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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.

Mathematical optimization plays an important role in engineering design, leading to greatly improved performance. Deterministic optimization however, can lead to undesired choices because it neglects input and model uncertainty. Reliability-based design optimization (RBDO) and robust design improve optimization by considering uncertainty. A design is called reliable if it meets all performance targets in the presence of variation/uncertainty and robust if it is insensitive to variation/uncertainty. Ultimately, a design should be optimal, reliable, and robust. Usually, some of the deterministic optimality is traded-off in order for the design to be reliable and/or robust. This paper describes the state-of-the-art in assessing reliability and robustness in engineering design and proposes a new unifying formulation. The principles of deterministic optimality, reliability and robustness are first defined.

Early in the engineering design cycle, it is difficult to quantify product reliability or compliance to performance targets due to insufficient data or information for modeling the uncertainties. Design decisions are therefore, based on fuzzy information that is vague, imprecise qualitative, linguistic or incomplete. The uncertain information is usually available as intervals with lower and upper limits. In this work, the possibility theory is used to assess design reliability with incomplete information. The possibility theory can be viewed as a variant of fuzzy set theory. A possibility-based design optimization method is proposed where all design constraints are expressed possibilistically. It is shown that the method gives a conservative solution compared with all conventional reliability-based designs obtained with different probability distributions.