Sequential gauss-newton MCMC algorithm for high-dimensional bayesian model updating
Paper i proceeding, 2016

Bayesian model updating provides a rigorous framework to account for uncertainty induced by lack of knowledge about engineering systems in their respective mathematical models through updates of the joint probability density function (PDF), the so-called posterior PDF, of the unknown model parameters. The Markov chain Monte Carlo (MCMC) methods are currently the most popular approaches for generating samples from the posterior PDF. However, these methods often found wanting when sampling from difficult distributions (e.g., high-dimensional PDFs, PDFs with flat manifolds, multimodal PDFs, and very peaked PDFs). This paper introduces a new multi-level sampling approach for Bayesian model updating, called Sequential Gauss-Newton algorithm, which is inspired by the Transitional Markov chain Monte Carlo (TMCMC) algorithm. The Sequential Gauss-Newton algorithm improves two aspects of TMCMC to make an efficient and effective MCMC algorithm for drawing samples from difficult posterior PDFs. First, the statistical efficiency of the algorithm is enhanced by use of the systematic resampling scheme. Second, a new MCMC algorithm, called Gauss-Newton MCMC algorithm, is proposed which is essentially an M-H algorithm with a Gaussian proposal PDF tailored to the posterior PDF using the gradient and Hessian information of the negative log posterior. The effectiveness of the proposed algorithm for solving the Bayesian model updating problem is illustrated using three examples with irregularly shaped posterior PDFs.

Bayesian model updating

Hessian

Uncertainty quantification

Markov chain monte carlo

Gauss-Newton

Optimal scale factor tuning

Författare

Majid Khorsand Vakilzadeh

Chalmers, Tillämpad mekanik, Dynamik

Anders Sjögren

Chalmers University of Technology

Volvo

Anders Johansson

Chalmers, Tillämpad mekanik, Dynamik

Thomas Abrahamsson

Chalmers, Tillämpad mekanik, Dynamik

Conference Proceedings of the Society for Experimental Mechanics Series

21915644 (ISSN) 21915652 (eISSN)

Vol. 3 Part F2 303-314

Ämneskategorier

Maskinteknik

DOI

10.1007/978-3-319-54858-6_30

ISBN

978-331954857-9