Local and Global Structural Health Monitoring via Stochastic Functional Time Series Methods: A Critical Assessment and Comparison

In the arena of structural health monitoring (SHM), ultrasonic guided wave-based and vibration-based damage detection and identification methods constitute two seemingly distinct approaches, oftentimes treated separately. Guided-waves-based methods are typically used for ``local'' damage diagnosis due to their increased sensitivity while vibration-based methods are based on the premise that damage has an impact on the global structural dynamic response, therefore are typically used for tackling ``global'' damage diagnosis. In this work, we present the comparison and critical assessment of the two state-of-the-art time-series-based methods, a local method based on guided waves and a global method based on structural vibrations, via a series of progressive damage analysis (PDA) numerical simulations and experiments on a composite unmanned aerial vehicle (UAV) wing structure. At first, a finite element model is established for progressive damage analysis on a composite plate fitted with piezoelectric sensors/actuators. Then, ultrasonic guided wave signals are generated and collected in a pitch-catch configuration as damage progression occurs while the low-frequency vibratory response and modal analysis results are also generated to allow the comparison of the local and global diagnostic methods. Next, both methods are implemented and assessed on a composite UAV wing structure, outfitted with accelerometers and piezoelectric sensors, to collect active-sensing pitch-catch ultrasonic and vibration response signals under different damage locations and magnitudes. The diagnostic methods presented are based on: (i) stochastic functional series time-varying autoregressive (FS-TAR) models to represent the ultrasonic guided wave propagation and enable the subsequent FS-TAR model-based local damage detection and identification tasks, and (ii) functionally pooled autoregressive models with exogenous excitation (FP-ARX) models to enable the vibration-based global damage diagnosis. It is shown that by incorporating a local guided wave-based damage diagnosis scheme within the global vibration-based damage detection and identification framework, both the sensitivity and robustness for detecting and identifying (localizing and quantifying) minor damage can be significantly increased.