A PC-kriging-HDMR Integrated with an Adaptive Sequential Sampling Strategy for High-Dimensional Approximate Modeling

High-dimensional complex multi-parameter problems are ubiquitous in engineering, as traditional surrogate models are limited to low/medium-dimensional problems (referred to p≤10 ). They are limited to the dimensional disaster that greatly reduce the modelling accuracy with the increase of design parameter space. Moreover, for the case of high nonlinearity, the coupling between design variables fail to be identified due to the lack of parameter decoupling mechanism. In order to improve the prediction accuracy of high-dimensional modeling and reduce the sample demand, this paper considered embedding the PCKriging surrogate model into the high-dimensional model representation framework of Cut- HDMR. Accordingly, a PC-Kriging-HDMR approximate modeling method based on the multi-stage adaptive sequential sampling strategy (including first-stage adaptive proportional sampling criterion and second stage central-based maximum entropy criterion) is proposed.