Probabilistic State Estimation Under Varying Loading States via the Integration of Time-Varying Autoregressive and Gaussian Process Models

In this work, probabilistic damage quantification under varying loading conditions in a non-stationary, guided-wave environment is being tackled via the synergistic integration between Time-varying Autoregressive (TAR) models and Gaussian Process regression models (GPRMs). Applying these TAR-GPRMs onto an aluminum coupon with simulated damage under different loading conditions fitted with piezoelectric sensors/actuators, the TAR models show the capability of capturing the non-stationarity in the ultrasonic guided-wave signals generated by the actuators under varying plate-loading conditions. They also provide insights to the maintainer by showing when in time the guided-wave time series deviate the most. In order to take advantage of that, a time instant selection algorithm was developed to allow flexibility in choosing the time instant(s) at which probabilistic damage quantification should be done. Finally, this quantification task is tackled by GPRMs, in which multiple GPRMs are trained using the TAR model parameters under varying conditions, and then used to predict damage size and/or loading state. While this framework is much more powerful in terms of tapping into the dynamics of how guided-waves change with varying conditions compared to simpler forms of GPRMs (such as damage index-trained GPRMs), training of TAR-GPRMs is far more complex. The advantages and challenges associated with the proposed TAR-GPRM approach is presented herein along with potential open areas for research in this regard.