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勒让德多项式 1

厄米多项式 1

同相/正交分量不平衡；正交频分复用；标准独立 1

基于观测器同步；混沌系统；勒让德多项式；安全通信 1

广义哈密尔顿—雅可比—贝尔曼方程；非线性最优控制；伽辽金逼近（Galerkin approximation）；勒让德多项式（Legendre polynomials） 1

拉盖尔多项式 1

求根 1

科里奥利质量流量计；数字信号处理方法；两相流工况；正交解调；滑动离散傅里叶变换；希尔伯特变换 1

高斯积分 1

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Anisotropy of multi-layered structure with sliding and bonded interlayer conditions

Lingyun YOU, Kezhen YAN, Jianhong MAN, Nengyuan LIU

《结构与土木工程前沿（英文）》 2020年第14卷第3期页码 632-645 doi: 10.1007/s11709-020-0617-4

摘要： A better understanding of the mechanical behavior of the multi-layered structure under external loading is the most important item for the structural design and the risk assessment. The objective of this study are to propose and develop an analytical solution for the mechanical behaviors of multi-layered structure generated by axisymmetric loading, and to investigate the impact of anisotropic layers and interlayer conditions on the multi-layered structure. To reach these objectives, first, according to the governing equations, the analytical solution for a single layer was formulated by adopting the spatial Hankel transform. Then the global matrix technique is applied to achieve the analytical solution of multi-layered structure in Hankel domain. The sliding and bonded interlayer conditions were considered in this process. Finally, the numerical inversion of integral transform was used to solve the components of displacement and stress in real domain. Gauss-Legendre quadrature is a key scheme in the numerical inversion process. Moreover, following by the verification of the proposed analytical solution, one typical three-layered flexible pavement was applied as the computing carrier of numerical analysis for the multi-layered structure. The results have shown that the anisotropic layers and the interlayer conditions significantly affect the mechanical behaviors of the proposed structure.

关键词： multi-layered structure Hankel transformation anisotropic transversely isotropic interlayer condition Gauss-Legendre quadrature

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高阶高斯积分节点的高精度数值计算

张庆礼,王晓梅,殷绍唐,江海河

《中国工程科学》 2008年第10卷第2期页码 35-40

摘要：

在工程数值计算、X射线衍射线形分析、光谱学等领域常使用高斯数值积分，高斯积分的节点及权重因子是数值积分的必须数据。研究了高次勒让德、拉盖尔和厄米多项式的零点，即高斯-勒让德、高斯-拉盖尔、高斯-厄米积分的节点的计算方法，给出了一种有效的高精度数值算法——搜索迭代方法（scan-iteration method，SIM）。根据勒让德、拉盖尔、厄米多项式的特点，对拉盖尔多项式、厄米多项式的定义稍做变化后，获得了计算多项式值的稳定递推关系。求它们的根时，先在一定范围内以一定的步长搜索根所在的

关键词：高斯积分勒让德多项式拉盖尔多项式厄米多项式求根

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Anefficient quadrature demodulator for medical ultrasound imaging

Hao ZHOU,Yin-fei ZHENG

《信息与电子工程前沿（英文）》 2015年第16卷第4期页码 301-310 doi: 10.1631/FITEE.1400205

摘要： Quadrature demodulation is used in medical ultrasound imaging to derive the envelope and instantaneous phase of the received radio-frequency (RF) signal. In quadrature demodulation, RF signal is multiplied with the sine and cosine wave reference signal and then low-pass filtered to produce the base-band complex signal, which has high computational complexity. In this paper, we propose an efficient quadrature demodulation method for B-mode and color flow imaging, in which the RF signal is demodulated by a pair of finite impulse response filters without mixing with the reference signal, to reduce the computational complexity. The proposed method was evaluated with simulation and in vivo experiments. From the simulation results, the proposed quadrature demodulation method produced similar normalized residual sum of squares (NRSS) and velocity profile compared with the conventional quadrature demodulation method. In the in vivo color flow imaging experiments, the time of the demodulation process was 5.66 ms and 3.36 ms, for the conventional method and the proposed method, respectively. These results indicated that the proposed method can maintain the performance of quadrature demodulation while reducing computational complexity.

关键词： B-mode ultrasound imaging Color flow imaging Quadrature demodulation Finite impulse response filter

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连续非线性最优控制问题的勒让德—伽辽金逼近方法 Article

Xue-song CHEN

《信息与电子工程前沿（英文）》 2017年第18卷第10期页码 1479-1487 doi: 10.1631/FITEE.1601101

摘要：由于勒让德多项式（Legendre polynomials）具有正交性，在计算函数内积时，该方法可以明显减少积分计算量。详细证明了此方法的稳定性和收敛性。

关键词：广义哈密尔顿—雅可比—贝尔曼方程；非线性最优控制；伽辽金逼近（Galerkin approximation）；勒让德多项式（Legendre polynomials）

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利用勒让德多项式同步两种不同的混沌系统及其在安全通信中的应用 None

Saeed KHORASHADIZADEH, Mohammad-Hassan MAJIDI

《信息与电子工程前沿（英文）》 2018年第19卷第9期页码 1180-1190 doi: 10.1631/FITEE.1601814

摘要：提出一种新的由状态反馈控制器和鲁棒控制项组成的混沌同步控制器，采用勒让德多项式补偿不确定性，还考虑截断错误。由于正交函数定理，勒让德多项式可逼近任意小的近似误差的非线性函数。因此，勒让德多项式可取代模糊系统和神经网络来估计和补偿控制系统中的不确定性。勒让德多项式具有比模糊系统和神经网络更少的调整参数，它的调整过程更为简单。与模糊系统的参数类似，使用从稳定性分析获得的自适应规则在线估计勒让德系数。假设主系统和从系统分别是Lorenz混沌系统和Chen混沌系统。安全通信系统需要基于观测器同步，因为主系统通过信道只发送一个状态变量。讨论了使用基于观测器同步获得其他状态变量的方法。仿真结果表明该方法的有效性。与模糊滑模控制器的比较表明，所提的控制器表现出优异的瞬态响应。此外，解释了安全通信问题，并测试了安全通信中控制器的性能。

关键词：基于观测器同步；混沌系统；勒让德多项式；安全通信

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Analytical and numerical investigation into the longitudinal vibration of uniform nanotubes

null

《机械工程前沿（英文）》 2014年第9卷第2期页码 142-149 doi: 10.1007/s11465-014-0292-z

摘要：

In recent years, prediction of the behaviors of micro and nanostructures is going to be a matter of increasing concern considering their developments and uses in various engineering fields. Since carbon nanotubes show the specific properties such as strength and special electrical behaviors, they have become the main subject in nanotechnology researches. On the grounds that the classical continuum theory cannot accurately predict the mechanical behavior of nanostructures, nonlocal elasticity theory is used to model the nanoscaled systems. In this paper, a nonlocal model for nanorods is developed, and it is used to model the carbon nanotubes with the aim of the investigating into their longitudinal vibration. Following the derivation of governing equation of nanorods and estimation of nondimensional frequencies, the effect of nonlocal parameter and the length of the nanotube on the obtained frequencies are studied. Furthermore, differential quadrature method, as a numerical solution technique, is used to study the effect of these parameters on estimated frequencies for both classical and nonlocal theories.

关键词： continuum theory differential quadrature method nanorod longitudinal vibration

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Velocity gradient elasticity for nonlinear vibration of carbon nanotube resonators

Hamid M. SEDIGHI, Hassen M. OUAKAD

《结构与土木工程前沿（英文）》 2020年第14卷第6期页码 1520-1530 doi: 10.1007/s11709-020-0672-x

摘要： In this study, for the first time, we investigate the nonlocality superimposed to the size effects on the nonlinear dynamics of an electrically actuated single-walled carbon-nanotube-based resonator. We undertake two models to capture the nanostructure nonlocal size effects: the strain and the velocity gradient theories. We use a reduced-order model based on the differential quadrature method (DQM) to discretize the governing nonlinear equation of motion and acquire a discretized-parameter nonlinear model of the system. The structural nonlinear behavior of the system assuming both strain and velocity gradient theories is investigated using the discretized model. The results suggest that nonlocal and size effects should not be neglected because they improve the prediction of corresponding dynamic amplitudes and, most importantly, the critical resonant frequencies of such nanoresonators. Neglecting these effects may impose a considerable source of error, which can be amended using more accurate modeling techniques.

关键词： velocity gradient elasticity theory nanotube resonators differential-quadrature method nonlinear vibration

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Uncertainty propagation analysis by an extended sparse grid technique

X. Y. JIA, C. JIANG, C. M. FU, B. Y. NI, C. S. WANG, M. H. PING

《机械工程前沿（英文）》 2019年第14卷第1期页码 33-46 doi: 10.1007/s11465-018-0514-x

摘要： In this paper, an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle, aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function (PDF) of the system response. The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis. Moreover, assisted by the Rosenblatt transformation, the various types of extended integration points are transformed into the extended Gauss-Hermite integration points, which makes the method suitable for any type of continuous distribution. Subsequently, within the sparse grid numerical integration framework, the statistical moments of the system response are obtained based on the transformed points. Furthermore, based on the maximum entropy principle, the obtained first four-order statistical moments are used to fit the PDF of the system response. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed method, which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.

关键词： uncertainty propagation analysis extended sparse grid maximum entropy principle extended Gauss integration Rosenblatt transformation high-order moments analysis

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OFDM直接变频接收机中通用的I/Q不平衡估计与补偿方法 None

Fang-lin GU, Shan WANG, Wen-wu WANG

《信息与电子工程前沿（英文）》 2018年第19卷第3期页码 388-397 doi: 10.1631/FITEE.1700003

摘要：直接变频接收机由于具有低功耗的特点，受到广泛关注，但是它存在较严重的同相/正交（I/Q）分量不平衡问题：I/Q不平衡会恶化接收信号的信噪比，进而影响系统的传输容量和能够支持的调制方式。本文首先分析了I/Q不平衡对OFDM接收机接收信号的影响，在此基础上，定义了一个统计量用于刻画OFDM系统的I/Q不平衡特性，并提出一种实现I/Q不平衡参数估计与补偿的方法。特别地，进一步证明该统计量不受传输信道影响，因而该方法适用于高斯白噪声和多径衰落信道等不同场景。仿真结果表明，该方法可以实现对OFDM系统I/Q不平衡的准确估计与补偿，使补偿后系统的误比特率性能接近于不存在I/Q不平衡的情形。更重要的是，由于该方法不依赖于导频信号，因而可以应用于采用不同标准的OFDM系统。

关键词：同相/正交分量不平衡；正交频分复用；标准独立

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科里奥利质量流量计气液两相流信号处理的改进

李春辉1,孙立军1,刘佳荣1,张扬1,李海洋2,王化祥1

《信息与电子工程前沿（英文）》 2021年第22卷第2期页码 141-286 doi: 10.1631/FITEE.1900558

摘要：科里奥利质量流量计作为一种日益流行的流量测量仪表，在单相流条件下表现出较高测量精度，并在工业上得到广泛应用。但在复杂流动条件下，例如两相流工况，由于各种因素（包括不合适的信号处理方法），测量精度会大大降低。本文分析了3种数字信号处理方法——正交解调（QD）、希尔伯特和滑动离散傅立叶变换法，分别用于处理传感器信号并在两相流工况下测试算法性能。在此基础上，分别改进了两相流条件下的信号处理方法。在仿真中使用随机游走模型分别建立单相流和两相流工况下的传感器信号，评估这3种方法的相位差跟踪性能。基于数字信号处理器，在其评估板上完成转换器程序设计。将转换器在单相流和两相流工况下测试，根据测量精度和算法复杂度评估改进的信号处理方法性能，结果表明QD算法在单相流工况下性能最佳。在两相流条件下，QD算法在160、250和420 kg/h流量点的测量指示误差和重复性能优于改进的希尔伯特算法，而希尔伯特算法在600 kg/h流量点的性能优于QD算法。

关键词：科里奥利质量流量计；数字信号处理方法；两相流工况；正交解调；滑动离散傅里叶变换；希尔伯特变换

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标题作者时间类型操作

Anisotropy of multi-layered structure with sliding and bonded interlayer conditions

Lingyun YOU, Kezhen YAN, Jianhong MAN, Nengyuan LIU

期刊论文

高阶高斯积分节点的高精度数值计算

张庆礼,王晓梅,殷绍唐,江海河

期刊论文

Anefficient quadrature demodulator for medical ultrasound imaging

Hao ZHOU,Yin-fei ZHENG

期刊论文