Integration Of Multivariate Functions By Orthogonal Arrays And Application

Integration of multivariate functions and global sensitivity analysis are very impor-tant concepts in theory, how to calculate the integration of multivariate functions and global sensitivity indices are also very important to solve engineering and theoretical problems. We are all concerned about how to obtain them effectively and quickly.In the first part of this paper, I presented how to compute the integration of multi-variate functions by orthogonal arrays based on ANOVA high-dimensional model repre-sentation. Especially, when the multivariate functions are very complicated or unknown but experimental data are known. By using SAS language and some examples are given to show the feasibility and effectiveness of replacing Monte Carlo (MC) or quasi-Monte Carlo (quasi-MC) simulation by design of experiment.Due to the calculation of global sensitivity indices are similar with the methodology of calculating the integration of functions, so in the next part of this paper, I presented how to compute the global sensitivity indices by orthogonal arrays when the form of the objective function f is known, I use DOE to estimate the global sensitivity indices instead of Monte Carlo simulation. The feasibility and effectiveness of the method are verified by given a classic example.