CN111783559A - Time-frequency domain joint fault diagnosis method based on vibration signals - Google Patents

Time-frequency domain joint fault diagnosis method based on vibration signals Download PDF

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CN111783559A
CN111783559A CN202010536722.4A CN202010536722A CN111783559A CN 111783559 A CN111783559 A CN 111783559A CN 202010536722 A CN202010536722 A CN 202010536722A CN 111783559 A CN111783559 A CN 111783559A
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vector
matrix
threshold
data
fault
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李晓
张竹青
张玉华
孟华
田彦彦
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Henan Boteli Intellectual Property Services Co ltd
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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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
    • G01M13/04—Bearings
    • G01M13/045—Acoustic or vibration analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The invention belongs to the field of fault diagnosis methods of rotating machinery, and particularly relates to a time-frequency domain joint fault diagnosis method based on vibration signals, which comprises the steps of firstly, based on the characteristic that sampling of rotating signals has periodicity, representing sampling signals in a period as a multi-dimensional vector, representing sampling signals in a plurality of periods as a data matrix, solving characteristic values of the sampling signals by using an established covariance matrix, and establishing a characteristic value threshold vector for detecting real-time faults; and secondly, transforming the time domain matrix into a frequency domain matrix by utilizing wavelet packet transformation, further rewriting each row vector of the matrix into a matrix form based on certain periodicity, and solving a characteristic value to establish a corresponding threshold vector so as to judge which frequency band the fault occurs in, so that the positioning precision of the fault detection is improved, and more favorable support is provided for maintenance, management and the like of a system.

Description

Time-frequency domain joint fault diagnosis method based on vibration signals
Technical Field
The invention relates to the field of fault diagnosis methods for rotary machines, in particular to a time-frequency domain joint fault diagnosis method based on vibration signals.
Background
In the existing rotary machine fault diagnosis method, the effect is often poor because only the correlation based on one-dimensional vibration signals is utilized.
In the prior art, the most common one-dimensional vibration signal is collected from a rotary mechanical system, and time domain and frequency domain analysis is usually performed by methods such as wavelet transformation, neural network and the like. Wavelet transformation processes only the low-frequency part of a signal, which is unbalanced for frequency domain analysis, and the BP neural network has the defects of slow learning speed, easy falling into local minimum values and the like.
However, the above diagnostic method is still based on the analysis of the one-dimensional signal in the time domain, and only can improve the accuracy of the fault in the time domain. However, after determining the failure, one would want to know which frequency band the failure is carried on. If the method can be realized, the positioning precision of the fault is certainly improved, and a foundation is laid for further system maintenance and health management.
Disclosure of Invention
The invention aims to provide a time-frequency domain joint fault diagnosis method based on vibration signals.
The technical scheme for solving the technical problems is as follows:
a time-frequency domain joint fault diagnosis method based on vibration signals comprises the following steps:
1) the multivariate fault diagnosis method based on the time domain comprises the following steps: measuring vibration signal of rotary mechanical system, amplifying, transmitting and displaying the acquired vibration signal to obtain original vibration signal sequence
X(i)＝[x(i)(1),x(i)(2),L,x(i)(L)]
Set forth below: i is 1,2, L, N, N +1, L, wherein i represents the ith group of data, L represents the length of each group of data, the first N groups are normal data and are used for training a diagnosis threshold value, and the rest groups of data are test data;
2) the sampled signal of the rotating mechanical system in one period is expressed as a vector, as follows: y is(i)＝[x(i)(1)，x(i)(2)，Lx(i)(r)]TWherein r is the number of sampling points in a period;
the sampled signals over a number of cycles can be written in the form of a matrix as follows:
Figure BDA0002537320870000021
wherein, b ═ L/r ], i ═ 1,2, L, N;
order:
Figure BDA0002537320870000022
obtaining a symmetric matrix E(i)And satisfy the characteristic value of
Figure BDA0002537320870000023
Note E(i)The vector of eigenvalues of
Figure BDA0002537320870000024
3) Determination of the threshold vector:
and recording the eigenvalue matrix as D:
Figure BDA0002537320870000031
order to
Figure BDA0002537320870000032
Then there is
Figure BDA0002537320870000033
Selecting
Figure BDA0002537320870000034
The vector of the threshold eigenvalue is obtained from the first N normal data, wherein α is a threshold coefficient used for adjusting the size of the selected threshold;
4) establishing an online fault discriminator:
new obtained data set
Figure BDA0002537320870000035
The feature vector is obtained as in step 3,
Figure BDA0002537320870000036
note also that:
Figure BDA0002537320870000037
and recording a deviation vector:
Figure RE-GDA0002642168250000038
wherein
Figure RE-GDA0002642168250000039
5) By means of the step function concept: order to
Figure BDA00025373208700000310
6) Obtaining a fault discriminator:
Figure BDA0002537320870000041
7) the method is based on a fault diagnosis method on a frequency domain:
the wavelet packet operator matrix is recorded as W ∈ Rr×rAnd (3) carrying out wavelet packet transformation on the matrix form in the step (2) to obtain the following formula:
Figure BDA0002537320870000042
where i is 1,2, L, N, a row vector
Figure BDA0002537320870000043
Is Y(i)Projection on the s-th frequency band;
8) determining wavelet threshold values on each frequency range:
for the matrix obtained in step 7(i)The signal of the s-th frequency band is
Figure BDA0002537320870000044
Will be provided with
Figure BDA0002537320870000045
Rewrite to matrix form as in step 2:
Figure BDA0002537320870000046
the above equation is recorded as the eigenvalue matrix form in step 3, and the eigenvalues are calculated:
Figure BDA0002537320870000051
to obtain
Figure BDA0002537320870000052
Then, there is a matrix of feature values as in step 3:
Figure BDA0002537320870000053
recording:
Figure BDA0002537320870000054
Figure BDA0002537320870000055
selecting a threshold vector:
Figure BDA0002537320870000056
wherein w αsThe threshold coefficient is used for adjusting the size of the selected threshold;
9) and judging the frequency band fault:
when there is new data Y(i)When coming, the feature vector is obtained based on the processes of the steps 7 to 8,
Figure BDA0002537320870000061
note that its deviation vector from the threshold vector is:
Figure BDA0002537320870000062
the same idea with the help of step function as in step 5 is that:
Figure BDA0002537320870000063
the discriminator for obtaining faults in step 6:
Figure BDA0002537320870000064
preferably, the total number L of sample points in step 2 is an integer multiple of r, and if not, the sample points are truncated or subjected to bit-filling processing.
Preferably, the total number b of sample points in step 8 is an integer multiple of l, and if not, the sample points are truncated or subjected to bit-filling processing.
The invention has the beneficial effects that: firstly, based on the characteristic that the sampling of a rotation signal has periodicity, a sampling signal in one period is expressed as a multi-dimensional vector, sampling signals in a plurality of periods are expressed in the form of a data matrix, a characteristic value of the sampling signal is solved by utilizing an established covariance matrix, and a threshold vector of the characteristic value is established for detecting real-time faults, so that whether the faults occur or not is judged in a time domain, a one-dimensional vibration signal is rewritten into the multi-dimensional signal, and whether the faults occur or not is judged by solving the threshold vector and establishing an online fault discriminator;
then, the time domain matrix is converted into a frequency domain matrix by wavelet packet conversion, each row vector of the matrix is further rewritten into a matrix form based on certain periodicity, and characteristic values are obtained again to establish corresponding threshold vectors so as to judge which frequency the fault occurs at, thereby judging the frequency band of the fault occurrence in the frequency domain. The time domain signal is transformed to the frequency domain by wavelet packet transformation, and a fault discriminator is established to discriminate which frequency band the fault occurs in by solving the threshold vector of the frequency band, so that people can know which frequency the fault occurs at, and the problems that the detection and diagnosis method is not good and the maintenance, management and the like of the system are inconvenient because the diagnosis method in the prior art can only know whether the fault exists in the time domain and can not know which frequency band the fault is carried on.
Detailed Description
The following examples are only for illustrating the technical solutions of the present invention more clearly, and therefore are only examples, and the protection scope of the present invention is not limited thereby.
A time-frequency domain joint fault diagnosis method based on vibration signals comprises the following steps:
1) the multivariate fault diagnosis method based on the time domain comprises the following steps: measuring vibration signals of a rotary mechanical system, amplifying, transmitting and displaying the acquired vibration signals, wherein the obtained original vibration signal sequence is as follows:
Figure BDA0002537320870000071
wherein i represents the ith group of data, L represents the length of each group of data, the first N groups of data are normal data for training a diagnostic threshold, and the rest data groups are test data;
2) the sampled signal of the rotating mechanical system in one period is expressed as a vector, as follows: y is(i)＝[x(i)(1)，x(i)(2)，Lx(i)(r)]TWherein r is the number of sampling points in a period;
the sampled signals over a number of cycles can be written in the form of a matrix as follows:
Figure BDA0002537320870000072
wherein, b ═ L/r ], i ═ 1,2, L, N;
order:
Figure BDA0002537320870000081
obtaining a symmetric matrix E(i)And satisfy the characteristic value of
Figure BDA0002537320870000082
Note E(i)The vector of eigenvalues of
Figure BDA0002537320870000083
3) Determination of the threshold vector:
and recording the eigenvalue matrix as D:
Figure BDA0002537320870000084
order to
Figure BDA0002537320870000085
Then there is
Figure BDA0002537320870000086
Selecting
Figure BDA0002537320870000087
The vector of the threshold eigenvalue is obtained from the first N normal data, wherein α is a threshold coefficient used for adjusting the size of the selected threshold;
4) establishing an online fault discriminator:
new obtained data set
Figure BDA0002537320870000091
The feature vector is obtained as in step 3,
Figure BDA0002537320870000092
note also that:
Figure BDA0002537320870000093
and recording a deviation vector:
Figure BDA0002537320870000094
wherein
Figure BDA0002537320870000095
5) By means of the step function concept: order to
Figure BDA0002537320870000096
6) Obtaining a fault discriminator:
Figure BDA0002537320870000097
7) the method is based on a fault diagnosis method on a frequency domain:
the wavelet packet operator matrix is recorded as W ∈ Rr×rAnd (3) carrying out wavelet packet transformation on the matrix form in the step (2) to obtain the following formula:
Figure BDA0002537320870000098
where i is 1,2, L, N, a row vector
Figure BDA0002537320870000099
Is Y(i)Projection on the s-th frequency band;
8) determining wavelet threshold values on each frequency range:
for the matrix obtained in step 7(i)The signal of the s-th frequency band is
Figure BDA0002537320870000101
Will be provided with
Figure BDA0002537320870000102
Rewrite to matrix form as in step 2:
Figure BDA0002537320870000103
the above equation is recorded as the eigenvalue matrix form in step 3, and the eigenvalues are calculated:
Figure BDA0002537320870000104
to obtain
Figure BDA0002537320870000105
Then, there is a matrix of feature values as in step 3:
Figure BDA0002537320870000106
recording:
Figure BDA0002537320870000107
Figure BDA0002537320870000111
selecting a threshold vector:
Figure BDA0002537320870000112
wherein w αsThe threshold coefficient is used for adjusting the size of the selected threshold;
9) and judging the frequency band fault:
when there is new data Y(i)When coming, the feature vector is obtained based on the processes of the steps 7 to 8,
Figure BDA0002537320870000113
note that its deviation vector from the threshold vector is:
Figure BDA0002537320870000114
the same idea with the help of step function as in step 5 is that:
Figure BDA0002537320870000115
the discriminator for obtaining faults in step 6:
Figure BDA0002537320870000116
in the time-frequency domain joint fault diagnosis method based on the vibration signal, when in use, the judgment on the time domain is to judge whether the group data has faults or not, the process is as in the step 2 to the step 6, the judgment on the frequency domain is to judge which frequency band the faults occur in the fault data group, the process is as in the step 7 to the step 9,
firstly, as the process steps 2 to 6, a sampling signal in one period is expressed into a multidimensional vector, sampling signals in a plurality of periods are expressed into a data matrix form, the characteristic value of the sampling signal is obtained by utilizing the established covariance matrix, and a threshold vector of the characteristic value is established for detecting real-time faults, so that whether the faults occur or not is judged in a time domain, a one-dimensional vibration signal is rewritten into the multidimensional signal, and whether the faults occur or not is judged by obtaining the threshold vector and establishing an online fault discriminator;
then, as in the procedure from step 7 to step 9, the time domain matrix is transformed into a frequency domain matrix by wavelet packet transformation, each row vector of the matrix is further rewritten into a matrix form based on a certain periodicity, and the eigenvalue is obtained again to establish a corresponding threshold vector, thereby discriminating the frequency band in which the fault occurs in the frequency domain. Transforming the time domain signal to a frequency domain by utilizing wavelet packet transformation, and establishing a fault discriminator by solving a threshold vector of a frequency band to discriminate which frequency band a fault occurs;
thereby judging the frequency of the fault, improving the positioning precision of the fault detection, providing more favorable support for the maintenance, management and the like of the system,
therefore, people can know which frequency the fault occurs at, and the problems that the diagnosis method in the prior art can only know whether the fault exists in the time domain and cannot know which frequency band the fault is carried on, so that the detection diagnosis method is poor, and the system is inconvenient to maintain, manage and the like are solved.
Further, the total number L of sample points in step 2 is an integer multiple of r, and if not, the sample points are truncated or bit-complemented.
Further, the total number b of sample points in the step 8 is an integral multiple of l, and if not, the sample points are truncated or subjected to bit-filling processing.
Furthermore, the invention can know which frequency the fault occurs in through the method, and can combine deep learning to solve the problem when a plurality of faults are in a plurality of frequency bands.
Further, in order to verify the aforementioned method, a failure needs to be added to the test data. Since the fault on the frequency band is needed, firstly, the fault data group to be added is rewritten into a matrix form, and a wavelet packet matrix is obtained through wavelet packet transformation, namely, different frequency bands are obtained. And adding the fault into different frequency bands, carrying out wavelet packet reconstruction on the fault, and processing the reconstructed data serving as an original signal. Here we choose to add the fault as 0.8 times the maximum deviation of the relevant frequency band in the normal data.
In this embodiment: the simulation adopts data of a bearing data center website of the university of western storage, 76 groups of data are extracted from data with the rotating speed of 1797rpm and the load of 0HP, the first 60 groups are used as training data, and the last 16 groups are used as test data;
the simulation results obtained by performing 18 sets of tests on different data sets with faults added on different frequency bands are shown in tables 1 and 2:
TABLE 1 time domain discrimination results
Fault data set Time domain discrimination result
67 67
61 61
75 75
67 67
61 61
75 75
70 70
72 72
69 69
68 68
67 67
61 61
75 75
70 70
72 72
69 69
68 68
64 None
TABLE 2 frequency domain discrimination results
Frequency band of faults Frequency domain discrimination result
5 5
2 2
5 4 5
2 5 2 5
5 7 5 7
5 7 4 5 7
3 8 3 8
1 8 1 8
2 4 2 4 8
4 7 4 7
1 4 5 1 4 5
1 5 7 1 5 7
2 5 7 2 4 5 7
3 6 8 3 6 8
1 4 8 1 4 8
2 4 8 2 4 8
2 4 7 2 4 7
None None
From the simulation results, the method can not only detect which group of data fails, but also detect the type of the failed frequency band. As in the 17 th test in the table, faults were added to the low, mid and high frequency bands in the 68 th set of data, and the test results were all good. However, the test results of groups 3, 6, 9 and 13 show that the 4 th frequency band has faults all the time, and the faults are false alarms through simulation verification, so the effectiveness of the method is verified through simulation.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; the modifications and the substitutions do not cause the essence of the corresponding technical solutions to depart from the scope of the technical solutions of the embodiments of the present invention, and the corresponding technical solutions are all covered in the claims and the specification of the present invention.

Claims (3)

1. A time-frequency domain joint fault diagnosis method based on vibration signals is characterized by comprising the following steps:
1) the multivariate fault diagnosis method based on the time domain comprises the following steps: measuring vibration signals of a rotary mechanical system, amplifying, transmitting and displaying the acquired vibration signals, wherein the obtained original vibration signal sequence is as follows:
Figure FDA0002537320860000011
wherein i represents the ith group of data, L represents the length of each group of data, the first N groups of data are normal data for training a diagnostic threshold, and the rest data groups are test data;
2) the sampled signal of the rotating mechanical system in one period is expressed as a vector, as follows: y is(i)＝[x(i)(1)，x(i)(2)，Lx(i)(r)]TWherein r is the number of sampling points in a period;
the sampled signals over a number of cycles can be written in the form of a matrix as follows:
Figure FDA0002537320860000012
wherein, b ═ L/r ], i ═ 1,2, L, N;
order:
Figure FDA0002537320860000021
obtaining a symmetric matrix E(i)And satisfy the characteristic value of
Figure FDA0002537320860000022
Note E(i)The vector of eigenvalues of
Figure FDA0002537320860000023
3) Determination of the threshold vector:
and recording the eigenvalue matrix as D:
Figure FDA0002537320860000024
order to
Figure FDA0002537320860000025
Then there is
Figure FDA0002537320860000026
Selecting
Figure FDA0002537320860000027
The vector of the threshold eigenvalue is obtained from the first N normal data, wherein α is a threshold coefficient used for adjusting the size of the selected threshold;
4) establishing an online fault discriminator:
new obtained data set
Figure FDA0002537320860000031
The feature vector is obtained as in step 3,
Figure FDA0002537320860000032
note also that:
Figure FDA0002537320860000033
and recording a deviation vector:
Figure FDA0002537320860000034
wherein
Figure FDA0002537320860000035
5) By means of the step function concept: order to
Figure FDA0002537320860000036
6) Obtaining a fault discriminator:
Figure FDA0002537320860000037
7) the method is based on a fault diagnosis method on a frequency domain:
the wavelet packet operator matrix is recorded as W ∈ Rr×rAnd C, performing wavelet packet transformation on the matrix form in the step 2 to obtain the following formula:
Figure FDA0002537320860000041
where i is 1,2, L, N, a row vector
Figure FDA0002537320860000042
Is Y(i)Projection on the s-th frequency band;
8) determining wavelet threshold values on each frequency range:
for the matrix obtained in step 7(i)S thThe signal of one frequency band is
Figure FDA0002537320860000043
Will be provided with
Figure FDA0002537320860000044
Rewrite to matrix form as in step 2:
Figure FDA0002537320860000045
the above equation is recorded as the eigenvalue matrix form in step 3, and the eigenvalues are calculated:
Figure FDA0002537320860000051
to obtain
Figure FDA0002537320860000052
Then, there is a matrix of feature values as in step 3:
Figure FDA0002537320860000053
recording:
Figure FDA0002537320860000054
Figure FDA0002537320860000055
selecting a threshold vector:
Figure FDA0002537320860000056
wherein w αsThe threshold coefficient is used for adjusting the size of the selected threshold;
9) and judging the frequency band fault:
when there is new data Y(i)When coming, the feature vector is obtained based on the processes of the steps 7 to 8,
Figure FDA0002537320860000061
note that its deviation vector from the threshold vector is:
Figure FDA0002537320860000062
the same idea with the help of step function as in step 5 is that:
Figure FDA0002537320860000063
the discriminator for obtaining faults in step 6:
Figure FDA0002537320860000064
2. the method according to claim 1, wherein the total number L of sample points in step 2 is an integer multiple of r, and if not, the method performs truncation or bit-filling processing on the sample points.
3. The method according to claim 1, wherein the total number b of the sample points in the step 8 is an integer multiple of l, and if not, the total number b of the sample points is truncated or subjected to bit-filling processing.
CN202010536722.4A 2020-06-12 2020-06-12 Time-frequency domain joint fault diagnosis method based on vibration signals Withdrawn CN111783559A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113177537A (en) * 2021-06-29 2021-07-27 湖北博华自动化系统工程有限公司 Fault diagnosis method and system for rotary mechanical equipment

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113177537A (en) * 2021-06-29 2021-07-27 湖北博华自动化系统工程有限公司 Fault diagnosis method and system for rotary mechanical equipment
CN113177537B (en) * 2021-06-29 2021-09-17 湖北博华自动化系统工程有限公司 Fault diagnosis method and system for rotary mechanical equipment

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