Parameter identification in non-smooth gap systems with an improved spherical simplex-radial cubature quadrature kalman filter and strong tracking techniques

Abstract

Accurate parameter identification is critical for the effective modeling and control of dynamic systems, especially those exhibiting complex, nonlinear behaviors such as non-smooth gap systems. These systems, characterized by abrupt changes in dynamics due to physical constraints, discontinuities, or contact phenomena, pose significant challenges for traditional parameter identification methods, often resulting in inaccurate models and suboptimal system performance. To address these challenges, this study introduces the Strong Tracking Square Root Spherical Simplex-Radial Cubature Quadrature Kalman Filter (STSR-SSRCQKF), an advanced filtering algorithm designed to enhance parameter identification accuracy in non-smooth gap systems. The STSR-SSRCQKF provides several key benefits, including improved numerical stability through the adoption of QR decomposition, which avoids the need for positive-definite matrices, rapid adaptation to sudden system changes via strong tracking techniques, increased accuracy through a two-fold increase in sampling points, and computational simulations by utilizing acceleration data for alignment with commonly available measurements. The effectiveness of this method is validated on both 1-DoF and 5-DoF non-smooth systems. Through extensive simulations and comparisons under varying noise levels, large initial errors and limited measurement, the proposed approach demonstrates good performance. The capability of the STSR-SSRCQKF to accurately identify unknown switching points and ensure reliable state tracking in complex, non-smooth systems highlight its potential for broader applications in structural health monitoring, robotics, and dynamic system analysis.