Sensor Informativeness, Identifiability, and Uncertainty in Bayesian Inverse Problems for Structural Health Monitoring

TL;DR

This paper introduces a Bayesian inverse problem framework for Structural Health Monitoring that quantifies sensor informativeness, parameter identifiability, and uncertainty, demonstrated through a case study on a research bridge.

Contribution

It presents a novel Bayesian approach that unifies parameter identification with uncertainty quantification, enabling optimal sensor placement and more reliable SHM diagnostics.

Findings

Sensor layouts significantly influence the spatial resolution of parameter recovery.

The Bayesian framework identifies regions of non-identifiability in the parameter field.

Data from controlled vehicle passages provide high information content for the target parameters.

Abstract

In Structural Health Monitoring (SHM), the recovery of distributed mechanical parameters from sparse data is often ill-posed, raising critical questions about identifiability and the reliability of inferred states. While deterministic regularization methods such as Tikhonov stabilise the inversion, they provide little insight into the spatial limits of resolution or the inherent uncertainty of the solution. This paper presents a Bayesian inverse framework that rigorously quantifies these limits, using the identification of distributed flexural rigidity from rotation (tilt) influence lines as a primary case study. Fisher information is employed as a diagnostic metric to quantify sensor informativeness, revealing how specific sensor layouts and load paths constrain the recoverable spatial features of the parameter field. The methodology is applied to the full-scale openLAB research bridge (TU Dresden) using data from controlled vehicle passages. Beyond estimating the flexural rigidity profile, the Bayesian formulation produces credible intervals that expose regions of practical non-identifiability, which deterministic methods may obscure. The results demonstrate that while the measurement data carry high information content for the target parameters, their utility is spatially heterogeneous and strictly bounded by the experiment design. The proposed framework unifies identification with uncertainty quantification, providing a rigorous basis for optimising sensor placement and interpreting the credibility of SHM diagnostics.