass inclusions in frequencies lower than the quarter-wavelength resonance of the porous material is discussed. We show that absorption peaks can be achieved not only by what is known in literature as the trapped mode effect, but also by the resonance of small elastic inclusions at low frequencies, which can be interpreted as a mass-spring effect. In this work, the inclusion and the porous skeleton is considered elastic and fully coupled to each other, therefore accounting for all types of energy dissipation i.e. viscous, thermal, and structural losses and energy dissipated due to the relative motion of the fluid phase and the frame excited by the resonating inclusion. Additionally, the inclusions are also modeled as motionless and rigid to distinguish between the trapped mode and/or the modified frame mode effect and the mass-spring effect. Moreover, the distinction between these two effects are explained in more detail by comparing the dissipated energy by each mechanism (viscous, thermal and structural effect).

Meta-porous material, Biot-Allard poroelastic model, Mass-spring effect

This contribution deals with the inverse problem of indirect identification of moving loads. The identification is performed based on the recorded response of the loaded structure and its numerical model. A specific feature of such problems is a very large number of the degrees of freedom (DOFs) that can be excited and a limited number of available sensors. As a result, unless the solution space is significantly limited, the identification problem is underdetermined: it has an infinite number of exact, observationally indistinguishable solutions. We propose an approach based on the assumption of sparsity of the excitation, which can be expressed in the form of a requirement of a bounded l1 norm of the solution. As long as the loads are sparse, the approach allows them to be freely moving, without the usual assumption of a constant velocity. We first test the approach in a numerical example with 10% rms measurement noise. A good qualitative agreement of the numerical results allows to proceed with experimental investigations, and the moving load identification is then carried out based on the response measured experimentally on a lab test stand.

The paper presents a novel method for sensor placement optimized towards effective identification of structural damages. The derivation of the method is based on the concept of virtual distortions together with information provided by a set of strain gauges. Then, a gradient oriented optimization is applied to identify sensor locations, which are the most sensitive to potential damage scenarios. Steepest descent method is utilized to determine the optimal values of the objective function. Additionally, dependence of the method on the applied excitation signal is discussed. Finally, effectiveness of the proposed methodology is demonstrated on an example of optimal search for sensor placement on a 6-bay planar truss structure.

optimal sensor placement, virtual distortion method, damage identification

Vibration mitigation in space structures creates a unique class of a technical problem where resistant for outgassing and non-fluidic solutions are preferable. Additionaly, a vibration induced by time-varying excitations needs to be effectively reduced. The vibration mitigation task is speciffically difficult in the case of light, slender and inherently flexible structures of various types, such as supporting structures, deployable structures, modular structures or wide-span skeletal roofing structures. This study presents a concept of a vibration attenuation method based on semi-active joints and dedicated to frame structures under forced vibration excitation. The presented investigation contains an analysis of the problem of the optimal control of a structure fitted with semi-active structural members. Furthermore, an adequate model of the semi-active joints is developed and a numerical example is presented. Finally, the research provides an experimental verification of the developed control algorithms, which is conducted on a test stand in a laboratory environment.

This contribution proposes a quantitative criterion for optimization of actuator placement for the Prestress–Accumulation Release (PAR) strategy of mitigation of vibrations. The PAR strategy is a semi-active control approach that relies on controlled redistribution of modal energy into high-frequency high-order modes, where it is effectively dissipated by means of the natural mechanisms of material damping. The energy transfer is achieved by a controlled temporary removal of selected structural constraints. An example is a short-time decoupling of rotational degrees of freedom in a frame node, so that the bending moments are no longer transferred between the involved beams. If it such a decoupling is performed at the maximum of the shear/bending strain energy of adjacent beams, it results in an almost instantaneous energy release into high-frequency local vibrations and quick dissipation of energy. We propose and test a quantitative criterion for placement of such actuators. The criterion is based on local modal strain energy that can be released into high-order modes. The numerical time complexity is linear with respect to the number of actuators, which facilitates quick selection of placements in large structures.

semi-active control, damping of vibrations, actuator placement, smart structures, Prestress-Accumulation Release (PAR)

Semi-active systems for mitigation of vibrations proved to be effective in many applications. Their prominent advantage is that they combine strong points of passive and active damping systems. Proper design can ensure their reliability, which is what passive systems are praised for. A high effectiveness in vibration damping links them with active systems. At the same time they do not have many deficiencies of active systems. They are adaptive, so they can stay effective in different environmental conditions, which is the factor that eliminates passive systems from many implementations. Their mass and energy consumption is very low, and the controlled structure can stay in the safe configuration even in case of power supply failure, which puts them in contrast to many active systems. The mentioned attributes make them a good choice for many structures subjected to vibrations, especially when there is a strong emphasis on maximization of the efficiency/mass ratio of the damping system.
This contribution presents a decentralized closed-loop control strategy and applies it in a frame structure equipped with controllable truss-frame nodes. Such nodes can be switched between frame-like and truss-like states in a controllable manner. In the frame-like state the node transmits all forces and moments, while in the truss-like state only axial and shearing forces are transmitted. These nodes allow for structural reconfiguration, which can be utilized by semi-active control strategies for the purpose of vibration damping. The implemented control algorithm applies the Prestress-Accumulation Release (PAR) strategy based on the transmission of the accumulated potential energy to high modes of vibration, which are highly dissipative. Strain measurements are conducted locally on selected elements. A similar strategy proved its effectiveness in mitigation of free structural vibrations. This research studies the concept of its application to mitigation of forced structural vibrations, caused by variable external conditions.

Semi-active damping, Truss-frame nodes, Prestress-Accumulation Release (PAR), Decentralized control

In this paper, a damage localization method based on additional virtual mass and dynamic test of simple harmonic excitation is proposed. Firstly, when additional masses are added to the structure, a large number of virtual structures can be constructed; then the virtual construction formula is derived in order to obtain the dynamic response of virtual structures without adding real mass. After dynamic test of simple harmonic excitation, the dynamic response of virtual structures can be obtained using the acceleration response and virtual construction formula. Furthermore, when the applied harmonic excitation frequency is close to the natural frequency of the structure, the structural response can reach a maximum by adding advisable mass and the mass value can be calculated. When the local structure is damaged, the extreme value and the corresponding position of the additional mass are found by adding mass at different positions in the structure. Thus, the approximate location of the damage is determined according to the results. Finally, the numerical simulation of the elastic foundation beam model simplified by track structure is carried out, and the results show that the damage can be localized.

structural health monitoring, damage identification, slab track, virtual mass

This contribution proposes a decentralized closed-loop control algorithm for semi-active mitigation of free vibrations in frame structures. The control uses dedicated dissipative devices, which consist of two controllable structural nodes placed pairwise in both ends of selected structural beams. The nodes are capable of a controlled transition between the standard frame mode of operation (full moment-bearing ability) and the truss mode in which they do not bear any moments and constitute in fact structural hinges. Synchronous switching is equivalent to reconfiguration of the global structure by (dis)allowing the involved beams to transmit moments and to accumulate vibration energy in the form of their bending strain. Upon switching to the truss mode, the accumulated energy is released into high-frequency local vibrations, which undergo quick dissipation by standard mechanisms of material damping. The approach is illustrated in a numerical example and verified in a preliminary experimental test.

Mitigation of vibrations, Semi-active control, Decentralized control, Structural reconfiguration

Extensive research efforts have been recently devoted to semi-active structural control with its paradigms of smart self-adaptivity and low consumption of energy, which is used for local adaptation rather than to generate external control forces. Considered application areas include adaptive landing gears, seismic isolation systems, vehicle-track/span systems, power train electro-mechanical systems, damping of flexible space structures, vehicle crashworthiness, arctic engineering, wind turbines, etc. A part of the research concerns semi-active management of strain energy for damping of structural vibrations. Early works considered truss structures with stiffness-switched bars. They later evolved into either standalone one degree of freedom stiffness-switched dampers and isolators or investigations in triggering modal energy transfer to highly-damped high-order modes. The latter researches seem all to study the fundamental vibration mode of a cantilever beam with two detachable layers and differ mainly in the actuator technologies; the main idea is to employ actuators for a quick release of the vibration-related strain energy. This research extends the problem to general 2D frames. Controllable truss-frame nodes are incorporated into the structure. Thanks to their controllable ability to transmit moments, they allow for a quick transition between truss and frame modes. We propose a new, decentralized, closed-loop control strategy based on local energy measures. Vibration damping is more effective than in the previously studied control scheme based on a global energy measure, especially for higher vibration modes. Mitigation of vibrations will be presented in representative numerical examples, including a comparison to the global energy-based control strategy. Finally, results of experimental study, conducted on a structure analogous to the one from numerical simulations, will be demonstrated.

Vibration damping, Smart structures, Semi-active control, PAR strategy, Decentralized damping strategy

Truss-Z (TZ) is an Extremely Modular System (EMS). Such systems allow for creation of structurally sound free-form structures, are comprised of as few types of modules as possible, and are not constrained by a regular tessellation of space. Their objective is to create spatial structures in given environments connecting given terminals without self-intersections and obstacle-intersections. In an EMS, the assembly, reconfiguration and deployment difficulty is moved towards the module, which is relatively complex and whose assembly is not intuitive. As a result, an EMS requires intensive computation for assembling its desired free-form geometrical configuration, while its advantage is the economization of construction and reconfiguration by extreme modularization and mass prefabrication. TZ is a skeletal modular system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic module (Truss-Z module, TZM) subjected to affine transformations (mirror reflection and rotation). The previous research on TZ focused on global discrete optimization of the spatial configuration of modules. This contribution reports on the first attempts at structural optimization of the TZM for a single-branch TZ. Namely, the internal topology of a TZM and sizing of its elements are subject to optimization. An important challenge is due the fact that TZM is to be universal, i.e., it must be designed for the worst case scenario. There are four variations of each module, and due to symmetries there are thus 4^4 = 256 unique 5-unit configurations. The structural performance of all of them needs to be evaluated in terms of a typical structural criterion (the maximum von Mises effective stress), and used for structural optimization at the level of a single TZM.

Extremely Modular System, Truss-Z, Structural optimization, Effective stress

This paper discusses passive and semi-active techniques of structural control by means of smart joints, and then it proposes a specific smart joints system for frame structures and tests its capability in mitigation of free vibrations. Basically, the proposed solution modifies frame beams by addition of truss-type hinges, and its effectiveness relies on the softening effect that occurs in compression due to geometric nonlinearities and which triggers the highly-damped high-frequency response modes of the structure. First, the finite element (FE) model of the specific frame structure with geometrical nonlinearities is derived, and the proposed passive joints are described and incorporated into the model. Then, their principle of operation and effectiveness is examined numerically for the first two natural modes of vibrations with various initial displacement amplitudes. An objective function is proposed to assess joints placement, based on the efficiency in mitigation of the excited vibrations.

Vibration Damping, Structure Response, Smart Structure, Structural Control

Truss-Z (TZ) is an Extremely Modular System (EMS). Such systems allow for creation of structurally sound free-form structures, are comprised of as few types of modules as possible, and are not constrained by a regular tessellation of space. Their objective is to create spatial structures in given environments connecting given terminals without self-intersections and obstacle-intersections. In an EMS, the assembly, reconfiguration and deployment difficulty is moved towards the module, which is relatively complex and whose assembly is not intuitive. As a result, an EMS requires intensive computation for assembling its desired free-form geometrical configuration, while its advantage is the economization of construction and reconfiguration by extreme modularization and mass prefabrication. TZ is a skeletal modular system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic module (Truss-Z module, TZM) subjected to affine transformations (mirror reflection and rotation). The previous research on TZ focused on global discrete optimization of the spatial configuration of modules. This contribution is the first attempt at structural optimization of the TZM for a single-branch TZ. The result is a multicriterial optimization, where the Pareto front provides the means to strike the optimal balance between geometric and structural assessment criteria.

multicriterial optimization, Truss-Z, effective stress, modular systems

In recent years, vibration damping strategies based on semi-active management of strain energy have attracted a large interest and were proven highly effective. However, most of published research considers simple one degree of freedom systems or study the same basic example (the first vibration mode of a cantilever beam) with the same control strategy. This contribution focuses on truss-frame nodes with controllable moment-bearing ability. It proposes and tests an approach that allows the control strategy to be extended to more complex structures and vibration patterns.

adaptive impact absorption, smart structures, semi-active control, safety engineering

This contribution reviews the challenges in adaptive self-protection of structures. A proper semi-active control strategy can significantly increase structural ability to absorb impact-type loads and damp the resulting vibrations. Discussed systems constitute a new class of smart structures capable of a real-time identification of loads and vibration patterns, followed by a low-cost optimum absorption of the energy by structural adaptation. Given the always surging quest for safety, such systems have a great potential for practical applications (in landing gears, road barriers, space structures, etc.). Compared to passive systems, their better performance can be attributed to the paradigm of self-adaptivity, which is ubiquitous in nature, but still sparsely applied in structural engineering. Being in the early stages of development, their ultimate success depends on a concerted effort in facing a number of challenges. This contribution discusses some of the important problems, including these of a conceptual, technological, methodological and software engineering nature.

adaptive impact absorption, smart structures, semi-active control, safety engineering

This contribution presents and overviews a new class of strategies for Adaptive Impact Absorption (AIA) and illustrates a selected strategy in a numerical example. The proposed strategies are based on a challenging approach of a semi-active management and dissipation of structural kinetic and potential energy. The entire process of AIA is considered, including its two main phases: semi-actively controlled reception of an impact and semi-actively controlled damping of the resulting structural vibrations. Management and redistribution of impact energy seems to be one of the most promising and challenging problems in the field of AIA, which requires a substantial theoretical progress in semi-active control strategies and in structural optimization, besides a technological progress in semi-active actuators.

Adaptive impact absorption, smart structures, adaptive structures, impact energy management, bilinear control, switched systems

This paper presents a frequency-domain, nonparametric method for identification of added masses, and reports on its experimental verification. The identification is directly based on experimentally collected characteristics of the unmodified structure, so that no parametric numerical model of the monitored structure is required. Consequently, there is no need for the initial stage of model updating. This is a continuation of and an improvement over a previous research that resulted in a time-domain identification method, which was tested to be accurate but significantly time-consuming. For the experimental verification, a 4~m long 3D truss structure with 26 nodes and 70 elements is used. A total of 12 modification cases is tested: in each of 3~selected nodes, 4~additional masses are separately added and successfully identified.

Structural damage identification plays a critical role in structural health monitoring on evaluating structural safety and maintaining structural integrity. This paper presents a damage identification approach based on Virtual Distortion Method (VDM) using random response. VDM is a fast structural reanalysis method in which virtual distortions are introduced to simulate structural damages or modifications. Via VDM, responses of damaged structure can be computed quickly without reanalysis of the whole structure. In this paper, firstly the frequency response of damaged structure is constructed efficiently using VDM, and then damage extents are optimized using the objective function which is computed using the MAC (modal assurance criterion) of the power spectrum of theoretical response and measured responses. At last, a plane truss is proposed to verify the proposed method.

This paper presents a damage identification method using virtual structure. The main concept is based on Virtual Distortion method (VDM), which belongs to a fast structural reanalysis method and employs the virtual distortions or virtual forces to simulate the structural modifications. In this paper, the structure with virtual mass, damping or stiffness is defined as virtual structure. Firstly, the frequency response of the virtual structure is constructed by VDM method; Secondly, the natural frequencies of virtual structure with additional masses or stiffness are estimated; At last, the estimated natural frequencies of the virtual structure are used for damage optimization of the structure. A numerical beam model is used to describe and verify the proposed method.

This paper presents the substructure isolation method, which a novel method for substructural analysis and structural health monitoring (SHM) at the local level. The motivation behind it are the facts that global SHM of large and complex structures is generally difficult and that often only small substructures are crucial and require monitoring. These facts suggest that there is a need for ways of applying global SHM approaches locally, which is impossible with typical substructuring methods. The paper offers an overview of the common substructuring approaches and describes the substructure isolation method. The method splits the task of local monitoring into two stages: (1) Isolation; the outside influences are numerically eliminated from the measured response of the substructure. (2) Local SHM; all methods aimed originally at global SHM can be used with the constructed response of the isolated substructure. Local analysis is possible in time domain as well as in frequency domain; in offline and in online time regimes. The method is illustrated in a numerical example and substantiated in an experimental study using a damaged cantilever beam; the robustness of the isolation with respect to unknown modifications of the outside structure is tested.

Substructuring, Structural Health Monitoring, SHM, Damage identification, Local analysis

Substructure Isolation Method (SIM) is used for large substructure identification. It utilizes the responses of global structure to construct the responses of the isolated substructure, which is a virtual and independent structure with the same system parameters as the real substructure. Then, the substructure identification is carried out equivalently via the isolated substructure and flexibly by some of the existing identification methods which aim originally at the large structure. Therefore, the performance of the SIM offers the possibility that the large substructure can be identified. A numerical bridge model is used to verify the proposed method, which preforms efficiently and accurately.

Structural Health Monitoring (SHM), Damage identification, Substructure, Interface force

This paper presents a Substructure Virtual Distortion Method (SVDM) for damage identification based on Virtual Distortion Method (VDM). VDM is a fast structural reanalysis method by introducing virtual distortions to simulate structural damages. SVDM extends the virtual distortions regard to the damaged elements to the related substructures. Such that the required number of virtual distortions depends on the substructure other than the elements, which reduces the computational work a lot. In addition, for a structure under a certain external force, the dynamic responses may be reflected by a few of main eigenvectors, and thus it only needs to compute the virtual distortions which are relative with these main eigenvectors. This further reduces the computational work. In this paper, first the relation among the virtual distortions of the substructure, actual distortions, and the substructure damage extents are derived; then the main distortions of the substructure are chosen by the contribution analysis of the distortions to the structural responses. In this way, the damages are optimized and identified by minimizing the least square distance between the measured response and the estimated response. A numerical frame model is used to verify the proposed method.

structural health monitoring (SHM), damage identification, Virtual Distortion Method, substructure

This paper presents a theoretical derivation and an experimental verification of a model-free method for identification of stiffness-related damages. The proposed method requires no parametric numerical model of the monitored structure, which obviates the need for initial model updating and fine tuning. The paper introduces the general methodology, including the inverse problem, focuses it on stiffness-related damages, and reports on an experimental verification. A 4-meter-long, 70-element truss steel structure made of a commercially available system of nodes and connecting tubes is used for that purpose. Damage is simulated by an intentional replacement of a structural element.

This paper proposes a Substructure Isolation Method based on time series (SIM-TM) of measured local response and intended for local online monitoring of substructures. The method consists of two key steps: (numerical) construction of the isolated substructure, and local identification. The isolated substructure is an independent virtual structure, which is separated from the global structure with virtual supports placed in their interface. In the first step, the response of the isolated substructure is constructed by linear combinations of sub-time series of the measured local responses. Then, natural frequencies of the isolated substructure are identified based on the constructed response and used for local identification. The method has no requirements on the initial state of the structure. The isolation can be carried out time section by time section using the successive fragments of the measured responses, so that the approach can be used for online monitoring. A numerical frame model is used to verify the proposed online monitoring method.

This paper proposed a frequency domain method of substructure identification for local health monitoring. The substructure isolation method (SIM) consists of two steps: the first is the construction of isolated substructure which is the key of the method, and the second is damage identification of substructure. The isolated substructure is a virtual and independent structure, and it have the same physical parameters of the real substructure with the additional virtual supports on boundary, which is realized by operating the measured response. This paper extends the SIM method to frequency domain, which could make the method employ more measured response and compute more efficiently. A mass-spring numerical model is used to verify the theory of the SIM method, and a cantilever beam is experimented to test the method. The method preformed efficiently and accurately in the both numerical model and experiment.

This paper presents the concept of smart structures dedicated to improving structural safety in case of unpredictable impact loadings. The concept is developed by bringing together two different ideas: adaptive impact absorption (AIA) and structural health monitoring (SHM). The potential for safe energy dissipation is maximized by optimum structural adaptation to impact loading parameters, for which the AIA subsystem is responsible. The SHM subsystem is used for on-line identification of impact type loadings, which is necessary in order to trigger optimum adaptation, as well as for post-impact damage assessment. Both subsystems depend on smart material technologies: optimum adaptation can be implemented through a small number of optimally distributed structural fuses, that is elements with controllable yield stresses, which can be implemented using magneto-rheological fluids, while the health and loading monitoring require a reliable sensing system, e.g. based on piezo-materials. The paper presents the general concept, provides a literature review and discusses in detail the challenges related to the SHM part.

This paper presents the concept of smart structures dedicated to improving structural safety in case of unpredictable impact loadings. The concept is developed by bringing together two different ideas: adaptive impact absorption (AIA) and structural health monitoring (SHM). The potential for safe energy dissipation is maximized by optimum structural adaptation to impact loading parameters, for which the AIA subsystem is responsible. The SHM subsystem is used for on-line identification of impact type loadings, which is necessary in order to trigger optimum adaptation, as well as for post-impact damage assessment. Both subsystems depend on smart material technologies: optimum adaptation can be implemented through a small number of optimally distributed structural fuses, that is elements with controllable yield stresses, which can be implemented using magneto-rheological fluids, while the health and loading monitoring require a reliable sensing system, e.g. based on piezo-materials. The paper presents the general concept, provides a literature review and discusses in detail the challenges related to the SHM part.

adaptivity, crashworthiness, inverse problems, structural monitoring, smart materials

Torsional vibrations are in general rather troublesome to control from the viewpoint of proper control torque generation as well as because of difficulties of imposing the control torques on quickly rotating parts of the drive- or rotor-shaft systems. In this paper there is proposed an active control technique based on the linear actuators with the magneto-rheological fluid (MRF) connecting the drive system planetary gear housing with the immovable rigid support. Here, by means of the magneto-rheological fluid of adjustable viscosity control damping torques are generated. Such actuators can effectively suppress amplitudes of severe transient and steady-state rotational fluctuations of the gear housing position and in this way they are able to minimize dangerous oscillations of dynamic torques transmitted by successive shaft segments in the entire drive system. The general purpose of the considerations is to control torsional vibrations of the power-station coal-pulverizer drive system driven by means of the asynchronous motor and the single stage planetary gear. In the computational examples drive system transient torsional vibrations induced by the electromagnetic motor torques during start-ups as well as steady-state vibrations excited by the variable dynamic retarding torques generated by the coal pulverizer during nominal operation have been significantly attenuated.

Torsional vibrations, rotational fluctuation, magneto-rheological fluid

This paper proposes a simple lab-size benchmark for testing algorithms in two identification problems related to global structural health monitoring (SHM): identification of structural modifications and identification of inelastic impacts. A 3D truss-like structure, constructed of a commercial tube/node system, is used. Structural modifications are implemented by attaching additional nodal masses or by cutting a selected element to reduce its stiffness. Inelastic impact is simulated by an impulsive excitation of an additional nodal mass. Technical specification and experimental characteristics of the unmodified structure are provided for model updating. Several modification and impact cases are experimentally tested. All the data and measurements are freely accessible in Internet. An evaluation system is proposed for assessing the solutions, based on identification accuracy, instrumentation and source lines of code. The authors encourage the readers to test their approaches on the provided data. With each solution received, the evaluations will be calculated and published online.

This paper presents a Substructure Isolation method for substructural damage identification using time series of local measured response. Isolated Substructure is a virtual and independent structure which is numerically separated from the global structure by adding virtual supports on the substructure interface. The basic concept of the isolation method is that: first time series of substructural responses are divided into several sub-series with overlap; through the linear combination of all the sub-series, when the boundary response are constrained to zeros, the corresponding inner responses are the constructed responses of the Isolated Substructure; then the substructural damage identification can be performed equivalently by the modes of the Isolated Substructure which are identified from the constructed inner responses. Numerical model of a six-span truss and an experiment of a cantilever beam are used to validate the method. Both the isolation and damage identification are preformed very well using local measured responses.

This paper presents and experimentally verifies a method for identification of structural damage. The work is focused on such damage types as cracks, delamination or excessive allowances, which may not cause significant stiffness degradation but induce noticeable additional damping. Damaged elements are located and the damage is assessed in terms of the damage-induced damping and also the stiffness degradation. The Virtual Distortion Method (VDM) is used for modeling of the modifications.

This paper presents and verifies experimentally a model-free methodology for off-line damage identification of truss structures. The Virtual Distortion Method (VDM) is used, which allows the approach to be based entirely on experimentally obtained non-parametric characteristics of the monitored structure, so that no parametric numerical modeling is necessary. The damage is modeled using certain damage-equivalent pseudo-loads, which are convolved with experimentally obtained local responses of the original structure to compute the response of the damaged structure. An effective sensitivity analysis is possible via the adjoint variable method.

A substructuring method is presented for substructure identification and local health monitoring. The concerned substructure is numerically separated from the global structure to be a so-called Isolated Substructure by adding virtual supports on the substructure interface. The isolated substructure is a small and independent structure; its virtual supports are constructed using the FFT of measured local responses of the global structure. The damage of the substructure can be then identified easily by any of the classical methods which perform well on global structures. An experiment of a cantilever beam, of which the upper part is chosen as the substructure, is used to validate the method.

This paper presents a method for fast identification of coexistent loads and damages, in which the number of sensors is mainly decided by the number of unknown loads.The computational efficiency is improved by Virtual Distortion Method (VDM), with which the repeated estimation of system impulse response is performed efficiently and by a local interpolation of perturbations of the structural response with respect to damage parameters. The proposed methodology is verified by a numerical example of a multi-span frame.

In the paper control of transient and steady-state torsional vibrations of the driven by the asynchronous motor laboratory drive system of the imitated coal pulverizer is performed by means of actuators with the magneto-rheological fluid. The main purpose of these studies is a minimisation of vibration amplitudes in order to increase the fatigue durability of the most responsible elements. The theoretical investigations are based on a hybrid and finite element structural model of the vibrating mechanical system as well as on sensitivity analysis of the response with respect to the actuator damping characteristics. For suppression of transient torsional vibrations excited by electro-magnetic torques generated by the motor and by the coal pulverizer tool there is proposed a control strategy based on actuators in the form of rotary control dampers.

Semi-active control, torsional vibrations, electro-mechanical drive system, control dampers, magneto-rheological fluid

This paper presents a substructuring method on damage identification using Local Primary Frequency (LPF).When a local excitation is applied on a concerned substructure, if the caused vibration mainly consists of only one single modal which represents most of the substructural distortion, then the corresponding frequency is defined as the substructural LPF. LPF reflects more information of the substructure and hence is more sensitivity to the substructural damage. Therefore, LPF can be used for substructural model updating and identification. However, generally substructures don’t own LPF. In this case, virtual supports constructed by Substructure Isolation Method are applied on the substructural boundary, such that it can enhance the constraint on the boundary, and decrease the influence from elements outside the substructure. In this way, the substructure sensitivity is enhanced and correspondingly the LPF of the substructure can be constructed. Numerical simulation of a three-story space frame structure testifies that substructural damages are identified effectively by this method.

Structure Health Monitoring (SHM), Damage Identification, substructuring method, Substructure Isolation Method, Local Primary Frequency (LPF), Virtual Supports

This paper describes an effective method of substructure isolation for local structural health monitoring (SHM). In practice, often only a small part of a larger structure is critical and needs monitoring [1]. However, typical SHM methods require modeling or analysis of the global structure, which can be costly, time-consuming and error-prone. The proposed approach is based on the virtual distortion method [2]; the substructure is isolated from the entire structure by placing modeled fixed supports in all nodes of their mutual boundary. Therefore, given an excitation of the substructure and a measured response, the response of the substructure treated as fixed supported can be computed. Only experimental data are used for isolation, and no numerical modeling is required. A numerical experiment of damage identification in a frame-truss will be presented during the talk to validate the methodology at 5% rms measurement error level. It is omitted here due to space constraints.

This paper proposes a new approach for modeling and identification of damping in linear structures. The approach is based on the Virtual Distortion Method (VDM), which is a reanalysis methodology for fast modeling and identification of structural parameters. The VDM is extended in the sense of considering structural damping in frequency domain. The assumed damping model is a modified version of the proportional damping, which allows to distinguish between and to modify independently the damping properties of each element and in each degree of freedom. In this way, a precise formulation of the task of remodeling of damping is possible. Moreover, the proposed approach is used to state and solve the (basically nonlinear) inverse problem of identification of material damping by decomposing it into two linear subproblems.

damping identification, structural reanalysis, Virtual Distortion Method (VDM)

Identification of damage and moving load (or mass) are crucial problems in structural health monitoring (SHM). However, it seems there is not much investigation on simultaneous identification of the two factors, although in practice they usually exist together. This paper proposes a methodology to solve the coupled problem based on the Virtual Distortion Method (VDM): the damaged structure is modeled by an equivalent intact structure (called the distorted structure) subjected to the same moving mass (or in fact to the equivalent response-coupled moving load) and to certain virtual distortions which model the damage. The measured structural response is used to identify the moving mass and the damage; unknown mass and damage extents are used as the optimization variables instead of the usually chosen moving mass-equivalent force. In this way well-conditioning of the identification is ensured and the number of the necessary sensors is decreased. The numerical costs are considerably reduced by using the introduced concept of the moving dynamic influence matrix. The proposed identification method can be used both off-line and online by a repetitive application in a moving time window. A numerical experiment of a beam with 5% measurement error demonstrates that the moving masses can be identified along with the damage extents.

Structural health monitoring (SHM), Moving mass (load) identification, Damage identification, Virtual distortion method (VDM)

This paper presents and experimentally validates a model-free methodology for off-line identification of modifications of structural mass. The proposed approach makes use of the Virtual Distortion Method (VDM) and is based entirely on experimentally measured data of the original unmodified structure, which is a significant advantage: no numerical modeling of the structure and tedious updating of the model are necessary. The mass modification is modeled using equivalent virtual distortion forces and experimentally obtained local impulse-responses of the unmodified structure. The identification amounts to solving an optimization problem of minimizing the mean-square distance between measured and modeled responses of the modified structure; a quick first- and second-order sensitivity analysis using the adjoint variable method is proposed. The method is validated experimentally using a 4-meter-long 70-element truss structure.

mass identification, model-free SHM, virtual distortion method (VDM), adjoint variable method

This paper presents an improved numerical tool for identification of damage in skeletal structures. The problem of identification has been formulated in the time domain within the framework of the Virtual Distortion Method (VDM). VDM generally belongs to fast structural reanalysis methods and can be applied to Structural Health Monitoring problems, among others. The major computational asset of VDM is the influence matrix, containing all the local-global inter-relations for a structure due to given perturbations e.g. initial strain or external force. A non-linear least squares problem with strains, entering the objective function, is the subject of consideration. Strains are used in order to have relatively smooth variations (compared to accelerations) of the analyzed signal in time. The change of stiffness is the design variable. Analytical gradients are implemented in the optimization code based on the Levenberg-Marquardt algorithm with some penalty function terms. The efficiency of the software tool is demonstrated for a numerical example of a 2D truss structure. A breakthrough in terms of computational time reduction has been observed compared to the previously used steepest-descent optimization. The presented software assumes the feasibility of reliable measurements of strains in time for real skeletal structures (e.g. truss bridges). Future research will include experimental verification of the idea with piezoelectric sensors acting as tensometers.

This paper presents a novel method to identify coexistent load and damage based on the idea of Virtual Distortion Method (VDM), which is significant for structural healthy monitoring. This method models a system with unknown damage and load by an equivalent undamaged system with the same load and certain virtual distortions, which are estimated stepwise via measured response. Then damage size can be computed by the estimated virtual distortions. It could be used for both off-line and online identification. A numerical experiment validates that two kinds of damage sizes can be identified as well as coexistent continuous and triangular loads. Moreover two methods (load shape function and initial system iterates) are proposed and incorporated to improve the computational accuracy and to reduce the numerical effort.

This paper proposes a new model-less method for off-line identification of a mass impacting an elastic structure. The method is aimed at the identification of both mass and its velocity, makes use of the Virtual Distortion Method (VDM) and assumes the inelastic impact case, i.e. permanent modification of structural properties. Since the proposed approach is completely based on experimentally measured data, no numerical modeling and tedious fine-tuning of the model are necessary. The impacting mass is modeled using virtual distortion forces and an experimentally obtained system transfer matrix. The identification amounts to solving an optimization problem of minimizing the mean-square distance between measured and modeled structural responses, the latter is based on previously recorded responses of the unaffected structure.

This contribution reviews a recently proposed semi-active control approach based on the Prestress-Accumulation Release strategy, which aims at damping of structural vibrations by promoting vibration energy transfer from lower- into higher-order modes that have significant material damping. Unlike typical semi-active control, which focuses on local dissipation in actuators, the aim is to trigger natural global damping mechanisms. The actuators are controllable truss-frame nodes: lockable hinges that can change their mode of operation from a frame node (locked hinge) into truss node (free rotation). Sudden removal of such a kinematic constraint releases the accumulated bending energy into high-frequency quickly damped local vibrations. Two formulations are reviewed: decentralized with local-only feedback, and global, which aims at a targeted energy transfer between specific modes. Experimental results confirm the effectiveness using free, forced harmonic and random vibrations.

In practice, the broadly used finite element (FE) models can have very large number of degrees of freedom (DOFs). A small subset of DOFs representing sensor locations that provides an extremum of a selected objective function corresponding to a metric of the expected measurement accuracy is sought. Thus, optimal sensor placement is characterized by its complex combinatorial nature and tremendous computational effort required. With the aid of convex relaxation, the proposed approach allows one to transform the original combinatorial problem into its continuous counterpart, which requires smaller computational effort – by a few orders of magnitude than famous Effective Independence method. The effectiveness of the method has been demonstrated using an example of a FE model of an existing railway bridge. First, the FE model has been calibrated with measured responses of the bridge under the moving load of a passing train. Then, sensor layout has been obtained in such a way that it optimises the estimate of modal coordinates of the mode shapes participating most significantly in the measured structural response. The authors acknowledge the support of the National Science Centre, Poland (grant agreement 2018/31/B/ST8/03152).

Vibration damping is a very important aspect of engineering practice. The basic strategy of coping with vibrations is to properly design the structure, which will either eliminate or at least limit this phenomenon. When structural changes are not sufficient, a vibration damping system shall be introduced. We have developed a semi-active vibration damping system for 2D frame structures which proved to be efficient in various load conditions. Mitigation of vibration amplitudes, with very satisfying results, can be achieved both in free, as well as in forced vibrations which can have harmonic or purely random characteristics. In all cases numerical findings were confirmed with experimental investigations conducted on a similar structure, which authenticates the quality of the proposed control algorithm. Decentralization of the control system contributes to improving the safety and efficiency of the control. It also simplifies its implementation in the real structure, which is an additional advantage over the centralized control systems. The authors acknowledge the support of the National Science Centre, Poland (grant agreement 2020/39/B/ST8/02615).

Parametric identification of structures and their components can be encountered in many engineering problems such as damage assessment or model updating for the control purposes. In the present study the attention is on two approaches to model updating. The first approach is the classical penalty func-tion that minimizes the square norm of the error between experimental and numerical modal data. The second one is a probabilistic Bayesian framework that maximizes the a posteriori probability density function of the unknown parameters based on the experimental data. The main difference between these two approaches is related to the fact that the penalty function methods requires matching of the numerical data with those obtained experimentally. The Bayesian approach is not vulnerable to this problem, but it requires more weighting parameters to be selected. An improper selection of these parameters leads to a worse identification accuracy. In this work, the two approaches are compared using data obtained from experiments on a laboratory-scale frame with highly uncertain bolted connec-tions. 17 uncertain stiffness parameters are to be identified: 16 of them correspond to the bolted con-nections and one to the Young modulus of the beams. 82 degrees of freedom are measured with the aid of 4 bidirectional accelerometers and roving sensor technique. Experimental modal data used for model updating contain nine mode shapes and the corresponding natural frequencies within the fre-quency range from 0 to 1 kHz. The research is divided into three steps: (1) model class selection, (2) assessment of the parameter identifiability and (3) updating of the selected model with the aid of both examined model updating methods.

This contribution reviews a recently proposed control strategy for mitigation of vibrations based on the Prestress-Accumulation Release (PAR) approach [1]. The control is executed by means of semi-actively controllable truss-frame nodes. Such nodes have an on/off ability to transfer bending moments: they are able to temporary switch their operational characteristics between the truss-like and the frame-like behaviors. The focus is not on local energy dissipation in the nodes treated as friction dampers, but rather on stimulating the global transfer of vibration energy to high-order modes. Such modes are high-frequency and thus highly dissipative by means of the standard mechanisms of material damping. The transfer is triggered by temporary switches to the truss-like state performed at the moments of a high local bending strain. A sudden removal of a kinematic constraint releases the locally accumulated strain energy into high-frequency and quickly damped vibrations.
The first formulation investigated global control laws [1]. Recent approaches generalized it to decen-tralized control with a local-only feedback, which was tested in damping of free vibrations [2] as well as forced vibrations [3]. Recently, a global formulation was proposed that aims at a targeted energy transfer between specific vibration modes [4], and attempts were made to go beyond skeletal struc-tures [5]. Numerical and experimental results will be presented to confirm the high effectiveness of the approach in mitigation of free, forced random and forced harmonic vibrations.

This contribution concerns a snake-like robotic manipulator arm proposed first in [1]. The manipulator is composed of linearly but nonaxially joined identical modules with a possibility of relative twist, which amounts to one degree of freedom per module. It is an example of an extremely modular system [2], and its advantages are: economization (due to modularity and possible mass production) and robustness (easy repair by replacement of a failed module). The hitherto research involved the possible geometric transformations of the manipulator arm [3], but not its structural optimization. However, structural design of the involved modules is a challenging task, as the process has to take into account the relative position of the module along the arm, as well as the variety of global configurations of the deployed manipulator. It leads to a multi-load structural optimization problem with a significantly large number of loads. This contribution considers topology optimization of such a modular manipulator structure. Due to the large variety of possible load conditions, the initial analysis involves a 2D model of the structure with a discrete set of two possible relative arrangements of adjacent modules. Such a formulation allows the proposed approach to be preliminarily explored, tested and optimized in a numerically manageable simplified environment. The support of the National Science Centre, Poland, granted under the grant agreement 2019/33/B/ST8/02791 is gratefully acknowledged.

Despite significant advances in structural health monitoring (SHM), the design of contact sensor networks and their power supply for large-scale structures is still expensive and difficult. Due to the recent progress in computer vision (CV) it is possible to monitor structural components or even whole structures with the aid of digital cameras that allow to avoid the use of the contact sensors. However, CV-based measurements have a significantly lower accuracy than the techniques based on the contact sensors. Moreover, the amount of benchmark data available for development, testing and comparison of CV-based methods is limited. This problem has been partially overcome in recent years by the use of the physics-based graphical models (PBGM) in generation of synthetic but realistic video data. In this work, a comparison of two popular methods of CV-based object tracking applicable in SHM is discussed. PBGM-based videos used in this study are a part of The 2nd International Competition for Structural Health Monitoring'. Exact structural displacements are available due to the fact that PBGM-based video are generated using the structural model. Hence, calculation of the error metrics is straightforward and reliable. The PBGM-based videos show a spatial truss subjected to an unknown excitation.

Nowadays engineering studies require the use of the sophisticated finite element (FE) models consisting of hundreds if not thousands of degrees of freedom. However, using only such models does not allow for accurate reproduction of physical properties of real structures. To overcome this problem usually model updating (MU) techniques are employed. MU usually has one of two goals: 1) modification of some parameters of the model in order to minimize error between output of the FE model and experimental data obtained from the real system, and 2) identification of some properties of the real system using both experimental data and updated FE model. The former case relates to finding the model for performing simulations of the behaviour of the real system. In the later case MU can be applied in damage assessment process. Due to modelling uncertainties minimization of the error between measured and model output does not always provides the most accurate parametric identification. In this research unknown parameters describing rotational stiffness of bolted connections in a frame structure are estimated. Effectiveness of the two competitive model updating methods are compared. The first is based on modal sensitivities and minimizes error between numerical and experimental modal data. It requires matching of the numerical modes with the experimental ones, hence it is often called mode matching. The second is based on probabilistic Bayesian framework. In this approach maximum a posteriori (MAP) estimate of the unknown parameters is searched. It provides an augmented optimization allowing for model updating without mode matching. Moreover, this method is intended for parametric identification and explicitly includes the modelling errors into the problem formulation. In this study vibration modes are obtained from laboratory-scale frame with uncertain bolted connections. It is shown that assembly imperfections have significant influence on the mode shapes of the frame. The results also show that the two methods for model updating provide significantly different values of the identified stiffness parameters for the investigated bolted connections.

In the present study a benchmark test of selected methods of template matching-bated methods for computer vision-based object tracking is performed. The attention is paid to compare these methods in terms of estimation of nodal displacements in a flexible truss structure, aiming at assessment of their reliability in Structural Health Monitoring (SHM) applications. Thanks to the use of synthetic but realistic videos generated with the aid of physics-based graphics models (PBGM), exact displacement of tracked structural nodes are known. Therefore, reliable assessment of the accuracy of the examined methods is possible.

computer vision, structural health monitoring, physics-based graphics models (PBGM)

The uNET neural network architecture has shown very promising results when applied to semantic segmentation of biomedical images. The aim of this work is to check whether this architecture is equally applicable to semantic segmentation distinguishing the structural elements of railway viaducts. Artificial images generated by a computer graphics program rendering the 3D model of the viaduct in a photorealistic manner will be used as data sets. This approach produces a large number of
images that provide a solid training set for machine learning model.

Computer vision, deep learning, semantic segmentation

The paper presents the parametric identification of structural connections characterised by highly uncertain stiffness. Such uncertainties often appear in structural bolted connections. One of the common problems in parametric identification with the use of modal data is the problem of the mode matching. In this work the model updating method based on the Bayesian approach was used to identify the unknown parameters. Due to the probabilistic framework it allows to avoid the problem of the mode matching. A laboratory-scale frame structure is considered in this research, however this structure contains bolted connections common also in large-scale light-weight structures. The problem of parametric identification has been decomposed into the following tasks: (a) selection of the finite element model, (b) evaluation of the identifiability of the parameters, and (c) updating the finite element model with the use of available measurement data.

Bayesian approach, mode matching, system identification, model updating, bolted connections

In the present work, we propose a distributed collaborative controller to stabilize the vibration of modular systems. The method relies on the partitioning the structure, in a way that leads to a set of dynamically interconnected subsystems, each operated with an individual subcontroller. The key novelty in the proposed approach lies in the introduction of a collaboration between the neighboring subcontrollers. This collaboration is realized by exchanging some of the state information, allowing the establishment of short-term predictions of the interaction forces, identifying the boundary conditions for the subsystems. For the predictions, we employ autoregressive linear dynamical models which preserve the linear representation of the subsystems' dynamics. This allows, for each of the subsystems, defining and solving the problem of optimal stabilization based on the LQR method. The proposed method is examined for an actively controlled cantilever structure equipped with electromagnetic actuators. The performance of the designed controller is tested by comparing it to the optimal controller established by the solution to the centralized LQR problem. In addition, the distributed controller is compared to the decentralized case, where we assume a set of local independent subcontrollers. The computational complexity of the distributed control method is analyzed for different settings in the modeling of the predictions of the interaction forces.

This contribution is devoted to the problem of indirect identification of 2D trajectories of moving loads based on the measured mechanical responses of the loaded structure. This is an inverse problem of load identification, and such problems have been intensively studied. Such problems are typically characterized by (1) a very large number of structural degrees of freedom that can be excited by the moving load and (2) a limited number of sensors that are used to measure the response. In effect, the na¨ıve formulation based on minimization of the residuum norm is underdetermined, and the corresponding identification problem has an infinite number of exact solutions. Thus, in order to guarantee the uniqueness of the solution, the generality of the load is typically limited by assuming that the trajectory of the moving load is known (most often, the problem is reduced to the case of a single vehicle moving over a 1D bridge at a constant velocity) and that only the magnitude of the load is subject to identification. In contrast, our aim here is to identify more general loads, and in particular trajectories of loads that are freely moving on 2D structures like plates.

moving load identification, inverse problem, trajectory identification

The inerter is a subject of intensive research in the field of structural dynamics and control since 2002, when it was introduced by Malcolm Smith. Inerter-based devices are implemented in various practical applications, which include protective systems in earthquake engineering, suspensions of trains, road vehicles and aircraft landing gears. The majority of inerter applications proposed in the literature concerns vibration mitigation problems, e.g., implementation of the inerter in tuned mass dampers. In contrast, this contribution discusses an application of the inerter for solving the problem of impact absorption. The inerter was previously considered as a shock-absorber in [Ref.] but optimal impact mitigation was not provided. Recently, the authors have studied a simple inerter device based on the ball-screw mechanism with a variable thread lead, which ensures minimization of the generated reaction force and the optimal impact absorption. This contribution sums up the results obtained in the full-length journal paper, currently under review.

ball-screw inerter, impact absorption, passive absorber, variable inertance, variable moment of inertia, inertial damping