A parameter identification method for continuous-time nonlinear systems and its realization on a Miura-origami structure

Abstract

Abstract Many mechanical systems are nonlinear and often high-dimensional. Constructing accurate models for continuous-time nonlinear systems calls for effectively identifying their parameters, whereas measurement noise and sensitivity to initial conditions make the identification challenging. This paper proposes a new parameter identification method for ordinary differential equations based on the idea of B-Spline Galerkin finite element. In this approach, the system’s solution is globally constructed by a set of B-Splines. With Galerkin weak formulation, instead of taking analytical derivatives on basis functions, the differential terms are eliminated through integration by parts so that the measurement noise will not be amplified. Then least square algorithms can be adopted for solving the optimization problem to estimate the parameters. By solving two intractable testbed problems, the coupled Chua’s circuits and the Tank reactor equations, we show that the new approach is effective and efficient in dealing with systems with high-dimensionality, complex nonlinearity, discontinuous input and output, and noisy data without specific pre-processing. In addition, this method is employed to identify the geometrical and mechanical parameters of a Miura-origami structure under base excitation, which possesses complex global nonlinearity, exhibits chaotic responses, and suffers from significant measurement noise. The proposed method gains success in dealing with this system; based on the identified parameters, the corresponding constituent force-displacement relation and the simulation results agree well with the experiments.