A comprehensive Bayesian approach for model updating and quantification of modeling errors

• Published in: Probabilistic engineering mechanics Vol. 26; no. 4; pp. 550 - 560
• Main Authors: Zhang, E.L., Feissel, P., Antoni, J.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2011; Elsevier
• Subjects: Acoustics; Bayesian analysis; Bayesian approach; Chaos theory; Computer simulation; Engineering Sciences; Error analysis; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Markov Chain Monte Carlo; Mathematical models; Mathematics; Measurement and testing methods; Mechanics; Model updating; Modeling error; Monte Carlo methods; Multisine excitation; Permissible error; Physics; Polynomial chaos; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Solid mechanics; Stochastic processes; Structural and continuum mechanics; Multisine excitation; Bayesian approach; Polynomial chaos; Markov Chain Monte Carlo; Modeling error; Model updating; Costs; Stochastic process; Modeling; Model matching; Probability density function; System identification; Random variable; Measurement error; Linearization; Bayes estimation; Statistical analysis; Probabilistic approach; Random error; Frequency domain method; Experimental study; Orthogonal polynomial; Probability space; Confidence interval; Posterior probability; Predictability; Structural model; Non linear distortion; Structural analysis
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2011.07.001

This paper presents a comprehensive Bayesian approach for structural model updating which accounts for errors of different kinds, including measurement noise, nonlinear distortions stemming from the linearization of the model, and modeling errors due to the limited predictability of the latter. In particular, this allows the computation of any type of statistics on the updated parameters, such as joint or marginal probability density functions, or confidence intervals. The present work includes four main contributions that make the Bayesian updating approach feasible with general numerical models: (1) the proposal of a specific experimental protocol based on multisine excitations to accurately assess measurement errors in the frequency domain; (2) two possible strategies to represent the modeling error as additional random variables to be inferred jointly with the model parameters; (3) the introduction of a polynomial chaos expansion that provides a surrogate mapping between the probability spaces of the prior random variables and the model modal parameters; (4) the use of an evolutionary Monte Carlo Markov Chain which, in conjunction with the polynomial chaos expansion, can sample the posterior probability density function of the updated parameters at a very reasonable cost. The proposed approach is validated by numerical and experimental examples. ► Bayesian model updating is investigated by accounting for errors of various kinds. ► The modeling error is represented and inferred jointly with model parameters. ► The measurement error is assessed by multisine excitations in the frequency domain. ► The polynomial chaos expansion is introduced for rapid uncertainty propagation. ► Surrogate model based sampling strategy is implemented by an evolutionary MCMC.