Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method

Abstract A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport （SST） k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation （NFFD） method based on the non-uniform rational B-spline （NURBS） basis function is introduced to the airfoil parameterization. The non-dominated sorting genetic algorithm-II （NSGA-II） is used as the search algo- rithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.

The Method for Optimum Design of Water Rocket Flight Stability Performance Conditions Using CAE with T Method and Robust Parameter Design

A water rocket is a rocket system that obtains thrust by injecting water with compressed air of up to about 8 atmospheres. It is usually manufactured using a pressure-resistant PET bottle. The mechanical elements and principles contained in the water rocket have much in common with the actual small rocket system, and are suitable as educational and research teaching materials in the field of mechanics. Especially in the field of disaster prevention and mitigation, the use of water rockets is being researched and developed as a rescue tool in the event of a flood or earthquake as a disaster countermeasure. However, since the water rocket is a flying object based on the mechanical principle, it is important to ensure the accuracy and stability of the flight path. In this paper, a mechanical simulator is developed with a numerical calculation program based on the mechanical consideration of water rocket flight performance. In addition, the correlation between the flight distance obtained in the simulation and the estimated flight distance is analyzed by applying a multivariate analysis method and verifying the validity of the flight distance calculated from the result. Based on the verification results, we will apply a statistical optimization method to approach the optimization of flight stability performance conditions for water rockets.

Investigation and Optimization of Sn/Gr Lubricants Effects on Cold Extrudability of Fe-TiC Nanocomposite Using Taguchi Robust Design Method

The present study deals with the effects of both tin (Sn) and graphite (Gr) powders on the cold extrudability of Fe-TiC nanocomposites as lubricant. The production process includes low-energy ball milling, powder metallurgy and cold direct Extrusion. Due to various factors influencing the extrudability of the Fe-TiC nanocomposites, such as milling time, rate of extrusion, type and content of lubricant and etc, Taguchi robust design method of system optimization was used to determine the approximate contribution percent (% &#961) of each factor. In order to investigation of Fe-TiC properties, samples with best quality of extrusion were analyzed by XRD and SEM investigations. The results indicate that, sitting the atomic layers of Sn lubricant between Fe and TiC particles leads to decreasing the friction. In this case sliding the particles on each other is easier and a part of the load is applied on lubricant. The results of extrusion of samples indicate that using 2% Sn admixed and die wall graphite lubrication can improve cold extrudability of Fe-TiC nanocomposites.

A Robust Design Method in Product Quality Applications

In order to express information on the quality grade of product designed, thetarget value of product quality design was described with a fuzzy number in this paper. Analternative to Taguchi's, the robustness application design method has been recently presented.However, neither Taguchi's method nor the alternative method is capable of dealing satisfactorilywith the frequently encountered situations in which all the noise variables cannot be studiedsimultaneously. Based on the ideas from response surface modeling, linear models theory, and randomeffects models, we provide a method for estimation in the robustness application design method inproduct quality applications. With this new method used, the high-quality ratio of the productdesigned could be increased, and the ability to resist the influence of various disturbing factorsand noise factors could be enhanced.

Robust Optimum Design of Thrust Hydrodynamic Bearings for Hard Disk Drives

This paper describes the robust optimum design which combines the geometrical optimization method proposed by Hashimoto and statistical method. Recently, 2.5″ hard disk drives (HDDs) are widely used for mobile devices such as laptops, video cameras and car navigation systems. In mobile applications, high durability towards external vibrations and shocks are essentials to the bearings of HDD spindle motor. In addition, the bearing characteristics are influenced by manufacturing error because of small size of the bearings of HDD. In this paper, the geometrical optimization is carried out to maximize the bearing stiffness using sequential quadratic programming to improve vibration characteristics. Additionally, the bearing stiffness is analyzed considering dimensional tolerance of the bearing using statistical method. The dimensional tolerance is assumed to distribute according to the Gaussian distribution, and then the bearing stiffness is estimated by combining the expectation and standard deviation. As a result, in the robust optimum design, new groove geometry of bearing can be obtained in which the bearing stiffness is four times higher than the stiffness of conventional spiral groove bearing. Moreover, the bearing has lower variability compared with the result of optimum design neglecting dimensional tolerance.

Robust airfoil optimization based on improved particle swarm optimization method

A robust airfoil optimization platform is constructed based on the modified particle swarm optimization method （i.e., the second-order oscillating particle swarm method）, which consists of an efficient optimization algorithm, a precise aerodynamic analysis program, a high accuracy surrogate model, and a classical airfoil parametric method. There are two improvements for the modified particle swarm method compared with the standard particle swarm method. First, the particle velocity is represented by the combination of the particle position and the variation of position, which makes the particle swarm algorithm a second-order precision method with respect to the particle po- sition. Second, for the sake of adding diversity to the swarm and enlarging the parameter searching domain to improve the global convergence performance of the algorithm, an oscillating term is introduced to the update formula of the particle velocity. At last, tak- ing two airfoils as examples, the aerodynamic shapes are optimized on this optimization platform. It is shown from the optimization results that the aerodynamic characteristic of the airfoils is greatly improved in a broad design range.

Design Support Method Based on Analysis of Shape Impression

In recent years, aesthetic design is becoming increasingly important in industrial product development due to the growing maturity of product functions. The designer is required to reflect consumer needs in the aesthetic design while giving consideration to the applications and functions of the product. For this reason, effective techniques enabling design creation based on consumer preference and needs are indispensable. The Taguchi method has been effectively used for the robust design of products. In this study, we proposed a design support method applying the Taguchi Method to robust design in respect to the inconsistencies of human kansei（sensitivity）, and specifically applied it for quantitatively analyzing the robustness of design solutions created in accordance with the design concept of a digital camera.

Robust optimization design on impeller of mixed-flow pump

To increase the robustness of the optimization solutions of the mixed-flow pump,the impeller was firstly indirectly parameterized based on the 2D blade design theory.Secondly,the robustness of the optimization solution was mathematically defined,and then calculated by Monte Carlo sampling method.Thirdly,the optimization on the mixed-flow pump′s impeller was decomposed into the optimal and robust sub-optimization problems,to maximize the pump head and efficiency and minimize the fluctuation degree of them under varying working conditions at the same time.Fourthly,using response surface model,a surrogate model was established between the optimization objectives and control variables of the shape of the impeller.Finally,based on a multi-objective genetic optimization algorithm,a two-loop iterative optimization process was designed to find the optimal solution with good robustness.Comparing the original and optimized pump,it is found that the internal flow field of the optimized pump has been improved under various operating conditions,the hydraulic performance has been improved consequently,and the range of high efficient zone has also been widened.Besides,with the changing of working conditions,the change trend of the hydraulic performance of the optimized pump becomes gentler,the flow field distribution is more uniform,and the influence degree of the varia-tion of working conditions decreases,and the operating stability of the pump is improved.It is concluded that the robust optimization method proposed in this paper is a reasonable way to optimize the mixed-flow pump,and provides references for optimization problems of other fluid machinery.

基于6σ稳健性的拼焊板车门轻量化研究

将某拼焊板车门各板件厚度及内板拼焊线位置作为变量,综合试验设计、响应面法、优化算法和蒙特卡罗模拟技术,提出了基于6σ稳健性的轻量化方法。算例结果表明,该方法在减轻车门质量的同时,提高了设计变量的可靠性和响应的稳健性,因此具有较强的工程实用性。

基于响应面的结构疲劳寿命6σ稳健优化设计

针对结构疲劳寿命离散性较大的问题,将响应面法、6σ稳健设计与疲劳寿命设计相结合,提出一种提高结构疲劳寿命稳健性且减轻结构质量的方法。该方法先用对设计参数进行拉丁超立方采样,用有限元法计算结构疲劳关键点处的平均应力和对称应力谱;然后采用Miner法求出结构关键点处的疲劳寿命,构造出疲劳寿命的响应面模型;最后基于响应面模型对结构进行疲劳寿命的6σ稳健优化设计。对某型搅拌车副车架进行了疲劳寿命稳健优化设计的结果表明,该方法在保证副车架疲劳寿命可靠性满足设计要求的基础上,有效提高其疲劳寿命的稳健性,减轻其结构质量。

干姜中6-姜辣素包合工艺的优化

[目的]优化干姜(RHIZOMA ZINGIBERIS)中6姜-辣素、β-环糊精包合物的制备工艺,提高干姜产品的稳定性。[方法]采用研磨法制备包合物;采用单因素试验结合正交设计法优化包合条件;采用高效液相色谱法(HPLC)进行含量测定,以包合率(0.6)、包合物收率(0.2)及包合物含6姜-辣素的百分数(0.2)加权评分为评价指标。[结果]最佳的包合条件为:干姜提取物浓缩至相对密度为1.08(25℃),加入2倍量水研磨1.0 h,干姜醇提液∶β-环糊精为1.5∶10.0(W/W)。[结论]该包合工艺合理可行,重复性好,包合效果好,可指导6姜-辣素-β-环糊精包合物的生产。

System reliability-based robust design of deep foundation pit considering multiple failure modes

Recently,reliability-based design is a universal method to quantify negative influence of uncertainty in geotechnical engineering.However,for deep foundation pit,evaluating the system safety of retaining structures and finding cost-effective design points are main challenges.To address this,this study proposes a novel system reliability-based robust design method for retaining system of deep foundation pit and illustrated this method via a simplified case history in Suzhou,China.The proposed method included two parts:system reliability model and robust design method.Back Propagation Neural Network(BPNN)is used to fit limit state functions and conduct efficient reliability analysis.The common source random variable(CSRV)model are used to evaluate correlation between failure modes and determine the system reliability.Furthermore,based on the system reliability model,a robust design method is developed.This method aims to find cost-effective design points.To solve this problem,the third generation non-dominated genetic algorithm(NSGA-III)is adopted.The efficiency and accuracy of whole computations are improved by involving BPNN models and NSGA-III algorithm.The proposed method has a good performance in locating the balanced design point between safety and construction cost.Moreover,the proposed method can provide design points with reasonable stiffness distribution.

Robust Topology Optimization of Periodic Multi-Material Functionally Graded Structures under Loading Uncertainties

This paper presents a robust topology optimization design approach for multi-material functional graded structures under periodic constraint with load uncertainties.To characterize the random-field uncertainties with a reduced set of random variables,the Karhunen-Lo`eve(K-L)expansion is adopted.The sparse grid numerical integration method is employed to transform the robust topology optimization into a weighted summation of series of deterministic topology optimization.Under dividing the design domain,the volume fraction of each preset gradient layer is extracted.Based on the ordered solid isotropic microstructure with penalization(Ordered-SIMP),a functionally graded multi-material interpolation model is formulated by individually optimizing each preset gradient layer.The periodic constraint setting of the gradient layer is achieved by redistributing the average element compliance in sub-regions.Then,the method of moving asymptotes(MMA)is introduced to iteratively update the design variables.Several numerical examples are presented to verify the validity and applicability of the proposed method.The results demonstrate that the periodic functionally graded multi-material topology can be obtained under different numbers of sub-regions,and robust design structures are more stable than that indicated by the deterministic results.

Using the Taguchi Method and Grey Relational Analysis to Optimize the Performance of a Solar Air Heater

Solar energy is regarded as one of the promising renewable energy sources in the world.The main aim of this study is to use the Taguchi-Grey relational grade analysis to optimize the performance of two Solar Air Heaters(SAHs).A typical Grey–Taguchi method was applied.The Orthogonal Array,Signal-to-Noise ratio,Grey Relational Grade,and Analysis of Variance were employed to investigate the performance characteristics of SAH.Experimental observations were made in agreement with Jordanian climate 32°00′N latitude and 36°00′E longitude with a solar intensity of 500 W\m^(2).The operating factors selected for optimization are the tilt angle(T)with three levels(0°,22°,45°),inlet velocity(V)with two levels(1.2,1.8 m/s),and absorber plate material(M)with two levels(Aluminum,wood).In this study,the Grey–Taguchi approach is validated by performing 12 individual experiments.The results show that the process factors sequence required for a maximum SAH efficiency(SAHµ)is V>T>M.Using this approach,we combined the Orthogonal Array design with Grey Relational Analysis.As a result of that,the level of each operating conditions which optimizes both process responses(Temperature difference,ΔT and Solar air heater efficiency,SAHµ)can be specified with a minimum number of tests compared with classic Grey Relational Analysis.The optimal operating conditions of a SAH for multiple performance characteristics are determined as T2,M2,and V2,respectively,which are in congruence with the experimental results.

基于MIMO阵列的综合射频系统鲁棒波形设计算法研究

基于多输入多输出(MIMO)阵列的综合射频(MFRF)系统通过优化多波形,可以在不同角度辐射不同的信号,进而同时实现多种功能。然而,当存在角度误差时,综合射频系统所合成的信号会出现畸变,这将导致系统性能下降。该文主要考虑存在角度误差时,对综合射频系统鲁棒波形设计算法进行研究。首先,提出基于最小最大化(Min-Max)框架的MIMO阵列多波形优化问题。同时,为减少非线性功放引起的波形失真,对发射波形施加了峰均比(PAPR)约束。为求解此问题,该文提出了基于交替方向乘子法(ADMM)和Majorization-Minimization(MM)方法的波形优化算法。仿真实验结果表明,当存在角度误差时,所提算法能够获得更好的性能。

非正态响应稳健参数设计的贝叶斯建模与优化

针对非正态响应的稳健参数设计问题,提出一种考虑噪声因子的贝叶斯建模与参数优化方法。首先,考虑经验贝叶斯先验信息,利用贝叶斯广义线性模型构建设计因子与输出响应之间的函数关系;其次,假设噪声因子服从已知的分布,在此基础上利用贝叶斯抽样技术获得考虑噪声因子波动的输出响应模拟抽样值;然后,在给定产品规格的基础上,利用输出响应的抽样值构建符合性后验概率函数,并利用遗传算法对所构建的符合性后验概率函数进行优化,获得对噪声因子波动具有稳健性的参数设计值;最后,结合实际的案例验证了所提方法的有效性。研究结果表明,所提方法有效地刻画了噪声因子的波动对产品或过程质量的影响,从而获得了更为稳健可靠的参数设计值。

板式T型构件角接合多指标稳健优化设计

为增强板式家具角接合强度,提高家具结构质量的稳定性,对以18 mm厚刨花板为基材的T型构件进行角接合强度稳健优化设计。选取圆榫直径(6、8、10 mm)、圆榫长度(30、40、50 mm)、连接件种类(二合一连接件、三合一连接件、四合一连接件)及连接件长度(35、40、45 mm)为设计因素,采用L_9(3~4)正交表进行试验方案设计。使用ANSYA有限元软件,对构件进行模拟抗弯测试,将构件的形变量、连接件及圆榫的最大等效应力作为衡量指标,通过稳健设计田口法结合灰色关联分析法对板式T型构件角接合强度进行多指标稳健优化。结果表明:长40 mm的四合一连接件,配以长为30 mm,直径为8 mm的圆棒榫为本研究的稳健优化结果。选取各因素中间水平为初始对照组,优化后构件的形变量减少1.71 mm,连接件的等效应力减小207.94 MPa。虽圆榫的等效应力有所增加,但综合性能有所提升,灰色关联度由0.60增加至0.78,提高30%。试验证明:田口法结合灰色关联分析法可有效将板式家具研究中的多指标问题转化为单一问题进行研究,实现板式家具的稳健设计,进而实现家具结构质量稳定性的提升,延长家具的使用寿命。

Adjoint-based robust optimization design of laminar flow wing under flight condition uncertainties

It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions.In order to seek a more robust natural laminar flow control effect,it is necessary to develop an effective optimization design method.Meanwhile,attention must be given to the impact of crossflow(CF)instability brought on by the sweep angle.This paper constructs a robust optimization design framework based on discrete adjoint methods and non-intrusive polynomial chaos.Transition prediction is implemented by coupled Reynolds-Averaged Navier-Stokes(RANS)and simplified e^(N)method,which can consider both Tollmien-Schlichting(TS)wave and crossflow vortex instability.We have performed gradient enhancement processing on the general Polynomial Chaos Expansion(PCE),which is advantageous to reduce the computational cost of single uncertainty propagation.This processing takes advantage of the gradient information obtained by solving the coupled adjoint equations considering transition.The statistical moment gradient solution used for the robust optimization design also uses the derivatives of coupled adjoint equations.The framework is applied to the robust design of a 25°swept wing with infinite span in transonic flow.The uncertainty quantification and sensitivity analysis on the baseline wing shows that the uncertainty quantification method in this paper has high accuracy,and qualitatively reveals the factors that dominate in different flow field regions.By the robust optimization design,the mean and standard deviation of the drag coefficient can be reduced by 29%and 45%,respectively,and compared with the deterministic optimization design results,there is less possibility of forming shock waves under flight condition uncertainties.Robust optimization results illustrate the trade-off between the transition delay and the wave drag reduction.

Optimal design of 6-DOF vibration isolation platform based on transfer matrix method for multibody systems

The structure parameters of 6-degree of freedom(DOF)vibration isolation platform have a significant effect on its performance.To make the designed vibration isolation platform perform well,non-dominanted sorting genetic algorithm version II(NSGA-II)was applied to optimize its structure based on the transfer matrix method for multibody systems.Firstly,the Jacobian matrix of 6-DOF vibration isolation platform was solved based on kinematics.Secondly,the transfer equation of 6-DOF vibration isolation system was established by the linear transfer matrix method for multibody systems.And the formula of its natural frequency was derived according to the boundary conditions of the system.Thirdly,the manipulability index was constructed based on a dimensionless Jacobian matrix.And a new performance index function was established considering the influence of dynamic isotropic and legs mass.Fourthly,genetic algorithm(GA)and NSGA-II were used to optimize the structure of the 6-DOF vibration isolation platform under the same conditions,respectively.It showed that NSGA-II had higher optimization efficiency,better calculation accuracy and shorter optimization time than that of GA.Finally,NSGA-II was adopted for multi-objective optimization design of 6-DOF vibration isolation platform based on the constraint conditions.Optimal Pareto solutions were obtained,which provides structural parameters for subsequent design work.Therefore,the proposed optimization method and the performance index in this paper provide a theoretical basis for the optimal design of relevant vibration isolation mechanism.

干姜中3种姜酚类成分提取工艺研究

目的:建立干姜中姜酚的提取工艺。方法:采用超声辅助提取法考察乙醇浓度、提取时间、料液比3个因素对6-姜酚、8-姜酚、10-姜酚总提取率的影响,并利用响应面法优选姜酚最佳提取工艺。结果:优化后最佳提取条件设定为乙醇浓度为61%,提取时间为41 min,料液比为1∶34(g/mL)。结论:本方法简便,具备可行性,可用于干姜中姜酚提取物的提取、分离及纯化。