Efficient Multi-objective Aerodynamic Shape Optimization of 3D Supersonic Transport Using Proper Orthogonal Decomposition

Optimization problems in many industrial applications are very hard to solve. Many examples of them can be found in the design of aeronautical systems. In this field, the designer is frequently faced with the problem of considering not only a single design objective, but several of them, i.e., the designer needs to solve a Multi-Objective Optimization Problem (MOP). In aeronautical systems design, aerodynamics plays a key role in aircraft design, as well as in the design of propulsion system components, such as turbine engines. Thus, aerodynamic shape optimization is a crucial task, and has been extensively studied and developed. Multi-Objective Evolutionary Algorithms (MOEAs) have gained popularity in recent years as optimization methods in this area, mainly because of their simplicity, their ease of use and their suitability to be coupled to specialized numerical simulation tools. In this chapter, we will review some of the most relevant research on the use of MOEAs to solve multi-objective and/or multi-disciplinary aerodynamic shape optimization problems. In this review, we will highlight some of the benefits and drawbacks of the use of MOEAs, as compared to traditional design optimization methods. In the second part of the chapter, we will present a case study on the application of MOEAs for the solution of a multi-objective aerodynamic shape optimization problem.

A variable fidelity concept is introduced in the proper orthogonal decomposition (POD) based re-parameterization approach to efficiently solve multi-objective aerodynamic shape optimizations. The re-parameterization approach enables to extract dominant shape deformation modes from a database of good airfoil designs and to reduce the number of design variables. Our proposed variable fidelity approach is realized by utilizing low-fidelity functional evaluations to select the good airfoil designs. The validity of the proposed approach is investigated in a multi-objective aerodynamic shape optimization problem of 2D airfoil.

Surrogate-based method can dramatically reduce the number of expensive function evaluations in real-world multi- objective optimization problems (MOP). When the number of objectives is small, using surrogate models combined with expected hypervolume improvement (EHVI) infill sampling criterion (ISC) has been proved to be efficient to provide a set of solutions with good diversity and good proximity to the Pareto front (PF) in aerodynamic shape optimization. However, traditional hypervolume-based infilling strategies use only one kind of ISC to generate one or multiple sample points, the advantages of various kinds of ISC cannot be comprehensively utilized and the parallelization is not easy to implement. This paper proposes a combined multi-point infilling strategy based on Kriging models and develops an efficient global multi-objective constrained optimization method (EGMOCO) to solve multi- objective aerodynamic shape optimization with complex constraints. Multiple sample points are generated by using four ISC considering hypervolume at each iteration and then evaluated in parallel. Firstly, the performance of EGMOCO is compared with that of single criterion EHVI strategy on six benchmarks within the same computational budget to prove its effectiveness, and then EGMOCO is implemented in an aerodynamic shape optimization problem with complex constraints. The result shows that EGMOCO has good performance in balancing local exploitation and global exploration with faster convergence rate and high robustness, the whole PF can be fully explored in limited evaluations and the constraint handling is effective especially for real-world problems with complex and nonlinear constraints, the comprehensive aerodynamic performance of the airfoil is greatly improved. It can be confirmed that Kriging-based multi-objective optimization method combined with multi-point infilling strategy performs better than single infilling criterion EHVI, since different sample infilling criteria can complement with each other, both local exploitation and global exploration can be considered and well balanced.

The traditional multi-objective efficient global optimization (EGO) algorithms have been hybridized and adapted to solving the expensive aerodynamic shape optimization problems based on high-fidelity numerical simulations. Although the traditional EGO algorithms are highly efficient in solving some of the optimization problems with very complex landscape, it is not preferred to solve most of the aerodynamic shape optimization problems with relatively low-degree multi-modal design spaces. A new infill criterion encouraging more local exploitation has been proposed by hybridizing two traditional multi-objective expected improvements (EIs), namely, statistical multi-objective EI and expected hypervolume improvement, in order to improve their robustness and efficiency in aerodynamic shape optimization. Different analytical test problems and aerodynamic shape optimization problems have been investigated. In comparison with traditional multi-objective EI algorithms and a standard evolutionary multi-objective optimization algorithm, the proposed method is shown to be more robust and efficient in the tests due to its hybrid characteristics, easier handling of sub-optimization problems, and enhanced exploitation capability.

Numerical noise is an inevitable by-product of Computational Fluid Dynamics (CFD) simulations which can lead to challenges in finding optimum designs. This article draws attention to the issue, illustrating the difficulties it can cause for road vehicle aerodynamics simulations. Firstly a benchmark problem is used to assess a range of turbulence models and grid types. Large noise amplitudes up to 22% are evident for solutions computed on unstructured tetrahedral grids whereas computations on hexahedral and polyhedral grid structures exhibit substantially less noise. The Spalart Allmaras turbulence model is shown to be far less susceptible to noise levels than two other commonly-used models for this application. Secondly, multi-objective aerodynamic shape optimization is applied to a fairing for a practical road vehicle which is parameterised in terms of three design variables. Moving Least Squares (MLS) metamodels are constructed from 50 high-fidelity CFD solutions for two objective functions. Subsequent optimization is successful for the first objective, however numerical noise levels in excess of 7% give rise to difficulties for the second one. A revision to the problem leads to success and the construction of a small Pareto front. Further analysis underlines the inherent capability of MLS metamodels in dealing with noisy CFD responses.

Expedited constrained multi-objective aerodynamic shape optimization by means of physics-based surrogates

Constraints handling in Nash/Adjoint optimization methods for multi-objective aerodynamic design

In this paper, a numerical optimization of a radial turbine impeller is developed, which combines popular techniques such as artificial neural networks, genetic algorithm, database and CFD analysis tools. Multi-objective aerodynamic optimization is performed by using software FINETM/Design 3D. The performance parameters in the terms of total-to-static efficiency, expansion ratio are defined as optimized objectives. The performance of the new impeller is compared to the original one at the design point as well as at off-design points with a significant performance improvement. The design method provided very good predictions leading to an efficiency increase of 8.01 percent and an expansion ratio increase of 2.76 percent. An analysis of the CFD results is also discussed within the original and the new impeller. The whole results indicate that the multi-objective aerodynamic optimization process can be used in practical terms.

In this paper the use of Genetic Algorithms for multi objective optimisation in aerodynamic optimisation is outlined. After a review of existing GA methodologies the operators considered at present the most promising one are described. A simple mathematical test is used for preliminary algorithmic perfomance while in more applicative cases the pressure reconstruction problem of two conflicting aerodynamic profiles is used as benchmark. A full potential transonic solver is at first used showing the performances of the optimisation algorithm employed while final results are obtained using a commercial Navier-Stokes solver with k-e turbulence modelling to reconstruct the geometry of two airfoils working at Mach=0.2 Re=5E6 and Mach=0.77 Re=19.6E6. Even thogh the test case presented might not have a practical application, it shows that direct multi objective optimisation with Navier Stokes solver can be faced with GA.

This paper presents a novel methodology for realizing a computationally efficient multi-objective design optimization (CE-MODO) of switched reluctance motors (SRMs). Existing MODO approaches rely heavily on static and dynamic finite element analysis (FEA) to evaluate the electromagnetic performance parameters, which, despite their accuracy, incur significant computational costs. While analytical models reduce the dependence on static FEA, their limited accuracy constrains their applicability. Similarly, existing machine learning methods are inadequate for mapping multiple geometric parameters (GPs) to static characteristics across varied SRM designs. To overcome these limitations, this study proposes a novel integrated approach that combines K-means clustering with an artificial neural network (ANN) to enable accurate and efficient prediction of static characteristics. This technique led to a 52.16% decrease in the total computation time for determining the static characteristics of the SRM designs. Further, dynamic performance is evaluated using a MATLAB/Simulink-based SRM drive model, offering a computationally lightweight alternative to dynamic FEA. The proposed CE-MODO framework is applied to a four-phase 8/6 SRM topology designed for an electric three-wheeler, with average torque and electromagnetic losses as optimization objectives. Optimization is carried out by coupling the nondominated sorting genetic algorithm II (NSGA-II) with Kriging surrogate models, significantly reducing the computational load. The proposed methodology achieved an 11.01% improvement in average torque and a 4.56% reduction in electromagnetic losses compared to the initial design. The FEA models corresponding to both static and dynamic analyses employed in this study are further validated through experimental testing on a fabricated SRM prototype.

Intelligent sensor management is generally required for efficient and accurate data processing when the multi-sensor system is used for multi-target tracking (MTT). However, this is theoretically and computationally challenging. To deal with this problem, we propose a novel sensor management approach based on efficient multi-objective optimization for MTT under the framework of partially observed Markov decision process. The multi-Bernoulli filter is used in conjunction with two objective functions. To simplify the multi-objective optimization problem, we use the Euclidean distance (ED) between the feasible and utopian solution vectors as a measure of the objectives and then sequentially select sensors from the candidates. For the selected sensors, we rank them according to the obtained ED measure and implement the iterated-corrector fusion scheme after the ranking. Numerical studies demonstrate the effectiveness and efficiency of our approach in multi-sensor MTT scenarios.

Externally mounted sensors on autonomous vehicles can significantly affect their aerodynamic performance, especially under crosswind conditions. To improve the crosswind aerodynamic characteristics, a multi-objective aerodynamic optimization framework was developed for the shape optimization of externally mounted sensors. The Reynolds-averaged Navier–Stokes equations, coupled with the realizable k−ε turbulence model, were employed to simulate the turbulent flow, and the numerical method was validated through wind tunnel experiments. Six deformation parameters were selected as design variables, and the free-form deformation technique was applied to achieve smooth mesh deformation. Design samples were generated using the optimal Latin hypercube sampling method to analyze the relationships between the design variables and the aerodynamic responses and to identify the dominant influencing factors. Minimizing the aerodynamic drag and lateral force under crosswind conditions was defined as the optimization objective. The Non-Dominated Sorting Genetic Algorithm II based on the Kriging surrogate model was employed to optimize the sensor shapes, yielding a Pareto-optimal front. The optimal model selected from the Pareto-optimal front was compared with the baseline model. Under crosswind conditions, the drag and lateral force coefficients are reduced by 5.22% and 4.58%, respectively, demonstrating the effectiveness of the proposed optimization framework in improving the crosswind aerodynamic performance.

A computationally efficient procedure for multiobjective design optimization with variable-fidelity models and response surface surrogates is presented. The proposed approach uses the multiobjective evolutionary algorithm that works with a fast surrogate model, obtained with kriging interpolation of the low-fidelity model data enhanced by space-mapping correction exploiting a few high-fidelity training points. The initial Pareto front generated by multiobjective optimization of the surrogate using the multiobjective evolutionary algorithm can be iteratively refined by local enhancements of the surrogate model. The latter are realized with a space-mapping response correction based on a limited number of high-fidelity training points allocated along the initial Pareto front. The proposed method allows us to obtain, at a low computational cost, a set of designs representing tradeoffs between the conflicting objectives. The current approach is illustrated using examples of airfoil design: one in transonic flow, involving aerodynamics tradeoffs; and another one in low-speed flow, involving tradeoffs between the aerodynamic and the aeroacoustic performances.

A chaos ant colony optimization algorithm for continuous domain is proposed based on chaos optimization theory and ant colony optimization algorithm. The searching abilities of optimization algorithms with different coding methods are compared, and the results indicate that the proposed algorithm has better performance than genetic algorithm and particle swarm optimization algorithm. Based on the non-dominated sorting concept and niching method, a multi-objective chaos ant colony optimization algorithm is also constructed and numerical results show that the improved algorithm performs well at solving multi-objective optimization problems. An optimal support vector regression model based on radial basis kernel function is developed for the small sample size and nonlinear characteristics of streamlined head optimization. On the basis of the above work, a multi-objective optimization design for the aerodynamic head shape of high-speed train is developed using a modified vehicle modeling function parametric approach. The optimization results demonstrate that the new optimization design method has exceptional searching abilities and high prediction accuracy. After optimization, the aerodynamic drag of the simplified train with three carriages is reduced by 10.52% and the aerodynamic lift of the tail car is reduced by 35.70%. The optimization approach proposed in the present paper is simple yet efficient and sheds light on the engineering design of aerodynamic shape of high-speed trains.

In the aerodynamic shape design, the drag prediction has always been an extremely challenging mission for the exploration of a configuration. As for the more complex configurations, it is especially desired to the availability of a highly accurate and reliable aerodynamic numerical solution. For improving the drag prediction accuracy and promoting the aerodynamic shape designs, firstly, the characteristics of drag prediction based on far-field drag method and near-field drag method is analyzed and compared. Also, the merits and demerits of defining axial velocity defect with the current main far-field drag prediction approaches is summarized, which promotes the building of the improved method of axial velocity defect and the improved far-field drag prediction and decomposition approach. Moreover, during the establishment of the drag decomposition method, it is necessary to judge and decide on the selection of the drag region. Therefore, the discussions on the sensitivity of the relevant parameters are fulfilled. Furthermore, based on the far-field drag prediction and decomposition method constructed, the aerodynamic performance research of Common Research Model wing-body configuration is launched. The results show that it can effectively observe and analyze the changes in drag components, their impact on the total drag and the contribution percentage. Finally, combining the far-field drag prediction and decomposition method proposed in this paper with a gradient-based aerodynamic shape optimization design system, the aerodynamic shape optimization designs are studied with CRM wing-body configuration. The results can not only directly analyze the detailed change of the visualized drag region, but also can obtain the more accurate total drag and lift-to-drag ratio of the optimized configuration by removing the spurious drag.