CN114124038A - Deconvolution enhancement-based rolling bearing acoustic signal weak fault diagnosis method - Google Patents

Deconvolution enhancement-based rolling bearing acoustic signal weak fault diagnosis method Download PDF

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CN114124038A
CN114124038A CN202111331810.1A CN202111331810A CN114124038A CN 114124038 A CN114124038 A CN 114124038A CN 202111331810 A CN202111331810 A CN 202111331810A CN 114124038 A CN114124038 A CN 114124038A
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李宏坤
王树杰
代月帮
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Dalian University of Technology
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H21/00—Adaptive networks
    • H03H21/0012—Digital adaptive filters
    • H03H21/0043—Adaptive algorithms
    • 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
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02—Preprocessing
    • G06F2218/04—Denoising
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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Abstract

The invention belongs to the technical field of fault diagnosis of mechanical equipment and provides a deconvolution enhancement-based weak fault diagnosis method for an acoustic signal of a rolling bearing. The method comprises the following steps: collecting sound signals of a fault bearing during operation through a noise microphone; searching the optimal combination of the filter length and the fault period of the MCKD by using an improved cuckoo parameter optimization algorithm, and performing global optimization and local optimization through Levy flight and random preference migration; the optimized optimal parameter combination is used as a prior parameter of the MCKD, and a filter f is solved by maximizing the correlation kurtosis so as to solve a filtered signal; performing Hilbert envelope demodulation on the filtered signal; and carrying out fault diagnosis according to the fault characteristic frequency in the envelope spectrum. The invention overcomes the uncertainty of artificially selecting the length of the filter and the fault period, realizes the self-adaptive MCKD filtering, and has good noise reduction effect and fault feature extraction capability.

Description

Deconvolution enhancement-based rolling bearing acoustic signal weak fault diagnosis method
Technical Field
The invention belongs to the technical field of fault diagnosis of mechanical equipment, relates to rolling bearing acoustic signal fault feature extraction, and particularly relates to a deconvolution enhancement-based rolling bearing acoustic signal weak fault diagnosis method.
Background
Modern industry is developing rapidly, and mechanical equipment plays a vital role as an important tool for technological progress. The rolling bearing, which is a core component of a rotating machine, usually carries a large load, and when the rolling bearing fails, a mechanical transmission failure is caused, which causes a serious economic loss. Thus, diagnosis and monitoring of rolling bearings may improve safety and reliability of mechanical systems. Currently, monitoring and diagnostic methods are based primarily on vibration signal analysis. However, the vibration sensor is mounted in a contact manner, thereby limiting its use. The sound sensor adopts a non-contact mode, and is convenient to install. The sound signal contains abundant information, and when the mechanical equipment breaks down, the sound signal changes correspondingly.
Aiming at the problem of low signal-to-noise ratio of the sound signal, extracting weak fault information in the signal is a main research direction, and some scholars do related research. The Shenbovin and the like provide an acoustic signal fault feature extraction method based on MCKD and CEEMDAN, wherein the impact in an acoustic signal is enhanced by using an MCKD algorithm, then the kurtosis value of each empirical mode component is calculated, the optimal component is selected, and fault information is extracted. Zhan et al combine VMD and MCKD, and adopt PSO to optimize the parameter combination in VMD and MCKD. And the Liushankun and the like use the Teager energy operator and the MCKD for fault identification of the rolling bearing, firstly, the MCKD is adopted to reduce noise of signals, and then the Teager operator is used for enhancing periodic impact in the signals.
The Maximum Correlation Kurtosis Deconvolution (MCKD) algorithm can effectively extract fault period information in the rolling bearing acoustic signal, however, the MCKD algorithm depends on the selection of the filter length and the prior fault period. Cuckoo Search Algorithm (CSA) is a biological heuristic that simulates the behavior of Cuckoo birds in their eggs in nests of other birds. The CSA has excellent global optimization capability and local optimization capability, but the algorithm is the same as other biological heuristic algorithms, and has the problems of low later-stage optimization accuracy, low iteration speed and easy falling into local optimization. Tsipanitis and the like introduce static and dynamic penalty functions into the algorithm to enhance the CS optimization algorithm, and provide a CS mixing method with dynamic penalty by combining key parameters of a Bird Swarm Algorithm (BSA). The Lirongyu and the like improve the stability and the searching capability of the algorithm by adjusting the flight step length of Levy and introducing dynamic inertia weight and a memory strategy in preference random walk. The NGAs is used for synchronously optimizing the wavelet filter and the MCKD for bearing fault diagnosis, such as Zulong and the like, but the method needs to use the wavelet filter for preprocessing and synchronously optimize four parameters, thereby increasing the complexity and the parameter optimizing difficulty of the method.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a rolling bearing acoustic signal weak fault diagnosis method based on deconvolution enhancement, which overcomes the problems of low iteration speed and low search precision of a cuckoo search algorithm, and has better fault feature extraction effect by utilizing an Improved Cuckoo Search Algorithm (ICSA) to adaptively search the filter length and the fault period of MCKD.
The technical scheme of the invention is as follows:
the method for diagnosing the weak fault of the rolling bearing acoustic signal based on deconvolution enhancement is characterized by comprising the following steps of: the method comprises the following steps:
step 1: collecting a sound signal when a fault bearing operates by using a sound sensor;
step 2: the improved cuckoo parameter optimization algorithm finds the optimal combination of the filter length and the fault period, and the specific process is as follows:
2.1 initializing population parameters: the number n of the nests and the number m of the bird eggs in each nest are determined, because only the influence of the length L of the filter and the fault period T on the MCKD algorithm effect is considered, m is 2, the search interval of L and T is set, and the maximum iteration time T is setmaxObjective function AHSI (nest)i)；
The Adjusted Harmonic Significance Index (AHSI) is taken as a fitness function of the ICSA-MCKD and has the expression:
Figure BDA0003349165930000021
wherein, F (k omega) is the amplitude of the envelope spectrum of the deconvolution signal at k omega, and N (omega) is the average noise in the frequency conversion range around k omega;
2.2 calculating the target value of each nest, finding out the nest with the maximum target value of the current position as the optimal nest Xb；
And 2.3, carrying out Levy flight, updating the position, and keeping the optimal nest still. Calculating the target value AHSI (nest) of each nest under the new positioni) And comparing with the target value of the old position nest, if the target value of the new position nest is larger than the old target value, replacing the old nest, and flying the lavi by the following method:
Figure BDA0003349165930000022
in the formula (I), the compound is shown in the specification,
Figure BDA0003349165930000023
represents the position of the ith bird nest in the t generation; α is the step size;
Figure BDA0003349165930000024
a representative point multiplication operation; l (beta) represents a Levy flight path, and satisfies the following formula:
Figure BDA0003349165930000025
where μ and v follow a standard normal distribution, β ═ 1.5;
Figure BDA0003349165930000026
the step length alpha of the flight of the Levis is as follows:
Figure BDA0003349165930000027
where F is the step size factor, obey [0,1 ]]Uniformly distributed, XbRepresenting a current optimal solution;
the new positions reached by the hybrid flying of formulas (1) to (4) through the lewy flight are:
Figure BDA0003349165930000031
2.4 carry on preference random walk, calculate the goal value of the new nest, if greater than the goal value of the old nest, replace the old nest, preference random walk is specifically as follows:
generating a random number and a discovery probability
Figure BDA0003349165930000032
Comparing when the random number is greater than
Figure BDA0003349165930000033
Representative parasitic eggs were found, with a random walk of preference, creating new nests:
Figure BDA0003349165930000034
Figure BDA0003349165930000035
in which v obeys [0,1 ]]A random factor which is evenly distributed on the surface,
Figure BDA0003349165930000036
and
Figure BDA0003349165930000037
are two random solutions of the t-th generation,
Figure BDA0003349165930000038
is the discovery probability of the t generation, pa0.25, t is the current iteration number, tmaxIs the maximum iteration number;
2.5, selecting an optimal solution, judging whether an iteration stop condition is met, if so, outputting an optimal parameter combination, and if not, returning to the step 2.3 to continue circulation;
and step 3: performing MCKD filtering by using the optimal parameter combination in the step 2 to actually measure the signal xn(N ═ 1, 2.., N) is the source vibration signal sn(N ═ 1, 2.. times.n) is convolved with the transmission path h, and the Maximum Correlation Kurtosis Deconvolution (MCKD) is performed by finding an FIR filter and performing a deconvolution operation to obtain the source signal snApproximate solution y of (N ═ 1, 2.., N)n(n＝1,2,...,N)：
Figure BDA0003349165930000039
In the formula f (f)1,f2...,fL) Is a filter, L is the filter length, and is the convolution operation;
solving for the filter f by maximizing the correlation kurtosis, which is defined as:
Figure BDA00033491659300000310
wherein T is a fault period T ═ fs/fi，fsTo sample frequency, fiIs a fault signature frequency; m is the displacement number, and M is generally selected to be 7.
Solving filter f (f) by maximizing correlation kurtosis1,f2,...,fL)
Figure BDA0003349165930000041
The relative kurtosis is derived for the filter:
Figure BDA0003349165930000042
the coefficients of the filter are obtained from equations (9) to (12), and are expressed in a matrix form:
Figure BDA0003349165930000043
in the formula
Figure BDA0003349165930000044
Figure BDA0003349165930000045
The specific steps of MCKD are as follows:
3.1 initializing parameters such as a fault period T, a filter length L, a displacement number M and the like;
3.2 according to xnCalculating XT,
Figure BDA0003349165930000046
3.3 computing filtered yn，
Figure BDA0003349165930000047
3.4 according to ynCalculating alpha and beta;
3.5 updating the filter f;
3.6 determination of Δ CKM(T) whether the threshold value is smaller than the threshold value or not, if so, ending the iteration, and otherwise, repeating the steps 3.3-3.5.
And 4, step 4: carrying out envelope spectrum analysis on the signal subjected to deconvolution filtering in the step 3;
and 5: fault diagnosis is carried out according to the fault characteristic frequency in the envelope spectrum;
the invention has the beneficial effects that: the optimal combination of the filter length and the fault period of Maximum Correlation Kurtosis Deconvolution (MCKD) is searched by using an Improved Cuckoo Search Algorithm (ICSA), the uncertainty of artificial parameter selection is overcome, the filtering effect of the MCKD is improved, and the fault feature extraction capability is better.
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FIG. 1 is a flow chart of a method for diagnosing weak faults of rolling bearing acoustic signals based on deconvolution enhancement, provided by the invention;
FIG. 2 is a time domain graph and an envelope spectrum of the measured signal, wherein (a) is the time domain graph and (b) is the envelope spectrum of the measured signal after Hilbert envelope demodulation;
FIG. 3 is an optimization iteration graph of ICSA versus optimal combination of filter length and fault period, comparing the optimization with CSA and PSO for the same signal in order to highlight the higher optimization accuracy and iteration speed of ICSA;
FIG. 4 is an envelope spectrum after using the optimal parameter combination of the ICSA output for MCKD filtering;
FIG. 5 is a deconvolution envelope spectrum after adjusting the fault period of the MCKD to a theoretical value;
fig. 6 is a comparison graph of the envelope spectrum of an MED filtered signal at the same filter length.
Detailed Description
The following detailed description of the invention refers to the accompanying drawings.
In this embodiment, a deconvolution enhancement-based rolling bearing acoustic signal weak fault diagnosis method is shown in fig. 1, which is a flowchart of the fault diagnosis method and includes the following steps:
step 1: collecting sound signals of a fault bearing during operation by using a sound sensor:
the test is carried out on a QPZZ-II test platform, the direction of a measuring point is opposite to a bearing seat, the distance between a sound sensor and a tested bearing is 1.5m, the tested bearing has an inner ring fault, the machining mode is linear cutting, the model of the used bearing is NU205EM/PS, and the specific parameters are shown in Table 1. Collecting sound signals by using a PCB noise microphone and an NI9234 acquisition card, setting the sampling frequency to be 12800Hz, the sampling time to be 2 seconds and the rotating speed to be 900r/min, and calculating f according to a theoretical formulai116.25Hz, and T110. The time domain graph and the envelope spectrum of the actually measured signal are shown in fig. 2, the periodic component cannot be seen from the time domain graph of fig. 2(a), only obvious frequency conversion and double frequency conversion can be seen in the envelope spectrum of fig. 2(b), and the fault frequency is submerged by noise, so that the fault information cannot be judged;
TABLE 1 bearing dimensional information
Figure BDA0003349165930000051
Step 2: the improved cuckoo parameter optimization algorithm finds the optimal combination of the filter length and the fault period, and the specific process is as follows:
2.1 initializing ICSA parameters, setting bird nest number n as 15 and maximum iteration number tmaxThe objective function is AHSI (nest) 50i). The search interval for the filter length L is [100,1000]The error between the actual fault frequency and the theoretical fault frequency is generally within 2%, so the search interval of the fault period is [108,113]]；
2.2 calculating the target value of each nest, finding out the nest with the maximum target value of the current position as the optimal nest Xb；
And 2.3, carrying out Levy flight, updating the position, and keeping the optimal nest still. Calculating the target value AHSI (nest) of each nest under the new positioni) And comparing the target value with the target value of the nest at the old position, and replacing the old nest if the target value of the nest at the new position is larger than the old target value;
2.4, carrying out preference random walk, calculating the target value of the new nest, and replacing the old nest if the target value of the new nest is larger than the target value of the old nest;
2.5, selecting an optimal solution, judging whether an iteration stop condition is met, if so, outputting an optimal parameter combination, and if not, returning to the step 2.3 to continue circulation;
in order to verify that ICSA has good searching performance on actual signals, parameter optimization is carried out on the same experimental signals with CSA and PSO. FIG. 3 is an iterative graph of the parameter optimization algorithm, the initialization parameters of CSA and PSO are consistent with the simulation signal, and the search intervals of the filter length L and the fault period T are respectively [100,1000] and [108,113 ]. As can be seen from the figure, ICSA reached the optimal solution at 33 iterations, AHSI value 6.596, CSA reached the optimal solution at 39 iterations, AHSI value 6.482, PSO reached the optimal solution at 47 iterations, and AHSI value 6.41. Therefore, the ICSA has the maximum fitness function value when the iteration times are the minimum, so the ICSA has higher iteration speed and search precision.
And step 3: performing MCKD filtering by using the optimal parameter combination in the step 2 to actually measure the signal xn(N ═ 1, 2.., N) is the source vibration signal sn(N ═ 1, 2.. times.n) is convolved with the transmission path h, and the Maximum Correlation Kurtosis Deconvolution (MCKD) is performed by finding an FIR filter and performing a deconvolution operation to obtain the source signal snApproximate solution y of (N ═ 1, 2.., N)n(n＝1,2,...,N)：
Figure BDA0003349165930000061
In the formula f (f)1,f2...,fL) Is a filter, L is the filter length, and is the convolution operation;
solving filter f (f) by maximizing correlation kurtosis1,f2,...,fL)：
Figure BDA0003349165930000062
The relative kurtosis is derived for the filter:
Figure BDA0003349165930000063
the coefficients of the filter are obtained from equations (9) to (12), and are expressed in a matrix form:
Figure BDA0003349165930000064
in the formula
Figure BDA0003349165930000071
Figure BDA0003349165930000072
The specific steps of MCKD are as follows:
3.1 initializing fault period T as 111.5, filter length L as 622, and displacement M as 7;
3.2 according to xnComputing
Figure BDA0003349165930000073
3.3 computing filtered yn，
Figure BDA0003349165930000074
3.4 according to ynCalculating alpha and beta;
3.5 updating the filter f;
3.6 determination of Δ CKM(T) whether the threshold value is smaller than the threshold value or not, if so, ending the iteration, and otherwise, repeating the steps 3.3-3.5.
And 4, step 4: envelope spectrum analysis is carried out on the signal subjected to deconvolution filtering in the step 3, the envelope spectrum of the MCKD deconvolution signal under the parameter is shown in figure 4, fault characteristic frequency 115.5Hz and frequency multiplication thereof can be obviously seen in the figure, and effectiveness of the invention is proved;
and 5: and fault diagnosis is carried out according to fault characteristic frequency in the envelope spectrum, and the main frequency component 115.5Hz in the signal is determined to be very close to the fault of the inner ring of the rolling bearing and contain high-order frequency multiplication through deconvolution filtering and envelope spectrum analysis of the measured signal, so that the fault of the inner ring of the bearing can be judged.
To verify that the selection of the fault period may affect the deconvolution effect of the MCKD on the actual signal, the fault period in the optimal parameter combination [622,111.5] is now changed to the theoretical fault period 110, and the MCKD deconvolution is performed, where fig. 5 is an envelope spectrum after deconvolution. The higher order multiples of the fault frequency in fig. 5 are heavily disturbed by noise and the amplitude of the overall spectral line is reduced compared to fig. 4. The practical engineering problem is that the actual fault characteristic frequency has a certain error with a theoretical calculation value due to the rotation speed fluctuation and the rolling body slippage, and the fault characteristic is not obvious and the fault diagnosis is difficult due to the theoretical value serving as the prior parameter of the MCKD.
In order to highlight the superiority of MCKD to actual signal processing, the same actual signal is filtered by the MED, for the sake of fairness, the filter length of the MED is 622 equal to the consistent L of MCKD, and the envelope analysis is performed on the signal filtered by the MED as shown in fig. 6, in which although the fault characteristic frequency can be found, the noise interference is serious, as can be seen from comparing fig. 4 and fig. 6, MCKD has better fault characteristic extraction capability.
The invention provides a deconvolution enhancement-based rolling bearing acoustic signal weak fault diagnosis method, and although the measured signal is from a rolling bearing, the person skilled in the art can apply the principle and the method of the invention to fault diagnosis of other objects in the field.

Claims (1)

1. A method for diagnosing weak faults of rolling bearing acoustic signals based on deconvolution enhancement is characterized by comprising the following steps: the method comprises the following steps:
step 1: collecting a sound signal when a fault bearing operates by using a sound sensor;
step 2: the improved cuckoo parameter optimization algorithm finds the optimal combination of the filter length and the fault period, and the specific process is as follows:
2.1 initializing population parameters: the number n of the nests and the number m of the bird eggs in each nest are determined, because only the influence of the length L of the filter and the fault period T on the MCKD algorithm effect is considered, m is 2, the search interval of L and T is set, and the maximum iteration time T is setmaxObjective function AHSI (nest)i)；
And (3) taking the adjusted harmonic significance index as a fitness function of the ICSA-MCKD, wherein the expression is as follows:
Figure FDA0003349165920000011
wherein, F (k omega) is the amplitude of the envelope spectrum of the deconvolution signal at k omega, and N (omega) is the average noise in the frequency conversion range around k omega;
2.2 calculating the target value of each nest, finding out the nest with the maximum target value of the current position as the optimal nest Xb；
2.3, carrying out Laiwei flight, updating the position, and keeping the optimal nest still; calculating the target value AHSI (nest) of each nest under the new positioni) And comparing with the target value of the old position nest, if the target value of the new position nest is larger than the old target value, replacing the old nest, and flying the lavi by the following method:
Figure FDA0003349165920000012
in the formula (I), the compound is shown in the specification,
Figure FDA0003349165920000013
represents the position of the ith bird nest in the t generation; α is the step size;
Figure FDA0003349165920000014
a representative point multiplication operation; l (beta) represents a Levy flight path, and satisfies the following formula:
Figure FDA0003349165920000015
where μ and v follow a standard normal distribution, β ═ 1.5;
Figure FDA0003349165920000016
the step length alpha of the flight of the Levis is as follows:
Figure FDA0003349165920000017
wherein F is a step size factor, obey [0,1 ]]Uniformly distributed, XbRepresenting a current optimal solution;
the new positions reached by the hybrid flying of formulas (1) to (4) through the lewy flight are:
Figure FDA0003349165920000018
2.4 carry on preference random walk, calculate the goal value of the new nest, if greater than the goal value of the old nest, replace the old nest, preference random walk is specifically as follows:
generating a random number and a discovery probability
Figure FDA0003349165920000021
Comparing when the random number is greater than
Figure FDA0003349165920000022
Representative parasitic eggs were found, with a random walk of preference, creating new nests:
Figure FDA0003349165920000023
Figure FDA0003349165920000024
in which v obeys [0,1 ]]A random factor which is evenly distributed on the surface,
Figure FDA0003349165920000025
and
Figure FDA0003349165920000026
are two random solutions of the t-th generation,
Figure FDA0003349165920000027
is the discovery probability of the t generation, pa0.25, t is the current iteration number, tmaxIs the maximum iteration number;
2.5, selecting an optimal solution, judging whether an iteration stop condition is met, if so, outputting an optimal parameter combination, and if not, returning to the step 2.3 to continue circulation;
and step 3: performing MCKD filtering by using the optimal parameter combination in the step 2 to actually measure the signal xnIs a source vibration signal snConvolution with the transmission path h is performed, and deconvolution of the maximum correlation kurtosis is performed by searching an FIR filter and performing deconvolution operation to obtain a source signal snApproximate solution y ofn，n＝1,2,...,N：
Figure FDA0003349165920000028
Wherein f (f)1,f2...,fL) Is a filter, L is the filter length, and is the convolution operation;
solving for the filter f by maximizing the correlation kurtosis, which is defined as:
Figure FDA0003349165920000029
wherein T is a fault period, and T ═ fs/fi，fsTo sample frequency, fiIs a fault signature frequency; m is a displacement number, and M is 7; solving filter f (f) by maximizing correlation kurtosis1,f2,...,fL)
Figure FDA00033491659200000210
The relative kurtosis is derived for the filter:
Figure FDA00033491659200000211
the coefficients of the filter are obtained from equations (9) to (12) and expressed in a matrix form:
Figure FDA00033491659200000212
in the formula
Figure FDA0003349165920000031
Figure FDA0003349165920000032
The specific steps of MCKD are as follows:
3.1 initializing a fault period T, a filter length L and a displacement number M;
3.2 according to xnCalculating XT,
Figure FDA0003349165920000033
3.3 computing filtered yn，
Figure FDA0003349165920000034
3.4 according to ynCalculating alpha and beta;
3.5 updating the filter f;
3.6 determination of Δ CKM(T) whether the value is smaller than a threshold value or not, if so, ending the iteration, and otherwise, repeating the step 3.3-3.5;
and 4, step 4: carrying out envelope spectrum analysis on the signal subjected to deconvolution filtering in the step 3;
and 5: and carrying out fault diagnosis according to the fault characteristic frequency in the envelope spectrum.
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CN114894468B (en) * 2022-04-07 2023-01-03 大连理工大学 Chaos detection-based early weak fault diagnosis method for planetary gear box
CN114894481A (en) * 2022-04-21 2022-08-12 山东大学 Rolling bearing fault diagnosis method and system based on deconvolution algorithm
CN114894481B (en) * 2022-04-21 2023-02-17 山东大学 Rolling bearing fault diagnosis method and system based on deconvolution algorithm
CN115146688A (en) * 2022-09-06 2022-10-04 武昌理工学院 Variable speed rotating machine fault sparse feature extraction method based on time-frequency spectrum optimization
CN115859091B (en) * 2022-11-01 2023-05-26 哈尔滨工业大学 Bearing fault feature extraction method, electronic equipment and storage medium
CN115859091A (en) * 2022-11-01 2023-03-28 哈尔滨工业大学 Bearing fault feature extraction method, electronic device and storage medium
CN116404646A (en) * 2023-06-08 2023-07-07 国网江西省电力有限公司电力科学研究院 Power system scheduling method and system considering standby risk
CN116404646B (en) * 2023-06-08 2023-10-20 国网江西省电力有限公司电力科学研究院 Power system scheduling method and system considering standby risk
CN116520095A (en) * 2023-07-03 2023-08-01 昆明理工大学 Fault location method, system and computer readable storage medium
CN116520095B (en) * 2023-07-03 2023-09-12 昆明理工大学 Fault location method, system and computer readable storage medium
CN117030268A (en) * 2023-10-07 2023-11-10 太原科技大学 Rolling bearing fault diagnosis method
CN117030268B (en) * 2023-10-07 2024-01-23 太原科技大学 Rolling bearing fault diagnosis method

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