Damage Identification Results Research Articles

Physics-guided deep learning based on modal sensitivity for structural damage identification with unseen damage patterns

Recently, wide attention has been paid to develop deep learning-based models for structural damage identification. However, in most of the studies, the pure deep learning-based structural damage identification methods lack physical interpretability and scientific consistency for generalization. Therefore, although such methods can achieve good damage identification results when data with similar damage patterns used for training and testing the network model, they usually give poor predictions in the unseen domain, i.e., the network’s extrapolation ability is limited. In this research, a physics-guided deep learning neural network (PGDLNN) is proposed by incorporating the physical loss constructed by structural modal parameters sensitivity analysis into the original Convolutional Neural Network (CNN) for structural damage identification. The model’s physical interpretability is improved, which can lead to more accurate damage identification results, especially in the domain with unseen damage patterns in training the network model. Numerical and experimental studies on simply supported beams are carried out to demonstrate the feasibility and effectiveness of the proposed method. The influences of measurement noise and incomplete measurements are also investigated. The results show that the incorporation of physical knowledge to deep learning model can enhance the generalization of the network, and hence improve the accuracy of damage severity quantification. This study not only performs damage localization and quantification simultaneously using the physics-guided deep learning neural network, but also demonstrates the superiority of incorporating physical knowledge into data-driven deep learning models for structural health monitoring.

Frequency Recognition of a Free Damped Vibration Signal Based on Improved Elias Aboutanios Interpolation Method

The free damped vibration signal of engineering structures is an energy-limited signal, and the effective signal length is limited by the damped factor. The classical periodic graph method is affected by signal damped coefficient and noise, and it is difficult to obtain satisfactory recognition accuracy. This article proposes the IEAI method for frequency estimation of freely damped vibration signal, considering the influence of initial phase. By combining discrete Fourier transform with complex operations, the signal is iteratively interpolated to improve the accuracy of frequency estimation .The simulation results show that the mean error of the IEAI method is 1.3%~26.5% of the traditional Periodogram method, A&M method and Welch method, and the Root-mean-square deviation is 7.4%~40.3% of the latter three methods under the condition of high signal-to-noise ratio; In the case of low signal-to-noise ratio, the mean error of the IEAI method is 16.2%~43.0% of the latter three, and the Root-mean-square deviation is 20.8%~81.8% of the latter three. The experimental results of cantilever beam damage identification show that the IEAI method is more sensitive to small structural damages and can be used for the identification and diagnosis of small structural damages.

Cross-domain damage identification of bridge based on generative adversarial and deep adaptation networks

Model-driven bridge damage identification based on video measurement frequently encounters challenges due to low data quality, which leads to significant discrepancy between numerical model and actual bridge, exacerbating the cross-domain problem. To address this issue, the generative adversarial network (GAN) and Deep Adaptation Network (DAN) are introduced in this paper. The principles and utilizations of the two networks are introduced, while GAN is used to generate a large number of high-quality artificial samples to enhance the learning, and DAN is used to extract generic damage features to cross the source and target domains. A damage experiment of a steel truss model bridge is conducted to validate the proposed method, and the damage identification results of the proposed method and the traditional method are compared. The identification results illustrate that the proposed method can generate a substantial number of artificial samples only using a limited number of real target samples. These artificial samples facilitate the learning of cross-domain damage features, which ultimately contributes to achieving higher accuracy in damage identification.

Uncertain damage identification methods based on residual force vector under the influence of measurement noise

This paper proposes probabilistic and interval methods, grounded in the residual force vector technique, to quantify measurement uncertainties and effectively integrate them into the identification process. In the probabilistic method, the measurement noise is assumed to be a zero-mean normal distribution, while the stiffness parameters of structural elements are assumed to follow a normal distribution, represented by mean values and standard deviations. In the interval method, the measurement noise is modelled as interval numbers, and the interval perturbation technique is employed to derive interval bounds for elemental stiffness parameters. A two-step model updating strategy is implemented, separately addressing pristine and damaged structures, to mitigate modeling errors. By using the results of probabilistic damage identification, a novel damage index termed damage expectation capable of capturing both the extent and probability of damage is introduced. Furthermore, an interval damage index is introduced to quantify the damage based on interval damage identification results. The impact of noise levels on the statistical properties of uncertain damage indices is also investigated. Numerical examples reveal that deterministic indexes exhibit a monotonic increase in average values with increasing noise levels. Particularly, as noise levels rise, the standard deviation of the combination index initially surpasses the deterministic damage index but eventually diminishes. Through the proposed methodology, structural damage can be identified even in the presence of uncertainties. The efficacy of the proposed damage identification technique is also validated by experimental data.

Evaluation of BFRP strengthening and repairing effects on concrete beams using DIC and YOLO-v5 object detection algorithm

In this study the effectiveness of using Basalt Fiber Reinforced Polymer (BFRP) for strengthening and repairing concrete beams after pre-damage was investigated. Four-point bending tests were conducted on concrete beams, and their strain nephograms were analyzed using 3D-DIC (Digital Image Correlation) to assess the BFRP reinforcement and repair effects on concrete. A damage indicator model based on stress-displacement curves was proposed to quantify concrete damage and evaluate the BFRP strengthening effect. Additionally, the YOLO-v5 object detection algorithm was employed to detect surface damage on concrete specimens, and its results were cross-verified with the damage indicator. The study reveals that BFRP reinforcement primarily affects the concrete beams beyond the elastic limit, enhancing their load-bearing capacity by 37.91% and improving ductility. The proposed damage indicator proves successful in quantifying damage in BFRP-reinforced concrete beams, distinguishing the transition points between elastic, cracking, and failure stages. The YOLO-v5 algorithm accurately detects damage in strain nephograms, providing sensitive and timely identification of concrete damage. Results proves that the offset ratio between the damage identification results of YOLO-v5 and the experimental stress-displacement curve data is between − 3.03% and 8.66%. The proposed damage indicator and YOLO-v5 detection offer valuable tools for evaluating damage and monitoring the health of concrete structures in engineering applications.

Output-only structural damage identification based on Q-learning hybrid evolutionary algorithm and response reconstruction technique

Various structural damage identification methods have been developed and employed, while the absence of input excitation measurements may pose a huge challenge in their application since the input forces such as seismic load, traffic load, wind load, are not directly measurable. To address this issue, in the present paper, a novel output-only structural damage detection approach based on Q-learning hybrid evolutionary algorithm (QHEA) and response reconstruction technique is presented. On the one hand, the external excitation and structural acceleration responses are reconstructed with the aid of response reconstruction and Tikhonov regularization techniques in time domain. Structural damage identification can be formulated as an optimization-based inverse problem. On the other hand, a new optimization framework QHEA integrating Jaya algorithm, differential evolution, Q-learning algorithm is developed as search tool. The unknown structural parameters and unmeasured input force are iteratively updated by using two different measurement sets until the reconstructed acceleration responses agree well with the measured responses. Numerical examples involving a cantilever beam structure under single excitation and a simply-supported 51-bar truss structure under multiple excitations, as well as an experimental five-floor steel frame structure in the laboratory are carried out to validate the effectiveness of the proposed method. The final results demonstrate that the proposed method can accurately detect damage locations and quantify damage extents without the information of input excitation. In addition, the superiority of QHEA over other heuristic algorithms, the uncertainties of measurement noise and modeling errors on damage identification results are further examined.

Non-Destructive Damage Evaluation Based on Static Response for Beam-like Structures Considering Shear Deformation

Shear deformation plays an important role in certain structures, and neglecting shear deformation can affect the accuracy of structural response. This paper proposes a non-destructive damage evaluation method that considers shear deformation, based on static response, for identifying corrosion in beam-like structures. The influence of shear deformation on nodal displacement for simply supported beams with different cross-sections was analyzed. The results indicate that even small errors yield inaccurate identification results when neglecting shear deformation. To solve this problem, analytical displacements of the structure were determined based on the Timoshenko beam theory, and the objective function was established. Additionally, the damage identification results were obtained by minimizing the objective function using the interior point method. Several progressively complex examples were used to demonstrate the effectiveness of the proposed method in identifying damage in beam-like structures.

Structural Damage Identification Based on Convolutional Neural Network Group Considering the Sensor Fault

This article proposes a structural damage identification method based on one-dimensional convolutional neural network group considering sensor faults. The method aims to reduce the damage misjudgment caused by sensor faults. In the proposed method, according to the sensor layout, some convolutional neural network sub-models are established to extract the features from raw vibration data for sensor fault diagnosis and structural damage identification; then two convolutional neural networks groups, namely the sensor fault diagnosis group and the damage identification group are designed on the basis of the functions of each sub-model. The sensor fault diagnosis group determines whether the sensor data is abnormal and truncates the abnormal signal. The remaining normal signal are entered into the damage identification group and the final damage identification results are calculated according to the statistical decision module. The effectiveness of the devised method is verified by the IASC-ASCE benchmark structure and laboratory experiments. The results demonstrate that the sensor fault diagnosis and damage identification accuracy of each sub-model ranges from 98.54% to 99.77% and from 87.21% to 91.74% respectively at different noise levels; the damage identification group can reduce the impact of sub-model misjudgment on the structural damage identification. The accuracy of the final damage identification results is 100%. The identification time of all samples in the test set is 53.09 s and 22.93 s, respectively, for SHM benchmark and Laboratory experiment cases. And the average judgment time of each submodel in the sensor fault diagnosis group was 278 and 94 ms, and that of each submodel in the damage identification group was 294 and 105 ms, respectively, for a single test sample, which fulfills the requirements of online damage identification for structural health monitoring.

Chilling injury monitoring and intensity identification of dryland maize in Heilongjiang.

Accurate and timely access to large-scale crop damage information provides an essential reference for responding to agricultural disaster prevention and mitigation needs and ensuring food production security. This study aims to reveal the new characteristics of low-temperature cold damage to maize in the context of climate warming. Taking Heilongjiang, one of the provinces with the highest latitude, the most significant climate change and the largest maize production in China, as the study area, we combined meteorological stations and MODIS remote sensing data to spatially identify the occurrence and intensity of cold damage to maize based on the growing season temperature distance level index, and to assess the extent of cold damage. The main findings are as follows. (1) The frequency and intensity range of cold damage in the growing season (May-September) in Heilongjiang Province from 1991 to 2020 against climate warming showed a decreasing trend. Among them, the average temperature from 1991 to 2000 was 17.777°C, with seven occurrences of maize cold damage years, of which five years were widespread cold damage and two years was regional cold damage. The average temperature from 2000 to 2010 was 18.137°C, with cold damage three times, of which two years were regional cold damage and one year was widespread cold damage. The average temperature from 2010-2020 was 18.130°C, with one maize cold damage year occurring, which was regional cold damage. The frequency of maize chilling injury decreased significantly from 1991 to 2020, from 0.23 in 1991-2000 to 0.1 in 2000-2010 and finally to 0.03 in 2010-2020. (2) Based on the good consistency between MODIS_LST data and temperature data from meteorological stations, it can be used for temperature remote sensing estimation model for spatially extensive cold damage monitoring and intensity discrimination. (3) Taking 2009 as an example of a large-scale cold damage year, the spatial discrimination of maize cold damage intensity shows that the spatial distribution of chilling injury intensity has no obvious geographical features. The intensity of cold damage was mainly mild cold damage. According to administrative regions, the scope of chilling injury was the largest in Mudanjiang City, Heihe City, and Jixi City, accounting for 91.56%, 86.25%, and 84.91%, respectively. The areas with the most extensive range of severe chilling injuries were the Great Khingan Mountains region, Heihe City, Mudanjiang City, Yichun City, and Jixi City. In the context of climate warming, the frequency and intensity range of maize cold damage showed a decreasing trend from 1991-2020 in Heilongjiang Province. The results of cold damage identification based on MODIS_LST data are accurate and can improve the spatial accuracy. The results of the study provide reference and guidance for dealing with the occurrence and defence of spatially refined cold damage. This article is protected by copyright. All rights reserved.

Safety Monitor Symmetry Concerning Beam Bridge Damage Utilizing the Instantaneous Amplitude Square Method

It is critical for the safety monitoring of highway bridges that beam bridge damage can be identified from the dynamic response of passing vehicles. Numerical simulations of passing vehicles were conducted utilizing the vehicle–bridge coupling vibration theory and the indirect measurement method. Fast Fourier transform was performed on the time history response of vehicle acceleration, and the driving frequency component response and its instantaneous amplitude square value (IAS value) were obtained by band-pass filtering and Hilbert transform processing. The identified IAS value detected the damage location of the bridge. The identification method of IAS value is used to analyze the applicability of a simply supported beam bridge, a continuous beam bridge, and an irregular skew beam bridge. The effects of vehicle speed, vehicle damping, bridge damping, and a social vehicle on damage identification are discussed. The results show that the effect of damage location is better when the vehicle speed is less than 4 m/s. In the presence of social vehicles, the excitation on the bridge increases, and the damage location can still be accurately determined by the IAS method. Vehicle damping and bridge damping have little effect on the results of damage identification. In structural health monitoring for bridges, this paper can provide a theoretical reference for the application of IAS motion sensing to identify the damage location indirectly.

Probabilistic Structural Model Updating with Modal Flexibility Using a Modified Firefly Algorithm.

Structural model updating is one of the most important steps in structural health monitoring, which can achieve high-precision matching between finite element models and actual engineering structures. In this study, a Bayesian model updating method with modal flexibility was presented, where a modified heuristic optimization algorithm named modified Nelder-Mead firefly algorithm (m-NMFA) was proposed to find the most probable values (MPV) of model parameters for the maximum a posteriori probability (MAP) estimate. The proposed m-NMFA was compared to the original firefly algorithm (FA), the genetic algorithm (GA), and the particle swarm algorithm (PSO) through the numerical illustrative examples of 18 benchmark functions and a twelve-story shear frame model. Then, a six-story shear frame model test was performed to identify the inter-story stiffness of the structure in the original and the damage states, respectively. By comparing the two, the position and extent of damage were accurately found and quantified in a probabilistic manner. In terms of optimization, the proposed m-NMFA was powerful to find the MPVs much faster and more accurately. In the incomplete measurement case, only the m-NMFA achieved target damage identification results. The proposed Bayesian model updating method has the advantages of high precision, fast convergence, and strong robustness in MPV finding and the ability of parameter uncertainty quantification.

Structural damage detection based on cross-correlation function with data fusion of various dynamic measurements

To take advantage of various types of dynamic measurement data for structural damage detection, an identification strategy based on cross-correlation function with data fusion of various dynamic measurements was proposed to improve the accuracy of damage identification in the present study. First of all, the cross-correlation functions among the easily acquired strain, acceleration, and displacement responses were theoretically derived when the structure was subjected to ambient excitations. Furthermore, an identification strategy was proposed for structural damage detection with the objective function of minimizing the difference between the measured and computed cross-correlation function under multiple unknown ambient excitations. In the proposed strategy, four optimization methods, namely, gradient search, genetic algorithm, particle swarm optimization, and the hybrid method of particle optimization method and gradient search were applied as the search engine to identify structural unknown damage index. Moreover, the performance of the proposed identification strategy was examined by the numerical studies on a two-dimensional and a three-dimensional truss as well as the experimental study on a cantilever beam. These results showed that the cross-correlation function among different types of vibration measurements could significantly improve the accuracy of the identification results, meanwhile, the proposed strategy exhibited excellent robustness to the measurement noise. In addition, the performance of the proposed strategy with different combinations of vibration data and the influence of reference data on the accuracy of damage identification results were further investigated.

Solution to the problem of bridge structure damage identification by a response surface method and an imperialist competitive algorithm

To increase the efficiency of structural damage identification (SDI) methods and timeously and accurately detect initial structural damage, this research develops an SDI method based on a response surface method (RSM) and an imperialist competitive algorithm (ICA). At first, a Latin hypercube design method is used for experimental design and selection of sample points based on RSM. Then, a high-order response surface surrogate model for the target frequency response and stiffness reduction factor is established. Finally, analysis of variance is performed to assess the overall goodness-of-fit and prediction accuracy of the established model. Then the results obtained are combined with structural dynamic response data to construct objective functions; furthermore, the optimal solution of parameter vector in the objective function is solved based on the ICA. Then damage positioning and quantification can be achieved according to location and degree of change in each parameter; finally, the RSM-ICA-based SDI method proposed is applied to damage identification of high-dimensional damaged simply-supported beam models. To verify the effectiveness of the proposed method, the damage identification results are compared with the results obtained from traditional optimization algorithms. The results indicate that: average errors in the structural stiffness parameters and natural frequency that are identified by the proposed method are 6.104% and 0.134% respectively. The RSM-ICA-based SDI method can more accurately identify the location and degree of damages with more significantly increased identification efficiency and better precision compared to traditional algorithms. This approach provides a novel means of solving SDI problems.

Nonlinear damage identification method of transmission tower structure based on general expression for linear and nonlinear autoregressive model and Itakura distance

Fatigue cracks and bolt looseness are two kinds of common nonlinear damage in a transmission tower structure. However, due to the complexity of the transmission tower structure, it is difficult to identify the nonlinear damage accurately by using traditional damage identification methods. To solve this problem effectively, a time domain damage identification method based on general expression for linear and nonlinear autoregressive model (GNAR model) and Itakura distance is proposed. To describe the stochastic characteristics of time series more concisely and accurately, the optimized structure of GNAR model was selected by the stochastic pruning algorithm based on greedy strategy. And Itakura distance was used as a damage indicator for nonlinear damage identification. The nonlinear damage experiment of three-story frame model in Los Alamos laboratory was used to verify the effectiveness of the proposed method, and this method was applied to the nonlinear damage identification experiment of a transmission tower steel frame model. In the transmission tower model experiment, two kinds of nonlinear damage types are considered: component breathing cracks and joint bolt loosening. The results show that the proposed nonlinear damage identification method can easily identify the nonlinear damage of the frame model and the transmission tower model effectively. The change of floor mass barely has effects on the damage identification results. The damage probability of the damaged stories calculated by the proposed method is significantly higher than that of the undamaged stories, so that it is helpful to find the location of the nonlinear damage source efficiently. And the proposed method is a damage identification method based on sub-structure story, which can identify the transmission tower model with two nonlinear damage sources at the same time.

An efficient stochastic-based coupled model for damage identification in plate structures

Mode shape-based method has shown its dominance in failure identification of beams. However, it is a challenge for fault detection in a plate structure. It requires combined information in two directions to determine the damage location. In this study, a damage index, namely mode shape derivative based damage identification (MSDBDI), is applied to localize damage in fixed-free plate structures. Two-dimensional (2D) displacement mode shapes and their derivatives are used to identify the MSDBDI index. It is a fact that this indicator is stuck in indicating the damage severity. Hence, a coupled model between an artificial neural network (ANN) and antlion optimizer (ALO), so-called ALOANN is used to overcome this drawback. In this method, ALO instead of a backpropagation algorithm is used to look for the best initial values of learnable parameters of ANN i.e. weights and biases through mean squared error (MSE). These obtained parameters are added to ANN for damage identification. The efficiency of the proposed approach is tested with two numerical studies of the plate structures with single and multiple damage scenarios. In the first application, damage scenarios in a plate-like structure are detected. In the second application, ALO first is used to build a FE model of a composite structure based on a vibration experiment. Then the slab of the updated model is assumed to be suffered several damage scenarios. In both applications, failures are localized by using damage index. Then, the proposed approach is used to quantify the corresponding extent by means of changes in frequencies and displacement mode shapes. Values of damage index are achieved from modal properties of one or three out of the first five modes of the two considered structures. A conventional ANN also is investigated for comparison. Results of damage identification indicate that the damage indicator coupled with ALOANN show better performance compared with using ANN alone even when a noise level is assigned to modal properties.

Sensitivity Analysis Using a Reduced Finite Element Model for Structural Damage Identification.

Sensitivity analysis is widely used in engineering fields, such as structural damage identification, model correction, and vibration control. In general, the existing sensitivity calculation formulas are derived from the complete finite element model, which requires a large amount of calculation for large-scale structures. In view of this, a fast sensitivity analysis algorithm based on the reduced finite element model is proposed in this paper. The basic idea of the proposed sensitivity analysis algorithm is to use a model reduction technique to avoid the complex calculation required in solving eigenvalues and eigenvectors by the complete model. Compared with the existing sensitivity calculation formulas, the proposed approach may increase efficiency, with a small loss of accuracy of sensitivity analysis. Using the fast sensitivity analysis, the linear equations for structural damage identification can be established to solve the desired elemental damage parameters. Moreover, a feedback-generalized inverse algorithm is proposed in this work in order to improve the calculation accuracy of damage identification. The core principle of this feedback operation is to reduce the number of unknowns, step by step, according to the generalized inverse solution. Numerical and experimental examples show that the fast sensitivity analysis based on the reduced model can obtain almost the same results as those obtained by the complete model for low eigenvalues and eigenvectors. The feedback-generalized inverse algorithm can effectively overcome the ill-posed problem of the linear equations and obtain accurate results of damage identification under data noise interference. The proposed method may be a very promising tool for sensitivity analysis and damage identification based on the reduced finite element model.

Damage Detection of Transmission Tower Based on Stochastic Subspace and Statistic Model

During the long service period of the transmission tower, the severe environment, material aging and fatigue effects result in the damage accumulation and resistance fading of the transmission tower, which even lead to the structural failure. In this paper, a stochastic subspace-based damage detection algorithm combined with statistical model is proposed for the damage identification of transmission tower structures through processing and analysing its vibration signals. Based on the structural modal parameters identified from the structural vibration response, the nominal modal parameters are defined. Considering that the Hankel matrixes constructed by the system observability matrix and the system output covariance matrix have the same kernel space, the damage index sensitive to the modal parameters is constructed. In the manuscript, firstly, the damage index establishment method and process of the algorithm are presented; and then the vibration data of transmission tower structure simulation under different damage conditions are obtained through numerical simulations; finally, above data are analysed to obtain the damage identification results of transmission tower. The results show that the method proposed in this work can effectively identify the local damage of transmission tower structure.

An Ensemble Neural Network for Damage Identification in Steel Girder Bridge Structure Using Vibration Data

Damage detection has the ability to prevent the occurrence of unpredictable failures and increase the serviceability of structures. Vibration-based damage detection methods are due to the fact that the damages will change the dynamic characteristics of a structure, such as natural frequencies, mode shapes and damping ratios. Resultantly, structural capacity is usually impacted, which subsequently, adversely affects performance. Fortunately, artificial neural networks (ANNs) have emerged as one of the most powerful learning tools, inspired by biological nervous systems. Unsurprisingly, the said technique has been applied for structural damage identification in the past decades. Relatedly, the objective of this study was to investigate the potential of ensemble neural network-based damage detection techniques in a scaled steel girder bridge structure using dynamic parameters. Experimental and finite element analyses of the structure were performed to generate modal parameters and study the efficiency of the ensemble neural networks in order to improve structural damage identification. Pursuant to the damage identification results, the ensemble ANN-based damage identification method was able to detect and locate damage with a high level of accuracy.

Post-earthquake damage identification of an RC school building in Nepal using ambient vibration and point cloud data

This paper presents a damage identification and performance assessment study of a four-story masonry-infilled reinforced concrete building in Sankhu, Nepal, using ambient vibration and point cloud data measurements. The building was severely damaged during the 2015 Gorkha earthquake. A set of accelerometers was used to record the ambient response of the building in order to extract its modal parameters, and a series of lidar scans were collected to estimate the surface defects of certain structural components. An initial model of the structure is created using a recently proposed strut model for masonry infills and a novel modeling approach for infilled RC frames. Dimensions are extracted from lidar-derived point cloud data in the absence of as-built drawings. The FE model updating is first performed through a deterministic formulation where optimal model parameters are estimated through a least squares optimization, and then through a Bayesian inference formulation where the joint posterior probability distribution of the updating parameters are estimated based on the prior knowledge of updating parameters and likelihood of measured data. The error functions for both formulations are defined as the difference between identified and model-predicted modal parameters. Two cases of model updating are performed using different parameterizations and different prior information about the damage. In the first case, updating parameters include walls and columns along the four stories of the building and exclude structural components observed to be severely damaged. The prior knowledge about structural component stiffness values is based on the expected material properties. In the second case of model updating, updating parameters include walls and columns of only the first story, and the prior stiffness values are estimated from the point-cloud measurements. The prior values are then updated using the vibration measurements. The damage identification results are in good agreement with visual observations and point cloud damage quantifications. The most probable model parameters in the Bayesian approach are also found to be in good agreement with the optimal results obtained in the deterministic formulation. Finally, it is shown that the probabilistic natural frequency predictions provide more realistic confidence bounds when both modeling errors and parameter uncertainties are accounted for in the prediction process.

Structural damage identification based on modal frequency strain energy assurance criterion and flexibility using enhanced Moth-Flame optimization

The development of structural damage identification based on dynamic characteristics has been suffering from certain issues, such as low computational efficiency and lack of high-sensitivity damage indicators. In addition, the application of damage-sensitive objective function and efficient optimization technique control the success of damage identification as two key factors. To this regard, a damage identification framework based on modal frequency strain energy assurance criterion (MFSEAC), modal flexibility and enhanced moth-flame optimization is presented in this paper. To evaluate the performance of the proposed method, three benchmark functions are firstly used to validate the optimization performance of enhanced moth-flame optimization. The results indicate that enhanced moth-flame optimization can achieve better optimization results compared to moth-flame optimization, particle swarm optimization and cuckoo search. Three numerical examples, a 3-span concrete continuous beam considering gradient temperature variations, a 40-story shear frame under random noise and a 31-bar truss structure under the double influences of random noise and temperatures, are then practiced as comparisons by frequency change ratio (FCR) and modal assurance criterion (MAC), modal strain energy (MSE) and modal flexibility, in order to evaluate the damage identification accurateness of the proposed objective function. Finally, two laboratory examples, a simply supported steel beam and a 3-story shear steel frame, are applied to further verify the proposed method. According to the damage identification results, the proposed method features good environmental noise robustness, which boosts the efficiency of symmetric location damage identification.