Physically Consistent Modeling & Identification of Nonlinear Friction with Dissipative Gaussian Processes

Abstract

Friction modeling has always been a challenging problem due to the complexity of real physical systems. Although a few state-of-the-art structured data-driven methods show their efficiency in nonlinear system modeling, deterministic passivity as one of the significant characteristics of friction is rarely considered in these methods. To address this issue, we propose a Gaussian Process based model that preserves the inherent structural properties such as passivity. A matrix-vector physical structure is considered in our approaches to ensure physical consistency, in particular, enabling a guarantee of positive semi-definiteness of the damping matrix. An aircraft benchmark simulation is employed to demonstrate the efficacy of our methodology. Estimation accuracy and data efficiency are increased substantially by considering and enforcing more structured physical knowledge. Also, the fulfillment of the dissipative nature of the aerodynamics is validated numerically.