CN112179651A - Gear degradation index extraction method based on DRS processing and principal component analysis - Google Patents

Gear degradation index extraction method based on DRS processing and principal component analysis Download PDF

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CN112179651A
CN112179651A CN202011045863.2A CN202011045863A CN112179651A CN 112179651 A CN112179651 A CN 112179651A CN 202011045863 A CN202011045863 A CN 202011045863A CN 112179651 A CN112179651 A CN 112179651A
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gear
principal component
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臧家林
王欣
张福海
杨少杰
王俊
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Nuclear Power Operation Research Shanghai Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms
    • G01M13/021—Gearings
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention discloses a gear degradation index extraction method based on DRS processing and principal component analysis, which comprises the following steps: step 1: acquiring a vibration signal x (N) generated by gear operation through a vibration acceleration sensor, and adding a window function w with the length of N to the acquired vibration signal at the kth moment corresponding to the signal lengthN(n) constructing a windowed time-domain signal xk(n) satisfies xk(n)＝x(n+kT)wN(n); step 2: respectively extracting the edge frequency information corresponding to the 1-4 times of meshing frequency of the gear from the noise reduction signal by a narrow-band filtering method, and performing Hilbert demodulation on the extraction result to obtain the edge frequency envelope spectrum information of the 1-4 times of meshing frequency; and step 3: and calculating the RMS value of the edge frequency envelope information of the meshing frequency of 1 to 4 times, constructing a corresponding matrix for the calculated RMS data, and normalizing the matrix based on the mean value and the variance of each datum. The beneficial effects are that: using vibration acceleration sensorsAnd collecting a gear vibration signal of the equipment, and acquiring a time domain graph and a frequency spectrum graph of the signal.

Description

Gear degradation index extraction method based on DRS processing and principal component analysis
Technical Field
The invention belongs to the field of equipment state monitoring, and particularly relates to a gear degradation index extraction method based on DRS processing and principal component analysis.
Background
The gear is used as an important structural part and a transmission part in mechanical equipment, and plays an indispensable important role in the fields of aerospace, transportation, agricultural production, power transmission and the like. However, due to the complex working conditions of the gears and the like, the gears and the gear box are easily damaged in the operation process, so that the operation faults of the gears are caused, the transmission precision of the gears is influenced, even the operation reliability of equipment is influenced, and great potential safety hazards are caused. Therefore, the gear running performance index is extracted, and the real-time monitoring of the gear running state is very important.
The gear can vibrate during operation due to production and manufacturing defects, installation errors, abrasion, cracks and other phenomena in the operation process. The gear vibration signal is mainly expressed as a modulation characteristic, namely, the gear meshing frequency is modulated by the frequency conversion of the shaft on which the gear is positioned, and the gear shaft frequency conversion is a modulation signal. The frequency spectrum of the vibration signal shows that the gear meshing frequency is taken as the center, the modulation signal is in a side frequency form and is symmetrically distributed at equal intervals on the left and right of the meshing frequency, the gear fault degrees are different, and the modulation degrees of the gear rotation frequency on the meshing frequency are also different. Therefore, the modulation frequency of the gear vibration signal is extracted, and the running state characteristics of the gear can be effectively detected. Antoni proposes a Discrete Random Separation (DRS) method, which can separate modulation frequency from gear vibration signals to extract gear fault features. And a Principal Component Analysis (abbreviated PCA) proposed by Karl Pearson converts a set of variables which may have correlation into a set of linearly uncorrelated variables through orthogonal transformation, thereby realizing the dimensionality reduction and feature fusion of the original data. The method extracts the gear meshing modulation signal based on the DRS method, and fuses the edge frequency effective values (namely RMS values) of gear meshing by utilizing a principal component analysis method to obtain the gear degradation index.
Disclosure of Invention
The invention aims to provide a gear degradation index extraction method based on DRS processing and principal component analysis.
The technical scheme of the invention is as follows: a gear degradation index extraction method based on DRS processing and principal component analysis comprises the following steps:
step 1: acquiring a vibration signal x (N) generated by gear operation through a vibration acceleration sensor, and adding a window function w with the length of N to the acquired vibration signal at the kth moment corresponding to the signal lengthN(n) constructing a windowed time-domain signal xk(n) satisfies xk(n)＝x(n+kT)wN(n)；
Step 2: respectively extracting the edge frequency information corresponding to the 1-4 times of meshing frequency of the gear from the noise reduction signal by a narrow-band filtering method, and performing Hilbert demodulation on the extraction result to obtain the edge frequency envelope spectrum information of the 1-4 times of meshing frequency;
and step 3: and calculating the RMS value of the edge frequency envelope information of the meshing frequency of 1 to 4 times, constructing a corresponding matrix for the calculated RMS data, and normalizing the matrix based on the mean value and the variance of each datum.
The step 1 comprises adding a window function w with the length of N to the acquired vibration signal at the time corresponding to kT-N-deltaN(n) constructing a corresponding windowed time-domain signal xkd (n) and satisfy
Figure BDA0002707934040000021
The step 1 comprises the steps of constructing a DRS optimal filter based on the principle of minimum mean square error prediction error, and carrying out DRS processing on the windowed signal to improve the signal-to-noise ratio of the signal.
The optimal filter based on the minimum mean square error prediction error principle in the step 1 is constructed based on the following frequency response characteristics:
Figure BDA0002707934040000022
wherein p iskFor windowing signal xk(n) a deterministic component of the composition,
Figure BDA0002707934040000031
for windowing signals
Figure BDA0002707934040000032
The deterministic component of the composition of matter,
Figure BDA0002707934040000033
for windowing signals
Figure BDA0002707934040000034
The non-deterministic component of (a) is,
Figure BDA0002707934040000035
for windowing signals
Figure BDA0002707934040000036
And xk(n) a cross-power spectrum of (n),
Figure BDA0002707934040000037
for windowing signals
Figure BDA0002707934040000038
The self-power spectrum of (a) a,
Figure BDA0002707934040000039
being deterministic components
Figure BDA00027079340400000310
And pkThe cross-power spectrum of (a) a,
Figure BDA00027079340400000311
being deterministic components
Figure BDA00027079340400000312
The self-power spectrum of (a) a,
Figure BDA00027079340400000313
as non-deterministic components
Figure BDA00027079340400000314
The self-power spectrum of (a).
And 3, solving a correlation matrix of the standardized matrix according to a principal component analysis method, and calculating the eigenvalue and the eigenvector of the normalized matrix.
And 3, calculating the accumulated variance of each characteristic component based on the characteristic vector, selecting the characteristic components with the accumulated variance contribution rate of more than 75% for fusion, and finally obtaining the gear degradation index.
The invention has the beneficial effects that: acquiring a gear vibration signal of equipment by using a vibration acceleration sensor, and acquiring a time domain graph and a frequency spectrum graph of the signal, wherein the time domain graph and the frequency spectrum graph are shown in attached drawings 1 and 2; performing DRS processing on the signals, selecting an optimal filter corresponding to the DRS based on the principle of minimum mean square error prediction error, performing noise reduction processing on the original signals based on the selected filter, acquiring 1-4 times of meshing frequency side frequency information of gear meshing through narrow-band filtering, and acquiring an envelope spectrum corresponding to the side frequency information through Hilbert demodulation, wherein the 1 time of meshing frequency side frequency envelope spectrum information is shown in figure 3; and calculating the RMS value of the 1-4 times of meshing frequency side frequency envelope spectrum by a principal component analysis method, and selecting characteristic components with the cumulative variance contribution rate of each component of more than 75% for fusion to obtain the gear degradation index. The degradation trend of the gear operation plotted against the gear degradation index is shown in fig. 4.
Drawings
FIG. 1 is a time domain diagram of an original signal;
FIG. 2 is a spectrum diagram of an original signal;
fig. 3 is 1-fold meshing frequency side frequency information extracted by DRS;
FIG. 4 is a degradation trend graph of gear operation;
fig. 5 is a schematic flow chart of a gear degradation index extraction method based on DRS processing and principal component analysis provided by the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
As shown in fig. 5, a gear degradation indicator extraction method based on DRS processing and principal component analysis includes the following steps:
step 1: acquiring a vibration signal x (N) generated by gear operation through a vibration acceleration sensor, and adding a window function w with the length of N to the acquired vibration signal at the kth moment corresponding to the signal lengthN(n) constructing a windowed time-domain signal xk(n) satisfies xk(n)＝x(n+kT)wN(n); setting delta as the signal time interval between two adjacent window functions of the signal, and adding the window function w with the length of N to the acquired vibration signal at the time corresponding to kT + N + deltaN(n) constructing a corresponding windowed time-domain signal by
Figure BDA0002707934040000041
The time domain signal satisfies
Figure BDA0002707934040000042
And constructing a DRS optimal filter based on the principle of minimum mean square error prediction error, and performing DRS processing on the windowed signal to improve the signal-to-noise ratio of the signal. The optimal filter based on the minimum mean square error prediction error principle is constructed based on the following frequency response characteristics H (f):
Figure BDA0002707934040000043
wherein p iskFor windowing signal xk(n) a deterministic component of the composition,
Figure BDA0002707934040000044
for windowing signals
Figure BDA0002707934040000045
The deterministic component of the composition of matter,
Figure BDA0002707934040000046
for windowing signals
Figure BDA0002707934040000047
The non-deterministic component of (a) is,
Figure BDA0002707934040000048
for windowing signals
Figure BDA0002707934040000049
And xk(n) a cross-power spectrum of (n),
Figure BDA00027079340400000410
for windowing signals
Figure BDA00027079340400000411
The self-power spectrum of (a) a,
Figure BDA00027079340400000412
being deterministic components
Figure BDA00027079340400000413
And pkThe cross-power spectrum of (a) a,
Figure BDA00027079340400000414
being deterministic components
Figure BDA00027079340400000415
The self-power spectrum of (a) a,
Figure BDA00027079340400000416
as non-deterministic components
Figure BDA00027079340400000417
The self-power spectrum of (a).
Step 2: respectively extracting the edge frequency information corresponding to the 1-4 times of meshing frequency of the gear from the noise reduction signal by a narrow-band filtering method, and performing Hilbert demodulation on the extraction result to obtain the edge frequency envelope spectrum information of the 1-4 times of meshing frequency;
and step 3: and calculating the RMS value of the edge frequency envelope spectrum of the meshing frequency of 1 to 4 times, constructing a corresponding matrix for the calculated RMS data, and normalizing the matrix based on the mean value and the variance of each datum. And solving a correlation matrix of the standardized matrix according to a principal component analysis method, and calculating the eigenvalue and the eigenvector of the normalized matrix. And calculating the accumulated variance of each feature component based on the feature vector, selecting the feature components with the accumulated variance contribution rate of more than 75% for fusion, and finally obtaining the gear degradation index.

Claims (7)

1. A gear degradation index extraction method based on DRS processing and principal component analysis is characterized by comprising the following steps:
step 1: acquiring a vibration signal x (N) generated by gear operation through a vibration acceleration sensor, and adding a window function w with the length of N to the acquired vibration signal at the kth moment corresponding to the signal lengthN(n) constructing a windowed time-domain signal xk(n) satisfies xk(n)＝x(n+kT)wN(n)；
Step 2: respectively extracting the edge frequency information corresponding to the 1-4 times of meshing frequency of the gear from the noise reduction signal by a narrow-band filtering method, and performing Hilbert demodulation on the extraction result to obtain the edge frequency envelope spectrum information of the 1-4 times of meshing frequency;
and step 3: and calculating the RMS value of the edge frequency envelope information of the meshing frequency of 1 to 4 times, constructing a corresponding matrix for the calculated RMS data, and normalizing the matrix based on the mean value and the variance of each datum.
2. The gear degradation indicator extraction method based on DRS processing and principal component analysis of claim 1, wherein: the step 1 comprises adding a window function w with the length of N to the acquired vibration signal at the time corresponding to kT-N-deltaN(n) constructing a corresponding windowed time-domain signal
Figure FDA0002707934030000011
And satisfy
Figure FDA0002707934030000012
3. The gear degradation indicator extraction method based on DRS processing and principal component analysis of claim 1, wherein: the step 1 comprises the steps of constructing a DRS optimal filter based on the principle of minimum mean square error prediction error, and carrying out DRS processing on the windowed signal to improve the signal-to-noise ratio of the signal.
4. The gear degradation indicator extraction method based on DRS processing and principal component analysis of claim 1, wherein: the optimal filter based on the minimum mean square error prediction error principle in the step 1 is constructed based on the following frequency response characteristics:
Figure FDA0002707934030000013
wherein p iskFor windowing signal xk(n) a deterministic component of the composition,
Figure FDA0002707934030000014
for windowing signals
Figure FDA0002707934030000015
The deterministic component of the composition of matter,
Figure FDA0002707934030000021
for windowing signals
Figure FDA0002707934030000022
The non-deterministic component of (a) is,
Figure FDA0002707934030000023
for windowing signals
Figure FDA0002707934030000024
And xk(n) a cross-power spectrum of (n),
Figure FDA0002707934030000025
for windowing signals
Figure FDA0002707934030000026
The self-power spectrum of (a) a,
Figure FDA0002707934030000027
being deterministic components
Figure FDA0002707934030000028
And pkThe cross-power spectrum of (a) a,
Figure FDA0002707934030000029
being deterministic components
Figure FDA00027079340300000210
The self-power spectrum of (a) a,
Figure FDA00027079340300000211
as non-deterministic components
Figure FDA00027079340300000212
The self-power spectrum of (a).
5. The gear degradation indicator extraction method based on DRS processing and principal component analysis of claim 1, wherein: and 3, solving a correlation matrix of the standardized matrix according to a principal component analysis method, and calculating the eigenvalue and the eigenvector of the normalized matrix.
6. The gear degradation indicator extraction method based on DRS processing and principal component analysis of claim 1, wherein: and 3, calculating the accumulated variance of each characteristic component based on the characteristic vector, selecting the characteristic components with the accumulated variance contribution rate of more than 75% for fusion, and finally obtaining the gear degradation index.
7. The gear degradation indicator extraction method based on DRS processing and principal component analysis of claim 2, wherein: and 3, calculating the accumulated variance of each characteristic component based on the characteristic vector, selecting the characteristic components with the accumulated variance contribution rate of more than 75% for fusion, and finally obtaining the gear degradation index.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102192845A (en) * 2010-03-18 2011-09-21 施耐德东芝换流器欧洲公司 Method for diagnosing heat radiation system
CN102200489A (en) * 2010-03-23 2011-09-28 施耐德东芝换流器欧洲公司 Method for diagnosing heat radiation system
CN103954450A (en) * 2014-05-19 2014-07-30 重庆交通大学 Bearing life degradation performance evaluation index construction method based on main component analysis
CN107121283A (en) * 2017-06-19 2017-09-01 苏州微著设备诊断技术有限公司 A kind of gear condition monitoring index extracting method based on Discrete Stochastic separation algorithm

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102192845A (en) * 2010-03-18 2011-09-21 施耐德东芝换流器欧洲公司 Method for diagnosing heat radiation system
CN102200489A (en) * 2010-03-23 2011-09-28 施耐德东芝换流器欧洲公司 Method for diagnosing heat radiation system
CN103954450A (en) * 2014-05-19 2014-07-30 重庆交通大学 Bearing life degradation performance evaluation index construction method based on main component analysis
CN107121283A (en) * 2017-06-19 2017-09-01 苏州微著设备诊断技术有限公司 A kind of gear condition monitoring index extracting method based on Discrete Stochastic separation algorithm

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