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Computer programs and models are playing an increasing role in simulating vehicle crashworthiness, dynamic, and fuel efficiency. To maximize the effectiveness of these models, the validity and predictive capabilities of these models need to be assessed quantitatively. For a successful implementation of Computer Aided Engineering (CAE) models as an integrated part of the current vehicle development process, it is necessary to develop objective validation metric that has the desirable metric properties to quantify the discrepancy between multiple tests and simulation results. However, most of the outputs of dynamic systems are multiple functional responses, such as time history series. This calls for the development of an objective metric that can evaluate the differences of the multiple time histories as well as the key features under uncertainty.

Particle swarm optimization (PSO) is a relatively new stochastic optimization algorithm and has gained much attention in recent years because of its fast convergence speed and strong optimization ability. However, PSO suffers from premature convergence problem for quick losing of diversity. That is to say, if no particle discovers a new superiority position than its previous best location, PSO algorithm will fall into stagnation and output local optimum result. In order to improve the diversity of basic PSO, design of experiment technique is used to initialize the particle swarm in consideration of its space-filling property which guarantees covering the design space comprehensively. And the optimization procedure of PSO is divided into two stages, optimization stage and improving stage. In the optimization stage, the basic PSO initialized by Optimal Latin hypercube technique is conducted.