Efficient Decoupling of Multiphysics Systems for Uncertainty Propagation

Uncertainty propagation through coupled multiphysics systems is often intractable due to computational expense. In this work, we present a novel methodology to enable uncertainty analysis of expensive coupled systems. The approach consists of offline discipline level analyses followed by an online synthesis that results in accurate approximations of full coupled system level uncertainty analyses. Coupling is handled by an efficient procedure for approximating the map from system inputs to fixed point sets that makes use of state of the art L1-minimization techniques and cut high dimensional model representations. The methodology is demonstrated on an analytic numerical example and a fire detection satellite system where it is shown to perform well as compared to brute force Monte Carlo simulation

Multifidelity Uncertainty Propagation via Adaptive Surrogates in Coupled Multidisciplinary Systems

Fixed point iteration is a common strategy to handle interdisciplinary coupling within a feedback-coupled multidisciplinary analysis. For each coupled analysis, this requires a large number of disciplinary high-fidelity simulations to resolve the interactions between different disciplines. When embedded within an uncertainty analysis loop (e.g., with Monte Carlo sampling over uncertain parameters), the number of high-fidelity disciplinary simulations quickly becomes prohibitive, because each sample requires a fixed point iteration and the uncertainty analysis typically involves thousands or even millions of samples. This paper develops a method for uncertainty quantification in feedback-coupled systems that leverage adaptive surrogates to reduce the number of cases forwhichfixedpoint iteration is needed. The multifidelity coupled uncertainty propagation method is an iterative process that uses surrogates for approximating the coupling variables and adaptive sampling strategies to refine the surrogates. The adaptive sampling strategies explored in this work are residual error, information gain, and weighted information gain. The surrogate models are adapted in a way that does not compromise the accuracy of the uncertainty analysis relative to the original coupled high-fidelity problem as shown through a rigorous convergence analysis.United States. Army Research Office. Multidisciplinary University Research Initiative (Award FA9550-15-1-0038

A decomposition-based approach to uncertainty analysis of feed-forward multicomponent systems

To support effective decision making, engineers should comprehend and manage various uncertainties throughout the design process. Unfortunately, in today's modern systems, uncertainty analysis can become cumbersome and computationally intractable for one individual or group to manage. This is particularly true for systems comprised of a large number of components. In many cases, these components may be developed by different groups and even run on different computational platforms. This paper proposes an approach for decomposing the uncertainty analysis task among the various components comprising a feed-forward system and synthesizing the local uncertainty analyses into a system uncertainty analysis. Our proposed decomposition-based multicomponent uncertainty analysis approach is shown to be provably convergent in distribution under certain conditions. The proposed method is illustrated on quantification of uncertainty for a multidisciplinary gas turbine system and is compared to a traditional system-level Monte Carlo uncertainty analysis approach.SUTD-MIT International Design CentreUnited States. Defense Advanced Research Projects Agency. META Program (United States. Air Force Research Laboratory Contract FA8650-10-C-7083)Vanderbilt University (Contract VU-DSR#21807-S7)United States. Federal Aviation Administration. Office of Environment and Energy (FAA Award 09-C-NE-MIT, Amendments 028, 033, and 038

Hybrid Sampling/Spectral Method for Solving Stochastic Coupled Problems

peer reviewedIn this paper, we present a hybrid method that combines Monte Carlo sampling and spectral methods for solving stochastic coupled problems. After partitioning the stochastic coupled problem into subsidiary subproblems, the proposed hybrid method entails iterating between these subproblems in a way that enables the use of the Monte Carlo sampling method for subproblems that depend on a very large number of uncertain parameters and the use of spectral methods for subproblems that depend on only a small or moderate number of uncertain parameters. To facilitate communication between the subproblems, the proposed hybrid method shares between the subproblems a reference representation of all the solution random variables in the form of an ensemble of samples; for each subproblem solved by a spectral method, it uses a dimension-reduction technique to transform this reference representation into a subproblem-specific reduced-dimensional representation to facilitate a computationally efficient solution in a reduced-dimensional space. After laying out the theoretical framework, we provide an example relevant to microelectomechanical systems