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Multi-fidelity surrogates from shared principal components

Application to structural design exploration and optimization

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Abstract

Computational cost of high-fidelity simulations limits the number of evaluations which may be performed in design exploration and optimization. Surrogates based on samples of multiple fidelities are used to decrease computational cost and lower error from single-fidelity surrogates. This paper develops a novel multi-fidelity surrogate model based on principal components which are shared between multiple fidelities of finite element model samples. This method does not require a common grid between the fidelities, further reducing computational cost. The new method was tested on various design spaces of the Transonic Purdue Research Compressor and compared to other common and novel multi-fidelity methods. The new method was more accurate and required less computational cost than the other tested methods. Little to no increase in computational cost was needed to reduce surrogate error to 50% of the single-fidelity error. For fixed error, the computational cost was reduced by more than 75%. These results were also validated by testing the method on a more complex turbomachinery blade, Parametric Blade Study Rotor 4. The decreased error and computational cost improve effectiveness of design exploration and optimization. Such improvements help meet the demand for cleaner and safer engines by allowing high-fidelity design exploration within reasonable time frames.

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Authors and Affiliations

  1. Mechanical Engineering, Brigham Young University, Provo, UT, 84602, USA

    Spencer Bunnell, Steven Gorrell & John Salmon

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  1. Spencer Bunnell
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  2. Steven Gorrell
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  3. John Salmon
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Correspondence to Spencer Bunnell.

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Replication of results

The research code, developed in Python, to duplicate the SPC method with Space-Mapping as the secondary surrogate is given in the appendix. In order to replicate the other methods which were tested, the reader is directed to the cited publications in which those methods were developed and used. LF and HF FEA samples for the nine-dimensional design space are given as supplementary material. This data contains 35 HF samples and 1000 LF samples of the Purdue Blade. Replication of the error for this set may be performed from this data. Replication of the computational cost requires using CAD and FEA software to produce the samples. Differing software may produce different results, but should yield similar trends.

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Bunnell, S., Gorrell, S. & Salmon, J. Multi-fidelity surrogates from shared principal components. Struct Multidisc Optim 63, 2177–2190 (2021). https://doi.org/10.1007/s00158-020-02793-z

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  • DOI: https://doi.org/10.1007/s00158-020-02793-z

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