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.

翻译：在结构健康监测中，从稀疏数据中恢复分布力学参数通常是不适定的，这引发了关于可识别性与推断状态可靠性的关键问题。虽然确定性正则化方法（如Tikhonov方法）能稳定反演过程，但它们对分辨率的空间限制或解的内在不确定性提供的信息有限。本文提出一种贝叶斯反演框架，以从旋转（倾斜）影响线识别分布抗弯刚度为主要案例，严格量化这些限制。采用Fisher信息作为诊断指标来量化传感器信息性，揭示特定传感器布局与荷载路径如何约束参数场可恢复的空间特征。该方法通过受控车辆通行数据应用于德累斯顿工业大学全尺寸openLAB研究桥梁。除估计抗弯刚度分布外，贝叶斯框架生成的置信区间能揭示实际不可识别区域，而确定性方法可能掩盖这些区域。结果表明，虽然测量数据对目标参数具有高信息量，但其效用存在空间异质性，且严格受实验设计限制。所提框架将识别与不确定性量化相统一，为优化传感器布设及解释结构健康监测诊断的可信度提供了严谨基础。