Research on multi-fidelity aerodynamic optimization methods

 Constructing high approximation accuracy surrogate model with lower computational cost has great engineering significance. In this paper, using co-Kriging method, an efficient multifidelity 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.     

Stationary flow fields prediction of variable physical domain based on proper orthogonal decomposition and kriging surrogate model

In this paper a new flow field prediction method which is independent of the governing equations, is developed to predict stationary flow fields of variable physical domain. Predicted flow fields come from linear superposition of selected basis modes generated by proper orthogonal decomposition(POD). Instead of traditional projection methods, kriging surrogate model is used to calculate the superposition coefficients through building approximate function relationships between profile geometry parameters of physical domain and these coefficients. In this context,the problem which troubles the traditional POD-projection method due to viscosity and compressibility has been avoided in the whole process. Moreover, there are no constraints for the inner product form, so two forms of simple ones are applied to improving computational efficiency and cope with variable physical domain problem. An iterative algorithm is developed to determine how many basis modes ranking front should be used in the prediction. Testing results prove the feasibility of this new method for subsonic flow field, but also prove that it is not proper for transonic flow field because of the poor predicted shock waves.     

Optimization of aerodynamic efficiency for twist morphing MAV wing

Twist morphing(TM) is a practical control technique in micro air vehicle(MAV) flight.However, TM wing has a lower aerodynamic efficiency(CL/CD) compared to membrane and rigid wing. This is due to massive drag penalty created on TM wing, which had overwhelmed the successive increase in its lift generation. Therefore, further CL/CDmaxoptimization on TM wing is needed to obtain the optimal condition for the morphing wing configuration. In this paper, two-way fluid–structure interaction(FSI) simulation and wind tunnel testing method are used to solve and study the basic wing aerodynamic performance over(non-optimal) TM, membrane and rigid wings. Then,a multifidelity data metamodel based design optimization(MBDO) process is adopted based on the Ansys-DesignXplorer frameworks. In the adaptive MBDO process, Kriging metamodel is used to construct the final multifidelity CL/CDresponses by utilizing 23 multi-fidelity sample points from the FSI simulation and experimental data. The optimization results show that the optimal TM wing configuration is able to produce better CL/CDmaxmagnitude by at least 2% than the non-optimal TM wings. The flow structure formation reveals that low TV strength on the optimal TM wing induces low CDgeneration which in turn improves its overall CL/CDmaxperformance.     

Variable-fidelity optimization with design space reduction

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.     

An optimization method for metamorphic mechanisms based on multidisciplinary design optimization

The optimization of metamorphic mechanisms is different from that of the conventional mechanisms for its characteristics of multi-configuration. There exist complex coupled design variables and constraints in its multiple different configuration optimization models. To achieve the compatible optimized results of these coupled design variables, an optimization method for metamorphic mechanisms is developed in the paper based on the principle of multidisciplinary design optimization（MDO）. Firstly, the optimization characteristics of the metamorphic mechanism are summarized distinctly by proposing the classification of design variables and constraints as well as coupling interactions among its different configuration optimization models. Further, collaborative optimization technique which is used in MDO is adopted for achieving the overall optimization performance. The whole optimization process is then proposed by constructing a two-level hierarchical scheme with global optimizer and configuration optimizer loops. The method is demonstrated by optimizing a planar five-bar metamorphic mechanism which has two configurations,and results show that it can achieve coordinated optimization results for the same parameters in different configuration optimization models.     

Parameter optimization of controllable local degree of freedom for reducing vibration of flexible manipulator

 Parameter optimization of the controllable local degree of freedom is studied for reducing vibration of the flexible manipulator at the lowest possible cost. The controllable local degrees of freedom are suggested and introduced to the topological structure of the flexible manipulator, and used as an effective way to alleviate vibration through dynamic coupling. Parameters introduced by the controllable local degrees of freedom are analyzed and their influences on vibration reduction are investigated. A strategy to optimize these parameters is put forward and the corresponding optimization method is suggested based on Particle Swarm Optimization (PSO). Simulations are conducted and results of case studies confirm that the proposed optimization method is effective in reducing vibration of the flexible manipulator at the lowest possible cost.     

Kriging模型在机翼气动外形优化中的应用

针对粒子群等随机优化算法计算量大的缺点,发展了基于Kriging模型的优化方法.采用改进的量子粒子群算法对Kriging模型的相关模型参数进行优化,以提高代理模型预测精度,并与具有双层结构的粒子群算法相结合.采用雷诺平均N-S方程流场求解器与多目标非线性适应值加权方法,对高维度多目标多约束的跨声速机翼进行了优化,设计的机翼具有理想的压力分布,降低了机翼阻力系数,并且有效控制了低头力矩和翼根弯矩,表明该方法具有较强的工程实用性.     

Multi-disciplinary design optimization with variable complexity modeling for a stratosphere airship

This paper proposes a hybrid architecture based on Multi-disciplinary Design Optimization(MDO) with the Variable Complexity Modeling(VCM) method, to solve the problem of general design optimization for a stratosphere airship. Firstly, MDO based on the Concurrent SubSpace Optimization(CSSO) strategy is improved for handling the subsystem coupling problem in stratosphere airship design which contains aerodynamics, structure, and energy. Secondly, the VCM method based on the surrogate model is presented for reducing the computational complexity in high-fidelity modeling without loss of accuracy. Moreover, the global-to-local optimization strategy is added to the architecture to enhance the process. Finally, the result gives a prominent stratosphere airship general solution that validates the feasibility and efficiency of the optimization architecture. Besides, a sensitivity analysis is conducted to outline the critical impact upon stratosphere airship design.     

Uncertainty analysis and design optimization of hybrid rocket motor powered vehicle for suborbital flight

In this paper, we propose an uncertainty analysis and design optimization method and its applications on a hybrid rocket motor(HRM) powered vehicle. The multidisciplinary design model of the rocket system is established and the design uncertainties are quantified. The sensitivity analysis of the uncertainties shows that the uncertainty generated from the error of fuel regression rate model has the most significant effect on the system performances. Then the differences between deterministic design optimization(DDO) and uncertainty-based design optimization(UDO) are discussed. Two newly formed uncertainty analysis methods, including the Kriging-based Monte Carlo simulation(KMCS) and Kriging-based Taylor series approximation(KTSA), are carried out using a global approximation Kriging modeling method. Based on the system design model and the results of design uncertainty analysis, the design optimization of an HRM powered vehicle for suborbital flight is implemented using three design optimization methods: DDO, KMCS and KTSA. The comparisons indicate that the two UDO methods can enhance the design reliability and robustness. The researches and methods proposed in this paper can provide a better way for the general design of HRM powered vehicles.In this paper,we propose an uncertainty analysis and design optimization method and its applications on a hybrid rocket motor(HRM)powered vehicle.The multidisciplinary design model of the rocket system is established and the design uncertainties are quantified.The sensitivity analysis of the uncertainties shows that the uncertainty generated from the error of fuel regression rate model has the most significant effect on the system performances.Then the differences between deterministic design optimization(DDO)and uncertainty-based design optimization(UDO)are discussed.Two newly formed uncertainty analysis methods,including the Kriging-based Monte Carlo simulation(KMCS)and Kriging-based Taylor series approximation(KTSA),are carried out using a global approximation Kriging modeling method.Based on the system design model and the results of design uncertainty analysis,the design optimization of an HRM powered vehicle for suborbital flight is implemented using three design optimization methods:DDO,KMCS and KTSA.The comparisons indicate that the two UDO methods can enhance the design reliability and robustness.The researches and methods proposed in this paper can provide a better way for the general design of HRM powered vehicles.     

Aerodynamic optimization design for high pressure turbines based on the adjoint approach

A first study on the continuous adjoint formulation for aerodynamic optimization design of high pressure turbines based on S2surface governed by the Euler equations with source terms is presented.The objective function is defined as an integral function along the boundaries,and the adjoint equations and the boundary conditions are derived by introducing the adjoint variable vectors.The gradient expression of the objective function then includes only the terms related to physical shape variations.The numerical solution of the adjoint equation is conducted by a finitedifference method with the Jameson spatial scheme employing the first and the third order dissipative fluxes.A gradient-based aerodynamic optimization system is established by integrating the blade stagger angles,the stacking lines and the passage perturbation parameterization with the quasi-Newton method of Broyden–Fletcher–Goldfarb–Shanno(BFGS).The application of the continuous adjoint method is validated through a single stage high pressure turbine optimization case.The adiabatic efficiency increases from 0.8875 to 0.8931,whilst the mass flow rate and the pressure ratio remain almost unchanged.The optimization design is shown to reduce the passage vortex loss as well as the mixing loss due to the cooling air injection.     

Automatic differentiation based discrete adjoint method for aerodynamic design optimization on unstructured meshes

A systematic methodology for formulating, implementing, solving and verifying discrete adjoint of the compressible Reynolds-averaged Navier-Stokes (RANS) equations for aerodynamic design optimization on unstructured meshes is proposed. First, a general adjoint formulation is con-structed for the entire optimization problem, including parameterization, mesh deformation, flow solution and computation of the objective function, which is followed by detailed formulations of matrix-vector products arising in the adjoint model. According to this formulation, procedural components of implementing the required matrix-vector products are generated by means of auto-matic differentiation (AD) in a structured and modular manner. Furthermore, a duality-preserving iterative algorithm is employed to solve flow adjoint equations arising in the adjoint model, ensur-ing identical convergence rates for the tangent and the adjoint models. A three-step strategy is adopted to verify the adjoint computation. The proposed method has several remarkable features:the use of AD techniques avoids tedious and error-prone manual derivation and programming;duality is strictly preserved so that consistent and highly accurate discrete sensitivities can be obtained; and comparable efficiency to hand-coded implementation can be achieved. Upon the cur-rent discrete adjoint method, a gradient-based optimization framework has been developed and applied to a drag reduction problem.     

先进复合材料制造工艺成本估算模型研究现状

降低制造成本是复合材料推广使用的必经之路,建立成本估算模型是定量评价复合材料工艺成本的基础和降低复合材料工艺成本的重要技术手段。复合材料制造设计的核心就是针对特定产品选择最佳的材料和制造工艺,实现产品性能与成本的最佳平衡。而成本估算模型可以在工艺过程与成本之间建立定量关系,这是制造设计的关键组成部分。本文对国外先进复合材料制造成本估算模型研究的现状进行了总结和评述,给出了主要成本估算模型的类型、建模方法以及各自的特点及适用范围,提出了基于成本估算模型的工艺 性能 成本集成分析的未来研究方向。     

A numerical optimization of high altitude testing facility for wind tunnel experiments

High altitude test facilities are required to test the high area ratio nozzles operating at the upper stages of rocket in the nozzle full flow conditions.It is typically achieved by creating the ambient pressure equal or less than the nozzle exit pressure.On average,air/GN2is used as active gas for ejector system that is stored in the high pressure cylinders.The wind tunnel facilities are used for conducting aerodynamic simulation experiments at/under various flow velocities and operating conditions.However,constructing both of these facilities require more laboratory space and expensive instruments.Because of this demerit,a novel scheme is implemented for conducting wind tunnel experiments by using the existing infrastructure available in the high altitude testing(HAT)facility.This article presents the details about the methods implemented for suitably modifying the sub-scale HAT facility to conduct wind tunnel experiments.Hence,the design of nozzle for required area ratio A/A*,realization of test section and the optimized configuration are focused in the present analysis.Specific insights into various rocket models including high thrust cryogenic engines and their holding mechanisms to conduct wind tunnel experiments in the HAT facility are analyzed.A detailed CFD analysis is done to propose this conversion without affecting the existing functional requirements of the HAT facility.     

Flight strategy optimization for high-altitude long-endurance solar-powered aircraft based on Gauss pseudo-spectral method

Solar-powered aircraft have attracted great attention owing to their potential for longendurance flight and wide application prospects.Due to the particularity of energy system, flight strategy optimization is a significant way to enhance the flight performance for solar-powered aircraft.In this study, a flight strategy optimization model for high-altitude long-endurance solar-powered aircraft was proposed.This model consists of three-dimensional kinematic model,aerodynamic model, energy collection model, energy store model and energy loss model.To solve the nonlinear optimal control problem with process constraints and terminal constraints, Gauss pseudo-spectral method was employed to discretize the state equations and constraint equations.Then a typical mission flying from given initial point to given final point within a time interval was considered.Results indicate that proper changes of the attitude angle contribute to increasing the energy gained by photovoltaic cells.Utilization of gravitational potential energy can partly take the role of battery pack.Integrating these two measures, the optimized flight strategy can improve the final state of charge compared with current constant-altitude constant-velocity strategy.The optimized strategy brings more profits on condition of lower sunlight intensity and shorter daytime.     

Multipoint optimization on fuel efficiency in conceptual design of wide-body aircraft

Aircraft conceptual design optimizations that maximize the performance at a design condition (single-point) may result in designs with unsatisfying off-design performance. To further improve aircraft efficiency under actual flight operations, there is a need to consider multiple flight conditions (multipoint) in aircraft conceptual design and optimization. A new strategy for multipoint optimizations in aircraft conceptual design is proposed in this paper. A wide-body aircraft is taken as an example for both single-point and multipoint optimizations with the objective of maximizing the specific hourly productivity. Boeing 787-8 flight data was used in the multipoint optimization to reflect the true objective function. The results show that the optimal design from the multipoint optimization has a 7.72% total specific hourly productivity increase of entire flight missions compared with that of the baseline aircraft, while the increase in the total specific hourly productivity from the single-point optimal design is only 5.73%. The differences between the results of single-point and multipoint optimizations indicate that there is a good option to further improve aircraft efficiency by considering actual flight conditions in aircraft conceptual design and optimization.     

Air route network optimization in fragmented airspace based on cellular automata

Air route network optimization,one of the essential parts of the airspace planning,is an effective way to optimize airspace resources,increase airspace capacity,and alleviate air traffic con gestion.However,little has been done on the optimization of air route network in the fragmented airspace caused by prohibited,restricted,and dangerous areas (PRDs).In this paper,an air route network optimization model is developed with the total operational cost as the objective function while airspace restriction,air route network capacity,and non-straight-line factors (NSLF) are taken as major constraints.A square grid cellular space,Moore neighbors,a fixed boundary,together with a set of rules for solving the route network optimization model are designed based on cellular automata.The empirical traffic of airports with the largest traffic volume in each of the 9 flight information regions in mainland China is collected as the origin-destination (OD) air port pair demands.Based on traffic patterns,the model generates 35 air routes which successfully avoids 144 PRDs.Compared with the current air route network structure,the number of nodes decreases by 41.67％,while the total length of flight segments and air routes drop by 32.03％ and 5.82％ respectively.The NSLF decreases by 5.82％ with changes in the total length of the air route network.More importantly,the total operational cost of the whole network decreases by 6.22％.The computational results show the potential benefits of the model and the advantage of the algorithm.Optimization of air route network can significantly reduce operational cost while ensuring operation safety.     

风险投资中三类经典优化模型等价性分析

风险投资中有三类经典优化模型,分别是风险极小化模型、期望收益极大化模型、风险厌恶模型。这三类模型的等价会为投资组合分析提供更多的方法。文中证明了三类优化模型产生相同的有效前沿,并在此意义下得出这三类优化模型的等价性。另外,引用MSCI世界股价指数数据对三个模型有效前沿的等价性,进行实际算例验证。     

SA和SST湍流模型对高超声速边界层强制转捩的适应性

凸起物是高超声速流动中常用的一种人工转捩装置。采用高阶精度算法模拟了高超声速进气道压缩面上的强制转捩流动,转捩装置为一排高度为1mm的钻石型凸起物和斜坡型凸起物。考察了Spalart-Allmaras(SA)模型和剪切应力输运(SST)湍流模型对该问题的适应性。在考察过程中通过丰富的算例分析了网格规模、可压缩修正和空间离散格式等对计算结果的影响。在层流区,计算能与试验取得非常一致的结果。但在湍流区,计算得到的热流通常高出试验数据。经分析发现其原因是强制转捩的湍流边界层与自然转捩的湍流边界层在涡结构上存在较大差别,使得湍流模型的效果较差。针对高超强制转捩湍流涡结构丰富的特点,对SST湍流模型进行了修改。计算结果表明,该修改方法对提高热流精度具有一定效果。     

Design and optimization of a novel electrically controlled high pressure fuel injection system for heavy fuel aircraft piston engine

The heavy fuel compression ignition engines are widely equipped as aircraft piston engines. The fuel injection system is one of the key technologies that determines the performance of engine. One of the main challenges is to precisely control the injected fuel quantity and flow rate in the presence of pressure fluctuation. This challenge is even more serious for heavy fuel. An original design for electrically controlled high pressure fuel injection system called Multi-Pumppressure-reservoirs fuel injection System(MPS) was demonstrated to reduce the pressure fluctuation and help keep injection stable. MPS was compared with an ordinary high pressure Common Rail fuel injection System(CRS). This work established one-dimensional AMESim and mathematical models for both CRS and MPS to study the effect of different structures and geometric parameters on the pressure fluctuations. The calculations show that the average fuel pressure fluctuation of MPS can be reduced by 57% for the crankshaft speed of 1900 r/min, and the pressure fluctuation before injection reduced by 100%. It is concluded that the pressure performance of MPS is less sensitive to pressure reservoir volume than that of CRS, and there is an opportunity for further volume reduction.     

Methods to determine stress profile in ALT based on theoretical life models

With the recent products being more reliable,engineers cannot obtain enough failure or degradation information through the design period and even the product lifetime,therefore,accelerated life test(ALT)has become the most popular way to quantify the life characteristics of products.Test design is the most essential topic,such as testing duration,stress profile,data inference,etc.In this paper,a method and procedure based on theoretical life models is proposed to determine the accelerated stress profile.Firstly,the method for theoretical life calculation is put forward based on the main failure mechanism analysis and the theoretical life models.Secondly,the method is provided to determine the accelerated stress profile,including the method to determine the accelerated stress types and the stress range on the basis of the main failure mechanism analysis,the method to determine the acceleration factor and the accelerated stress level based on life quantitative calculation models,and the collaborative analysis method of the accelerated test time while taking the multiple failure mechanisms into consideration.Lastly,the actuator is taken as an example to describe the procedure of the method and the engineering applicability and the validity are verified.