Analysis and Application of an Improved FFT Algorithm for Energy Centrobaric Correction Method
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摘要: 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。Abstract: The effect of wrong location of spectral bins caused by noise on frequency estimation was studied in the energy centrobaric correction method. In order to improve accuracy of frequency estimation, an improved FFT correction algorithm was proposed to decrease the ratio of wrong choices of spectral bins, based on the theory of the energy centrobaric correction method and existing methods for selecting spectral bins. The improved method, based on the D. Macleod method, selected the spectral bins by means of phase difference between the spectral lines, and reduced the occurrence of wrong location of spectral bins. Finally, a general formula of frequency correction was presented. The simulation results showed that the improved algorithm had a lower ratio of wrong choices of spectral bins and better anti-noise performance; And the method had a smaller root-mean-square error(RMSE) than the other methods when estimating the frequency in Gauss white noise. The application of pipeline length detection in the simulation of downhole casing further indicated that the improved method had higher frequency estimation accuracy and effectively decreased length measurement errors.
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表 1 管道长度误差
m 管道长度 21 30 60 84 未校正 0.157 6 0.321 3 0.990 5 1.532 1 幅值法 0.125 9 0.257 3 0.782 1 1.232 8 D.Macleod法 0.079 11 0.162 5 0.502 7 0.777 3 改进算法 0.046 13 0.101 6 0.316 1 0.505 2 
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