应用序列二次规划的波达方向与多普勒频率联合估计

为了快速准确地联合估计阵列信号波达方向(DOA)与多普勒频率,提出了将序列二次规划(SQP)应用于最大似然函数优化的联合谱估计算法。该方法利用空时信号模型通过Hankel矩阵构造出阵列流型中包含DOA与多普勒频率信息的广义天线阵模型,并推导出其最大似然函数,从而将参数估计问题转化为非线性函数优化问题。然后,将SQP方法应用于似然函数的优化求解中,得到DOA与多普勒频率的估计值。最后应用SQP方法、微分进化法、遗传算法和量子粒子群算法分别进行了优化的仿真对比实验。结果表明:提出的算法具有寻优时间短,估计精度高,参数自动配对等特点,在信噪比为0dB时估计两个目标信号源的DOA与多普勒频率的均方根误差分别为0.263 6°和0.007 6rad,基本达到了阵列信号处理中参数联合估计方法的设计要求。     

轴空间多约束下的五轴B样条路径速度规划

针对五轴机床刀具位姿与驱动轴非线性映射导致的驱动轴加速度、跃度超过电机限制问题,提出一种考虑驱动轴性能限制的进给速度规划方法.基于机床的运动学反解,推导了驱动轴的速度、加速度、跃度与进给速度的映射关系,建立加工过程驱动轴的约束条件;以加工效率为优化目标,建立多约束条件下高维度非线性最优化模型;应用序列二次型规划(SQP...     

基于序列二次规划算法的机械弹性车轮的结构优化

在保证结构与实际车轮模型结构相同的条件下,建立机械弹性车轮的有限元模型,实现了车轮受力时的结构协调性和弹簧的回位功能。利用ANSYS软件对车轮进行了有限元分析,得出车轮的径向刚度。根据结构优化问题的特点,以轮辐的每段长度作为设计变量,轮胎径向刚度为优化目标,利用序列二次规划(SQP)算法,对车轮结构进行优化设计。结果表明:基于SQP算法的机械弹性车轮的结构优化,在允许范围内有效的增大了车轮的径向刚度。     

履带式工程车机械液压差速转向装置参数设计

机械液压差速转向装置作为一种双功率流转向装置,其参数设计是一个非线性、多目标和多参数优化问题。在对履带式工程车参数设计、目标评价和约束条件理论分析的基础上,提出了一种基于多岛遗传算法(Multi Island Genetic Algorithm, MIGA)和序列二次规划(Sequential Quadratic Programming, SQP)法的组合优化方法。根据组合优化的思想,对履带式工程车机械液压差速转向装置参数进行全局寻优,结合实例样车设计需要,将机械液压差速转向装置参数进行优化,优化后的参数可满足设计需要,表明所给出的组合优化方法可用于工程车机械液压差速转向装置参数设计。     

面齿轮磨削齿面齿形误差修正

以面齿轮齿面的形状误差为研究对象,建立了面齿轮齿面数学方程,通过三坐标测量仪（CMM）对面齿轮齿面进行了误差测量。为提高面齿轮齿面的精度,提高其理论和工程的应用价值,提出了一种基于序列二次规划（SQP）的面齿轮齿面误差评定方法。建立了齿面误差的识别方程,应用序列二次规划算法对机床加工参数进行优化求解,并与最小二乘优化法进行对比,应用修正后的机床调整参数,再次通过三坐标测量仪对修正后的齿面误差进行检测,验证了该方法的可行性。     

基于序列二次规划算法的圆柱度误差评定方法

圆柱的形状误差为研究对象,为提高圆柱体形状误差评定精度,增强其理论和工程应用价值,提出一种基于序列二次规划算法的圆柱度误差评定方法。定义了测量点到圆柱面的符号距离函数,建立了圆柱度误差评定的数学模型,应用最小二乘方法将圆柱进行粗定位,将拟合圆柱和测量点进行坐标变换简化了误差评定数学模型,运用运动几何学的知识和序列二次规划(SQP)算法解决了满足最小区域原则的圆柱度评定的优化问题。实验结果表明:提出的圆柱度的评定算法稳定性较好,效率和精度较高,所得到的误差值是有效的。     

区间不确定多目标优化算法在薄板冲压成形中的应用研究

提出一种薄板冲压成形不确定多目标优化方法,该方法将冲压成形中的摩擦因数作为不确定参数,采用区间描述,以厚度不均最小和起皱最小为目标函数,以压边力和拉深筋阻力作为设计变量。基于非线性区间数值规划将不确定多目标优化问题转换为确定的多目标优化问题。采用Kriging近似模型提高优化效率,基于多目标遗传算法和序列二次规划算法的混合优化算法取得Pareto解集。应用算例说明了该算法的有效性。     

凸优化方法在工作站负荷优化配置中的应用

在不考虑设备故障的前提下,一个工作站的服务质量主要取决于其负荷大小。本文建立了工作站负荷最小的优化模型,设计了一种变量转换方法,并经适当的约束条件合并将该非线性的、具有不等式约束的模型转化为凸优化模型。推导给出该凸优化模型对应的拉格朗日函数及其最优解存在的KKT条件,并引入凸优化内点法作为负荷配置的有效计算工具。实例计算结果表明,凸优化内点算法具有迭代次数少、收敛速度快的优点;实际应用中可以将非线性的复杂优化问题凸性化,从而得到其最优解。     

基于可靠性优化的风电齿轮箱传动系统安全系数预可控设计

针对风电齿轮箱传动系统设计过程中各级安全系数难以预先定量控制的问题,建立了完整的风电齿轮箱传动系统可靠性优化模型.结合标准ISO6336将轮齿疲劳安全系数进行分类和整理,并将其表示成关于优化变量的显式函数形式,在此基础上制定了合理的目标函数,应角序列二次规划法(SQP)求解优化模型.算例表明:优化后的风电齿轮箱传动系统较好地体现了设计者的预先期望,能够实现各级啮合安全系数预先可控,从而有效避免了传统选配法在这方面的局限性.     

基于AMESim和SQP算法的爬行焊接机温控系统优化设计

为了提高爬行焊接机温度控制系统的精度和稳定性,提出了一种基于AMESim和序列二次规划(SQP)算法的温控系统优化设计方法.通过ANSYS温度场分析优化热楔的结构,采用理论分析和试验相结合的方法获取系统各个元件的模型参数,建立符合实际工况的热楔等关键部件的数学模型,根据工作条件确定爬焊机温控系统的约束条件,运用AMESim和序列二次规划(SQP)算法对爬行焊接机温控系统的PID参数进行优化.结果表明:采用SQP算法对爬行焊接机温控系统PID参数进行优化是可行的,系统稳态温度偏差控制在1℃以内,满足快速稳定的焊接作业要求.     

Straightness and flatness evaluation using data envelopment analysis

In today's world of precision engineering, robustness and accuracy in the evaluation of the form tolerances are considered as competitive advantages for manufacturing enterprises. Amongst various methods for accurate and robust evaluation, which have been studied, nonlinear optimization methods based on operational research have proved to be successful as far as they can ensure unique and global convergence in practical applications. However, it is well known that ensuring the convergence is the most difficult thing to deal with for a nonlinear optimization technique because the performance is in general highly sensitive to parameter setting. Therefore, this paper introduces a robust linear programming formulation-based algorithm in which the performance is not dependent on the quality of parameters. Interestingly, in this algorithm, the data envelopment analysis technique is used to form a convex hull that decides the minimum enclosed zone in a robust manner. From the computational experiments, it is shown that the proposed algorithm can be a promising alternative to the traditional nonlinear optimization method for straightness and flatness evaluation.     

Conicity error evaluation using sequential quadratic programming algorithm

Form error evaluation plays an important role in processing quality evaluation. Conicity error is evaluated as a typical example in this paper based on sequential quadratic programming (SQP) algorithm. The evaluation is carried out in three stages. Signed distance function from the measured points to conical surface is defined and the cone is located roughly by the method of traditional least-squares (LS) firstly; the fitted cone and the measured point coordinates are transformed to simplify the optimal mathematical model of conicity error evaluation secondly; and then optimization problem on conicity error evaluation satisfying the minimum zone criterion is solved by means of SQP algorithm and kinematic geometry, where approximate linear differential movement model of signed distance function is deduced in order to reduce the computational complexity. Experimental results show that the conicity error evaluation algorithm is more accurate, and has good robustness and high efficiency. The obtained conicity error is effective.     

A combinatorial optimization approach for evaluating minimum-zone spatial straightness errors

This paper presents a new and robust approach for the accurate evaluation of minimum-zone spatial straightness error from a set of coordinate measurement data points. The algorithm iteratively searches for the specific data points that define the minimum bound of the spatial straightness zone using combinatorial optimization. It is based on the fact that the minimum circumscribed cylinder of a point set, which is equivalent to the minimum spatial straightness zone of the measurement data, will pass through three, four, or five of the data points that constitute the convex hull vertices of the entire data set. Computed results have shown that although the presented approach may lead to increased computational time, it is robust and able to construct the exact minimum circumscribed cylinder for a given point set. The minimum-zone spatial straightness error can thus be evaluated with the best possible accuracy. The advantage of the presented algorithm is demonstrated via comparison with published computed results of existing algorithms.     

以线性逼近算法模式实现形状误差包容评定

根据形状误差定义及数学规划理论,建立形状误差包容评定的非线性规划模型,提出一种线性逼近算法摸式。其核心是利用线性规划模型的迭代运算,结合坐标变换去逼近非线性规划模型最优解。理论分析和大量计算表明算法能精确地评定形状误差,且快速收敛、计算稳定。     

A method for axis straightness error evaluation based on improved artificial bee colony algorithm

An improved artificial bee colony (IABC) optimization algorithm for the accurate evaluation of minimum zone axis straightness error from a set of coordinate measurement data points was proposed. In the proposed algorithm, the opposition-based learning method was employed to produce initial population and scouts, the employed bees used greedy selection mechanism to update the best food source achieved so far one by one, and a new search mechanism inspired by differential evaluation was used for onlookers. The nonlinear mathematical model for axis straightness error evaluation and the fitness function of IABC were introduced in detail. Four classical test functions were selected in the experiments; the simulation results verified the feasibility of IABC algorithm. According to two practical examples, the results obtained by the IABC algorithm are more accurate and efficient than other conventional methods. It is a unified approach for other form and position error evaluations and is well suited for high-precision measuring equipments such as the CMM.     

Profile error evaluation of free-form surface using sequential quadratic programming algorithm

Profile error of free-form surface is evaluated in this paper based on sequential quadratic programming (SQP) algorithm. The optimal localization model is established with the minimum zone criterion firstly. Subsequently, the surface subdivision method or STL (STeror Lithography) model is used to compute the point-to-surface distance and the approximate linear differential movement model of signed distance is deduced to simplify the updating process of alignment parameters. Finally, the optimization model on profile error evaluation of free-form surface is solved with SQP algorithm. Simulation examples indicate that the results acquired by SQP method are closer to the ideal results than the other algorithms in the problem of solving transformation parameters. In addition, real part experiments show that the maximum distance between the measurement points and their corresponding closest points on the design model is shorter by using SQP-based algorithm. Lastly, the results obtained in the experiment of the workpiece with S form illustrate that the SQP-based profile error evaluation algorithm can dramatically reduce the iterations and keep the precision of result simultaneously. Furthermore, a simulation is conducted to test the robustness of the proposed method. In a word, this study purposes a new algorithm which is of high accuracy and less time-consuming.     

Evaluation method for spatial straightness errors based on minimum zone condition

A nonlinear mathematical model for spatial straightness error evaluation based on the minimum zone condition is established in this paper. According to the error analysis, it is proved that the mathematical model for spatial straightness error evaluation cannot be linearized. A criterion for verification of the existence and uniqueness of the minimum zone solution is proposed. A new computational method is also proposed, and practical examples are given. Finally, the correctness of this method is demonstrated using a geometrical solution. This new method is convenient for computation of uniqueness and exactness of the minimum zone solution.     

Straightness and flatness tolerance evaluation: an optimization approach

This paper presents an optimization approach that could be used to calculate exact values of straightness and flatness errors as defined by the ANSI Y14.5M standards on geometric dimensioning and tolerancing. The straightness and flatness error evaluation problems are formulated as nonlinear optimization problems with linear objective function and nonlinear constraints. Because of the special structure of the problem, a linear search method is developed that reduces the nonlinear problem to a linear programming problem with only two constraints. Examples are presented to compare the optimization approach with the least-squares method and some exact methods. The results show that the optimization procedures presented in this paper provide exact values of straightness and flatness errors and are superior to the existing methods in terms of computation time.     

Semidefinite programming for Chebyshev fitting of spatial straight line with applications to cutter location planning and tolerance evaluation

This paper presents a novel model for fitting of spatial straight line based on Chebyshev norm. The problem is firstly formulated as a minimax problem, and then reformulated as a semidefinite programming (SDP) problem, which could be solved by many interior-point algorithms. The application of the proposed approach to two problems arising from manufacturing engineering, i.e. planning of the initial location of cylindrical cutter for flank milling and evaluation of the spatial straightness error, is discussed. Examples and numerical simulations illustrate the efficiency of the novel model.     

间歇过程PSO SQP混合优化算法研究*

针对SQP算法在求解具有复杂约束的间歇过程优化时容易陷入局部极值点的问题,本文提出一种PSO-SQP混合优化算法。该算法首先采用外点罚函数法将间歇过程有约束的优化问题转换为无约束的优化问题,利用PSO强大的全局搜索能力对其进行求解,并把搜索结果作为SQP搜索初始点,以此弥补SQP全局搜索弱的缺点,再利用SQP良好的局部收敛性和较强的非线性收敛速度对原优化问题进行精细搜索,弥补了PSO局部搜索弱的缺点,通过不断的迭代最终获得优化问题的全局最优解。该算法充分利用了SQP和PSO的优缺点,增强了其对复杂约束优化问题的求解能力。将本文提出的算法用于连续搅拌化学反应系统温度控制中,仿真结果表明产物浓度能够充分逼近期望值,且反应器的温度轨迹收敛,从而验证了该算法的有效性和实用价值。