Multi-objective Aerodynamic Optimization Research Articles

Multi-Objective Hybrid Algorithm Integrating Gradient Search and Evolutionary Mechanisms

The current multi-objective evolutionary algorithm (MOEA) has attracted much attention because of its good global exploration ability, but its local search ability near the optimal value is relatively weak, and for optimization prob lems with large-scale decision variables, the number of populations and iterations required by MOEA are very large, so the optimization efficiency is low. Gradient-based optimization algorithms can overcome these problems well, but they are difficult to be applied to multi-objective problems (MOPs). Therefore, this paper introduced random weight function on the basis of weighted average gradient, developed multi-objective gradient operator, and combined it with non-dominated genetic algorithm based on reference points (NSGA- III) proposed by Deb in 2013 to develop multi-objective optimization algorithm (MOGBA) and multi-objective Hybrid Evolutionary algorithm (HMOEA). The latter greatly enhances the local search capability while retaining the good global exploration capability of NSGA-III. Numerical experiments show that HMOEA has excellent capture capability for various Pareto formations, and the efficiency is improved by times compared with typical multi-objective algorithms. And further HMOEA is applied to the multi-objective aerodynamic optimization problem of the RAE2822 airfoil, and the ideal Pareto front is obtained, indicating that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.

A parallel variable-fidelity algorithm for efficient constrained multi-objective aerodynamic design optimization

Modern aerodynamic design optimization aims to discover optimal configurations using computational fluid dynamics under complex flow conditions, which is a typical expensive multi-objective optimization problem. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) combined with efficient global optimization is a promising method but requires enhanced efficiency and faces limitations in its application to multi-objective aerodynamic design optimization (MOADO). To address the issues, an efficient parallel MOEA/D assisted with variable-fidelity optimization (VFO) is proposed for solving MOADO, called the MOEA/D-VFO algorithm. Variable-fidelity surrogates are built for objectives and constraints, achieving higher accuracy using fewer high-fidelity samples and a great number of low-fidelity samples. By retaining more good candidates, the sub-optimization problems defined by decomposing original objectives are capable of discovering more favorable samples using MOEA/D, which prompts optimization convergence. A constraint-handling strategy is developed by incorporating the probability of feasibility functions in the sub-optimizations. The selection of new samples for parallel evaluation is improved by filtering out poor candidates and selecting effective promising samples, which improves the feasibility and diversity of solved Pareto solutions. A Pareto front (PF) can be efficiently found in a single optimization run. The proposed approach is demonstrated by four analytical test functions and verified by two aerodynamic design optimizations of airfoils with and without constraints, respectively. The results indicate that the MOEA/D-VFO approach can greatly improve optimization efficiency and obtain the PF satisfying constraints within an affordable computational budget.

Prescreening surrogate-model-assisted multi-objective aerodynamic optimization design of highly loaded axial compressor in heavy-duty gas turbine

To address the challenges of numerous design variables and high evaluation costs in the aerodynamic optimization of advanced highly-loaded axial compressors, this paper presents an axial compressor aerodynamic optimization platform based on directly manipulated free-form deformation (DFFD) parameterization method, a data-driven multi-objective differential evolution optimizer, and computational fluid dynamics. The DFFD method allows for direct geometric manipulation of the target compressor, enabling efficient parameterization of the blades and flow path and reducing the number of design variables. A prescreening surrogate-model-assisted multi-objective differential evolution (Pre-MODE) optimizer is developed to obtain competitive solutions within a limited number of iterations. The surrogate model in Pre-MODE conducts real evaluations only on selected individuals in each generation, thereby reduce evaluation costs while ensuring prediction accuracy. Additionally, a parallel task management system is integrated to improve optimization efficiency. To verify the effectiveness of the optimization platform, a 1.5-stage highly-loaded compressor is aerodynamically optimized. After optimization, the adiabatic efficiency at the design point and the surge margin are increased by 2.42% and 9.04%, respectively. These results confirm the effectiveness and speed of the aerodynamic optimization platform, promoting the establishment of an integrated optimization design system for axial compressors.

A stacking-based ensemble prediction method for multiobjective aerodynamic optimization of high-speed train nose shape

A stacking-based ensemble prediction method is proposed in order to improve the efficiency and accuracy of aerodynamic shape optimization. This can be divided into a two-level model. The first-level model uses various base learners to predict the training dataset and obtain various combinations of predictions. In the second-level model, the meta-learner is trained using various combinations of predictions as inputs and the true response values as outputs. The RMSE and R-Square metrics results show that the performance metrics of the stacked models are significantly better than those of the original surrogate models, except for the stacked RBFNN model. The stacked Kriging model and LSSVR model achieved the best results with RMSE and R-Square index values of 0.0039 and 0.8418 for aerodynamic drag coefficient, respectively. The stacked Kriging model, RBFNN model, and LSSVR model achieved the best results with RMSE and R-Square index values of 0.0024 and 0.76 for aerodynamic lift coefficient, respectively. Four state-of-the-art multiobjective optimization algorithms are used to perform the optimization process. The results of hypervolume and Pareto fronts demonstrate the effectiveness of the selected FDV-NSGAII algorithm. After optimization, the drag and lift coefficients before and after optimization are reduced by 1.9% and 12.7%, respectively.

Manifold-guided multi-objective gradient algorithm combined with adjoint method for supersonic aircraft shape design

The aerodynamic design of supersonic aircraft necessitates the comprehensive consideration of multiple conflicting design objectives and multi-disciplinary characteristics. However, the efficiency of heuristic algorithms in solving multi-objective aerodynamic problems significantly decreases with the increase in the number of design variables and objectives. Although gradient-based adjoint optimization methods can eliminate the constraints of design variables on aerodynamic optimization and have high optimization efficiency, they are prone to getting stuck in local optima and are difficult to apply in multi-objective optimization. To overcome these shortcomings, a manifold-guided multi-objective gradient-based algorithm (MG-MOGBA) is proposed. This algorithm enhances the optimization efficiency of the algorithm by coupling the multi-objective gradient operator with the predicted Pareto front (PF) manifold structure to guide the population search direction and reduce the search space. A multi-objective aerodynamic optimization framework based on the discrete adjoint method is developed to automate the aerodynamic optimization process. Test functions and airfoil optimization results confirm that the proposed algorithm achieves superior results with fewer iterations and is more efficient than heuristic algorithms. The four-objective supersonic civil aircraft example demonstrates that the algorithm can effectively handle high-dimensional multi-objective aerodynamic optimization problems. A potential equilibrium solution increased the cruise factor by 17.5% and 12.8% under supersonic and transonic conditions respectively, reduced the maximum overpressure of the sonic boom by 25.1%, and decreased the root bending moment by 20.3%. Overall, MG-MOGBA can efficiently solve high-dimensional multi-objective aerodynamic optimization problems and has good scalability for the dimensions of design objectives and variables.

Multi-objective aerodynamic optimization of expansion–deflection nozzle based on B-spline curves

An expansion–deflection nozzle (EDN) is an altitude-compensated nozzle that can accommodate a wide range of nozzle pressure ratio (NPR) variations. An EDN design with good thrust performance under both high- and low-NPR conditions can effectively improve the launch capability of the vehicle. In this study, a multi-objective aerodynamic optimization design is developed considering the performance of the EDN in both open and closed wake modes. The design method of the outer wall and pintle of the EDN is developed using B-spline curves. The design variables are the coordinates of the control points of the curves, and the objective functions are the thrust efficiencies of the EDN at NPRs of 30 and 400. The nozzle thrust is obtained using a Reynolds Averaged Navier–Stokes (RANS) equation solver and validated by experimental results. A radial basis function neural network and a non-dominated sorting genetic algorithm II (NSGA-II) are used to construct the surrogate model and search for the Pareto front, respectively. The relationship between the nozzle contour geometry and the nozzle thrust characteristics of the four optimised individuals on the Pareto front is discussed and analysed. The results demonstrate the effectiveness of the multi-objective optimization design for an EDN. One of the optimized designs improved the thrust efficiency at NPR = 30 by 3.5 % while improving the thrust efficiency at NPR = 400 by 0.6 %. Moreover, to ensure superior performance of the EDN in both operating modes, the nozzle length and pintle ending angle must be designed as a compromise, whereas a larger nozzle exit angle is favoured for both conditions. This study demonstrates the potential of the B-spline method for nozzle optimization design.

Aerodynamic optimization of NACA 0012 airfoils with attached Gurney flap in the rarefied gas flow

The aerodynamic optimization of a Gurney flap attached to the NACA 0012 airfoil in rarefied gas flow is studied in this study. In order to investigate the effects of Gurney flap geometry (height, mounting angle, and mounting location) and angle of attack on the aerodynamic characteristics of the airfoil in the rarefied gas flow, the flow fields around NACA 0012 airfoils with Gurney flap attached are simulated by using the direct simulation Monte Carlo method. Furthermore, the multi-objective aerodynamic optimization of the airfoil with Gurney flap is performed at the single design point, and the Pareto front is obtained. Based on the benchmark configuration (obtained from the Pareto front), aerodynamic optimization by controlling the mounting angle of the Gurney flap and the angle of attack is investigated over a wide range of Mach numbers (ranging from 2 to 4) and Knudsen numbers (ranging from 0.024 to 0.24) by constructing an artificial neural network model. The results show that through optimization, the lift-to-drag ratio of the airfoil is increased by up to 29.25% under the combination of different Mach numbers and Knudsen numbers, which significantly improves the aerodynamic characteristics.

An Improved Multi-Objective Particle Swarm Optimization Method for Rotor Airfoil Design

In this study, a multi-objective aerodynamic optimization is performed on the rotor airfoil via an improved MOPSO (multi-objective particle swarm optimization) method. A database of rotor airfoils containing both geometric and aerodynamic parameters is established, where the geometric parameters are obtained via the CST (class shape transformation) method and the aerodynamic parameters are obtained via CFD (computational fluid dynamics) simulations. On the basis of the database, a DBN (deep belief network) surrogate model is proposed and trained to accurately predict the aerodynamic parameters of the rotor airfoils. In order to improve the convergence rate and global searching ability of the standard MOPSO algorithm, an improved MOPSO framework is established. By embedding the DBN surrogate model into the improved MOPSO framework, multi-objective and multi-constraint aerodynamic optimization for the rotor airfoil is performed. Finally, the aerodynamic performance of the optimized rotor airfoil is validated through CFD simulations. The results indicate that the aerodynamic performance of the optimized rotor airfoil is improved dramatically compared with the baseline rotor airfoil.

Multi-fidelity and multi-objective aerodynamic short nacelle shape optimisation under different flight conditions

AbstractThroughout the course of a flight mission, a range of aerodynamic conditions, including design-point conditions and off-design conditions, are encountered. As the bypass ratio increases and the fan-pressure ratio decreases to reduce the engine’s specific fuel consumption, the engine diameters increase, which results in an increase in the nacelle weight and overall drag. To reduce its weight and drag, a shorter nacelle with a length-to-diameter ratio $L/D = 0.35$ is investigated. In this study, an adaptive cokriging-based multi-objective optimisation method is applied to the design of a short aero-engine nacelle. Two nacelle performance metrics were employed as the objective functions for the optimisation routine. The cruise drag coefficient is evaluated under cruise conditions, whereas the intake pressure recovery is evaluated under takeoff conditions. The cokriging metamodel are refined using an effective infilling strategy, where high-fidelity samples are infilled via the modified Pareto fitness, and low-fidelity samples are infilled via the Pareto front. By combining parameterised geometry generation, automated mesh generation, numerical simulations, surrogate model construction, Pareto front exploration based on the non-dominated sorting genetic algorithm-II and sample infilling, an integrated multi-objective optimisation framework for short aero-engine nacelles is developed. Two-objective and three-objective test functions are used to validate the effectiveness of the proposed framework. After the optimisation process, a set of non-dominated nacelle designs is obtained with better aerodynamic performance than the original design, demonstrating the effectiveness of the optimisation framework. Compared with the kriging-based optimisation framework, the cokriging-based optimisation framework outperforms the single-fidelity method with a higher hypervolume value at the same number of iteration loops.

Multi-objective aerodynamic shape design optimization of canard-controlled missiles for reducing induced roll

Multi-objective aerodynamic shape design optimization of canard-controlled missiles for reducing induced roll

Multi-Objective Aerodynamic and Aeroelastic Coupled Design Optimization Using a Full Viscosity Discrete Adjoint Harmonic Balance Method

Abstract With increasing requirements for high-loading and high-efficiency turbomachines, blades become thinner and thinner and thus design optimizations considering both aerodynamic performances and aeroelastic stability become more and more necessary. In this study, a full viscosity discrete adjoint harmonic balance solver has been developed using algorithmic differentiation (AD), verified by a discrete linear solver based upon duality property, and then adopted to perform multi-disciplinary coupled design optimizations. To this end, a framework of multi-objective adjoint design optimizations has been developed to improve both aerodynamic performances and the aeroelastic stability of turbomachinery blades. This framework is divided into two steps: aeroelastic design initialization and aerodynamic Pareto front determination. First, the blade profiles are optimized to improve the aeroelastic stability only and constrain the variations of aerodynamic performances. Second, the optimized blade profiles in the first step are used as the initial ones and then further optimized with the objective function of aerodynamic parameters and the constraints of aeroelastic parameters. The effectiveness of the multi-objective design optimization method is demonstrated by comparing the optimization results with those from a single-objective aerodynamic and aeroelastic coupled design optimization method. The results from the transonic NASA Rotor 67 subjected to a hypothetical vibration mode show that the multi-objective coupled design optimization method is capable of improving performances in both disciplines.

Multi-objective aerodynamic optimization of an axisymmetric variable-geometry inlet with a Mach 5 design point

The inlet is a critical component of the air-breathing system of an aircraft engine and an appropriate inlet design can address the issue of aerodynamic contradiction between low and high Mach numbers, restricting aircraft flight over a wide speed range. Therefore, in this study, an axisymmetric variable-geometry inlet with a Mach 5 design point was designed. A multi-point multi-objective optimization design, based on the Kriging surrogate model and non-dominated sorting genetic algorithm-II algorithm, was performed. Wind tunnel tests and numerical simulations were conducted to investigate the inlet performance and flow field details. The steady-state pressure distribution was recorded, and shadowgraph images were obtained simultaneously to comprehensively evaluate the inlet performance. The experimental and numerical results indicate that the design and optimization methods of the inlet are effective. The inlet operated appropriately and stably over a wide range of speeds, and the total pressure recovery (TPR) coefficient reaches 0.421 at the design point. The optimization results show that a 21.36% gain in the TPR coefficient at Ma = 3.0 was achieved at the cost of a 2.44% loss of total pressure recovery at Ma = 5.0. It is also beneficial in terms of the total pressure distortion at Ma = 5.0, which is reduced by 6.54%. This indicates that the inlet design and optimization framework developed in this study is promising for wide use in practical engineering applications.

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

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

A Fast and Efficient Method for Multiobjective Aerodynamic Optimization of a Civil Aircraft Fuselage

This study presents a new method for aerodynamic optimization of a civil aircraft fuselage. Typically, the fuselage is designed for minimum drag force at cruise conditions, which is essential for determining the flight cost. Evolutionary optimization methods, as a powerful tool, require the accurate computations of flows around several hundreds of candidate geometries, which in turn are too costly and time-consuming. One strategy is to use two-dimensional simulations that reduce the computational cost by at least one order of magnitude. This approach was applied in the current work, and the results were obtained with the aim of minimizing the drag coefficient and maximizing the lift coefficient. A genetic algorithm (GA) was used for shape optimization, and the objective function evaluation was carried out using computational fluid dynamics (CFD). A fuselage shape parameterization method is presented that accounts for important flow features. The 150-seat aircraft model designed in Amirkabir University of Technology was considered as a reference body. In the first step, the optimization is carried out for the single objective of minimizing the drag coefficient. Then, the multiobjective optimization is performed with the simultaneous drag coefficient minimization and lift coefficient maximization. Finally, the two-dimensional (2D) side view of the optimum fuselages is used for generation of the corresponding three-dimensional (3D) geometry. The results show that such 3D optimum fuselage reduced the drag coefficient by about 11% while increasing the lift coefficient by 29% in comparison with the original geometry.

Comparing Gradient-Free and Gradient-Based Multi-Objective Optimization Methodologies on the VKI-LS89 Turbine Vane Test Case

Abstract The present paper addresses the multi-objective aerodynamic shape optimization of the two-dimensional LS-89 turbine cascade. The objective is to minimize the entropy generation at subsonic and transonic flow conditions while maintaining the same flow turning. Nineteen design variables are used to parametrize the geometry. The optimization problem is used to compare two major classes of optimization algorithms and at the same time deduce if this problem has multiple local solutions or one global optimum. A first optimization strategy uses a gradient-based Sequential Quadratic Programming (SQP) algorithm. This SQP algorithm allows to directly handle the non-linear constraints during the optimization process. An adjoint solver is used for computing the sensitivities of the flow quantities with respect to the design variables, such that the additional gradient computational cost is nearly independent of the number of design variables. In addition, the same optimization problem is performed with a gradient-free-metamodel assisted-evolutionary algorithm. A comparison of the two Pareto-fronts obtained with both methods shows that the gradient-based approach allows to find the same optimum at a reduced computational cost. Moreover, the results suggest that the considered optimization problem is uni-modal. In other terms, it is characterized by a single optimal solution.

Multi-objective aerodynamic optimization design of high-speed maglev train nose

PurposeThe nose length is the key design parameter affecting the aerodynamic performance of high-speed maglev train, and the horizontal profile has a significant impact on the aerodynamic lift of the leading and trailing cars Hence, the study analyzes aerodynamic parameters with multi-objective optimization design.Design/methodology/approachThe nose of normal temperature and normal conduction high-speed maglev train is divided into streamlined part and equipment cabin according to its geometric characteristics. Then the modified vehicle modeling function (VMF) parameterization method and surface discretization method are adopted for the parametric design of the nose. For the 12 key design parameters extracted, combined with computational fluid dynamics (CFD), support vector machine (SVR) model and multi-objective particle swarm optimization (MPSO) algorithm, the multi-objective aerodynamic optimization design of high-speed maglev train nose and the sensitivity analysis of design parameters are carried out with aerodynamic drag coefficient of the whole vehicle and the aerodynamic lift coefficient of the trailing car as the optimization objectives and the aerodynamic lift coefficient of the leading car as the constraint. The engineering improvement and wind tunnel test verification of the optimized shape are done.FindingsResults show that the parametric design method can use less design parameters to describe the nose shape of high-speed maglev train. The prediction accuracy of the SVR model with the reduced amount of calculation and improved optimization efficiency meets the design requirements.Originality/valueCompared with the original shape, the aerodynamic drag coefficient of the whole vehicle is reduced by 19.2%, and the aerodynamic lift coefficients of the leading and trailing cars are reduced by 24.8 and 51.3%, respectively, after adopting the optimized shape modified according to engineering design requirements.

Multi-Objective Aerodynamic Optimization of a High-Speed Train Head Shape Based on an Optimal Kriging Model

An optimal Kriging surrogate model based on a 5-fold cross-validation method and improved artificial fish swarm optimization is developed for improving the aerodynamic optimization efficiency of a high-speed train running in the open air. The developed optimal Kriging model is compared with the original Kriging model in two test sample points, and the prediction errors are all reduced to within 5%. Thus, the optimal Kriging model is selected for use in each iteration to approximate the CFD simulation model of a high-speed train in subsequent optimization. After that, the strong Pareto evolutionary algorithm II (SPEA2) is adopted to obtain a series of Pareto-optimal solutions. Based on the above work, a multi-objective aerodynamic optimization design for the head shape of a high-speed train is performed using a free-form deformation (FFD) parameterization approach. After optimization, the aerodynamic drag coefficient of the head car and the aerodynamic lift coefficient of the tail car are reduced by 5.2% and 32.6%, respectively. The results demonstrate that the optimization framework developed in this paper can effectively improve optimization efficiency.

Multi-objective aerodynamic optimization of two-dimensional hypersonic forebody-inlet based on the heuristic algorithm

Nowadays, the forebody-inlet integrated design optimization becomes more and more important in improving the performance of hypersonic vehicles. And several achievements have been made to improve the performance of the two-dimensional hypersonic forebody-inlet integrated vehicle. However, all these works are faced with many defects. For example, the work adopting the gradient algorithm is easy to be trapped in the local optimum solution. The data-driven optimization method is with a low level of accuracy. Moreover, the geometry parameterization methods adopted in those optimization procedures are hardly implemented to complex configurations. In this study, a global-searching multi-objective optimization framework is proposed to overcome these limitations and to carry out multi-objective optimization of the two-dimensional hypersonic forebody-inlet shape. The framework includes the Free-Form Deformation (FFD) method, the mesh deformation method, the high-accuracy Reynolds Averaged Navier-Stokes (RANS) solver, and the global-searching heuristic algorithm. Results obtained by this framework indicate that the total pressure recovery coefficient, the pressure rising ratio, and the mass flow coefficient are increased by 3.97%, 9% and 7.35%, respectively, which suggests that the optimization framework proposed in this study is promising to be widely used in practical engineering applications.

Multi-objective aerodynamic shape optimization of a streamlined high-speed train using Kriging model

Multi-objective aerodynamic shape optimization of a streamlined high-speed train using Kriging model

Multi-objective aerodynamic optimization design of variable camber leading and trailing edge of airfoil

Variable camber is an effective method for improving the flight efficiency of large aircraft, and has attracted the attention of researchers. This work focused on the optimization of a variable camber airfoil. First, the influences of the variable camber of the leading and trailing edges on the airfoil aerodynamic performance were investigated using a computational fluid dynamics numerical simulation. An initial database was established for a deep neural network. Second, an iterative algorithm was constructed to optimize the variable camber airfoil in terms of the rotation angle of the leading edge, deflection position of the leading edge, rotation angle of the trailing edge, and deflection position of the trailing edge. A genetic algorithm was used in each iteration to maximize the lift coefficient and lift-to-drag ratio, as predicted using a deep neural network (DNN). The optimal results were validated using Fluent. If the DNN result approximated the Fluent results, the iterative process was stopped. Otherwise, the Fluent results were inserted into the database to update the DNN prediction model. The optimization results showed that the lift-to-drag ratio of the 2D airfoil could be increased by more than 14 when the angle of attack was less than 8° relative to the original airfoil. Furthermore, to validate the 2D optimal results, the optimized 2D airfoil was stretched into 3D, and it was discovered that the aerodynamic performance trend of the 3D airfoil with respect to the angle of attack was basically the same as that of the 2D airfoil. In addition, the corresponding 3D airfoil improved the aerodynamic performance and reduced the noise at a high frequency (by approximately 16 dB). In contrast, the noise in the low and medium frequencies remained unchanged. Therefore, the optimization method and results can provide a reference for the aerodynamic design and acoustic design of large civil aircraft wings.