Institute of Fundamental Technological Research

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

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

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

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

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

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

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

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

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

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.

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)

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 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)

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

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 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

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 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 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.

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 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.