FFT+FT离散频谱校正法参数估计精度

研究用FFT谱连续细化傅里叶变换分析法进行离散频谱校正时的参数估计误差。分析无噪声情况下频率﹑相位﹑幅值的估计误差随细化倍数的变化规律,估计精度随细化倍数的增大而提高,当细化倍数大于40时,最大估计误差几乎可忽略不计。在高斯白噪声的影响下,细化后频谱序列最大值找错的概率随细化倍数的增加而增加,综合考虑频率分辨率对频率估计精度的影响及频谱序列最大值找错的概率,提出用归一化频率估计综合误差和归一化频率估计最大可能误差两个指标评价此校正法对频率的估计精度,并基于此给出不同信噪比条件下的最优细化倍数。采用非线性最小二乘拟合法对噪声影响下的FFT谱连续细化傅里叶变换分析校正法进行改进,通过仿真模拟验证改进后该校正方法具备更高的校正精度和抗噪能力。     

能量重心法的改进FFT算法分析及应用研究

研究噪声引起的谱线定位错误对能量重心法校正精度的影响。为了提高频率校正精度,在分析能量重心法理论和现有谱线选择方法的基础上,提出了一种减少谱线定位错误率的改进FFT校正算法。该算法在D. Macleod法基础上,利用谱线间的相位差确定谱线,减少了谱线定位错误。最后给出了通用的频率校正公式。仿真结果表明,改进算法谱线定位错误率低,抗噪性强,高斯白噪声条件下进行频率估计时较其他方法具有更小的均方根误差。在模拟井下套管的管道长度检测应用中进一步表明,改进方法具有更高的校正精度,有效地减少了长度测量误差。     

考虑电网频率变化率的改进相位差校正法研究

针对电网信号基波频率动态变化时相位差校正法测量结果存在较大误差,甚至可能测量失败的问题,提出了一种考虑频率变化率的改进相位差校正法。指出了非同步采样造成的频谱泄漏是相位差校正法测量误差的主要来源,尤其当基频动态变化导致基波频率偏移较大时,非同步采样使测量精度严重降低。推导了基于频率变化率修正的归一化频率校正量公式,在线测量时,频率变化率用前次与当次测得的基波频率进行差商运算求得,再据此对测量结果进行了修正。分别使用考虑频率变化率的方法和原方法对变频电网信号进行了数值仿真研究。研究结果表明,改进相位差校正法有更高的测量精度,对基波的测量精度提高一个数量级,采样窗长为IEC标准规定窗长的50%,能满足频率动态变化时谐波在线测量的精度与实时性要求。     

计及负频率的极高频信号离散频谱校正新方法

对于机械振动与故障诊断等领域中常见的极高频(接近奈奎斯特频率)信号,传统的离散频谱校正方法存在着较大误差,负频率成分干涉严重是影响其频谱分析精度的重要因素。为提高极高频信号的频谱分析与校正精度,给出了一种计及负频率影响的离散频谱校正新方法。该方法基于Blackman窗,依据离散频谱的周期性并利用局部谱峰附近的3条谱线,建立包含正负频率贡献的离散频谱校正模型,通过对模型的求解获得频率、幅值和相位校正公式。采用频段内扫描的方式对频谱校正公式进行了仿真验证,结果表明所提方法可有效降低负频率成分对极高频信号频谱的干涉影响,提高其频率、幅值和相位校正精度。     

适用于频率偏移情况下谐波参数估计的改进算法

针对电网信号基波频率偏移时传统相位差校正法测量结果存在较大误差,甚至可能产生测量失败的问题,提出了一种基于传统相位差的改进算法。将电网电压信号加入Blackman-Harris窗,通过分析加窗信号的频谱表达式,研究了电参量估计的误差来源,将频谱表达式进行了多项式变换从而加快了旁瓣衰减速度,进一步减轻频谱泄漏和各谱线之间的干扰,再依据传统相位差法的估计公式和多项式变换所得的新频谱表达式对电参量进行了重新估计。分别使用传统相位差法和经多项式变换的改进相位差法进行了数值仿真对比。研究结果表明:改进算法较传统相位差法相比各次谐波的测量精度提高了至少一个数量级,适用于频率偏移情况下电力系统谐波参数的高准确度估计;即使在噪声条件下,改进算法的优势也比较明显。     

基于双窗全相位FFT双谱线校正电力谐波分析

基于快速傅里叶变换的电力谐波分析在非同步采样情况下存在频谱泄露,影响测量精度。为抑制频谱泄露对谐波分析的影响,分析对比了双窗全相位FFT与传统加窗FFT在抑制频谱泄露方面的特点,并通过计算证明了双窗全相位FFT在电力谐波分析中的独特优势。针对全相位频谱分析通常采用的时移相位差法存在计算量大、实时性差及存在相位模糊现象等不足,提出了一种基于双窗全相位FFT双谱线校正的谐波分析算法,利用基波频点附近的两条谱线幅值计算基波频率,进而推导了简洁实用的谐波幅值校正公式。该算法实现方便,且实时性优于相位差法。通过与传统加Hanning窗、Nuttall窗插值FFT的仿真对比验证了新算法具有更高精度,基于该算法的实验结果也验证了算法的有效性。     

基于双窗全相位FFT双谱线校正的电力谐波分析

基于快速傅里叶变换的电力谐波分析在非同步采样情况下存在频谱泄露,影响测量精度。为抑制频谱泄露对谐波分析的影响,分析对比了双窗全相位FFT与传统加窗FFT在抑制频谱泄露方面的特点,并通过计算证明了双窗全相位FFT在电力谐波分析中的独特优势。针对全相位频谱分析通常采用的时移相位差法存在计算量大、实时性差及存在相位模糊现象等不足,提出了一种基于双窗全相位FFT双谱线校正的谐波分析算法,利用基波频点附近的两条谱线幅值计算基波频率,进而推导了简洁实用的谐波幅值校正公式。该算法实现方便,且实时性优于相位差法。通过与传统加Hanning窗、Nuttall窗插值FFT的仿真对比验证了新算法具有更高精度,基于该算法的实验结果也验证了算法的有效性。     

一种不依赖窗谱函数的校正方法及应用

在系统分析了对谐波信号进行离散频谱校正的4种方法（比值法、能量重心法、FFT＋FT法和相位差法）对窗谱函数的依赖关系的基础上,将相位差法和连续傅立叶变换法有机结合起来,提出了一种精确的、不依赖窗谱函数的通用离散频谱校正方法,并通过仿真分析和工程实例验证了该方法的正确性和有效性。     

基于Rife-Vincent窗衰减信号插值离散傅里叶变换

频谱泄漏和栅栏效应是影响衰减信号离散傅里叶变换精度的主要因素。为了提高多频衰减信号离散傅里叶变换频谱参数的校正精度,提出一种加窗两点矢量插值校正算法。对信号加M阶余弦窗并计算加窗后信号的离散傅里叶变换,利用真实频率附近的两根谱线的矢量比建立方程,通过求解方程获得频率偏移量和衰减因子,利用上述获得的两个参数计算出信号的频率、幅值和相位。余弦窗的最大旁瓣衰减特性能有效的降低频谱泄漏的影响,两点矢量频域插值可以消除栅栏效应,两者结合极大地提高了算法的参数校正精度。仿真和试验结果表明,算法具有较高的参数校正精度和稳定性,且计算效率较高,适用于实时处理及对计算资源要求苛刻的场合,为多频衰减信号的特征提取提供了一种可选的方法。     

基于极值法和重心法的离散频谱校正方法

针对多频率信号,在分析矩形窗函数的频谱泄漏特点的基础上,应用极值法搜索需校正的频率,然后用重心法求得校正后的频率、幅值和相位。该方法计算量小,能够快速找到需校正的谱线并进行校正,满足工程实时监测的需要。     

Anti-Noise Performance of the FT Continuous Zoom Analysis Method for Discrete Spectrum

As a discrete spectrum correction method,the Fourier transform(FT) continuous zoom analysis method is widely used in vibration signal analysis,but little effort had been made on this method's anti-noise performance.It is widely believed that the analysis accuracy of the method can be substantially improved by increasing the zoom multiple,however,with the zoom multiple increases,the frequency estimation accuracy may decline sometimes in practices.Aiming at the problems above,this paper analyzes the sources of frequency estimation error when a harmonic signal mixed with and without noise is processed using the FT continuous zoom analysis.According to the characteristics that the local maximum of the zoom spectrum may be wrongly selected when the signal is corrupted with noise,the number of wrongly selected spectrum lines is deduced under different signal-to-noise ratio and local zoom multiple,and then the maximum frequency estimation error is given accordingly.The validity of the presented analysis is confirmed by simulations results.The frequency estimation accuracy of this method will not improve any more under the influence of noise,and there is a best zoom multiple,when the zoom multiple is larger than the best zoom multiple;the maximum frequency estimation error will fluctuate back and forth.The best zoom multiple curves under different signal-to-noise ratios given provide a theoretical basis for the choice of the appropriate zoom multiples of the FT continuous zoom analysis method in engineering applications.     

Non-parametric estimation of the amplitude ratio of sinusoidal signals with common frequency

The systematic bias error of the amplitude ratio estimation owed to leakage effect can be effectively reduced by employment of the non-parametric multi-point interpolation of the discrete Fourier transform in the quotient of amplitudes. Simple single-step algorithms for fast measurement and estimation of the amplitude ratio of sinusoidal signals with the same frequency from two channels are presented. The paper analyzes and compares the systematic bias errors and the noise error behaviors of the amplitude ratio estimation changing the order of Rife–Vincent windows class I, which are designed for maximization of the window spectrum side-lobe fall-off, and minimum side-lobe level (MSL) windows, which are designed for minimization of the energy in the window spectrum main lobe. Estimation errors are shown in relation to the number of signal cycles in the measurement interval.     

噪声激振下的油井动液面测量方法研究

油井动液面深度是原油开采中的关键工作参数,也是油田合理安排开采计划的重要依据。针对目前声共振法存在测量范围不足和测量精度较低的问题,论文提出了噪声激振下的油井动液面测量优化方法。本文首先探究了激励频带变化对测量结果的影响,并建立了强噪声激励下系统输出响应信号的数学模型。然后,根据建立的数学模型提出了共振信号的提取算法,通过功率谱估计和自适应同态滤波有效抑制了强噪声对共振信号的干扰。最后,研究了基于双线性插值的离散频谱校正算法,实现了共振特征参数的精确估计。实验结果表明,该方法能在强噪声干扰下提取出共振信号,实现了超过1 700 m的动液面稳定测量,且波动小于2 m。     

PHASE DIFFERENCE CORRECTION METHOD FOR PHASE AND FREQUENCY IN SPECTRAL ANALYSIS

A new method, phase difference corrections method is developed to correct the frequency and phase of spectrum peak. The continuous time-domain signal is separated into two segments and fast Fourier translation (FFT) is carried out for them, respectively. The frequency and phase are corrected using the phase difference of corresponding discrete spectral lines. Furthermore, the amplitude can also be rectified using the formula of window function spectrum. This method, with good adaptability, high speed and accuracy, is theoretically simple. It can resolve the frequency by means of phase difference directly without the formula of window function. Simulation shows that the single-component frequency, phase and amplitude of theoretical signal can be corrected satisfactorily, with frequency error less than 0.0002 frequency resolution, phase 0.1° and amplitude 0.0002. If the signal involves noise, the mean corrected errors are less than 0.001 frequency resolution, 1° for phase, and 0.01 for amplitude, respectively, and the maximum corrected errors of one segment are less than 0.01 frequency resolution, 1° and 0.03, respectively.     

Energy based signal parameter estimation method and a comparative study of different frequency estimators

The influences of window functions and noise on the performance of the energy-based signal parameter estimation method are investigated, and the appropriate parameters and algorithm are recommended accordingly. The frequency, amplitude and phase estimation variances of the energy based method are deduced and verified by computer simulation. The performances of four frequency estimation methods are compared: the energy based method, the interpolation based method, the phase difference based method and the Fourier transform (FT) continuous zoom based method. For the second and third methods, the Quinn algorithm and the phase difference based method with factor η=0.5 are recommended, respectively. It was found that each method has its own advantages. The energy based method has the best stability compared with others. The interpolated method has the lowest frequency estimation variance when the frequency biasδ is large, while the phase-difference based method does better when δ is low. The change of δ does not influence the maximum frequency estimation error of the FT continuous zoom based method. Comparatively speaking, the phase-difference based method has the least frequency estimation error.     

Subsample interpolation bias error in time of flight estimation by direct correlation in digital domain

This work presents an investigation of the bias error introduced in time of flight estimation realized by subsample interpolation in digital domain. The time of flight estimation is accomplished based on the evaluation of the peak position of the cross correlation function. In order to cope with the discrete nature of the cross-correlation function, subsample estimation exploits three time domain interpolation techniques: parabolic, cosine, Gaussian and frequency domain interpolation using phase angle. An empirical equation relating the maximum value of the bias error to sampling frequency and signal parameters (center frequency and envelope bandwidth) has been derived. It is found that the maximum value of the bias error is in inverse cubic relation to sampling frequency and in quadratic relation envelope bandwidth for cosine interpolation. The maximum value of the bias error is in inverse cubic relation to sampling frequency and in quadratic relation to center frequency and envelope bandwidth for parabolic interpolation. The coefficients related to the approximation technique are given. Results can be applied for bias errors estimation or correction when fast subsample interpolation is used and application of phase domain interpolation is unacceptable due to processing speed limitations. The equations for minimum required sampling frequency are derived by balancing the interpolation error against Cramer–Rao lower bound.     

S-修正的自适应卡尔曼滤波与模糊卡尔曼滤波相结合的汽车状态估计算法

精确的汽车状态信息的获取是汽车动态控制系统正常工作的前提。建立了二自由度汽车动力学模型,提出了将S-修正的自适应卡尔曼滤波与模糊卡尔曼滤波相结合进行汽车关键状态估计的方法。模糊卡尔曼滤波利用所设计的模糊控制器通过实时监测信息实际方差与理论方差的比值,实现对时变量测噪声的协方差矩阵的实时在线估计,提高了算法在时变量测噪声情况下的鲁棒性;S-修正的自适应卡尔曼滤波算法基于滤波不发散理论推导得出实时修正因子S,进而对估计误差协方差矩阵直接加权。两种方法的结合在总体上提高了在汽车动力学系统过程噪声与量测噪声协方差矩阵不准确情况下算法的鲁棒性与估计精度,最后通过基于ADAMS的虚拟试验验证了该方法的有效性。     

Estimation of time-varying power quality indices using a computationally efficient algorithm

In this paper a new recursive adaptive filter based on a fast Gauss–Newton method has been proposed for the estimation of power quality (PQ) indices for time-varying voltage and current signals in an electric power system. The presented algorithm is based on the minimization of a weighted forgetting factor based error cost function by the use of Recursive Gauss–Newton method. Further a Hessian matrix approximation is used to produce a fast recursive algorithm, which is immune to random noise, waveform distortion and increases the speed of convergence and accuracy. The algorithm models the typical time-varying signal and the accompanied distortions due to harmonics and random noise in a manner that will be suitable for real-time PQ indices estimation. Further, the forgetting factor is tuned in accordance with signal error covariance to provide improved performance. Also power system frequency variations are estimated and correction factors are derived. The effects of sub harmonics, and interharmonics in the signal have been considered while estimating the various PQ indices.