A progressive trigonometric mixed response surface method for double-loop interval optimization

• Main Authors: Zheng, Guanchao, Xu, Wen, Mohd Ariffin, Mohd Khairol Anuar, Abdul Aziz, Nuraini, Ahmad, Siti Azfanizam
• Format: Article
• Language: English
• Published: Multidisciplinary Digital Publishing Institute (MDPI) 2023
• Online Access: http://psasir.upm.edu.my/id/eprint/106655/1/106655.pdf; http://psasir.upm.edu.my/id/eprint/106655/; https://www.mdpi.com/2077-1312/11/7/1394
• Institution: Universiti Putra Malaysia

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.