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For the simultaneous identification (SI) problem on the moving vehicle loads and bridge damage, the existing methods fail to appropriately consider the sparse characteristics of structural damage and ignore the prior information of vehicle loads, which make them suffering from challenges such as prolonged computation cost, poor noise robustness, and limited identification accuracy. To address this issue, a novel semi-convex function is proposed to construct a theoretical framework for the SI problem using the bridge dynamic responses subjected to moving vehicles in this study. Firstly, the bridge damage-induced virtual forces are conceptualized as a new form of moving residual forces characterized by block sparsity properties, and the damage location is then determined by the frequency characteristics with the largest fundamental frequency amplitude of moving residual forces. Secondly, a semi-convex function model encompassing moving forces and moving residual forces is defined. Combined with sparse regularization strategy, an improved alternating direction method of multipliers algorithm is proposed and applied to simultaneously solve for both moving vehicle loads and damage degrees. To assess the effectiveness and feasibility of the proposed method, extensive numerical validations are conducted in various bridge damage scenarios. Additionally, a series of truss bridge experiments are performed in laboratory under multiple damage and vehicle axle-weight conditions. The results show that compared with the existing outstanding methods, the proposed semi-convex function method can significantly reduce the identification cost, enhance robustness to noise, and demonstrate notable improvements in accuracy for the SI problem, which provides an innovative and more efficient solution to the SI problem in bridge engineering. [ABSTRACT FROM AUTHOR]

Physics-driven and data-driven methods are commonly used for impact force identification. Due to system identification errors, physics-driven methods often suffer from force oscillations and peak underestimations, leading to poor accuracy. Data-driven methods generally require massive experimental data, incurring expensive costs. Hence, achieving accurate and low-cost impact force identification in the presence of system identification errors remains a significant challenge. In this paper, we proposed a data-physics hybrid-driven deep learning method for impact force identification, named DPH-TrLSTM. The method utilizes the time-reversed long short-term memory (TrLSTM) network to establish the causal relationship from response to force. The data-physics hybrid (DPH) loss function is employed to mitigate the adverse effect of system identification errors. The DPH-TrLSTM method only requires the transfer matrix and a small amount of experimental data obtained from the system identification step, eliminating the need for additional experiments. Experimental results from 40 impact forces at eight locations on a composite plate demonstrated that the DPH-TrLSTM method could achieve mean peak and relative errors below 1.0% and 2.5%, respectively, significantly outperforming the three regularization methods. This result suggests that the proposed method can perform high-accuracy impact force identification even when system identification errors exist. Moreover, the effect of system identification errors on the method's performance can be evaluated using the min–max curve, thereby determining its applicable scope. The study further reveals that system identification errors are the key reason for the poor performance of the three regularization methods. The choice of measurement points may affect the performance of DPH-TrLSTM, primarily due to system identification errors rather than the condition number of the transfer matrix. [ABSTRACT FROM AUTHOR]

This paper discusses isotropic sparse regularization for a random field on the unit sphere S 2 in R 3 , where the field is expanded in terms of a spherical harmonic basis. A key feature is that the norm used in the regularization term, a hybrid of the ℓ 1 and ℓ 2 -norms, is chosen so that the regularization preserves isotropy, in the sense that if the observed random field is strongly isotropic then so too is the regularized field. The Pareto efficient frontier is used to display the trade-off between the sparsity-inducing norm and the data discrepancy term, in order to help in the choice of a suitable regularization parameter. A numerical example using Cosmic Microwave Background (CMB) data is considered in detail. In particular, the numerical results explore the trade-off between regularization and discrepancy, and show that substantial sparsity can be achieved along with small L 2 error. [ABSTRACT FROM AUTHOR]

The present work proposes a seismic response estimation framework for post-earthquake structural condition assessment via acceleration measurements. An augmented sparse state space model is first derived to represent the underlying governing equations of the system of interest with hysteresis nonlinearity. A Bayesian filter is then utilized to provide the displacement estimate under an earthquake excitation by fusing the identified sparse state space model with the measured system acceleration. To avoid subjective assumptions on the process and observation noises in the Bayesian filter, a double-loop process is proposed, where the inner loop is an online Bayesian filtering by the unscented Kalman filter with Robbins-Monro algorithm, while the outer loop is an offline Bayesian updating by the transitional Markov chain Monte Carlo method. The feasibility of the framework is demonstrated on a simple illustrative example and a followed engineering application to the state estimation of a bridge pier finite element model. The results indicate the capability of the framework to properly infer the system displacement, including its residual components. [ABSTRACT FROM AUTHOR]

• This paper proposes an improved Jaya algorithm for damage identification. • Objective function is improved based on sparse regularization and Bayesian inference. • Benchmark studies are conducted to demonstrate the improvement of this approach. • Numerical and experimental investigations are conducted to demonstrate the performance. • Good identification results are obtained with a limited quantity of modal data. Structural damage identification can be considered as an optimization problem, by defining an appropriate objective function relevant to structural parameters to be identified with optimization techniques. This paper proposes a new heuristic algorithm, named improved Jaya (I-Jaya) algorithm, for structural damage identification with the modified objective function based on sparse regularization and Bayesian inference. To improve the global optimization capacity and robustness of the original Jaya algorithm, a clustering strategy is employed to replace solutions with low-quality objective values and a new updated equation is used for the best-so-far solution. The objective function that is sensitive and robust for effective and reliable damage identification is developed through sparse regularization and Bayesian inference and used for optimization analysis with the proposed I-Jaya algorithm. Benchmark tests are conducted to verify the improvement in the developed algorithm. Numerical studies on a truss structure and experimental validations on an experimental reinforced concrete bridge model are performed to verify the developed approach. A limited quantity of modal data, which is distinctively less than the number of unknown system parameters, are used for structural damage identification. Significant measurement noise effect and modelling errors are considered. Damage identification results demonstrate that the proposed method based on the I-Jaya algorithm and the modified objective function based on sparse regularization and Bayesian inference can provide accurate and reliable damage identification, indicating the proposed method is a promising approach for structural damage detection using data with significant uncertainties and limited measurement information. [ABSTRACT FROM AUTHOR]

Highlights • A new sensitivity-free damage identification approach is proposed with the incomplete modal data. • The sparse regularization is introduced to circumvent the drawback that the identification results are very sensitive to the measurement noise due to the insufficient amount of the measured incomplete modal data. • A new decoupled goal function (with respect to the damage parameters) is proposed and the alternating minimization approach is called to get the solution. • A simple and efficient threshold setting method is proposed to determine a proper sparse regularization parameter. • Numerical and experimental examples show that the present damage identification approach with the sparse regularization obviously performs better than the approach without the sparse regularization and the sensitivity approach with the Tikhonov regularization. • The present approach can also work for only frequency measurements. Abstract The incomplete modal data is mostly measured for experimental and engineering structures, however, its application into structural damage identification suffers from the drawback that the amount of the incomplete modal data is often insufficient, rendering the identification very sensitive to the measurement noise. Aiming to overcome this drawback, this paper proposes a new damage identification approach that combines the incomplete modal data with the sparse regularization. The realization of the proposed damage identification approach is mainly threefold: (a) The first is the establishment of a new goal function which is decoupled with respect to the damage parameters. To this end, the decomposition of the stiffness matrix so that the damage parameters are contained in a diagonal matrix must be introduced. (b) The second is the application of the alternating minimization approach to get the solution of the new goal function. (c) The third is the development of a novel and simple threshold setting method to properly determine the sparse regularization parameter. The feature of the proposed damage identification approach lies in that the sensitivity analysis is not involved and the exact orders of the modal data are not demanded. Numerical and experimental examples are conducted to verify the proposed damage identification approach. As a result, the proposed new goal function along with the sparse regularization indeed improves the accuracy and robustness for damage identification, in comparison to the cases when no regularization is used with the new goal function and when the Tikhonov regularization is incorporated into the conventional nonlinear least-squares goal function. Moreover, the proposed damage identification approach can work for various types of structures and even for only frequency measurements. [ABSTRACT FROM AUTHOR]

Abstract The objective of this paper is to provide a new damage identification method using frequency response data. In this approach, the inverse identification problem is treated as a nonlinear optimization problem whose objective function is just the constitutive relation error (CRE). To circumvent the ill-posedness of the inverse problem which is caused by use of the possibly insufficient data and enhance the robustness of the identification process, the sparse regularization is introduced where the ℓ 1 -norm regularization term is added to the original CRE function. In regard to the minimum solution of the sparse-regularized CRE objective function, the alternating minimization (AM) method is established. The attractive features of the present damage identification approach are: (a) while coping with the sparse regularization, a closed-form solution is obtained due to the decoupling of the CRE function with respect to the damage parameters and hence the sparse regularization term would introduce little computational complexity; (b) the sparse regularization parameters are directly determined by a simple threshold setting method; (c) no sensitivity analysis is involved herein. Numerical examples are conducted to verify the proposed approach and the results show that the sparse regularization obviously improves the accuracy and robustness for the identified damages. [ABSTRACT FROM AUTHOR]

Highlights • Method is applicable to systems with nonlinear elastic and inelastic behavior. • The method allows one to extract the force-displacement behavior with memory. • Discovery of the nonlinear/inelastic features embedded within the system. • Extraction of equations of motion and physics of the system. • Method is applicable for systems in Civil, Mechanical, and Aerospace engineering. Abstract A system identification technique suitable for single degree of freedom (SDOF) and multiple degree of freedom (MDOF) structural systems with either nonlinear elastic or inelastic/hysteretic behavior is proposed in this paper. The method is a parametric modeling technique based on sparse regularization. The proposed framework is capable of discovering the underlying governing equations of the system of interest from input-output data. We build on the work of Brunton et al. (2016) by including functions that allow the discovery of significant nonlinearities, and hystertic or inelastic behavior with permanent deformation. We also present model selection using sparse regularization and cross validation using Akaike criteria. We demonstrate through experimental validation that the technique presented in this paper is applicable to a significantly broader class of problems. The effectiveness of the proposed method is evaluated through numerical examples of a 2-story nonlinear or inelastic building with a adjustable stiffness device. We also present experimental validation using a unique nonlinear structural system that consists of a MDOF structural system and a nonlinear negative stiffness device (NSD) to illustrate the significant ability of the proposed framework. We successfully identify the following structural systems from experimental data: a SDOF yielding frame without NSD; a SDOF yielding frame with NSD; and a 3-DOF frame with NSD. The extracted sparse model also shows potential for generalization. [ABSTRACT FROM AUTHOR]

• Novel method is proposed for eliminating mass loading effect during impact force identification. • Proposed method introduces pseudo-forces to re-express accelerometer mass loading effects. • Proposed method can simultaneously identify impact force and accelerometer masses. • Application of proposed sparse regularization-based method is effective and robust. Identifying impact force from measured structural responses has been extensively studied. Contact sensors such as accelerometers are often applied for recording the structural responses. Masses of the contact sensors would change the structural dynamic properties, especially for lightweight structures. To eliminate the effects of additional masses in force identification, this paper proposes a novel method for reconstructing the impact force. The proposed method is developed from existing sparse regularization-based method. In the process of forward analysis, a key step is to introduce some pseudo-forces for simulation of the additional mass loading effects. The measured responses are regarded as the sum of two components. One is induced by the impact force, and the other one is caused via pseudo-forces. In the process of inverse analysis, impact force identification involving notable sensor mass is treated as a problem of multi-force identification, in which both impact force and pseudo-forces are simultaneously identified. The impact force is identified via sparse regularization which determines more accurate results insensitive to noise. Masses of installed sensors are estimated from the identified pseudo-forces because the pseudo-forces are a translated expression of mass loading effects. Therefore, the effects of additional masses can be eliminated in force identification. Numerical simulations and experimental studies on a cantilever beam are carried out. Cases studies show that the proposed method can be applied for estimating the impact force and additional masses with high accuracy and strong robustness. Some related issues are discussed as well. [ABSTRACT FROM AUTHOR]

We propose a constrained inpainting model to recover an image from its incomplete and/or inaccurate wavelet coefficients. The objective functional of the proposed model uses the ℓ 0 norm to promote the sparsity of the resulting image in a tight framelet system. To overcome the algorithmic difficulty caused by the use of the ℓ 0 norm, we approximate the ℓ 0 norm by its Moreau envelope. A fixed-point proximity algorithm is developed to solve the new approximation optimization model and the convergence analysis of the algorithm is provided. The proposed algorithm can be accelerated by the FISTA technique and we also develop an adaptive method to determine the approximation parameter to further speed up the algorithm. We demonstrate that the rows of the discrete cosine transform matrix can generate a redundant tight framelet system with symmetric boundary condition, which has good ability to extract information from incomplete wavelet coefficients. Using the tight framelet system, our numerical experiments show that the proposed model and the related fixed-point algorithm can recover images with much higher quality in terms of the PSNR values and visual quality of the restored images than the models based on the ℓ 1 norm and the total variation. [ABSTRACT FROM AUTHOR]

The classical function expansion method based on minimizing l 2 -norm of the response residual employs various basis functions to represent the unknown force. Its difficulty lies in determining the optimum number of basis functions. Considering the sparsity of force in the time domain or in other basis space, we develop a general sparse regularization method based on minimizing l 1 -norm of the coefficient vector of basis functions. The number of basis functions is adaptively determined by minimizing the number of nonzero components in the coefficient vector during the sparse regularization process. First, according to the profile of the unknown force, the dictionary composed of basis functions is determined. Second, a sparsity convex optimization model for force identification is constructed. Third, given the transfer function and the operational response, Sparse reconstruction by separable approximation (SpaRSA) is developed to solve the sparse regularization problem of force identification. Finally, experiments including identification of impact and harmonic forces are conducted on a cantilever thin plate structure to illustrate the effectiveness and applicability of SpaRSA. Besides the Dirac dictionary, other three sparse dictionaries including Db6 wavelets, Sym4 wavelets and cubic B-spline functions can also accurately identify both the single and double impact forces from highly noisy responses in a sparse representation frame. The discrete cosine functions can also successfully reconstruct the harmonic forces including the sinusoidal, square and triangular forces. Conversely, the traditional Tikhonov regularization method with the L-curve criterion fails to identify both the impact and harmonic forces in these cases. [ABSTRACT FROM AUTHOR]

• A novel MFI method based on learning dictionary with double sparsity is proposed. • Dictionary learning technique is employed to design a better fit force dictionary based on the measured response data. • The force dictionary is assumed to be expressed sparsely over the base dictionary, and the moving force is sparse over the force dictionary simultaneously. • Sparse K-SVD algorithm is employed to realize the learning process through alternatively updating between double sparse codes. Moving force identification (MFI) is essential for the bridge safety as it is one of the major loads acting on the bridge deck. MFI techniques based on force dictionary are promising owing to their prominent performance in solving ill-posed problems and calculation efficiency. Since the specific forms of authentic moving forces are complex and unknown, a fixed dictionary normally adopted tends to fail in expressing moving forces sparsely enough. In this study, dictionary learning (DL) is introduced into the field of MFI to design a better fit force dictionary based on the measured response data. A novel MFI method based on learning dictionary with double sparsity is proposed. Firstly, the MFI equation in time domain which describes the relationship between moving force and measured structural responses is established. Then a sparse dictionary model is designed in which the force dictionary is assumed to be expressed sparsely over the base dictionary, and the moving force is sparse over the force dictionary simultaneously. Moreover, the sparse K-singular-value-decomposition (K-SVD) algorithm is employed to realize the learning process through alternatively updating between double sparse codes. Finally, the learned force dictionary and moving forces are estimated through base force dictionary and double sparse codes. Numerical simulations and experimental studies are carried out to investigate the performance of the proposed method, and the results clearly certify its effectiveness and robustness. [ABSTRACT FROM AUTHOR]

For impact force identification, as a severe ill-posed inverse problem, the wavelet-transform method individually requires a large and accurate decomposition level to obtain a robust and accurate result. However, continuing to increase the number of cubic B-spline dual scaling functions will make the cost of calculation too expansive. To overcome the above mentioned difficulties of impact force identification, sparse regularization is used as a post-processing to solve the residual ill-posed problems. During the iteration process of sparse regularization, the two-step iterative shrinkage-thresholding algorithm (TwIST) algorithm is applied rather than the original iterative shrinkage-thresholding (IST) algorithm, which is more suitable for sparse solution. By combining cubic B-spline scaling functions as pre-processing and TwIST sparse regularization algorithm as post-processing, the proposed method TwIST-SpaR-CB can obtain better impact force identification accuracy with improved computational efficiency. The effectiveness and accuracy of the proposed method compared with the two individual method were verified by experimental and numerical results. • Cubic B-spline dual scaling functions compose a dictionary. • Cubic B-spline require appropriate but low decomposition levels. • Sparse regularization as a post-processing to solve the residual ill-posed problem. • The number of calculation iterations can be reduced. • The recognition accuracy can be improved. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron microscopy, etc. Since the acquired tomographic data is highly incomplete, the reconstruction problem is severely ill-posed and the traditional reconstruction methods, e.g. filtered backprojection (FBP), do not perform well in such situations. To stabilize the reconstruction procedure additional prior knowledge about the unknown object has to be integrated into the reconstruction process. In this work, we propose the use of the sparse regularization technique in combination with curvelets. We argue that this technique gives rise to an edge-preserving reconstruction. Moreover, we show that the dimension of the problem can be significantly reduced in the curvelet domain. To this end, we give a characterization of the kernel of the limited angle Radon transform in terms of curvelets and derive a characterization of solutions obtained through curvelet sparse regularization. In numerical experiments, we will show that the theoretical results directly translate into practice and that the proposed method outperforms classical reconstructions. [Copyright &y& Elsevier]

Ø Sparse regularization and moving average constraint are used for moving force identification. Ø Identified moving forces have sparse representation and stable local average values. Ø Identified moving forces are robust and not sensitive to calibration errors of sensors. Ø Performance is better than l 1 -norm regularization and moving average Tikhonov methods. An accurate input-output mathematical model is the basis of moving force identification (MFI). However, an absolutely accurate mathematical model between moving forces and structural responses is difficult to be established due to some practical reasons, such as calibration error, modelling error, and so on. An inaccurate input-output relationship may lead to some unreasonable MFI results, for example, an obvious fluctuation of the trend lines in moving forces. To tackle this problem, a constrained sparse regularization-based method is proposed for MFI in this study. Wherein, structural responses obtained from sensors with calibration errors are taken as the inputs. A system matrix reflecting the input-output relationship is formulated in the consideration of unknown moving forces and initial conditions. Sparse regularization is adopted for ensuring that the identified forces are sparse and robust. The constrained condition is expressed as a non-negative function. This function is defined via a strategy named moving average and applied for reflecting the degree of fluctuation of the trend lines for the moving forces. The constrained problem is solved as a standard form of l 1 -norm regularization via relaxing the constrained condition appropriately. Numerical simulations and experimental studies are conducted for assessing the effectiveness and feasibility of the proposed method. Effects of different calibration errors of sensors are discussed in detail. Illustrated results show that the proposed method can reconstruct the moving forces with a good performance. Some related issues are discussed as well. [ABSTRACT FROM AUTHOR]

This paper proposes a method for separating rail and wheel noise contributions via sparse regularization of microphone array data. The underlying idea is to promote sparse solutions, which jointly approximate the two noise contributions with few non-zero coefficients. The main hypothesis is that the acoustic field radiated by the rail is sparse in a dictionary of plane waves, that the acoustic field radiated by the wheels is sparse in a dictionary of moving sources, and that both acoustic fields are dense in the opposite dictionaries. How well this happens is studied with the coherence between the plane waves and the moving sources. The strength of the proposed approach is that it does not require static tests prior to the pass-by. The separation is performed in three main steps, executed in the time-frequency domain. First, the rail contribution is separated from the total pass-by noise using matching pursuit optimization, promoting solutions with a limited number of plane waves per frequency. Second, the residual between the total pass-by noise and the estimated rail noise is calculated. And third, the wheel contribution is separated from the residual via ℓ 1 -norm minimization, promoting solutions that are row-sparse at all frequencies. The separation performance is investigated with synthetic data, and validated with experimental data against reference predictions with the TWINS software, for pass-by noise measurements of trains running at 40, 80 and 160 km/h. [ABSTRACT FROM AUTHOR]

As a typical inverse problem, impact force identification tends to be a challenge owing to its ill-posedness. Recently, the sparse characteristic of the impact force in time domain are taken into consideration to convert the ill-posed problem into a sparse recovery task. The classic way to obtain sparse approximate solutions of impact force is to use the L1-norm regularization. However, underestimating the exact solution inevitably happens when applying the L1-norm regularization to impact force identification. In this paper, a novel sparse regularization method with generalized minimax-concave (GMC) penalty is proposed to deal with the impact force identification problem. Even if the GMC penalty turns out to be a nonconvex regularizer to promote sparsity in the sparse estimation, it retains the convexity of the sparsity-regularized least squares cost function and the global optimal solution can be found by convex optimization. Additionally, an approach to adaptively set regularization parameters is presented. Finally, simulations and experiments are conducted to verify the performances of the proposed method, and the results are compared with those of the L1-norm regularization method. Results demonstrate that the nonconvex sparse regularization based on GMC can produce more accurate estimations for impact force identification. • A non-sparse regularization method with generalized minimax-concave(GMC) penalty is proposed for impact force identification. • The GMC penalty not only ensures the convexity of the cost function, but also enhances the sparsity and accuracy of the solution. • A strategy to set regularization parameter is presented. • Compared with the L1-norm, performances of the proposed method are validated through simulations and experiments. [ABSTRACT FROM AUTHOR]

• Novel method based on matrix regularization with sparse penalty term is proposed for force identification. • Unknown force and initial conditions are together used for establishing matrix-based identified equations. • System matrix with relatively small size can be used for solving large-scale problem of force identification. • Application of proposed matrix regularization-based method is effective and time-saving. Identification of force via structural responses has been widely studied due to the force is always difficult or even impossible to be measured directly. Force identification is a typical ill-posed problem. To overcome this drawback, regularization methods have been widely studied. However, existing regularization methods used for force identification belong to the vector-based method, in which unknown force and structural responses are organized in two vectors, respectively. This characteristic decides that the identified process of a long-duration problem will be time-consuming because the size of system matrix is large. In view of this, a novel matrix regularization-based method is proposed for force identification in this paper. Combing with moving time windows, the structural responses are extracted and organized in a form of matrix. A system matrix is formulated by considering both unknown force and unknown initial conditions. Then a governing equation is established, in which structural excitation sources such as force and initial condition are orderly stored in a form of matrix. To obtain a stable solution, matrix regularization is introduced for improving the matrix-based governing equation. Herein, the sparse penalty term is considered as the sum of absolute values of elements in the matrix of excitation sources. Fast iterative shrinkage-thresholding algorithm (FISTA) is applied for solving the matrix regularization model. The regularization parameter is selected according to Bayesian information criterion (BIC). Finally, numerical simulations and experimental studies are carried out for assessing the feasibility and effectiveness of the proposed method. Illustrated results show that the proposed method is effective and time-saving. It can use a system matrix with a relatively small size to dealing with a large-scale problem of force identification. Some related issues are discussed as well. [ABSTRACT FROM AUTHOR]

• A novel method is proposed for MFI based on CS with redundant dictionaries. • An indirect way to design dictionary for different types of structural responses. • A MFI governing equation is formulated by exploiting compressed coefficients directly. • Compressed coefficients rather than structural responses can be directly used for MFI. • The identified moving forces are in good agreement with the true ones. Moving force identification (MFI) techniques have been widely studied in recent years. However, the contradiction between response acquisition and energy consumption limits applications of existing MFI methods and has become one of the most prominent issues in the field of structural health monitoring (SHM). In fact, sample length of response data can be shortened by exploiting compressed coefficients of responses based on compressed sensing (CS) theory. In order to mitigate this contradiction and to study if these compressed coefficients can be efficiently exploited for MFI, a novel method is proposed for MFI based on CS with redundant dictionaries in this study. Firstly, a redundant dictionary is designed for creating a sparse expression on each moving force based on prior knowledge of moving forces. Then, by the aid of relationship between moving forces and responses, an indirect way is presented to design dictionaries for different types of structural responses, sparse expression of responses is established simultaneously, and a MFI governing equation is formulated by directly exploiting compressed coefficients of responses via CS. Moreover, sparse regularization is introduced to ensure the accuracy of MFI results. Finally, the proposed method is validated by both numerical simulations and experimental verifications. The illustrated results show that the sample length of each acquired data can be obviously shortened and the compressed coefficients rather than structural responses can be directly used for MFI. The identified moving forces are in good agreement with the true ones, which shows the effectiveness and applicability of the proposed method. In addition, the proposed method can estimate the total weight of the car with a good accuracy and a strong robustness to noise. [ABSTRACT FROM AUTHOR]

• Guidance for the application of power spectrum density data based on minimum constitutive relation error principle has been provided. • Only measurement power spectrum density data from few limited sensors are needed for damage identification. • Sparse regularization has demonstrated a pronounced effect on the accuracy and robustness for the identification results. This paper proposes a novel model-based damage identification strategy based on minimum constitutive relation error and sparse regularization using the power spectrum density data. Firstly, the stationary random vibration problem is transformed into a series of harmonic vibrations by the pseudo excitation method and the error in constitutive relation is established by the admissible stress field and admissible displacement field. A much more general and simpler strategy so as to build the admissible stress field is addressed by requiring only an extra decomposition of the stiffness matrix. Then, the sparse regularization is added to the original constitutive relation error objective function to circumvent the ill-posedness of the inverse problem. Finally, the solution of this nonlinear optimization problem is solved by the alternating minimization method. The proposed method has the advantage that only measurement power spectrum density data from few limited sensors are needed in the inverse analysis. Numerical and experimental results show the effectiveness and robustness of this approach. [ABSTRACT FROM AUTHOR]