Curse of Dimensionality in Bayesian Model Updating

TL;DR

This paper investigates the challenges posed by high-dimensional spaces in Bayesian model updating for structural health monitoring, highlighting the impact of the curse of dimensionality and proposing strategies to address it.

Contribution

It provides an analytical framework to understand the curse of dimensionality in Bayesian updating and explores factors affecting the prior-posterior distance in high dimensions.

Findings

High-dimensional Bayesian updating faces significant challenges due to the curse of dimensionality.

The prior-posterior distance is crucial for parameter estimation accuracy in high dimensions.

Multi-modality and degeneracy further complicate Bayesian model updating in high-dimensional spaces.

Abstract

Bayesian approach provides a coherent framework to address the model updating problem in structural health monitoring. The current practice, however, only focuses on low-dimension model (generally no more than 20 parameters), which limits the accuracy and predictability of the updated model. This paper aims at understanding the curse of dimensionality in Bayesian model updating, and thus proposing feasible strategies to overcome it. An analytical investigation is conducted, which allows us to answer fundamental questions in Bayesian analysis, e.g., where the posterior mass locates and how large of it comparing to the prior volume. The key concept here is the distance from the prior to the posterior, which makes the parameter estimation really difficult in high-dimension problems. In this sense, not only the dimensionality matters, but also the multi-modality, the pronounced degeneracy, and other factors that influence the prior-posterior distance matter.