Application of clouds for modeling uncertainties in robust space system design

Abstract

This report discusses a case study for modeling uncertainties in a Matlab model for space system design, with the goal of determining robust feasible designs for the model. An initial analysis of the original model (provided without uncertainties) revealed a number of anomalies that were resolved. In addition, the problem structure revealed the presence of all difficulties an optimization problem can have: discrete variables, strong nonlinearities, discontinuities due to branching decisions, multiple objectives, multiple local minima. To aid in providing reliable uncertainty information, an uncertainty elicitation interface (implemented in Matlab) is described. The uncertainty information actually provided by ESA consisted in independent worst case bounds (intervals) for a number of variables. To be able to automatically insert the uncertainty information into the model, semiautomatic conversion tools into the modeling languages AMPL (cf. [6]) and LINGO (cf. [13]) are discussed. The formal modeling of uncertainty by means of clouds, and the robust optimization of a resulting uncertain model was considered from a theoretical point of view, with a toy example demonstration. The sensitivity approach to the robust optimization requires tools from automatic differentiation which turned out not to be realizable for the model problem under discussion. Instead, a heuristic approach using surrogate function modeling, corner searches, and discrete line searches was used to solve the robust optimization problem in case of interval uncertainties. This approach works satisfactorily for the model problem for the case of interval uncertainty. Solving the model problem with uncertainty revealed significant robustness advantages of the approach using uncertainty. The influence on assumed knowledge about additional uncertainty information was illustrated by for a few model choices.