Likelihood-based Approach for Uncertainty Propagation in Multidisciplinary Analysis

Abstract

This paper proposes a new methodology for uncertainty quantification in systems that require multidisciplinary iterative analysis between two or more coupled component models. This methodology is based on computing the probability of satisfying the interdisciplinary compatibility equations, conditioned on specific values of the coupling (or feedback) variables, and this information is used to estimate the probability distributions of the coupling variables. The estimation of the coupling variables is analogous to likelihoodbased parameter estimation in statistics and thus leads to the proposed likelihood approach for multidisciplinary analysis (LAMDA). Using the distributions of the feedback variables, the coupling can be removed in any one direction without loss of generality, while still preserving the mathematical relationship between the coupling variables. The calculation of the probability distributions of the coupling variables is theoretically exact and does not require a fully coupled system analysis. The proposed method is illustrated using a mathematical example and an aerospace system application - a fire detection satellite. I. Introduction Multidisciplinary systems analysis and optimization is an extensive area of research, and numerous studies in the literature have dealt with the various aspects of coupled multidisciplinary analysis in several engineering disciplines. Researchers have focused both on the development of computational methods 1,2 and the application of these methods to several types of multi-physics interaction, for example, fluid-structure, 3 thermal-structural, 4 fluid-thermal-structural, 5 etc. Studies have considered these methods and applications either for multidisciplinary analysis (MDA) or for multidisciplinary optimization (MDO). The coupling between individual disciplinary analyses may be one-directional (feed-forward) or bi-directional (feedback). Feed-forward coupling is straightforward to deal with; this paper focuses on bi-directional (feedback) coupling. Computational methods for MDA can be classified into three different groups of approaches 6 - field elimination method, 6 monolithic method, 6,7 and partitioned methods. The well-known fixed point iteration approach (repeated analysis until convergence of coupling variables), and the staggered solution approach 6,8 are examples of partitioned methods. Further, two types of approaches – single-level and multi-level approaches – have been pursued for MDO. An important factor in the analysis and design of multidisciplinary systems is the presence of uncertainty in the system inputs. It is necessary to account for the various sources of uncertainty in both MDA and MDO problems. The MDA problem focuses on uncertainty propagation to calculate the uncertainty in the outputs. In the MDO problem, the objective function and/or constraints may become stochastic if the inputs are random. The focus of the present paper is only on uncertainty propagation in multidisciplinary analysis and not on optimization. While most of the aforementioned methods for deterministic MDA can easily be extended to nondeterministic MDA using Monte Carlo sampling, this may be computationally expensive due to repeated evaluations of disciplinary analyses. Hence, researchers have focused on developing more efficient alternatives. Gu et al. 9 proposed worst case uncertainty propagation using derivative-based sensitivities. Kokkolaras et al. 10 used the advanced mean value method for uncertainty propagation and reliability analysis, and this