Hybrid physics-based and machine learning model with interpretability and uncertainty for real-time estimation of unmeasurable parts

Physics-based models are used to estimate the behavior of dynamic systems. However, these models contain uncertainties, i.e., "parameter uncertainty"and "structural uncertainty,"which cause the gap between real phenomena and physics-based models (reality gap). Kaneko et al., (2022) proposed a hybrid physics-based and machine learning model for the real-time estimation of unmeasurable parts and demonstrated the high performance for the "parameter uncertainty."This study verifies the hybrid model performance for the "structural uncertainty."Additionally, two new concepts are discussed, interpretability and uncertainty, and implemented in the hybrid model.The hybrid model performance for the structural uncertainty is examined by numerical experiments and application to measured data using a deep-water offshore drilling system as an application case study. The results show that the hybrid model gives robust estimation for the structural uncertainty. Additionally, the hybrid model accuracy increases as the physics-based model accuracy used for training increases. Furthermore, several seconds of future data could improve the model performance for the transient response. Finally, we show that two new outputs could effectively explain the reality gap; the model outputs the estimation of the uncertain parameter to give interpretability within the parameter uncertainty and the structural uncertainty metric outside the parameter uncertainty.