Damage Identification in Simply Supported Bridge Based on Rotational-Angle Influence Lines Method

To locate and quantify local damage in a simply supported bridge, in this study, we derived a rotational-angle influence line equation of a simply supported beam model with local damage. Using the diagram multiplication method, we introduce an analytical formula for a novel damage-identification indicator, namely the diff erence of rotational-angle influence linescurvature(DRAIL-C). If the initial stiff ness of the simply supported beam is known, the analytical formula can be effectively used to determine the extent of damage under certain circumstances. We determined the effectiveness and anti-noise performance of this new damage-identification method using numerical examples of a simply supported beam, a simply supported hollow-slab bridge, and a simply supported truss bridge. The results show that the DRAIL-C is directly proportional to the moving concentrated load and inversely proportional to the distance between the bridge support and the concentrated load and the distance between the damaged truss girder and the angle measuring points. The DRAIL-C indicator is more sensitive to the damage in a steel-truss-bridge bottom chord than it is to the other elements.

Damage Identification of A TLP Floating Wind Turbine by Meta-Heuristic Algorithms

Damage identification of the offshore floating wind turbine by vibration/dynamic signals is one of the important and new research fields in the Structural Health Monitoring（SHM）. In this paper a new damage identification method is proposed based on meta-heuristic algorithms using the dynamic response of the TLP（Tension-Leg Platform） floating wind turbine structure. The Genetic Algorithms（GA）, Artificial Immune System（AIS）, Particle Swarm Optimization（PSO）, and Artificial Bee Colony（ABC） are chosen for minimizing the object function, defined properly for damage identification purpose. In addition to studying the capability of mentioned algorithms in correctly identifying the damage, the effect of the response type on the results of identification is studied. Also, the results of proposed damage identification are investigated with considering possible uncertainties of the structure. Finally, for evaluating the proposed method in real condition, a 1/100 scaled experimental setup of TLP Floating Wind Turbine（TLPFWT） is provided in a laboratory scale and the proposed damage identification method is applied to the scaled turbine.

Structural damage identification using test static data based on grey system theory

A new structural damage identification method using limited test static displacement based on grey system theory is proposed in this paper. The grey relation coefficient of displacement curvature is defined and used to locate damage in the structure, and an iterative estimation scheme for solving nonlinear optimization programming problems based on the quadratic programming technique is used to identify the damage magnitude. A numerical example of a cantilever beam with single or multiple damages is used to examine the capability of the proposed grey-theory-based method to localize and identify damages. The factors of meas-urement noise and incomplete test data are also discussed. The numerical results showed that the damage in the structure can be localized correctly through using the grey-related coefficient of displacement curvature, and the damage magnitude can be iden-tified with a high degree of accuracy, regardless of the number of measured displacement nodes. This proposed method only requires limited static test data, which is easily available in practice, and has wide applications in structural damage detection.

Damage identification of steel truss bridges based on deep belief network

To improve the accuracy and anti-noise ability of the structural damage identification method,a bridge damage identification method is proposed based on a deep belief network(DBN).The output vector is used to establish the nonlinear mapping relationship between the mode shape and structural damage.The hidden layer of the DBN is trained through a layer-by-layer pre-training.Finally,the backpropagation algorithm is used to fine-tune the entire network.The method is validated using a numerical model of a steel truss bridge.The results show that under the influence of noise and modeling uncertainty,the damage identification method based on the DBN can identify the accurate damage location and degree identification compared with the traditional damage identification method based on an artificial neural network.

Experimental study of structural damage identification based on WPT and coupling NN

Too many sensors and data information in structural health monitoring system raise the problem of how to realize multi-sensor information fusion. An experiment on a three-story frame structure was conducted to obtain vibration test data in 36damage cases. A coupling neural network (NN) based on multi-sensor information fusion is proposed to achieve identification of damage occurrence, damage localization and damage quantification, respectively. First, wavelet packet transform (WPT) is used to extract features of vibration test data from structure with different damage extent. Then, data fusion is conducted by assembling feature vectors of different type sensors. Finally, three sets of coupling NN are constructed to implement decision fusion and damage identification. The results of experimental study proved the validity and feasibility of the proposed methodology.

Structural Damage Identification System Suitable for Old Arch Bridge in Rural Regions: Random Forest Approach

A huge number of old arch bridges located in rural regions are at the peak of maintenance.The health monitoring technology of the long-span bridge is hardly applicable to the small-span bridge,owing to the absence of technical resources and sufficient funds in rural regions.There is an urgent need for an economical,fast,and accurate damage identification solution.The authors proposed a damage identification system of an old arch bridge implemented with amachine learning algorithm,which took the vehicle-induced response as the excitation.A damage index was defined based on wavelet packet theory,and a machine learning sample database collecting the denoised response was constructed.Through comparing three machine learning algorithms:Back-Propagation Neural Network(BPNN),Support Vector Machine(SVM),and Random Forest(R.F.),the R.F.damage identification model were found to have a better recognition ability.Finally,the Particle Swarm Optimization(PSO)algorithm was used to optimize the number of subtrees and split features of the R.F.model.The PSO optimized R.F.model was capable of the identification of different damage levels of old arch bridges with sensitive damage index.The proposed framework is practical and promising for the old bridge’s structural damage identification in rural regions.

Non-probabilistic information fusion technique for structural damage identification based on measured dynamic data with uncertainty

Based on measured natural frequencies and acceleration responses,a non-probabilistic information fusion technique is proposed for the structural damage detection by adopting the set-membership identification（SMI） and twostep model updating procedure.Due to the insufficiency and uncertainty of information obtained from measurements,the uncertain problem of damage identification is addressed with interval variables in this paper.Based on the first-order Taylor series expansion,the interval bounds of the elemental stiffness parameters in undamaged and damaged models are estimated,respectively.The possibility of damage existence（PoDE） in elements is proposed as the quantitative measure of structural damage probability,which is more reasonable in the condition of insufficient measurement data.In comparison with the identification method based on a single kind of information,the SMI method will improve the accuracy in damage identification,which reflects the information fusion concept based on the non-probabilistic set.A numerical example is performed to demonstrate the feasibility and effectiveness of the proposed technique.

Development of a software platform for bridge modal and damage identification based on ambient excitation

Modal and damage identification based on ambient excitation can greatly improve the efficiency of high-speed railway bridge vibration detection.This paper first describes the basic principles of stochastic subspace identification,peak-picking,and frequency domain decomposition method in modal analysis based on ambient excitation,and the effectiveness of these three methods is verified through finite element calculation and numerical simulation,Then the damage element is added to the finite element model to simulate the crack,and the curvature mode difference and the curvature mode area difference square ratio are calculated by using the stochastic subspace identification results to verify their ability of damage identification and location.Finally,the above modal and damage identification techniques are integrated to develop a bridge modal and damage identification software platform.The final results show that all three modal identification methods can accurately identify the vibration frequency and mode shape,both damage identification methods can accurately identify and locate the damage,and the developed software platform is simple and efficient.

An Improved Damage Identification Method Based on Mode Information

This paper presents a new algorithm to predict locations and severities of damage in structures by changing modal parameters. An existing algorithm of damage detection is reviewed and the new algorithm is formulated to improve the accuracy of damage locating and severity estimation by eliminating the erratic assumptions and limits in the existing algorithm. The damage prediction accuracy is numerically assessed for each algorithm when applied to a two-dimensional frame structure for which pre-damage and post-damage modal parameters are available for only a few modes of vibration. The analysis results illustrate the improved accuracy of the new algorithm when compared to the existing algorithm.

Three-Step Damage Identification Method Based on Dynamic Characteristics

A three-step damage identification method based on dynamic characteristics is proposed to improve the structure reliability and security and avoid serious accident. In the proposed method, the frequency and difference of modal curvature(DMC) are used as damage indexes. Firstly, the detection of the occurrence of damage is addressed by the frequency or the square of frequency change. Then the damage location inside the structure is measured by the DMC. Finally, with the stiffness reduction rate as a damage factor, the amount of damage is estimated by the optimization algorithm. The three-step damage identification method has been validated by conducting the simulation on a cantilever beam and the shaking table test on a submerged bridge. The results show that the method proposed in this paper can effectively solve the damage identification problem in theory and engineering practice.

Mooring Damage Identification of Floating Wind Turbine Using a Non-Probabilistic Approach Under Different Environmental Conditions

This paper discusses the damage identification in the mooring line system of a floating wind turbine(FWT)exposed to various environmental loads.The proposed method incorporates a non-probabilistic method into artificial neural networks(ANNs).The non-probabilistic method is used to overcome the problem of uncertainties.For this purpose,the interval analysis method is used to calculate the lower and upper bounds of ANNs input data.This data contains some of the natural frequencies utilized to train two different ANNs and predict the output data which is the interval bounds of mooring line stiffness.Additionally,in order to reduce computational time and more importantly,identify damage in various conditions,the proposed method is trained using constant loads(CL)case(deterministic loads,including constant wind speed and airy wave model)and is tested using random loads(RL)case(including Kaimal wind model and JONSWAP wave theory).The superiority of this method is assessed by applying the deterministic method for damage identification.The results demonstrate that the proposed non-probabilistic method identifies the location and severity of damage more accurately compared to a deterministic one.This superiority is getting more remarkable as the difference in uncertainty levels between training and testing data is increasing.

Damage Identification in Beam-Type Structures Using Pseudo Strain Energy Density and Grey Relation Coefficient

Based on pseudo strain energy density (PSED) and grey relation coefficient (GRC), an index is proposed to locate the damage of beam-type structures in time-domain. The genetic algorithm (GA) is utilized to identify the structural damage severity of confirmed damaged locations. Furthermore, a systematic damage identification program based on GA is developed on MATLAB platform. ANSYS is employed to conduct the finite element analysis of complicated civil engineering structures, which is embedded with interface technique. The two-step damage identification is verified by a finite element model of Xinxingtang Highway Bridge and a laboratory beam model based on polyvinylidens fluoride (PVDF). The bridge model was constructed with 57 girder segments, and simulated with 58 measurement points. The damaged segments were located accurately by GRC index regardless of damage extents and noise levels. With stiffness reduction factors of detected segments as variables, the GA program evolved for 150 generations in 6 h and identified the damage extent with the maximum errors of 1% and 3% corresponding to the noise to signal ratios of 0 and 5%, respectively. In contrast, the common GA-based method without using GRC index evolved for 600 generations in 24 h, but failed to obtain satisfactory results. In the laboratory test, PVDF patches were used as dynamic strain sensors, and the damage locations were identified due to the fact that GRC indexes of points near damaged elements were smaller than 0.6 while those of others were larger than 0.6. The GA-based damage quantification was also consistent with the value of crack depth in the beam model.

A METHOD OF ONLINE DAMAGE IDENTIFICATION FOR STRUCTURES BASED ON AMBIENT VIBRATION

A method of damage identification for engineering structures based on ambient vibration is put forward, in which output data are used only. Firstly, it was identification of the statistic parameters to associate with the exterior excitation for undamaged structures. Then it was detection and location of the structural damages for damaged structures. The ambient identification method includes a theoretical model and numerical method. The numerical experiment results show the method is precise and effective. This method may be used in health monitoring for bridges and architectures.

HOMOTOPY CONTINUATION ALGORITHM FOR STRUCTURAL DAMAGE IDENTIFICATION

A new method is put forward for structural damage identification based on the homotopy continuation algorithm. A numerical example is presented to verify the method. The beams with different damage locations and different damage extents are identified by this method. The numerical examples have proved that this new method is capable of easy convergence, which is not sensitive to the initial iterative values. It is effective for accurately identifying multiple damages. By incorporating the finite element method into the homotopy continuation algorithm, the damage identifying ability of the new method can be greatly enhanced.

Ensemble 1D DenseNet Damage Identification Method Based on Vibration Acceleration

Convolution neural networks in deep learning can solve the problem of damage identification based on vibration acceleration.By combining multiple 1D DenseNet submodels,a new ensemble learning method is proposed to improve identification accuracy.1D DenseNet is built using standard 1D CNN and DenseNet basic blocks,and the acceleration data obtained from multiple sampling points is brought into the 1D DenseNet training to generate submodels after offset sampling.When using submodels for damage identification,the voting method ideas in ensemble learning are used to vote on the results of each submodel,and then vote centrally.Finally,the cantilever damage problem simulated by ABAQUS is selected as a case study to discuss the excellent performance of the proposed method.The results show that the ensemble 1D DenseNet damage identification method outperforms any submodel in terms of accuracy.Furthermore,the submodel is visualized to demonstrate its operation mode.

Impact Damage Identification of Aluminum Alloy Reinforced Plate Based on GWO-ELM Algorithm

As a critical structure of aerospace equipment,aluminum alloy stiffened plate will influence the stability of spacecraft in orbit and the normal operation of the system.In this study,a GWO-ELM algorithm-based impact damage identification method is proposed for aluminum alloy stiffened panels to monitor and evaluate the damage condition of such stiffened panels of spacecraft.Firstly,together with numerical simulation,the experimental simulation to obtain the damage acoustic emission signals of aluminum alloy reinforced panels is performed,to establish the damage data.Subsequently,the amplitude-frequency characteristics of impact damage signals are extracted and put into an extreme learning machine(ELM)model to identify the impact location and damage degree,and the Gray Wolf Optimization(GWO)algorithm is employed to update the weight parameters of the model.Finally,experiments are conducted on the irregular aluminum alloy stiffened plate with the size of 2200 mm×500 mm×10 mm,the identification accuracy of impact position and damage degree is 98.90% and 99.55% in 68 test areas,respectively.Comparative experiments with ELM and backpropagation neural networks(BPNN)demonstrate that the impact damage identification of aluminum alloy stiffened plate based on GWO-ELM algorithm can serve as an effective way to monitor spacecraft structural damage.

Structural Damage Identification via Pseudo Strain Energy Density and Wavelet Packet Transform

Based on strain signals, a new time-domain methodology for detecting the beam local damage has been developed. The pseudo strain energy density （PSED） is defined and used to build two major damage indexes, the average pseudo strain energy density （APSED） and the average pseudo strain energy density rate （APSEDR）. Probability and mathematical statistics are utilized to derive a standardized damage index. Furthermore, by applying the analytic relation between the strain energy release rate and the stress intensity factor, an analytic solution of crack depth is derived. For the dynamic strain signals, the wavelet packet transform is used to pre-process measured data. Finally, a numerical simulation indicates that this method can effectively identify the damage location and its absolute severity.

Improved modal truncation error in the directly analytical method for damage identification of frame structures

The damage identification is made by the numerical simulation analysis of a five-storey-and-two-span RC frame structure, using improved and unimproved direct analytical method respectively; and the fundamental equations were solved by the minimal least square method （viz. general inverse method）. It demonstrates that the feasibility and the accuracy of the present approach were impoved significantly, compared with the result of unimproved damage identification.

Damage Identification in Footbridges from Natural Frequency Measurements

The present study aims to develop a robust structural damage identification method that can be used for the evaluation of bridge structures. An approach for the structural damage identification based on the measurement of natural frequencies is presented. The structural damage model is assumed to be associated with a reduction of a contribution to the element stiffness matrix equivalent to a scalar reduction of the material modulus. A computational procedure for the direct iteration technique based on the non-linear perturbation theory is proposed to identify structural damage. The presented damage identification technique is applied to the footbridge over the Slunjcica River near Slunj to demonstrate the effectiveness of the proposed approach. Using a limited number of measured natural frequencies, reduction in the stiffness of up to 100% at multiple sites is detected. The results indicate that the proposed approach can be successful in not only predicting the location of damage but also in determining the extent of structural damage.

Damage Identification under Incomplete Mode Shape Data Using Optimization Technique Based on Generalized Flexibility Matrix

A generalized flexibility–based objective function utilized for structure damage identification is constructed for solving the constrained nonlinear least squares optimized problem. To begin with, the generalized flexibility matrix (GFM) proposed to solve the damage identification problem is recalled and a modal expansion method is introduced. Next, the objective function for iterative optimization process based on the GFM is formulated, and the Trust-Region algorithm is utilized to obtain the solution of the optimization problem for multiple damage cases. And then for computing the objective function gradient, the sensitivity analysis regarding design variables is derived. In addition, due to the spatial incompleteness, the influence of stiffness reduction and incomplete modal measurement data is discussed by means of two numerical examples with several damage cases. Finally, based on the computational results, it is evident that the presented approach provides good validity and reliability for the large and complicated engineering structures.