Vibration-based damage detection of planar and space trusses using differential evolution algorithm

Abstract In this study, an efficient damage detection technique using the differential evolution (DE) algorithm and vibration data is proposed to properly detect the locations and extents of multiple damages of truss structures. The general equilibrium equations in which the reaction forces at notes are taken into account are considered. The compatibility equations in terms of forces are presented using the singular value decomposition (SVD) technique and then the extended equations of motion are developed based on the force method. As an optimization algorithm, the differential evolution (DE) algorithm is utilized and the objective function for damage detection is based on vibration data such as natural frequencies and mode shapes. Three numerical examples for planar and space truss structures are considered to verify the effectiveness and practical applicability of the present study. The numerical results show that the proposed method based on DE and vibration data can provide a reliable tool on determining the locations and extents of multiple damages of truss structures when it compares with those obtained from the genetic algorithm.

[1]  Kalmanje Krishnakumar,et al.  Micro-Genetic Algorithms For Stationary And Non-Stationary Function Optimization , 1990, Other Conferences.

[2]  S. M. Seyedpoor,et al.  Structural damage detection using an efficient correlation-based index and a modified genetic algorithm , 2011, Math. Comput. Model..

[3]  Hong Hao,et al.  Vibration-based Damage Detection of Structures by Genetic Algorithm , 2002 .

[4]  E. J. Williams,et al.  STRUCTURAL DAMAGE DETECTION BY A SENSITIVITY AND STATISTICAL-BASED METHOD , 1998 .

[5]  J. Mahu,et al.  Real-Time Structural Damage Assessment Using Artificial Neural Networks and Antiresonant Frequencies , 2014 .

[6]  T. Coleman,et al.  The null space problem I. complexity , 1986 .

[7]  J. C. C. De Henderson,et al.  A Problem in Applied Topology: on the Selection of Cycles for the Flexibility Analysis of Skeletal Structures , 1969 .

[8]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[9]  Robert D. Adams,et al.  The location of defects in structures from measurements of natural frequencies , 1979 .

[10]  V. Ho-Huu,et al.  Damage Detection in Laminated Composite Plates Using Modal Strain Energy and Improved Differential Evolution Algorithm , 2016 .

[11]  Seung Wook Baek,et al.  Inverse radiation analysis using repulsive particle swarm optimization algorithm , 2008 .

[12]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[13]  Dexuan Zou,et al.  A novel modified differential evolution algorithm for constrained optimization problems , 2011, Comput. Math. Appl..

[14]  Kamran Behdinan,et al.  Particle swarm approach for structural design optimization , 2007 .

[15]  S. Patnaik.  The integrated force method versus the standard force method , 1986 .

[16]  Dan Simon,et al.  Evolutionary Optimization Algorithms , 2013 .

[17]  Shailendra S. Aote,et al.  A Brief Review on Particle Swarm Optimization : Limitations & Future Directions , 2013 .

[18]  J. C. Henderson,et al.  TOPOLOGICAL ASPECTS OF STRUCTURAL ANALYSIS , 1960 .

[19]  S. M. Seyedpoor.  A two stage method for structural damage detection using a modal strain energy based index and particle swarm optimization , 2012 .

[20]  James Kennedy,et al.  The particle swarm: social adaptation of knowledge , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[21]  Ting-Yu Chen,et al.  IMPROVEMENTS OF SIMPLE GENETIC ALGORITHM IN STRUCTURAL DESIGN , 1997 .

[22]  S. S. Law,et al.  DAMAGE LOCALIZATION BY DIRECTLY USING INCOMPLETE MODE SHAPES. TECHNICAL NOTE , 2000 .

[23]  A. Topcu,et al.  Sparse self‐stress matrices for the finite element force method , 2001 .

[24]  Ali Kaveh,et al.  Efficient finite element analysis by graph-theoretical force method; triangular and rectangular plate bending elements , 2008 .

[25]  Alex Pothen,et al.  Sparse null basis computations in structural optimization , 1989 .

[26]  Andries Petrus Engelbrecht,et al.  Binary Differential Evolution , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[27]  Z. Yao,et al.  Structural damage identification using static test data and changes in frequencies , 2001 .

[28]  K. Moslem,et al.  Structural Damage Detection by Genetic Algorithms , 2002 .

[29]  Ikuyo Kaneko,et al.  On computational procedures for the force method , 1982 .

[30]  J. Gilbert.  Computing a sparse basis for the null space , 1987 .

[31]  Chunming Yang,et al.  A new particle swarm optimization technique , 2005, 18th International Conference on Systems Engineering (ICSEng'05).

[32]  Donald E. Grierson,et al.  Comparison among five evolutionary-based optimization algorithms , 2005, Adv. Eng. Informatics.

[33]  Ali Kaveh,et al.  Efficient finite element analysis by graph-theoretical force method , 2007 .

[34]  T. Coleman,et al.  The null space problem II. Algorithms , 1987 .

[35]  Zbigniew Michalewicz.  GAs: What Are They? , 1996 .

[36]  Prabir Kumar Jena,et al.  Differential Evolution: An Inverse Approach for Crack Detection , 2013 .

[37]  John Robinson,et al.  Integrated theory of finite element methods , 1973 .

[38]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..

[39]  José Elias Laier,et al.  A hybrid Particle Swarm Optimization - Simplex algorithm (PSOS) for structural damage identification , 2009, Adv. Eng. Softw..

[40]  H. Schek.  The force density method for form finding and computation of general networks , 1974 .

[41]  Shirley J. Dyke,et al.  Structural health monitoring for flexible bridge structures using correlation and sensitivity of modal data , 2007 .

[42]  E. Maunder,et al.  Topological and linear analysis of skeletal structures , 1971 .

[43]  Jaehong Lee,et al.  Damage Detection in Truss Structures using Anti-Optimization , 2013 .

[44]  Z. R. Lu,et al.  Structural damage detection using artificial bee colony algorithm with hybrid search strategy , 2016, Swarm Evol. Comput..

[45]  Hoang Chi Tran,et al.  Force methods for trusses with elastic boundary conditions , 2013 .

[46]  Narayana Prasad Padhy,et al.  Comparison of Particle Swarm Optimization and Genetic Algorithm for TCSC-based Controller Design , 2007 .

[47]  S. Patnaik.  The variational energy formulation for the integrated force method , 1986 .

[48]  Trung Nguyen-Thoi,et al.  A two-stage assessment method using damage locating vector method and differential evolution algorithm for damage identification of cross-ply laminated composite beams , 2017 .

[49]  Zhengliang Li,et al.  A two-stage method to identify structural damage sites and extents by using evidence theory and micro-search genetic algorithm , 2009 .

[50]  Herbert Martins Gomes,et al.  Some comparisons for damage detection on structures using genetic algorithms and modal sensitivity method , 2008 .