Polynomial Response Surface based on basis function selection by multitask optimization and ensemble modeling

Abstract

Polynomial Regression Surface (PRS) is a commonly used surrogate model for its simplicity, good interpretability, and computational efficiency. The performance of PRS is largely dependent on its basis functions. With limited samples, how to correctly select basis functions remains a challenging problem. To improve prediction accuracy, a PRS modeling approach based on multitask optimization and ensemble modeling (PRS-MOEM) is proposed for rational basis function selection with robustness. First, the training set is partitioned into multiple subsets by the cross validation method, and for each subset a sub-model is independently constructed by optimization. To effectively solve these multiple optimization tasks, an improved evolutionary algorithm with transfer migration is developed, which can enhance the optimization efficiency and robustness by useful information exchange between these similar optimization tasks. Second, a novel ensemble method is proposed to integrate the multiple sub-models into the final model. The significance of each basis function is scored according to the error estimation of the sub-models and the occurrence frequency of the basis functions in all the sub-models. Then the basis functions are ranked and selected based on the bias-corrected Akaike’s information criterion. PRS-MOEM can effectively mitigate the negative influence from the sub-models with large prediction error, and alleviate the uncertain impact resulting from the randomness of training subsets. Thus the basis function selection accuracy and robustness can be enhanced. Seven numerical examples and an engineering problem are utilized to test and verify the effectiveness of PRS-MOEM.

Vertical accuracy evaluation free access digital elevation models (DEMs): case Fergana Valley in Uzbekistan

“…To improve its accuracy parametric models (or a corrective surface) introduced when refining heights (Fotopoulos et al, 2003). Such models include high-order polynomials with interpolation with different basis functions (Zhao et al, 2022), least squares collocation (Lyszkowicz et al, 2014), finite element method (Zaletnyik et al, 2007), Fourier series (Grigoriadis et.al., 2021), and artificial neural networks (Konakoglu & Akar, 2021). Interpolation methods (such as inverse distance weighting, bilinear interpolation, polynomial regression, triangulation, radial basis functions and nearest-neighbor interpolation) were considering according the application area, surface features, distribution of data and their accuracy.…”

MTHSA-DHEI: multitasking harmony search algorithm for detecting high-order SNP epistatic interactions

“…Gao et al designed a transfer strategy based on the multidirectional prediction method to improve the performance of the multiobjective multitasking optimization approach [48]. Zhao et al proposed a polynomial regression surface modelling approach based on multitasking optimization for rational basis function selection [49]. EMO can efficiently address multiple different optimization problems simultaneously, enhance the global search ability and improve the performance of each task via knowledge transfer between tasks [48].…”

Data science assisted cohesive finite element modelling of impact behaviour of AP‐HTPB crystal binder composite

“…This allows the creation of a local approximate relationship between input and output factors in a response surface methodology (RSM), defined by Box et al [ 21 ] RSM is used to find a regression model that fits the given data. [ 22 ] Such response surfaces have been used in mechanics to model, predict and optimise structural responses in many systems. For example, Olabi et al [ 23 ] used RSM to describe the residual stress distribution in welding, Safeen et al [ 24 ] used RSM to predict mechanical properties of an aluminium alloy, and Gallant et al [ 25 ] used RSM to quantify the contributions of individual ingredients on the burning rates of an energetic material.…”