CN109740535B - Reciprocating motion signal extraction method based on multi-observer likelihood ratio detection method - Google Patents

Reciprocating motion signal extraction method based on multi-observer likelihood ratio detection method Download PDF

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CN109740535B
CN109740535B CN201910000343.0A CN201910000343A CN109740535B CN 109740535 B CN109740535 B CN 109740535B CN 201910000343 A CN201910000343 A CN 201910000343A CN 109740535 B CN109740535 B CN 109740535B
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reciprocating motion
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柳小勤
伍星
谢俊杰
刘畅
刘韬
蔡正
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Shanghai Huayang Measuring Instruments Co ltd
Kunming University of Science and Technology
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Abstract

The invention discloses a reciprocating motion signal extraction method based on a multi-observer likelihood ratio detection method, and belongs to the technical field of rotating machinery state monitoring. The invention adopts a multi-observer likelihood ratio detection method, does not need to install a key phase device, can find out the signal period consistent with actual reciprocation only by analyzing the test signal, and extracts the reciprocating motion signal. Experiments have been carried out on the industrial robot, and the experiments show that the method has high precision and stability and can accurately detect the reciprocating motion of the robot.

Description

Reciprocating motion signal extraction method based on multi-observer likelihood ratio detection method
Technical Field
The invention relates to a reciprocating motion signal extraction method based on a multi-observer likelihood ratio detection method, and belongs to the technical field of rotating machinery state monitoring.
Background
With the continuous improvement of the industrial automation degree, the joint type industrial robot has very wide application in various fields of automobile and automobile part manufacturing industry, machining industry, electronic and electrical industry and the like. The heart of the industrial robot transmission system is the RV reducer, accounting for over 1/3 of its total cost. As a main rotating member in an industrial robot, reliability gradually decreases and a failure rate increases as a service time increases. The assembly line is interrupted when the robot stops working, and the robot needs to be transferred away from the station when replacing the speed reducer, so that a large amount of time is consumed, and great economic loss is brought to enterprises. Because the robot has a large amplitude movement in the working process and causes structural vibration, the vibration intensity is far greater than the vibration caused by internal faults, and the frequency ranges of the robot and the structural vibration are close to each other, and fault signals are difficult to obtain. Therefore, it is necessary to separate a signal corresponding to the movement of the robot from continuously recorded data in a complete cycle, remove noise corresponding to the standstill, and obtain a signal corresponding to the reciprocating oscillation of the robot, so as to more accurately identify the failure of the robot rotary mechanical system.
Disclosure of Invention
The invention provides a reciprocating motion signal extraction method based on a multi-observer likelihood ratio detection method, which is used for realizing reciprocating motion signal extraction.
The technical scheme of the invention is as follows: a reciprocating motion signal extraction method based on a multi-observer likelihood ratio detection method comprises the following steps:
step1, dividing the test signal into M sub-frames, and dividing one of the M sub-frames into xlThe binary assumption is made for the reciprocating signal or noise:
Figure BDA0001933367820000011
in the formula Sl、N、XlAre respectively signal framing xlDiscrete Fourier transform coefficient vector of contained motion signal, discrete Fourier transform coefficient vector of noise, signal framing xlThe length of each discrete Fourier transform coefficient vector is L, and the (k + 1) th elements in the three coefficient vectors are respectively
Figure BDA0001933367820000012
NkAnd
Figure BDA0001933367820000013
l＝1,2,3...M；k＝0,1,2...L-1；
step2, dividing the signal into frames xlPerforming discrete Fourier transform to obtain XlAnd XlK elements of (a); taking the signal with the lowest energy as noise, carrying out discrete Fourier transform to obtain N,and k elements of N, and calculating the k +1 th element N of NkVariance λ ofN(k)；
Step3, hypothesis
Figure BDA0001933367820000021
Belonging to noise, conditional probability density function thereof
Figure BDA0001933367820000022
Expressed as:
Figure BDA0001933367820000023
suppose that
Figure BDA0001933367820000024
Belonging to reciprocating motion signals, conditional probability density functions thereof
Figure BDA0001933367820000025
Expressed as:
Figure BDA0001933367820000026
will be provided with
Figure BDA0001933367820000027
And
Figure BDA0001933367820000028
for representing
Figure BDA0001933367820000029
Likelihood of (2):
Figure BDA00019333678200000210
in the formula:
Figure BDA00019333678200000211
Figure BDA00019333678200000212
is that
Figure BDA00019333678200000213
The variance of (a) is determined,
Figure BDA00019333678200000214
step4, obtaining the superposition relationship between the noise and the motion signal
Figure BDA00019333678200000215
Is estimated as
Figure BDA00019333678200000216
By using
Figure BDA00019333678200000217
Substitution formula
Figure BDA00019333678200000218
In (1)
Figure BDA00019333678200000219
Obtaining:
Figure BDA00019333678200000220
step5 based on
Figure BDA00019333678200000221
Likelihood ratio of
Figure BDA00019333678200000222
Obtaining signal frames xlGeometric mean of likelihood ratios across frequency bands
Figure BDA00019333678200000223
And defining a discrimination signal frame xlThe rules pertaining to noise or reciprocating signals are:
Figure BDA00019333678200000224
by introducing and framing xlAdjacent 2m subframes { xl-m,...xl,...,xl+mImproving the quality of discrimination to obtain a discrimination function of the multi-observer likelihood ratio detection method comprising a plurality of sub-frames:
Figure BDA00019333678200000225
in the formula: eta is a discrimination threshold value, and l represents the signal framing sequence number currently being analyzed;
step6, substituting the optimal discriminant threshold into the discriminant function
Figure BDA00019333678200000226
Each frame of the signal is classified into a reciprocating motion signal and noise according to a discriminant function, and the frames belonging to the reciprocating motion signal are extracted, i.e., the reciprocating motion signal is extracted from the test signal.
In Step6, the optimal discrimination threshold value obtaining method is as follows:
1) equally dividing the test signal into M sub-frames, wherein one signal sub-frame is xl,l∈[1,...,M]；
2) Calculating the periodicity of the reciprocating motion: for a discrimination threshold η, frame xlBy discriminant function
Figure BDA0001933367820000039
To judge that it belongs to the reciprocating motion signal H1Or noise H0(ii) a If each reciprocation period includes Z sub-frames, if frame xlIs H1Then frame xl+zShould also belong to H1(ii) a The periodicity of the reciprocating motion signal can be defined as:
Figure BDA0001933367820000031
in the formula (I), the compound is shown in the specification,
Figure BDA0001933367820000032
q is of signal H1The number of frames;
3) maximization of calculationSignal-to-noise ratio of the classified reciprocating motion signal to noise: for a discrimination threshold η, the signal-to-noise ratio is defined as the ratio of the power of the reciprocating signal frame to the power of the noise frame:
Figure BDA0001933367820000033
Figure BDA0001933367820000034
in the formula
Figure BDA0001933367820000035
For a set of frame-wise fractions of the reciprocating signal,
Figure BDA0001933367820000036
for a noise framing set, rms represents the root mean square value of the computed signal;
4) combining the periodicity of the reciprocating motion and the signal-to-noise ratio of the reciprocating motion signal and the noise after maximum classification, and defining an optimized objective function of a discrimination threshold as follows:
Figure BDA0001933367820000037
search for optimal discrimination thresholds over a range, i.e.
Figure BDA0001933367820000038
And the eta corresponding to the maximum time is the optimal discrimination threshold.
The invention has the beneficial effects that: the invention adopts a multi-observer likelihood ratio detection method, does not need to install a key phase device, can find out the signal period consistent with actual reciprocation only by analyzing the test signal, and extracts the reciprocating motion signal. Experiments have been carried out on the industrial robot, and the experiments show that the method has high precision and stability and can accurately detect the reciprocating motion of the robot.
Drawings
FIG. 1 is a flow chart of the method steps of the present invention;
FIG. 2 is an example of a test signal for a reciprocating motion of a robot;
FIG. 3 is a relationship and fit curve of an objective function and an optimized objective function for a discrimination threshold;
FIG. 4 is a discriminant function of a measurement signal;
fig. 5 is a graph of experimental reciprocation signals versus noise classification results.
Detailed Description
The invention will be further described with reference to the following figures and examples, without however restricting the scope of the invention thereto.
In the running process of the reciprocating motion equipment, sensors such as vibration, sound and acoustic emission are used for picking up running state signals, and the running state signals are converted into digital signals through data acquisition equipment. The invention distinguishes the reciprocating motion signal and the noise in the test signal through analyzing the test signal to obtain the motion period signal in the signal, thereby laying a foundation for further deep analysis. The reciprocating period is only the noise part + the overlapping part of the noise and the action signal, and the overlapping part of the noise and the action signal is the reciprocating signal
Example 1: as shown in fig. 1 to 5, a reciprocating motion signal extraction method based on the multi-observer likelihood ratio detection method, the present example illustrates the implementation of the present invention with an actual test signal on the welding robot joint of a certain automobile factory:
step1, dividing the test signal into 469 sub-frames with length of 0.0256s, and dividing one signal into x sub-frameslThe binary assumption is made for the reciprocating signal or noise:
Figure BDA0001933367820000041
in the formula Sl、N、XlAre respectively signal framing xlDiscrete Fourier transform coefficient vector of motion signal, discrete Fourier transform coefficient vector of noise, and signal frame xlThe length of each discrete Fourier transform coefficient vector is L, and the (k + 1) th elements in the three coefficient vectors are respectively
Figure BDA0001933367820000042
NkAnd
Figure BDA0001933367820000043
1,2,3.. 469; l-1, 0,1, 2; the test signal is shown in fig. 2 (time (seconds) on the abscissa and amplitude (mv) on the ordinate).
Step2, dividing the signal into frames xlPerforming discrete Fourier transform to obtain XlAnd XlK elements of (a); taking the signal frame with the lowest energy as noise, carrying out discrete Fourier transform on the signal frame to obtain N and k elements of the N, and calculating the k +1 th element N of the NkVariance λ ofN(k)；
Step3, hypothesis
Figure BDA0001933367820000044
Belonging to noise, conditional probability density function thereof
Figure BDA0001933367820000045
Expressed as:
Figure BDA0001933367820000046
suppose that
Figure BDA0001933367820000047
Belonging to reciprocating motion signals, conditional probability density functions thereof
Figure BDA0001933367820000048
Expressed as:
Figure BDA0001933367820000049
will be provided with
Figure BDA00019333678200000410
And
Figure BDA00019333678200000411
for representing
Figure BDA00019333678200000412
Likelihood of (2):
Figure BDA00019333678200000413
in the formula:
Figure BDA00019333678200000414
Figure BDA00019333678200000415
is that
Figure BDA00019333678200000416
The variance of (a) is determined,
Figure BDA00019333678200000417
step4, obtaining the superposition relationship between the noise and the motion signal
Figure BDA00019333678200000418
Is estimated as
Figure BDA00019333678200000419
By using
Figure BDA00019333678200000420
Substitution formula
Figure BDA00019333678200000421
In (1)
Figure BDA00019333678200000422
Obtaining:
Figure BDA0001933367820000051
obtained in step2
Figure BDA0001933367820000052
Substitution into
Figure BDA00019333678200000518
Can obtain
Figure BDA0001933367820000053
Step5 based on
Figure BDA0001933367820000054
Likelihood ratio of
Figure BDA0001933367820000055
Obtaining signal frames xlGeometric mean of likelihood ratios in the 0 to L-1 frequency bands
Figure BDA0001933367820000056
And defines the frame x of the discrimination signallThe rules pertaining to noise or reciprocating signals are:
Figure BDA0001933367820000057
by introducing and framing xlAdjacent 2m subframes { xl-m,...xl,...,xl+mImproving the quality of discrimination to obtain a discrimination function of the multi-observer likelihood ratio detection method comprising a plurality of sub-frames:
Figure BDA0001933367820000058
in the formula: eta is a discrimination threshold value, and l represents the signal framing sequence number currently being analyzed;
step6, obtaining an optimal discrimination threshold value:
1) equally dividing the test signal into M sub-frames, wherein one signal sub-frame is xl,l∈[1,...,M]；
2) Calculating the periodicity of the reciprocating motion: for a discrimination threshold η, frame xlBy discriminant function
Figure BDA00019333678200000519
To judge that it belongs to the reciprocating motion signal H1Or noise H0(ii) a If each reciprocation period includes Z sub-frames, if frame xlIs H1Then frame xl+ZShould also belong to H1(ii) a The periodicity of the reciprocating motion signal can be defined as:
Figure BDA0001933367820000059
in the formula (I), the compound is shown in the specification,
Figure BDA00019333678200000510
q is of signal H1The number of frames;
3) calculating the signal-to-noise ratio of the reciprocating motion signal and the noise after maximum classification: for a discrimination threshold η, the signal-to-noise ratio is defined as the ratio of the power of the reciprocating signal frame to the power of the noise frame:
Figure BDA00019333678200000511
Figure BDA00019333678200000512
in the formula
Figure BDA00019333678200000513
For a set of frame-wise fractions of the reciprocating signal,
Figure BDA00019333678200000514
for a noise framing set, rms represents the root mean square value of the computed signal;
4) combining the periodicity of the reciprocating motion and the signal-to-noise ratio of the reciprocating motion signal and the noise after maximum classification, and defining an optimized objective function of a discrimination threshold as follows:
Figure BDA00019333678200000515
setting the search range of the discriminant threshold (1 ≦ eta ≦ 14) as the bottom portion of the discriminant function, calculating the target function
Figure BDA00019333678200000516
And (3) performing 4-order curve fitting on the data, and finding out a value corresponding to the highest point on a fitting curve, namely 3.3 serving as an optimal discrimination threshold eta. The results are shown in FIG. 3, where the discontinuities are the correspondences calculated for different values of η
Figure BDA00019333678200000517
The continuous curve is a fourth order polynomial fitted curve of the discontinuity point.
The discrimination threshold η is substituted into Step5 by 3.3 to obtain a discrimination function
Figure BDA00019333678200000520
Obtaining the final discriminant function
Figure BDA0001933367820000061
The calculated discriminant function is shown in fig. 4.
The discriminant function is substituted into the test signal, and each frame of the test signal is classified into a noise or a reciprocating signal, as shown in fig. 5, a dotted line indicates a classification result, corresponding to the right coordinate axis, 0 is a noise, and 1 is a portion where the noise overlaps with the motion signal, i.e., the reciprocating signal. The solid line represents the test signal. It can be seen that the higher intensity motion signals can be separated from the noise.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.

Claims (2)

1. A reciprocating motion signal extraction method based on a multi-observer likelihood ratio detection method is characterized by comprising the following steps: the method comprises the following steps:
step1, dividing the test signal into M sub-frames, and dividing one of the M sub-frames into xlThe binary assumption is made for the reciprocating signal or noise:
Figure FDA0001933367810000011
in the formula Sl、N、XlAre respectively signal framing xlDiscrete Fourier transform coefficient vector of motion signal, discrete Fourier transform coefficient vector of noise, and signal frame xlDiscrete Fourier ofThe transform coefficient vectors are all L in length, and the k +1 th elements in the three coefficient vectors are respectively
Figure FDA0001933367810000012
NkAnd
Figure FDA0001933367810000013
l＝1,2,3...M；k＝0,1,2...L-1；
step2, dividing the signal into frames xlPerforming discrete Fourier transform to obtain XlAnd XlK elements of (a); taking the signal frame with the lowest energy as noise, carrying out discrete Fourier transform on the signal frame to obtain N and k elements of the N, and calculating the k +1 th element N of the NkVariance λ ofN(k)；
Step3, hypothesis
Figure FDA0001933367810000014
Belonging to noise, conditional probability density function thereof
Figure FDA0001933367810000015
Expressed as:
Figure FDA0001933367810000016
suppose that
Figure FDA0001933367810000017
Belonging to reciprocating motion signals, conditional probability density functions thereof
Figure FDA0001933367810000018
Expressed as:
Figure FDA0001933367810000019
will be provided with
Figure FDA00019333678100000110
And
Figure FDA00019333678100000111
for representing
Figure FDA00019333678100000112
Likelihood of (2):
Figure FDA00019333678100000113
in the formula:
Figure FDA00019333678100000114
Figure FDA00019333678100000115
is that
Figure FDA00019333678100000116
The variance of (a) is determined,
Figure FDA00019333678100000117
step4, obtaining the superposition relationship between the noise and the motion signal
Figure FDA00019333678100000118
Is estimated as
Figure FDA00019333678100000119
By using
Figure FDA00019333678100000120
Substitution formula
Figure FDA00019333678100000121
In (1)
Figure FDA00019333678100000122
Obtaining:
Figure FDA0001933367810000021
step5 based on
Figure FDA0001933367810000022
Likelihood ratio of
Figure FDA0001933367810000023
Obtaining signal frames xlGeometric mean of likelihood ratios across frequency bands
Figure FDA0001933367810000024
And defines the frame x of the discrimination signallThe rules pertaining to noise or reciprocating signals are:
Figure FDA0001933367810000025
by introducing and framing xlAdjacent 2m subframes { xl-m,...xl,...,xl+mImproving the quality of discrimination to obtain a discrimination function of the multi-observer likelihood ratio detection method comprising a plurality of sub-frames:
Figure FDA0001933367810000026
in the formula: eta is a discrimination threshold value, and l represents the signal framing sequence number currently being analyzed;
step6, substituting the optimal discriminant threshold into the discriminant function
Figure FDA00019333678100000216
Each frame of the signal is classified into a reciprocating signal and noise according to a discriminant function, and the frames belonging to the reciprocating signal are extracted, i.e., the reciprocating signal is extracted from the test signal.
2. The method of extracting a reciprocating motion signal based on the multi-observer likelihood ratio detection method according to claim 1, characterized in that: in Step6, the optimal discrimination threshold value obtaining method is as follows:
1) equally dividing the test signal into M sub-frames, wherein one signal sub-frame is xl,l∈[1,...,M]；
2) Calculating the periodicity of the reciprocating motion: for a discrimination threshold η, frame xlBy discriminant function
Figure FDA00019333678100000215
To judge that it belongs to the reciprocating motion signal H1Or noise H0(ii) a If each reciprocation period includes Z sub-frames, if frame xlIs H1Then frame xl+zShould also belong to H1(ii) a The periodicity of the reciprocating motion signal can be defined as:
Figure FDA0001933367810000027
in the formula (I), the compound is shown in the specification,
Figure FDA0001933367810000028
q is of signal H1The number of frames;
3) calculating the signal-to-noise ratio of the reciprocating motion signal and the noise after maximum classification: for a discrimination threshold η, the signal-to-noise ratio is defined as the ratio of the power of the reciprocating signal frame to the power of the noise frame:
Figure FDA0001933367810000029
Figure FDA00019333678100000210
in the formula
Figure FDA00019333678100000211
For a set of frame-wise fractions of the reciprocating signal,
Figure FDA00019333678100000212
for noise framing, rms represents the mean square of the computed signalA root value;
4) combining the periodicity of the reciprocating motion and the signal-to-noise ratio of the reciprocating motion signal and the noise after maximum classification, and defining an optimized objective function of a discrimination threshold as follows:
Figure FDA00019333678100000213
search for optimal discrimination thresholds over a range, i.e.
Figure FDA00019333678100000214
And the eta corresponding to the maximum time is the optimal discrimination threshold.
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