Neural network-aided simulation of non-Gaussian stochastic processes

Simulation of non-Gaussian stochastic processes is of paramount importance to dynamic reliability assessment of structures driven by non-Gaussian loads. In this paper, a novel translation model based on neural network is proposed to convert the target non-Gaussian power spectrum to the underlying Gaussian power spectrum for simulating non-Gaussian stochastic processes. First, a valid neural network model, whose structure is similar to the transformation from a non-Gaussian power spectrum to its underlying Gaussian power spectrum, is established. Then, starting with an initial underlying Gaussian power spectrum, the non-Gaussian power spectrum corresponding to the target non-Gaussian distribution is obtained through the Wiener-Khintchine transform and translation process. After that, the discrete data of non-Gaussian power spectrum is employed as the input layer in the neural network above, while the discrete data of Gaussian power spectrum serves as the output layer. With the trained neural network, the required underlying Gaussian power spectrum can be directly obtained by inputting the target non-Gaussian power spectrum. Finally, Gaussian samples can be generated by using the spectral representation method, which are then converted into non-Gaussian samples via the translation process. The effectiveness, accuracy, and applicability of the proposed method are demonstrated through two numerical examples.