A Progressive Trigonometric Mixed Response Surface Method for Double-Loop Interval Optimization

Abstract

For some highly nonlinear problems, the general second-order response surface method (RSM) cannot satisfy the accuracy requirement. To improve accuracy, the highest order number has to be determined in advance. Thus, a progressive trigonometric mixed response surface method (PTMRSM) was proposed to enhance the approximation accuracy and define the highest order number, rather than determining it in advance. After that, a double-loop interval optimization process could be constructed using this PTMRSM to save time while maintaining accuracy when compared to other experimental or computational methods. Unfortunately, the traditional double-loop interval optimization method had issues with the probability of reliable constraints. Then, for the construction of this double-loop interval optimization process, the modified reliable constraints were introduced. A more reliable and effective double-loop interval optimization was introduced for addressing practical engineering problems using the effective approximate method of the PTMRSM and the amended reliable constraints. Two numerical test functions and a composite submersible hull were performed to verify the accuracy and effectiveness of the PTMRSM and the double-loop interval optimization.