High dimensional model representation (HDMR) coupled intelligent sampling strategy for nonlinear problems Original Research Article

High-dimensional model representation (HDMR) is a general set of metamodel assessment and analysis tools to improve the efficiency of high dimensional underlying system behavior. Compared with the current popular modeling methods, such as Kriging (KG), radial basis function (RBF), and the moving least square approximation method (MLS), the distinctive characteristic of the HDMR is to decouple the input variables. Therefore, a high dimensional problem can be transformed as a low, middle or combination of middle dimensional function. Although the HDMR is a feasible method for high dimensional problems, the computational cost is still a bottleneck for complex engineering problems. To improve the efficiency of the HDMR method further, the purpose of this study is to use an intelligent sampling method for the HDMR. Because the HDMR cannot be integrated with the sampling method directly, a projection-based intelligent method is suggested. Compared with the popular HDMR methods, the construction procedure for the HDMR-based model is optimized. To validate the performance of the suggested method, multiple mathematical test functions are given to illustrate the modeling principles, procedures, and the efficiency and accuracy of HDMR models with problems of a wide scope of dimensionalities.