Optimal Sample Augmentation and Resource Allocation for Design With Inadequate Uncertainty Data

Uncertainty modeling in reliability-based design optimization problems requires a large amount of measurement data that are generally too costly in engineering practice. Instead, engineers are constantly challenged to make timely design decisions with only limited information at hand. In the literature, Bayesian binomial inference techniques have been used to estimate the reliability values of functions of uncertainties with limited samples. However, existing methods assume one sample as the entire set of measurements with one for each uncertain quantity while in reality one sample is one measurement on a specific quantity. As a result, effective yet efficient allocating resources in sample augmentation is needed to reflect the relative contributions of uncertainties on the final optimum. We propose a sample augmentation process that uses the concept of sample combinations. Uncertain quantities are sampled with respect to their relative ‘importance’ while the impacts of bad measurements, which affect the evaluation of reliability inference, are alleviated via a Markov-Chain Monte Carlo filter. The proposed method could minimize the efforts and resources without assuming distributions for uncertainties. Several examples are used to demonstrate the validity of the method in product development.