Efficiency comparison of MCMC and Transport Map Bayesian posterior estimation for structural health monitoring

Authored by

Jan Grashorn, Matteo Broggi, Ludovic Chamoin, Michael Beer

Abstract

In this paper, an alternative to solving Bayesian inverse problems for structural health monitoring based on a variational formulation with so-called transport maps is examined. The Bayesian inverse formulation is a widely used tool in structural health monitoring applications. While Markov Chain Monte Carlo (MCMC) methods are often implemented in these settings, they come with the problem of using many model evaluations, which in turn can become quite costly. We focus here on recent developments in the field of transport theory, where the problem is formulated as finding a deterministic, invertible mapping between some easy to evaluate reference density and the posterior. The resulting variational formulation can be solved with integration and optimization methods. We develop a general formulation for the application of transport maps to vibration-based structural health monitoring. Further, we study influences of different integration approaches on the efficiency and accuracy of the transport map approach and compare it to the Transitional MCMC algorithm, a widely used method for structural identification. Both methods are applied to a lower-dimensional dynamic model with uni- and multi-modal properties, as well as to a higher-dimensional neural network surrogate system of an airplane structure. We find that transport maps have a significant increase in accuracy and efficiency, when used in the right circumstances.

Details

Organisation(s): Institute for Risk and Reliability
International RTG 2657: Computational Mechanics Techniques in High Dimensions
External Organisation(s): École normale supérieure Paris-Saclay (ENS Paris-Saclay)
University of Liverpool
Tongji University
Type: Article
Journal: Mechanical Systems and Signal Processing
Volume: 216
No. of pages: 16
ISSN: 0888-3270
Publication date: 01.07.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Control and Systems Engineering, Signal Processing, Civil and Structural Engineering, Aerospace Engineering, Mechanical Engineering, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.ymssp.2024.111440 (Access: Open )