采样序列长度及周波数对正弦参数拟合的影响

doi:10.3969/j.issn.1000-1158.2022.08.04

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摘要针对波形拟合法估计正弦参数时,测量条件对拟合参数带来的误差影响,进行了拟合误差界的搜索研究。选取的条件变量分别是A/D位数、幅度、序列所含波形的周波数、初始相位、直流分量以及序列数据点数。以两两联动的双条件组合方式进行误差界搜索,获得了幅度、频率、相位、直流分量、动态有效位数等拟合参数的误差界随不同条件变化而变化的曲线规律,筛分出了显著影响量和不显著影响量。并对A/D位数、序列所含波形的周波数、以及序列数据点数带来的影响进行了深入研究,获得了拟合参数的误差界呈现量子化阶梯特征的显著规律,并获得了量子化阶梯边界点估计的经验公式。该结果可用于拟合正弦参数的误差评价和不确定度估计,也可以用于在设定拟合误差和不确定度情况下,选择测量条件。

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	梁志国

关键词 ：计量学, 正弦波, 曲线拟合, 误差界, 量化, 幅度, 频率, 相位

Abstract：Aiming at the influence of measurement conditions on the error of the curve-fit parameters by the sine fitting method, a study on the fitting error bounds is carried out. The selected condition variables are the A/D bits number, the signals amplitude, the number of signal cycles in sampling sequence, the initial phase, the DC bias, and the number of data points in sampling sequence. The error bounds search is carried out in the dual condition combination method, and the error of curve-fit parameters via the changes of different conditions is obtained, both the significant influence and the insignificant influence are screened out. Through the study of the influence of the number of A/D bits, the number of signals cycles in sequence, and the number of data points, some laws has been carried out, and the significant law that the error boundary showing the characteristics of the quantization step has been obtained, and the estimation of the boundary point of the quantization step has been obtained by empirical formula. The result can be used to estimate the error and uncertainty of the sine-fit parameters, and can also be used to select the measurement conditions under the fitting error and uncertainty.

Key words： metrology sine wave curve fitting error bounds quantization amplitude frequency phase

收稿日期: 2021-06-23 发布日期: 2022-08-20

PACS:

TB973

作者简介: 梁志国(1962-),男,黑龙江巴彦县人,博士,北京长城计量测试技术研究所研究员,博士研究生导师,主要研究方向为数字化测量与校准,模式识别,动态校准,精确测量。Email: Lzg304@sina.com

引用本文:

梁志国. 采样序列长度及周波数对正弦参数拟合的影响[J]. 计量学报, 2022, 43(8): 989-1000.
LIANG Zhi-guo. The Influence of Both Data Number and Signal Cycles to the Sinusoidal Parameter’s Error in Sine-Fit Method. Acta Metrologica Sinica, 2022, 43(8): 989-1000.

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［1］IEEE Std 1057-1994 IEEE standard for digitizing waveform recorders ［S］. 1994.
［2］JJF 1048-1995 数据采集系统校准规范［S］. 北京: 中国计量出版社, 1995.
［3］JJF 1057-1998 数字存储示波器校准规范［S］. 北京: 中国计量出版社, 1998.
［4］IEEE Std 1241-2010, IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters ［S］. 2010.
［5］Peetz B E. Dynamic Testing of Waveform Recorders ［J］. IEEE Transactions on Instrumentation and Measurement, 1983, 32(1): 12-17.
［6］Doerfler D W. Dynamic Testing of a Slow Sample Rate High-Resolution Data Acquisition System ［J］. IEEE Transactions on Instrumentation and Measurement, 1986, 35(4): 477-482.
［7］魏燕定. 超低频标准振动台波形失真度近似解析解［J］. 振动与冲击, 2000, 19(3): 49-51.
Wei Y D. Approximate Analytical Solution of Waveform Distortion of Ultra-low Frequency Standard Vibrator ［J］. Journal of Vibration and Shock, 2000, 19(3): 49-51.
［8］田光明, 陈光踽. 正弦扫描振动响应的时频分析［J］. 振动与冲击, 2005, 24(6): 13-16.
Tian G M, Chen G J. Time-Frequency Analysis of the Response in a Sine-Swept Vibration Test ［J］. Journal of Vibration and Shock, 2005, 24(6): 13-16.
［9］于梅. 低频振动传感器幅值和相移测量的不确定度［J］. 振动与冲击, 2009, 28(4): 106-109.
Yu M. Measurement uncertainty of magnitude and phase shift for sensitivity of a low frequency vibration transducer with amplifier ［J］. Journal of Vibration and Shock, 2009, 28(4): 106-109.
［10］王宇, 张力, 洪宝林, 等. 正弦力校准中降低质量块振动响应不均匀影响的设计方案［J］. 振动与冲击, 2010, 29(7): 228-231.
Wang Y, Zhang L, Hong B L, et al. Mass design plan in sinusoidal force calibration to avoid nonuniform vibration response ［J］. Journal of Vibration and Shock, 2010, 29(7): 228-231.
［11］张根辈, 臧朝平. 基于振动测试的非线性参数识别方法［J］. 振动与冲击, 2013, 32(1): 83-88.
Zhang G B, Zang C P. A novel method for nonlinear parametric identification based on vibration tests ［J］. Journal of Vibration and Shock, 2013, 32(1): 83-88.
［12］梁志国, 朱振宇, 邵新慧, 等. 正弦波形局域失真及相变分析［J］. 振动与冲击, 2013, 32(18): 179-182,188.
Liang Z G, Zhu Z Y, Shao X H, et al. Definition and measurement method for local distortion of a sinusoidal waveform ［J］. Journal of Vibration and Shock, 2013, 32(18): 179-182,188.
［13］严鲁涛, 杨志鹏, 王有杰. 基于联合振动试验系统的正弦加随机振动研究［J］. 振动与冲击, 2015, 34(2): 91-95.
Yan L T, Yang Z P, Wang Y J. Sine on random vibration based on combined vibration test system. ［J］. Journal of Vibration and Shock, 2015, 34(2): 91-95.
［14］Deyst J P, Soulders T M, Solomon Jr O M. Bounds on Least-Squares Four-Parameter Sine-Fit Errors Due to Harmonic Distortion and Noise ［J］. IEEE Transaction on Instrumentation & Measurement, 1995, 44 (3): 637-642.
［15］Handel P. Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm ［J］. IEEE Transactions on Instrumentation and Measurement, 2000, 49(6): 1189-1193.
［16］Chiorboli G, Franco G, Morandi C. Uncertainties in quantization-noise estimates ［J］. IEEE Transactions on Instrumentation and Measurement, 1997, 46(1): 56-60.
［17］林俊武. 高速A/D转换的动态精度研究［D］. 福州: 福州大学, 2005.
［18］桑龙, 陈静. 基于正弦曲线拟合算法的ADC测试改进方法［J］. 电讯技术, 2010, 50(2): 69-72.
Sang L, Chen J. Improved ADC Measurement approach Based on sine wave fitting ［J］. Telecommunication engineering, 2010, 50(2): 69-72.
［19］张智慧. ADC的测量不确定度评估方法研究［D］. 西安: 陕西科技大学, 2015.
［20］梁志国. 正弦波形参量对A/D有效位数评价的影响［J］. 计量学报, 2017, 38(1): 91-97.
Liang Z G. The influence of Sinusoidal Parameters in Evaluation of Effective Bit of ADC Converts by Curve-fit Method ［J］. Acta Metrologica Sinica, 2017, 38(1): 91-97.
［20］梁志国. 非均匀采样条件下残周期正弦波形的最小二乘拟合算法［J］. 计量学报, 2021, 42(3): 358-364.
Liang Z G. The Sinewave Fit Algorithm Based on Total Least-Square Method with Partial Period Waveforms and Non-uniform Sampling［J］. Acta Metrologica Sinica, 2021, 42(3): 358-364.
［21］梁志国. 正弦波拟合参数的不确定度评定［J］. 计量学报, 2018, 39(6): 888-894.
The measurement uncertainty of curve-fit parameters of sinusoidal ［J］. Acta Metrologica Sinica, 2018, 39(6): 888-894.