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Bayesian Updating and Model Class Selection for Hysteretic Structural Models Using Stochastic Simulation

Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125 USA

James L. Beck

Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125 USA, jimbeck{at}its.caltech.edu

System identification of structures using their measured earthquake response can play a key role in structural health monitoring, structural control and improving performance-based design. Implementation using data from strong seismic shaking is complicated by the nonlinear hysteretic response of structures. Furthermore, this inverse problem is ill-conditioned; for example, even if some components in the structure show substantial yielding, others will exhibit nearly elastic response, producing no information about their yielding behavior. Classical least-squares or maximum likelihood estimation will not work with a realistic class of hysteretic models because it will be unidentifiable based on the data. It is shown here that Bayesian updating and model class selection provide a powerful and rigorous approach to tackle this problem when implemented using a recently developed stochastic simulation algorithm called Transitional Markov Chain Monte Carlo. The updating and model class selection is performed on a previously-developed class of Masing hysteretic structural models that are relatively simple yet can give realistic responses to seismic loading. The theory for the Masing hysteretic models, and the theory used to perform the updating and model class selection, are presented and discussed. An illustrative example is given that uses simulated dynamic response data and shows the ability of the algorithm to identify hysteretic systems even when the class of models is unidentifiable based on the data.

Key Words: Bayesian methods • Masing hysteretic models • system identification • Markov Chain Monte Carlo simulation • model class selection

Journal of Vibration and Control, Vol. 14, No. 1-2, 7-34 (2008)
DOI: 10.1177/1077546307079400


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