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 PC-Kriging 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. This method makes full use of the high precision of PC-Kriging and optimizes the layout of test points to improve the modeling efficiency. Numerical tests and a cantilever beam practical application are showed that: (1) The performance of the traditional single-surrogate model represented by Kriging in high-dimensional nonlinear problems is obviously much worser than that of the combined- surrogate model under the framework of Cut-HMDR (mainly including Kriging-HDMR, PCE-HDMR, SVR-HDMR, MLS-HDMR and PC-Kriging-HDMR);(2)The number of samples for PC-Kriging-HDMR modeling increases polynomially rather than exponentially with the expansion of the parameter space, which greatly reduces the computational cost;(3)None of the existing Cut-HDMR can be superior to any in all aspects. Compared with PCEHDMR and Kriging-HDMR, PC-Kriging-HDMR has improved the modeling accuracy and efficiency within the expected improvement range, and also has strong robustness.