Institute of Fundamental Technological Research

In this paper, the authors propose, investigate, and discuss a concept of novel type of deployable helium-filled aerostat as a low-cost mean of transport. Internal construction of the aerostat is based on ultra-light tensegrity structure equipped with prestressed tensioned elements of controllable lengths. Such tensegrity structure allows for adaptive morphing of the aerostat understood as simultaneous controllable modifications of aerostat volume and shape during the flight. The controlled volume changes enable influencing buoyancy force and obtaining desired vertical motion during the ascending and descending process. In turn, external shape changes allow for lowering the aerodynamic drag and energy usage needed to uphold stable horizontal position or maintain the desired flight path. Moreover, such internal structure allows for convenient storage, transportation and deployment of the aerostat construction on the ground or in required point at the atmosphere. The article presents an analysis of the exemplary operational mission of the aerostat. The authors introduce the mechanical model capturing interaction of the internal tensegrity structure and aerostat envelope based on the finite-element method, as well as dynamic model allowing for simulation of the aerostat’s vertical and horizontal motion influenced by buoyancy and drag forces. Both these models are used to positively verify the feasibility of the proposed concept of deployable tensegrity-based aerostat with adaptive morphing and its efficiency in realization of the assumed flight mission.

tensegrity structure, internal construction, shape modification, helium-filled aerostat, vertical mobility, horizontal mobility

Measurements of displacements of bridges under dynamic load are particularly difficult in the case of structures where access to the area under the tested structure is impossible. Then, remote measurement methods are preferred, such as interferometric radar. Interferometric radar has high accuracy when measuring displacement in the direction of its target axis. The problems appear when a bridge vibrates in two directions: horizontal (lateral or longitudinal) and vertical. The use of one radar to measure those vibrations may be impossible. This paper presents the application of a set of two interferometric radars to measure vertical vibration and horizontal longitudinal vibration with high accuracy. The method was positively verified by experimental tests on two railway bridges characterized by different levels of horizontal displacement. The accuracy of the radar measurements was tested by the direct measurement of vertical displacements using inductive gauges. In conclusion, in the case of vertical displacement measurements using one interferometric radar, the influence of horizontal displacements should be excluded. In the case of locating radars at the area of bridge supports, it is necessary to either use a set of two radars or first investigate the magnitude of possible horizontal displacements in relation to vertical displacements.

bridge monitoring, interferometric radar, remote measurements, dynamic vertical and horizontal displacements

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 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

In the case of the monitoring of bridges, the determination of vertical displacements is one of the most important issues. A new measuring system has been developed and implemented for assessment of railway bridges based on measurements of the structural response to passing trains. The system uses inertial sensors: Inclinometers and accelerometers that do not need any referential points. The system records signals related to the passage of a train over a monitored bridge. The signals from inclinometers before the train's entry are used to determine the static movement. Integrated signals from inclinometers and accelerometers are used to determine dynamic displacements when the train goes through the bridge. Signals from inclinometers are used to determine the so-called "quasi-static" component of the displacement and signal from the accelerometer to determine the dynamic component. Field tests have been carried out on a viaduct along a high-speed railway line. Periodic comparative measurements are carried out using a Total Station to verify static measurements and using inductive sensors to verify dynamic measurements. Tests of the system carried out so far have proven its usefulness for monitoring bridges in a high-speed railway (up to 200 km/h) with high accuracy while determining dynamic displacements.

bridge monitoring, dynamic and static displacements, inertial sensors, total station, indirect measurement

This paper describes an application of wavelet analysis for damage detection of a steel frame structure with bolted connections. The wavelet coefficients of the acceleration response for the healthy and loosened connection structure were calculated at each measurement point. The difference of the wavelet coefficients of the response of the healthy and loosened connection structure is selected as an indicator of the damage. At each node of structure the norm of the difference of the wavelet coefficients matrix is then calculated. The point for which the norm has the higher value is a candidate for location of the damage. The above procedure was experimentally verified on a laboratory-scale 2-meter-long steel frame. The structure consists of 11 steel beams forming a four-bay frame, which is subjected to impact loads using a modal hammer. The accelerations are measured at 20 different locations on the frame, including joints and beam elements. Two states of the structure are considered: healthy and damaged one. The damage is introduced by means of loosening two out of three bolts at one of the frame connections. Calculating the norm of the difference of the wavelet coefficients matrix at each node the higher value was found to be at the same location where the bolts were loosened. The presented experiment showed the effectiveness of the wavelet approach to damage detection of frame structures assembled using bolted connections.

complex bolted lap connection, frame structure, wavelet analysis, damage detection

An experimental and analytical study of the relation between local defect, in a steel structure, and its higher frequencies and higher modes is discussed. The structure is a plane steel frame, assembled of beams, joined together with bolted connections. Removing some bolts from a given connection simulates the damage. In the experiment, an impulse force induced structural vibrations. Effects of vibrations were shown by data from gages, measuring accelerations with a high accuracy. From the data, it could be observed, that mode shapes, for the healthy and damaged structures didn’t show any differences for low frequencies. Only modes around thirteen showed significant gap between picks of Frequency Response Functions, for healthy and damaged frame. Moreover, looking at mode shapes, it could be observed that structural configuration may have some influence on defects to be observable. This aspect is discussed in a separate section. The experiment performed on the whole structure allows finding the place where the defect is localized. However, it can’t give detailed information on the defect itself, here defect of a bolt. For finding it, an ultrasonic measurement of pre-tensioning forces in bolts was applied. It allowed not only to determine stresses in the bolt, but also to verify, if in the process of assembling the structure was not pre-stressed.

Detectable damages, Bolted connections, Experimental modal analysis, Ultrasonic measurements, Steel frames, Analytical dynamics

A railway bridge has been the object of investigation in the context of structural health monitoring (SHM). The current work is focused on utilization of experimental data for refining a numerical model of the structure as well as on tests of dynamic excitations using a controlled hydraulic shaker and passing trains. The numerical model has been matched to experimental measurements using experimental modal analysis - classical and operational. The tailored SHM system for monitoring of the bridge consists of 15 piezoelectric strain sensors taking advantage of wireless communication for data transfer. Experimental responses of the bridge collected by the SHM system are confronted with the ones produced by the FE numerical model of the bridge. The long-term objective of the investigation is to elaborate a method for assessment of structural condition and prediction of remaining lifetime of the bridge.

Bridge Monitoring, Experimental Measurements, Modal Analysis, Wireless SHM

A railway bridge has been the object of investigation since mid 2007 as a response to increasing interest in structural health monitoring (SHM) from Polish Railways. It is a typical 40 m long, steel truss structure spanning a channel in Nieporet near Warsaw. There is over 1500 similar bridges in the railway network in Poland. The integrated system consists of two components – weigh in motion (WIM) part for identification of train load and SHM part for assessing the state of the bridge. Two aspects of wireless transmission are considered – short range (in the vicinity of the bridge, 2.4GHz) and far range (from the bridge to the data analysis center, GSM). The system is designed to be energetically self-sufficient, batteries are recharged by solar panels. Both the subsystems use piezoelectric strain sensors. Numerical model of the bridge corresponds well to the experimental data and provides a good starting point for considering different scenarios of simulated damage in the structure.

SHM, Piezo sensors, Wireless transmission, Bridge dynamics, Railway infrastructure

The paper presents some results of research on the Weight-in-motion (WIM) system. The device is used for identification of loads on the road surface generated by traveling vehicles. The proposed approach utilizes the piezoelectric measurement techniques to monitor strain development in a deformable body and eventually these measurements are used for tire- pavement load identification. An advantage of the proposed concept is that no additional limitation for a vehicle velocity and direction is required in order to make the measurement feasible. The device allow to identify many parameters which can be stored for statistical and planning purposes. When an overload or an exceed in speed limit is detected the data can be sent for penalization purposes. The research includes a computer simulation of the bending plate detector using the Finite Element Method (FEM). Its objective is to validate the concept as well as to test some factors which are important with respect to the proposed load identification methodology. An experimental research involved field tests on the WIM system using a bending plate detector and inductive loops to detect a vehicle.

Weigh-in-Motion, Load identification, Piezoelectric sensors, Sensitivity analysis

This paper presents results of in situ investigation of a railway truss bridge in the context of structural health monitoring (SHM). Three experimental methods are examined. Dynamic responses of the bridge recorded by strain gauges are confronted with alternative ways of acquisition using piezoelectric patch sensors and ultrasonic probeheads. All types of sensors produce similar output. Also the corresponding responses of the numerical model of the bridge match experimental data.

The paper is a continuation of research on the application of a structural reanalysis method—the virtual distortion method—to structural health monitoring. The first approach, formulated previously in the time domain, suffered from a considerable numerical cost. In order to reduce it, this paper presents an alternative approach, formulated in the frequency domain thanks to the assumption of using harmonic excitation (quasi-static problem). The hardware devices supposed to collect structural responses are piezoelectric patch sensors. The software tool for damage identification solves a nonlinear least squares optimization problem by employing analytically derived sensitivities. Strains are the analyzed quantities, contributing to the objective function. Considerations are restricted to skeletal structures and a simplified dynamic problem with no damping. Effectiveness of the frequency-domain identification is demonstrated in numerical examples. Experimental verification is envisaged.

Damage identification, Inverse problem, Frequency domain, Skeletal structures, Reanalysis methods

Frequency-Based Analysis, Inverse Problem, Piezo Devices, Structural Damage Identification

The contribution describes three innovative external airbag systems developed by the
authors for the protection of flying objects during emergency landings. The first one is the
AdBag system dedicated for small drones, which is designed to protect the carried equipment
and prevent damages to objects or injuries to people at the crash location. The second system
is external airbag designed for ultralight aircraft Skyleader 600, which provides significant
reduction of touchdown velocity and deceleration levels during emergency landings, thereby
improving protection of the pilot and the passengers. Finally, the last presented solution is the
Spring-Drop system with specialized airbag deployment technique, which is dedicated for
specialised airdrop operations where the touchdown conditions can be extremely harsh and
unexpected, while protection of transported cargo is of crucial importance. Both conceptual
studies, numerical simulations and experimental tests of the three proposed systems are
presented and discussed.

External airbags, adaptive system, emergency landing, human safety

This contribution introduces the concept of sky sailing, which combines the
advantages of airships and standard fixed-wing aircraft, albeit in a vertical plane alignment.
The proposed vehicle is equipped with rigid aerodynamic sails and auxiliary engines, enabling
navigation and control with minimal power consumption along the desired trajectory. The
proper orientation of the airship relative to the wind direction is achieved through the
adjustment of the sails' angle of attack and the use of auxiliary lateral engines. Consequently,
the system enables efficient maneuvering, particularly in windy conditions, while requiring low
energy input. In the current stage of our research, we focus on 2D sky sailing in a horizontal
plane. This study formulates mathematical model which employs a combined approach of
analytical methods and numerical simulations based on finite volume method. Then, the
corresponding control problem aimed at following the desired fly path with the lowest possible
energetic cost. The motivation behind this work stems from the potential applications of aerial
monitoring, such as crop or forest surveillance.

Airship, flight control, optimization, aerospace

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

In this contribution, the authors propose a concept of novel type of an ultra-light helium-filled aerostat. The internal construction of the proposed aerostat is based on a self-deployable tensegrity structure equipped with prestressed tensioned elements of controllable lengths. Such construction enables convenient transportation of the aerostat and its fast deployment at the required operational point at the atmosphere. The controllable tensegrity structure can be used for simultaneous changes of the aerostat volume and external shape during the flight. This enables modification of buoyancy and drag forces and obtaining a desired vertical and horizontal motion as well as a desired flight path. The authors propose a method of numerical modelling of self-deployable helium-filled aerostats based on the finite element method as well as CFD and FSI models presenting behaviour of aerostat during typical operational conditions. The presented results show the interaction of the internal tensegrity structure and aerostat envelope and positively verify the feasibility of the proposed concept of tensegrity-based aerostats.

tensegrity structure, internal construction, helium-filled aerostat, numerical modelling

In this contribution the authors propose and investigate the concept of adaptive morphing for recently introduced tensegrity-based helium-filled aerostats. The proposed aerostat is based on an ultra-light tensegrity structure equipped with prestressed ensioned elements of controllable lengths. Such internal structure allows for adaptive morphing of the aerostat defined as simultaneous controllable modifications of aerostat volume and external shape during the flight. The controlled volume changes enable influencing buoyancy forces acting on the envelope and obtaining desired vertical motion of the aerostat during the ascending and descending process (“vertical mobility”). In turn, the controlled changes of external shape of the aerostat can be used either for lowering the aerodynamic drag forces and reducing energy usage needed to maintain stable horizontal position or to follow the desired path of aerostat horizontal motion (“horizontal stability”). The authors effectively apply the previously introduced mechanical FEM model of the tensegrity-based aerostat and dynamic model of the aerostat’s vertical and horizontal motion to conduct simulations of the process of adaptive morphing and maintain a proper position in the atmosphere. The obtained results positively verify the idea of adaptive morphing and its efficiency in controlling vertical and horizontal motion of the aerostat.

tensegrity structure, helium-filled aerostat, adaptive morphing, vertical mobility, horizontal stability

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

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.

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

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 article is devoted to space truss-like structures commonly used for solar panel installations or telecommunication antennas. Such structures have obvious advantage of beneficial ratio of their stiffness to mass. One of challenges in satellite engineering is focused on special design of ultra-light structures, compacted during transportation to the orbit, able to deploy into large cantilever with e.g. photovoltaic panels (being on the orbit). This approach allows for better withstands the launch loads in compact configuration. The proposed smart topology (SMARTOP) of the structure enables for easy, zero-energetic transformation from the compact, two-dimensional form into the final, tree-dimensional configuration, making use of stored pre-stress energy, released with use of specially controlled clutches. Main innovations are in specially design topology and so-called smart clutches performing controlled release of stored strain energy in a proper timing. Numerical simulations of the SMARTOP structure functionalities are presented.

self-deployable structures, prestressed truss-like structures, rod-cable structures, joint connections, vibration reduction

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

The article presents the railway bridge structures monitoring system, which takes advantage of the dynamic response measurement and evaluation method. The monitoring system is focused on steel structures with the spans exceeding 30 m. The elaboration of the method which uses inclinometers together with an accelerometer for indirect displacement measurement under the dynamic load is the main achievement of the project.

monitoring, railway bridges, inclinometer, accelerometer

This work is focused on experimental verification of existing techniques for localization of a loosened bolted connection. To this end, a laboratory-scale 2-meter-long steel frame is used. The structure consists of 11 steel beams forming a four-bay frame, which is subjected to impact loads using a modal hammer. The accelerations are measured at 20 different locations on the frame, including joints and beam elements. Two states of the structure are considered: a healthy and a damaged one. The damage is introduced by means of loosening two out of three bolts at one of the frame connections. Experimental modal analysis reveals that the loosened bolts in the connection cause a shift only in some of the frame’s natural frequencies, while the others remain insensitive to the damage.

bolted lap connection, frame structure, experimental modal analysis, damage location

In this paper we numerically study simple two dimensional frame structure loaded by impulse-like excitations. Various configurations of time duration of a single impact load and location of this excitation are investigated. The aim of this research is to indicate the best possible load case for identification of a specific damage. Two kinds of structural modifications are considered. The first group concerns the element stiffness changes (axial and bending) which can be simulated by alternating the Young‘s modulus. The second group covers the modifications of stiffness nodal connections. In a numerical model, these kinds of defects can be implemented using rotational spring with different characteristics. Obtained selected responses for the original and modified structure are numerically generated.

structural modification, semi-rigid joint, virtual distortion method, gradient-based optimization

This study presents the numerical analysis and experimental tests of a planar frame structure with semi-rigid joints. Based on structural responses the identification of nodal parameters is performed.

Frame structures, Semi-rigid joints, Inverse problem, SHM

The nodal connections in the standard analysis of frame structures are idealized assuming either pinned or fully rigid joints. State of such structural connections is highly important for safe operation of skeletal structures. In this work, the authors propose modeling, detection and identification of semi-rigid joints, i.e. nodal connections covering the range between pinned and fully rigid joints. The presented approach is based on the Virtual Distortion Method (VDM) and dedicated to statically or dynamically loaded two-dimensional frame structures.

In the last years one can observe an increasing interest in structural health monitoring (SHM) from Polish Railways. There are several hundreds of steel truss bridges of various spans and similar topologies in Polish railway infrastructure. One of them, located over a canal in Nieporęt near Warsaw with span of 40m became an object of investigation and implementation of an integrated SHM system. The system consists of two components – weigh in motion (WIM) part for identification of train load and SHM part for assessing the bridge state. The WIM module supplies load data required for SHM inverse analyses, however it can operate as an independent system for monitoring of railway traffic providing information about axle loads and rolling stock identification. Many in-situ installations of SHM systems suffer from a troublesome and time- consuming way of data acquisition via standard cables. In order to facilitate data collection related with this way of acquisition, an alternative solution of wireless transmission of the measured data from the field to analysis centre is proposed. Two aspects of wireless transmission are considered – short range (in the vicinity of the bridge) and far range (from the bridge to the centre of analysis). This paper takes up the practical issue of design and implementation of the integrated SHM system for truss steel railway bridge with a special insight into the monitoring of railway traffic.

Structural Health Monitoring, monitoring of steel railway bridges

The authors propose an idea of monitoring the state of skeletal structures of high importance (e.g. roof structures over large area buildings) with the aim of identification of slowly-developing plastic zones. This is formulated as an inverse problem within the framework of the Virtual Distortion Method, which was used previously to identify stiffness/mass modifications in similar manner. Permanent plastic strains developed in a truss element can be modeled by an initial strain (virtual distortion) introduced to the structure. The formation of subsequent plastic zones in the structure is assumed to be slow. Consequently, the design variable (plastic strain) is time-independent, which makes the inverse analysis efficient. This article presents problem formulation and numerical algorithm for identification of the plastic strains in truss structures. The identification relies on gradient-based optimization. A numerical example is included to demonstrate the efficiency of the algorithm.

In the last years one can observe an increasing interest in structural health monitoring (SHM) from Polish Railways. There are several hundreds of steel truss bridges of various spans and similar topologies in Polish railway infrastructure. One of them, located over a canal in Nieporęt near Warsaw with span of 40m became an object of investigation and implementation of an integrated SHM system.
The system consists of two components – weigh in motion (WIM) part for identification of train load and SHM part for assessing the bridge state. The WIM module supplies load data required for SHM inverse analyses, however it can operate as an independent system for monitoring of railway traffic providing information about axle loads and rolling stock identification.
Many in-situ installations of SHM systems suffer from a troublesome and time-consuming way of data acquisition via standard cables. In order to facilitate data collection related with this way of acquisition, an alternative solution of wireless transmission of the measured data from the field to analysis centre is proposed. Two aspects of wireless transmission are considered – short range (in the vicinity of the bridge) and far range (from the bridge to the centre of analysis).
This paper takes up the practical issue of design and implementation of the integrated SHM system for truss steel railway bridge with a special insight into the monitoring of railway traffic.

SHM systems, monitoring of railway bridges

The paper presents results of in-situ investigation of a railway truss bridge in the context of SHM. Three experimental methods are examined. Dynamic responses of the bridge recorded by strain gauges are confronted with alternative ways of acquisition using piezoelectric sensors and ultrasonic probeheads. Numerical model corresponds to experimental data.

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.

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).

The present study provides a comprehensive framework for sensor layout optimization aiming at accurate estimation of the modal coordinates coming from the structural response. The proposed procedure consists of two steps briefly described below. The first step is a selection of vibrational modes taking part in the motion of structures during their normal operation – in this case subjected to traveling load. Among these structures there are various types of bridges especially railway bridges. In the case of present study structural responses are obtained from rigorous finite element (FE) model of the bridge. The FE model is calibrated with measured response of real bridge located in Huta Zawadzka. The calibration process is based on the displacement signals of the bridge under the traveling load. In the second step modes of interest are selected and a set of candidate sensor locations is proposed. It is a subset of all degrees of freedom (DOFs) of the FE model from which several locations are chosen as best possible locations for the displacement sensors. The above sensor placement problem is a combinatorial task. Many methods for solving such problems have been developed previously, but in the case of large scale structures they require tremendous computational effort. To reduce this effort the so-called convex relaxation is incorporated into optimization process. The technique consists in reformulation of combinatorial problem into continuous convex one. Then, the convex relaxation is achieved by introducing the so-called sensor density function, which assigns a certain metric for individual candidate sensor location. Next, the value of this function is optimized in such a way that it maximize determinant of the Fisher Information Matrix. It has been shown that above algorithm is very effective and is distributing a number of sensors in several iterations only. Finally, it is worth noting that presented method can be used to distribute sensors for structural health monitoring. Moreover, it can be also applied in modal control strategies in vibration suppression.