STOCHASTIC OPTIMIZATION FOR DESIGN UNDER UNCERTAINTY WITH DEPENDENT PROBABILITY MEASURES

Sponsor:                           U.S. National Science Foundation

Project No.:                      CMMI-1462385

Duration:                          August 15, 2015 – June 31, 2018

Principal Investigator:  Professor Sharif Rahman

Graduate Student:         Mr. Hamid Reza Fazeli

 

SUMMARY

     The objectives of this proposal are to build a solid mathematical foundation, devise efficient numerical algorithms, and develop practical computational tools for stochastic design optimization of large-scale complex systems subject to random input following arbitrary dependent probability distributions. The proposed effort will involve: (1) a new theoretical development of the generalized analysis-of-variance (ANOVA) dimensional decomposition (ADD) for dependent random variables, leading to the generalized polynomial dimensional decomposition (PDD) of a high-dimensional stochastic response; (2) new formulae and scalable algorithms associated with the generalized PDD method for calculating the statistical moments and reliability, followed by design sensitivity analysis; and (3) new reliability-based and robust optimization algorithms for shape and topology designs from a single or at most a few stochastic simulations.  Due to innovative calculation of the expansion coefficients, the generalized decomposition method will be efficiently implemented regardless of the size of the stochastic design problem. The innovative formulation of the statistical moment and reliability analyses and design sensitivities, which requires a single or at most a few stochastic simulations for all possible designs, will markedly accelerate the optimization process, potentially producing breakthrough solutions to stochastic design problems.