Support Vector Machines Approach to Conditional Simulation of Non-Gaussian Stochastic Process

Abstract

The problem of conditional simulation of non-Gaussian stochastic processes and fields has gained a significant interest recently because of its applications in many fields, such as wind engineering, ocean engineering, and soil engineering. In this paper, the support vector machines (SVM) approach is developed for the conditional simulation of non-Gaussian stochastic processes and fields. To show the advantages of the presented method, the conditional simulation of non-Gaussian fluctuating wind pressures is carried out by using SVM and artificial neural networks (ANN). SVM considers three kinds of kernel function, such as linear function, Gaussian radial basis function, and exponential radial basis function, whereas ANN employs back-propagation and generalized regression. In machine learning of these artificial intelligences, two ways (interpolation and extrapolation) are employed to train finite non-Gaussian samples. The feasibility and validity of these algorithms are evaluated through the correlation coefficients, root mean square errors, skewness errors, and kurtosis errors between simulated samples and target samples and probability density functions (PDF), power spectral density (PSD) functions, and autocorrelation functions (ACF) of the simulated non-Gaussian fluctuating wind pressures versus their corresponding targets. The results show that the accuracy and effectiveness of SVM with an appropriate kernel function are superior to the back-propagation neural network (BPNN) and generalized regression neural network (GRNN). Furthermore, the advantage of the presented SVM approach is very obvious when the trained non-Gaussian samples are few.