Abstract

The second part of the multi-objective design and optimization with parametric and model-form uncertainty quantification (MDO with P&MF-UQ) is dedicated to incorporating MF-UQ into the MDO framework. MF-UQ is used to estimate the error due to modeling inaccuracies and to validate the mathematical models used in the MDO framework. In this approach, the sensitivity index introduced in the first part of the article is modified too so that it is a quantitative measure of system design robustness with regards to modeling inaccuracies as well as the manufacturing variability in the design of systems with multiple performance functions. The optimum design solution is finally realized by exploring the Pareto Front of the enhanced performance space, where the model-form error associated with each design is used to modify the estimated performance measures and the parametric sensitivity of each design point is considered to discern between cases and help identify the most parametrically robust of the Pareto-optimal design solutions. To demonstrate the benefits of incorporating uncertainty quantification analysis into the design optimization from a more practical standpoint, design of a robust high-efficiency high-power-density 1.25 kW Vienna-type rectifier is used as a case study to compare the theoretical analysis with a comprehensive experimental validation. It is shown that the final design selected using the MDO with P&MF-UQ reduces the design sensitivity and system loss by 33% and 5%, respectively, compared to the optimal design selected using the conventional MDO.