Bayesian system identification for structures considering spatial and temporal correlation

TL;DR

This paper develops a Bayesian system identification method that accounts for spatial and temporal correlations in large, dense sensor datasets, improving accuracy over traditional uncorrelated error assumptions.

Contribution

It introduces an efficient likelihood evaluation approach and uses nested sampling for model evidence, enabling accurate Bayesian identification with correlated data.

Findings

Correlation in model errors is strongly supported by data.

The method effectively handles large datasets with many uncertain parameters.

Improved parameter estimation accuracy demonstrated on real-world bridge data.

Abstract

The decreasing cost and improved sensor and monitoring system technology (e.g. fiber optics and strain gauges) have led to more measurements in close proximity to each other. When using such spatially dense measurement data in Bayesian system identification strategies, the correlation in the model prediction error can become significant. The widely adopted assumption of uncorrelated Gaussian error may lead to inaccurate parameter estimation and overconfident predictions, which may lead to sub-optimal decisions. This paper addresses the challenges of performing Bayesian system identification for structures when large datasets are used, considering both spatial and temporal dependencies in the model uncertainty. We present an approach to efficiently evaluate the log-likelihood function, and we utilize nested sampling to compute the evidence for Bayesian model selection. The approach is first demonstrated on a synthetic case and then applied to a (measured) real-world steel bridge. The results show that the assumption of dependence in the model prediction uncertainties is decisively supported by the data. The proposed developments enable the use of large datasets and accounting for the dependency when performing Bayesian system identification, even when a relatively large number of uncertain parameters is inferred.