Reliability-based robust design optimization using the eigenvector dimension reduction (EDR) method

This paper presents an effective methodology for reliability-based robust design optimization (RBRDO). The eigenvector dimension reduction (EDR) method plays a pivotal role in making RBRDO effective because the EDR method turns out to be very efficient and accurate for probability analysis. The use of the EDR method provides three benefits to RBRDO. First, an approximate response surface facilitates sensitivity calculation of reliability and quality where the response surface is constructed using the eigenvector samples. Thus, sensitivity analysis becomes very efficient and simple. Second, one EDR execution evaluates a set of quality (objective) and reliability (constraint) functions. In general, the EDR requires 2N + 1 or 4N + 1 simulation runs where N is the total number of random variables. The EDR execution does not require an iterative process, so the proposed RBRDO methodology has a single-loop structure. Moreover, the EDR execution time can be much shorter by taking advantage of a parallel computing power, and RBRDO can be far more efficient. Third, the EDR method allows solving problems with statistically correlated and non-normally distributed random inputs. Three practical engineering problems are used to demonstrate the effectiveness of the proposed RBRDO method using the EDR method.