Bayesian system identification based on probability logic

Probability logic with Bayesian updating provides a rigorous framework to quantify modeling uncertainty and perform system identification. It uses probability as a multi-valued propositional logic for plausible reasoning where the probability of a model is a measure of its relative plausibility within a set of models. System identification is thus viewed as inference about plausible system models and not as a quixotic quest for the true model. Instead of using system data to estimate the model parameters, Bayes' Theorem is used to update the relative plausibility of each model in a model class, which is a set of input–output probability models for the system and a probability distribution over this set that expresses the initial plausibility of each model. Robust predictive analyses informed by the system data use the entire model class with the probabilistic predictions of each model being weighed by its posterior probability. Additional robustness to modeling uncertainty comes from combining the robust predictions of each model class in a set of candidates for the system, where each contribution is weighed by the posterior probability of the model class. This application of Bayes' Theorem automatically applies a quantitative Ockham's razor that penalizes the data-fit of more complex model classes that extract more information from the data. Robust analyses involve integrals over parameter spaces that usually must be evaluated numerically by Laplace's method of asymptotic approximation or by Markov Chain Monte Carlo methods. An illustrative application is given using synthetic data corresponding to a structural health monitoring benchmark structure