Norms of Dual Complex Vectors and Dual Complex Matrices

In this paper,we investigate some properties of dual complex numbers,dual complex vectors,and dual complex matrices.First,based on the magnitude of the dual complex number,we study the Young inequality,the Hölder inequality,and the Minkowski inequality in the setting of dual complex numbers.Second,we define the p-norm of a dual complex vector,which is a nonnegative dual number,and show some related properties.Third,we study the properties of eigenvalues of unitary matrices and unitary triangulation of arbitrary dual complex matrices.In particular,we introduce the operator norm of dual complex matrices induced by the p-norm of dual complex vectors,and give expressions of three important operator norms of dual complex matrices.

ON THE DECOMPOSITION OF COMPLEX VECTOR SPACES AND THE JORDAN CANONICAL FORM OF COMPLEX LINEAR TRANSFORMATIONS

New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.

Accurate two-degree-of-freedom discrete-time current controller design for PMSM using complex vectors

Properties of the current controller are essential for permanent magnet synchronous machine(PMSM)drives,but the conventional continuous-time current controller cannot fully decouple the cross-coupling terms when applied in the digital processor.Its performance is related closely to the rotational speed.To improve the performance of the current loop,the direct design method in the discrete-time domain is adopted using the accurate discrete-time complex vector model.An integrated accurate hold-equivalent discrete model for PMSM is derived considering the difference between the output of the voltage source inverter and the back electro-motive force.Then an accurate two-degree-of-freedom(2DOF)current controller with a third-order closed-loop transfer function is designed.The 2DOF controller has more freedom in pole placement,and two schemes with a different cancelled pole-zero pair are investigated.Analysis is conducted by the robust root locus method via the complex vector root locus and sensitivity functions,showing properties in disturbance rejection and sensitivity to parameter variation of two schemes.Both schemes have their own advantages.Finally,the dynamic performance and flexibility of the proposed current controller is verified on a 2.5-kW PMSM test bench.

WAVE SUPERPOSITION METHOD BASED ON VIRTUAL SOURCE BOUNDARY WITH COMPLEX RADIUS VECTOR FOR SOLVING ACOUSTIC RADIATION PROBLEMS

By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.

Nonlinear Dynamic Characteristics of the Vectored Thruster AUV in Complex Sea Conditions

The mobility of the vectored thruster AUV in different environment is the important premise of control system design. The new type of autonomous underwater vehicle (AUV) equipped with rudders and vectored thrusters which are combined to control the course is studied. Firstly, Euler angles representation and quaternion method are applied to establish six-DOF kinematic model respectively, then Newton second law and Lagrangian approach are used to deduce the vectored thruster AUV’s nonlinear dynamic equations with six degrees of freedom (DOF) respectively in complex sea conditions based on the random wave theory according to the structural and kinetic characteristics of the vectored thruster AUV in this paper. The kinematic models and dynamic models based on different theories have the same expression and conclusion, which shows that the kinematic models and dynamic models of the vectored thruster AUV are accurate. The Runge-Kutta arithmetic is used to solve the dynamic equations, which not only can simulate the motions such as cruise and hover but also can describe the vehicle’s low-frequency and high-frequency motion. The results of computation show that the mobility of the vectored thruster AUV in interference-free environment and the integrated signals including low-frequency motion signal and high-frequency motion signal in environmental disturbance accord with practical situation, which not only solve the problem of especial singularities when the pitch angle θ = ±90° but also clears up the difficulties of computation and display of the coupled nonlinear motion equations in complex sea conditions. Moreover, the high maneuverability of the vectored thruster AUV equipped with rudders and vectored thrusters is validated, which lays a foundation for the control system design.

Complex Spacetime Frame: Four-Vector Identities and Tensors

This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.

Support vector regression model for complex target RCS predicting

The electromagnetic scattering computation has developed rapidly for many years; some computing problems for complex and coated targets cannot be solved by using the existing theory and computing models. A computing model based on data is established for making up the insufficiency of theoretic models. Based on the ＂support vector regression method＂, which is formulated on the principle of minimizing a structural risk, a data model to predicate the unknown radar cross section of some appointed targets is given. Comparison between the actual data and the results of this predicting model based on support vector regression method proved that the support vector regression method is workable and with a comparative precision.

双向驱动井径测井仪推靠系统工作行为分析

针对单向驱动井径测井仪存在的启动响应慢、速度集中和初始运动冲击等问题,提出一种具有双向驱动特征的新型结构井径测井仪,并对其推靠系统(实现测量臂伸缩)双向驱动过程进行矢量化建模求解及工作行为分析(运动性能仿真、测量性能仿真)。首先进行双向驱动测井仪推靠系统物理建模和理论研究,以双驱动丝杠系统参数(速度、位移)为输入,采用复数矢量法对测井仪推靠系统运动性能参数(位移、速度、加速度)进行参数化表征;然后以实际双驱动推靠系统为对象进行实例分析,对其运动特性进行理论求解,得到推靠杆端口和推靠销钉的运动曲线,并对双驱动速度匹配特性进行研究;最后基于ADAMS进行测井仪工作行为分析,将仿真与理论结果进行对比,结果表明推靠系统仿真运动曲线与理论解析曲线具有较高的吻合度,证明了测井仪推靠系统矢量化建模求解的正确性。

考虑频率耦合特性的D-PMSG复数域阻抗建模及其特征分析

阻抗分析法因其简单有效被广泛用于含电力电子变换器的互联系统稳定性研究。然而,采用传统方法对频域序阻抗建模时,需通过非线性变换(Park变换及其反变换)进行坐标系转换,这会导致不同周期分量的卷积运算及相应的频移,其过程较为烦琐。针对上述问题,基于复向量时域微分算子,提出了永磁直驱同步发电机(D-PMSG)等效阻抗建模方法。该方法在时域周期系统稳定运行轨迹的邻域内直接进行小信号线性化,并采用指数旋转因子灵活反映系统受扰后的时变特性,结合时域微分算子等效表征互联系统控制环节的动态特性,避免了频域阻抗建模时坐标系的反复变换,大幅降低了解析建模的复杂度。此外,所提方法能够更加清晰地阐释互联系统受到扰动时D-PMSG并网逆变器产生频率耦合现象的物理意义;同时,能够说明基频电压初始相位对耦合分量相频特性的影响。最后,利用仿真验证了所提算法的有效性。

Optimized Complex Power Quality Classifier Using One vs. Rest Support Vector Machines

Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power quality classification techniques focused on single power quality events and did not include an optimal feature selection process. This paper presents a classification system that employs Wavelet Transform and the RMS profile to extract the main features of the measured waveforms containing either single or complex disturbances. A data mining process is designed to select the optimal set of features that better describes each disturbance present in the waveform. Support Vector Machine binary classifiers organized in a “One Vs Rest” architecture are individually optimized to classify single and complex disturbances. The parameters that rule the performance of each binary classifier are also individually adjusted using a grid search algorithm that helps them achieve optimal performance. This specialized process significantly improves the total classification accuracy. Several single and complex disturbances were simulated in order to train and test the algorithm. The results show that the classifier is capable of identifying >99% of single disturbances and >97% of complex disturbances.

低复杂度永磁同步电机三矢量固定开关频率模型预测电流控制策略

针对传统永磁同步电机(permanent magnet synchronous motor,PMSM)三矢量模型预测电流控制(three-vector model predictive current control,TV-MPCC)存在开关频率不固定和计算复杂的问题,提出一种固定开关频率TV-MPCC策略。利用前一周期的零电压矢量和参考电压矢量所在扇区来快速筛选所需最优电压矢量和次优电压矢量,避免了无效枚举计算,从而降低了开关频率和计算复杂度。引入系统d和q轴电流差参数,计算各电压矢量的作用时间,确保电压矢量作用时间恒大于零和开关频率固定。以三相两电平电压型逆变器驱动的表贴式PMSM为被控对象,通过仿真和实验对传统TV-MPCC策略和所提三矢量固定开关频率模型预测电流控制策略进行对比研究,仿真和实验结果表明,所提策略在保证系统稳态和动态性能的基础上,在固定和降低开关频率的同时,降低了计算复杂度。

基于复矢量及HSS的MMC交直流侧阻抗建模

模块化多电平换流器(modular multilevel converter,MMC)具有运行稳定、控制多样化等优点,对其精确建模成为当前研究热点。提出了一种基于复矢量的MMC交直流侧阻抗建模方法。该方法根据复矢量建模的基本原理分析了换流器的正负序转换关系,并在考虑三相耦合的前提下,从差共模角度简述了三相MMC的建模要点,建立了三相系统的完整时域模型。引入谐波状态空间理论(harmonic state space,HSS)对所建模型进行处理来提高建模精度,并利用接口矩阵及阻抗求解的基本原理建立了MMC的交直流侧阻抗模型。最后在仿真平台进行了对比实验,证实了建模方法的可行性。

高速永磁同步电机解耦控制——低载波比数字延时与Smith预估控制

永磁同步电机(PMSM)运行在高速工况时,由于逆变器的开关频率受限使得载波比较低,会出现数字延时加剧的问题,直接影响了系统的控制性能,甚至造成系统失稳。针对低载波比工况下的数字延时问题,首先对数字延时环节进行精确的复矢量建模,并基于转速及电流环带宽的根轨迹、闭环零极点图及波特图分析数字延时对系统性能的影响,并给出考虑延时后系统的临界失稳转速。结合复矢量解耦策略,提出一种改进的基于Smith预估控制的解耦延时补偿电流控制策略,能够避免高速低载波比工况下系统失稳的问题,提高了电流环的稳定性,同时具有较好动态响应能力和解耦性能。采用Simulink仿真对比验证了所提的解耦延时补偿控制策略的有效性。

考虑换相过程的电网换相换流器小信号阻抗建模

建立准确的数学模型对于判断电力系统稳定性具有重要意义,其中阻抗模型凭借简单有效的优势成为判断系统稳定性的常用工具。为完成考虑换相过程的电网换相换流器阻抗建模,在dq坐标系下采用了基于平均化的小信号建模方法。首先,将换相重叠过程中各物理量的非线性变化过程利用小信号法线性化,建立了物理量之间的传递函数;然后,加入了交流电源侧的交流网络简化模型,同时考虑了定电压控制方式和锁相环的建模,得到电网换相换流器直流侧和交流侧的等效阻抗模型;最后,通过对比PSCAD/EMTDC仿真结果和模型计算结果,证明了阻抗模型的准确性。

自注意力机制下复杂文本实体关系抽取方法

为了能够明确语义关系,快速识别所需信息,提出一种自注意力机制下复杂文本实体关系抽取方法。通过复杂文本向量模型把全部词映射为低度实数向量,使文本转变成矢量模式,按照单词的外在情境学习嵌入,可将句子内的所有字转化为嵌入矩阵。利用LSTM网络建立文本向量,存取以往和将来的上下文,融合前后两种输出矢量。运用激活函数压缩单词维度,计算句子上下文本语义贡献权重,在双向LSTM层和输出层间加入自注意力机制,从多角度获取矩阵层次的句子语义,计算组合句子特征矢量在关系上的分数,根据给定概率随机抽样权值参变量,完成复杂文本实体关系抽取。通过实验证明所提方法对复杂文本实体关系抽取效果较好,具有极高的精准度。

基于改进支持向量回归的空战飞行动作识别

针对空战中飞机的飞行动作愈发复杂导致识别准确率低的问题,提出了改进支持向量回归的空战飞行动作识别方法,该方法采用高斯核函数作为线性核函数,利用混沌初始化和反向学习策略改进麻雀搜索算法,利用改进后的麻雀算法优化支持向量回归算法,具体表现为对支持向量回归算法中高斯核函数的参数进行优化,通过优化后的支持向量回归算法进行飞机动作识别。采用了五种基本的飞行动作和几种复杂的飞行动作验证该方法的识别准确率。仿真表明,优化后的支持向量回归算法与传统的支持向量回归算法、模糊支持向量机算法、传统聚类算法、神经网络算法相比,对基本飞行动作的平均识别率至少提升了2.2%,对复杂飞行动作的平均识别率至少提升了3.7%。

多连杆锻造重载机械臂运行轨迹分析及算法研究

针对多连杆机械臂在运动轨迹计算繁杂,解析计算难度较大的问题,提出采取复数矢量法进行计算,在MATLAB中求解机械臂的末端轨迹,并在ADAMS中对多连杆机械臂建立运动学和动力学模型,完成仿真分析,验证理论计算的轨迹。

高速磁悬浮用直线同步电机电流控制策略研究

高速磁悬浮列车采用直线同步电机作为其驱动装置,其电流控制效果直接影响列车运行稳定性及舒适性。针对直线电机功率较大的特点,单相驱动时采用多H桥串联方案,并可实现高低速运行时驱动拓扑切换,矢量控制中电机电流经过坐标变换后dq轴电流存在严重的交叉耦合,并且耦合分量随着车速的增加不断增大,从而降低了电流控制性能。为了提升电机动态控制效果,提出复矢量电流控制方法,并采用虚拟电阻解决了不同调制方式下电流振荡问题,通过半实物仿真平台对控制性能进行了验证,仿真和实验结果表明了电流控制策略的可行性和有效性。

远东燃料动力综合体产业结构偏离度的空间分析

俄罗斯东向能源政策对远东燃料动力综合体产业投资产生冲击效应,燃料动力综合体为增加向亚太地区国家的燃料动力资源出口实施了一系列投资项目。2012—2019年,远东燃料动力资源的产业结构出现偏离度。相关计算采用产业指数增长率结构分解法(偏离—比重分析法)的传统模型和空间模型。从国家、宏观区域(区域间)、地区等不同空间层面,对远东燃料动力综合体年均就业人数和总增加值增长率进行结构分解,并得出以下结论:在俄罗斯东向能源政策框架下燃料动力综合体采掘业的发展获得强大推动力,其竞争力分量为正值,弥补了导致全俄经济失稳的负面冲击影响;影响燃料动力综合体采掘业经济发展态势的重要因素在于区域间竞争成败,而非空间外部性;区别于煤炭产业,油气产业具备形成空间外部性的潜力;采掘业的发展领先于其他产业,仍是地区经济飞地。原文发表于俄罗斯《空间经济》杂志2022年第4期((1)),经作者同意以中文刊发于《西伯利亚研究》。

Discrete Differential Geometry and the Structural Study of Protein Complexes

This paper proposes a novel four-dimensional approach to the structural study of protein complexes. In the approach, the surface of a protein molecule is to be described using the intersection of a pair of four-dimensional triangular cones (with multiple top vertexes). As a mathematical toy model of protein complexes, we consider complexes of closed trajectories of n-simplices (n=2,3,4...), where the design problem of protein complexes corresponds to an extended version of the Hamiltonian cycle problem. The problem is to find “a set of” closed trajectories of n-simplices which fills the n-dimensional region defined by a given pair of n+1 -dimensional triangular cones. Here we give a solution to the extended Hamiltonian cycle problem in the case of n=2 using the discrete differential geometry of triangles (i.e., 2-simplices).