Bayesian Structural Identification using Gaussian Process Discrepancy Models

TL;DR

This paper develops a Bayesian framework for structural identification using Gaussian Process models, focusing on kernel selection to improve out-of-sample prediction accuracy and model robustness.

Contribution

It introduces a new Bayesian model selection method for choosing kernel functions, balancing accuracy, generalizability, and simplicity in GP-based structural modeling.

Findings

Proposes an exponential-trigonometric covariance function justified by Bayesian selection.

Demonstrates improved prediction robustness through numerical and experimental examples.

Provides algorithms for kernel selection using Laplace approximation and sampling.

Abstract

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting accuracy in the training data set, their out-of-sample predictions can be highly inaccurate. This paper investigates this problem by reformulating the problem on a consistent probabilistic foundation, reviewing common choices of kernel covariance functions, and proposing a new Bayesian model selection for kernel function selection, aiming to create a balance between fitting accuracy, generalizability, and model parsimony. Computational aspects are addressed via Laplace approximation and sampling techniques, providing detailed algorithms and strategies. Numerical and experimental examples are included to demonstrate the accuracy and robustness of the proposed framework. As a result, an exponential-trigonometric covariance function is characterized and justified based on the Bayesian model selection approach and observations of the sample autocorrelation function of the response discrepancies.