CN107391935A - The instantaneous Frequency Estimation method examined based on non-delayed cost function and Grubbs - Google Patents
The instantaneous Frequency Estimation method examined based on non-delayed cost function and Grubbs Download PDFInfo
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Abstract
The invention discloses the instantaneous Frequency Estimation method based on non-delayed cost function and Grubbs inspections, primary signal is converted to by time-frequency spectrum using Short Time Fourier Transform, more vallate bands are obtained using Canny detection algorithms, the exceptional value excluded per vallate band is examined using Grubbs, by being superimposed one synthesis ridge band with complete sharp edge of structure, the exceptional value for excluding synthesis ridge band is examined using Grubbs, calculate the Mean curve of synthesis ridge band, Mean curve is smoothed, calculate the confidential interval of the smooth Mean curve in 95% confidence level, smooth Mean curve and its confidential interval are mapped on target crestal line, obtain the reference line of target crestal line and the local region of search, target crestal line is extracted using non-delayed cost function.The present invention is suitable for estimating the instantaneous frequency of complicated multi -components frequency variation signal, overcomes conventional method in the defects of mechanical oscillation signal instantaneous Frequency Estimation, and the accuracy and precision of estimated result is high, is easy to engineer applied.
Description
Technical field
The present invention relates to condition monitoring for rotating machinery and fault diagnosis field, and in particular to based on non-delayed cost function and
The instantaneous Frequency Estimation method that Grubbs is examined.
Background technology
Due to the complexity of working environment, rotating machinery is often operated under Variable Velocity Condition.Instantaneous Frequency Estimation is to assess
Running state of rotating machine and the important prerequisite for carrying out fault diagnosis.Currently used instantaneous Frequency Estimation method is a step cost
Function method（one-step cost function）.One step cost function method can search for ridge point in the range of local frequencies, but
It is that the central point of local frequencies scope depends on the position of a upper ridge point, this causes a step cost function, and there is delay.This
Outside, the width of local frequencies hunting zone is rule of thumb arbitrarily set, and width at any time be all it is fixed, no
It can vary over, this causes a step cost function to lack enough adaptivitys.Drawbacks described above causes a step cost
Function method accuracy and precision when estimating instantaneous frequency is relatively low.
The content of the invention
The problem to be solved in the present invention is the deficiency for more than, proposes what is examined based on non-delayed cost function and Grubbs
Instantaneous Frequency Estimation method.Compared with the conventional method, ginseng of the present invention using the smooth Mean curve after mapping as target crestal line
Line is examined, the Local Search section using the confidential interval after mapping as target crestal line, therefore the center of local frequencies hunting zone
Position of the point independent of a upper ridge point, without any delay, local frequencies hunting zone can be set automatically, search for bandwidth energy
Reach change over time and change automatically, the accuracy and precision of instantaneous Frequency Estimation result is high.
To solve above technical problem, the present invention uses following technical scheme：There is provided based on non-delayed cost function and
The instantaneous Frequency Estimation method that Grubbs is examined, it is characterised in that comprise the following steps：
Step 1：Using Short Time Fourier Transform algorithm by signal x（k）（k=1, 2, …,N）Time-frequency spectrum is converted to, N is represented
The length of signal；
Step 2：One piece of regional area having compared with high s/n ratio is chosen from time-frequency spectrum, should using Canny detection algorithms
Regional area is converted into bianry image, and bianry image includes more vallate bands；Regional area refers to comprise at least two vallate bands, noise
Than the region more than 80dB；
Step 3：Excluded using Grubbs check algorithms per exceptional value of the vallate with lower edges；
Step 4：Above-mentioned more vallate bands are most complete according to the mutual kinematics proportionate relationship wherein profile that is added to
Ridge band on, structure one have complete sharp edge synthesis ridge band；Kinematics proportionate relationship refers to the machine corresponding to ridge band
Gearratio between device part；
Step 5：Above-mentioned exceptional value of the synthesis ridge with lower edges is excluded using Grubbs check algorithms；
Step 6：Calculate the Mean curve of above-mentioned synthesis ridge band, using 5 points three times smoothing algorithm Mean curve is smoothly located
Reason, obtains smooth Mean curve, calculates the confidential interval of the smooth Mean curve in 95% confidence level；
Step 7：By above-mentioned smooth Mean curve and its confidential interval according between smooth Mean curve and target crestal line to be estimated
Kinematics proportionate relationship be mapped on target crestal line；
Step 8：Reference line using the smooth Mean curve after mapping as target crestal line, using the confidential interval after mapping as mesh
Mark the Local Search section of crestal line；
Step 9：Ridge point is searched in the Local Search section corresponding to each moment using non-delayed cost function, it is determined that each
Instantaneous frequency corresponding to moment, finally obtain the instantaneous frequency on whole time interval.
Further, Short Time Fourier Transform algorithm comprises the following steps in the step 1：
1）To signal x（k）Carry out Short Time Fourier Transform：
,
TF (t, f) representation signal x（k）Short Time Fourier Transform result, t represents time factor, and f represents scale factor, function
W (z) represents window function of the independent variable as z；
2）Calculate signal x（k）Time-frequency spectrum：
,
Spectrogram (t, f) represents x（k）Time-frequency spectrum.
Further, Canny detection algorithms comprise the following steps in the step 2：
1) image f (x, y) is smoothed using Gaussian filter, eliminates noise and Extraneous details in image：
,
,
Image after g (x, y) representatives are smooth, G (x, y) represent 2-d gaussian filterses device, the time point of x representative images, and y is represented
The Frequency point of image, symbol * represent convolutional calculation, and it is poor that σ represents Gauss standard, σ=1 in the present invention；
2) amplitude and direction of g (x, y) intensity gradient are calculated
,
,
,
M (x, y) represents the amplitude of intensity gradient, and θ (x, y) represents the direction of intensity gradient, gxIt is right that (x, y) represents g (x, y)
X partial derivative, gy(x, y) represents partial derivatives of the g (x, y) to y；
3) false edge is eliminated using non-maximum coercion Acts：
On gradient direction θ (x, y), if non-zero gradient value is more than two adjacent Grad, the non-zero gradient value is kept
It is constant, otherwise, the non-zero gradient value zero setting；
4) image after above-mentioned elimination false edge is filtered using two threshold values of different sizes, two threshold values are designated as
T1And T2, T1<T2, by T1Obtained image is designated as I1, by T2Obtained image is designated as I2；In the present invention, T1=0.0063, T2=
0.0156；
5) from I2It is middle to reject the weak edge not being connected with strong edge, then connect I1And I2In edge formed continuous boundary.
Further, Grubbs check algorithms comprise the following steps in the step 3：
1）To signal xn（n=1, 2, …,N）, establish Grubbs test statistics,Representative sample average, σ
Representative sample standard deviation, N representative sample length；
2）Significance is set as α, according to new probability formulaDetermine g0(N, α), g0(N, α)
Data length is represented as N, significance be α corresponding to Grubbs critical values, the present invention in α=0.05；
If 3), （b=1, 2, …,N）, then x is rejectedb。
Further, non-delayed cost function comprises the following steps in the step 9：
1）Local Search section FB corresponding to k-th of momentkIt is defined as
,
fk(pmc) value of the smooth Mean curve after mapping k-th of moment is represented,It is bent to represent the smooth average after mapping
For line confidential interval in the half of k-th of moment width, m represents the length of target crestal line；
2）Non-delayed cost function CF corresponding to k-th of momentkIt is defined as：
,
,
fk(i) represent in FBkIn the range of the frequency values that are taken, TF (tk, fk) represent values of the TF (t, f) k-th of moment, tk
Represent values of the t k-th of moment, fkRepresent values of the f k-th of moment, ekRepresent weight factor.
Further, relative error≤0.561%, average relative error≤0.046%.
The present invention uses above technical scheme, and compared with prior art, the present invention has advantages below：
1) present invention has real-time：The present invention using the smooth Mean curve of synthesis ridge band after mapping as reference line, can be
When determine the central point of current time local frequencies hunting zone, avoid the dependence to previous ridge point, eliminating the time prolongs
Late, there is real-time.
2) present invention has adaptivity：The present invention utilizes the confidence area for synthesizing the smooth Mean curve of ridge band after mapping
Between be used as the local frequencies region of search, adaptive can should determine that the local frequencies hunting zone corresponding to each moment, searching strip
Width can be over time change and change automatically, it is not necessary to by virtue of experience set search bandwidth, so as to eliminate due to artificial
Reason and caused error.
3) test result indicates that：Maximum between the instantaneous Frequency Estimation value and measured value that are obtained by the present invention is relative by mistake
Difference is 0.561%, average relative error 0.046%, and compared with the result of a step cost function method, maximum relative error reduces
96.58%, average relative error reduces by 97.85%.
The present invention will be further described with reference to the accompanying drawings and examples.
Brief description of the drawings
Accompanying drawing 1 is the instantaneous Frequency Estimation method examined in the embodiment of the present invention based on non-delayed cost function and Grubbs
Flow chart；
Accompanying drawing 2 is epicyclic gearbox vibration signal in the embodiment of the present invention；
Accompanying drawing 3 is the time-frequency spectrum of epicyclic gearbox vibration signal in the embodiment of the present invention；
Accompanying drawing 4 is the regional area with high s/n ratio chosen in the embodiment of the present invention from time-frequency spectrum；
Accompanying drawing 5 is the edge of the local image region detected in the embodiment of the present invention by Canny algorithms；
Accompanying drawing 6 is to be eliminated in the embodiment of the present invention using Grubbs check algorithms per vallate with the result after abnormity point；
Accompanying drawing 7 is the synthesis ridge band being formed by stacking in the embodiment of the present invention using the kinematics proportionate relationship between ridge band（It is most lower
The ridge band of layer is to synthesize ridge band）；
Accompanying drawing 8 is to eliminate synthesis ridge with the result after abnormity point using Grubbs check algorithms in the embodiment of the present invention；
Accompanying drawing 9 is the mean value smoothing curve and its 95% confidential interval that ridge band is synthesized in the embodiment of the present invention；
Accompanying drawing 10 is mean value smoothing curve and its confidential interval for mapping to obtain in the embodiment of the present invention；
Accompanying drawing 11 is instantaneous Frequency Estimation value in the embodiment of the present invention.
Embodiment
Embodiment, as shown in figure 1, the instantaneous Frequency Estimation method examined based on non-delayed cost function and Grubbs, bag
Include following steps：
Step 1：Using Short Time Fourier Transform algorithm by signal x（k）（k=1, 2, …,N）Time-frequency spectrum is converted to, N is represented
The length of signal；
Step 2：One piece of regional area having compared with high s/n ratio is chosen from time-frequency spectrum, should using Canny detection algorithms
Regional area is converted into bianry image, and bianry image includes more vallate bands；Regional area refers to comprise at least two vallate bands, noise
Than the region more than 80dB；
Step 3：Excluded using Grubbs check algorithms per exceptional value of the vallate with lower edges；
Step 4：Above-mentioned more vallate bands are most complete according to the mutual kinematics proportionate relationship wherein profile that is added to
Ridge band on, structure one have complete sharp edge synthesis ridge band；Kinematics proportionate relationship refers to the machine corresponding to ridge band
Gearratio between device part；
Step 5：Above-mentioned exceptional value of the synthesis ridge with lower edges is excluded using Grubbs check algorithms；
Step 6：Calculate the Mean curve of above-mentioned synthesis ridge band, using 5 points three times smoothing algorithm Mean curve is smoothly located
Reason, obtains smooth Mean curve, calculates the confidential interval of the smooth Mean curve in 95% confidence level；
Step 7：By above-mentioned smooth Mean curve and its confidential interval according between smooth Mean curve and target crestal line to be estimated
Kinematics proportionate relationship be mapped on target crestal line；
Step 8：Reference line using the smooth Mean curve after mapping as target crestal line, using the confidential interval after mapping as mesh
Mark the Local Search section of crestal line；
Step 9：Ridge point is searched in the Local Search section corresponding to each moment using non-delayed cost function, it is determined that each
Instantaneous frequency corresponding to moment, finally obtain the instantaneous frequency on whole time interval.
Short Time Fourier Transform algorithm comprises the following steps in step 1：
1）To signal x（k）Carry out Short Time Fourier Transform：
,
TF (t, f) representation signal x（k）Short Time Fourier Transform result, t represents time factor, and f represents scale factor, function
W (z) represents window function of the independent variable as z；
2）Calculate signal x（k）Time-frequency spectrum：
,
Spectrogram (t, f) represents x（k）Time-frequency spectrum.
Further, Canny detection algorithms comprise the following steps in the step 2：
1) image f (x, y) is smoothed using Gaussian filter, eliminates noise and Extraneous details in image：
,
,
Image after g (x, y) representatives are smooth, G (x, y) represent 2-d gaussian filterses device, the time point of x representative images, and y is represented
The Frequency point of image, symbol * represent convolutional calculation, and it is poor that σ represents Gauss standard, σ=1 in the present invention；
2) amplitude and direction of g (x, y) intensity gradient are calculated
,
,
,
M (x, y) represents the amplitude of intensity gradient, and θ (x, y) represents the direction of intensity gradient, gxIt is right that (x, y) represents g (x, y)
X partial derivative, gy(x, y) represents partial derivatives of the g (x, y) to y；
3) false edge is eliminated using non-maximum coercion Acts：
On gradient direction θ (x, y), if non-zero gradient value is more than two adjacent Grad, the non-zero gradient value is kept
It is constant, otherwise, the non-zero gradient value zero setting；
4) image after above-mentioned elimination false edge is filtered using two threshold values of different sizes, two threshold values are designated as
T1And T2, T1<T2, by T1Obtained image is designated as I1, by T2Obtained image is designated as I2；In the present invention, T1=0.0063, T2=
0.0156；
5) from I2It is middle to reject the weak edge not being connected with strong edge, then connect I1And I2In edge formed continuous boundary.
Grubbs check algorithms comprise the following steps in step 3：
1）To signal xn（n=1, 2, …,N）, establish Grubbs test statistics,Representative sample average, σ
Representative sample standard deviation, N representative sample length；
2）Significance is set as α, according to new probability formulaDetermine g0(N, α), g0(N, α)
Data length is represented as N, significance be α corresponding to Grubbs critical values, the present invention in α=0.05；
If 3), （b=1, 2, …,N）, then x is rejectedb。
Non-delayed cost function comprises the following steps in step 9：
1）Local Search section FB corresponding to k-th of momentkIt is defined as
,
fk(pmc) value of the smooth Mean curve after mapping k-th of moment is represented,It is bent to represent the smooth average after mapping
For line confidential interval in the half of k-th of moment width, m represents the length of target crestal line；
2）Non-delayed cost function CF corresponding to k-th of momentkIt is defined as：
,
,
fk(i) represent in FBkIn the range of the frequency values that are taken, TF (tk, fk) represent values of the TF (t, f) k-th of moment, tk
Represent values of the t k-th of moment, fkRepresent values of the f k-th of moment, ekRepresent weight factor.
The performance of algorithm of the present invention is verified using blower fan turbine epicyclic gearbox vibration data.
Vibration data gathers from the gearbox-case of epicyclic train, data length N=2736825, sample frequency
fs= 5000 Hz。
The epicyclic gearbox vibration data collected is as shown in Figure 2.
Epicyclic gearbox vibration data shown in Fig. 2 is converted to by time-frequency spectrum using Short Time Fourier Transform algorithm, obtained
The time-frequency spectrum arrived is as shown in Figure 3.
The regional area with high s/n ratio, obtained regional area such as Fig. 4 institutes are chosen from the time-frequency spectrum shown in Fig. 3
Show.
Rim detection is carried out to regional area as shown in Figure 4 using Canny detection algorithms, obtained image border is as schemed
Shown in 5.
The abnormity point of each vallate band in Fig. 5 is eliminated using Grubbs check algorithms, obtained result is as shown in Figure 6.
Each vallate band is added to the most complete ridge band of a wherein profile according to the kinematics proportionate relationship between ridge band
On, constructed synthesis ridge band is as shown in Figure 7（Undermost ridge band is to synthesize ridge band）.
The abnormity point of synthesis ridge band is eliminated using Grubbs check algorithms, as a result as shown in Figure 8.
The smooth Mean curve and its 95% confidential interval of synthesis ridge band are calculated, as a result as shown in Figure 9.
According to the kinematics proportionate relationship between smooth Mean curve and target crestal line by smooth Mean curve and its confidence
Interval Maps are on target crestal line, as a result as shown in Figure 10.
Using the ridge point of non-delayed cost function search target crestal line, obtained instantaneous frequency profile is as shown in figure 11.
Show through many experiments, the maximum relative error between the instantaneous Frequency Estimation value and measured value that are obtained by the present invention
For 0.561%, average relative error 0.046%, and use the instantaneous Frequency Estimation value that a step cost function method obtains and actual measurement
Maximum relative error between value is 16.39%, and average relative error 2.14%, maximum relative error of the present invention reduces
96.58%, average relative error reduces by 97.85%.
According to experimental result, think after analysis：
1) a traditional step cost function it is determined that current search section central point when need rely on a ridge point position
Put, there is time delay phenomenon, the present invention can determine to work as immediately by the use of the smooth Mean curve after mapping as reference line
The center of the preceding region of search, completely independent of a upper ridge point, therefore there is real-time.
2) a traditional step cost function method lacks adaptivity, it is necessary to artificially set the region of search, and search width
It is fixed, thus inevitably brings error, the present invention is using the smooth Mean curve confidential interval after mapping come automatic
Local Search section is determined, the change that bandwidth can be over time is searched for and changes automatically, it is not necessary to it is artificial to participate in, therefore have
Adaptivity.
3) compared with a traditional step cost function method, accuracy of the invention and the degree of accuracy are high.
One skilled in the art would recognize that above-mentioned embodiment is exemplary, it is in order that ability
Field technique personnel can be better understood from present invention, should not be understood as limiting the scope of the invention, as long as
According to technical solution of the present invention improvements introduced, protection scope of the present invention is each fallen within.
Claims (6)
1. the instantaneous Frequency Estimation method examined based on non-delayed cost function and Grubbs, it is characterised in that including following step
Suddenly：
Step 1：Using Short Time Fourier Transform algorithm by signal x（k）（k=1, 2, …,N）Time-frequency spectrum is converted to, N is represented
The length of signal；
Step 2：One piece of regional area having compared with high s/n ratio is chosen from time-frequency spectrum, should using Canny detection algorithms
Regional area is converted into bianry image, and bianry image includes more vallate bands；
Step 3：Excluded using Grubbs check algorithms per exceptional value of the vallate with lower edges；
Step 4：Above-mentioned more vallate bands are most complete according to the mutual kinematics proportionate relationship wherein profile that is added to
Ridge band on, structure one have complete sharp edge synthesis ridge band；
Step 5：Above-mentioned exceptional value of the synthesis ridge with lower edges is excluded using Grubbs check algorithms；
Step 6：Calculate the Mean curve of above-mentioned synthesis ridge band, using 5 points three times smoothing algorithm Mean curve is smoothly located
Reason, obtains smooth Mean curve, calculates the confidential interval of the smooth Mean curve in 95% confidence level；
Step 7：By above-mentioned smooth Mean curve and its confidential interval according between smooth Mean curve and target crestal line to be estimated
Kinematics proportionate relationship be mapped on target crestal line；
Step 8：Reference line using the smooth Mean curve after mapping as target crestal line, using the confidential interval after mapping as mesh
Mark the Local Search section of crestal line；
Step 9：Ridge point is searched in the Local Search section corresponding to each moment using non-delayed cost function, it is determined that each
Instantaneous frequency corresponding to moment, finally obtain the instantaneous frequency on whole time interval.
2. the instantaneous Frequency Estimation method according to claim 1 examined based on non-delayed cost function and Grubbs, its
It is characterised by, Short Time Fourier Transform algorithm comprises the following steps in the step 1：
1）To signal x（k）Carry out Short Time Fourier Transform：
,
TF (t, f) representation signal x（k）Short Time Fourier Transform result, t represents time factor, and f represents scale factor, function
W (z) represents window function of the independent variable as z；
2）Calculate signal x（k）Time-frequency spectrum：
,
Spectrogram (t, f) represents x（k）Time-frequency spectrum.
3. the instantaneous Frequency Estimation method according to claim 1 examined based on non-delayed cost function and Grubbs, its
It is characterised by, Canny detection algorithms comprise the following steps in the step 2：
1) image f (x, y) is smoothed using Gaussian filter, eliminates noise and Extraneous details in image：
,
,
Image after g (x, y) representatives are smooth, G (x, y) represent 2-d gaussian filterses device, the time point of x representative images, and y is represented
The Frequency point of image, symbol * represent convolutional calculation, and it is poor that σ represents Gauss standard；
2) amplitude and direction of g (x, y) intensity gradient are calculated
,
,
,
M (x, y) represents the amplitude of intensity gradient, and θ (x, y) represents the direction of intensity gradient, gx(x, y) represents g (x, y) to x
Partial derivative, gy(x, y) represents partial derivatives of the g (x, y) to y；
3) false edge is eliminated using non-maximum coercion Acts：
On gradient direction θ (x, y), if non-zero gradient value is more than two adjacent Grad, the non-zero gradient value is kept
It is constant, otherwise, the non-zero gradient value zero setting；
4) image after above-mentioned elimination false edge is filtered using two threshold values of different sizes, two threshold values are designated as T1
And T2, T1<T2, by T1Obtained image is designated as I1, by T2Obtained image is designated as I2；
5) from I2It is middle to reject the weak edge not being connected with strong edge, then connect I1And I2In edge formed continuous boundary.
4. the instantaneous Frequency Estimation method according to claim 1 examined based on non-delayed cost function and Grubbs, its
It is characterised by：Grubbs check algorithms comprise the following steps in the step 3：
1）To signal xn（n=1, 2, …,N）, establish Grubbs test statistics,Representative sample average, σ
Representative sample standard deviation, N representative sample length；
2）Significance is set as α, according to new probability formulaDetermine g0(N, α), g0(N, α) generation
Table data length is N, and significance is the Grubbs critical values corresponding to α；
If 3), （b=1, 2, …,N）, then x is rejectedb。
5. the instantaneous Frequency Estimation method according to claim 1 examined based on non-delayed cost function and Grubbs, its
It is characterised by：Non-delayed cost function comprises the following steps in the step 9：
1）Local Search section FB corresponding to k-th of momentkIt is defined as
,
fk(pmc) value of the smooth Mean curve after mapping k-th of moment is represented,It is bent to represent the smooth average after mapping
For line confidential interval in the half of k-th of moment width, m represents the length of target crestal line；
2）Non-delayed cost function CF corresponding to k-th of momentkIt is defined as：
,
,
fk(i) represent in FBkIn the range of the frequency values that are taken, TF (tk, fk) represent values of the TF (t, f) k-th of moment, tk
Represent values of the t k-th of moment, fkRepresent values of the f k-th of moment, ekRepresent weight factor.
6. the instantaneous Frequency Estimation method according to claim 1 examined based on non-delayed cost function and Grubbs, its
It is characterised by：Relative error≤0.561%, average relative error≤0.046%.
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| CN116962123A (en) * | 2023-09-20 | 2023-10-27 | 大尧信息科技(湖南)有限公司 | Raised cosine shaping filter bandwidth estimation method and system of software defined framework |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114674410A (en) * | 2022-03-24 | 2022-06-28 | 安徽大学 | Component number time-varying underwater acoustic signal instantaneous frequency estimation method |
| CN116962123A (en) * | 2023-09-20 | 2023-10-27 | 大尧信息科技(湖南)有限公司 | Raised cosine shaping filter bandwidth estimation method and system of software defined framework |
| CN116962123B (en) * | 2023-09-20 | 2023-11-24 | 大尧信息科技(湖南)有限公司 | Raised cosine shaping filter bandwidth estimation method and system of software defined framework |
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