Beck, James L.
(2010)
*Bayesian system identification based on probability logic.*
Structural Control and Health Monitoring, 17
(7).
pp. 825-847.
ISSN 1545-2255.
https://resolver.caltech.edu/CaltechAUTHORS:20101207-111319772

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## Abstract

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.

Item Type: | Article | |||||||||
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Additional Information: | © 2010 John Wiley & Sons, Ltd. Received 2 February 2010; Revised 13 July 2010; Accepted 17 September 2010. Article first published online: 28 Oct. 2010 The author dedicates this paper to the memory of Professor George W. Housner. He was a scholar, a leader, a gentleman, a mentor and a valued colleague at the California Institute of Technology. The author also wishes to thank Dr Sai-Hung Cheung for permission to include the state-space example from his PhD thesis. | |||||||||

Subject Keywords: | system identification; probability logic; Bayesian updating; robust predictions; model assessment | |||||||||

Issue or Number: | 7 | |||||||||

Record Number: | CaltechAUTHORS:20101207-111319772 | |||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20101207-111319772 | |||||||||

Official Citation: | Beck, J. L. (2010), Bayesian system identification based on probability logic. Structural Control and Health Monitoring, 17: 825–847. doi: 10.1002/stc.424 | |||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||

ID Code: | 21214 | |||||||||

Collection: | CaltechAUTHORS | |||||||||

Deposited By: | Tony Diaz | |||||||||

Deposited On: | 11 Dec 2010 00:48 | |||||||||

Last Modified: | 03 Oct 2019 02:21 |

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