Performance of Iterative Network Uncertainty Quantification for Multicomponent System Qualification

Abstract

In order to impact design decisions and realize the full promise of high-fidelity computational tools, simulation results must be integrated at the earliest stages in the design process. This is particularly challenging when dealing with uncertainty and optimizing for system-level performance metrics as full-system models (often notoriously expensive and time-consuming to develop) are generally required to propagate uncertainties to system-level quantities of interest. Methods for propagating parameter and boundary condition uncertainty in networks of interconnected components hold promise for enabling design under uncertainty in real-world applications. These methods preclude the need for time consuming mesh generation of full-system geometries when changes are made to components or subassemblies. Additionally, they explicitly tie full-system model predictions to component/subassembly validation data which is valuable for qualification. This is accomplished by taking advantage of the fact that many engineered systems are inherently modular, being comprised of a hierarchy of components and subassemblies which are individually modified or replaced to define new system designs. We leverage this hierarchical structure to enable rapid model development and the incorporation of uncertainty quantification and rigorous sensitivity analysis earlier in the design process. The resulting formulation of the uncertainty propagation problem is iterative. We express the system model as a network of interconnected component models which exchange stochastic solution information at component boundaries. We utilize Jacobi iteration with Anderson acceleration to converge stochastic representations of system level quantities of interest through successive evaluations of component or subassembly forward problems. We publish our open-source tools for uncertainty propagation in networks remarking that these tools are extensible and can be used with any simulation tool (including arbitrary surrogate modeling tools) through the construction of a simple Python interface class. Additional interface classes for a variety of simulation tools are currently under active development. The performance of the uncertainty quantification method is determined by the number of iterations needed to achieve a desired level of accuracy. Performance of these networks for simple canonical systems from both a heat transfer and solid mechanics perspective are investigated; the models are examined with thermal and mechanical Dirichlet and Neumann type boundary conditions separately imposed and the impact of varying governing equations and boundary condition type on the performance of the networks is analyzed. The form of the boundary conditions is observed to have a large impact on the convergence rate with Neumann-type boundary conditions corresponding to significant performance degradation compared to the Dirichlet boundary conditions. Nonmonotonicity is observed in the solution convergence in some cases.