Hierarchical Bayesian model updating for structural identification

Abstract A new probabilistic finite element (FE) model updating technique based on Hierarchical Bayesian modeling is proposed for identification of civil structural systems under changing ambient/environmental conditions. The performance of the proposed technique is investigated for (1) uncertainty quantification of model updating parameters, and (2) probabilistic damage identification of the structural systems. Accurate estimation of the uncertainty in modeling parameters such as mass or stiffness is a challenging task. Several Bayesian model updating frameworks have been proposed in the literature that can successfully provide the “parameter estimation uncertainty” of model parameters with the assumption that there is no underlying inherent variability in the updating parameters. However, this assumption may not be valid for civil structures where structural mass and stiffness have inherent variability due to different sources of uncertainty such as changing ambient temperature, temperature gradient, wind speed, and traffic loads. Hierarchical Bayesian model updating is capable of predicting the overall uncertainty/variability of updating parameters by assuming time-variability of the underlying linear system. A general solution based on Gibbs Sampler is proposed to estimate the joint probability distributions of the updating parameters. The performance of the proposed Hierarchical approach is evaluated numerically for uncertainty quantification and damage identification of a 3-story shear building model. Effects of modeling errors and incomplete modal data are considered in the numerical study.

[1]  S. Alampalli,et al.  EFFECTS OF TESTING, ANALYSIS, DAMAGE, AND ENVIRONMENT ON MODAL PARAMETERS , 2000 .

[2]  Hoon Sohn,et al.  A review of structural health monitoring literature 1996-2001 , 2002 .

[3]  F. Hemez,et al.  Updating finite element dynamic models using an element-by-element sensitivity methodology , 1993 .

[4]  Babak Moaveni,et al.  Effects of changing ambient temperature on finite element model updating of the Dowling Hall Footbridge , 2012 .

[5]  Babak Moaveni,et al.  Environmental effects on the identified natural frequencies of the Dowling Hall Footbridge , 2011 .

[6]  A. Kiureghian,et al.  Aleatory or epistemic? Does it matter? , 2009 .

[7]  M. Baruch.  Optimal correction of mass and stiffness matrices using measured modes , 1982 .

[8]  François M. Hemez,et al.  Uncertainty and Sensitivity Analysis of Damage Identification Results Obtained Using Finite Element Model Updating , 2009, Comput. Aided Civ. Infrastructure Eng..

[9]  P. Gustafson,et al.  Conservative prior distributions for variance parameters in hierarchical models , 2006 .

[10]  I. Smith,et al.  Structural identification with systematic errors and unknown uncertainty dependencies , 2013 .

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

[12]  Costas Papadimitriou,et al.  Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models , 2015, J. Comput. Phys..

[13]  François M. Hemez,et al.  Uncertainty analysis of system identification results obtained for a seven‐story building slice tested on the UCSD‐NEES shake table , 2014 .

[14]  Sankaran Mahadevan,et al.  Separating the contributions of variability and parameter uncertainty in probability distributions , 2013, Reliab. Eng. Syst. Saf..

[15]  Christophe Andrieu,et al.  A tutorial on adaptive MCMC , 2008, Stat. Comput..

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

[17]  Sondipon Adhikari,et al.  A second-moment approach for direct probabilistic model updating in structural dynamics , 2012 .

[18]  Siu-Kui Au,et al.  Development of a practical algorithm for Bayesian model updating of a coupled slab system utilizing field test data , 2014 .

[19]  Guido De Roeck,et al.  One-year monitoring of the Z24-Bridge : environmental effects versus damage events , 2001 .

[20]  John E. Mottershead,et al.  The sensitivity method in finite element model updating: A tutorial (vol 25, pg 2275, 2010) , 2011 .

[21]  Tadeusz Uhl,et al.  Advanced structural damage detection : from theory to engineering applications , 2013 .

[22]  Andreas Stavridis,et al.  Nonlinear finite element model updating of an infilled frame based on identified time-varying modal parameters during an earthquake , 2014 .

[23]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[24]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[25]  Shirley J. Dyke,et al.  Damage Detection Accommodating Varying Environmental Conditions , 2006 .

[26]  James L. Beck,et al.  A Bayesian probabilistic approach to structural health monitoring , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[27]  Ka-Veng Yuen,et al.  Bayesian Methods for Updating Dynamic Models , 2011 .

[28]  Costas Papadimitriou,et al.  On prediction error correlation in Bayesian model updating , 2013 .

[29]  Babak Moaveni,et al.  Bayesian FE Model Updating in the Presence of Modeling Errors , 2014 .

[30]  Jon D. Collins,et al.  Statistical Identification of Structures , 1973 .

[31]  Costas Papadimitriou,et al.  Bayesian uncertainty quantification and propagation in molecular dynamics simulations: a high performance computing framework. , 2012, The Journal of chemical physics.

[32]  P. G. Bakir,et al.  Damage identification on the Tilff bridge by vibration monitoring using optical fiber strain sensors , 2005 .

[33]  Babak Moaveni,et al.  Probabilistic identification of simulated damage on the Dowling Hall footbridge through Bayesian finite element model updating , 2015 .

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

[35]  James L. Beck,et al.  Statistical System Identification of Structures , 1989 .

[36]  K. F. Alvin,et al.  Finite Element Model Update via Bayesian Estimation and Minimization of Dynamic Residuals , 1996 .

[37]  Joel P. Conte,et al.  Uncertainty Quantification in the Assessment of Progressive Damage in a 7-Story Full-Scale Building Slice , 2013 .

[38]  B. Goller,et al.  Investigation of model uncertainties in Bayesian structural model updating , 2011, Journal of sound and vibration.

[39]  J. Beck.  Bayesian system identification based on probability logic , 2010 .

[40]  P. Koumoutsakos,et al.  Bayesian Hierarchical Models for Uncertainty Quantification in Structural Dynamics , 2014 .

[41]  S. E. Ahmed,et al.  Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference , 2008, Technometrics.

[42]  Hoon Sohn,et al.  A Bayesian Probabilistic Approach for Structure Damage Detection , 1997 .

[43]  M. Friswell,et al.  Uncertainty identification by the maximum likelihood method , 2005 .

[44]  K. Yuen.  Bayesian Methods for Structural Dynamics and Civil Engineering , 2010 .

[45]  James L. Beck,et al.  New Bayesian Model Updating Algorithm Applied to a Structural Health Monitoring Benchmark , 2004 .

[46]  Glauco Feltrin,et al.  Damage Identification Using Modal Data: Experiences on a Prestressed Concrete Bridge , 2005 .

[47]  Hoon Sohn,et al.  Environmental variability of modal properties , 1999 .

[48]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[49]  James L. Beck,et al.  Structural damage detection and assessment by adaptive Markov chain Monte Carlo simulation , 2004 .

[50]  E. Peter Carden,et al.  Vibration Based Condition Monitoring: A Review , 2004 .

[51]  D. Warner North,et al.  A Tutorial Introduction to Decision Theory , 1968, IEEE Trans. Syst. Sci. Cybern..

[52]  Hoon Sohn,et al.  An experimental study of temperature effect on modal parameters of the Alamosa Canyon Bridge , 1999 .

[53]  James L. Beck,et al.  Bayesian Updating and Model Class Selection for Hysteretic Structural Models Using Stochastic Simulation , 2008 .

[54]  Thomas H. Heaton,et al.  The Observed Wander of the Natural Frequencies in a Structure , 2006 .

[55]  John E. Mottershead,et al.  Finite Element Model Updating in Structural Dynamics , 1995 .

[56]  G. Roeck,et al.  Structural damage identification of the highway bridge Z24 by FE model updating , 2004 .

[57]  Eleni Chatzi,et al.  Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty , 2010 .

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

[59]  Tshilidzi Marwala,et al.  Model selection in finite element model updating using the Bayesian evidence statistic , 2011 .

[60]  Stochastic Relaxation , 2014, Computer Vision, A Reference Guide.

[61]  James L. Beck,et al.  Bayesian Analysis of the Phase II IASC–ASCE Structural Health Monitoring Experimental Benchmark Data , 2004 .

[62]  J. Beck,et al.  Bayesian Updating of Structural Models and Reliability using Markov Chain Monte Carlo Simulation , 2002 .

[63]  A. Gelman.  Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[64]  J. Ching,et al.  Transitional Markov Chain Monte Carlo Method for Bayesian Model Updating, Model Class Selection, and Model Averaging , 2007 .

[65]  Dennis V. Lindley.  Introduction to decision theory , 1978 .

[66]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[67]  Siu-Kui Au,et al.  Connecting Bayesian and frequentist quantification of parameter uncertainty in system identification , 2012 .

[68]  Shamim N. Pakzad,et al.  Generalized Response Surface Model Updating Using Time Domain Data , 2014 .

[69]  Costas Papadimitriou,et al.  Bridge health monitoring system based on vibration measurements , 2008 .

[70]  M. Friswell,et al.  Perturbation methods for the estimation of parameter variability in stochastic model updating , 2008 .

[71]  Jeff Gill,et al.  Bayesian Methods : A Social and Behavioral Sciences Approach , 2002 .

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

[73]  Gerhart I. Schuëller,et al.  Evidence-Based Identification of Weighting Factors in Bayesian Model Updating Using Modal Data , 2012 .

[74]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[75]  C. Papadimitriou,et al.  Structural identification based on optimally weighted modal residuals , 2007 .

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