Structural Anomaly Detection with Probabilistic Distance Metric of Transmissibility Measurements

This chapter introduces two data-driven algorithms designed to rigorously account for variability in transmissibility functions by employing probabilistic distance metrics for structural anomaly detection. The first approach utilizes the symmetric Kullback–Leibler divergence between baseline and damaged-state transmissibility measurements, which are modeled as circularly symmetric complex Gaussian ratio random variables, to derive damage indices that remain effective under non-Gaussian uncertainties in TF estimates. To improve decision-making reliability under ambient vibration conditions, a Bayesian Monte Carlo hybrid thresholding technique is implemented. The second algorithm integrates agglomerative hierarchical clustering with multivariate probabilistic distances obtained via Laplace asymptotic expansions, thereby circumventing the need for high-dimensional integration while maintaining the correlation structure among transmissibility functions. An unsupervised clustering framework is facilitated through a bootstrapped Monte Carlo threshold, eliminating the requirement for predefined damage categories. Empirical validation through field studies demonstrates that these methodologies outperform deterministic approaches by systematically incorporating uncertainties inherent in transmissibility measurements. Collectively, these frameworks advance the vibration-based structural damage detection by leveraging probabilistic distance metrics and robust thresholding strategies.