Computational methods for modeling and design of complex engineering systems under uncertainty

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Computation-based design is starting to become the norm in many engineering sectors and high-fidelity models are now increasingly used to support decision making in industrial design practice. Despite the significant progress that has been made in this area, a number of challenges remain to be overcome in order to fully realize the potential of computation-based design workflows to accelerate complex systems design. One of the main challenges is computational cost. With the increasing push towards high-fidelity models, evaluation of a wide range of design alternatives/concepts can be computationally infeasible even on massively parallel computers. Another challenge arises from the fact that uncertainty is ubiquitous in the mathematical modeling and characterization of engineering systems. Existing approaches can be computationally prohibitive when dealing with uncertainty, e.g., when engineers wish to predict performance statistics using a high-fidelity model and/or decide on parameter settings that can help mitigate the impact of uncertainty. These two challenges are exacerbated by the fact that computer models of complex real-world engineering systems are often parametrized in terms of a huge number of design variables and uncertain parameters. There is a pressing need for scalable and efficient algorithms to tackle high-dimensional problems in computational modeling and design optimization, especially in the presence of uncertainty. The proposed research program will address these important challenges and the main research topics of focus are: (i) novel data-driven and Galerkin/Petrov-Galerkin projection based algorithms for constructing real-time emulators of high-dimensional parametrized systems along with rigorous error estimation capabilities, (ii) low-rank tensor decomposition strategies for efficiently dealing with high-dimensional problems, (iii) algorithms for rapid calculation of decision analytics for computational engineering under uncertainty that will enable engineers to gain deeper insights and allow near real-time decision making, and (iv) parallel software tools for heterogeneous multicore computer clusters. Breakthroughs in these areas are key to overcoming the computational challenges associated with design under uncertainty and developing the next generation of immersive collaborative environments for multidisciplinary analysis and robust design of complex engineering systems. The application areas of particular focus include gas turbine system/component level design, aerodynamic shape design and multidisciplinary aircraft design. The proposed research program will greatly enhance and find applications in the applicant's ongoing research partnerships that cover various topics in computational science and engineering as well as collaboration with Pratt & Whitney Canada who is a global leader in gas turbine engines.