Physics-informed neural networks for friction-involved nonsmooth dynamics problems

Physics-informed neural networks for friction-involved nonsmooth dynamics problems

19 March 2024 | Zilin Li · Jinshuai Bai · Huajiang Ouyang · Saulo Martelli · Ming Tang · Yang Yang · Hongtao Wei · Pan Liu · Ronghan Wei · Yuantong Gu
This paper presents a new physics-informed neural network (PINN) approach for solving nonsmooth dynamic problems involving friction-induced vibration. The proposed framework integrates the theoretical formulations of nonsmooth multibody dynamics into the neural network training process, enabling more accurate simulation of nonsmooth dynamic behaviors and improving computational efficiency by eliminating the need for small time steps typically used in conventional time-stepping methods. Four PINN strategies were proposed: single PINN, dual PINN, advanced single PINN, and advanced dual PINN. Two typical dynamics problems with nonsmooth contact were simulated: a 1-dimensional stick-slip problem and a 2-dimensional problem involving separation-reattachment and stick-slip. Both single and dual PINN methods showed advantages in handling the 1-dimensional stick-slip problem, outperforming conventional methods in difficult friction models. In contrast, the advanced single and dual PINN methods provided better accuracy in simulating the 2-dimensional problem, even when conventional methods failed. Friction-induced vibration (FIV) is a self-excited vibration associated with various engineering issues, including squealing brakes, squeaky joints, and inaccurate robotic positioning. The dynamics of systems with friction are complex and nonlinear, with nonsmoothness manifestations such as direction-changing friction forces, stick-slip vibration, and separation-reattachment events. Research on FIV focuses on low-degree-of-freedom models and complex structures. The conventional approach for determining FIV involves tracking motion states, which is tedious and time-consuming. The proposed PINN approach offers a promising alternative for efficiently simulating nonsmooth dynamics involving friction.This paper presents a new physics-informed neural network (PINN) approach for solving nonsmooth dynamic problems involving friction-induced vibration. The proposed framework integrates the theoretical formulations of nonsmooth multibody dynamics into the neural network training process, enabling more accurate simulation of nonsmooth dynamic behaviors and improving computational efficiency by eliminating the need for small time steps typically used in conventional time-stepping methods. Four PINN strategies were proposed: single PINN, dual PINN, advanced single PINN, and advanced dual PINN. Two typical dynamics problems with nonsmooth contact were simulated: a 1-dimensional stick-slip problem and a 2-dimensional problem involving separation-reattachment and stick-slip. Both single and dual PINN methods showed advantages in handling the 1-dimensional stick-slip problem, outperforming conventional methods in difficult friction models. In contrast, the advanced single and dual PINN methods provided better accuracy in simulating the 2-dimensional problem, even when conventional methods failed. Friction-induced vibration (FIV) is a self-excited vibration associated with various engineering issues, including squealing brakes, squeaky joints, and inaccurate robotic positioning. The dynamics of systems with friction are complex and nonlinear, with nonsmoothness manifestations such as direction-changing friction forces, stick-slip vibration, and separation-reattachment events. Research on FIV focuses on low-degree-of-freedom models and complex structures. The conventional approach for determining FIV involves tracking motion states, which is tedious and time-consuming. The proposed PINN approach offers a promising alternative for efficiently simulating nonsmooth dynamics involving friction.
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