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This work introduces a new design algorithm to optimize progressively folding thin-walled structures and in order to improve automotive crashworthiness. The proposed design algorithm is composed of three stages: conceptual thickness distribution, design parameterization, and multi-objective design optimization. The conceptual thickness distribution stage generates an innovative design using a novel one-iteration compliant mechanism approach that triggers progressive folding even on irregular structures under oblique impact. The design parameterization stage optimally segments the conceptual design into a reduced number of clusters using a machine learning K-means algorithm. Finally, the multi-objective design optimization stage finds non-dominated designs of maximum specific energy absorption and minimum peak crushing force.

A common scenario in engineering design is the evaluation of expensive black-box functions: simulation codes or physical experiments that require long evaluation times and/or significant resources, which results in lengthy and costly design cycles. In the last years, Bayesian optimization has emerged as an efficient alternative to solve expensive black-box function design problems. Bayesian optimization has two main components: a probabilistic surrogate model of the black-box function and an acquisition functions that drives the design process. Successful Bayesian optimization strategies are characterized by accurate surrogate models and well-balanced acquisition functions. The Gaussian process (GP) regression model is arguably the most popular surrogate model in Bayesian optimization due to its flexibility and mathematical tractability. GP regression models are defined by two elements: the mean and covariance functions.