Polynomial-rooting based fourth-order MUSIC for direction-of-arrival estimation of noncircular signals

A polynomial-rooting based fourth-order cumulant algorithm is presented for direction-of-arrival（DOA） estimation of second-order fully noncircular source signals, using a uniform linear array（ULA）. This algorithm inherits all merits of its spectralsearching counterpart except for the applicability to arbitrary array geometry, while reducing considerably the computation cost.Simulation results show that the proposed algorithm outperforms the previously developed closed-form second-order noncircular ESPRIT method, in terms of processing capacity and DOA estimation accuracy, especially in the presence of spatially colored noise.

DESIGN OF NONCIRCULAR GEARS WITH DISCONTINUOUS PITCH CURVE

When the noncircular gear pair is applied to the continuously variable transmission （CVT） with gear, the transmission ratio function is discontinuous. In accordance with this unique characteristic, a new approach to design and analyze noncircular gears with discontinuous pitch curve is proposed. The design courses of various noncircular gear pairs with discontinuous pitch curve are unified based on the numerical algorithm of spline fitting and ＂fairing boundary condition＂. According to the particularity of discontinuous pitch curve, the rules and procedures for teeth distribution are recommended. It is explained in detail why the undercut is formed and how to manage the undercut based on meshing principle.In addition, the calculation formulas for each tooth profile segment are also derived. If the tooth profile data are calculated, the measurement and the incision process for noncircular gear can be conducted and the CAD simulation can be achieved easily. To ensure the continuity of the transmission, the transmission interference of the tooth which is located at the pitch curve joint point is managed by utilizing Bezier curve with CAD software. And the contact ratio of gear pair is obtained. The case study shows that this approach is successful and opens up a new way for the design of noncircular gear.

A Real-Valued 2D DOA Estimation Algorithm of Noncircular Signal via Euler Transformation and Rotational Invariance Property

The problem of two-dimensional(2 D)direction of arrival(DOA)estimation for double parallel uniform linear arrays is investigated in this paper.A real-valued DOA estimation algorithm of noncircular(NC)signal is proposed,which combines the Euler transformation and rotational invariance(RI)property between subarrays.In this work,the effective array aperture is doubled by exploiting the noncircularity of signals.The complex arithmetic is converted to real arithmetic via Euler transformation.The main contribution of this work is not only extending the NC-Euler-ESPRIT algorithm from uniform linear array to double parallel uniform linear arrays,but also constructing a new 2 Drotational invariance property between subarrays,which is more complex than that in NCEuler-ESPRIT algorithm.The proposed 2 DNC-Euler-RI algorithm has much lower computational complexity than2 DNC-ESPRIT algorithm.The proposed algorithm has better angle estimation performance than 2 DESPRIT algorithm and 2 D NC-PM algorithm for double parallel uniform linear arrays,and is very close to that of 2 D NC-ESPRIT algorithm.The elevation angles and azimuth angles can be obtained with automatically pairing.The proposed algorithm can estimate up to 2(M-1)sources,which is two times that of 2 D ESPRIT algorithm.Cramer-Rao bound(CRB)of noncircular signal is derived for the proposed algorithm.Computational complexity comparison is also analyzed.Finally,simulation results are presented to illustrate the effectiveness and usefulness of the proposed algorithm.

WIDELY LINEAR RLS CONSTANT MODULUS ALGORITHM FOR COMPLEX-VALUED NONCIRCULAR SIGNALS

Based on the constant modulus criterion, a new Widely Linear(WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance for complex-valued noncircular signals. The new algorithm takes advantage of the WL filtering theory by taking full use of second-order statistical information of the complex-valued noncircular signals. Therefore, the weight vector contains the complete second-order information of the real and imaginary parts to decrease the residual inter-symbol interference effectively. Theoretical analysis and simulation results show that the proposed scheme can significantly improve the equalization performance for complex-valued noncircular signals compared with traditional blind equalization algorithms.

Low-Complexity DOA Estimation of Noncircular Signals for Coprime Sensor Arrays

This paper presents a low?complexity method for the direction?of?arrival(DOA)estimation of noncircular signals for coprime sensor arrays.The noncircular property is exploited to improve the performance of DOA estimation.To reduce the computational complexity,the rotational invariance propagator method(RIPM)is included in the algorithm.First,the extended array output is reconstructed by combining the array output and its conjugated counterpart.Then,the RIPM is utilized to obtain two sets of DOA estimates for two subarrays.Finally,the true DOAs are estimated by combining the consistent results of the two subarrays.This illustrates the potential gain that both noncircularity and coprime arrays provide when considered together.The proposed algorithm has a lower computational complexity and a better DOA estimation performance than the standard estimation of signal parameters by the rotational invariance technique and Capon algorithm.Numerical simulation results illustrate the effectiveness and superiority of the proposed algorithm.

Effect of noncircular orifice plates on the near flow field of turbulent free jets

In this paper, we experimentally investigate the near-field flow characteristics of turbulent free jets respectively issued from circular, triangular, diamond, rectangular, and notched-rectangular orifice plates into air surroundings. All the orifice plates have identical opening areas or equivalent diameters（De） and their aspect ratios（AR） range from 1 to 6.5. Planar particle image velocimetry（PIV） is used to measure the velocity field at the same Reynolds number of Re = 5 × 10^4,where Re = Ue De/ν with Ue being the exit bulk velocity and ν the kinematic viscosity of fluid. The mean and turbulent velocity fields of all the five jets are compared in detail. Results show that the noncircular jets can enhance the entrainment rate, reflected by the higher acceleration rates of mean velocity decay and spread, shorten the length of the unmixed core,expedite the increase of turbulent intensity compared with the circular counterpart shortened unmixed core, and increase turbulent intensity comparing to the circular counterpart. Among the five jets, the rectangular jet（AR = 6.5） produces the greatest decay rate of the near-field mean velocity, postpones the position at which the 鈥榓xis-switching鈥檖henomenon occurs. This supports that axis switching phenomenon strongly depends on jet initial conditions. In addition, the hump in the centerline variation of the turbulence intensity is observed in the rectangular and triangular jets, but not in the circular jet, nor in diamond jet nor in notched-rectangular jet.

Effects of Finite Aspect Ratio and Noncircular Plasma Flux Surface on Electron Temperature Gradient Driven Modes

A gyrokinetic model with integral eigenmode equations is developed based on the local equilibrium of shaped tokamak plasmas. Effects of main geometric parameters （finite aspect ratio, elongation, triangularity, and Shafranov shift gradient） on the electrostatic electron temper- ature gradient （ETG） driven modes are investigated numerically. It is found that the finite aspect ratio has a general stabilizing effect, while the elongation can be either stabilizing or destabilizing, depending on the poloidal wavelength of the mode and other parameters. It is shown that a low aspect ratio enhances the stabilizing effect of elongation, and weakens its destabilizing effect as well.

Effects of Noncircular Inlet on the Flow Structures in Turbulent Jets

Turbulent jet flows with noncircular nozzle inlet are investigated by using a Reynolds Stress Model. In order to analyze the effects of noncircular inlet, the cross section of inlet are selected as circular, square, and equilateral triangular shape. The jet half-width, vorticity thickness, and developments of the secondary flow are presented. From the result, it is confirmed that the secondary flows of square and equilateral triangular nozzle are more vigorous than that of the circular jet. This development of secondary flows is closely related to the variations of vortical motions in axial and azimuthal directions.

Cutting Force Fluctuation Suppression and Error Homogenization of Noncircular Gear Hobbing Based on the Tool Shifting Method

The current research on noncircular hobbing mainly focuses on the linkage model and motion realization.However,the intermittent cutting characteristics of hobbing would increase uncertainties in the manufacturing process.In this paper,a hobbing machining model with tool-shifting characteristics was proposed to solve the problems of cutting force fluctuation and inconsistency of tooth profile envelope accuracy at different positions of the pitch curve in noncircular gear hobbing.Based on the unit cutting force coefficient method,the undeformed chip volume generated by interrupted cutting was used to characterize the fluctuation trend of the hobbing force.The fluctuation characteristics of the cutting force generated by different hobbing models were compared and analyzed.Using the equivalent gear tooth and hob slotting numbers,an analysis model of the tooth profile envelope error of the noncircular gear was constructed.Subsequently,the tooth profile envelope errors at different positions of the pitch curve were compared and analyzed based on the constructed model.The transmission structure of the electronic gearbox was constructed based on the proposed hobbing model,and the hobbing experiment was conducted based on the selfdeveloped noncircular gear CNC hobbing system.This paper proposes a hobbing method that can effectively suppress the fluctuation of the peak and whole circumference cutting force and reduce the maximum envelope error of the whole circumference gear teeth.

Design of Linear Functional Noncircular Gear with High Contact Ratio Used in Continuously Variable Transmission

Continuously variable transmission(CVT)of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency.The key technology of CVT with noncircular gear has been broken through some countries,and is in the stage of deep application research.Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China,the noncircular gear CVT is still in the preliminary exploration and research stage.The linear functional noncircular gear pair,whose transmission ratio is a linear function in the working section,to realize continuously variable transmission was the research object in this paper.According to the required transmission ratio in the working section,the transmission ratio function in the non-working section was constructed by using a polynomial.And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair.In addition,for improving the stability and bearing capacity of gear transmission,the noncircular gear pair transmission with high contact ratio was designed.Furthermore,the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile,from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment.Finally,an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.

Efficient tensor decomposition method for noncircular source in colocated coprime MIMO radar

An effective method via tensor decomposition is proposed to deal with the joint direction-of-departure(DOD)and direction-of-arrival(DOA)estimation of noncircular sources in colocated coprime MIMO radar.By decomposing the transmitter and receiver into two sparse subarrays,noncircular property of source can be used to construct new extended received signal model for two sparse subarrays.The new received model can double the virtual array aperture due to the elliptic covariance of imping sources is nonzero.To further exploit the multidimensional structure of the noncircular received model,we stack the subarray output and its conjugation according to mode-1 unfolding and mode-2 unfolding of a third-order tensor,respectively.Thus,the corresponding extended tensor model consisted of noncircular information for DOA and DOD can be obtained.Then,the higher-order singular value decomposition technique is utilized to estimate the accurate signal subspace and angular parameter can be automatically paired via the rotational invariance relationship.Specifically,the ambiguous angle can be eliminated and the true targets can be achieved with the aid of the coprime property.Furthermore,a closed-form expression for the deterministic CRB under the NC sources scenario is also derived.Simulation results verify the superiority of the proposed estimator.

Research and Test of Three-Pulley Noncircular Synchronous Pulley Transmission Mechanism with Minimum Slack

The noncircular synchronous belt drive mechanism has demonstrated certain achievements and has been used in special fields.Research regarding noncircular synchronous belt drive mechanisms has focused on optimization design and kinematic analysis in China,whereas two pulley noncircular synchronous belt transmissions have been developed overseas.However,owing to the noncircular characteristics of the belt pulley,the real-time variation in the belt length slack during the transmission of the noncircular synchronous belt is significant,resulting in high probabilities of skipping and vibration.In this study,a noncircular tensioning pulley is added to create a stable three-pulley noncircular synchronous belt driving mechanism and a good synchronous belt tensioning,with no skipping;hence,the non-uniform output characteristic of the driven pulley is consistent with the theoretical value.In the circular noncircular noncircular three-pulley noncircular synchronous belt mechanism,the pitch curve of the driving synchronous belt pulley is circular,whereas those of the driven synchronous belt and tensioning pulleys are noncircular.To minimize the slack of the belt length of the synchronous belt and the constraint of the concavity and circumference of the tensioning pulley,an automatic optimization model of the tensioning pulley pitch curve is established.The motion simulation,analysis,and optimization code for a three-belt-pulley noncircular synchronous belt drive mechanism is written,and the variation in belt length slack under different speed ratios is analyzed based on several examples.The testbed for a circular-noncircular-noncircular three-pulley noncircular synchronous belt transmission mechanism is developed.The test shows that the three-pulley noncircular synchronous belt drives well.This study proposes an automatic optimization algorithm for the tensioning pulley pitch curve of a noncircular synchronous belt transmission mechanism;it yields a stable transmission of the noncircular synchronous belt transmission mechanism as well as non-uniform output characteristics.

Air Cooling of Mini-Channel Heat Sink in Electronic Devices

Heat transfer experiments were conducted to investigate the thermal performance of air cooling through mini-channel heat sink with various configurations. Two types of channels have been used, one has a rectangular cross section area of 5 × 18 mm2 and the other is triangular with dimension of 5 × 9 mm2. Four channels of each configuration have been etched on copper block of 40 mm width,30 mm height, and 200 mm length. The measurements were performed in steady state with air flow rates of 0.002 - 0.005 m3/s, heating powers of 80 - 200 W and channel base temperatures of 48°C, 51°C, 55°C and 60°C. The results showed that the heat transfer to air stream is increased with increasing both of air mass flow rate and channel base temperature. The rectangular channels have better thermal performance than trian- gular ones at the same conditions. Analytical fin approach of 1-D and 2-D model were used to predict the heat transfer rate and outlet air temperature from channels heat sink. Theoretical results have been compared with experimental data. The predicted values for outlet air temperatures using the two models agree well with a deviation less than ±10%. But for the heat transfer data, the deviation is about +30% to –60% for 1-D model, and –5% to –80% for 2-D model. The global Nusselt number of the present experimental data is empirically correlated as with accuracy of ±20% for and compared with other literature correlations.

模型误差影响下基于CNN+BiLSTM神经网络的非圆信号目标直接跟踪算法

针对运动观测阵列状态误差与接收频率抖动同时影响下的非圆信号无源跟踪问题,提出了一种基于卷积神经网络(Convolutional Neural Network,CNN)+双向长短时记忆网络(Bi-directional Long Short-Term Memory,BiL⁃STM)的直接跟踪算法.该算法首先利用多运动观测阵列信号各频带间的相关性与辐射源信号的非圆特性,建立模型误差影响下的扩展多站观测矢量;接着利用多个观测时隙内扩展多站观测矢量的信号子空间构造空时特征输入序列;然后设计基于CNN与BiLSTM混合神经网络的直接跟踪模型,通过训练实现对非圆目标的轨迹矢量直接估计.本文算法是从原始数据信号子空间中估计轨迹矢量的直接跟踪模式,相比传统“观测参数估计+滤波轨迹跟踪”的两步估计模式,具有更高的估计精度.由于本文算法在神经网络训练过程中学习到模型误差的信息,因此能够实现对多种误差的校正.仿真结果表明,本文算法较传统两步跟踪算法与现有直接跟踪算法均具有更高的轨迹估计精度,能够明显提升模型误差影响下多站协同跟踪的鲁棒性.

非圆截面及非对称型面高速精密车削关键技术研究

针对非圆截面及非对称型面的高速精密车削加工难题,提出一种基于快速刀具进给伺服系统的该类型面数控车削加工方法。通过分析非圆截面及非对称表面数控车削原理、快速刀具进给伺服机构及其控制方法,并通过车削实验验证了方法的有效性。首先,分析了非圆截面与非对称表面车削的原理、复杂几何形状工件的轮廓数据处理机制和方法,为高速精密车削提供准确的工件描述。其次,快速刀具进给伺服机构是实现高速精密车削的关键,分析了各种快速进给系统优缺点,提出了采用直线电机的快速刀具进给伺服机构,采用自抗扰控制算法控制快速刀具伺服系统。最后,通过试制的实验样机车削实验验证了基于自抗扰控制的快速刀具进给伺服机构及其数控车削系统的技术和方法的可行性。实验结果表明,该技术能够成功地实现非圆截面及非对称型面工件加工,并能够实现较高的尺寸精度和表面质量,满足复杂型面工件的加工需求。

非圆间歇齿轮的节曲线设计及其周转缺陷的最速回转修复

针对非圆齿轮不能实现单向连续回转的问题,提出了一种等时间歇的N叶任意非圆齿轮节曲线的设计方法。通过分析节曲线的设计过程,将节曲线分为功能型和非功能型2类,其中,功能型节曲线用于满足任意给定的传动要求,非功能型节曲线用于补偿功能型节曲线以修复周转缺陷。为了提高非圆间歇齿轮的传动效率,基于变分原理构建了一种非功能型节曲线设计的最速回转修复模型,研究了该模型的实现机理。以功能型节曲线的边界条件为依据,利用欧拉-拉格朗日方程推导了该模型的解析解,给出了与其共轭的外啮合和内啮合非圆齿轮的节曲线方程。数值实例验证了该非圆间歇齿轮设计方法的实用性和最速回转修复模型的有效性。

非圆小通道内氮气-水气液二相流流型特性

通过可视化手段对水力直径为1.15 mm的矩形小通道(w×h=2 mm×0.81 mm)和正三角形小通道(边长2 mm)内氮气-水气液二相绝热垂直向上流动进行了实验研究。在表观气速0.1—30 m/s和表观液速0.01—5 m/s范围内,由实验结果得到2种小通道内的氮气-水典型流型图和流型转变界限。通过对比实验结果发现,在水力直径相同的情况下,小通道的截面形状对流型转变界限有显著影响。

内啮合非圆齿轮加工的数学模型及图形仿真

根据范成法加工内啮合非圆齿轮时刀具和齿轮节曲线间的位置关系,建立了插齿加工的数学模型,分析了加工非圆齿轮时其节曲线为凸的条件。根据所建模型和节曲线为凸的条件,将加工内啮合非圆齿轮的范成过程用计算机进行了动态图形仿真。根据图形仿真结果,可以分析和判断所加工非圆齿轮的齿形特征,为设计和制造节曲线封闭型内啮合非圆齿轮提供了直观的判断方法。

高阶变性椭圆锥齿轮传动模式设计与分析

高阶变性椭圆锥齿轮是球面大端节曲线为高阶椭圆或变性椭圆的非圆锥齿轮。针对目前非圆锥齿轮的设计与分析方法较繁复的问题,根据齿轮空间啮合原理,提出一种仿真加工获得高阶变性椭圆锥齿轮齿形的方法。模拟加工刀具与高阶变性椭圆锥齿轮的节曲线作纯滚动的齿形生成过程,推导出齿形形成过程中的运动参数,并对其节曲线、齿顶曲线及齿根曲线进行设计。重点分析高阶椭圆锥齿轮与变性椭圆锥齿轮齿廓的传动模式及其运动学特性,建立以高阶变性椭圆为基础的椭圆锥齿轮族的仿真模型,统一各种椭圆锥齿轮的传动模式及其设计过程,获得高阶变性椭圆锥齿轮齿廓在传动过程中的运动变化规律及齿轮副匹配模式的通式。通过试验验证该仿真加工获得高阶变性椭圆锥齿轮齿形的方法的正确性。此齿形获得方法可推广应用到任意球面节曲线形状及任意轴间夹角的非圆锥齿轮,从而实现非圆锥齿轮的通用参数化设计。

数控车削中凸变椭圆型面的成形方法

主要研究数控车削中凸变椭圆型面的成形方法。提出了将型面先分解、后合成的成形机理 ,将中凸变椭圆的型面分解为“椭圆”、“变椭圆”和“中凸”三个基本特征 ,对每一种特征进行了数学描述 ,并提出了相应的成形方法。采用微椭圆柱逼近整个型面 。