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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Acknowledgements
The author would like to thank the anonymous reviewers and the editors for carefully reading the paper and for making useful comments and suggestions that improved the appearance of the paper. This work was supported by the National Supercomputing Center in Zhengzhou. The authors acknowledge HEXAGON MSC CRADLE for the CFD solver licenses provided. The authors also want to acknowledge Mr.Bruno Demory and Dr.Manuel Henner of Valeo Thermal Systems for the inspiring talks during coffee breaks.
Funding
This work was financed by the National Natural Science Foundation of China [Grant number 12272354 and 52375270], and the Natural Science Foundation of Henan (Grant number 222300420547).
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All authors contributed to the study conception and design. Conceptualization and resources were provided by Z.Z.. Methodology was proposed by Z.Z. and S.J.. Funding acquisition was provided by Z.Z. and Y.L.. Data collection, analysis and validation were performed by S.J.. The first draft of the manuscript was written by Z.Z. and S.J. and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Zhang, Z., Jing, S., Li, Y. et al. Corner error reduction by Chebyshev transformed orthogonal grid. Engineering with Computers 40, 3717–3734 (2024). https://doi.org/10.1007/s00366-024-01991-3
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DOI: https://doi.org/10.1007/s00366-024-01991-3