An Integrated Framework for Probabilistic Optimization Using Inverse Reliability Strategy

In this work, we propose an integrated framework for probabilistic optimization that can bring both the design objective robustness and the probabilistic constraints into account. The fundamental development of this work is the employment of an inverse reliability strategy that uses percentile performance for assessing both the objective robustness and probabilistic constraints. The percentile formulation for objective robustness provides an accurate probabilistic measure for robustness and more reasonable compound noise combinations. For the probabilistic constraints, compared to a traditional probabilistic model, the proposed formulation is more efficient since it only evaluates the constraint functions at the required reliability levels. The other major development of this work is a new search algorithm for the Most Probable Point of Inverse Reliability (MPPIR) that can be used to efficiently evaluate the performance robustness and percentile performance in the proposed formulation. Multiple techniques are employed in the MPPIR search, including the steepest decent direction and an arc search. The algorithm is applicable to general non-concave and non-convex functions of system performance with random variables following any continuous distributions. The effectiveness of the MPPIR search algorithm is verified using example problems. Overall, an engineering example on integrated robust and reliability design of a vehicle combustion engine piston is used to illustrate the benefits of the proposed method.