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. 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, uncertainties in the excitations caused by earthquakes, and limited constraining information 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 method for combining prior knowledge of a system with measured data and for choosing between competing model classes. Similar approaches have been used in the field of system identification, but these methods (referred to as asymptotic-approximation-based methods) often focus on the model defined by the set of most plausible parameter values and have difficulty dealing with ill-conditioned problems, where there may be many models with high plausibility. 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 modal data for the purposes of structural health monitoring, and (3) identification of hysteretic structural models, including degrading models, from seismic structural response. In cases where asymptotic approximation-based methods are appropriate, the results obtained using stochastic simulation show good agreement with results from asymptotics. For cases involving ill-conditioned problems based on simulated data, stochastic simulation methods are successfully applied to obtain results in situations where the use of asymptotics is infeasible. Finally, preliminary studies using stochastic simulation to identify a deteriorating hysteretic model with sparse real data from a structure damaged in an 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.