A new sequential sampling method for constructing the high-order polynomial surrogate models

Abstract

Purpose This paper aims to study the sampling methods (or design of experiments) which have a large influence on the performance of the surrogate model. To improve the adaptability of modelling, a new sequential sampling method termed as sequential Chebyshev sampling method (SCSM) is proposed in this study. Design/methodology/approach The high-order polynomials are used to construct the global surrogated model, which retains the advantages of the traditional low-order polynomial models while overcoming their disadvantage in accuracy. First, the zeros of Chebyshev polynomials with the highest allowable order will be used as sampling candidates to improve the stability and accuracy of the high-order polynomial model. In the second step, some initial sampling points will be selected from the candidates by using a coordinate alternation algorithm, which keeps the initial sampling set uniformly distributed. Third, a fast sequential sampling scheme based on the space-filling principle is developed to collect more samples from the candidates, and the order of polynomial model is also updated in this procedure. The final surrogate model will be determined as the polynomial that has the largest adjusted R-square after the sequential sampling is terminated. Findings The SCSM has better performance in efficiency, accuracy and stability compared with several popular sequential sampling methods, e.g. LOLA-Voronoi algorithm and global Monte Carlo method from the SED toolbox, and the Halton sequence. Originality/value The SCSM has good performance in building the high-order surrogate model, including the high stability and accuracy, which may save a large amount of cost in solving complicated engineering design or optimisation problems.

Dynamic Response of Dual-Disk Rotor System with Uncertainties Based on Chebyshev Convex Method

“…Compared with perturbation technique or Taylor expansion, it is not limited by small uncertainty. The overestimation caused by the wrapping effect is also controlled effectively [30]. Chebyshev expansion function is an approximate proxy model.…”

A Novel Sparse Polynomial Expansion Method for Interval and Random Response Analysis of Uncertain Vibro‐Acoustic System

“…is section presents the sparse grids' sequential sampling scheme to calculate the coefficient of the IRMAPC expansion. In the proposed sequential sampling scheme, the integration points of sparse grids' Shock and Vibration quadrature [46][47][48] are used as the candidates of the sampling method, while the sequential sampling scheme, used in [49], is used to select the sampling points from the candidates. A new method called the SGS-IRAPC method is proposed based on the developed sequential sampling scheme.…”

“…In order to improve the precision of the IRMAPC expansion method, a simple format is adopted in the IRMAPC expansion method to reduce the number of the expansion coefficients [49,50]. Equation ( 3) can be rewritten as…”

Uncertainty-based design optimization of NLF airfoil for high altitude long endurance unmanned air vehicles

“…For multi-dimensional uncertainty input, especially for high-order polynomial approximation in complex engineering design, many studies including efficient sampling strategies have been widely performed (Zhao et al , 2018b) to improve the UQ estimate accuracy and efficiency of high-dimensional and high-order PCE, e.g. Latin Hypercube sampling, coherence motivated sampling and Chebyshev tensor product sampling (Wu et al , 2018, 2016), etc. This paper uses Monte Carlo (MC) sampling method to obtain a specified number of samples according to given PDF.…”