An evolutionary hybrid approach to identify multibody systems with partially known physics

Abstract

Although the recent development of sensing techniques and machine learning approaches have contributed to the motion prediction and simulation of dynamical systems, the cost of data acquisition is still prohibitive. There also are critical locations of mechanisms inaccessible for instrumentation [1]. Subsequently, one is encountered with partial information from a physical identity, resulting in inaccurate training of neural networks. In addition, a feasible challenge in working with multibody systems is that one knows the physics of a given system partially due to associated complexity and nonlinearity, and lack of information. Linking the known physics to data-driven models to compensate for unknown physics can be helpful such that physical equations guide the training towards the right solution quickly by confining the space of admissible solutions, reducing discrepancies between a fully known physics and an incompletely known one [1, 2]. This approach improves predictions and mitigates the training issue of neural networks with limited data [3]. However, this hybrid method of physics-based simulation and deep neural network can result in a black-box function for the unknowns in multibody systems, which are not physically interpretable and generalizable. Combining statistical learning concepts with classical approaches in applied mechanics and mathematics, Schmidt and Lipson [4] used the genetic algorithm to distill motion equations from experimental data, which are interpretable. Brunton et al. also developed a popular approach for the model discovery of dynamical systems, the so-called SINDy [5]. As the latter is limited to a function dictionary built by a user, Askari and Crevecoeur suggested an evolutionarily symbolic regression method to generate an adaptive function dictionary [6]. In this study, we intend to extend the algorithm in [6] and develop an evolutionary hybrid procedure of physics-based modeling and symbolic regression procedure for the model discovery of an unknown subsystem of a multibody mechanism, Fig. 1. The governing equations of the subsystem can be identified in an interpretable fashion. The applications of this strategy encompass digital twins, system identification, control, and condition monitoring.