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Variable-fidelity optimization with design space reduction

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Chinese Journal of Aeronautics 2013年第4期26卷 841-849页

作者： Mohammad Kashif Zahir gao zhenghong School of Aeronautics Northwestern Polytechnical University

Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity （LF） model provides physics-based approximation of the high-fidelity （HF） model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.

关键词： Airfoil optimization Curse of dimensionality Design space reduction Genetic algorithms Kriging Surrogate models Surrogate update strategies Variable fidelity

Research on multi-fidelity aerodynamic optimization methods

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Chinese Journal of Aeronautics 2013年第2期26卷 279-286页

作者： Huang Likeng gao zhenghong Zhang Dehu National Key Laboratory of Aerodynamic Design and Research Northwestern Polytechnical University

Constructing high approximation accuracy surrogate model with lower computational cost has great engineering significance. In this paper, using co-Kriging method, an efficient multi-fidelity surrogate model is constructed based on two independent high and low fidelity samples. Co-Kriging method can use a greater quantity of low-fidelity information to enhance the accuracy of a surrogate of the high-fidelity model by modeling the correlation between high and low fidelity model, thus computational cost of building surrogate model can be greatly reduced. A wing-body problem is taken as an example to compare characteristics of co-Kriging multi-fidelity （CKMF） model with traditional Kriging based multi-fidelity （KMF） model. A sampling convergence of the CKMF model and the KMF model is conducted, and an appropriate sampling design is selected through the sampling convergence analysis. The results indicate that CKMF model has higher approximation accuracy with the same high-fidelity samples, and converges at less high-fidelity samples. A wing-body drag reduction optimization design using genetic algorithm is implemented. Satisfying design results are obtained, which validate the feasibility of CKMF model in engineering design.

关键词： Aerodynamics Co-Kriging Multi-fidelity Optimization Surrogate model

A new grid deformation technology with high quality and robustness based on quaternion

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Chinese Journal of Aeronautics 2014年第5期27卷 1078-1085页

作者： Huang Jiangtao gao zhenghong Wang Chao China Aerodynamics Research and Development Center National Key Laboratory of Aerodynamic Design and Research Northwestern Polytechnical University

Quality and robustness of grid deformation is of the most importance in the field of aircraft design, and grid in high quality is essential for improving the precision of numerical simulation. In order to maintain the orthogonality of deformed grid, the displacement of grid points is divided into rotational and translational parts in this paper, and inverse distance weighted interpolation is used to transfer the changing location from boundary grid to the spatial grid. Moreover, the deformation of rotational part is implemented in combination with the exponential space mapping that improves the certainty and stability of quaternion interpolation. Furthermore, the new grid deformation technique named ‘‘layering blend deformation＇＇ is built based on the basic quaternion technique, which combines the layering arithmetic with transfinite interpolation（TFI） technique. Then the proposed technique is applied in the movement of airfoil, parametric modeling, and the deformation of complex configuration, in which the robustness of grid quality is tested. The results show that the new method has the capacity to deal with the problems with large deformation, and the ‘‘layering blend deformation＇＇ improves the efficiency and quality of the basic quaternion deformation method significantly.

关键词： Basis quaternion grid deformation Exponential mapping Inverse distance weighting(IDW) Lie algebra space Transfinite interpolation

Flight dynamics characteristics of canard rotor/wing aircraft in helicopter flight mode

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Chinese Journal of Aeronautics 2019年第7期32卷 1577-1587页

作者： Honggang gao Ao HE zhenghong gao Yang NA Yangping DENG School of Aeronautics Northwestern Polytechnical University

The aerodynamic layout of the Canard Rotor/Wing(CRW) aircraft in helicopter flight mode differs significantly from that of conventional helicopters. In order to study the flight dynamics characteristics of CRW aircraft in helicopter mode, first, the aerodynamic model of the main rotor system is established based on the blade element theory and wind tunnel test results. The aerodynamic forces and moments of the canard wing, horizontal tail, vertical tail and fuselage are obtained via theoretical analysis and empirical formula. The flight dynamics model of the CRW aircraft in helicopter mode is developed and validated by flight test data. Next, a method of model trimming using an optimization algorithm is proposed. The flight dynamics characteristics of the CRW are investigated by the method of linearized small perturbations via Simulink. The trim results are consistent with the conventional helicopter characteristics, and the results show that with increasing forward flight speed, the canard wing and horizontal tail can provide considerable lift,which reflects the unique characteristics of the CRW aircraft. Finally, mode analysis is implemented for the linearized CRW in helicopter mode. The results demonstrate that the stability of majority modes increases with increasing flight speed. However, one mode that diverges monotonously,and the reason is that the CRW helicopter mode has a large vertical tail compared to the conventional helicopter. The results of the dynamic analysis provide optimization guidance and reference for the overall design of the CRW aircraft in helicopter mode, and the model developed can be used for control system design.

关键词： Canard rotor/wing aircraft Dynamics analysis Flight dynamics Helicopter Linearization Model building

Aerodynamic design optimization of nacelle/pylon position on an aircraft

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Chinese Journal of Aeronautics 2013年第4期26卷 850-857页

作者： Li Jing gao zhenghong Huang Jiangtao Zhao Ke National Key Laboratory of Aerodynamic Design and Research Northwestern Polytechnical University

The arbitrary space-shape free form deformation （FFD） method developed in this paper is based on non-uniform rational B-splines （NURBS） basis function and used for the integral parameterization of nacelle-pylon geometry. The multi-block structured grid deformation technique is established by Delaunay graph mapping method. The optimization objects of aerodynamic characteristics are evaluated by solving NavierStokes equations on the basis of multi-block structured grid. The advanced particle swarm optimization （PSO） is utilized as search algorithm, which com-bines the Kriging model as surrogate model during optimization. The optimization system is used for optimizing the nacelle location of DLR-F6 wing-body-pylon-nacelle. The results indicate that the aerodynamic interference between the parts is significantly reduced. The optimization design system established in this paper has extensive applications and engineering value.

关键词： Delaunay graph mapping Free form deformation (FFD) Kriging model Navier-Stokes equations Particle swarm optimization (PSO) Space-shape

Mechanism of unconventional aerodynamic characteristics of an elliptic airfoil

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Chinese Journal of Aeronautics 2015年第3期28卷 687-694页

作者： Sun Wei gao zhenghong Du Yiming Xu Fang School of Aeronautics Northwestern Polytechnical University

Abstract The aerodynamic characteristics of elliptic airfoil are quite different from the case of con ventional airfoil for Reynolds number varying from about 104 to 106. In order to reveal the funda mental mechanism, the unsteady flow around a stationary two-dimensional elliptic airfoil with 16% relative thickness has been simulated using unsteady Reynolds-averaged NavieStokes equations and the 7 Reot transition turbulence model at different angles of attack for flow Reynolds number of 5 x 10^5. The aerodynamic coefficients and the pressure distribution obtained by computation are in good agreement with experimental data, which indicates that the numerical method works well. Through this study, the mechanism of the unconventional aerodynamic characteristics of airfoil is analyzed and discussed based on the computational predictions coupled with the wind tunnel results. It is considered that the boundary layer transition at the leading edge and the unsteady flow separation vortices at the trailing edge are the causes of the case. Furthermore, a valuable insight into the physics of how the flow behavior affects the elliptic airfoil＇s aerodynamics is provided.

关键词： Aerodynamic characteristicsBoundary layer transition Elliptic aerofoil section Flow separation Numerical analysis

Aerodynamic optimization of rotor airfoil based on multi-layer hierarchical constraint method

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Chinese Journal of Aeronautics 2016年第6期29卷 1541-1552页

作者： Zhao Ke gao zhenghong Huang Jiangtao Li Quan The First Aircraft Institute of AVIC Xi’an 710089China National Key Laboratory of Aerodynamic Design and Research Northwestern Polytechnical UniversityXi’an 710072China China Aerodynamics Research and Development Center Mianyang 621000China

Rotor airfoil design is investigated in this paper. There are many difficulties for this highdimensional multi-objective problem when traditional multi-objective optimization methods are used. Therefore, a multi-layer hierarchical constraint method is proposed by coupling principal component analysis(PCA) dimensionality reduction and e-constraint method to translate the original high-dimensional problem into a bi-objective problem. This paper selects the main design objectives by conducting PCA to the preliminary solution of original problem with consideration of the priority of design objectives. According to the e-constraint method, the design model is established by treating the two top-ranking design goals as objective and others as variable constraints. A series of bi-objective Pareto curves will be obtained by changing the variable constraints, and the favorable solution can be obtained by analyzing Pareto curve spectrum. This method is applied to the rotor airfoil design and makes great improvement in aerodynamic performance. It is shown that the method is convenient and efficient, beyond which, it facilitates decision-making of the highdimensional multi-objective engineering problem.

关键词： Multi-layer hierarchical constraint method Multi-objective optimization NSGA II Pareto front Principal component analysis Rotor airfoil

Double-stage Metamodel and Its Application in Aerodynamic Design Optimization

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Chinese Journal of Aeronautics 2011年第5期24卷 568-576页

作者： ZHANG Dehu gao zhenghong HUANG Likeng WANG Mingliang National Key Laboratory of Science and Technology on Aerodynamic Design and Research Northwestern Polytechnical University Xi＇an 710072 China National Key Laboratory of Science and Technology on Test Physics ＆ Numerical Mathematical Beijing 100076 China

Constructing metamodel with global high-fidelity in design space is significant in engineering design. In this paper, a double-stage metamodel （DSM） which integrates advantages of both interpolation metamodel and regression metamodel is constructed. It takes regression model as the first stage to fit overall distribution of the original model, and then interpolation model of regression model approximation error is used as the second stage to improve accuracy. Under the same conditions and with the same samples, DSM expresses higher fidelity and represents physical characteristics of original model better. Besides, in order to validate DSM characteristics, three examples including Ackley function, airfoil aerodynamic analysis and wing aerodynamic analysis are investigated, In the end, airfoil and wing aerodynamic design optimizations using genetic algorithm are presented to verify the engineering applicability of DSM.

关键词： optimization genetic algorithm double-stage metamodel Kriging BP neural network Latin hypercube Parsecmethod

An improved adaptive sampling and experiment design method for aerodynamic optimization

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Chinese Journal of Aeronautics 2015年第5期28卷 1391-1399页

作者： Huang Jiangtao gao zhenghong Zhou Zhu Zhao Ke Computational Aerodynamics Institute China Aerodynamics Research and Development Center National Key Laboratory of Aerodynamic Design and Research Northwestern Polytechnical University

Experiment design method is a key to construct a highly reliable surrogate model for numerical optimization in large-scale project. Within the method, the experimental design criterion directly affects the accuracy of the surrogate model and the optimization efficient. According to the shortcomings of the traditional experimental design, an improved adaptive sampling method is proposed in this paper. The surrogate model is firstly constructed by basic sparse samples. Then the supplementary sampling position is detected according to the specified criteria, which introduces the energy function and curvature sampling criteria based on radial basis function （RBF） network. Sampling detection criteria considers both the uniformity of sample distribution and the description of hypersurface curvature so as to significantly improve the prediction accuracy of the surrogate model with much less samples. For the surrogate model constructed with sparse samples, the sample uniformity is an important factor to the interpolation accuracy in the initial stage of adaptive sam- pling and surrogate model training. Along with the improvement of uniformity, the curvature description of objective function surface gradually becomes more important. In consideration of these issues, crowdness enhance function and root mean square error （RMSE） feedback function are introduced in C criterion expression. Thus, a new sampling method called RMSE and crowd- ness enhance （RCE） adaptive sampling is established. The validity of RCE adaptive sampling method is studied through typical test function firstly and then the airfoil/wing aerodynamic opti- mization design problem, which has high-dimensional design space. The results show that RCE adaptive sampling method not only reduces the requirement for the number of samples, but also effectively improves the prediction accuracy of the surrogate model, which has a broad prospects for applications.

关键词： Aerodynamic optimization Crowdness enhance function RBF model RCE adaptive sampfing RMSE feedback