A Machine Learning Enabled MDO for Bio-Inspired Autonomous Underwater Gliders

The preliminary design of AUGs is intrinsically challenging due to the strong coupling between the external hydrodynamic shape, the hydrostatic balance, the structural integrity, and internal packaging constraints. This complexity is further amplified for bio-inspired configurations, whose rich geometric parametrizations lead to high-dimensional design spaces that are difficult to explore using conventional optimization approaches. This work presents a ML-enabled bi-level multidisciplinary design optimization (MDO) framework for the performance-driven design of a manta-ray-inspired AUG. At the upper level, hydrodynamically efficient external geometries are explored in a reduced design space obtained through physics-driven parametric model embedding, which identifies a low-dimensional latent representation directly correlated with the lift, drag, and pressure distributions. At the lower level, a constrained internal sizing problem determines the minimum feasible empty weight by accounting for structural, hydrostatic, geometric, and payload constraints. To render the resulting bi-level problem computationally tractable, a multi-fidelity surrogate-based optimization strategy is adopted, combining low- and high-fidelity hydrodynamic models with stochastic radial basis function surrogates and adaptive Bayesian sampling. The framework enables efficient exploration of the coupled design space while rigorously managing model uncertainty and computational cost. The optimized configurations exhibit a 14.7% improvement in maximum hydrodynamic efficiency and a 12.8% reduction in empty weight relative to the baseline design, while satisfying all disciplinary constraints. These results demonstrate that the integration of physics-driven dimensionality reduction and multi-fidelity machine learning enables scalable and physically consistent MDO of complex bio-inspired underwater vehicles.

💡 Research Summary

The paper presents a comprehensive machine‑learning‑enabled multidisciplinary design optimization (MDO) framework tailored for the preliminary design of bio‑inspired autonomous underwater gliders (AUGs), specifically a manta‑ray‑shaped vehicle. The authors recognize that the early‑stage design of AUGs is intrinsically difficult because external hydrodynamics, hydrostatic balance, structural integrity, and internal packaging are tightly coupled, and that bio‑inspired geometries introduce a high‑dimensional shape parameter space that is intractable for conventional optimization methods.

To address these challenges, a bi‑level architecture based on the BLISS (Bi‑Level Integrated System Synthesis) paradigm is adopted. The upper level optimizes the external hull geometry for maximum hydrodynamic efficiency (lift‑to‑drag ratio) while the lower level determines the minimum feasible empty weight of the internal pressure hull and buoyancy system, subject to structural buckling, hydrostatic equilibrium, positive surface buoyancy, geometric containment, and payload‑volume constraints.

A key innovation is the use of physics‑driven parametric model embedding (PD‑PME) to reduce the original 32 design variables (four NACA‑based sections, each with airfoil, position, and orientation parameters) to a low‑dimensional latent space that directly correlates with lift, drag, and pressure distributions. Large ensembles of low‑fidelity potential‑flow simulations (PUFFIn) are used to extract physically meaningful modes, ensuring that the reduced variables retain interpretability and improve surrogate learning efficiency.

The framework employs a multi‑fidelity surrogate modeling strategy based on stochastic radial basis functions (SRBF). Low‑fidelity data are generated cheaply with PUFFIn at multiple mesh resolutions, while high‑fidelity data are obtained from steady RANS simulations in OpenFOAM (k‑ω SST with γ‑Reθ transition) and unsteady ISIS‑CFD runs. The SRBF surrogate provides both predictions and uncertainty estimates, which are exploited by a batch Bayesian optimization algorithm. The acquisition function is expected hypervolume improvement (EHVI) computed in an augmented feature space; candidate points are clustered to promote diversity along the Pareto front.

Results show that the optimized manta‑ray designs achieve a 14.7 % increase in maximum lift‑to‑drag ratio and a 12.8 % reduction in empty weight compared with a baseline configuration, while satisfying all multidisciplinary constraints. Surrogate validation against high‑fidelity CFD yields average relative errors below 3 %, and the multi‑fidelity approach reduces the number of expensive CFD evaluations by more than 95 %, making the overall process computationally tractable for early‑stage design cycles.

The paper’s contributions are threefold: (1) a complete mathematical formulation of a bi‑level, multi‑objective, multi‑constraint MDO problem for bio‑inspired AUGs; (2) a physics‑based dimensionality reduction technique that improves surrogate accuracy and sampling efficiency; (3) an integrated multi‑fidelity surrogate and batch Bayesian optimization workflow that delivers high‑quality Pareto‑optimal designs with dramatically reduced computational cost.

The authors conclude that integrating physics‑driven dimensionality reduction with multi‑fidelity machine learning creates a scalable, physically consistent MDO framework applicable not only to underwater gliders but also to other early‑stage shape optimization problems involving complex physics and strong multidisciplinary coupling. Future work is suggested on experimental validation, inclusion of environmental variability (temperature, depth‑dependent density, currents), and extension to more intricate biomimetic geometries.