Details
| Original language | English |
|---|---|
| Article number | 111440 |
| Number of pages | 16 |
| Journal | Mechanical Systems and Signal Processing |
| Volume | 216 |
| Early online date | 30 Apr 2024 |
| Publication status | Published - 1 Jul 2024 |
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.
Keywords
- Bayesian updating, Markov chain Monte Carlo, Structural health monitoring, Transport maps, Variational inference
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
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In: Mechanical Systems and Signal Processing, Vol. 216, 111440, 01.07.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Efficiency comparison of MCMC and Transport Map Bayesian posterior estimation for structural health monitoring
AU - Grashorn, Jan
AU - Broggi, Matteo
AU - Chamoin, Ludovic
AU - Beer, Michael
N1 - Publisher Copyright: © 2024 The Author(s)
PY - 2024/7/1
Y1 - 2024/7/1
N2 - 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.
AB - 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.
KW - Bayesian updating
KW - Markov chain Monte Carlo
KW - Structural health monitoring
KW - Transport maps
KW - Variational inference
UR - http://www.scopus.com/inward/record.url?scp=85191653620&partnerID=8YFLogxK
U2 - 10.1016/j.ymssp.2024.111440
DO - 10.1016/j.ymssp.2024.111440
M3 - Article
AN - SCOPUS:85191653620
VL - 216
JO - Mechanical Systems and Signal Processing
JF - Mechanical Systems and Signal Processing
SN - 0888-3270
M1 - 111440
ER -