Parametric uncertainty analysis for complex engineering systems

Abstract

With the rapid advancement of computational science, modeling and simulation have become standard methods to study the behavior of complex systems. As scientists and engineers try to capture more detail, the models become more complex. Given that there are inevitable uncertainties entering at every stage of a model's life cycle, the challenge is to identify those components that contribute most to uncertainties in the predictions. This thesis presents new methodologies for allowing direct incorporation of uncertainty into the model formulation and for identifying the relative importance of different parameters. The basis of these methods is the deterministic equivalent modeling method (DEMM), which applies polynomial chaos expansions and the probabilistic collocation approach to transform the stochastic model into a deterministic equivalent model. By transforming the model the task of determining the probability density function of the model response surface is greatly simplified. In order to advance the representation method of parametric uncertainty. a theoretical study of polynomial chaos representation of uncertain parameters has been performed and an Adomian polynomial expansion for functions of random variables has been developed. While DEMM is applied to various engineering systems to study the propagation of uncertainty in complex models, a systematic framework is introduced to quantitatively assess the effect of uncertain parameters in stochastic optimization problems for chemical product and process design. Furthermore, parametric uncertainty analysis techniques for discrete and correlated random variables have been developed such that the deterministic equivalent modeling method can be applied to a broader range of engineering problems. As a result of these developments, uncertainty analysis can now be performed 2 to 3 orders faster than conventional methods such as Monte Carlo. Examples of models in various engineering systems suggest both the accuracy and the practicality of the new framework for parametric uncertainty analysis established in this thesis.