Reliability Based Design Optimization of Dynamic Vehicle Performance Using Bond Graphs and Time Dependent Metamodels

A vehicle drivetrain is designed to meet specific vehicle performance criteria which usually involve trade-offs among conflicting performance measures. This paper describes a methodology to optimize the drivetrain design including the axle ratio, transmission shift points and transmission shift ratios considering uncertainty. A complete vehicle dynamic model is developed using the bond graph method. The model includes the vehicle, engine, transmission, torque converter, driveline, and transmission controller. An equivalent MATLAB Simulink model performs the nonlinear dynamic analysis. In order to reduce the computational effort, a time-dependent metamodel is developed based on principal component analysis using singular value decomposition. The optimization is performed using both the Simulink vehicle dynamic model and the metamodel. A deterministic optimization first determines the optimum design in terms of fuel economy, without considering variations or uncertainties. Subsequently, a Reliability-Based Design Optimization is carried out to find the optimum design in the presence of uncertainty. All analyses are exclusively performed in the MATLAB environment. A vehicle example illustrates the design methodology in detail.