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In damage detection the number of elements is generally more than the number of measured frequencies. Consequently, the corresponding damage detection equation is undetermined and thus has infinite solutions. Since in the damaged structures most of their elements remain healthy, the sparsest solution for the damage detection equation is mostly the actual damage. In the proposed method, the damage equation is first linearized in various ways using random finite difference increments. The sparsest solutions for created linear system of equations are derived using basis pursuit. These solutions are considered as the first population for a continuous genetic algorithm to obtain the damage solution. For investigation of the proposed method three case studies are considered. Simulation results confirm the efficiency of the proposed method compared to those found in the literature.

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A novel two-stage algorithm for detection of damages in large-scale structures under static loads is presented. The technique utilizes the vector of response change (VRC) and sensitivities of responses with respect to the elemental damage parameters (RSEs). It is shown that VRC approximately lies in the subspace spanned by RSEs corresponding to the damaged elements. The property is leveraged in the first stage of the proposed method by seeking RSEs whose spanned subspace best contains the VRC. Consequently, the corresponding elements are regarded as damage candidates. To alleviate the exploration among RSEs, they are first partitioned into several clusters. Subsequently, discrete ant colony optimization (ACO) is utilized to find the clusters containing the RSEs of damaged elements. In the second stage of the algorithm, damage amounts for the restricted elements are determined using a continuous version of ACO. Two numerical examples are studied. The results illustrate that the method is both robust and efficient for detection of damages in large-scale structures.

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In this study, efficient methods for optimal sensor placement (OSP) based on a new geometrical viewpoint for damage detection in structures is presented. The purpose is to minimize the effects of noise on the damage detection process. In the geometrical viewpoint, a sensor location is equivalent to projecting the elliptical noise on to a face of response space which is corresponding to the sensor. The large diameters of elliptical noise make the damage detection process problematic. To overcome this problem, the diameters of the elliptical noise are scaled by filter factor to obtain an elliptical called equivalent elliptical noise. Based on the geometrical viewpoint, six simple forward algorithms are introduced to find the OSP. To evaluate the merits of the proposed method, a two-dimensional truss, under both static and dynamic loads, is studied. Numerical results demonstrate the efficiency of the proposed method.

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Chaos is embedded to the he Charged System Search (CSS) to solve practical optimization problems. To improve the ability of global search, different chaotic maps are introduced and three chaotic-CSS methods are developed. A comparison of these variants and the standard CSS demonstrates the superiority and suitability of the selected variants for practical civil optimization problems.

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In this study, an approach for damage detection of large-scale structures is developed by employing kinetic and modal strain energies and also Heuristic Particle Swarm Optimization (HPSO) algorithm. Kinetic strain energy is employed to determine the location of structural damages. After determining the suspected damage locations, the severity of damages is obtained based on variations of modal strain energy between the analytical models and the responses measured in damaged models using time history dynamic analysis data. In this paper, damages are modeled as a reduction of elasticity modulus of structural elements. The detection of structural damages is formulated as an unconstrained optimization problem that is solved by HPSO algorithm. To evaluate the performance of the proposed method, the results are compared with those provided in previous studies. To demonstrate the ability of this method for detection of multiple structural damages, different types of damage scenarios are considered. The results show that the proposed method can detect the exact locations and the severity of damages with a high accuracy in large-scale structures.

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Vibration based techniques of structural damage detection using model updating method, are computationally expensive for large-scale structures. In this study, after locating precisely the eventual damage of a structure using modal strain energy based index (MSEBI), To efficiently reduce the computational cost of model updating during the optimization process of damage severity detection, the MSEBI of structural elements is evaluated using properly trained cascade feed-forward neural network (CFNN). In order to achieve an appropriate artificial neural network (ANN) model for MSEBI evaluation, a set of feed-forward artificial neural networks which are more suitable for non-linear approximation, are trained. All of these neural networks are tested and the results demonstrate that the CFNN model with log-sigmoid hidden layer transfer function is the most suitable ANN model among these selected ANNs. Moreover, to increase damage severity detection accuracy, the optimization process of damage severity detection is carried out by particle swarm optimization (PSO) whose cost function is constructed based on MSEBI. To validate the proposed solution method, two structural examples with different number of members are presented. The results indicate that after determining the damage location, the proposed solution method for damage severity detection leads to significant reduction of computational time compared to finite element method. Furthermore, engaging PSO algorithm by efficient approximation mechanism of finite element (FE) model, maintains the acceptable accuracy of damage severity detection.

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Damage assessment is one of the crucial topics in the operation of structures. Multiplicities of structural elements and joints are the main challenges about damage assessment of space structure. Vibration-based damage evaluation seems to be effective and useful for application in industrial conditions and the low-cost. A method is presented to detect and assess structural damages from changes in mode shapes. First, the mechanism of using two-dimensional continuous wavelet transform is applied for damage localization. Second, finite element model updating technique is utilized as an inverse optimization problem by applying the charged system search algorithm to assess the damage in each element sited in the first stage. The study indicates the potentiality of the developed code to assess the damages of space structures without concerning about the size and shape of structure. A series of numerical examples with different damage scenarios have been carried out in the double layer space structures and the results confirm the reliability and applicability of introduced method.

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This paper aims to introduce topology optimization as a robust tool for damage detection in plane stress structures. Two objective functions based on natural frequencies and shape modes of the structure are defined to minimize discrepancy between dynamic specifications of the real damaged structure and the updating model. Damage area is assumed as a porous material where amount of porosity signifies the damage intensity. To achieve this, Solid Isotropic Material with Penalization (SIMP) model is employed. Sensitivity analysis is achieved and a mathematical based method is used for solving the optimization problems. In order to demonstrate efficiency and robustness of the method to identify various type of damages in terms of both location and intensity, several numerical examples are presented and the results are discussed.

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The purpose of the present study is the damage detection in the thin plates in terms of the wide application of such structures in various branches of engineering such as structural, mechanical, aerospace, shipbuilding, etc. using gradient-based second-order numerical optimization techniques. The technique used for optimization in this study is the second-order Levenberg-Marquardt algorithm (SOLMA). Using the acceleration response in a number of structural nodes under dynamic excitation, identification of the location and extent of damage in the plate elements are obtained by the proposed algorithm over an iterative cycle and by updating the sensitivity matrix. The damage has been assumed in the form of decreased modulus of elasticity in linear mode. A numerical problem has been solved and presented in order to verify and compare the proposed damage detection method with other methods. Also several numerical problems have been solved and its results have been presented in order to evaluate different scenarios such as one or more damages, small or large damage extent, absence or presence of noise with different levels, number of measured responses (number of sensors), position of measured points and the dynamic analysis time of the damage detection problem with the proposed method. The results show the appropriate accuracy, efficiency and performance of the proposed damage detection method.

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The damage identification of truss constructions was investigated in this work. Damage detection is defined through an inverse optimization problem. A function defined as a combination of mode shapes and natural frequencies is examined to minimize damage structures. This guided approach considerably reduces the computational cost and increases the accuracy of optimization. This index mostly exhibits an acceptable performance. Gold Rush Optimization (GRO), an artificial intelligence system based on the power of human thinking and decision-making, was employed to address damage detection. The programming was done in MATLAB. Validation and verification were carried out using a 10, 25, 200, 272, and 582 bar truss. A comparison between the GRO, MCSS, PSO and TLBO is conducted to show the efficiency of the GRO in finding the global optimum. The results show that utilizing the proposed function and the GRO optimization technique to discover truss damaged structure in the quickest time possible is both reliable and stable.

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An efficient method is proposed by using time domain responses and topology optimization to identify the location and severity of damages in two-dimensional structures under plane stress assumption. Damage is assumed in the form of material density reduction in the finite element model of the structure. The time domain responses utilized here, are the nodal accelerations measured at certain points of the structure. The responses are obtained by the Newmark method and contaminated with uniformly random noise in order to simulate real conditions. Damage indicators are extracted from the time domain responses by using Singular Value Decomposition (SVD). The problem of damage detection is presented as a topology optimization problem and the Solid Isotropic Material with Penalization (SIMP) method is used for appropriate damage modeling. The objective function is formed based on the difference of singular values of the Hankel matrix for responses of real structure and the analytical model. In order to evaluate the correctness of the proposed method, some numerical examples are examined. The results indicate efficiency of the proposed method in structural damage detection and its parameters such as resampling length in SVD, penalty factor in the SIMP method and number and location of sensors are effective parameters for improving the results.

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This paper proposes a method for structural damage detection through the sensitivity analysis of modal shapes in the calculation of modal strain energy (MSE). For this purpose, sensitivity equations were solved to determine the strain energy based on dynamic data (i.e., modal shapes). An objective function was then presented through the sensitivity-based MSE to detect structural damage. Due to the nonlinearity of sensitivity equations, the objective function of the proposed formulation can be minimized through the shuffled shepherd optimization algorithm (SSOA). The first few modes were employed for damage detection in solving the inverse problem. The proposed formulation was evaluated in a few numerical examples under different conditions. The numerical results indicated that the proposed formulation was efficient and effective in solving the inverse problem of damage detection. The proposed method not only minimized sensitivity to measurement errors but also effectively identified the location and severity of structural damage.
 

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In order to evaluate the damage state, value, and position of structural members more accurately, a multi-objective optimization (MO) method is utilized that is based on changes in natural frequency. The multi-objective optimization dynamic-based damage detection method is first introduced. Two objective functions for optimization are then introduced in terms of changing the natural frequencies and mode shapes. The multi-objective optimization problem (MOP) is formulated by using the two objective functions. Three considered MO algorithms consist of Colliding Bodies Optimization (MOCBO), Particle Swarm Optimization (MOPSO), and non-dominated sorting genetic algorithm (NSGA-II) to achieve the best structural damage detection. The proposed methods are then applied to three planar steel frame structures. Compared to the traditional optimization methods utilizing the single-objective optimization (SO) algorithms, the presented methods provide superior results.

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The contourlet transform as an extension of the wavelet transform in two dimensions uses the multiscale and directional filter banks, and has a more adequate performance in comparison with the classical multi-scale representations. In this study, the efficiency of the contourlet transform is assessed for identifying the damage of plate structures in various conditions. The conditions include single damage and multi–damages with different shapes and severities, the different supports (i.e., boundary conditions), and the higher mode shapes,. For achieving this purpose, the process of the damage detection of plate structures using contourlet transform is implemented in the three steps. In the first step, the first mode shapes of a damaged plate and a reference state as the intact plate are obtained using the finite element method. In the second step, the damage indices are achieved by applying the contourlet transform to the responses of the first mode shapes for the damaged and intact plates. Finally, the location and the approximate shape of the damage are identified by plotting the damage indices. The obtained results indicate that the various conditions influence the performance of the contourlet transform for identifying the location and approximate shape of damages in plate structures.