高精密热敏电阻温度计校准方法的探讨

文章介绍了高精密热敏电阻温度计的特点。从校准条件、操作方法、数据处理三个方面对校准方法进行了阐述,其中数据拟合使用切比雪夫多项式法,最后进行了测量不确定度评定。     

基于自适应切比雪夫滤波器的非线性有源噪声控制

提出一种基于自适应切比雪夫滤波器的非线性有源噪声控制算法FCLMS。FCLMS算法使用传统的Fx LMS结构,将初级噪声使用第一类切比雪夫多项式展开,进而拟合该信号,而后使用LMS自适应算法进行噪声控制。该算法的计算复杂度低于2阶VFx LMS和1阶FS LMS算法。在不同的仿真模型下的仿真结果表明,该算法控制效果均达到或优于VFx LMS和FS LMS算法,且收敛速度快。     

一种求非线性振动系统周期解的切比雪夫级数方法

将切比雪夫级数理论和非线性优化算法结合,提出了一种求非线性振动系统周期解的方法。本方法将状态矢量中未知切比雪夫系数的求解,转化为对主周期上系统残差求最小值的无约束最优化问题,计算出了具有较高精度的切比雪夫级数周期解。所得周期解可通过积分运算直接求得系统的Floquet转移矩阵,从而分析周期解的稳定性。最后,以Duffing系统方程和直升机旋翼系统运动方程为例,验证了本方法正确、有效,也证明了将切比雪夫级数理论引入直升机气动弹性响应与稳定性研究正确可行。     

边缘识别的二维正交多项式拟合及结构变形检测

数字图像中边缘附近的灰度是沿边缘方向和跨边缘方向二维变化的,以前边缘识别的多项式拟合大多采用跨边缘方向的一维拟合.介绍一种采用二维正交多项式进行边缘识别的新方法,由于二维拟合更符合边缘附近小区域内像素灰度二维变化的实际,因此拟合结果优于一维拟合.在进行拟合时,利用正交多项式的正交性将优化方程对角化,避免求逆或解方程,没有多项式拟合优化方程的病态问题,采用高阶多项式拟合可以提高拟合精度.对生成图像的边缘识别结果表明,二维正交多项式拟合识别边缘的精度和稳定性较好.简支梁模型试验表明,采用正交多项式边缘拟合方法检测梁的静变形,图像变形检测精度在0.1像素之内,适当选择图像采集设备和采集范围,点检测精度与传统检测方法的精度相当,边缘检测属线状高密度检测,检测范围远大于传统方法.     

基于通用切比雪夫滤波器的有源噪声控制研究

针对前馈管道非线性有源噪声控制系统,提出一种基于通用切比雪夫滤波器的次级通道建模方法和通用切比雪夫滤波x最小均方误差算法(GCFXLMS,general Chebyshev filtered-x least mean square)。通用切比雪夫滤波器由第一类切比雪夫滤波器扩展获得,交叉项部分可通过对角结构实现,根据对角结构的性质,可以采用减少通道信号的实现策略以降低结构复杂度;使用该滤波结构建模次级通道,并给出了稀疏虚拟次级通道模型,基于此模型推导了GCFXLMS算法。该方法性能比较包括计算复杂度对比和控制效果对比。实验结果表明,在非线性有源噪声控制系统中,通用切比雪夫滤波器可达到与Volterra次级通道建模类似的建模效果,相比于传统的前馈滤波器,通用切比雪夫滤波器具有更优的控制性能。     

基于零相位滤波的聚焦形貌恢复技术

在聚焦形貌恢复技术中,为获取更好的恢复精度,提出了一种高精度的聚焦形貌恢复算法,该方法用零相位滤波器对窗口序列图像的评价函数值进行滤波,在消除干扰的同时,保持各空间数据点的位置不变.设计了基于切比雪夫Ⅱ滤波器的零相位滤波器;利用二次曲线的最小二乘拟合峰值位置作为窗口序列的聚焦位置,进一步提高了峰值定位精度;采用三次曲面...     

基于第二类切比雪夫多项式的语音线性谱对参数的计算

对线性谱对(LSP)参数的计算方法提出改进算法，该算法利用第二类切比雪夫多项式的迭代性质对初始函数降阶。理论分析表明，改进算法可以获得更简洁的数学表达式。实验结果显示，改进算法中基本消除了乘法运算，同时随着线性预测分析阶数的增加可以进一步降低算法复杂度。     

低温用NTC热敏电阻校准方程的评估

选用4个校准方程拟合应用于航天领域的两种NTC热敏电阻温度计,采用最小二乘法计算校准方程的系数,通过几个统计数据比较校准方程的性能并确定最佳拟合方程,同样的方法可用于评估其它NTC热敏电阻温度计校准方程的拟合能力.     

基于稀疏信号分解和分段拟合积分逼近的无转速计阶比方法与应用

针对传统无转速阶比存在低阶拟合阶次模糊和高阶拟合频率积分方程难求解的问题,提出了一种基于稀疏信号分解和分段拟合积分逼近的无转速计阶比方法。根据啮合频率的稀疏信号分解动态时间支撑区对瞬时转频分段,并进行低阶多项式拟合,采用积分逼近方法代替求解方程,确定等角度重采样时刻,准确实现无转速计下的阶比分析。仿真和实测信号试验结果表明：基于啮合频率动态时间支撑区对瞬时转频分段,既能保证各段内频率变化简单,又能使分段最少;在各分段内采用2阶多项式就能准确拟合,解决了单个多项式整体拟合精度不高、缺乏自适应性的问题;积分逼近求解等角度重采样时刻,不需要求解方程,有效解决了方程无解、无实数解影响阶比结果的问题;基于稀疏信号分解和分段拟合积分逼近的无转速计阶比方法,为无转速计条件下旋转机械变转速过程信号阶比分析提供了一种新的有效途径。     

稀疏信号分解-分段拟合逼近及其无转速计阶比应用

针对传统无转速阶比存在低阶拟合阶次模糊和高阶拟合频率积分方程难求解的问题,提出了一种基于稀疏信号分解和分段拟合积分逼近的无转速计阶比方法。根据啮合频率的稀疏信号分解动态时间支撑区对瞬时转频分段,并进行低阶多项式拟合,采用积分逼近方法代替求解方程,确定等角度重采样时刻,准确实现无转速计下的阶比分析。仿真和实测信号试验结果表明:基于啮合频率动态时间支撑区对瞬时转频分段,既能保证各段内频率变化简单,又能使分段最少;在各分段内采用2阶多项式就能准确拟合,解决了单个多项式整体拟合精度不高、缺乏自适应性的问题;积分逼近求解等角度重采样时刻,不需要求解方程,有效解决了方程无解、无实数解影响阶比结果的问题;基于稀疏信号分解和分段拟合积分逼近的无转速计阶比方法,为无转速计条件下旋转机械变转速过程信号阶比分析提供了一种新的有效途径。     

A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials

The accuracy of metamodelling is determined by both the sampling and approximation. This article proposes a new sampling method based on the zeros of Chebyshev polynomials to capture the sampling information effectively. First, the zeros of one-dimensional Chebyshev polynomials are applied to construct Chebyshev tensor product (CTP) sampling, and the CTP is then used to construct high-order multi-dimensional metamodels using the ‘hypercube’ polynomials. Secondly, the CTP sampling is further enhanced to develop Chebyshev collocation method (CCM) sampling, to construct the ‘simplex’ polynomials. The samples of CCM are randomly and directly chosen from the CTP samples. Two widely studied sampling methods, namely the Smolyak sparse grid and Hammersley, are used to demonstrate the effectiveness of the proposed sampling method. Several numerical examples are utilized to validate the approximation accuracy of the proposed metamodel under different dimensions.     

Problem of Contact of Two Half Spaces with a Ring-Shaped Groove in One of Them. Part 2. Numerical Method and Results

A numerical algorithm is proposed for the solution of a singular integral equation of the axisymmetric elastic problem of contact of two half spaces one of which contains a ring-shaped groove. By the methods of orthogonal polynomials and collocations, the singular integral equation is reduced to a system of nonlinear algebraic equations for the geometric parameters of the gap and the coefficients of Fourier expansion of the required function in Chebyshev polynomials of the first kind. A numerical solution of the posed problem is constructed and used for the analysis of contact parameters regarded as functions of the radii of the ring-shaped groove of fixed width.     

A Chebyshev collocation method for computing the eigenvalues of the Laplacian

Chebyshev collocation techniques are developed in this paper to compute the eigenvalues of the Laplacian based on a boundary integral formulation for two-dimensional domains with piecewise smooth boundaries. Unlike the traditional domain methods (for example, the finite element method) which discretizes the eigenfunctions on the two-dimensional domain, only a one-dimensional function defined on the boundary is discretized. Global expansions in terms of Chebyshev polynomials are used in each smooth piece of the boundary to solve the integral equation. Comparing with the boundary element method, this method obtains higher accuracy for a smaller discretized matrix. Finally, an efficient algorithm for generating the discretized matrix (say, n × n) is developed that requires only O(n² log n) operations.     

Spectral collocation methods for the primary two-point boundary value problem in modelling viscoelastic flows

Expansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two-point boundary value problem within a spectral collocation formulation. The performance of the methods is analysed in terms of accuracy and robustness relative to the level of non-linearity. Accurate results are obtained with Chebyshev polynomials and the performance of these trial functions is insensitive to the level of non-linearity whereas the behaviour of the beam functions shows great sensitivity to the level of non-linearity. The use of Newton's method to solve the mixed linear-non-linear system for the Chebyshev coefficients is successful for highly non-linear problems without the need for parameter continuation.     

Reliability-based design optimization of a car body using dimension- reduced Chebyshev polynomial

A reliability-based design optimization (RBDO) method of a car body is presented on basis of dimension-reduced Chebyshev polynomial method (DCM). To improve calculation efficiency and save computational time, complex models are often approximated by metamodels in reliability analysis. Traditional metamodels require a large number of sample points, which is time-consuming. To improve the efficiency, DCM is proposed to approximate the performance function of the car body. First, the performance function is decomposed by the dimension-reduction method into a sum of univariate functions, which are then fitted through Chebyshev polynomials. The reliability of the car body is predicted by the Taylor expansion method and the fourth-moment method. Finally, the result of RBDO is obtained using an improved adaptive genetic algorithm. The proposed method saves on the calculation time with high precision. Besides, the improved adaptive genetic algorithm reduces the number of iterations in the car body optimization and improves the efficiency.     

Determination of mixed mode cohesive laws

A novel approach is proposed for the determination of mixed mode cohesive laws for large scale crack bridging problems. The approach is based on a plane, two-dimensional analysis utilizing the J integral applied a double cantilever beam specimens loaded with uneven bending moments. The normal and shear stresses of the cohesive laws are obtained from consecutive values of the fracture resistance, the normal and tangential displacements of the end of the cohesive zone. The data analysis involves fitting and determination of partial differentials. This is done by a numerical method using Chebyshev polynomials. The accuracy of the numerical procedure is investigated by the use of synthetic data. It is found that both the shape and peak stress of the cohesive law can be determined with high accuracy, providing that the data possess low noise and a sufficiently high number of datasets are used. The investigation leads to some practical guidelines for experimental use of the proposed approach.     

一种新的会话密钥协商算法

对Chebyshev多项式的定义进行了扩展,形成了有限域Zp上的Chebyshev多项式。利用有限域上Chebyshev多项式的单向性和半群特性,构造了一种新的会话密钥协商算法。该算法具有会话密钥协商的公平性。与Diffie—Hellman算法相比,该算法的运行无需寻找有限域中的本原元,只需选用普通的整数即可,且算法的破译更为复杂。对算法的安全性进行了分析,指出任何在实数域上具有半群特性的代数多项式都可用来构造会话密钥协商算法。     

A Method of Estimating the Process Capability Index from the First Four Moments of Non‐normal Data

A method is presented to estimate the process capability index (PCI) for a set of non‐normal data from its first four moments. It is assumed that these four moments, i.e. mean, standard deviation, skewness, and kurtosis, are suitable to approximately characterize the data distribution properties. The probability density function of non‐normal data is expressed in Chebyshev–Hermite polynomials up to tenth order from the first four moments. An effective range, defined as the value for which a pre‐determined percentage of data falls within the range, is solved numerically from the derived cumulative distribution function. The PCI with a specified limit is hence obtained from the effective range. Compared with some other existing methods, the present method gives a more accurate PCI estimation and shows less sensitivity to sample size. A simple algebraic equation for the effective range, derived from the least‐square fitting to the numerically solved results, is also proposed for PCI estimation. Copyright © 2004 John Wiley & Sons, Ltd.     

用幂基多项式拟合频向函数的几点技巧

提出了用幂基多项式拟合频响函数的几点技巧。运用幂基多项式和最小二乘法对频响函数拟合的计算公式进行了推导,得到了用于问题求解的线性代数方程组,为改善该方程组系统矩阵的条件数,对频率变量和系数矩阵进行了规范化处理;频率变量被规范化到0＝－1的无量纲正实数区域,两个相关矩阵的每列模长被规范为1。然后用奇异值分解的方法求解该方程组,得到拟合频响函数所用的幂基多项式的系数。最后,根据幂基多项式的系数,求出系统的极点和留数,从而识别出系统的模糊态参数,文中给出了一个悬臂梁模拟算例,结果表明本文算法具有较好的计算精度。     

The method of particular solutions for solving axisymmetric polyharmonic and poly-Helmholtz equations

In this paper we derive analytical particular solutions for the axisymmetric polyharmonic and poly-Helmholtz partial differential operators using Chebyshev polynomials as basis functions. We further extend the proposed approach to the particular solutions of the product of Helmholtz-type operators. By using this formulation, we can approximate the particular solution when the forcing term of the differential equation is approximated by a truncated series of Chebyshev polynomials. These formulas were further implemented to solve inhomogeneous partial differential equations (PDEs) in which the homogeneous solutions were obtained by the method of fundamental solutions (MFS). Several numerical experiments were carried out to validate our newly derived particular solutions. Due to the exponential convergence of Chebyshev interpolation and the MFS, our numerical results are extremely accurate.