A Comparative study on multiobjective reliable and robust optimization for crashworthiness design of vehicle structure

Abstract

Design optimization without considering uncertainties of system variables and parameters can be problematic in real 
life. In order to take into account the effect of uncertainties, reliable and robust design schemes have proven 
effective, but limited studies have been reported to compare their difference in a multiobjective framework. This 
paper takes a typical vehicle structure subject to offset frontal crashing scenario as an example to compare reliable 
and robust designs with their deterministic counterpart. The thicknesses of some key components of vehicle frontal 
structures were selected as design variables, the vehicle weight and energy absorption as the objectives, deceleration 
and firewall intrusion as the constraints. The deterministic multiobjective optimization problem was first solved by 
adopting Design of Experimental (DOE), metamodels and Non-dominated Sorting Genetic Algorithm II (NSGA-II). 
Take into account the uncertainties, a Monte Carlo Simulation (MCS) is adopted to generate random distributions 
of the objective and constraint functions for each design. For the reliability-based optimization the desired reliabilities 
of 90 %, 95 % and 99 % are considered, respectively. For the robustness-based optimization, two different formulation 
strategies are adopted. The optimization showed that the reliable and robust Pareto fronts are shifted away from their 
deterministic counterpart due to uncertainties. The different Pareto fronts yielded from the deterministic, reliable and 
robust designs are compared to provide some quantitative insights into how to apply these different design schemes 
for resolving uncertainty problems. It is shown that, compared with the baseline design, the optimizations enhance 
the crashworthiness of vehicle, though more conservative solutions could have been generated from the reliable 
and robust optimizations.