Probabilistic optimization of engineering system with prescribed target design in a reduced parameter space

A novel probabilistic robust design optimization framework is presented using a Bayesian inference framework. The objective of the study is to obtain probabilistic descriptors of the system parameters conditioned on the user-prescribed target probability distributions of the output quantities of interest or figures of merit of a system. A criterion-based identification of a reduced important parameter space is performed from the typically high number of parameters modeling the stochastically parametrized physical system. The criterion can be based on sensitivity indices, design constraints or expert opinion or a combination of these. The posterior probabilities on the reduced or important parameters conditioned on prescribed target distributions of the output quantities of interest are derived using the Bayesian inference framework. The probabilistic optimal design proposed here offers the distinct advantage of prescribing probability bounds of the system performance functions around the optimal design points such that robust operation is ensured. The proposed method has been demonstrated with two numerical examples including the optimal design of a structural dynamic system based on user-prescribed target distribution for the resonance frequency of the system.