Inverse Problem Of Damage Identification Research Articles

Quantitative method for the probability of structural damage based on moment theory

In the context of uncertainty in the inverse problem of damage identification, this study proposes a moment theory based probabilistic damage identification (MbPDI) method. Noise errors in the identification process are treated as uncertain parameters, while structural stiffness parameters are treated as functions of noise errors. A limit state function for damage identification is defined, and its probability is computed. Utilizing the concept of moment theory, the expansion series is performed for the limit state function around the most probable point of failure, with gradient information derived using sensitivity matrices. Based on the gradient information and uncertainty inputs, damage probabilities for various elements can be obtained. Additionally, this paper addresses the calculation of structural damage probabilities under the non-normal distribution of random variables by transforming non-normal variables into equivalent normal variables. The proposed probability index and expected index of structural damage in the probabilistic damage identification method has a clear physical meaning, and the calculation has high accuracy. The proposed method is validated through a mathematical example and a numerical simulation. Meanwhile, the influence of damage extent, noise level, and modal order on identification results are analyzed. Experimental validation of the method is also presented.

Generalized Integral Transform and Hamiltonian Monte Carlo for Bayesian structural damage identification

The present work addresses the inverse problem of damage identification within the Bayesian framework. The inverse problem is formulated as a parameter estimation one and it is built on the response of the continuous model of the structure provided by the Generalized Integral Transform technique. The Hamiltonian Monte Carlo (HMC) method is considered for sampling the posterior probability density function of the cohesion parameters, which are the ones considered for the description of the damage state of the structure. Numerical simulations considering an Euler-Bernoulli beam were carried out in order to assess the applicability of the proposed damage identification approach. The numerical results shown that the HMC method was able to identify the considered damage scenarios, yielding Markov chains with relatively high convergence rates and with uncorrelated states right at the beginning of the chains.

Ultrasonic guided wave based structural damage detection and localization using model assisted convolutional and recurrent neural networks

The inverse problem of damage identification involves real-time, continuous observation of structures to detect any undesired, abnormal behavior and ultrasonic guided waves are considered as one of the preferred candidates for this. A parallel implementation of a reduced-order spectral finite element model is utilized to formulate the forward problem in an isotropic and a composite waveguide. In this work, along with a time-series dataset, a 2D representation of continuous wavelet transformation based time–frequency dataset is also developed. The datasets are corrupted with several levels of Gaussian random noise to incorporate different kinds of uncertainties and noise present in the real scenario. Deep learning networks like convolutional and recurrent neural networks are utilized to numerically approximate the solution of the inverse problem. A hybrid strategy of classification and regression in a supervised setting is proposed for combined damage detection and localization. The performance of the networks is compared based on metrics like accuracy, loss value, mean absolute error, mean absolute percentage error, and coefficient of determination. The predictions from conventional machine learning algorithms, trained on feature engineered dataset are compared with the deep learning algorithms. The generalization of the trained deep networks on different excitation frequencies and a higher level of uncertainties is also highlighted in this work.

A new adaptive approach of the Metropolis-Hastings algorithm applied to structural damage identification using time domain data

In the present work, the formulation and solution of the inverse problem of structural damage identification is presented based on the Bayesian inference, a powerful approach that has been widely used for the formulation of inverse problems in a statistical framework. The structural damage is continuously described by a cohesion field, which is spatially discretized by the finite element method, and the solution of the inverse problem of damage identification, from the Bayesian point of view, is the posterior probability densities of the nodal cohesion parameters. In this approach, prior information about the parameters of interest and the quantification of the uncertainties related to the magnitudes measured can be used to estimate the sought parameters. Markov Chain Monte Carlo (MCMC) method, implemented via the Metropolis-Hastings (MH) algorithm, is commonly used to sample such densities. However, the conventional MH algorithm may present some difficulties, for instance, in high dimensional problems or when the parameters of interest are highly correlated or the posterior probability density is very peaked. In order to overcome these difficulties, a new adaptive MH algorithm (P-AMH) is proposed in the present work. Numerical results related to an inverse problem of damage identification in a simply supported Euler-Bernoulli beam are presented. Synthetic experimental time domain data, obtained with different damage scenarios, and noise levels, were addressed with the aim at assessing the proposed damage identification approach. An adaptive MH algorithm (H-AMH) and the conventional MH algorithm, already consolidated in the literature, were also considered for comparison purposes. The numerical results show that both adaptive algorithms outperformed the conventional MH. Besides, the P-AMH provided Markov chains with faster convergence and better mixing than the ones provided by the H-AMH.

A robust optimization for damage detection using multiobjective genetic algorithm, neural network and fuzzy decision making

ABSTRACTAn inverse problem of damage identification and localization in a structure is modelled as a robust optimization problem. In the robust optimization problem, the optimum value and small variations around this optimum value are considered. The structural health monitoring damage detection problem is solved using a multiobjective genetic algorithm. So, the robust optimum value is obtained by solving a multiobjective problem where a functional and a variance function of this functional are used. This variance function is obtained by a Design of Experiment with regression and also through a relation between functional variance and damage parameters found by artificial neural network. As a multiobjective genetic algorithm obtains multiple solutions, a fuzzy decision making technique finds the better tradeoff solution for the problem. Boundary element method is utilized to obtain the distribution of stress to elastostatic problem. Numerical results clearly show that the proposed strategy and the use an optimized fuzzy decision making results in accurate damage identification and represents a powerful tool for structural health monitoring. Based on the analysis and numerical results, suggestions to potential researchers have also been provided for future scopes.

Structural damage identification built on a response surface model and the flexibility matrix

The present work is concerned with the inverse problem of structural damage identification. The damage state of the structure is continuously described by a cohesion field, spatially discretized by the finite element method, and a response surface model (RSM) is considered to provide a polynomial relation between the nodal cohesion parameters and elements of the flexibility matrix of the system. Here, the inverse problem of damage identification is posed as an optimization one, where the objective is to minimize, with respect to the nodal cohesion parameters, the squared norm of the difference between an experimental response vector, composed with elements of the flexibility matrix obtained from a modal test on the supposed damaged structure, and the corresponding one predicted by a RSM. The Particle Swarm Optimization method was considered for solving the resulting inverse problem of damage identification. A simply supported Euler-Bernoulli beam, with three different damage scenarios and the synthetic experimental mode shapes corrupted with two different levels of noise, was considered in the numerical assessment of the proposed damage identification approach. The numerical results show that the proposed approach, built on a RSM of the flexibility matrix, presented results comparable with those obtained with the approach built on the FEM of the structure and it also presented an extremely higher computational performance.

Structural damage identification via time domain response and Markov Chain Monte Carlo method

The present work addresses the problem of structural damage identification built on the statistical inversion approach. Here, the damage state of the structure is continuously described by a cohesion parameter, which is spatially discretized by the finite element method. The inverse problem of damage identification is then posed as the determination of the posterior probability densities of the nodal cohesion parameters. The Markov Chain Monte Carlo method, implemented with the Metropolis–Hastings algorithm, is considered in order to approximate the posterior probabilities by drawing samples from the desired joint posterior probability density function. With this approach, prior information on the sought parameters can be used and the uncertainty concerning the known values of the material properties can be quantified in the estimation of the cohesion parameters. The assessment of the proposed approach has been performed by means of numerical simulations on a simply supported Euler–Bernoulli beam. The damage identification and assessment are performed considering time domain response data. Different damage scenarios and noise levels were addressed, demonstrating the feasibility of the proposed approach.

Identificação de Danos Estruturais utilizando Dados no Domínio do Tempo e Critério D-ótimo

The present work deals with the damage identification problem in mechanical structures from their impulse response. In the adopted model, the structural integrity is continually described by a cohesion parameter and the finite element model (FEM) is used to spatially discretize the displacement and cohesion fields. The damage identification problem is then posed as an optimization one, whose objective is to minimize, with respect to the vector of nodal cohesion parameters, a functional based on the difference between the experimentally obtained impulse response and the corresponding one predicted by an FEM of the structure. The damage identification problem built on the time domain presents some advantages, as the applicability in linear systems with high levels of damping an/or closed spaced modes, and in nonlinear systems. Numerical studies were carried out considering a simply supported Euler-Bernoulli beam. The D-optimal criterion was considered with the aim at determining the optimal position of the displacement sensor. The Differential Evolution (DE) optimization method was considered to solve the inverse problem of damage identification. Numerical analysis were carried out in order to assess the influence, on the identification results, of noise in the synthetic experimental data and of the sensor position. The presented results shown the potentiality of the proposed damage identification approach and also the importance of the optimal experiment design for the quality of the damage identification results.

Damage diagnosis in steel structures with different noise levels via optimization algorithms

In this paper, the main objective is to solve the inverse problem of damage identification with the help of the Imperialist Competitive Algorithm (ICA) optimization. Three different numerical cases, including a clamped-free beam, a 2D truss and a 2D plate-type structure are modelled by using Finite Element Method (FEM) and used to evaluate the proposed damage identification procedure. The proposed objective function for the optimization procedure is formed by using modal parameters. Those parameters are obtained from the damage state, where cracks are simulated with the assumption of reducing the local stiffness of the structure. Then, proposed damage detection/characterization process is performed by implementing an optimization algorithm, called Imperialist Competitive Algorithm (ICA). Results obtained from the numerical case studies show that this algorithm is trustworthy and can be used to identify the severity and location of the damage with a good accuracy. Furthermore, the effects of noise on the results of damage identification process are studied so as to investigate the tolerance of the method in the face of environmental noise. Finally, the results obtained by the ICA are compared to the ones obtained by using two commonly used algorithms, i.e. the binary genetic algorithm (BGA) and particle swarm optimization (PSO).

The Differential Evolution method applied to continuum damage identification via flexibility matrix

In the present work, a structural damage identification approach, built on the flexibility matrix, is proposed. Here, the damage state of the structure is continuously described by a cohesion parameter, which, in turn, is spatially discretized by the finite element method. Then, the inverse problem of damage identification is defined as an optimization one, where the objective is to minimize, with respect to the nodal cohesion parameters, a functional based on the difference between the experimentally obtained flexibility matrix and the corresponding one predicted by a finite element model of the structure. The Differential Evolution stochastic optimization method was considered for solving the resulting damage identification problem. The assessment of the proposed approach has been performed by means of numerical simulations on a simply supported Euler–Bernoulli beam. A brief analysis of the influence of different damage positions and severities on the undamped natural frequencies and on the flexibility matrix of the structure is presented. Then, the influence of damage and different levels of noise on the mode shapes of the structure is also considered. In the damage identification problem, different damage scenarios and noise levels were addressed. For comparison purposes, other stochastic optimization methods, namely, Particle Swarm Optimization, Luus–Jaakola and Simulated Annealing, were also considered for the identification of one damage scenario in the presence of noise corrupted data.

Application of generalized flexibility matrix in damage identification using Imperialist Competitive Algorithm

In this article, a new objective function which is formed by using generalized flexibility matrix is presented with the aim of solving the constrained optimization problem in damage detection procedure. The main purpose is to decrease the effects of truncation error which ensue from cutting off the higher order modes. Two different case studies are used to evaluate the proposed approach. These cases include, a 2D-frame and a Howe-Truss structure. In this study, each structure is modeled by finite element method and damages are induced by considering a reduction in the stiffness of the elements. Finally, the inverse problem of damage identification is solved by using the Imperialist Competitive Algorithm (ICA) for each damage scenario. Not only the effect of noise on the obtained results is studied but also a comparison is drawn between the proposed method based on ICA and other conventional optimization algorithms, namely PSO and GA.

Damage diagnostic technique combining POD with time-frequency analysis and dynamic quantum PSO

A novel damage identification procedure is presented that is ideally suited for continuous structural health monitoring of large civil engineering structures. The procedure for damage detection, location and quantification is developed by combining Hilbert Huang transformation (HHT) and proper orthogonal decomposition with dynamic quantum particle swarm optimisation algorithm (DQPSO). The damaged structure is modeled using finite elements, in which the damage is represented by a section having reduced flexural rigidity. Forward analyses are first used to identify time instant of damage using HHT and location of damage using proper orthogonal decomposition. The inverse damage identification problem is later set up as an optimization problem and solved using a newly developed DQPSO algorithm. The proposed method exhibited robustness in identifying the exact time instant of damage occurrence, spatial locations of the damage and also the extent of damage correctly for a wide range of locations and damage severities. The effect of measurement error/noise is also investigated.

Damage identification in bars with a wave propagation approach: Performance comparison of five hybrid optimization methods

The formulation and solution of the inverse problem of damage identification based on an one-dimensional wave propagation approach are presented in this paper. Time history responses, obtained from pulse-echo synthetic experiments, are used to damage identification. The identification process is built on the minimization of the squared residue between the synthetic experimental echo, obtained by using a sequential algebraic algorithm, and the corresponding analytical one. Fivedifferent hybrid optimization methods areinvestigated. The hybridization is performed combining the deterministic Levenberg-Marquardt method and each one of the following stochastic techniques: The Particle Swarm Optimization; the Luus-Jaakola optimization method; the Simulated Annealing method; the Particle Collision method; and a Genetic Algorithm. A performance comparison of the five hybrid techniques is presented. Different damage scenarios are considered and, in order to account for noise corrupted data, signals with 10 dB of signal to noise ratio are also considered. It is shown that the damage identification procedure built on the Sequential Algebraic Algorithm yielded to very fast and successful solutions. In the performance comparison, it is also shown that the hybrid technique combining the Luus-Jaakola and the Levenberg-Marquardt optimization methods provides the faster damage recovery.

Damage Identification in Bars with a Wave Propagation Approach: Performance Comparison of Five Hybrid Optimization Methods

The formulation and solution of the inverse problem of damage identification based on an one-dimensional wave propagation approach are presented in this paper. Time history responses, obtained from pulse-echo synthetic experiments, are used to damage identification. The identification process is built on the minimization of the squared residue between the synthetic experimental echo, obtained by using a sequential algebraic algorithm, and the corresponding analytical one. Five different hybrid optimization methods are investigated. The hybridization is performed combining the deterministic Levenberg-Marquardt method and each one of the following stochastic techniques: The Particle Swarm Optimization; the Luus-Jaakola optimization method; the Simulated Annealing method; the Particle Collision method; and a Genetic Algorithm. A performance comparison of the five hybrid techniques is presented. Different damage scenarios are considered and, in order to account for noise corrupted data, signals with 10 dB of signal to noise ratio are also considered. It is shown that the damage identification procedure built on the Sequential Algebraic Algorithm yielded to very fast and successful solutions. In the performance comparison, it is also shown that the hybrid technique combining the Luus-Jaakola and the Levenberg-Marquardt optimization methods provides the faster damage recovery.

Damage identification in bars with a wave propagation approach and a hybrid optimization method

The formulation and solution of the inverse problem of damage identification based on wave propagation approach are presented. Different damage scenarios for a bar are considered. Time history responses, obtained from pulse-echo synthetic experiments, are used toidentify damage position, severity and shape. In order to account for noise corrupted data, different levels of signal to noise ratio - varying from 30 to 0 dB - are introduced. In the identification process, different optimization methods are investigated: the deterministic Levenberg-Marquardt; the stochastic Particle Swarm Optimization; and a hybrid technique combining the aforementioned methods. It is shown that the damage identification procedure built on the wave propagation approach was successful, even for highly corrupted noisy data. Test case results are presented and a few comments on the advantages of deterministic and stochastic methods and their combination are also reported. Finally, an experimental validation of the sequential algebraic algorithm, used for modeling the direct problem, is presented.

Damage Identification in Bars with a Wave Propagation Approach and a Hybrid Optimization Method

The formulation and solution of the inverse problem of damage identification based on wave propagation approach are presented. Different damage scenarios for a bar are considered. Time history responses, obtained from pulse-echo synthetic experiments, are used to identify damage position, severity and shape. In order to account for noise corrupted data, different levels of signal to noise ratio – varying from 30 to 0 dB – are introduced. In the identification process, different optimization methods are investigated: the deterministic Levenberg-Marquardt; the stochastic Particle Swarm Optimization; and a hybrid technique combining the aforementioned methods. It is shown that the damage identification procedure built on the wave propagation approach was successful, even for highly corrupted noisy data. Test case results are presented and a few comments on the advantages of deterministic and stochastic methods and their combination are also reported. Finally, an experimental validation of the sequential algebraic algorithm, used for modeling the direct problem, is presented.

Detection of holes in a plate using global optimization and parameter identification techniques

In this work, an inverse problem of damage identification and localization is modelled using independent techniques, both for the direct model and for the inverse model. The damage is characterized by a hole in the structure, which modifies existing temperature and stress fields. Direct models for the thermal (conduction) and elastostatic problems are needed to obtain the distribution of these quantities in the domain, for a particular configuration. The boundary element method is used here as the direct problem, and two different and independent techniques are used for the inverse problem, in order to localize and to identify a damage in a structure. The first technique adopted is a global optimization technique using genetic algorithms and the second approach is a parameter identification technique using artificial neural networks. The identification and localization of a hole in the structure is performed using these two techniques for the inverse problem, with comparable results.

Dead Load Based Damage Identification Method for Long-term Structural Health Monitoring

A novel damage identification procedure is presented that is ideally suited for long-term structural health monitoring of large civil structures. The procedure is based on the redistribution of dead load stress that occurs in a structure when damage takes place. The damaged structure is modeled using finite elements, in which the damage is represented by a section of reduced flexural rigidity. Forward analyses are first presented to show how the dead load is redistributed for different damage scenarios. The inverse damage identification problem is set up as a constrained optimization problem and solved using a real coded genetic algorithm. The proposed method correctly identified damage for a wide range of locations and damage severities. Results show that damage is difficult to identify when it is close to the inflection points of the structure, where the dead load strain is zero, and when the damage is not located between two sensors. The effect of measurement error is investigated.

Identification of Concentrated Damages in Euler-Bernoulli Beams under Static Loads

An identification procedure of concentrated damages in Euler-Bernoulli beams under static loads is presented in this work. The direct analysis problem is solved first by modeling concentrated damages as Dirac’s delta distributions in the flexural stiffness. Closed-form solutions for both statically determinate and indeterminate beams are presented in terms of damage intensities and positions. On this basis, for the inverse damage identification problem, a nonquadratic optimization procedure is proposed. The presented procedure relies on the minimization of an error function measuring the error between the analytical model response and experimental data. The procedure allows to recognize “a posteriori” some sufficient conditions for the uniqueness of the solution of the damage identification problem. The influence of the instrumental noise on the identified parameters is also explored.

A frequency response function-based damage identification method for cylindrical shell structures

In this paper, a structural damage identification method (SDIM) is developed for cylindrical shells and the numerically simulated damage identification tests are conducted to study the feasibility of the proposed SDIM. The SDIM is derived from the frequency response function solved from the structural dynamic equations of damaged cylindrical shells. A damage distribution function is used to represent the distribution and magnitudes of the local damages within a cylindrical shell. In contrast with most existing modal parameters-based SDIMs which require the modal parameters measured in both intact and damaged states, the present SDIM requires only the FRF-data measured in the damaged state. By virtue of utilizing FRF-data, one is able to make the inverse problem of damage identification well-posed by choosing as many sets of excitation frequency and FRF measurement point as needed to obtain a sufficient number of equations.