Reliability assessment of stochastic dynamical systems using physics informed neural network based PDEM
提出一种基于物理信息神经网络的概率密度演化法，用于高效求解广义密度演化方程，并通过三个数值算例验证了该方法在随机动力系统可靠性评估中的准确性和计算效率。
In the recent decade, the reliability analysis of a stochastic system coupled with the uncertainty related to the system’s parameter has attracted much attention. Probability density evolution method (PDEM) is one of the viable options that estimates the probability density function of the structural response by solving generalized density evolution equations (GDEEs). The advantage of PDEM is that it is derived based on the principle of probability conservation, where GDEEs are decoupled from the physical system. In general, GDEEs in PDEM are solved using a finite difference scheme in which the accuracy of the numerical solution depends on the number of temporal and spatial discretizations , leading to computationally inefficient for high-fidelity models. With this in view, this study proposes a physics-informed neural network (PINN), a novel deep learning method, based PDEM, for solving the GDEEs. PINN utilizes physical information in the form of differential equations to enhance the performance of the neural networks. This method does not need any interpolation or coordinate transformation, which is often seen in any numerical scheme , thus the computational budget is reduced. Three numerical examples are presented in this study to illustrate the proposed PINN-based PDEM, including a Van-der-Pol oscillator subjected to Gaussian white noise, a one-storey moment resisting frame coupled with a nonlinear energy sink with negative stiffness and sliding friction , and a high-rise timber building coupled with shape memory alloy-based outriggers . The first example is utilized to show the accuracy of the proposed method by comparing results with the Fokker–Planck–Kolmogorov equation and Monte Carlo simulation . The rest two examples are investigated for estimating time-dependent probability of failure. Numerical results show that the proposed PINN-based PDEM can estimate the probability of failure efficiently.