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An effective method utilizing the differential evolution algorithm (DEA) as an optimisation solver is suggested here to detect the location and extent of single and multiple damages in structural systems using time domain response method. Changes in acceleration response of structure are considered as a criterion for damage occurrence. The acceleration of structures is obtained using Newmark method. Damage is simulated by reducing the elasticity modulus of structural members. Three illustrative examples are numerically investigated, considering also measurement noise effect. All the numerical results indicate the high accuracy of the proposed method for determining the location and severity of damage.

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In the present study, ten steel-moment resisting frames (SMRFs) having different numbers of stories ranging from 3 to 20 stories and fundamental periods of vibration ranging from 0.3 to 3.0 second were optimized subjected to a set of earthquake ground motions using the concept of uniform damage distribution along the height of the structures. Based on the step-by-step optimization algorithm developed for uniform damage distribution, ductility-dependent strength reduction factor spectra were computed subjected to a given far-fault earthquake ground motion. Then, the mean ductility reduction factors subjected to 20 strong ground motions were computed and compared with those designed based on load pattern of ASCE-7-16 (similar to standard No. 2800) code provision. Results obtained from parametric studies indicate that, except in short-period structures, for moderate and high levels of inelastic demand the structures designed based on optimum load pattern with uniform damage distribution along the height require larger seismic design base shear strength when compared to the frames designed based on the code provisions, which is more pronounced for long-period structures i.e., the structural system becomes more flexible. This phenomenon can be associated to the P-delta effect tending to increase the story drift ratios of flexible structures, especially at the bottom stories. For practical purpose, a simplified expression which is a function of fundamental period and ductility demand to estimate ductility-dependent strength reduction factors of designed SMRFs according to code-based lateral load pattern is proposed.

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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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In this paper, topology optimization is utilized for damage detection in three dimensional elasticity problems. In addition, two mode expansion techniques are used to derive unknown modal data from measured data identified by installed sensors. Damages in the model are assumed as reduction of mass and stiffness in the discretized finite elements. The Solid Isotropic Material with Penalization (SIMP) method is used for parameterizing topology of the structure. Difference between mode shapes of the model and real structure is minimized via a mathematical based algorithm. Analytical sensitivity analysis is performed to obtain derivatives of objective function with respect to the design variables. In order to illustrate the accuracy of the proposed method, four numerical examples are presented.

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Dampers can reduce structural response under dynamic loads. Since dampers are costly, the design of structures equipped with dampers should make their application economically justifiable. Among the effective cost reduction factors is optimal damper placement. Hence, this study intended to find the optimal viscous damper placement using efficient optimization methods. Taking into account the nonlinear behavior of structure, this optimal distribution can be determined through meeting story-wise damping requirements such that the structure provides the minimum dynamic response and becomes economically justified. To compare the effect of different damper placement layouts on structural response and determine the objective function of optimization, the ratio of peak structural displacement to yield displacement was used as the damage index and objective function of optimization. Colliding Bodies' Optimization (CBO) algorithm was used for optimal damper placement. In this study, the 3- and 4-story concrete frames with different damper placement conditions were studied. Results confirmed the efficiency of the proposed method and algorithm in optimal viscous damper placement in each story. It was also discovered that the application of dampers on higher stories partially uniforms height-wise damage distribution and works towards the design goals.

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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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This paper presents an optimization-based model updating approach for structural damage detection and quantification. A new damage-sensitive objective function is proposed using a condensed form of the modal flexibility matrix. The objective function is solved using Chaotic Imperialist Competitive Algorithm (CICA), as an enhanced version of the original Imperialist Competitive Algorithm (ICA), and the optimal solution is reported as the damage detection results. The application of the CICA in vibration-based damage detection and quantification has been successfully investigated in a feasibility study published by the authors of the present paper and herein, its application is generalized for a case in which a complex (but more sensitive) objective function is utilized to formulate the damage detection problem as an inverse model updating problem. The method is validated by studying different damage patterns simulated on three numerical examples of the engineering structures. Comparative studies are carried out to evaluate the accuracy and repeatability of the proposed method in comparison with other vibration-based damage detection methods. The obtained results introduce the proposed damage detection approach as a robust method with high level of accuracy even in the presence of noisy inputs.

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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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In this study, the finite element model updating was simulated by reducing the stiffness of the members. Due to lack of access to the experimental results, the data obtained from an analytical model were used in the proposed structural damage scenarios. The updating parameters for the studied structures were defined as a reduction coefficient applied to the stiffness of the members. Parameter variations were calculated by solving an unconstrained nonlinear optimization problem. The objective function in the optimization problem was proposed based on the Multi-Degree-of-Freedom (MDOF) equations of motion as well as the dynamic characteristics of the studied structure. Only the first natural frequency of the damaged structure was used in the proposed updating process, and only one vibration mode was used in the updating problem and damage identification procedure. In addition, as elimination of high-order terms in the proposed formula introduced errors in the final response, the variations of natural frequency and vibration mode for higher-order terms were included in the free vibration equation of the proposed objective function. The Colliding Bodies Optimization (CBO) algorithm was used to solve the optimization problem. The performance of the proposed method was evaluated using the numerical examples, where different conditions were applied to the studied structures. The results of the present study showed that, the proposed method and formulation were capable of efficiently updating the dynamic parameters of the structure as well as identifying the location and severity of the damage using only the first natural frequency of the structure.
 

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Beyond common practice that treats structural damage detection as an optimization problem, the present work offers another approach that updates boundaries of the damage ratios. In this approach the bandwidth between such lower and upper boundaries, is adaptively reduced aiming to coincide at the true damage state. Formulation of the proposed method is developed using modal strain energy in a system of finite elements. A resolution-based technique is applied so that the search space cardinality can be defined and then reduced. The proposed method is validated on different structural types including beam, frame and truss examples with various damage scenarios. The results exhibit high cardinality reduction and capability of the proposed iterative method in squeezing the design space for more efficient search.
 

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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.