Reliability-based Multi-Objective Optimization and Visualization using LS-OPT Version 4

This study expounds the multi-objective optimization of a realistic crashworthiness problem with special reference to the incorporation of uncertainty and the visualization of the Pareto Optimal Frontier (POF). LS-OPT® and LS-DYNA® are used for the optimization based on the C2500 truck model developed by NHTSA. The design problem is set up as a Reliability-Based Design Optimization (RBDO) problem which includes specifications for the variation of the input parameters. For the purpose of design, reliability-based constraints on the displacements and stage pulses (interval-based integrals over the acceleration history) are specified. Nine thickness variables were assigned to various parts affecting the crashworthiness performance. Solution of the example employs Radial Basis Function networks as surrogate functions with Space Filling sampling as well as the NSGA-II algorithm for determining the POF starting from an infeasible design. Post-processing is done to determine a subset of optimal points of interest using the Viewer of LS-OPT® Version 4. This post- processor is based on a new architecture which allows window splitting and detachable windows for flexible viewing. It also includes the following new features: (1) Correlation Matrix, (2) Parallel Coordinate plot (POF) and (3) Hyper-Radial Visualization (POF). Thus 3 types of POF viewing are available, including the current 3D scatter plot. The study shows that a complex decision-making process such as optimal design involving uncertainty and multiple objectives can be simplified by using appropriate analysis and visualization tools.