Damage detection in CFRP composite beams based on vibration analysis using proper orthogonal decomposition method with radial basis functions and cuckoo search algorithm

Abstract This paper presents a new fast approach for crack identification using vibration analysis based on model reduction using proper orthogonal decomposition method with radial basis function (POD-RBF). The method is formulated as an inverse problem for detecting the position, length and depth of crack in Carbon Fibre Reinforced Polymer (CFRP) composite structures, where Genetic and Cuckoo search algorithms are used to minimize the cost function based on numerical and experimental natural frequencies. The results show that the POD-RBF combined with Cuckoo search algorithm is an efficient and a feasible methodology of predicting the width, depth and position of double rectangular notches in CFRP beams. The stability of this technique is tested by introducing a white Gaussian noise in the frequencies data input. The results show that the proposed approach is stable when the noise level is lower than 6%.

[1]  Ted Belytschko,et al.  Cracking particles: a simplified meshfree method for arbitrary evolving cracks , 2004 .

[2]  H. Nguyen-Xuan,et al.  An isogeometric approach for size-dependent geometrically nonlinear transient analysis of functionally graded nanoplates , 2017 .

[3]  SamirĀ Khatir,et al.  Multiple damage detection and localization in beam-like and complex structures using co-ordinate modal assurance criterion combined with firefly and genetic algorithms , 2016 .

[4]  Hung Nguyen-Xuan,et al.  Isogeometric analysis of functionally graded carbon nanotube reinforced composite nanoplates using modified couple stress theory , 2018 .

[5]  Timon Rabczuk,et al.  Detection of multiple flaws in piezoelectric structures using XFEM and level sets , 2014 .

[6]  Timon Rabczuk,et al.  Damage and fracture algorithm using the screened Poisson equation and local remeshing , 2016 .

[7]  A. Vakakis,et al.  PROPER ORTHOGONAL DECOMPOSITION (POD) OF A CLASS OF VIBROIMPACT OSCILLATIONS , 2001 .

[8]  Brian F. Feeny,et al.  On Proper Orthogonal Co-Ordinates as Indicators of Modal Activity , 2002 .

[9]  Dinh Chi Pham,et al.  EXPERIMENTAL AND COMPUTATIONAL STUDIES ON PROGRESSIVE FAILURE ANALYSIS OF NOTCHED CROSS-PLY CFRP COMPOSITE , 2012 .

[10]  H. P. Lee,et al.  PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS—PART I: THEORY , 2002 .

[11]  A. Barr,et al.  One-dimensional theory of cracked Bernoulli-Euler beams , 1984 .

[12]  Chien H. Thai,et al.  A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis , 2016 .

[13]  Qui X. Lieu,et al.  Size-dependent isogeometric analysis of functionally graded carbon nanotube-reinforced composite nanoplates , 2017 .

[14]  Behzad V. Farahani,et al.  Extending a radial point interpolation meshless method to non-local constitutive damage models , 2016 .

[15]  Ugo Galvanetto,et al.  Numerical investigation of a new damage detection method based on proper orthogonal decomposition , 2007 .

[16]  Guang Meng,et al.  Modeling of wave propagation in plate structures using three-dimensional spectral element method for damage detection , 2009 .

[17]  Chien H. Thai,et al.  A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis , 2016 .

[18]  Mario Köppen,et al.  Application of proper orthogonal decomposition and radial basis functions for crack size estimation using particle swarm optimization , 2017 .

[19]  Loc V. Tran,et al.  Isogeometric analysis for nonlinear thermomechanical stability of functionally graded plates , 2016 .

[20]  Timon Rabczuk,et al.  Detection of material interfaces using a regularized level set method in piezoelectric structures , 2016 .

[21]  Angel C. Aparicio,et al.  Structural Damage Identification from Dynamic‐Test Data , 1994 .

[22]  H. Nguyen-Xuan,et al.  Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory , 2015 .

[23]  R. Batra,et al.  Modeling damage in polymeric composites , 2008 .

[24]  Timon Rabczuk,et al.  Element-wise fracture algorithm based on rotation of edges , 2013 .

[25]  Timon Rabczuk,et al.  Dual‐horizon peridynamics , 2015, 1506.05146.

[26]  H. Nguyen-Xuan,et al.  A simple and robust three-dimensional cracking-particle method without enrichment , 2010 .

[27]  R. Capozucca,et al.  Notched CFRP laminates under vibration , 2015 .

[28]  Timon Rabczuk,et al.  Finite strain fracture of 2D problems with injected anisotropic softening elements , 2014 .

[29]  Xin-She Yang,et al.  Engineering optimisation by cuckoo search , 2010 .

[30]  Stéphane Bordas,et al.  An efficient computational approach for control of nonlinear transient responses of smart piezoelectric composite plates , 2015 .

[31]  Timon Rabczuk,et al.  A level-set based IGA formulation for topology optimization of flexoelectric materials , 2017 .

[32]  Idir Belaidi,et al.  Crack identification using model reduction based on proper orthogonal decomposition coupled with radial basis functions , 2016 .

[33]  Timon Rabczuk,et al.  Steiner-point free edge cutting of tetrahedral meshes with applications in fracture , 2017 .

[34]  Hung Nguyen-Xuan,et al.  Isogeometric analysis for functionally graded microplates based on modified couple stress theory , 2016, ArXiv.

[35]  Loc V. Tran,et al.  Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads , 2017 .

[36]  Loc V. Tran,et al.  Vibration analysis of cracked FGM plates using higher-order shear deformation theory and extended isogeometric approach , 2015 .

[37]  Roger Serra,et al.  Damage detection and localization in composite beam structures based on vibration analysis , 2016 .

[38]  Chien H. Thai,et al.  Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements , 2015 .

[39]  Israel Herszberg,et al.  Damage detection in repairs using frequency response techniques , 2009 .

[40]  Timon Rabczuk,et al.  Dual-horizon peridynamics: A stable solution to varying horizons , 2017, 1703.05910.

[41]  Wing Kong Chiu,et al.  Disbond detection in adhesively bonded composite structures using vibration signatures , 2006 .

[42]  Gaëtan Kerschen,et al.  Feature extraction using auto-associative neural networks , 2004 .

[43]  R. Capozucca A reflection on the application of vibration tests for the assessment of cracking in PRC/RC beams , 2013 .

[44]  R. Capozucca,et al.  Vibration of CFRP cantilever beam with damage , 2014 .

[45]  Hung Nguyen-Xuan,et al.  Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory , 2014, ArXiv.

[46]  M. Abdel Wahab,et al.  An isogeometric finite element approach for thermal bending and buckling analyses of laminated composite plates , 2017 .

[47]  Yun-Lai Zhou,et al.  Multiple damage detection in composite beams using Particle Swarm Optimization and Genetic Algorithm , 2017 .