Metamodeling of nonlinear structural systems with parametric uncertainty subject to stochastic dynamic excitation

Within the context of Structural Health Monitoring (SHM), it is often the case that structural systems are described by uncertainty, both with respect to their parameters and the characteristics of the input loads. For the purposes of system identification, efficient modeling procedures are of the essence for a fast and reliable computation of structural response while taking these uncertainties into account. In this work, a reduced order metamodeling framework is introduced for the challenging case of nonlinear structural systems subjected to earthquake excitation. The introduced metamodeling method is based on Nonlinear AutoRegressive models with eXogenous input (NARX), able to describe nonlinear dynamics, which are moreover characterized by random parameters utilized for the description of the uncertainty propagation. These random parameters, which include characteristics of the input excitation, are expanded onto a suitably defined finite-dimensional Polynomial Chaos (PC) basis and thus the resulting representation is fully described through a small number of deterministic coefficients of projection. The effectiveness of the proposed PC-NARX method is illustrated through its implementation on the metamodeling of a five-storey shear frame model paradigm for response in the region of plasticity, i.e., outside the commonly addressed linear elastic region. The added contribution of the introduced scheme is the ability of the proposed methodology to incorporate uncertainty into the simulation. The results demonstrate the efficiency of the proposed methodology for accurate prediction and simulation of the numerical model dynamics with a vast reduction of the required computational toll.

[1]  S. Gholizadeh,et al.  OPTIMAL DESIGN OF STRUCTURES SUBJECTED TO TIME HISTORY LOADING BY SWARM INTELLIGENCE AND AN ADVANCED METAMODEL , 2009 .

[2]  Chung Bang Yun,et al.  Identification of Linear Structural Dynamic Systems , 1982 .

[3]  L. Piroddi,et al.  An identification algorithm for polynomial NARX models based on simulation error minimization , 2003 .

[4]  Erik A. Johnson,et al.  NATURAL EXCITATION TECHNIQUE AND EIGENSYSTEM REALIZATION ALGORITHM FOR PHASE I OF THE IASC-ASCE BENCHMARK PROBLEM: SIMULATED DATA , 2004 .

[5]  Sheng Chen,et al.  Modelling and analysis of non-linear time series , 1989 .

[6]  Dionisio Bernal,et al.  State Estimation in Structural Systems with Model Uncertainties , 2008 .

[7]  Keith Worden,et al.  Genetic algorithm with an improved fitness function for (N)ARX modelling , 2007 .

[8]  Richard W. Longman,et al.  On‐line identification of non‐linear hysteretic structural systems using a variable trace approach , 2001 .

[9]  Filippo Ubertini,et al.  System identification of a super high-rise building via astochastic subspace approach. , 2011 .

[10]  Steve A. Billings,et al.  Term and variable selection for non-linear system identification , 2004 .

[11]  J. Beck,et al.  Updating Models and Their Uncertainties. I: Bayesian Statistical Framework , 1998 .

[12]  G. Fraraccio,et al.  Identification and Damage Detection in Structures Subjected to Base Excitation , 2008 .

[13]  B. Sudret,et al.  An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis , 2010 .

[14]  Joel P. Conte,et al.  Damage identification study of a seven-story full-scale building slice tested on the UCSD-NEES shake table , 2010 .

[15]  Spilios D. Fassois,et al.  A functional model based statistical time series method for vibration based damage detection, localization, and magnitude estimation , 2013 .

[16]  K. Worden,et al.  Past, present and future of nonlinear system identification in structural dynamics , 2006 .

[17]  A. Corigliano,et al.  Parameter identification in explicit structural dynamics: performance of the extended Kalman filter , 2004 .

[18]  Elias B. Kosmatopoulos,et al.  Development of adaptive modeling techniques for non-linear hysteretic systems , 2002 .

[19]  Costas Papadimitriou,et al.  Joint input-response estimation for structural systems based on reduced-order models and vibration data from a limited number of sensors , 2012 .

[20]  Charles R. Farrar,et al.  Non-linear feature identifications based on self-sensing impedance measurements for structural health assessment , 2007 .

[21]  C. Papadimitriou,et al.  Structural model updating and prediction variability using Pareto optimal models , 2008 .

[22]  Roger G. Ghanem,et al.  Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure , 2005, SIAM J. Sci. Comput..

[23]  Spilios D. Fassois,et al.  Aircraft Virtual Sensor Design Via a Time-Dependent Functional Pooling NARX Methodology , 2013 .

[24]  Charles R. Farrar,et al.  Classifying Linear and Nonlinear Structural Damage Using Frequency Domain ARX Models , 2002 .

[25]  Achintya Haldar,et al.  Health Assessment at Local Level with Unknown Input Excitation , 2005 .

[26]  Spilios D. Fassois,et al.  Parametric time-domain methods for non-stationary random vibration modelling and analysis — A critical survey and comparison , 2006 .

[27]  Eleni Chatzi,et al.  The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non‐collocated heterogeneous sensing , 2009 .