Improved Hybrid Response Surface Method Based on Double Weighted Regression and Vector Projection

Abstract

In order to increase the accuracy and stability of the classical response surface method and relevant method, a new improved response surface method based on the idea of double weighting factors and vector projection method is proposed. The response surface is fitted by the weighted regression technique, which allows the sampling points to be weighted by their distance from the true failure surface and that from the estimated design point. It uses the vector of the gradient projection method to get new sampling points in the process of iteration, in order to make the sampling points closer to the design point, and the value of deviation coefficient is constantly adjusted. To some extent, these strategies increase the accuracy and stability of the response surface method, while the calculation time is decreased. At last, the rationality and efficiency of the proposed method are demonstrated through five examples. Besides, as revealed from this investigation, compared with other conventional algorithms, this method has a few obvious advantages; this algorithm not only has high precision and efficiency, but also has solid stability.

Optimization of G1 Micromixer Structure in Two-Fluid Mixing Based on CFD and Response Surface Methodology

“…The core of the RSM is to seek the best fit of an equation or expressions for the optimization objectives based on the experimental or simulation data. It enables statistical predictions to reduce the simulation time [22][23][24]. With its short cycle and high precision, RSM can fully capture the interactions between multiple factors.…”

Propagation algorithm for hybrid uncertainty parameters based on polynomial chaos expansion

“…39 As the core of constructing the PCE model, the methods to obtain the PCE coefficients are the Galerkin projection method and the stochastic response surface method (regression method). [40][41][42] However, inevitably, as the dimensionality of the uncertain parameters of the system and the accuracy of the solution increase, the number of orders required for the PCE model will become higher so that the computational cost of both methods increases (i.e., dimensional curse). To overcome this drawback, some methods have been proposed to filter and discard terms in the Galerkin projection that have less impact on the results, for example, the adaptive method, 43 the sparse grid numerical integration method (SGNIM).…”

“…As research progressed, a PCE based on Askey's law was proposed to solve the uncertainty propagation problem for uncertain variables with various types of distributions 39 . As the core of constructing the PCE model, the methods to obtain the PCE coefficients are the Galerkin projection method and the stochastic response surface method (regression method) 40‐42 . However, inevitably, as the dimensionality of the uncertain parameters of the system and the accuracy of the solution increase, the number of orders required for the PCE model will become higher so that the computational cost of both methods increases (i.e., dimensional curse).…”

Improved Response Surface Method Based on Linear Gradient Iterative Criterion

“…Wei et al [16] proposed a modifed iterative response surface method (called NDIRSM) to improve the accuracy and efciency of structural reliability analysis. Based on the idea of double weight factor and vector projection method, Xia and Wang [17] proposed a new improved response surface method. However, these methods improve the accuracy while increasing the amount of calculation, and some improve the computational efciency but afect the accuracy.…”