Instantaneous frequency estimation method based on LoG operator and PauTa test

An instantaneous frequency and operator technology, applied in the field of rotating machinery condition monitoring and fault diagnosis, can solve the problems of one-step cost function delay, low accuracy and precision, and cannot change with time, so as to eliminate time delay and avoid The effect of relying on and eliminating errors

Active Publication Date: 2017-11-10
WEIFANG UNIVERSITY
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AI-Extracted Technical Summary

Problems solved by technology

The one-step cost function method can search for ridge points in the local frequency range, but the center point of the local frequency range depends on the position of the previous ridge point, which leads to a delay in the one-step cost function
In addition, the width of the local frequency range is set arb...
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Method used

1) traditional one-step cost function needs to depend on the position of last ridge point when determining the central point of current search interval, there is time delay phenomenon, the present invention util...
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Abstract

The invention discloses an instantaneous frequency estimation method based on an LoG operator and a PauTa test. According to the method, an original signal is transformed into a time-frequency spectrogram based on short-time Fourier transform; a plurality of ridge bands are obtained according to a LoG detection algorithm; with PauTa testing, an abnormal value of each ridge band is removed; superposition is carried out to construct a synthesis ridge band with the complete and clear edge; an abnormal value of the synthesis ridge band is eliminated by PauTa testing; a mean value curve of the synthesis ridge band is calculated, smoothing processing is carried out on the mean value curve, and a confidence interval of the smooth mean value curve at the 95% of confidence level is calculated; the smooth mean value curve and the confidence interval are mapped to a target ridge line to obtain a reference line and a local searching zone of the target ridge line; and the target ridge line is extracted by using a non-delay cost function. The instantaneous frequency estimation method is suitable for estimating an instantaneous frequency of a complicated multi-component variable-frequency signal; defects in instantaneous frequency estimation of a mechanical vibration signal according to the traditional method are overcome; the accuracy and precision of the estimation result are high; and the method is convenient to engineering application.

Application Domain

Geometric CADMachine gearing/transmission testing +2

Technology Topic

Fourier transformRidge +11

Image

  • Instantaneous frequency estimation method based on LoG operator and PauTa test
  • Instantaneous frequency estimation method based on LoG operator and PauTa test
  • Instantaneous frequency estimation method based on LoG operator and PauTa test

Examples

  • Experimental program(1)

Example Embodiment

[0059] example, as figure 1 As shown, the instantaneous frequency estimation method based on LoG operator and PauTa test includes the following steps:
[0060] Step 1: Use the short-time Fourier transform algorithm to convert the signal x(k) (k=1, 2, …, N) into a time-spectrogram, where N represents the length of the signal;
[0061] Step 2: Select a local area with a high signal-to-noise ratio from the time-spectrogram, and use the LoG detection algorithm to convert the local area into a binary image. The binary image contains multiple ridges; a local area refers to at least two Ridges, areas where the signal-to-noise ratio is greater than 80dB;
[0062] Step 3: Use the PauTa test algorithm to exclude outliers on the upper and lower edges of each ridge;
[0063] Step 4: The above-mentioned multiple ridges are superimposed on one of the ridges with the most complete outline according to the kinematic proportional relationship between them, and a synthetic ridge with a complete and clear edge is constructed; The transmission ratio between the corresponding machine parts;
[0064] Step 5: Use the PauTa test algorithm to exclude the abnormal values ​​of the upper and lower edges of the above-mentioned synthetic ridges;
[0065] Step 6: Calculate the mean curve of the above-mentioned synthetic ridge, and use the five-point cubic smoothing algorithm to smooth the mean curve to obtain a smooth mean curve, and calculate the confidence interval of the smooth mean curve at the 95% confidence level;
[0066] Step 7: Map the above-mentioned smoothed mean curve and its confidence interval to the target ridgeline according to the kinematic proportional relationship between the smoothed mean curve and the target ridgeline to be estimated;
[0067] Step 8: use the mapped smooth mean curve as the reference line of the target ridge, and use the mapped confidence interval as the local search interval of the target ridge;
[0068] Step 9: Use the non-delay cost function to search for ridge points in the local search interval corresponding to each moment, determine the instantaneous frequency corresponding to each moment, and finally obtain the instantaneous frequency in the entire time interval.
[0069] The short-time Fourier transform algorithm in step 1 includes the following steps:
[0070] 1) Take the short-time Fourier transform of the signal x(k):
[0071] ,
[0072] TF(t, f) represents the short-time Fourier transform result of the signal x(k), t represents the time factor, f represents the scale factor, and the function w(z) represents the window function whose independent variable is z;
[0073] 2) Calculate the time spectrum of the signal x(k):
[0074] ,
[0075] spectrogram(t, f) represents the time spectrum of x(k).
[0076] The LoG detection algorithm in step 2 includes the following steps:
[0077] 1) Use Gaussian filter to smooth the original image I(x, y):
[0078] ,
[0079] parameter G σ (x, y) represents the Gaussian kernel function with standard deviation σ, L(x, y) represents the image after Gaussian filtering, x represents the time point of the image, y represents the frequency point of the image, and * represents the convolution calculation; In the invention, σ=1;
[0080] 2) Perform the Laplacian operation on L(x, y):
[0081] ,
[0082] Represents the result of L(x, y) after Laplacian operation;
[0083] 3) Set an appropriate threshold, if a certain point (x, y) on the image corresponds to If it is greater than the threshold, it is determined that the point is an edge; in the present invention, the threshold is set to 4.63×10 -7.
[0084] The PauTa test algorithm in step 3 includes the following steps:
[0085] 1) Estimate the signal x n (n=1, 2, …, N) standard deviation,
[0086] ,
[0087] represents the sample mean, σ represents the sample standard deviation, and N represents the sample length;
[0088] 2) If , then remove x n.
[0089] The non-delayed cost function in step 9 includes the following steps:
[0090] 1) The local search interval FB corresponding to the kth moment k defined as
[0091] ,
[0092] f k (pmc) represents the value of the smoothed mean curve after mapping at the kth moment, Represents half the width of the confidence interval of the smoothed mean curve after mapping at the k-th time, and m represents the length of the target ridge;
[0093] 2) The non-delayed cost function CF corresponding to the kth time k defined as:
[0094] ,
[0095] ,
[0096] f k (i) on behalf of FB k The frequency value taken in the range, TF(t k , f k ) represents the value of TF(t, f) at the kth moment, t k represents the value of t at the kth moment, f k represents the value of f at the kth moment, e k represents the weighting factor.
[0097] The performance of the algorithm described in the present invention is verified using the vibration data of the fan turbine planetary gearbox.
[0098] The vibration data is collected from the gearbox casing close to the planetary gear train, the data length is N=2736825, and the sampling frequency is fs=5000 Hz.
[0099] The collected vibration data of planetary gearboxes are as follows: figure 2 shown.
[0100] Using the short-time Fourier transform algorithm, the figure 2 The vibration data of the planetary gearbox shown is converted into a time-spectrogram, and the obtained time-spectrogram is as follows image 3 shown.
[0101] from image 3 Select the local area with high signal-to-noise ratio on the time-spectrogram shown, and the obtained local area is as follows: Figure 4 shown.
[0102] Using the LoG detection algorithm to detect Figure 4 The local area shown is subjected to edge detection, and the resulting image edge is as follows Figure 5 shown.
[0103] Eliminate the use of PauTa test algorithm Figure 5 The abnormal points of each ridge in the Image 6 shown.
[0104] According to the kinematic proportional relationship between the ridges, each ridge is superimposed on one of the ridges with the most complete outline, and the constructed synthetic ridge is as follows: Figure 7 (the lowermost ridge is the synthetic ridge).
[0105] The PauTa test algorithm is used to eliminate the abnormal points of the synthetic ridge, and the results are as follows Figure 8 shown.
[0106] Calculate the smoothed mean curve of the synthetic ridge and its 95% confidence interval, and the results are as follows Figure 9 shown.
[0107] According to the kinematic proportional relationship between the smoothed mean curve and the target ridge line, the smoothed mean curve and its confidence interval are mapped to the target ridge line, and the results are as follows: Figure 10 shown.
[0108] The non-delay cost function is used to search the ridge points of the target ridge, and the instantaneous frequency curve obtained is as follows Figure 11 shown.
[0109] After many experiments, it has been shown that the maximum relative error between the estimated value of instantaneous frequency obtained by the present invention and the measured value is 0.775%, and the average relative error is 0.068%. The maximum relative error between them is 16.39%, the average relative error is 2.14%, the maximum relative error of the present invention is reduced by 95.27%, and the average relative error is reduced by 96.82%.
[0110] According to the experimental results, it is concluded that:
[0111] 1) The traditional one-step cost function needs to rely on the position of the previous ridge point when determining the center point of the current search interval, and there is a time delay phenomenon. The present invention uses the mapped smooth mean curve as a reference line to instantly determine the current search interval. The center position of , completely independent of the previous ridge point, so it is real-time.
[0112] 2) The traditional one-step cost function method lacks self-adaptability, and needs to manually set the search interval, and the search width is fixed, which inevitably brings errors. The present invention uses the mapped smooth mean curve confidence interval to automatically determine the local search. In the interval, the search bandwidth can be changed automatically with the change of time without manual participation, so it is adaptive.
[0113] 3) Compared with the traditional one-step cost function method, the present invention has high precision and accuracy.
[0114] Those skilled in the art should realize that the above-mentioned specific embodiments are only exemplary, in order to enable those skilled in the art to better understand the content of the present invention, and should not be construed as a limitation on the protection scope of the present invention, as long as it is based on the present invention The improvements made by the technical solutions of the invention all fall into the protection scope of the present invention.

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