Probabilistic SHM under varying loads via the integration of Gaussian Process Regression and physics-based guided-wave propagation models

In this work, a probabilistic Structural Health Monitoring (SHM) framework integrating physics-based and data-based models for active-sensing, guided-wave SHM under varying damage and loading states is proposed. Physics-based models from the family of load-compensation algorithms are used to generate/synthesize baseline signals under varying loads in order to assist Gaussian Process Regression Models (GPRMs) in the training and prediction processes for probabilistic damage detection and quantification. For one-dimensional GPRMs trained using damage index (DI) values under varying damage states and zero load, physics model-reconstructed baseline signals are used to compensate the load effects in incoming DI test points at known load states but unknown damage states. This facilitates the accurate prediction of damage size using one-dimensional GPRMs trained using only zero-load data sets, without the need for any additional training data sets under loaded states. Also, for the case of two-dimensional GPRMs, where data sets from both loaded and unloaded under varying damage states are needed for training, physics-based models are used to synthesize the required training data sets for different damage states under any load state missing within the experimental training data sets. Both of these approaches are applied to an experimental Al coupon under varying damage and load states, and the GPRM predictions are compared with those from fully-experimental data sets in the case of one- and two-dimensional GPRMs. It is shown that, for one-dimensional GPRMs, the physics-based model-compensated DI test points lead to better predictions if the compensated load was small (~5 kN in this study). For higher loads, the predictions lose accuracy, which is attributed to the insufficiency of the assumptions of the physics-based model in reconstructing baseline signals under the higher loads. For the two-dimensional case, the accuracy of simultaneous damage and load state prediction is shown to be relatively good using the GPRMs trained with mixed experimentally- and model-compensated DI points. The proposed probabilistic SHM framework allows for highly-versatile models that capture the advantages of physics- and data-based models for entertaining accurate and robust damage detection and quantification.