New approach to uncertainty quantification and integration in single and multidisciplinary systems

Abstract

Representation and propagation of different types of uncertainties (aleatory and epistemic) are increasingly being acknowledged in the design and optimization of complex systems. Statistical moment-based existing uncertainty representation approaches quantify uncertainties in an input quantity through moment bounds, and for this purpose, estimate different moments of a random variable from different sample sets. However, being not independent of each other, all the moments of the same random variable should be calculated from the same sample dataset. Again, existing approaches compute the widest possible (most conservative) range for each of the moments which offer maximum possible alternative values of uncertain variable, and is regarded as worst case from the aspect of uncertainty quantification. Therefore, first part of this thesis proposes a new probabilistic uncertainty representation approach that bags all the advantages of probabilistic approaches and simultaneously eliminates the limitations of existing methods. Proposed method includes development of a function of interest, and optimization of this function yields effective estimation of all the moment bounds of a random variable described by either multiple interval data or a combination of multiple interval and sparse point data. Then, these moment bounds are used to fit uncertain data to bounded Johnson distribution through utilization of moment matching. Finally, proposed uncertainty representation method is demonstrated with four numerical problems, which include three challenge problems from Sandia Epistemic Uncertainty Workshop, and the results are compared with earlier studies. Again, uncertainty propagation through multidisciplinary system is difficult due to the presence of interdisciplinary coupling, and it becomes more difficult when uncertainty incorporates in the input quantity. Therefore, second part of this thesis presents a unified probabilistic framework for the representation and propagation of both aleatory and epistemic uncertainty through multidisciplinary system. Proposed framework exploits worst-case maximum likelihood estimation (WMLE) method to quantify uncertainty, and likelihood-based multidisciplinary analysis (LAMDA) method to propagate the uncertainty through multidisciplinary system. Finally, a numerical problem and an engineering problem (Fire detection satellite) are used to demonstrate our proposed framework.