Hybrid derivative functions for identification of unknown loads and physical parameters with application on slider-crank mechanism

Mechatronic systems are plagued by nonlinearities and contain uncertainties amongst others due to interactions with their environment. Having models of these systems that have accurate multistep predictive capabilities can be of value for control and decision making purposes. This paper proposes hybrid derivative functions that closely combine expert knowledge of the system, captured by ordinary differential equations, with data-driven feedforward neural networks. Euler's method is used to apprehend the system's multistep dynamics. The proposed formalism is dedicated to identifying unknown loads that are dependent on the state of the system together with the identification of physical parameter values. We apply the methodology on a slider-crank mechanism where synthetic data is used to investigate the feasibility and accuracy of the proposed approaches. Multiple numerical tests show that the network structure of the hybrid derivative function enables convergence and we show the ability to simultaneously uncover physical parameter values and explain unknown phenomena related to the unknown state dependent load. The latter suggest the possibility of discovering unknown loads without additional measurements. Further research should investigate the robustness of the presented approach