From Initial to Final State: Single Step Prediction of Structural Dynamic Response

Accurately predicting the structural response under dynamic loads is of great importance to evaluate the structure's performance, monitor the structure's health and control the vibration. The development of a real-time prediction method is challenging because the model must have a low computational burden and high running speed. Due to the computing convergence requirements and complexity constraints, traditional numerical methods such as the finite element method and the finite difference method must take thousands to millions of short-time steps to calculate the final structural dynamic response we really want. After costing a lot of computing resources and time, these internal steps are worthless but significantly reduced the efficiency of numerical methods. To tackle this problem, in this paper, we propose a single-step method named physics-informed implicit Runge-Kutta (PI-IRK) to predict the structure dynamic response straightly from the initial to the final state. Specifically, we fuse discrete-time physics-informed neural networks (PINNs) and implicit Runge-Kutta method with low-expense hide stages. In the proposed method, deep neural network models are employed as the core to predict the Runge-Kutta stages and the final state. We integrate physics information such as implicit Runge-Kutta form of structure vibration governing equation and boundary constraints as the prior information into the neural networks model. With the assistance of the prior information, the proposed PI-IRK model is an unsupervised learning model that can be trained without any measurement data. Without any internal steps, the PI-IRK model can straightly predict the final structural dynamic response after training. The accuracy of the proposed method is demonstrated by predicting the structural response of a cantilever beam under a distributed dynamic load even with a large time step.