Adaptive Radial-Basis-Function-Based Multifidelity Metamodeling for Expensive Black-Box Problems

摘要

The multifidelity metamodeling method provides an efficient way to approximate expensive black-box problems by using samples of different fidelities. Assisted by abundant cheap low-fidelity data, it can greatly improve the metamodeling efficiency by using relatively fewer expensive high-fidelity samples when compared with commonly used one-fidelity metamodeling methods. In this paper, a radial-basis-function-based multifidelity metamodeling method is proposed to approximate expensive black-box problems. This method has the following features: 1)it can be explicitly expressed almost in the simplest way; 2)it can be easily implemented through one-time matrix computation; and 3)it can be used to approximate black-box problems by samples with more than two fidelities. Besides, an adaptive sequential sampling method based on Voronoi partition and cross-validation is also developed to further improve the multifidelity metamodeling efficiency. To validate the proposed method, it is tested by several numerical benchmark problems and successfully applied in the optimal design of the drive axle in an all-direction propeller. Moreover, an overall comparison between the radial-basis-function-based multifidelity metamodeling method and several other metamodeling methods has been made. Results show that the proposed method is very efficient for metamodeling when using multifidelity samples, thus making it particularly suitable for engineering design problems involving computationally expensive simulations.