Bayesian collaborative sampling: Adaptive learning for multidisciplinary design

A Bayesian adaptive sampling method is developed for highly coupled multidisciplinary design problems. The method addresses a major challenge in aerospace design: exploration of a design space with computationally expensive analysis tools such as computational fluid dynamics (CFD) or finite element analysis. With a limited analysis budget, it is often impossible to optimize directly or to explore the design space with design of experiments (DoE) and surrogate models.;In such cases, the designer can conserve function calls by eliminating 'bad' regions within some confidence level. Exploration can then be concentrated in regions that probably contain a global optimum, in light of current data. However, current sampling methods, such as design of experiments (DoE), can be inefficient by attempting to represent all regions uniformly. Offline sampling techniques like DoE require selection of an entire input sample before evaluating any of them. If the analyses are executed serially, these strategies ignore valuable information since remaining sample points cannot be chosen in light of accumulating knowledge. As a result, such sampling methods can continue to run analyses in a 'bad' region long after there is sufficient certainty about its 'badness.' This inefficiency is magnified in multidisciplinary problems with feedbacks between disciplines since each design point may require iterative analyses to converge on a compatible solution between different disciplines.;To address these problems, this thesis describes Bayesian Collaborative Sampling (BCS). BCS is a bi-level architecture for design space sampling that uses Bayesian models with online, or adaptive, sampling. Bayesian adaptive sampling methods already exist, but BCS is tailored for strongly coupled multidisciplinary problems. It is novel because it simultaneously does the following: (1) concentrates disciplinary analyses in regions of a design space that are favorable to a system-level objective; (2) guides analyses to regions where interdisciplinary coupling variables are probably compatible.;BCS uses Bayesian sequential learning techniques along with elements of the collaborative optimization (CO) architecture for multidisciplinary optimization (MDO). Like CO, BCS decomposes a multidisciplinary problem into a system level and discipline level. In addition, it equips both of these levels with Bayesian models. In particular, BCS can borrow recent advances from machine learning literature and can use sparse Bayesian models for computational speed. At each iteration, BCS uses sequential learning criteria called expected improvement and probability of target match from the Bayesian models to select the next sample point for analysis.;The method is first tested with a subsonic glider wing design problem using low fidelity analysis. The results show favorable performance compared to an off-line DoE. Further performance tests investigate the method's dependence on coupling bandwidth, warm-start sample size, and replication error. Finally, BCS is demonstrated with CFD in coupled aero-propulsion design of a turbojet engine nacelle. Successful tests show that the BCS can be used for practical design with high fidelity analysis codes.