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Bayesian System Identification using auxiliary stochastic dynamical systems

Catanach, Thomas A. and Beck, James L. (2017) Bayesian System Identification using auxiliary stochastic dynamical systems. International Journal of Non-Linear Mechanics, 94 . pp. 72-83. ISSN 0020-7462. https://resolver.caltech.edu/CaltechAUTHORS:20171026-104414715

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Abstract

Bayesian approaches to statistical inference and system identification became practical with the development of effective sampling methods like Markov Chain Monte Carlo (MCMC). However, because the size and complexity of inference problems has dramatically increased, improved MCMC methods are required. Dynamical systems based samplers are an effective extension of traditional MCMC methods. These samplers treat the posterior probability distribution as the potential energy function of a dynamical system, enabling them to better exploit the structure of the inference problem. We present an algorithm, Second-Order Langevin MCMC (SOL-MC), a stochastic dynamical system based MCMC algorithm, which uses the damped second-order Langevin stochastic differential equation (SDE) to sample a posterior distribution. We design the SDE such that the desired posterior probability distribution is its stationary distribution. Since this method is based upon an underlying dynamical system, we can utilize existing work to develop, implement, and optimize the sampler's performance. As such, we can choose parameters which speed up the convergence to the stationary distribution and reduce temporal state and energy correlations in the samples. We then apply this sampler to a system identification problem for a non-linear hysteretic structure model to investigate this method under globally identifiable and unidentifiable conditions.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.ijnonlinmec.2017.03.012DOIArticle
http://www.sciencedirect.com/science/article/pii/S0020746217301889?via%3DihubPublisherArticle
ORCID:
AuthorORCID
Catanach, Thomas A.0000-0002-4321-3159
Additional Information:© 2017 Elsevier Ltd. Received 5 August 2016, Revised 25 February 2017, Accepted 11 March 2017, Available online 21 March 2017.
Subject Keywords:System identification; Bayesian methods; Markov Chain Monte Carlo; Stochastic differential equations; Masing hysteresis model
Record Number:CaltechAUTHORS:20171026-104414715
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171026-104414715
Official Citation:Thomas A. Catanach, James L. Beck, Bayesian System Identification using auxiliary stochastic dynamical systems, In International Journal of Non-Linear Mechanics, Volume 94, 2017, Pages 72-83, ISSN 0020-7462, https://doi.org/10.1016/j.ijnonlinmec.2017.03.012. (http://www.sciencedirect.com/science/article/pii/S0020746217301889)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82697
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Oct 2017 18:23
Last Modified:03 Oct 2019 18:57

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