Novel Two-Stage Method for Low-Order Polynomial Model

Abstract

One of the most popular statistical models is a low-order polynomial response surface model, i.e., a polynomial of first order or second order. These polynomials can be used for global metamodels in weakly nonlinear simulation to approximate their global tendency and local metamodels in response surface methodology (RSM), which has been studied in various applications in engineering design and analysis. The order of the selected polynomial determines the number of sampling points (input combinations) and the resulting accuracy (validity, adequacy). This paper derives a novel method to obtain an accurate high-order polynomial while requiring fewer sampling points. This method uses a two-stage procedure such that the second stage modifies the low-order polynomial estimated in the first stage; this second stage does not require new points. This paper evaluates the performance of the method numerically by using several test functions. These numerical results show that the proposed method can provide more accurate predictions than the traditional method.

Ensemble of Regression-Type and Interpolation-Type Metamodels

“…As a result, a large number of metamodels have been proposed, of which several types have gained wide acceptance in various applications. They are polynomial response surface (PRS) [12][13][14], support vector regression (SVR) [15][16][17], radial basis functions (RBF) [18,19], extended radial basis functions (E-RBF) [20], moving least squares (MLS) [21], artificial neural networks (ANN) [22,23], multivariate adaptive regressive splines (MARS) [24] and Kriging (KRG) [25,26]. These different metamodels give us more options for different tasks.…”

Multidisciplinary Design Optimization for a Centrifugal Compressor Based on Proper Orthogonal Decomposition and an Adaptive Sampling Method

“…The results have proved that the methods have the potential to satisfy industrial design needs. The commonly used surrogate models in these studies include Kriging [7,8], radial basis function (RBF) [9], artificial neural networks (ANNs) [10], polynomial response surface (PRS) [11], and support vector regression (SVR) [12]. The accuracy of surrogate models has a great influence on optimization results and may lead to the failure of optimization.…”