An Adaptive Dendrite-HDMR Metamodeling Technique for High-Dimensional Problems

Abstract

High-dimensional model representation (HDMR), decomposing the high-dimensional problem into summands of different order component terms, has been widely researched to work out the dilemma of “curse-of-dimensionality” when using surrogate techniques to approximate high-dimensional problems in engineering design. However, the available one-metamodel-based HDMRs usually encounter the predicament of prediction uncertainty, while current multi-metamodels-based HDMRs cannot provide simple explicit expressions for black-box problems, and have high computational complexity in terms of constructing the model by the explored points and predicting the responses of unobserved locations. Therefore, aimed at such problems, a new stand-alone HDMR metamodeling technique, termed as Dendrite-HDMR, is proposed in this study based on the hierarchical Cut-HDMR and the white-box machine learning algorithm, Dendrite Net. The proposed Dendrite-HDMR not only provides succinct and explicit expressions in the form of Taylor expansion but also has relatively higher accuracy and stronger stability for most mathematical functions than other classical HDMRs with the assistance of the proposed adaptive sampling strategy, named KKMC, in which k-means clustering algorithm, k-Nearest Neighbor classification algorithm and the maximum curvature information of the provided expression are utilized to sample new points to refine the model. Finally, the Dendrite-HDMR technique is applied to solve the design optimization problem of the solid launch vehicle propulsion system with the purpose of improving the impulse-weight ratio, which represents the design level of the propulsion system.