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

Abstract

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.

Bayesian topology optimization for efficient design of origami folding structures

“…Dominguez et al [37] applied BO to solve shape optimization problems in a non-linear finite element framework. Liu et al [38] also used BO in a finite element framework to design for structural crashworthiness. Another study using Kriging surrogate models for topology optimization of crash structures was conducted by Raponi et al [39].…”

A Bayesian Approach to Recovering Missing Component Dependence for System Reliability Prediction via Synergy Between Physics and Data

“…Q ′ V is the conditional PDF of the component load in the failure region, and [ Q is the unknown parameter. From the perspective of the Bayesian Theorem [31,32], . Q ′ V is the posterior PDF of the component load given that a failure has occurred, and its unknown parameter [ Q can be estimated from the observations or the sample of the component load.…”

LatticeOPT: A heuristic topology optimization framework for thin-walled, 2D extruded lattices

“…In the case of TO for thin-walled structures, several frameworks have been proposed and demonstrated. Notable ones are: (1) the equivalent static load approach, which seeks a static load that generates equivalent deformation to the true dynamic load, and thus converts the problem to a quasi-static TO problem [26,27]; (2) cellular automata-based approaches, which use a series of update rules to iteratively update the thickness of the shell elements defining the lattice walls [4,[28][29][30]; (3) the response surface method, which seeks to approximate the true response surface of the objective function through simple functions and repeated FE simulations [31,32]; and (4) various probabilistic and evolutionary methods like Bayesian optimization [33], ant colony method [34,35], and particle swarm method [36]. Most of these methods, although capable of improving the design, take many FE simulation and optimization iterations to do so [28], and can be computationally expensive for large scale problems.…”