Dynamic reliability analysis of stochastic structures under non-stationary random excitations based on an explicit time-domain method

For the analysis of the dynamic reliability of stochastic structures subjected to non-stationary random excitations, an effective hybrid approach is proposed. In this approach, the explicit time-domain method is employed to obtain the dynamic responses of each deterministic structure. Dynamic responses for the explicit time-domain method can be expressed as a series of products of deterministic coefficient matrices and random load vectors, which can significantly enhance computational efficiency. For the issue of stochastic structures, the double hidden-layer backpropagation neural network is introduced as a surrogate model for reconstructing the coefficient matrices to avoid repeated construction of the coefficient matrices for each sample with different structural parameters using the extremely time-intensive regular method. For more effective training of the back propagation neural network, the Latin hypercube sampling technique is introduced to generate representative samples of random structural parameters. In consideration of the intrinsic benefit of the explicit time-domain method, parallel computation is incorporated into the method. Finally, the explicit time-domain method is used to perform the Monte Carlo simulation in conjunction with the parallel computing technique to resolve the problem of small failure probabilities. To demonstrate the efficacy of the proposed method, numerical examples are presented.