A hybrid probabilistic framework for model validation with application to structural dynamics modeling

Abstract

Abstract Identifying useful mathematical models of physical systems is an essential part of computational modeling and simulation. Once appropriate models are identified, they can be used for applications such as response prediction, structural control, monitoring structural integrity, lifetime prognosis, etc. The number of models and model classes available to the modeler to represent a physical phenomenon, however, can be very large. Retaining all available models throughout a study can be computationally burdensome, so the modeler has the significant problem of identifying the valid models to be used in further studies. To address this challenge, a probabilistic framework is proposed herein for validating models by intertwining the concepts of model falsification and Bayesian model selection. Model falsification, based on the philosophy that measurements can only be used to falsify models, is used in this framework in both pre- and postprocessing steps to eliminate models and model classes, respectively, that cannot explain the measurements. This is the first study to propose a framework to integrate these two paradigms. A likelihood-bound model falsification, previously introduced by the authors, determines the validity of the initial candidate model classes, using the false discovery rate (FDR), and removes most of the incorrect ones without incurring any significant additional computational burden. Next, Bayesian model selection, which assigns posterior model class probabilities based on Bayes’ theorem, is applied to the remaining model classes to identify the model(s) and model class(es) that provide predictions that probabilistically best fit the data. Finally, a postprocessing likelihood-bound falsification checks the validity of the final model class(es). The proposed framework is first illustrated through two nonlinear structural dynamics examples that show the efficacy of the proposed framework in identifying models for these structures as well as reducing the computational burden relative to Bayesian model selection applied alone. Finally, a third example uses measurement data from experiments performed on a full-scale four-story base-isolated building at the world’s largest shake table in Japan’s “E-Defense” laboratory.