Abstract

Machine learning is gaining prominence in mechanical design, offering cost-effective surrogate models to replace computationally expensive models. Nevertheless, concerns persist regarding the accuracy of these models, especially when applied to safety-critical products. To address this challenge, this study investigates methods to account for model prediction errors by incorporating epistemic uncertainty within surrogate models while managing aleatory uncertainty in input variables. The paper clarifies key aspects of modeling coupled epistemic and aleatory uncertainty when using surrogate models derived from noise-free training data. Specifically, the study concentrates on quantifying the impacts of coupled uncertainty in mechanical design through the development of numerical methods based on the concept of the most probable point. This method is particularly relevant for mechanical component design, where failure prevention holds paramount importance, and the probability of failure is low. It is applicable to design problems characterized by probability distributions governing aleatory and epistemic uncertainties in model inputs and predictions. The proposed method is demonstrated using shaft and beam designs as two illustrative examples. The results demonstrate the method's effectiveness in quantifying and mitigating the influence of coupled uncertainty in the design process.

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