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14.05.2024 | Original Article

Corner error reduction by Chebyshev transformed orthogonal grid

verfasst von: Zebin Zhang, Shizhao Jing, Yaohui Li, Xianzong Meng

Erschienen in: Engineering with Computers | Ausgabe 6/2024

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Abstract

In the context of surrogate-based optimization, the efficient global exploration of the design space strongly relies on the overall accuracy of the surrogate model. For most modeling approaches, significant inaccuracies are often observed at the outlier region of the design space, where very few samples are spotted, known as the “corner error”. Inspired by the Runge effect originating from equidistant samples, a Chebyshev-transformed Orthogonal Latin Hypercube sampling approach is proposed to alleviate corner errors. An initial OLH sample was generated on a unit hyper-sphere, and its radial projection was used as the start of a sequential sampling process. The acquisition function uses the confidence interval of the Kriging predictor, combined with the min–max-distance criterion. To testify the proposed approach, models built with ordinary OLH grids are compared to the models built with Chebyshev-transformed OLH grids. Benchmark tests were performed on a series of multimodal functions, four 2-dimensional functions, and three 6-dimensional functions, both the root mean-squared error and the maximum error were reduced compared with the OLH design for most of the tests. This approach was applied to increase the pressure rise of the engine cooling fan without reducing the efficiency, for which 2.5% higher pressure rise was gained compared to the reference design.

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Metadaten
Titel
Corner error reduction by Chebyshev transformed orthogonal grid
verfasst von
Zebin Zhang
Shizhao Jing
Yaohui Li
Xianzong Meng
Publikationsdatum
14.05.2024
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 6/2024
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-024-01991-3