🤖 AI Summary
To address the ill-posedness, low identifiability, and difficulty in quantifying uncertainty in mechanical parameter inversion under sparse structural health monitoring (SHM) data, this paper proposes a unified framework integrating Fisher information matrix (FIM) analysis with Bayesian inversion. The FIM quantitatively characterizes the coupled influence of sensor placement and loading paths on parameter identifiability, revealing practically unidentifiable regions and fundamental spatial resolution limits. This enables robust identification of distributed mechanical parameters—such as flexural stiffness—and full-probabilistic uncertainty quantification. The method is validated on real-world bridge measurement data from the Open Laboratory at Technische Universität Dresden, successfully reconstructing spatially varying stiffness distributions and delivering physically interpretable credible intervals. It is the first to quantify spatial heterogeneity of data-informed information content and experimental design boundaries. The framework provides both theoretical foundations and practical tools for optimal sensor deployment and reliability assessment in SHM diagnostics.
📝 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.