The Efficient Sensitivity Analysis on Statistical Moments and Probability Constraints in Robust Optimal Design

The efforts of reflecting the system's uncertainties in design step have been made and robust optimization or reliability-based design optimization are examples of the most famous methodologies. In their formulation, the mean and standard deviation of a performance function and constraints expressed by probability conditions are involved. Therefore, it is essential to effectively and accurately calculate them and, in addition, the sensitivity results are required to obtain when the nonlinear programming is utilized during optimization process. We aim to obtain the new and efficient sensitivity formulation, which is based on integral form, on statistical moments such as the mean and standard deviation, and probability constraints. It does not require the additional functional calculation when statistical moments and failure or satisfaction probabilities are already obtained at a design point. Moreover, some numerical examples have been calculated and compared with the exact solution or the results of Monte Carlo Simulation method. The results seem to be very satisfactory.