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.

An Efficient Reliability Analysis Method Combining Improved EIF Active Learning Mechanism and Kriging Metamodel

Complex implicit performance functions widely exist in many engineering problems. The reliability analysis of these problems has always been a challenge. Using surrogate model instead of real performance function is one of the methods to solve this kind of problem. Kriging is one of the surrogate models with precise interpolation technique. In order to make the kriging model achieve higher accuracy using a small number of samples, i.e., improve its practicability and feasibility in practical engineering problems, some active learning equations are wildly studied. Expected improvement function (EIF) is one of them. However, the EIF has a great disadvantage in selecting the added sample point. Therefore, a joint active learning mechanism, J-EIF, is proposed to obtain the ideal added point. The J-EIF active learning mechanism combines the two active learning mechanisms and makes full use of the characters of kriging model. It overcomes the shortcoming of EIF active learning mechanism in the selection of added sample points. Then, using Monte Carlo Simulation (MCS) results as a reference, the reliability of two examples is estimated. The results are discussed showing that the learning efficiency and accuracy of the improved EIF are both higher than those of the traditional EIF.

Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

This study presents an efficient multimaterial design optimization algorithm that is suitable for nonlinear structures. The proposed algorithm consists of three steps: conceptual design generation, clustering, and metamodel-based global optimization. The conceptual design is generated using a structural optimization algorithm for linear models or a heuristic design algorithm for nonlinear models. Then, the conceptual design is clustered into a predefined number of clusters (materials) using a machine learning algorithm. Finally, the global optimization problem aims to find the optimal material parameters of the clustered design using metamodels. The metamodels are built using sampling and cross-validation and sequentially updated using an expected improvement function until convergence. The proposed methodology is demonstrated using examples from multiple physics and compared with traditional multimaterial topology optimization (MTOP) method. The proposed approach is applied to a nonlinear, multi-objective design problems for crashworthiness.