基于物理信息神经网络的时变可靠性分析方法

Time-dependent Reliability Analysis Based on Physics-Informed Neutral Network

传统时变可靠性分析(Time-dependent reliability analysis, TRA)往往通过大量实验设计样本(Design of experiments, DoE)构建代理模型,从而实现时变可靠性分析计算。在这个过程中,随着性能方程的非线性程度、响应求解难度等增加,Do E的计算成本愈发高昂,使得可靠性分析耗时冗长。针对该问题,创新性地提出了一种基于物理信息神经网络(Physics-informed neural network,PINN)的时变可靠性分析方法(PINN-based TRA, PBTRA)。该方法在TRA过程中将约束系统响应的偏微分方程(Partial differential equation, PDE)融入PINN模型训练的损失函数,使用PINN模型预测系统的实际响应,并基于此构建性能方程,解决了传统时变可靠性分析依赖大量仿真计算获取实验样本的难题,有效降低了TRA计算成本。同时针对传统PINN训练过程出现的收敛缓慢和模型欠拟合等问题,根据训练过程中PINN模型在不同采样区域的响应情况,判断相关区域是否接近系统响应的极限状态,并据此划分敏感区域,动态调整训练点采样分布,进一步结合神经网络的重采样机制,提出了一种基于区域响应权重的PINN模型动态采样训练方法,并且将其应用于TRA中。相较于传统的PINN,所提方法具有更快的训练速度与更高的性能响应计算精度,进而能够提升TRA精度与效率。文章中针对两个案例测试了所提出的PBTRA方法,并与传统TRA方法进行了对比,验证了所提出方法的优越性。

Traditional time-dependent reliability analysis(TRA)often constructs a surrogate model through a large number of design of experiments(DoE)samples,thereby achieving the calculation of time-dependent reliability analysis.As the nonlinearity of the performance function and the difficulty of response solution increase,the calculation cost of DoE becomes increasingly expensive,making the reliability analysis time-consuming and cumbersome.To address this problem,a time-dependent reliability analysis method based on physics-informed neural network(PINN-Based TRA,PBTRA)is proposed in this paper.This method incorporates the partial differential equation that constrains the system response into the loss function of the PINN training process,which uses the PINN model to predict the system's response.Based on the PINN model,the system performance function is constructed to preform TRA,which can solve the problem that traditional TRA relies on a large number of simulation calculations to obtain DoE samples,effectively reducing the calculation cost.At the same time,for the problems of slow convergence and underfitting that occur in the traditional PINN training process,the proposed method judges whether the relevant region is close to the limit state of the system response according to the response of the PINN model in different sampling regions during the training process and divide the sensitive regions accordingly.The distribution of training point sampling is dynamically adjusted,and combined with the resampling method of neural network,a dynamic sampling training method based on regional reaction weight function that suitable for PINN model is proposed and applied to TRA.Compared with traditional PINN,this method has faster training speed and higher accuracy of performance response calculation,which can improve the accuracy and efficiency of TRA.Two cases are analyzed by PBTRA and compared with traditional TRA methods to verify the superiority of the method proposed in this paper.