ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN

In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.

UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE NONLINEAR DIFFERENTIAL POLYNOMIALS SHARE ONE VALUE OR HAVE THE SAME FIXED POINTS IN AN ANGULAR DOMAIN

In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article improve Theorem 1 of Yang and Hua [26], and improve Theorem 1 of Fang and Qiu [6].

Uniqueness Theorems of Entire Functions with Shared-set in an Angular Domain

There have been lots of papers on the uniqueness theory of entire functions concerning shared-sets in the whole complex plane. However, it seems that the uniqueness theory in an angular domain is not widely investigated. In this paper, we study the uniqueness of entire functions concerning shared-sets in an angular domain instead of the whole complex plane, and we supply examples to show that Theorem 1 is sharp.

On Uniqueness of Meromorphic Functions and Their Derivatives in One Angular Domain

In this paper, applying the Nevanlinna theory of meromorphic function in one angular domain, we deal with a problem of uniqueness for meromorphic functions and their derivatives sharing three finite value ignoring multiplicities in an angular domain instead of the whole complex plane. Obtained results improve a recent result of Lin Weichuan and Seiki Mori.

The lifetime of conditioned Brownian motion in an angular domain

Conditioned Brownian motions in bounded domains have been extensively studied.However, we know little about the conditioned processes in an unbounded domain for the difficulty of techniques and methods. Only a few peculiar cases are investigated. In this note, we shall be devoted to investigating the integrability of the lifetime of conditioned Brownian motions in the angular domain A_m^d={(x^1,…, x^d)∈R^d, x^i】0, 1≤i≤m≤d} (d≥2).

Research on Instantaneous Angular Speed Signal Separation Method for Planetary Gear Fault Diagnosis

Planetary gear train is a critical transmission component in large equipment such as helicopters and wind turbines. Conducting damage perception of planetary gear trains is of great significance for the safe operation of equipment. Existing methods for damage perception of planetary gear trains mainly rely on linear vibration analysis. However, these methods based on linear vibration signal analysis face challenges such as rich vibration sources, complex signal coupling and modulation mechanisms, significant influence of transmission paths, and difficulties in separating damage information. This paper proposes a method for separating instantaneous angular speed (IAS) signals for planetary gear fault diagnosis. Firstly, this method obtains encoder pulse signals through a built-in encoder. Based on this, it calculates the IAS signals using the Hilbert transform, and obtains the time-domain synchronous average signal of the IAS of the planetary gear through time-domain synchronous averaging technology, thus realizing the fault diagnosis of the planetary gear train. Experimental results validate the effectiveness of the calculated IAS signals, demonstrating that the time-domain synchronous averaging technology can highlight impact characteristics, effectively separate and extract fault impacts, greatly reduce the testing cost of experiments, and provide an effective tool for the fault diagnosis of planetary gear trains.

THE POINCAR-BERTRAND FORMULA ON THE BUILDING DOMAIN OF COMPLEX BIBALLS

The Poincare-Bertrand formula takes an important position in the study of complex singular integral. The Poincare-Bertrand formula on the complex sphere in the multidimensional complex Euclidian spaces was given by Sheng Gong. Using the method of solid angular coefficient, the authors extend the Poincare-Bertrand formula on the complex sphere to the building domain of the complex biballs, and obtain a more general Poincare- Bertrand formula with the solid angular coefficients.

面向高机动目标检测的激光雷达探测图像分角域识别方法

高速移动和快速变换的运动模式容易导致目标模糊,从而无法准确识别目标的轮廓、形状和位置。为此,提出了面向高机动目标检测的激光雷达探测图像分角域识别方法。首先,通过邻域范围内像素点距离异常检测,去除激光雷达探测图像中的噪声和异常信号;然后,利用L-R算法解决目标高速移动造成的图像模糊问题;最后,采用基于互信息的自适应角域划分方法将图像分割成不同的角度域,并通过卷积神经网络在各角域中进行高精度目标识别,以实现高机动目标激光雷达探测。实验结果表明,该方法能够有效去除高机动目标造成的激光雷达探测图像模糊现象;相较于其他传统方法,该方法的目标识别率和全类平均精度较高、单图识别平均耗时较低,具有良好的识别效果。

基于时间序列森林的雷达高分辨距离像目标识别

为了提高雷达目标识别准确率与不完备角域数据下的识别性能,提出一种基于时间序列森林的高分辨距离像(HRRP)目标识别算法。详细介绍了时间序列森林算法的基本原理和用于HRRP目标识别的基本步骤。对实测HRRP数据的实验结果表明,相比于K-最近邻(KNN)、支持向量机(SVM)、随机森林(RF)、卷积神经网络(CNN)和长短时记忆网络(LSTM)等经典的目标识别算法,本文算法具有较优的识别性能与更好的角域推广能力。在只训练1/2和1/3角域数据的条件下,对全角域数据识别率均值优于85%,较上述方法平均提升5.2%。

复杂地物背景角域后向散射分布特性研究

针对采用平均后向散射系数进行对地空炸毫米波引信回波仿真时,因照射区域内入射角度散布较大造成仿真精度不足的问题,对复杂地物背景后向散射特性测试的远场条件进行了讨论,修正了复杂地物背景毫米波近场测试远场条件表达式,提出一种针对引信对地探测的复杂地物背景角域后向散射分布建模方法,构建基于实测数据优化的土耕地、水泥地等背景角域后向散射场,分析其对引信探测响应回波的影响。仿真结果表明,接近垂直入射情况下与传统乌拉比模型比较一致性较好,接近水平入射情况下比乌拉比模型后向散射系数小2~4 dB。利用该引信回波算法提高了毫米波引信探测仿真精度,可为对地空炸毫米波引信探测器设计提供数据支撑。

基于瞬时角速度信号窄带解调的RV减速器针齿故障检测

针对工业机器人实际工况下旋转矢量(rotary vector,RV)减速器低速级不完全旋转工况针齿故障特征提取困难的问题,研究结合编码器信号的优势,提出一种基于瞬时角速度(instantaneous angular speed,IAS)信号窄带解调的RV减速器针齿故障检测方法。首先,消除RV减速器换向过程产生的异常数据,获取非整周转RV减速器的IAS信号;接着,对IAS信号进行角域同步平均,消除非同步干扰对信号分析的影响;随后,设计带通滤波器对信号进行滤波;最后,通过幅值解调和相位解调进行针齿故障检测。试验结果显示,所提方法可有效实现RV减速器低速级不完全旋转工况下的针齿故障检测。

基于磁编码器和窄带解调的太阳轮故障检测

绝对式磁编码器具有价格低、安装方便等优势,适合于工程应用,但在低转速工况下其角度信号受测量误差的影响较大,需要对角度信号进行拟合以消除测量误差带来的干扰。传统的分段拟合方法在分段点处易出现不连续现象,角度信号的不连续导致由其计算的瞬时角速度(instantaneous angular speed,简称IAS)信号中出现虚假冲击,并对基于IAS信号的故障特征提取造成干扰。针对此问题,提出一种基于绝对式磁编码器IAS估计和窄带解调的太阳轮故障检测方法。首先,为保证IAS信号的连续性与平滑性,提出基于最小二乘拟合与5次Hermite插值的方法,实现了对IAS信号的拟合估计和平滑处理;其次,结合窄带解调技术实现了对行星齿轮减速器太阳轮故障特征的有效提取;最后,通过对正常与故障太阳轮的绝对式磁编码器信号分析对比,验证了所提方法的有效性。

基于角度域同步平均和阶次分析的低速斜齿轮故障诊断

为了准确识别转速波动的斜齿轮早期故障特征,提出了基于光电编码器等角度采样的角度域同步平均降噪与阶次分析相结合的故障诊断方法。首先基于时域同步平均原理提出了角度域同步平均算法,采用光电编码器作为外触发器对时域信号进行等角度采样,然后将重采样信号在角度域内进行同步平均,消除与给定频率无关的周期信号和随机噪声的干扰,再利用阶次分析提取故障特征,最后通过斜齿轮点蚀故障诊断试验验证了该方法的有效性。

基于线调频小波路径追踪阶比能量解调的齿轮轮齿裂纹故障诊断

针对变速下齿轮裂纹故障信号微弱,难以提取这一特点,提出了基于线调频小波路径追踪的阶比能量解调算法,并将其应用于变速下的齿轮裂纹故障诊断。该方法先采用线调频小波路径追踪算法提取齿轮的啮合频率分量,由此得到转速信号;然后利用转速信号对原始信号进行等角度采样得到角域平稳信号;接着对角域平稳信号进行带通滤波和角域平均运算以消除干扰噪声的影响;最后使用能量算子解调求取瞬时频率和瞬时幅值,根据瞬时频率和瞬时幅值进行故障诊断。应用实例表明,该方法能有效地提取变速下的齿轮裂纹故障。

方程f″+Af'+Bf=0的解在角域内的增长性及Borel方向

运用角域内值分布的理论和方法,研究了整系数2阶线性微分方程f″+Af'+Bf=0的解在角域内的增长性和Borel方向.在给定条件下,证明了方程的每一非零解在含有B的λ(λ>0)级Borel方向的任意角域内的增长级均为无穷,且B的λ级Borel方向与解的无穷级Borel方向一致.

关于Huxley方程高阶奇点的定性分析

Huxley方程在y轴两个方向上的无穷远点为不定号情况下的高阶奇点,利用水平等倾线与垂直等倾线构成的曲边扇形域来研究该类奇点轨线的定性结构,得到了y轴两个方向上的无穷远点有无数条积分曲线进入或走出的结论。

Borel方向与亚纯函数的唯一性

设f是复平面上的亚纯函数,argz=θ(0≤θ<2π)是f的一条Borel方向.如果亚纯函数g和f在包含argz=θ的角域内IM分担五个不同的值。a_i∈C(i=1,2,3,4,5),则f≡g.

角域多信息熵融合算法的EHA柱塞泵滑靴副状态评估方法

滑靴副是电静液执行器(Electro-hydrostatic Actuator,EHA)柱塞泵中受力最为复杂和薄弱环节,在变转速极端工况下对其健康状态进行有效评估对于EHA的安全稳定运行尤为重要。针对滑靴副在变转速工况下磨损故障特征机理复杂、难以揭示的问题。提出一种基于角域多信息熵融合算法的新状态评估方法,结合阶比分析与信息熵理论,针对EHA变转速极端工况提出“角域信息熵”新概念,运用BP神经网络和D-S证据理论构建基于角域多信息熵融合的滑靴磨损状态评估模型;最后在恒压变转速工况条件下,以滑靴外边缘偏磨磨损故障为例对评估模型进行测试试验验证和结果分析,证实状态评估方法有效性和评估结果的准确性。

基于阶次跟踪和小波包分析相结合的滚动轴承升速过程的故障诊断方法研究

滚动轴承在实际工况下并非全部都是恒速运转,在某些工况下一直处于变速工作,因此对变速过程的振动信号进行研究同样具有重要意义。在其变速工作过程中,振动信号包含大量的特征信息。并且由于此类信号所表现出非平稳性的特点,如果采用传统的频谱分析法分析,结果就会出现严重的"频率模糊"现象,很难提取到故障信息。所以提出了一种基于阶次跟踪和小波包分析相结合的诊断方法。首先对升速过程时测得的原始时域信号进行等角度重采样,然后对重采样后的角域信号进行小波包分解和重构,最后对重构信号进行阶次谱分析。通过仿真信号验证和实例分析,能够对滚动轴承故障进行有效诊断,从而表明本方法的有效性。

一种永磁电机齿槽转矩测量方法

针对当前齿槽转矩测量方法存在的局限性,提出一种简单易行的齿槽转矩测量方法。首先,利用砝码驱动装配在电机轴上的圆盘带动电机转动,通过编码器采集转子位置信号。其次,根据测试系统动力平衡方程得到齿槽转矩计算公式,并从角域分别对计算结果进行低通阶次滤波和角域傅里叶变换得到齿槽转矩角域曲线和其阶次成分及幅值。最后,利用该方法对一台8极12槽的永磁同步电机进行测试,实验结果与理论分析相符。此外,搭建与矢量控制实验平台相对应的电机控制模型,仿真所测齿槽转矩引起的转速谐波幅值大小,并与实验结果相对比,间接验证了所测齿槽转矩阶次成分准确性和幅值精度。结果表明:该方法不需搭建复杂的试验台,具有操作简单、成本低等优点。测试结果可用于评价齿槽转矩大小、电机结构优化及齿槽转矩相关谐波的抑制等。