Session: 01-02: Conceptual Design and Optimization I

Submission Number: 179485

A Probabilistic Machine Learning Approach for Uncertainty-Quantified Multi-Disciplinary Design Optimization of a 2D Vectoring Nozzle 

The design of two-dimensional (2D) vectoring nozzles for next-generation combat aircraft presents a formidable multi-disciplinary design optimization (MDO) challenge, demanding the concurrent reconciliation of competing objectives across aerodynamic performance, infrared (IR) signature suppression, and radar cross-section (RCS) reduction. The inherent physical conflicts—such as how geometric features that enhance thrust generation often lead to increased thermal and electromagnetic observability—necessitate a holistic approach to explore the complex, high-dimensional design space for Pareto-optimal solutions. However, navigating this space is severely hampered by the prohibitive computational expense associated with high-fidelity simulations for each discipline, rendering traditional optimization algorithms that require thousands of function evaluations impractical.

To address this critical challenge, this paper introduces a novel and highly efficient data-driven framework for the many-objective MDO of a 2D vectoring nozzle, built upon the principles of Bayesian optimization and advanced probabilistic surrogate modeling. The framework is specifically architected to deliver a rich set of optimal designs from a very limited budget of high-fidelity computational fluid dynamics (CFD), reverse Monte Carlo ray tracing (RMCRT), and full-wave electromagnetic (CEM) simulations.

At the core of our proposed methodology is a Multi-task Bayesian Neural Network (MT-BNN) that serves as a unified, global surrogate model. Unlike conventional approaches that build separate surrogates for each performance metric, the MT-BNN is designed with a shared-representation architecture that enables it to learn and leverage the underlying physical correlations between the disparate performance outputs (i.e., thrust coefficient,  IR intensities in multiple bands and planes, and RCS in different polarizations). This multi-task learning paradigm significantly enhances the model's predictive accuracy and generalization capability, especially in the crucial small-data regime typical of aerospace MDO problems. Furthermore, as a Bayesian model, the MT-BNN provides not only mean predictions but also a principled quantification of predictive uncertainty for each objective, which is the cornerstone of the subsequent optimization strategy.

This sophisticated probabilistic surrogate is then integrated into a many-objective Bayesian optimization (MOBO) loop. The search for new, informative design candidates to simulate is intelligently guided by the Expected Hypervolume Improvement (EHVI) acquisition function. The EHVI metric quantifies the expected increase in the dominated volume of the objective space, providing a theoretically sound mechanism to automatically balance the trade-off between exploiting known regions of high performance (exploitation) and reducing model uncertainty in unexplored regions of the design space (exploration). This active learning strategy ensures a rapid and efficient convergence towards the true Pareto front with a minimal number of costly high-fidelity simulations.

The framework is systematically applied to a 2D vectoring nozzle parameterized by seven key geometric variables. The performance of the MT-BNN surrogate is rigorously validated against a held-out test set, demonstrating its superior accuracy compared to standard single-task models. The convergence of the optimization process is tracked via the hypervolume indicator, confirming the efficiency of the EHVI-guided search. The final result is a well-distributed and comprehensive Pareto front, visualizing the intricate trade-offs between maximizing aerodynamic performance and minimizing multi-spectral signatures. In-depth analysis of representative designs selected from the Pareto front reveals the quantitative compromises required to achieve balanced or specialized performance characteristics. This work demonstrates a powerful and sample-efficient paradigm for tackling complex, multi-physics design problems in aerospace engineering, delivering a set of high-performance solutions under severe computational constraints.

Presenting Author: Rui Wang Northwestern Polytechnical University

Presenting Author Biography: Rui Wang received her M.S. degree from Northwestern Polytechnical University (NPU), China, in 2023. She is currently a Ph.D. student at the School of Power and Energy at the same university. Her research interests include computational electromagnetics, stealth technology, deep learning and artificial intelligence.

Authors:

Rui Wang Northwestern Polytechnical University
Qingzhen Yang Northwestern Polytechnical University
Lei Huang Northwestern Polytechnical University
Saile Zhang Northwestern Polytechnical University
Xu Sun Shenyang Aeroengine Research Institute