A functional series time-dependent framework for non-stationary modeling and statistical damage diagnosis via ultrasonic guided waves

This study presents a novel statistical structural damage diagnosis framework using ultrasonic guided wave signals. The approach employs functional series time-dependent autoregressive (FS-TAR) models to capture the non-stationary dynamics of guided wave propagation. Unlike traditional methods that analyze only initial wave packets, this framework utilizes complete guided wave signals, including reflected waves, providing a comprehensive assessment of structural state. The FS-TAR model represents time-varying parameters through deterministic evolution using orthogonal basis functions. Three basis function families, namely, wavelet, Chebyshev, and trigonometric, have been evaluated to determine optimal signal representation. The covariance structure of the estimated time-invariant coefficients of projection vector and time-varying model parameters is extensively investigated, and their role in damage diagnosis is assessed. Two complementary damage diagnosis approaches are developed: one based on time-invariant projection coefficients and another using time-dependent model parameters. Both approaches employ statistical hypothesis testing with established confidence bounds derived from the asymptotic properties of the parameter estimators. Experimental validation is conducted on an aluminum plate under various damage scenarios, including both damage-intersecting and non-intersecting wave propagation paths. Results demonstrate accurate and robust damage detection and classification across all tested states. The wavelet basis functions show superior performance, providing the clearest parameter separation between healthy and damaged states. Key advantages include (i) utilization of complete wave signals rather than isolated wave packets, (ii) response-only operation without requiring input measurements, (iii) established statistical framework with quantified uncertainties, and (iv) real-time applicability with minimal computational requirements.