Statistics knowledge-informed deep learning for simulation of univariate non-Gaussian wind pressure

To evaluate reliability performance and fatigue damage of building envelope components under winds, a stochastic simulation methodology is needed to efficiently and accurately generate a large number of sample functions of non-Gaussian wind pressure process with prescribed spectral and probabilistic features. While the translation process theory-based simulation models have been widely used for the non-Gaussian signal synthesis purpose, their accuracy is essentially limited by the incompatibility issue associated with a narrow-banded power spectral density (PSD) and/or a highly-skewed probability density function (PDF). Importantly, the convergence of these two-step learning methods (i.e., sequentially matching target PDF and PSD) to prescribed spectral and probabilistic contents is time consuming and not necessarily guaranteed. Motivated by the powerful multi-objective learning capability of neural networks, this study proposes to leverage deep learning methodology to generate non-Gaussian wind pressure time series. This one-step learning method (i.e., simultaneously matching both PDF and PSD) is expected to provide high simulation accuracy by integrating statistics knowledge (i.e., both spectral and probabilistic contents) into loss function consideration. To facilitate the learning process of the proposed statistics knowledge-informed deep neural network (SKI-DNN), an auto-regressive (AR) model is employed to generate underlying Gaussian process of target wind pressure as its input. Numerical examples demonstrate that the developed AR/SKI-DNN model can efficiently generate sample functions of non-Gaussian wind pressure process while accurately preserving both spectral and probabilistic contents.