A Non-Parametric Histogram Interpolation Method for Design Space Exploration

Abstract

A novel algorithm is presented to aid designers during the conceptual design phase of a new engineering product by rapidly assessing new areas of the design space. The algorithm presented here develops a Polynomial Chaos based meta-model that allows the designer to estimate the probability distribution for a candidate design's performance without requiring additional experiments or simulations. Probabilistic equivalence is used to map either a Probability Density Function (PDF) or a Cumulative-Distribution Function (CDF), continuous functions, into a reduced space in which interpolation functions can be developed. Data harvested from experiments or evaluations of an expensive computer code is used to train the meta-model. An advantage of this method over other histogram interpolation methods is that it is non-parametric: the training data is not assumed to belong to a particular family of probability distribution. The algorithm was validated using a standard benchmark test with synthetic data in a continuous-discrete design space. Finally, we exploited the variance of the Gaussian Process Emulators (GPEs) used as interpolation functions in order to develop a statistic that quantified the level of uncertainty associated with the algorithm's estimates. This is a key feature if the algorithm is to be of practical use.