Maximum-Projection-Based Bayesian Optimization Utilizing Sensitivity Analysis for High-Efficiency Radial Turbine Design with Scarce Data
Proposed a maximum-projection Bayesian optimization with sensitivity analysis for efficient turbine design under scarce CFD data, achieving a 6% efficiency increase.
Key Findings
Methodology
This study integrates MaxPro space-filling design, Gaussian process (GP) surrogate models, and polynomial chaos expansion (PCE) for efficient turbine efficiency optimization within a strict CFD simulation budget. MaxPro ensures uniform coverage and projection stability of initial samples, while GP models provide probabilistic predictions with uncertainty estimates. PCE enables fast Sobol sensitivity index computation, identifying influential parameters. Bayesian optimization iteratively refines the design by balancing exploration and exploitation via the upper confidence bound (UCB). Sensitivity analysis reduces the input dimension by focusing on key parameters, accelerating convergence. The workflow's modular structure allows flexible component replacement, maintaining robustness across different scenarios.
Key Results
- Within 330 CFD evaluations, turbine efficiency improved from 85.77% to 91.77%, outperforming baseline random and low-discrepancy sampling methods. MaxPro initial samples maintained excellent space coverage in high and low dimensions, leading to accurate surrogate models. Sobol indices identified a critical subspace, enabling focused optimization. Bayesian sampling in the full and reduced spaces progressively approached the optimum, demonstrating high efficiency and stability. The combined approach significantly reduced computational costs while achieving substantial performance gains.
Significance
This methodology addresses the challenge of high-cost CFD-based optimization by combining advanced experimental design, sensitivity-driven dimension reduction, and probabilistic surrogate modeling. It offers a practical framework for designing high-performance turbines with limited computational resources, applicable to aerospace and energy sectors. The integration of MaxPro design and sensitivity analysis enhances the reliability and efficiency of the optimization process, paving the way for smarter, resource-aware engineering workflows. Its success demonstrates a promising direction for high-dimensional, data-scarce engineering problems, potentially transforming traditional design paradigms.
Technical Contribution
The paper introduces a novel combination of MaxPro space-filling design with Bayesian optimization and PCE-based sensitivity analysis, enabling effective exploration and parameter reduction in high-dimensional, costly simulation environments. The workflow guarantees robust initial sampling, accurate surrogate modeling, and targeted parameter screening, resulting in faster convergence and improved design quality. Theoretical guarantees on space coverage and projection stability, along with empirical validation, differentiate this approach from existing methods. It also provides a scalable framework adaptable to various complex engineering systems.
Novelty
This work is the first to unify MaxPro design, Bayesian optimization, and PCE-based Sobol sensitivity analysis into an end-to-end turbine optimization workflow under limited data conditions. Unlike traditional random or low-discrepancy sampling, MaxPro ensures stable projection properties, crucial for effective sensitivity analysis. The combined use of surrogate models and parameter screening significantly reduces the number of expensive CFD evaluations needed, representing a major advancement in data-efficient high-dimensional optimization.
Limitations
- The current model assumes input independence; real-world dependencies require further methodological adjustments. The simplified CFD model used in early iterations omits phase change physics, potentially affecting accuracy. The approach's performance depends on proper tuning of MaxPro parameters and surrogate model hyperparameters. High-dimensional spaces still pose challenges despite dimension reduction, and scalability to very large parameter sets remains to be tested. Computational costs, although reduced, are still non-trivial for extremely complex models.
Future Work
Future directions include extending the framework to handle correlated inputs, multi-objective optimization, and real-time adaptive control. Integrating deep learning-based surrogate models could further improve scalability. Applying the workflow to other turbomachinery components or different physical phenomena, such as phase change effects, will broaden its applicability. Developing automated hyperparameter tuning and multi-fidelity strategies could enhance robustness and efficiency, making the approach more accessible for industrial deployment.
AI Executive Summary
Designing high-efficiency radial turbines traditionally relies on extensive high-fidelity CFD simulations, which are computationally expensive and limit exploration of the parameter space. This bottleneck hampers rapid development cycles, especially when physical phenomena like condensation further complicate simulations. To address this, the paper introduces an innovative workflow that combines advanced experimental design, surrogate modeling, and sensitivity analysis, enabling efficient optimization under scarce data conditions.
The core of the approach is the MaxPro design, which ensures that initial samples are well-distributed across the high-dimensional parameter space and maintain stability when projected onto lower dimensions. This property is critical for subsequent sensitivity analysis, which identifies the most influential parameters using Sobol indices computed via polynomial chaos expansion. By focusing the optimization on these key parameters, the workflow reduces the effective dimensionality, significantly decreasing the number of required CFD evaluations.
Bayesian optimization, leveraging Gaussian process models with an upper confidence bound acquisition function, iteratively refines the design by selecting promising candidates based on the surrogate’s predictions and uncertainties. The process alternates between exploring the full parameter space and exploiting the identified influential subspace, leading to rapid convergence. Experimental results demonstrate that, within just 330 CFD simulations, the turbine efficiency improved from 85.77% to 91.77%, a substantial gain over baseline methods.
This integrated methodology offers a practical solution for high-cost engineering design problems, balancing computational expense with optimization quality. Its modular structure allows adaptation to various physical systems and physical phenomena, making it a versatile tool for industry. The approach’s success paves the way for future enhancements, including multi-objective optimization, deep learning surrogates, and real-time adaptive control, promising a new paradigm for resource-efficient engineering design.
Deep Dive
Abstract
We propose a data-efficient workflow to optimize the efficiency of a radial turbine design under a strict budget of high-fidelity computational fluid dynamics simulations. Assuming anisotropic parameter impact, we use a maximum-projection initial experimental design to ensure space-filling and strong projection properties on low-dimensional subspaces. Bayesian optimization is performed using Gaussian process surrogates with an upper confidence bound acquisition function. In parallel, polynomial chaos expansions provide variance-based global sensitivity analysis metrics, which allow to identify a reduced subspace with the most influential parameters, wherein the optimization is continued. Turbine efficiency is increased from 85.77% initially to 91.77% at the end of the workflow, with a total budget of 330 simulations.