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Existing methods for design optimization under uncertainty assume that a high level of information is available, typically in the form of data. In reality, however, insufficient data prevents correct inference of probability distributions, membership functions, or interval ranges. In this article we use an engine design example to show that optimal design decisions and reliability estimations depend strongly on uncertainty characterization. We contrast the reliability-based optimal designs to the ones obtained using worst-case optimization, and ask the question of how to obtain non-conservative designs with incomplete uncertainty information. We propose an answer to this question through the use of Bayesian statistics. We estimate the truck's engine reliability based only on available samples, and demonstrate that the accuracy of our estimates increases as more samples become available.

This paper investigates the effects of manufacturing variations in fuel injectors on the engine performance with emphasis on emissions. The variations are taken into consideration within a Reliability-Based Design Optimization (RBDO) framework. A reduced version of Multi-Zone Diesel engine Simulation (MZDS), MZDS-lite, is used to enable the optimization study. The numerical noise of MZDS-lite prohibits the use of gradient-based optimization methods. Therefore, surrogate models are developed to filter out the noise and to reduce computational cost. Three multi-objective optimization problems are formulated, solved and compared: deterministic optimization using MZDS-lite, deterministic optimization using surrogate models and RBDO using surrogate models. The obtained results confirm that manufacturing variation effects must be taken into account in the early product development stages.