CN110457644B - Time-frequency ridge line extraction method based on LoG operator and Grubbs inspection - Google Patents

Time-frequency ridge line extraction method based on LoG operator and Grubbs inspection Download PDF

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CN110457644B
CN110457644B CN201910381317.7A CN201910381317A CN110457644B CN 110457644 B CN110457644 B CN 110457644B CN 201910381317 A CN201910381317 A CN 201910381317A CN 110457644 B CN110457644 B CN 110457644B
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窦春红
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Abstract

The invention discloses a time-frequency ridge line extraction method based on LoG operators and Grubbs test, which adopts short-time Fourier transform to convert original signals into time-frequency spectrograms, adopts LoG detection algorithm to obtain a plurality of ridge bands, adopts Grubbs test to eliminate abnormal values of each ridge band, constructs a synthetic ridge band with complete and clear edges through superposition, adopts Grubbs test to eliminate abnormal values of the synthetic ridge band, calculates a mean curve of the synthetic ridge band, smoothes the mean curve, calculates a confidence interval of the smooth mean curve at 95% confidence level, maps the smooth mean curve and the confidence interval thereof to a target ridge line to obtain a reference line and a local search interval of the target ridge line, and adopts a non-delay cost function to extract the target ridge line. The method is suitable for estimating the instantaneous frequency of the complex multi-component variable frequency signal, overcomes the defects of the traditional method in the estimation of the instantaneous frequency of the mechanical vibration signal, has high accuracy and precision of an estimation result, and is convenient for engineering application.

Description

Time-frequency ridge line extraction method based on LoG operator and Grubbs inspection
The invention is a divisional application with application number 2017106085670, application date 2017, 7, 24 and the title "instantaneous frequency estimation method based on LoG operator and Grubbs test".
Technical Field
The invention relates to the field of rotary machine state monitoring and fault diagnosis, in particular to a time-frequency ridge line extraction method based on LoG operator and Grubbs inspection.
Background
Due to the complexity of the operating environment, rotary machines often operate under variable speed conditions. Instantaneous frequency estimation is an important prerequisite for evaluating the operating state of a rotating machine and for fault diagnosis. The currently common instantaneous frequency estimation method is a one-step cost function (one-step cost function). The one-step cost function method can search ridge points in a local frequency range, but the center point of the local frequency range depends on the position of the last ridge point, which causes delay of the one-step cost function. Furthermore, the width of the local frequency range is set empirically at will and at any time is fixed and cannot change over time, which results in a one-step cost function that is not sufficiently adaptive. The above-mentioned drawbacks result in a one-step cost function method with low accuracy and precision in estimating the instantaneous frequency.
Disclosure of Invention
The invention aims to solve the problems and provides a time-frequency ridge line extraction method based on LoG operator and Grubbs inspection. Compared with the prior art, the method takes the mapped smooth mean curve as the reference line of the target ridge line and the mapped confidence interval as the local search interval of the target ridge line, so that the center point of the local frequency search range does not depend on the position of the last ridge point, no delay exists, the local frequency search range can be automatically set, the search bandwidth can be automatically changed along with the change of time, and the accuracy and precision of the instantaneous frequency estimation result are high.
In order to solve the technical problems, the invention provides a time-frequency ridge line extraction method based on LoG operator and Grubbs inspection, which is characterized by comprising the following steps:
step 1: converting the signal x (k) k =1, 2, …, N into a time-frequency spectrogram by using a short-time fourier transform algorithm, wherein N represents the length of the signal;
step 2: selecting a local area with a higher signal-to-noise ratio from the time-frequency spectrogram, and converting the local area into a binary image by adopting a LoG detection algorithm, wherein the binary image comprises a plurality of ridge bands; the local area is an area which at least comprises two ridge bands and has a signal-to-noise ratio of more than 80 dB;
and step 3: eliminating abnormal values of the upper edge and the lower edge of each ridge by adopting a Grubbs test algorithm;
and 4, step 4: superposing the ridge bands on one ridge band with the most complete contour according to the kinematic proportion relation between the ridge bands to construct a synthetic ridge band with complete and clear edges; the kinematic proportion relation refers to the transmission ratio between the machine parts corresponding to the ridge belt;
and 5: eliminating abnormal values of the upper edge and the lower edge of the synthesized ridge by adopting a Grubbs test algorithm;
step 6: calculating a mean value curve of the synthesized ridge, smoothing the mean value curve by adopting a five-point cubic smoothing algorithm to obtain a smooth mean value curve, and calculating a confidence interval of the smooth mean value curve on a 95% confidence level;
and 7: mapping the smooth mean curve and the confidence interval thereof to a target ridge line according to the kinematic proportion relation between the smooth mean curve and the target ridge line to be estimated;
and 8: taking the mapped smooth mean curve as a reference line of the target ridge line, and taking the mapped confidence interval as a local search interval of the target ridge line;
and step 9: searching ridge points in a local search interval corresponding to each moment by adopting a non-delay cost function, determining instantaneous frequency corresponding to each moment, and finally obtaining instantaneous frequency in the whole time interval;
the non-delayed cost function in step 9 comprises the steps of:
1) local search space FB corresponding to kth timekIs defined as
Figure 849705DEST_PATH_IMAGE001
，
fk(pmc) represents the value of the mapped smoothed mean curve at the kth time,
Figure 578627DEST_PATH_IMAGE002
representing half of the width of the confidence interval of the mapped smooth mean curve at the kth moment, wherein m represents the length of the target ridge line;
2) the non-delay cost function CF corresponding to the kth momentkIs defined as:
Figure 126283DEST_PATH_IMAGE003
,
Figure 624260DEST_PATH_IMAGE004
，
fk(i) is represented at FBkFrequency value, TF (t), taken within the rangek, fk) Represents the value of TF (t, f) at the kth time,tkrepresents the value of t at the kth time, fkRepresents the value of f at the k-th time, ekRepresents a weight factor;
the maximum relative error between the instantaneous frequency estimate and the measured value is 0.835%, and the average relative error is 0.071%.
Further, the short-time fourier transform algorithm in step 1 includes the following steps:
1) short-time fourier transform the signal x (k):
Figure 599170DEST_PATH_IMAGE005
，
TF (t, f) represents the result of the short-time fourier transform of the signal x (k), t represents a time factor, f represents a scale factor, and the function w (z) represents a window function with an argument z;
2) calculate the time-frequency spectrum of signal x (k):
Figure 815387DEST_PATH_IMAGE006
，
spectrogram (t, f) represents the time-frequency spectrum of x (k).
Further, the LoG detection algorithm in step 2 includes the following steps:
1) the original image I (x, y) is smoothed with a gaussian filter:
Figure 901155DEST_PATH_IMAGE007
，
Gσ(x, y) represents a gaussian kernel with standard deviation σ, L (x, y) represents a gaussian filtered image, x represents a time point of the image, y represents a frequency point of the image, and x represents a convolution calculation; in the present invention, σ = 1;
2) performing a Laplacian operation on L (x, y):
Figure 519218DEST_PATH_IMAGE008
,
Figure 914296DEST_PATH_IMAGE009
represents the result obtained by Laplacian operation of L (x, y);
3) setting a proper threshold value if a certain point (x, y) on the image corresponds to
Figure 352231DEST_PATH_IMAGE010
If the point is larger than the threshold value, the point is judged to be an edge; in the present invention, the threshold is set to 4.63 × 10-7。
Further, the Grubbs test algorithm in the step 3 comprises the following steps:
1) for signal xnN =1, 2, …, N, establishing Grubbs test statistics
Figure 304006DEST_PATH_IMAGE011
，
Figure 979838DEST_PATH_IMAGE012
Represents the sample mean, σ represents the sample standard deviation, and N represents the sample length;
2) setting the significance level as alpha according to a probability formula
Figure 296550DEST_PATH_IMAGE013
Determining g0(N, α)，g0(N, alpha) represents the data length N, and the significance level is the Grubbs critical value corresponding to alpha; in the present invention, α = 0.05;
3) if it is not
Figure 487360DEST_PATH_IMAGE014
B =1, 2, …, N, then x is rejectedb。
By adopting the technical scheme, compared with the prior art, the invention has the following advantages:
1) the invention has real-time property: the method takes the synthesized ridge smooth mean curve mapping as the reference line, can instantly determine the central point of the local frequency search range at the current moment, avoids the dependence on the previous ridge point, eliminates the time delay, and has real-time performance.
2) The invention has the self-adaptability: the invention utilizes the local range provided by the synthetic ridge smooth mean curve confidence interval mapping to adaptively determine the local frequency search range corresponding to each moment, the search bandwidth can automatically change along with the change of time, and the search bandwidth does not need to be set by experience, thereby eliminating the error caused by human factors.
3) The experimental results show that: the maximum relative error between the estimated value of the instantaneous frequency and the measured value obtained by the method is 0.835 percent, and the average relative error is 0.071 percent; compared with the result of the one-step cost function method, the maximum relative error is reduced by 94.91%, and the average relative error is reduced by 96.68%.
The invention is further illustrated with reference to the following figures and examples.
Drawings
FIG. 1 is a flow chart of a time-frequency ridge line extraction method based on a LoG operator and Grubbs inspection in the embodiment of the invention;
FIG. 2 is a planetary gearbox vibration signal in an embodiment of the present invention;
FIG. 3 is a time-frequency spectrum of a vibration signal of a planetary gearbox in an embodiment of the invention;
FIG. 4 is a local region with a high SNR selected from a time-frequency spectrogram in an embodiment of the present invention;
FIG. 5 is a diagram illustrating an edge of a local image region detected by a LoG algorithm according to an embodiment of the present invention;
FIG. 6 shows the result of eliminating outliers of each ridge by using the Grubbs test algorithm in the embodiment of the present invention;
FIG. 7 is a composite ridge stripe formed by stacking the kinematics proportion relationship between ridge stripes in the embodiment of the present invention (the ridge stripe at the lowest layer is the composite ridge stripe);
FIG. 8 shows the result of eliminating abnormal points of synthetic ridge by using Grubbs's test algorithm in the embodiment of the present invention;
FIG. 9 is a graph of the mean smooth curve of the synthesized ridge and its 95% confidence interval in an embodiment of the present invention;
FIG. 10 is a graph of a mean smoothing curve and its confidence interval mapped in an embodiment of the present invention;
FIG. 11 is a diagram illustrating an instantaneous frequency estimate in an embodiment of the present invention.
Detailed Description
In an embodiment, as shown in fig. 1, the time-frequency ridge line extraction method based on the LoG operator and Grubbs test includes the following steps:
step 1: converting the signal x (k) (k =1, 2, …, N) into a time-frequency spectrogram by using a short-time fourier transform algorithm, wherein N represents the length of the signal;
step 2: selecting a local area with a higher signal-to-noise ratio from the time-frequency spectrogram, and converting the local area into a binary image by adopting a LoG detection algorithm, wherein the binary image comprises a plurality of ridge bands; the local area is an area which at least comprises two ridge bands and has a signal-to-noise ratio of more than 80 dB;
and step 3: eliminating abnormal values of the upper edge and the lower edge of each ridge by adopting a Grubbs test algorithm;
and 4, step 4: superposing the ridge bands on one ridge band with the most complete contour according to the kinematic proportion relation between the ridge bands to construct a synthetic ridge band with complete and clear edges; the kinematic proportion relation refers to the transmission ratio between the machine parts corresponding to the ridge belt;
and 5: eliminating abnormal values of the upper edge and the lower edge of the synthesized ridge by adopting a Grubbs test algorithm;
step 6: calculating a mean value curve of the synthesized ridge, smoothing the mean value curve by adopting a five-point cubic smoothing algorithm to obtain a smooth mean value curve, and calculating a confidence interval of the smooth mean value curve on a 95% confidence level;
and 7: mapping the smooth mean curve and the confidence interval thereof to a target ridge line according to the kinematic proportion relation between the smooth mean curve and the target ridge line to be estimated;
and 8: taking the mapped smooth mean curve as a reference line of the target ridge line, and taking the mapped confidence interval as a local search interval of the target ridge line;
and step 9: and searching ridge points in the local search interval corresponding to each moment by adopting a non-delay cost function, determining the instantaneous frequency corresponding to each moment, and finally obtaining the instantaneous frequency in the whole time interval.
The short-time Fourier transform algorithm in the step 1 comprises the following steps:
1) short-time fourier transform the signal x (k):
Figure 914930DEST_PATH_IMAGE005
，
TF (t, f) represents the result of the short-time fourier transform of the signal x (k), t represents a time factor, f represents a scale factor, and the function w (z) represents a window function with an argument z;
2) calculate the time-frequency spectrum of signal x (k):
Figure 242006DEST_PATH_IMAGE006
，
spectrogram (t, f) represents the time-frequency spectrum of x (k).
The LoG detection algorithm in the step 2 comprises the following steps:
1) the original image I (x, y) is smoothed with a gaussian filter:
Figure 526357DEST_PATH_IMAGE015
，
Gσ(x, y) represents a gaussian kernel with standard deviation σ, L (x, y) represents a gaussian filtered image, x represents a time point of the image, y represents a frequency point of the image, and x represents a convolution calculation; in the present invention, σ = 1;
2) performing a Laplacian operation on L (x, y):
Figure 391414DEST_PATH_IMAGE008
,
Figure 684992DEST_PATH_IMAGE009
represents the result obtained by Laplacian operation of L (x, y);
3) setting a proper threshold value if a certain point (x, y) on the image corresponds to
Figure 69837DEST_PATH_IMAGE009
If the point is larger than the threshold value, the point is judged to be an edge; the threshold was set to 4.63 × 10-7。
The Grubbs test algorithm in the step 3 comprises the following steps:
1) for signal xn(N =1, 2, …, N), establishing Grubbs test statistics
Figure 790668DEST_PATH_IMAGE011
，
Figure 628174DEST_PATH_IMAGE012
Represents the sample mean, σ represents the sample standard deviation, and N represents the sample length;
2) setting the significance level as alpha according to a probability formula
Figure 459864DEST_PATH_IMAGE013
Determining g0(N, α)，g0(N, alpha) represents the data length N, and the significance level is the Grubbs critical value corresponding to alpha; in the present invention, α = 0.05;
3) if it is not
Figure 964795DEST_PATH_IMAGE014
(b =1, 2, …, N), then x is rejectedb。
The non-delayed cost function in step 9 comprises the steps of:
1) local search space FB corresponding to kth timekIs defined as
Figure 856527DEST_PATH_IMAGE016
，
fk(pmc) representing a mappingThe value of the smoothed mean curve at the kth time,
Figure 430597DEST_PATH_IMAGE017
representing half of the width of the confidence interval of the mapped smooth mean curve at the kth moment, wherein m represents the length of the target ridge line;
2) the non-delay cost function CF corresponding to the kth momentkIs defined as:
Figure 65978DEST_PATH_IMAGE018
,
Figure 425415DEST_PATH_IMAGE019
，
fk(i) is represented at FBkFrequency value, TF (t), taken within the rangek, fk) Represents the value of TF (t, f) at the kth time, tkRepresents the value of t at the kth time, fkRepresenting the value of f at the kth instant, i.e. the instantaneous frequency, ekRepresenting a weighting factor.
The performance of the algorithm of the invention was verified using the fan turbine planetary gearbox vibration data.
Vibration data is collected from a gearbox housing near the planetary gear train, with a data length of N =2736825 and a sampling frequency of fs = 5000 Hz.
The collected planetary gearbox vibration data is shown in FIG. 2.
The short-time Fourier transform algorithm is adopted to convert the vibration data of the planetary gearbox shown in FIG. 2 into a time-frequency spectrogram, and the obtained time-frequency spectrogram is shown in FIG. 3.
A local region with a high signal-to-noise ratio is selected from the time-frequency spectrogram shown in fig. 3, and the obtained local region is shown in fig. 4.
Edge detection is performed on the local area shown in fig. 4 by using a LoG detection algorithm, and the obtained image edge is shown in fig. 5.
The results obtained by eliminating outliers of each ridge in FIG. 5 using the Grubbs test algorithm are shown in FIG. 6.
The ridge bands are superimposed on one of the ridge bands with the most complete contour according to the kinematic proportion relationship between the ridge bands, and the constructed composite ridge band is shown in fig. 7 (the ridge band at the lowest layer is the composite ridge band).
The Grubbs test algorithm was used to eliminate outliers of the synthetic ridge, and the results are shown in FIG. 8.
The smoothed mean curve of the composite ridge and its 95% confidence interval were calculated and the results are shown in fig. 9.
The smooth mean curve and its confidence interval are mapped onto the target ridge line according to the kinematic proportional relationship between the smooth mean curve and the target ridge line, and the result is shown in fig. 10.
The non-delay cost function is used to search the ridge point of the target ridge line, and the obtained instantaneous frequency curve is shown in fig. 11.
Multiple experiments show that the maximum relative error between the instantaneous frequency estimation value and the measured value obtained by the method is 0.835%, the average relative error is 0.071%, the maximum relative error between the instantaneous frequency estimation value and the measured value obtained by the one-step cost function method is 16.39%, the average relative error is 2.14%, the maximum relative error of the method is reduced by 94.91%, and the average relative error is reduced by 96.68%. According to the experimental results, after analysis, it is considered that:
1) the traditional one-step cost function needs to depend on the position of the previous ridge point when determining the central point of the current search interval, and has a time delay phenomenon.
2) The traditional one-step cost function method is lack of adaptivity, a search interval needs to be set manually, and the search width is fixed, so errors are inevitably brought.
3) Compared with the traditional one-step cost function method, the method has high precision and accuracy.
It should be appreciated by those skilled in the art that the foregoing embodiments are merely exemplary for better understanding of the present invention, and should not be construed as limiting the scope of the present invention as long as the modifications are made according to the technical solution of the present invention.

Claims (4)

1. The time-frequency ridge line extraction method based on the LoG operator and Grubbs inspection is characterized by comprising the following steps of:
step 1: converting the signal x (k) k =1, 2, …, N into a time-frequency spectrogram by using a short-time fourier transform algorithm, wherein N represents the length of the signal;
step 2: selecting a region which at least comprises two ridge bands and has a signal-to-noise ratio larger than 80dB from the time-frequency spectrogram, and converting the local region into a binary image by adopting a LoG detection algorithm, wherein the binary image comprises a plurality of ridge bands;
and step 3: eliminating abnormal values of the upper edge and the lower edge of each ridge by adopting a Grubbs test algorithm;
and 4, step 4: superposing the ridge bands on one ridge band with the most complete contour according to the kinematic proportion relation between the ridge bands to construct a synthetic ridge band with complete and clear edges;
and 5: eliminating abnormal values of the upper edge and the lower edge of the synthesized ridge by adopting a Grubbs test algorithm;
step 6: calculating a mean value curve of the synthesized ridge, smoothing the mean value curve by adopting a five-point cubic smoothing algorithm to obtain a smooth mean value curve, and calculating a confidence interval of the smooth mean value curve on a 95% confidence level;
and 7: mapping the smooth mean curve and the confidence interval thereof to a target ridge line according to the kinematic proportion relation between the smooth mean curve and the target ridge line to be estimated;
and 8: taking the mapped smooth mean curve as a reference line of the target ridge line, and taking the mapped confidence interval as a local search interval of the target ridge line;
and step 9: searching ridge points in a local search interval corresponding to each moment by adopting a non-delay cost function, determining the instantaneous frequency corresponding to each moment, and finally obtaining the instantaneous frequency in the whole time interval:
the non-delayed cost function in step 9 comprises the steps of:
1) local search space FB corresponding to kth timekIs defined as
Figure 202389DEST_PATH_IMAGE001
，
fk(pmc) represents the value of the mapped smoothed mean curve at the kth time,
Figure 713005DEST_PATH_IMAGE002
representing half of the width of the confidence interval of the mapped smooth mean curve at the kth moment, wherein m represents the length of the target ridge line;
2) the non-delay cost function CF corresponding to the kth momentkIs defined as:
Figure 961583DEST_PATH_IMAGE003
,
Figure 950268DEST_PATH_IMAGE004
，
fk(i) is represented at FBkFrequency value, TF (t), taken within the rangek, fk) Represents the value of TF (t, f) at the kth time, tkRepresents the value of t at the kth time, fkRepresents the value of f at the k-th time, ekRepresents a weight factor;
the maximum relative error between the instantaneous frequency estimate and the measured value is 0.835%, and the average relative error is 0.071%.
2. The method for extracting time-frequency ridge lines based on LoG operator and Grubbs test according to claim 1, wherein the short-time Fourier transform algorithm in the step 1 comprises the following steps:
1) short-time fourier transform the signal x (k):
Figure 499061DEST_PATH_IMAGE005
，
TF (t, f) represents the result of the short-time fourier transform of the signal x (k), t represents a time factor, f represents a scale factor, and the function w (z) represents a window function with an argument z;
2) calculate the time-frequency spectrum of signal x (k):
Figure 790365DEST_PATH_IMAGE006
，
spectrogram (t, f) represents the time-frequency spectrum of x (k).
3. The method for extracting time-frequency ridge lines based on LoG operator and Grubbs test according to claim 1, wherein the LoG detection algorithm in the step 2 comprises the following steps:
1) the original image I (x, y) is smoothed with a gaussian filter:
Figure 650874DEST_PATH_IMAGE007
，
Gσ(x, y) represents a gaussian kernel with standard deviation σ, L (x, y) represents a gaussian filtered image, x represents a time point of the image, y represents a frequency point of the image, and x represents a convolution calculation;
2) performing a Laplacian operation on L (x, y):
Figure 318615DEST_PATH_IMAGE008
,
Figure 846549DEST_PATH_IMAGE009
represents the result obtained by Laplacian operation of L (x, y);
3) setting a proper threshold value if a certain point (x, y) on the image corresponds to
Figure 902229DEST_PATH_IMAGE010
If the value is larger than the threshold value, the point is judged to be an edge.
4. The method for extracting time-frequency ridge lines based on LoG operator and Grubbs test according to claim 1, characterized in that: the Grubbs test algorithm in the step 3 comprises the following steps:
1) for signal xnN =1, 2, …, N, establishing Grubbs test statistics
Figure 125400DEST_PATH_IMAGE011
，
Figure 596833DEST_PATH_IMAGE012
Represents the sample mean, σ represents the sample standard deviation, and N represents the sample length;
2) setting the significance level as alpha according to a probability formula
Figure 713694DEST_PATH_IMAGE013
Determining g0(N, α)，g0(N, alpha) represents the data length N, and the significance level is the Grubbs critical value corresponding to alpha;
3) if it is not
Figure 612379DEST_PATH_IMAGE014
B =1, 2, …, N, then x is rejectedb。
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