Data-driven Identification of Stochastic System Dynamics under Partial Observability Using Physics-Based Model Priors with Application to Acrobot

Accurate dynamical models form a main driver for high performance mechatronic applications. Conventional modeling of mechatronic systems is often limited in its ability to handle poorly understood phenomena and may not be adequate in instances where the underlying dynamics are not fully known nor fully captured by sensory data. To overcome these limitations, we propose a physics-based data-driven state-space modeling approach. We phrase the problem as a probabilistic representation learning problem. The hybrid model combines known physical relations with parametrized functions, represented as neural networks, to serve as substitutes for the previously unidentified substructures. The identification problem is solved using the Expectation-Maximization (EM) algorithm. In the Expectation step, Bayesian smoothers are utilized to provide complete state estimates from partial observations. In the M-step, the hybrid model is fitted onto the smoothed data. Although the physics based prior model comes at the loss of expressiveness, it serves as a strong model prior. The use of a physical model prior is beneficial both to improve the accuracy of the inference during the E-step as well as to reduce the complexity of the M-step. The proposed methodology is applied and validated for the identification of friction in both joints of an acrobat, with only measurements available in one joint. Numerical experiments demonstrate the methods capability of identifying comprehensive representations of the friction characteristics in both joints and possessing accurate predictive abilities.