Application of Stochastic Simulation Methods to System Identification

Abstract

Reliable predictive models for the response of structures are a necessity for many branches of earthquake engineering, such as design, structural control, and structural health monitoring. However, the process of choosing an appropriate class of models to describe a system, known as model-class selection, and identifying the specific predictive model based on available data, known as system identification, is difficult. Variability in material properties, complex constitutive behavior, uncertainty in the excitations caused by earthquakes, and limited constraining information (relatively few channels of data, compared to the number of parameters needed for a useful predictive model) make system identification an ill-conditioned problem. In addition, model-class selection is not trivial, as it involves balancing predictive power with simplicity. These problems of system identification and model-class selection may be addressed using a Bayesian probabilistic framework that provides a rational, transparent method for combining prior knowledge of a system with measured data and for choosing between competing model classes. The probabilistic framework also allows for explicit quantification of the uncertainties associated with modeling a system. The essential idea is to use probability logic and Bayes' Theorem to give a measure of plausibility for a model or class of models that is updated with available data. Similar approaches have been used in the field of system identification, but many currently used methods for Bayesian updating focus on the model defined by the set of most plausible parameter values. The challenge for these approaches (referred to as asymptotic-approximation-based methods) is when one must deal with ill-conditioned problems, where there may be many models with high plausibility, rather than a single v dominant model. It is demonstrated here that ill-conditioned problems in system identification and model-class selection can be effectively addressed using stochastic simulation methods. This work focuses on the application of stochastic simulation to updating and comparing model classes in problems of: (1) development of empirical ground motion attenuation relations, (2) structural model updating using incomplete modal data for the purposes of structural health monitoring, and (3) identification of hysteretic structural models, including degrading models, from seismic structural response. The results for system identification and model-class selection in this work fall into three categories. First, in cases where the existing asymptotic approximation-based methods are appropriate (i.e., well-conditioned problems with one highest-plausibility model), the results obtained using stochastic simulation show good agreement with results from asymptotic-approximation-based methods. Second, for cases involving ill-conditioned problems based on simulated data, stochastic simulation methods are successfully applied to obtain results in a situation where the use of asymptotics is not feasible (specfically, the identification of hysteretic models). Third, preliminary studies using stochastic simulation to identify a deteriorating hysteretic model with relatively sparse real data from a structure damaged in the 1994 Northridge earthquake show that the high-plausibility models demonstrate behavior consistent with the observed damage, indicating that there is promise in applying these methods to ill-conditioned problems in the real world.

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