Improved non-dominated sorting genetic algorithm （NSGA）-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm (NSGA) is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multiobjective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.     

Approximated-asymptotic solution of the complex variable equation of toroidal shells under axial symmetric loads

The series-approach and the asymptotic-approach are usually used to solve the complex variable equation of the toroidal shells under axial symmetric loads. As is known, the convergence of the series-solution is good only for small values of . On the other hand, the convergence of the asymptotic solution is good only for large values of μ. In this paper, based on an earlier work^[1], a new approach which may be called the approximated-asymptotic solution has been developed and it is valid for both small and large values of μ. It is shown that the results of the approximated-asymptotic solution for toroidal shell with μ=0.5 coincide very well with those of the series-solution, while the results of the asymptotic solution for this value of μ are not as good, and the results of the approximated-asymptotic solution for μ=15 agree with those of the asymptotic solution. This work has been carried out under the direction of Professor Zhang Wei.     

Wronskian and Grammian solutions for the (2+1)-dimensional BKP equation

The (2 + 1)-dimensional BKP equation in the Hirota bilinear form is studied during this work. Wronskian and Grammian techniques are applied to the construction of Wronskian and Grammian solutions of this equation, respectively. It is shown that these solutions can be expressed as not only Pfaffians but also Wronskians and Grammians.     

Aerodynamic optimization of 3D wing based on iSIGHT

A method for combining the CFD software,Fluent,with the iSIGHT design platform is presented to optimize a three-dimensional wing to ameliorate its aerodynamics performance.In the optimization design,two kinds of genetic algorithms,the Neighborhood Cultivation Genetic Algorithm（NCGA）and the Non-dominated Sorting Genetic Algorithm（NSGAII）,are employed and the Navier-Stoke（N-S）equations are adopted to derive the aerodynamics functions of the 3D wing.The aerodynamic performance of the optimized wing has been significantly improved,which shows that the approach can be extended and employed in other cases.     

柔性伸缩蒙皮支撑结构的多目标拓扑优化

针对柔性伸缩蒙皮支撑结构的多目标拓扑优化问题,分析了其实际应用中的优化对象及目标函数,提出使用六边形对设计域进行离散的方法,并建立离散模型与位矩阵的映射关系。采用基于位矩阵的NSGA-Ⅱ（Non-dominated Sorting Genetic Algorithm Ⅱ）进行求解。优化过程中引入个体连通性分析以提高计算效率。通过对可行个体进行有限元分析,获得其目标值;使用罚函数法对不可行个体加以惩罚,最终得到一组互不支配的支撑结构。结果表明,本方法可为柔性伸缩蒙皮支撑结构的多目标拓扑优化问题提供可行、有效的解,也可用于求解其它二维多目标拓扑优化问题。     

随机湍流工况低雷诺数风力机翼型优化研究

为改善小型风力机随机湍流工况适应性,以NACA0012翼型为研究对象,采用非嵌入式概率配置点法,获得随机湍流工况下小型风力机叶片翼型运行攻角分布规律;在气动优化中耦合层流分离预测,基于Transition SST模型、拉丁超立方试验设计、Kriging模型和带精英策略非支配排序遗传算法NSGA-II进行高湍流低雷诺数风力机翼型气动优化。结果表明,优化翼型叶片平均风能捕获效率分别提高3.01%和4.76%,标准差分别降低4.76%和14.93%,优化翼型湍流适应性增强。该方法将翼型设计与湍流风况相匹配,为湍流工况低雷诺数翼型及小型风力机设计提供参考。     

The wild solutions of the induced form under the spline wavelet basis in weakly damped forced KdV equation

In the paper what is studied is the wild solution of the induced form under the spline wavelet basis in weakly damped forced KdV equation. Project supported by the National Natural Science Foundation of China (19601020) and the Science-Technology Foundation of Minitry of Machine-building Industry of P. R. China     

大于切出风速的大型风力机运行控制策略研究

运用非定常叶素动量(BEM)理论计算气动载荷,叠加重力载荷和惯性载荷,建立并数值求解全机动力学模型。基于快速非支配排序遗传算法(NSGA),在切出风速以上,优化得到变速变桨和定速变桨两种控制规律曲线,实现大型风力机在25m/s~40m/s风速之间正常运行的目的。比较两种控制策略的输出功率、风轮推力和转矩,得出变速变桨控制策略更适合于25m/s~40m/s之间风力机运行控制的结论。计算稳态工况时8种叶根载荷的极限值,由各载荷的变化趋势可知,Fy在25m/s之后增大9%,其他载荷均安全。     

求解具有奇异性的桁架拓扑优化的遗传算法

采用遗传算法求解具有奇异最优解现象的桁架结构拓扑优化问题。在桁架结构拓扑优化的内力约束ε-放松列式基础上,根据遗传算法特点通过引入拓扑变量提出一种新的优化模型列式。在遗传算法中改进了适应度函数及约束处理方法、选择和交叉操作等,提高了求解算法的效率和可靠性。数值算例以及两种列式的对比分析表明,本文改进的遗传算法和新提出的优化模型列式,能够得到拓扑优化问题的全局最优解。     

Perturbation initial parameter method for solving the geometrical nonlinear problem of axisymmetrical shells

In the previous paper[7], the author presented a System of First-Order Differential Equations for the problem of axisynrm’trically loaded shells of revolution with small elastic. strains and arbitrarily large axial deflections, and a Method of Variable-Characteristic Nondimensionization with a Scale of Load Parameter. On this basis, by taking the weighted root-mean-square deviation of angular deflection from linearity as perturbation parameter, this paper pressents a perturbation system of nondimensional differential equations for the problem, thus transforms the geometrical nonlinear problem into several linear problems. This paper calculates these linear problems by means of the initial parameter method of numerical integration. The numerical results agree quite well with the experiments[4].     

地震作用下摩擦耗能减震结构优化

提出了地震作用下摩擦耗能支撑参数优化的一种新的数学模型。它的特点是在给定的几条地震波作用下,在满足框架的规范层间位移角限值要求下,框架各层安装的耗能支撑刚度之和最小,从而实现安装较少的耗能装置而能达到相同的抗震要求。本文利用遗传算法求解该优化问题,并编制了基于遗传算法的几条地震波分别作用下的摩擦耗能框架结构支撑参数弹塑性动力优化分析程序GAOFF。最后给出了一6层框架在三条地震波分别输入下的优化算例,分析结果表明本文方法是有效的。     

爆轰产物状态方程的水下爆炸反演理论研究

由于水下爆炸过程中爆轰产物的信息以水中压缩波形式向外传递,本文旨在探讨如何利用水下爆炸试验数据确定爆轰产物的状态方程。相较于常规圆筒试验,水下爆炸试验具有装置简单成本低、装药尺寸限制少、测定压力范围更广的特点,更适用于大药量或非理想炸药的现场测试。本文从水中冲击波轨迹和波后压力时程曲线出发,发展了由冲击波及其波后流场还原水气界面的逆特征线算法,以及根据水气界面确定爆轰产物状态方程的遗传算法。与水下爆炸正演结果对比,发现逆特征线法可以较准确地还原水气界面的位置和压力参数,有效压力下限可达2 MPa,远低于圆筒试验的测试下限0.1GPa。根据水气界面的反演结果,遗传算法也能稳定地优化JWL方程参数,8种常用炸药的等熵衰减压力误差在爆压至0.01 GPa的区间内都小于3%。结果表明,利用本文的逆特征线算法和遗传算法,理论上可以反演出压力范围较宽、准确性较高的爆轰产物状态方程。     

FLNG低温软管内衬波纹管多目标优化设计

低温柔性管道是海上浮式液化天然气生产储卸装置系统中输送液化天然气的核心装备之一。U型波纹管作为低温柔性管道最内层结构,直接影响低温管道的安全性。本文选取波径和环板长度作为独立结构设计参数进行结构分析,解决了在传统的U型波纹管灵敏度分析中,波高会随波距的改变而改变的耦合计算问题。构建了径向基函数神经网络代理模型,采用遗传算法对U型波纹管结构开展了多目标优化,获得以拉伸刚度最大和弯曲刚度最小为优化目标时的帕累托最优解集,为U型波纹管在实际工程应用中提供有益的设计参考。

     

Exact solutions of MHD second Stokes flow of generalized Burgers fluid

This work concerns with the exact solutions of magnetohydrodynamic (MHD) flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distribution and shear stress are expressed as a combination of steady-state and transient solutions computed by means of integral transformations. The effects of various parameters on the flow field are investigated. The MHD flow results in reduction of velocity distribution and associated thickness of the boundary layer.     

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

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 algorithm, 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.     

Analytical solutions for plane problem of functionally graded magnetoelectric cantilever beam

In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magneto-electro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.     

Investigation of horizontal-axis wind turbine (HAWT) blade threedimensional rotational effect based on field experiments

Field experiments are performed on a two-bladed 33 kW horizontal-axis wind turbine (HAWT). The pressures are measured with 191 pressure sensors positioned around the surfaces of seven spanwise section airfoils on one of the two blades. Three-dimensional (3D) and two-dimensional (2D) numerical simulations are performed, respectively, on the rotor and the seven airfoils of the blade. The results are compared with the experimental results of the pressure distribution on the seven airfoils and the lift coefficients. The 3D rotational effect on the blade aerodynamic characteristics is then studied with a numerical approach. Finally, some conclusions are drawn as follows. From the tip to the root of the blade, the experimental differential pressure of the blade section airfoil increases at first and then decreases gradually. The calculated 3D result of the pressure distribution on the blade surface is closer to that of the experiment than the 2D result. The 3D rotational effect has a significant impact on the blade surface flow and the aerodynamic load, leading to an increase of the differential pressure on the airfoils and their lift coefficient than that with the 2D one because of the stall delay. The influence of the 3D rotational effect on the wind turbine blade especially takes place on the sections with flow separation.     

旋转导向系统底部钻具组合力学计算新方法

底部钻具组合(Bottom Hole Assembly, BHA)的力学计算是进行旋转导向系统钻具组合设计和井眼轨迹控制的基础．本文在纵横弯曲法、加权余量法和有限元法的基础上,提出了一种基于管柱单元组合的BHA力学求解方法．该方法以保持微分方程特解相同的条件作为管柱单元划分依据,对底部钻具组合进行单元划分;将管柱单元的挠曲线通解替代传统加权余量法的试函数,结合单元节点类型和组合关系,构建出包含边界条件和通解系数的线性方程组．对于边界条件未知问题,以支点反力符号条件为约束条件,以挠曲线越界程度、切点处弯矩平衡条件为目标函数,建立了以边界条件未知量为变量的多目标优化数学模型．应用多目标优化算法求解出边界变量,进而得出通解系数;最后,得出管柱单元内各点位移和载荷．以推靠式旋转导向系统BHA力学计算为案例,对比本文方法与加权余量法的计算结果,发现两者计算结果相差较小,表明本文方法可用于旋转导向系统底部钻具组合的力学计算．     

A class of exact solutions for N-dimensional incompressible magnetohydrodynamic equations

In this paper, a sufficient and necessary condition is presented for existence of a class of exact solutions to N-dimensional incompressible magnetohydrodynamic(MHD)equations. Such solutions can be explicitly expressed by appropriate formulae. Once the required matrices are chosen, solutions to the MHD equations are directly constructed.     

可靠性优化问题中遗传算法适应值函数的建立

应用遗传算法进行优化,约束的处理成为建立适应值函数和算法进行的关键.可靠性优化是以系统可拿性指标作为优化问题的约束条件.首先结合外罚函数法建立数学模型,处理约束的惩罚因子时根据种群情况白适应取值,构造适应值函数的映射公式.随后采用拉格朗日秉子法建立了新的约束与目标函数向适应值函数的映射公式,该公式可以避免因罚函数病态所导致的搜索终止,收敛更加快速,使遗传算法得以成功应用于可靠性优化问题中.分析计算结果表明乘子法具有更好地收敛效果,两个公式构造合理.