An approach to Bayesian optimization for design feasibility check on discontinuous black-box functions

Arpan Biswas, Christopher Hoyle

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

The paper presents a novel approach to applying Bayesian Optimization (BO) in predicting an unknown constraint boundary, also representing the discontinuity of an unknown function, for a feasibility check on the design space, thereby representing a classification tool to discern between a feasible and infeasible region. Bayesian optimization is a low-cost black-box global optimization tool in the Sequential Design Methods where one learns and updates knowledge from prior evaluated designs, and proceeds to the selection of new designs for future evaluation. However, BO is best suited to problems with the assumption of a continuous objective function and does not guarantee true convergence when having a discontinuous design space. This is because of the insufficient knowledge of the BO about the nature of the discontinuity of the unknown true function. In this paper, we have proposed to predict the location of the discontinuity using a BO algorithm on an artificially projected continuous design space from the original discontinuous design space. The proposed approach has been implemented in a thin tube design with the risk of creep-fatigue failure under constant loading of temperature and pressure. The stated risk depends on the location of the designs in terms of safe and unsafe regions, where the discontinuities lie at the transition between those regions; therefore, the discontinuity has also been treated as an unknown creep-fatigue failure constraint. The proposed BO algorithm has been trained to maximize sampling toward the unknown transition region, to act as a high accuracy classifier between safe and unsafe designs with minimal training cost. The converged solution has been validated for different design parameters with classification error rate and function evaluations at an average of <1% and ∼150, respectively. Finally, the performance of our proposed approach in terms of training cost and classification accuracy of thin tube design is shown to be better than the existing machine learning (ML) algorithms such as Support Vector Machine (SVM), Random Forest (RF), and Boosting.

Original languageEnglish
Article number031716
JournalJournal of Mechanical Design
Volume143
Issue number3
DOIs
StatePublished - Mar 2021
Externally publishedYes

Funding

This research was funded in part by DOE NEUP DE-NE0008533. The opinions, findings, conclusions, and recommendations expressed are those of the authors and do not necessarily reflect the views of the sponsor.

FundersFunder number
U.S. Department of EnergyDE-NE0008533

    Keywords

    • Bayesian optimization
    • Design classification problem
    • Design space discontinuity
    • Metamodeling
    • Strain in design
    • Stress

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