CN113607415A - Bearing fault diagnosis method based on short-time stochastic resonance under variable rotating speed - Google Patents

Bearing fault diagnosis method based on short-time stochastic resonance under variable rotating speed Download PDF

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CN113607415A
CN113607415A CN202110712171.7A CN202110712171A CN113607415A CN 113607415 A CN113607415 A CN 113607415A CN 202110712171 A CN202110712171 A CN 202110712171A CN 113607415 A CN113607415 A CN 113607415A
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伏鹏
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Baoji University of Arts and Sciences
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Abstract

The invention discloses a bearing fault diagnosis method based on short-time stochastic resonance under variable rotating speed, which comprises the steps of collecting vibration time domain signals and rotating speed data of a rolling bearing of mechanical equipment to be diagnosed through an acceleration sensor and a rotating speed sensor, decomposing the vibration time domain signals into a plurality of short-time intervals, enabling the rotating speed change among the short-time intervals to be small, calculating four theoretical fault frequencies of each short-time interval according to the collected data, and carrying out stochastic resonance to obtain an output result. And carrying out Fourier transform on the output to obtain a spectrogram of the output, and extracting the frequency at the position with the maximum amplitude as the actual fault frequency. Whether the rolling bearing of the equipment has faults or not and the fault type can be diagnosed by comparing the change curves of the theoretical fault frequency and the search fault frequency relative to the rotating speed and calculating the average absolute error of the change curves. The method has good misdiagnosis preventing effect. The method can distinguish the fault bearing from the healthy bearing, reduces the economic loss caused by unnecessary misdiagnosis, and has high engineering application value.

Description

Bearing fault diagnosis method based on short-time stochastic resonance under variable rotating speed
Technical Field
The invention relates to the technical field of rolling bearing fault detection, in particular to a bearing fault diagnosis method based on short-time stochastic resonance under variable rotating speed.
Background
The rolling bearing mainly comprises an outer ring, an inner ring, a rolling body and a retainer, is a key part of rotary mechanical equipment, and the health state of the rolling bearing influences the performance, stability and life cycle of the whole rotary machine. According to incomplete statistics, in rotating machines using rolling bearings, about 30% of mechanical failures are caused by the bearings. Therefore, the diagnosis of the early fault characteristics of the bearing has great practical significance for avoiding serious faults and ensuring the normal operation of mechanical equipment. However, the characteristics of early failure are weak, and the extraction of the weak characteristics of early failure is very challenging.
In the field of bearing fault diagnosis, a modern signal processing method is used for processing bearing faults, and fault characteristic signals are accurately extracted from noisy signals, so that the fault characteristic signals are one of hot spots of current fault diagnosis. The traditional method for detecting weak characteristic information under a noise background is based on noise suppression and signal decomposition, such as wavelet transformation, empirical mode decomposition, local mean decomposition and the like, and the methods can suppress noise and weaken useful characteristic information to a certain extent.
The stochastic resonance does not adopt a direct noise reduction mode, but the optimal matching among the signal, the nonlinear system and the noise enables the system output to be optimal, and the conversion from noise energy to signal energy is realized, so that weak characteristic information under the noise background is enhanced or identified. Compared with the traditional method, the method strengthens weak characteristics while weakening noise, improves the signal-to-noise ratio and realizes the detection of weak signals. At present, most of rolling bearing fault detection methods adopting the stochastic resonance sampling method aim at the steady working condition that the rotating speed of mechanical equipment is unchanged. However, in the actual engineering environment, mechanical equipment is often under the variable-speed working condition, and the prior stochastic resonance detection method cannot cope with the variable-speed working condition.
Disclosure of Invention
In view of the above existing problems, the present invention aims to provide a bearing fault diagnosis method based on short-time stochastic resonance at a variable rotation speed, which decomposes a bearing fault vibration time-domain signal at the variable rotation speed into a plurality of short-time intervals, so that the rotation speed within each short-time interval does not change much (can be regarded as a fixed value), that is, the theoretical fault frequency of each short-time interval can be approximately calculated according to a bearing theoretical fault frequency calculation formula. And substituting the theoretical fault frequency into a signal-to-noise ratio calculation formula, and taking the formula as an optimization target of the stochastic resonance of each short-time interval to obtain the optimal stochastic resonance output of each short-time interval. And carrying out short-time Fourier transformation on the signals to obtain corresponding frequency spectrograms of the signals, extracting actual fault frequency from the frequency spectrograms, and comparing the actual fault frequency with theoretical fault frequency to judge whether a fault occurs and the fault type.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: a bearing fault diagnosis method based on short-time stochastic resonance under variable rotation speed is characterized by comprising the following steps:
s1, data acquisition: synchronously acquiring vibration time domain signals and rotating speed data of a rolling bearing;
s2, data partitioning: decomposing the vibration time domain signal in the whole acquisition time into M short time intervals according to the time domain, and keeping the rotating speed change in each short time interval consistent;
s3, data calculation: calculating theoretical fault frequency f of the rolling bearing according to the data collected in each short time intervaltWhich comprises the following aspects:
outer ring fault frequency:
Figure BDA0003134172160000021
inner ring failure frequency:
Figure BDA0003134172160000022
frequency of rolling element failure:
Figure BDA0003134172160000023
cage failure frequency:
Figure BDA0003134172160000031
wherein: f is the rotating speed of the input shaft, and the value is based on the first time point between the sampled rotating speed data and the short time zone; z represents the number of bearing rolling elements; d is the diameter of the rolling body; dmThe pitch diameter of the bearing is adopted; alpha is a contact angle; obtaining a curve graph of the change of theoretical fault frequency along with the rotation speed in a complete time domain;
the theoretical fault frequency value ftAnd substituting a signal-to-noise ratio (SNR) calculation formula:
Figure BDA0003134172160000032
in the formula, f is fault characteristic frequency; pS(f) Represents the power at frequency f; pT(f) Representing the local total power; k represents a frequency; f position in the power spectrum; x (k) represents a discrete fourier transform of a time series; j is calculating the local power; pTFinally obtaining an optimized reference value taking the optimal signal-to-noise ratio as the basis for stochastic resonance according to the selected signal length;
s4, self-adaptive stochastic resonance: performing adaptive stochastic resonance on the vibration signal in each short-time interval by taking the reference value as a target after being optimized by a quantum particle group optimization algorithm, and obtaining an optimal output signal in each short-time interval;
s5, data conversion: carrying out short-time Fourier transform on the optimal output signal of each short-time interval to obtain a corresponding spectrogram, extracting the frequency at the highest amplitude as the actual fault frequency, and drawing a curve graph of the actual fault frequency along with the change of the rotating speed;
s6, data comparison: comparing a curve graph of the theoretical fault frequency changing along with the rotating speed with a curve graph of the actual fault frequency changing along with the rotating speed, and calculating an average absolute error MAE;
Figure BDA0003134172160000033
in the formula (f)iIs the theoretical failure frequency; f. ofrIdentifying a failure frequency for the actual; n is the number of the intervals to be calculated, and then whether a fault occurs or not and the fault type are known are judged.
Preferably, the frequency resolution of the spectrogram satisfies
Figure BDA0003134172160000041
Wherein: f. of1For frequency resolution, fsIn order to be able to sample the frequency,
Figure BDA0003134172160000042
for the total number of samples in each short time interval, N is the total number of samplesNumber of samples in time.
Preferably, the mean absolute error value for the occurrence of a fault is identified to be in the range of 0.7-1.5.
The invention has the beneficial effects that: the invention decomposes the vibration signal into a plurality of short time intervals, optimizes the stochastic resonance between each short time interval and extracts the actual fault frequency. By comparing with the theoretical fault frequency, the effective diagnosis of the mechanical fault of the bearing is realized. The method overcomes the problem that the fault frequency of the variable-speed bearing fault vibration signal is difficult to capture under the background of strong noise, amplifies the weak fault information which is submerged by the noise and changes in real time, and has important significance for early fault diagnosis of the rolling bearing under the complex variable working condition.
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Fig. 1 is a flow chart of the unknown fault detection of the rolling bearing of the invention.
FIG. 2 is a time domain waveform and a frequency spectrum diagram of an original vibration signal of a bearing inner ring fault.
FIG. 3 is a graph of the change of the bearing rotation speed with time and a theoretical failure frequency curve obtained by calculation.
Fig. 4 shows 16 of the 300 decomposed original vibration signals in the short time interval (time domain diagram) according to the present invention.
FIG. 5 is a spectrum diagram of 16 short time intervals according to the present invention.
Fig. 6 is a spectrogram of the optimal stochastic resonance output obtained by using SNR calculated from the theoretical outer ring fault frequency as an optimization target in 16 short time intervals according to the invention.
Fig. 7 is a frequency spectrum diagram of the optimal stochastic resonance output obtained by using SNR calculated by the theoretical inner ring fault frequency as an optimization target in 16 short-time intervals according to the invention.
FIG. 8 is a frequency spectrum diagram of the optimal stochastic resonance output obtained by taking SNR calculated by theoretical rolling element fault frequency as an optimization target in 16 short time intervals.
Fig. 9 is a spectrum diagram of the optimal stochastic resonance output obtained by using SNR calculated by the theoretical cage fault frequency as an optimization target in 16 short time intervals according to the invention.
Fig. 10 is a comparison graph of theoretical fault frequency curves and actual identified fault frequency curves corresponding to four types of faults of the inner ring fault bearing.
Fig. 11 is a comparison graph of the Mean Absolute Error (MAE) calculation results corresponding to four types of faults of the inner ring faulty bearing according to the present invention.
Fig. 12 is a comparison graph of theoretical fault frequency curves and actual identified fault frequency curves corresponding to four types of faults for a healthy bearing of the present invention.
FIG. 13 is a comparison graph of the Mean Absolute Error (MAE) calculations for four types of faults for a healthy bearing of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood by those skilled in the art, the technical solutions of the present invention are further described below with reference to the accompanying drawings and the actual failed bearing case.
The invention is further described in detail with reference to the accompanying drawings, which show a bearing fault diagnosis method based on short-time stochastic resonance at variable rotation speed shown in fig. 1-13.
In order to more intuitively explain the steps of the method, a rolling bearing with a failed inner ring is taken as an authentication object for further detailed explanation. And in order to verify the misdiagnosis prevention capability of the method, the healthy bearing is used as a verification object to carry out a fault diagnosis misdiagnosis experiment.
Firstly, a vibration time domain signal of the rolling bearing with the inner ring fault is collected (preferably collected by an acceleration sensor), and as shown in fig. 2(a), a time domain waveform diagram of the fault signal of the inner ring of the bearing is shown. The sampling time was 300 seconds. In order to simulate the actual engineering working conditions, Levy noise with the intensity of 0.5 is added into the vibration signal, and a time domain diagram of the vibration signal containing the noise is shown in fig. 2(b), so that the vibration signal waveform can be found to be completely submerged by the noise and can not be separated.
Meanwhile, a rotating speed sensor is adopted to collect rotating speed data of the fault bearing in real time, and a curve of the rotating speed changing along with time is drawn, as shown in fig. 3 (left). And according to the theoretical failure frequency f of the four types of failures of the bearingtA calculation formula is used for calculating a theoretical fault frequency curve changing along with the rotating speed, and the theoretical fault frequency curve comprises the following aspectsAnd (3) calculating:
outer ring fault frequency:
Figure BDA0003134172160000061
inner ring failure frequency:
Figure BDA0003134172160000062
frequency of rolling element failure:
Figure BDA0003134172160000063
cage failure frequency:
Figure BDA0003134172160000064
wherein: f is the rotating speed of the input shaft, and the value is based on the first time point between the sampled rotating speed data and the short time zone; z represents the number of bearing rolling elements; d is the diameter of the rolling body; dmThe pitch diameter of the bearing is adopted; alpha is a contact angle; and obtaining a curve graph of the theoretical fault frequency changing along with the rotating speed in the complete time domain according to the calculation result.
As shown in fig. 3 (right), (a) is a theoretical inner ring failure frequency curve; (b) a theoretical outer ring fault frequency curve is obtained; (c) a theoretical rolling body fault frequency curve is obtained; (d) is a theoretical cage failure frequency curve.
Preferably, the time domain signal is averagely decomposed into 300 parts, that is, the sampling time of each short time interval is 1 second, and the whole vibration time domain signal is decomposed into a plurality of short time intervals, so that the rotating speed change in each short time interval is not large (can be regarded as a fixed value), and according to the theoretical fault frequency calculation formula, the change range of four theoretical fault frequencies in 1 second is far smaller than the change range of the fault frequency in the whole sampling time and can be regarded as a fixed value. The number of the short-time interval decompositions depends on the speed of the rotation speed change, namely, the short-time interval is larger when the rotation speed change is faster, and the short-time interval is smaller when the rotation speed change is opposite, so that the rotation speed change in each short-time interval is ensured to be small (preferably, the short-time interval decompositions are regarded as constant values). 16 of the short time intervals are selected from 300 short time intervals, and time domain diagrams and frequency spectrum diagrams of the short time intervals are respectively shown in fig. 4 and 5. It can be clearly found that the time domain fault pulse waveform is still buried by noise and can not be identified, and in addition, the fault frequency can not be identified in the spectrogram.
Will theory inner ring fault frequency ftTaking the calculated signal-to-noise ratio (SNR) as an optimization target, obtaining an optimal reference value taking the optimal signal-to-noise ratio as a basis for stochastic resonance, preferably performing self-adaptive stochastic resonance after a quantum particle swarm optimization algorithm to obtain an optimal output signal in each short-time interval, and performing short-time Fourier transform on the optimal output signal to obtain a corresponding spectrogram (as shown in FIG. 6);
wherein, the signal-to-noise ratio (SNR) calculation formula is as follows:
Figure BDA0003134172160000071
in the formula, f is fault characteristic frequency; pS(f) Represents the power at frequency f; pT(f) Representing the local total power; k represents a frequency; f position in the power spectrum; x (k) represents a discrete fourier transform of a time series; j is calculating the local power; pTThe selected signal length.
The signal-to-noise ratio (SNR) based objective function is preferably optimized with a quantum-behaved particle swarm algorithm. FIG. 7 is a graph of the spectrum of the optimal output for stochastic resonance with the signal-to-noise ratio (SNR) calculated for the theoretical outer-ring fault frequency as the optimization target; FIG. 8 is a frequency spectrum diagram of the optimal output obtained by taking the signal-to-noise ratio (SNR) calculated by the theoretical rolling element fault frequency as an optimization target and performing stochastic resonance; FIG. 9 is a graph of the spectrum of the optimal output for stochastic resonance with the signal-to-noise ratio (SNR) calculated for the theoretical cage failure frequency as the optimization target; the frequency resolution of each spectrogram satisfies
Figure BDA0003134172160000081
Wherein: f. of1For frequency resolution, fsIn order to be able to sample the frequency,
Figure BDA0003134172160000082
and N is the number of sampling points in the whole sampling time.
Respectively extracting the frequency with the maximum amplitude near the corresponding theoretical fault frequency in the frequency spectrograms as the actually identified fault frequency (and can be used as the search frequency of four faults, if the fault frequency has an interference frequency with the amplitude close to the amplitude on the frequency spectrograms, obtaining four optimized output results by using a cascade stochastic resonance method for the four output results, wherein the cascade stochastic resonance method is still optimized based on the four signal-to-noise ratio (SNR) target functions and the quantum particle swarm optimization), drawing a curve graph of the actual fault frequency along with the change of the rotating speed, and drawing a comparison graph of the four theoretical fault frequencies obtained by calculation and the change curve of the extracted actual identified fault frequency along with the change of the rotating speed, as shown in fig. 10;
(a) comparing results of inner ring faults; (b) the result is the outer ring fault comparison result; (c) comparing the rolling element faults; (d) comparing the fault of the retainer; the graph can visually show that the coincidence degree of a theoretical fault frequency curve corresponding to the inner ring fault and an actual recognition fault frequency curve is good.
In addition, the fault diagnosis can also be performed by comparing the Mean Absolute Error (MAE) values of the four fault frequencies, and the calculation formula is as follows:
Figure BDA0003134172160000091
in the formula (f)iIs the theoretical failure frequency; f. ofrIdentifying a failure frequency for the actual; n is the number of sections to be calculated, and as shown in fig. 11, the MAE value of the inner ring failure is smaller than the other three and is around 1. In conclusion, the bearing can be judged to have inner ring faults, and the bearing accords with the real situation. And the range value of the average absolute error value of the rolling bearing fault is determined to be 0.7-1.5 according to the detection of different parts of the rolling bearing for many times.
In order to prevent the method from making wrong fault diagnosis results on the healthy bearing, the method is also used for carrying out fault diagnosis on the healthy bearing. A comparison of the resulting theoretical fault frequency curve with the actual identified fault frequency curve is shown in fig. 12. The method can intuitively find that the coincidence degrees of theoretical fault frequency curves corresponding to the four fault types and actual recognition fault frequency curves are poor, and the situation that part of actual fault frequencies cannot be recognized occurs. Fig. 13 shows the MAE calculation results, and it can also be found that the MAEs corresponding to the four faults are much larger than 1. Therefore, the bearing is judged to be not in fault, namely the method has good anti-misdiagnosis effect.
The principle of the invention is as follows: bearing vibration time domain signals collected under the variable rotating speed are decomposed into a plurality of short time intervals, optimal stochastic resonance is respectively applied to enhance fault characteristics, and bearing faults under strong noise interference can be diagnosed. The method overcomes the problem that weak signals are difficult to extract under the background of strong noise and the problem that fault frequency is changed along with the change of the rotating speed in real time, so that the fault frequency is difficult to identify and extract.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made without departing from the spirit and scope of the present invention, which is intended to be covered by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (3)

1. A bearing fault diagnosis method based on short-time stochastic resonance under variable rotation speed is characterized by comprising the following steps:
s1, data acquisition: synchronously acquiring vibration time domain signals and rotating speed data of a rolling bearing;
s2, data partitioning: decomposing the vibration time domain signal in the whole acquisition time into M short time intervals according to the time domain, and keeping the rotating speed change in each short time interval consistent;
s3, data calculation: calculating theoretical fault frequency of the rolling bearing according to the data collected in each short time intervalRate ftWhich comprises the following aspects:
outer ring fault frequency:
Figure FDA0003134172150000011
inner ring failure frequency:
Figure FDA0003134172150000012
frequency of rolling element failure:
Figure FDA0003134172150000013
cage failure frequency:
Figure FDA0003134172150000014
wherein: f is the rotating speed of the input shaft, and the value is based on the first time point between the sampled rotating speed data and the short time zone; z represents the number of bearing rolling elements; d is the diameter of the rolling body; dmThe pitch diameter of the bearing is adopted; alpha is a contact angle; obtaining a curve graph of the change of theoretical fault frequency along with the rotation speed in a complete time domain;
the theoretical fault frequency value ftAnd substituting a signal-to-noise ratio (SNR) calculation formula:
Figure FDA0003134172150000015
in the formula, f is fault characteristic frequency; pS(f) Represents the power at frequency f; pT(f) Representing the local total power; k represents a frequency; f position in the power spectrum; x (k) represents a discrete fourier transform of a time series; j is calculating the local power; pTFinally obtaining an optimized reference value taking the optimal signal-to-noise ratio as the basis for stochastic resonance according to the selected signal length;
s4, self-adaptive stochastic resonance: performing adaptive stochastic resonance on the vibration signal in each short-time interval by taking the reference value as a target after being optimized by a quantum particle group optimization algorithm, and obtaining an optimal output signal in each short-time interval;
s5, data conversion: carrying out short-time Fourier transform on the optimal output signal of each short-time interval to obtain a corresponding spectrogram, extracting the frequency at the highest amplitude as the actual fault frequency, and drawing a curve graph of the actual fault frequency along with the change of the rotating speed;
s6, data comparison: comparing a curve graph of the theoretical fault frequency changing along with the rotating speed with a curve graph of the actual fault frequency changing along with the rotating speed, and calculating an average absolute error MAE;
Figure FDA0003134172150000021
in the formula (f)iIs the theoretical failure frequency; f. ofrIdentifying a failure frequency for the actual; n is the number of the intervals to be calculated, and then whether a fault occurs or not and the fault type are known are judged.
2. The bearing fault diagnosis method based on the short-time stochastic resonance at the variable rotation speed according to claim 1, characterized in that: the frequency resolution of the spectrogram satisfies
Figure FDA0003134172150000022
Wherein: f. of1For frequency resolution, fsIn order to be able to sample the frequency,
Figure FDA0003134172150000023
and N is the number of sampling points in the whole sampling time.
3. The bearing fault diagnosis method based on the short-time stochastic resonance at the variable rotation speed according to claim 2, characterized in that: the mean absolute error value for the occurrence of a fault is assumed to range from 0.7 to 1.5.
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Cited By (5)

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CN114486254A (en) * 2022-02-09 2022-05-13 青岛迈金智能科技股份有限公司 Bicycle bearing detection method based on time/frequency double-domain analysis
CN114563182A (en) * 2022-02-25 2022-05-31 明阳智慧能源集团股份公司 Method, system, medium and equipment for identifying collision and abrasion faults of main shaft bearing of wind turbine generator
CN115931319A (en) * 2022-10-27 2023-04-07 圣名科技(广州)有限责任公司 Fault diagnosis method, fault diagnosis device, electronic equipment and storage medium
CN116434372A (en) * 2023-06-12 2023-07-14 昆明理工大学 Intelligent data acquisition system and working condition identification system for variable working condition equipment
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114486254A (en) * 2022-02-09 2022-05-13 青岛迈金智能科技股份有限公司 Bicycle bearing detection method based on time/frequency double-domain analysis
CN114563182A (en) * 2022-02-25 2022-05-31 明阳智慧能源集团股份公司 Method, system, medium and equipment for identifying collision and abrasion faults of main shaft bearing of wind turbine generator
CN115931319A (en) * 2022-10-27 2023-04-07 圣名科技(广州)有限责任公司 Fault diagnosis method, fault diagnosis device, electronic equipment and storage medium
CN115931319B (en) * 2022-10-27 2023-10-10 圣名科技(广州)有限责任公司 Fault diagnosis method, device, electronic equipment and storage medium
CN116434372A (en) * 2023-06-12 2023-07-14 昆明理工大学 Intelligent data acquisition system and working condition identification system for variable working condition equipment
CN116434372B (en) * 2023-06-12 2023-08-18 昆明理工大学 Intelligent data acquisition system and working condition identification system for variable working condition equipment
CN117574779A (en) * 2024-01-12 2024-02-20 吉林大学 Groundwater monitoring network optimization method for improving quantum particle swarm
CN117574779B (en) * 2024-01-12 2024-03-26 吉林大学 Groundwater monitoring network optimization method for improving quantum particle swarm

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