Structural Damage Identification Method Research Articles

A Mahalanobis Distance Cumulant-Based Structural Damage Identification Method with IMFs and Fitting Residual of SHM Measurements

Data-driven damage identification based on measurements of the structural health monitoring (SHM) system is a hot issue. In this study, based on the intrinsic mode functions (IMFs) decomposed by the empirical mode decomposition (EMD) method and the trend term fitting residual of measured data, a structural damage identification method based on Mahalanobis distance cumulant (MDC) was proposed. The damage feature vector is composed of the squared MDC values and is calculated by the segmentation data set. It makes the changes of monitoring points caused by damage accumulate as “amplification effect,” so as to obtain more damage information. The calculation method of the damage feature vector and the damage identification procedure were given. A mass-spring system with four mass points and four springs was used to simulate the damage cases. The results showed that the damage feature vector MDC can effectively identify the occurrence and location of the damage. The dynamic measurements of a prestress concrete continuous box-girder bridge were used for decomposing into IMFs and the trend term by the EMD method and the recursive algorithm autoregressive-moving average with the exogenous inputs (RARMX) method, which were used for fitting the trend term and to obtain the fitting residual. By using the first n-order IMFs and the fitting residual as the clusters for damage identification, the effectiveness of the method is also shown.

Deep residual network framework for structural health monitoring

Convolutional neural networks have been widely employed for structural health monitoring and damage identification. The convolutional neural network is currently considered as the state-of-the-art method for structural damage identification due to its capabilities of efficient and robust feature learning in a hierarchical manner. It is a tendency to develop a convolutional neural network with a deeper architecture to gain a better performance. However, when the depth of the network increases to a certain level, the performance will degrade due to the gradient vanishing issue. Residual neural networks can avoid the problem of vanishing gradients by utilizing skip connections, which allows the information flowing to the next layer through identity mappings. In this article, a deep residual network framework is proposed for structural health monitoring of civil engineering structures. This framework is composed of purely residual blocks which operate as feature extractors and a fully connected layer as a regressor. It learns the damage-related features from the vibration characteristics such as mode shapes and maps them into the damage index labels, for example, stiffness reductions of structures. To evaluate the efficacy and robustness of the proposed framework, an intensive evaluation is conducted with both numerical and experimental studies. The comparison between the proposed approach and the state-of-the-art models, including a sparse autoencoder neural network, a shallow convolutional neural network and a convolutional neural network with the same structure but without skip connections, is conducted. In the numerical studies, a 7-storey steel frame is investigated. Four scenarios with considering measurement noise and finite element modelling errors in the data sets are studied. The proposed framework consistently outperforms the state-of-the-art models in all the scenarios, especially for the most challenging scenario, which includes both measurement noise and uncertainties. Experimental studies on a prestressed concrete bridge in the laboratory are conducted. The proposed framework demonstrates consistent damage prediction results on this beam with the state-of-the-art models.

Hybrid output-only structural system identification using random decrement and Kalman filter

A novel hybrid output-only structural identification and damage identification method is proposed. The method is developed by integration of Kalman filtering, as a model-based technique, and random decrement, as a data-driven technique. The random decrement method extracts free vibration from the measured responses of structural system under various types of loadings. The extracted free vibration is inputted to the Kalman filtering system to estimate the status of the structural system. In contrast to the traditional output-only techniques using Kalman filter, it is not required to estimate the input excitation in the damage detection process. The Kalman filter uses only the free vibration responses extracted from the random decrement. This also leads to downsizing the size of unknown state vector, which consequently decreases computational cost significantly. Since it is not required to use any parameter related to excitations in the mathematical model, the uncertainty of the physical model decreases. The proposed approach is numerically verified in three-degrees of freedom and ten-degrees of freedom systems under three different loading conditions. It is shown that the approach is robust to provide accurate estimation of states under physical changes due to structural damage assuming the input data is unknown. As another verification, the stiffness and damping matrices of a seven-story building on a shake table are estimated to show the capability of the method for damage identification of real structures. These numerical and experimental case studies demonstrate that the proposed technique is capable of detecting, localizing, and quantifying the extent of damage in a structure under a combination of any kinds of loadings.

Improved multi-objective sensor optimization method for structural damage identification based on genetic algorithm

An improved multi-objective sensor location optimization method based on genetic algorithm is proposed. According to the analytic relationship between structural response, mode shapes and damage quantities, the sensitivity matrix of structural dynamic response containing both structural modal information and damage information is firstly constructed, and then the objective function of multi-objective sensor location optimization method is established according to the minimum identification error criterion and the principle of ill- posedness in the inverse problem. In addition, a multi-objective genetic algorithm, NSGA-II, is used to solve the optimal location of measurement points. Finally, a simply supported box girder bridge is studied for validating the proposed method. Numerical simulations show that the improved optimization method based on genetic algorithm can achieve the optimization goal better, and the measurement points optimized by the improved method can get better damage identification results at the same level of measurement noise.

A Data-Driven Damage Identification Framework Based on Transmissibility Function Datasets and One-Dimensional Convolutional Neural Networks: Verification on a Structural Health Monitoring Benchmark Structure.

Vibration-based data-driven structural damage identification methods have gained large popularity because of their independence of high-fidelity models of target systems. However, the effectiveness of existing methods is constrained by critical shortcomings. For example, the measured vibration responses may contain insufficient damage-sensitive features and suffer from high instability under the interference of random excitations. Moreover, the capability of conventional intelligent algorithms in damage feature extraction and noise influence suppression is limited. To address the above issues, a novel damage identification framework was established in this study by integrating massive datasets constructed by structural transmissibility functions (TFs) and a deep learning strategy based on one-dimensional convolutional neural networks (1D CNNs). The effectiveness and efficiency of the TF-1D CNN framework were verified using an American Society of Civil Engineers (ASCE) structural health monitoring benchmark structure, from which dynamic responses were captured, subject to white noise random excitations and a number of different damage scenarios. The damage identification accuracy of the framework was examined and compared with others by using different dataset types and intelligent algorithms. Specifically, compared with time series (TS) and fast Fourier transform (FFT)-based frequency-domain signals, the TF signals exhibited more significant damage-sensitive features and stronger stability under excitation interference. The utilization of 1D CNN, on the other hand, exhibited some unique advantages over other machine learning algorithms (e.g., traditional artificial neural networks (ANNs)), particularly in aspects of computation efficiency, generalization ability, and noise immunity when treating massive, high-dimensional datasets. The developed TF-1D CNN damage identification framework was demonstrated to have practical value in future applications.

An iterative total least squares‐based estimation method for structural damage identification of 3D frame structures

An iterative total least squares‐based estimation method for structural damage identification of 3D frame structures

Model-Free Method for Damage Localization of Grid Structure

A model-free damage identification method for grid structures based on displacement difference is proposed. The inherent relationship between the displacement difference and the position of structural damage was deduced in detail by the Sherman–Morrison–Woodbury formula, and the basic principle of damage localization of the grid structure was obtained. That is, except for the tensile and compressive deformations of the damaged elements, the deformations of other elements were small, and only rigid body displacements occurred before and after the structural damage. According to this rule, a method for identifying the position of the damage was proposed for the space grid structure by using the rate of change of length for each element. Taking a space grid structure with a large number of elements as an example, the elastic modulus reduction method was used to simulate the damage to the elements, and the static and dynamic test parameters were simulated respectively to obtain the difference in displacement before and after the structural damage. The rate of change of length of each element was calculated based on the obtained displacement difference, and data noise was added to the simulation. The results indicated that the element with the larger length change rate in the structure was the most likely to be damaged, and the damaged element can be accurately evaluated even in the presence of noise in data.

Adaptive damage localization based on locally perturbed dynamic equilibrium and hierarchical clustering

Pseudo-excitation (PE) method is a recently developed damage identification method for flexible structures containing components like beams, plates and shells. Characterized by the high-order spatial derivatives, the approach has been shown to feature a high sensitivity to local damage. However, two major issues, i.e. susceptibility to measurement noise and unknown material/structural properties, hamper its practical applications. To tackle these problems, an adaptive damage localization method is proposed for plate-type structures, which combines the PE method with hierarchical clustering. In the proposed method, a general dynamic equilibrium model, involving unknown material/structural properties, is statistically identified and further used for damage localization. Moreover, noise-induced effects are quantified by using a hierarchical clustering for performance assessment of damage localization and process optimization of spatial derivative estimation to achieve more accurate damage localization. Meanwhile, a data fusion scheme is developed to avoid blind inspection zones, thus enhancing the capability of damage localization. Both numerical and experimental studies of cantilever plates containing two damage zones are conducted to validate the feasibility and the effectiveness of the proposed adaptive damage localization method. Results demonstrate that the proposed method outperforms the traditional PE method in terms of detection accuracy and robustness.

Non-contact structural health monitoring of a cable-stayed bridge: case study

In this article, the condition assessment of a cable-stayed bridge using remote sensing is presented. The displacement influence line (DIL) of the bridge under the live load tests is measured for a discrete number of target points. Three different remote sensing techniques including, laser scanning, terrestrial robotic total station and digital levelling are adopted for this purpose. It is demonstrated that DIL obtained by non-contact system is capable of identifying an emulated damage in an actual operating system. The contribution of the work is fourfold. First, a damage index based on the displacement profile of the bridge under the weigh-in-motion is extracted from the non-contact sensing system. Second, our study compares three different remote sensing techniques, namely, digital levelling, robotic total station and laser scanning and uses the measurements to validate the finite element model. Third, the effectiveness of the proposed method for structural damage identification is validated in a real-world large-scale operating structure. Finally, it is validated that strain-based influence line is highly likely to misidentify damage especially when the location of damage is not in the close proximity of the sensor; however, DIL is a better damage indicator even if damage occurs far from the measurement point.

Baseline updating method for structural damage identification using modal residual force and grey wolf optimization

ABSTRACTThis article presents two effective optimization-based model-updating approaches for structural damage identification using the modal residual force (MRF) concept. The first objective function employs a direct data-fitting procedure to inspect the amount of approaching between entries of the calculated MRF vectors for the monitored and analytical models of the structure. The second objective function uses the modal assurance criterion as a geometric tracing criterion to evaluate the amount of accordance between two vectors. The proposed objective functions are solved with a novel metaheuristic optimization technique, the grey wolf optimization algorithm. Four numerical examples are studied to demonstrate the efficiency of the proposed methods. Moreover, studies are conducted not only to assess the robustness of the methods in more realistic circumstances, but also to justify the necessity of using these techniques. Based on the obtained results, the second objective function is more sensitive to structural damage than the first objective function.

Experimental study on micro-damage identification in reinforced concrete beam with wavelet packet and DIC method

Abstract Structural damage identification has become a research hotspot in the field of science and engineering. Previous predominant lines of research on structural damage identification methods focused on macroscopic damage, which is visible to naked eyes, but there are few studies on structural micro-damage identification. Towards this end, this paper proposes a combination of digital image correlation (DIC) technique and wavelet packet analysis for micro-damage identification and to achieve real-time early warning of micro-damage initiation in concrete structures. This work implements a four-point bending test of reinforced concrete beams, as well as adopts the step loading and unloading method, following which, the beam acceleration response signal and the damage strain field are collected. Subsequently, the collected response and excitation are processed to obtain the excitation response function, reflecting the dynamic structural state. The wavelet packet is used to process the excitation response function and image under each load level to obtain the corresponding energy spectrum. In this way, the respective micro-damage identification indices are calculated for comparison. The experimental results show that the proposed methodology can properly characterize the damage state of structures under various stages of stress, provide a warning for the initiation of micro-damage, and even accurately determine the location and degree of micro-damage, based on the damage strain field.

Operational modal analysis using lifted continuously scanning laser Doppler vibrometer measurements and its application to baseline-free structural damage identification

A continuously scanning laser Doppler vibrometer (CSLDV) system is capable of efficient and spatially dense vibration measurements by sweeping its laser spot along a scan path assigned on a structure. This paper proposes a new operational modal analysis (OMA) method based on a data processing method for CSLDV measurements of a structure, called the lifting method, under white-noise excitation and applies a baseline-free method to identify structural damage using estimated mode shapes from the OMA method. The lifting method enables transformation of raw CSLDV measurements into measurements at individual virtual measurement points, as if the latter were made by use of an ordinary scanning laser Doppler vibrometer in a step-wise manner. It is shown that a correlation function with nonnegative time delays between lifted CSLDV measurements at two virtual measurement points on a structure under white-noise excitation and its power spectrum contain modal parameters of the structure, that is, natural frequencies, modal damping ratios, and mode shapes. The modal parameters can be estimated by using a standard OMA algorithm. A major advantage of the proposed OMA method is that curvature mode shapes associated with mode shapes estimated by the method can reflect local anomaly caused by small-sized structural damage, while those estimated by other existing OMA methods that use CSLDV measurements cannot. Numerical and experimental investigations are conducted to study the OMA method and baseline-free structural damage identification method. In the experimental investigation, effects of the scan frequency of a CSLDV system on the two methods were studied. It is shown in both the numerical and experimental investigations that modal parameters can be accurately estimated by the OMA method and structural damage can be successfully identified in neighborhoods with consistently high values of curvature damage indices.

Research on Damage Identification of Grid Structure Based on Genetic Algorithm

This paper proposes a genetic algorithm based damage identification method for grid structures. The genetic algorithm is used to process the modal information of the structure, and the damage identification of the truss structure is carried out. The stiffness reduction factor of the structural member is used as the optimization variable. The objective function is constructed according to the frequency and vibration mode, and the fitness function is established. The binary coding method is used to improve the crossover and mutation operators. In this paper, a grid structure model is used for numerical simulation analysis and verified by experiments. In the experimental stage, the grid structure is excited by hammering method, and the response data of each node and the modal information of the structure are obtained. Numerical simulation and experimental analysis show that the damage identification method based on genetic algorithm can effectively judge the location and extent of damage.

Definition of a load adaptive baseline by inverse finite element method for structural damage identification

Abstract One principle limitation to the implementation of Structural Health Monitoring (SHM) systems in real structures is the influence of different operational conditions with respect to those adopted during SHM system design, potentially leading to damage misclassifications. To overcome this issue, this work proposes a methodology to perform Structural Health Monitoring leveraging on the inverse Finite Element Method (iFEM). The iFEM methodology, based on the minimisation of a weighted least-squares functional defined as a comparison between the experimental strains and the corresponding numerical ones, enables the reconstruction of the strain field of a structure by means of a number of strain sensors without requiring any a-priori knowledge of the boundary load conditions. This allows providing a load-adaptive baseline based on an anomaly index that highlights the actual health state of the structure by comparing the strain reconstructed by the iFEM at some test locations with the strain measured by a test sensor in the same position, independently from the applied load and without training requirements for load cancelling. When the analysed structure is in a “healthy” condition, the two values match, otherwise they do not. If multiple test positions are considered, the damage position can also be inferred. Though the formulation of the diagnostic problem is general for an arbitrary component geometry and damage type, the proposed method is numerically demonstrated by means of a clamped plate subjected to different loads in the presence of single and multiple fatigue crack damages.

Structural Damage Recognition Based on Perturbations of Curvature Mode Shape and Frequency

A new method for structural damage identification is presented based on perturbations of curvature mode shape and frequency. Firstly, the structure’s mass and stiffness matrices are expressed as functions of its elements’ physical parameters, which reflect their damage states. According to differences in the curvature mode shape of the structure in undamaged and damaged states, possible damage equations and determined damage equations are established and used to solve for the elements’ damage parameters. Then, to ensure the accuracy of the recognition result, a reasonable solution is substituted into a damage-checking equation based on the change of frequency of the damaged structure. Numerical examples are used to show that, to identify the damage, only one order mode needs to be tested. When the degree of damage is low, first-order perturbation equations can be used to recognize the damage with sufficient accuracy. If the extent of the damage is high, second-order perturbation equations can be used to provide more accurate identification results.

Damage Identification for Underground Structure Based on Frequency Response Function.

Damage identification that is based on modal analysis is widely used in traditional structural damage identification. However, modal analysis is difficult in high damping structures and modal concentrated structures. Unlike approaches based on modal analysis, damage identification based on the frequency response function allows for the avoidance of error and easy verification through other test points. An updating algorithm is devised is this study by utilizing the frequency response function together with the dynamic reduction with respect to the selected design parameters. Numerical results indicate that the method can be used to define multiple parameters with large variation and incomplete measurement data and is robust against measurement noise. With the purpose of avoiding the occurrence of resonance and gaining additional information, the trial and error method has been used to choose a proper frequency. Furthermore, an experimental scale model in a soil box is subjected to the excitation of moving load to validate the effectiveness of the damage identification approach. The improved damage identification method for underground structures, which is based on the analysis of the frequency response function, can be adopted as an efficient and functional damage identification tool.

Wavelet entropy based structural damage identification under seismic excitation

In this work, an entropy based two-step structural damage identification method under seismic excitation is proposed. The measured signals are decomposed by means of wavelet packet transform, and the wavelet entropies are obtained on the basis of the information entropy theory. In the first step, the damage alarming indices, calculated with the wavelet entropies in undamaged and damaged conditions, are used as samples for Shewhart individuals control chart to alarm the structural damage. In the second step, the damage localization indices, constructed by calculating the differences of curvature of wavelet entropies in undamaged and damaged conditions, are fed to the back-propagation neural network to identify structure damage location. The numerical simulation and shaking table model test of an offshore platform under seismic excitation are implemented to verify the feasibility of the proposed two-step structural damage identification method. The results show that the proposed method needs only the non-stationary output data and has low sensitivity to signal noise.

A novel Tikhonov regularization-based iterative method for structural damage identification of offshore platforms

The structural damage identification, which entails finding a best approximate solution to an over-determined system of linear equations, is actually one of the practical problems encountered in structural health monitoring. A major challenge to structural damage identification is the ill-conditioned problem caused by noise contamination and spatially incomplete measurements. A novel Tikhonov regularization iterative method (TRIM) is proposed to solve the ill-conditioned system of linear equations. This method iteratively reconstructs the regularization matrix by gradually updating the regularized solution. A merit is that the false-positive indicators of damage are greatly reduced; and as a result this approach would be able to detect smaller damages that could not be detected by using traditional approaches. Another development embedded in TRIM is that a procedure, called singular value dichotomy, is developed to determine the regularization parameters. Several problems, such as the tremendous prior trials, due to the application of L-curve, are avoided. A numerical study is conducted on an offshore platform structure to demonstrate the effectiveness of the proposed method. The result shows that the new method outperforms the traditional Tikhonov regularization method in damage identification.

A Combined Modal Correlation Criterion for Structural Damage Identification with Noisy Modal Data

Structural damage identification is a scientific field that has attracted a lot of interest in the scientific community during the recent years. There have been many studies intending to find a reliable method to identify damage in structural elements both in location and extent. Most damage identification methods are based on the changes of dynamic characteristics and static responses, but the incompleteness of the test data is a great obstacle for both. In this paper, a structural damage identification method based on the finite element model updating is proposed, in order to provide the location and the extent of structural damage using incomplete modal data of a damaged structure. The structural damage identification problem is treated as an unconstrained optimization problem which is solved using the differential evolution search algorithm. The objective function used in the optimization process is based on a combination of two modal correlation criteria, providing a measure of consistency and correlation between estimations of mode shape vectors. The performance and robustness of the proposed approach are evaluated with two numerical examples: a simply supported concrete beam and a concrete frame under several damage scenarios. The obtained results exhibit high efficiency of the proposed approach for accurately identifying the location and extent of structural damage.

Sensitivity-based damage identification method for structures exposed to ground excitation

The purpose of this paper is to present a sensitivity-based finite element model (FEM) updating method using earthquake displacement response in the frequency domain and the frequency response function of structure due to ground excitation. The obtained sensitivity equation is solved by linear least square method through defining constraints on the design variables. Numerical examples of a plane truss and a plane frame support the fact that the proposed method is capable of reliable damage detection. In order to assess the effects of measurement and mass modelling errors on achieved results, model updating is conducted by adding random errors to numerically extracted displacement response and assigned mass properties. The issue of underlying soil foundation influences on obtained results is discussed and the proposed formulation is extended to more accurately capture the soil–structure behaviour. Results indicate that the proposed method is capable of identifying damage properties under different soil conditions with acceptable precision.