Misconceptions about the central limit theorem in uncertainty-based design optimization

Abstract

© 2021, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Uncertainty-based Design Optimization techniques present a powerful toolkit to achieve robust and reliable optimal designs in the presence of uncertainty, having probability theory as its backbone. The central limit theorem is a key concept in probability theory due to its notorious usefulness in a wide number of statistical problems. However, it seems that the theorem applicability to problems involving non-normal probability distributions has led to a mistaken belief that stochastic responses resulting from the propagation of input uncertainties naturally tend to be normally distributed. The purpose of this paper is to briefly discuss why this is not necessarily true and why this misconception can be detrimental. Three reasons are identified and illustrated through simple test cases using Monte Carlo simulations and Anderson-Darling test.