Damage detection of 2D elastic continuum structures incorporating finite cell method and particle swarm optimization

Document Type : Original Research

Authors
M. Nadi 1
P. Zakian 2
1 Arak University
2 Assistant Professor, Department of Civil Engineering, Arak University
10.22034/21.6.14
Abstract
There are many factors causing damages to a structure, including earthquakes, winds, environmental effects, etc. In order to repair a damaged structure, first its damage locations should be identified. Therefore, the damage identification of structures is considered as an important issue in civil engineering as well as mechanical engineering. Many methodologies have been devised for damage identification of structures, which are generally categorized to destructive and non-destructive cases. As a non-destructive damage identification approach, solving inverse problems for identifying the properties of a damaged structure is one of the popular methods which utilizes an optimization algorithm to minimize an error function in terms of measured strains or displacements. Since an iterative procedure with significant number of structural analyses should be carried out for the optimization process, an efficient numerical method should be employed to reduce the total computational cost. In this paper, the identification of hole in two-dimensional continuum structures is investigated with finite cell method and particle swarm optimization algorithm. The finite cell method is an efficient numerical method for solving the governing equations of continuum structures having geometrical complexity and/or discontinuities, which uses the concept of virtual domain method. The use of this concept makes the mesh generation easier such that the simple structured meshes can be utilized even for the curved boundaries of a structure, and hence mesh refinement is not necessary for the problems like damage detection. The finite cell method uses adaptive numerical integration for the cells including non-uniform material distribution. Accordingly, quadtree integration is utilized for the structural analysis using the finite cell method. Consequently, the computational time is significantly reduced. On the other hand, particle swarm optimization is a well-known meta-heuristic algorithm, and hence it does not require the gradient information of the problem. This population-based algorithm has been inspired by the social behaviour of animals such as fish schooling and birds flocking. The basis of this algorithm relies on the social influence and learning which enable individuals to preserve cognitive consistency. Thus, the exchange of ideas and interactions between individuals can lead them to solve optimization problems like damage detection. This study proposes the finite cell method and particle swarm optimization algorithm for damage detection of plate structures with single hole or multiple holes. As a non-gradient-based method, particle swarm optimization explores the search space to find the coordinates of the existing damage by minimizing an error function. This error function is evaluated by the strains or displacements calculated by the structural analysis utilizing the finite cell method. In order to evaluate the proposed methodology, numerical examples are provided to demonstrate the capability of finite cell method and particle swarm optimization algorithm in damage detection of two-dimensional structures. The first example considers the damage detection of a plate with a single hole, and it also considers the effects of mesh density. The second example employs a plate structure with three holes. The results demonstrate that the proposed methodology, with suitable computational efforts, can successfully be applied to damage detection of these structures.

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[1] Fan W, Qiao P. 2011. Vibration-based damage identification methods: a review and comparative study. Structural health monitoring, 10, 83-111.
[2] Broda D, Staszewski W, Martowicz A, Uhl T, Silberschmidt V. 2014. Modelling of nonlinear crack–wave interactions for damage detection based on ultrasound—A review. Journal of Sound Vibration, 333, 1097-1118.
[3] Lestari W, Qiao P. 2005. Application of wave propagation analysis for damage identification in composite laminated beams. Journal of composite materials, 39, 1967-1984.
[4] Sun H, Waisman H, Betti R. 2014. A multiscale flaw detection algorithm based on XFEM. International Journal for Numerical Methods in Engineering, 100, 477-503.
[5] Livani M, Khaji N, Zakian P. 2018. Identification of multiple flaws in 2D structures using dynamic extended spectral finite element method with a universally enhanced meta-heuristic optimizer. Structural and Multidisciplinary Optimization, 57, 605-623.
[6] Zakian P, Khaji N. 2018. A stochastic spectral finite element method for wave propagation analyses with medium uncertainties. Applied Mathematical Modelling, 63, 84-108.
[7] Zakian P, Khaji N. 2019. A stochastic spectral finite element method for solution of faulting-induced wave propagation in materially random continua without explicitly modeled discontinuities. Computational Mechanics, 64, 1017-1048.
[8] Noh G, Ham S, Bathe KJ. 2013. Performance of an implicit time integration scheme in the analysis of wave propagations. Computers Structures, 123, 93-105.
[9] Kim K-T, Bathe KJ. 2016. Transient implicit wave propagation dynamics with the method of finite spheres. Computers Structures, 173, 50-60.
[10] Ham S, Bathe KJ. 2012. A finite element method enriched for wave propagation problems. Computers structures, 94, 1-12.
[11] Komatitsch D, Tromp J. 1999. Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophysical journal international, 139, 806-822.
[12] Waisman H, Chatzi E, Smyth AW. 2010. Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms. International Journal for Numerical Methods in Engineering, 82, 303-328.
[13] Chatzi E, Hiriyur B, Waisman H, Smyth AW. 2011. Experimental application and enhancement of the XFEM–GA algorithm for the detection of flaws in structures. Computers Structures, 89, 556-570.
[14] Khaji N, Livani M, Zakian P. 2017. Crack Detection in 2D Domains Using Extended Finite Element Method and Particle Swarm Optimization. Modares Civil Engineering journal, 16, 177-189. ("In Persian")
[15] Du C, Zhao W, Jiang S, Deng X. 2020. Dynamic XFEM-based detection of multiple flaws using an improved artificial bee colony algorithm. Computer Methods in Applied Mechanics Engineering, 365, 112995
[16] Lotfollahi-Yaghin, M, Shamsai, A, Hesari, M. A. 2011. Application of Stationary Wavelet Transform (SWT) to the Crack Detection in Concrete Arch Dams by Frequency Analysis. Modares Civil Engineering journal, 11, 0-0. ("In Persian")
[17] Ma C, Yu T, Bui TQ. 2017. An effective computational approach based on XFEM and a novel three-step detection algorithm for multiple complex flaw clusters. Computers Structures, 193, 207-225.
[18] Sun H, Waisman H, Betti R. 2013. Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm. International Journal for Numerical Methods in Engineering, 95, 871-900.
[19] Parvizian J, Düster A, Rank E. 2007. Finite cell method. Computational Mechanics, 41, 121-133.
[20] Elhaddad M, Zander N, Kollmannsberger S, Shadavakhsh A, Nübel V, Rank E. 2015. Finite cell method: high-order structural dynamics for complex geometries. International Journal of Structural Stability Dynamics, 15, 1540018.
[21] Kennedy J, Eberhart R. Particle swarm optimization. Proceedings of ICNN'95-International Conference on Neural Networks. IEEE, 1942-1948.
[22] Shi Y, Eberhart R, editors. A modified particle swarm optimizer. 1998 IEEE international conference on evolutionary computation proceedings. IEEE world congress on computational intelligence, 1998. IEEE, 69-73.
[23] Kaveh A. 2014. Advances in Metaheuristic Algorithms for Optimal Design of Structures, Springer.
[24] Yan G, Sun H, Waisman H. 2015. A guided Bayesian inference approach for detection of multiple flaws in structures using the extended finite element method. Computers Structures, 152, 27-44.
Modares Civil Engineering journal
Volume 21, Issue 6
November and December 2021
Pages 205-214