Design for Crashworthiness of Categorical Multimaterial Structures Using Cluster Analysis and Bayesian Optimization

This work introduces a cluster-based structural optimization (CBSO) method for the design of categorical, multimaterial structures subjected to crushing, dynamic loading. The proposed method consists of three steps: conceptual design generation, design clustering, and Bayesian optimization. In the first step, a conceptual design is generated using the hybrid cellular automaton (HCA) algorithm. In the second step, threshold-based cluster analysis yields a lower-dimensional design. Here, a cluster validity index for structural optimization is introduced in order to qualitatively evaluate the clustered design. In the third step, the optimal design is obtained through Bayesian optimization, minimizing a constrained expected improvement function. This function allows to impose soft constraints by properly redefining the expected improvement based on the maximum constraint violation. The Bayesian optimization algorithm implemented in this work has the ability to search over: (i) a real design space for sizing optimization, (ii) a categorical design space for material selection, or (iii) a mixed design space for concurrent sizing optimization and material selection. With the proposed method, materials are optimally selected based on multiple attributes and multiple objectives without the need for material ranking. The effectiveness of this approach is demonstrated with the design for crashworthiness of multimaterial plates and thin-walled structures.