Damage evaluation of structures with uncertain parameters via interval analysis and FE model updating methods

Summary Experimental and numerical uncertainties are always present in structural identification problems. The quantification of the uncertainty on the results of a finite element updating procedure is commonly carried out in a probabilistic framework, which requires working with a-priori known probability distributions for the uncertain parameters. In this paper, the modal interval analysis method to estimate damage structural problems with uncertain-but-bounded parameters is presented. With this method only the bounds on the magnitude of uncertain parameters are required. The formulation of this method in a single objective framework is equivalent to minimizing the average value and the deviation of the uncertain objective function in the considered interval with which it is actually a multi-objective problem. Furthermore, its implementation requires the analytical evaluation of the sensitivities of the objective functions with respect to the uncertain parameters, which is derived. Numerical and experimental results evidence the accuracy and the effectiveness of the proposed approach to evaluate damage in uncertain environments. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  Ricardo Perera,et al.  Structural Damage Detection via Modal Data with Genetic Algorithms , 2006 .

[2]  Z. Qiu,et al.  Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach , 2003 .

[3]  Anjan Dutta,et al.  Damage detection in bridges using accurate modal parameters , 2004 .

[4]  Xiaojun Wang,et al.  Modal analysis of structures with uncertain-but-bounded parameters via interval analysis , 2007 .

[5]  M. Chandrashekhar,et al.  Uncertainty handling in structural damage detection using fuzzy logic and probabilistic simulation , 2009 .

[6]  Tadeusz Uhl,et al.  Reliability- and performance-based robust design optimization of MEMS structures considering technological uncertainties , 2012 .

[7]  Guido De Roeck,et al.  Dealing with uncertainty in model updating for damage assessment: A review , 2015 .

[8]  J. Mottershead,et al.  Interval model updating with irreducible uncertainty using the Kriging predictor , 2011 .

[9]  M. Chandrashekhar,et al.  Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic , 2009 .

[10]  Singiresu S. Rao,et al.  Analysis of uncertain structural systems using interval analysis , 1997 .

[11]  D. Moens,et al.  Interval sensitivity theory and its application to frequency response envelope analysis of uncertain structures , 2007 .

[12]  Ricardo Perera,et al.  A multistage FE updating procedure for damage identification in large-scale structures based on multiobjective evolutionary optimization , 2008 .

[13]  Ephrahim Garcia,et al.  Structural Damage Identification: A Probabilistic Approach , 1998 .

[14]  Guido De Roeck,et al.  Damage identification of a reinforced concrete frame by finite element model updating using damage parameterization , 2008 .

[15]  Geert Lombaert,et al.  Uncertainty quantification in the damage assessment of a cable-stayed bridge by means of fuzzy numbers , 2009 .

[16]  Ranjan Ganguli,et al.  Genetic fuzzy system for online structural health monitoring of composite helicopter rotor blades , 2007 .

[17]  In-Won Lee,et al.  An efficient algebraic method for the computation of natural frequency and mode shape sensitivities—Part I. Distinct natural frequencies , 1997 .

[18]  Hong Hao,et al.  Civil structure condition assessment by FE model updating: methodology and case studies , 2001 .

[19]  Hong Hao,et al.  Statistical damage identification of structures with frequency changes , 2003 .

[20]  Graeme Manson,et al.  Calculating frequency response functions for uncertain systems using complex affine analysis , 2005 .

[21]  Z. Qiu,et al.  The static displacement and the stress analysis of structures with bounded uncertainties using the vertex solution theorem , 2007 .

[22]  Xu Han,et al.  An uncertain structural optimization method based on nonlinear interval number programming and interval analysis method , 2007 .

[23]  R. Mullen,et al.  Uncertainty in mechanics problems-interval-based approach , 2001 .

[24]  Michael I Friswell,et al.  Damage identification using inverse methods , 2007, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[25]  J. Vehí,et al.  Structural assessment under uncertain parameters via interval analysis , 2008 .

[26]  Wang-Ji Yan,et al.  Statistic structural damage detection based on the closed-form of element modal strain energy sensitivity , 2012 .

[27]  M. Hanss,et al.  Review: Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances , 2011 .

[28]  John E. Mottershead,et al.  Model Updating In Structural Dynamics: A Survey , 1993 .

[29]  Tadeusz Uhl,et al.  Robustness analysis of a car windscreen using response surface techniques , 2011 .

[30]  Antonio Ruiz,et al.  An evolutionary multiobjective framework for structural damage localization and quantification , 2007 .

[31]  R. Fox,et al.  Rates of change of eigenvalues and eigenvectors. , 1968 .

[32]  Hui Li,et al.  A probabilistic damage identification approach for structures with uncertainties under unknown input , 2011 .

[33]  Z. Qiu,et al.  Exact bounds for the static response set of structures with uncertain-but-bounded parameters , 2006 .

[34]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[35]  Z. Qiu,et al.  Interval Analysis Method for Damage Identification of Structures , 2010 .

[36]  G. Muscolino,et al.  Interval analysis of structures with uncertain-but-bounded axial stiffness , 2011 .