CN114330417B - Bearing fault diagnosis method based on SAPSO-MCKD - Google Patents
Bearing fault diagnosis method based on SAPSO-MCKD Download PDFInfo
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Abstract
The invention discloses a bearing fault diagnosis method based on SAPSO-MCKD, which comprises the steps of adopting an annealing particle swarm algorithm to adaptively determine an optimal FIR filter of MCKD, adopting the optimal FIR filter to filter and reduce noise of bearing fault signals, reducing interference frequency components in the signals, and realizing deconvolution of the fault signals. And then, demodulating the filtered signal by using a Teager energy operator, and finally realizing the extraction and diagnosis of the bearing fault signal. The research result of the simulation signal verifies the effectiveness of the method, and the analysis result of the Kassi Chu Da bearing data also shows that the method can effectively realize the accurate diagnosis of the early failure of the bearing.
Description
Technical Field
The invention relates to a bearing and fault diagnosis method, in particular to a deconvolution bearing fault diagnosis method with maximum correlation kurtosis based on annealing particle swarm algorithm improvement, and belongs to the technical field of fault diagnosis.
Background
When the inner and outer rings, rollers and retainers of the rolling bearing are subjected to faults such as pitting, peeling and cracking, periodic impact is generated. In bearing fault diagnosis, the presence, intensity and frequency of the periodic impact signals represent whether or not a local fault occurs, the degree of the fault and the location of the fault. However, in actual operating conditions, the impact signals generated by bearing failure are often submerged in structural vibrations and significant background noise. It is difficult to obtain useful information directly from the original signal. And (3) deconvoluting the MED by using the minimum entropy value, taking the maximization of the kurtosis of the input signal x as an iteration termination condition, and finding out an optimal FIR filter to eliminate the transmission path effect, thereby recovering the pulse signal related to the fault in the signal. And then carrying out envelope demodulation on the filtered signals to diagnose the health state of the bearing, and the method is widely applied to the bearing diagnosis field. However, the conventional MED method is poor in robustness, mcDonald et al propose a novel method of MCKD on the basis of MED, define the relevant kurtosis as a novel evaluation index, and extract continuous pulses submerged in vibration signals by utilizing the characteristic of periodicity of fault impact numbers. The method is applied to gear fault detection, and good diagnosis effect is obtained.
In the existing fault diagnosis application, MCKD is often used as a pre-filter to perform noise reduction treatment on the original signal, and is combined with other diagnosis methods to be used as a comprehensive diagnosis method. The Teager energy operator as proposed by Liu Shangkun and the like combines MCKD filtering method, adopts a maximum correlation kurtosis deconvolution algorithm, and aims at maximizing the kurtosis of an envelope spectrum to perform noise reduction treatment on an original signal and detect periodic components in the signal. Li Zheng et al use MCKD as a noise reduction pre-filter to improve IEWT, effectively highlighting the fault signature.
The MCKD algorithm is limited by three parameters, namely the FIR filter length L, the fault period T and the number of displacements M. For the calculated parameters, the algorithm MCKD is improved by researching the self-adaption of the parameters. Tang et al propose a self-adaptive maximum correlation kurtosis deconvolution method, utilize the global optimizing capability of the cuckoo algorithm to carry out self-adaptive selection on the length L and the displacement number M of a filter, and obtain good diagnosis effect in the composite faults of the inner ring and the outer ring of the bearing. Miao et al propose an improved maximum correlation kurtosis deconvolution method IMCKD based on a fault period automatic selection program, which can adaptively select the displacement number M and the fault period T, and apply the displacement number M and the fault period T to bearing fault diagnosis to successfully extract fault characteristics.
In addition, heuristic optimization of the filter vector f is also a research hotspot. Cheng et al propose an improved MED algorithm for solving the inverse filter using a standard particle swarm optimization algorithm. And using the maximum kurtosis as an iteration termination condition, and performing particle optimization on the FIR filter vector to obtain an optimal FIR filter vector. The method is applied to bearing fault diagnosis, fault characteristics are successfully extracted, but the method does not consider the defect that a standard particle swarm is easy to fall into a local optimal solution, and meanwhile, the maximum kurtosis index is greatly influenced by random pulse components in fault signals. Inspired by the method, the improvement MCKD of the SAPSO based on the annealing particle swarm optimization algorithm is provided, the PSO is improved by utilizing the kick characteristic of the simulated annealing algorithm, the PSO is prevented from sinking into a local extremum, the maximum correlation kurtosis is used as an evaluation index of the filtering effect, the filter vector f is optimized, the random pulse signal interference is avoided, and the optimal FIR filter is obtained on the premise of inaccurate fault period T. And analyzing fault characteristics obtained by demodulating the envelope of the filtered signals to realize accurate diagnosis of the bearing.
Disclosure of Invention
The invention aims to provide a method for deconvoluting bearing faults based on maximum correlation kurtosis improved by an annealing particle swarm algorithm, so as to solve the technical problems of MCKD method in bearing fault diagnosis.
The innovation points of the technology are mainly as follows:
The global optimizing characteristic of the particle swarm algorithm and the kick characteristic of the annealing algorithm are utilized to improve MCKD algorithm, so that the local minimum is avoided being trapped while global optimizing is performed, and the acquisition of the FIR filter corresponding to the maximum correlation kurtosis is ensured. The phenomenon that the fault characteristic extraction fails due to inaccurate selection of the fault period T in MCKD algorithm is improved. The advantages of this method over the prior art are presented in: the method has simple calculation process and high speed; existing mature signal processing methods and diagnosis technologies, such as Wavelet Transformation (WT), inherent modal decomposition (EMD) and the like, are difficult to extract bearing faults containing random pulse signals, and the method is a method capable of effectively separating bearing fault signals containing random pulses; in addition, compared with the traditional MCKD method, when the fault period T is inaccurate in value, the method has a more obvious effect on extracting the bearing fault characteristics. The method has the innovation point and the advantages.
In order to achieve the above purpose, the technical scheme adopted by the invention is an improved maximum correlation kurtosis deconvolution fault diagnosis method SAPSO-MCKD based on annealing particle swarm optimization, which is characterized in that: the method comprises the steps of collecting bearing fault vibration signals, adopting an annealing particle swarm algorithm to improve MCKD algorithm, and obtaining a good deconvolution effect on the bearing fault signals containing random pulses on the premise of non-precise period. The method comprises the steps of firstly adopting a particle swarm algorithm improved by an annealing algorithm to adaptively determine MCKD an optimal filter, and realizing optimal deconvolution. And then solving the envelope spectrum of the 3-point symmetrical differential energy operator for the filtered fault signal, thereby judging the specific fault information of the bearing.
S1 annealing particle swarm algorithm:
The annealing particle swarm algorithm SAPSO is a particle swarm algorithm modified from the annealing algorithm. The method comprises the following specific steps:
s1.1 randomly initializing the velocities and positions of all particles,
S1.2, evaluating the fitness of all particles, storing the positions and the fitness values of the particles in an individual extremum P best of the particles, and storing the individual positions and the fitness values of the optimal fitness values in all P best in a global extremum g best.
S1.3, determining an initial temperature.
S1.4, and determining the adaptive value of each particle P i at the current temperature according to the following formula:
s1.5 is determined from all P i, the globally optimal surrogate value P' i, and the position and velocity of each particle are updated according to the following two formulas.
xi,j(t+1)＝xi,j(t)+vi,j(t+1)，j＝1，2，...，d
S1.6, calculating a particle target value, updating p best and g best, and then performing a temperature-reducing operation.
S1.7, stopping searching and outputting a result when the algorithm reaches the stopping condition, otherwise returning to S1.4 to continue searching.
S2, maximum correlation kurtosis deconvolution algorithm:
the filter coefficients of the maximum correlation kurtosis deconvolution algorithm MCKD are iteratively processed by maximizing the correlation kurtosis of the filtered signal. For any signal y (n), its MCKD algorithm objective function is:
wherein: y is an impact signal, and the calculation formula is as follows:
Wherein: l is the order of the filter, and f= [ f 1,f2,...,fL]T ] is the coefficient of the filter. M is the displacement number; t is a fault period, and the calculation formula is as follows:
T＝Fs/fm
Wherein: f m is the fault signature frequency and F s is the sampling frequency.
S3 3 point symmetric differential energy operator
The 3-point symmetrical differential energy operator is developed on the basis of the traditional Teager energy operator, so that the problems of the envelope edge end flying wing phenomenon generated by Hilbert demodulation and the larger demodulation amplitude and demodulation frequency error of the Teager energy operator are effectively solved, and the expression is as follows:
Wherein: x (n) is a discrete signal
The implementation steps of the MCKD algorithm of the S4 SAPSO improvement are as follows:
S4.1, initializing a particle swarm, initializing a start-stop temperature T 0,Tl and a cooling speed alpha, and starting annealing; randomly generating M populations;
S4.2, updating the optimal positions of the particles according to the formula (4), calculating a fitness value f (x i), and finding out the current optimal positions p id and the global optimal positions g id of all the particles;
s4.3, judging whether to replace the original particle position with the updated particles according to the formulas (10) and (11), if so, updating the system temperature according to the formula (12); otherwise, the temperature is unchanged;
S4.4, updating the position and the speed of the particles according to formulas (7) to (9), calculating the fitness f (x i) of each particle, and updating p id and g id;
s4.5, judging whether the system reaches the termination temperature; if so, stopping iteration; if not, turning to the step S4.2 to continue iteration;
G id at the end of the S4.6 iteration is the optimal FIR filter f. Which is used for filtering the vibration signal x (t).
S5, realizing steps of a bearing fault diagnosis method based on SAPSO-MCKD:
s5.1, collecting bearing fault signals; measuring a fault bearing experiment table by using an acceleration sensor to obtain a vibration acceleration signal as a signal x (k) to be analyzed;
s5.2, performing SAPSO-MCKD noise reduction filtering on the bearing fault vibration signal;
s5.3, demodulating the fault signal subjected to noise reduction and filtering by using a 3-point symmetrical differential energy operator;
S5.4, analyzing the extracted characteristics after envelope demodulation to judge the size and the position of the bearing fault.
Compared with the prior art, the invention has the following beneficial effects:
The invention provides a maximum correlation kurtosis deconvolution bearing fault diagnosis method based on annealing particle swarm algorithm improvement. The method comprises the steps of self-adaptively determining an optimal FIR filter of MCKD by adopting an annealing particle swarm algorithm, filtering and denoising a bearing fault signal by using the optimal FIR filter, reducing interference frequency components in the signal, and realizing deconvolution of the fault signal. And then, demodulating the filtered signals by using a Teager energy operator, and finally realizing the extraction and diagnosis of bearing fault signals to form a complete bearing fault diagnosis method.
Drawings
FIG. 1 is a flow chart of a fault diagnosis method of a SAPSO-MCKD-based bearing in the present invention.
Fig. 2 is a simulation of the bearing signal of the random pulse signal in the present invention.
Fig. 3 is a time domain diagram and a spectrum diagram (fault period t=120) of the signal shown in fig. 2 after the application method of the present invention.
Fig. 4 is a time domain diagram and a spectrum diagram (fault period t=122) of the signal shown in fig. 2 after the application method of the present invention.
Fig. 5 is a kesixi Chu Da bearing inner race failure experimental signal in the present invention.
Fig. 6 is a time domain plot and a spectral plot of the signal of fig. 5 after filtering by the application method of the present invention.
Detailed Description
The invention is further described below with reference to the drawings and the detailed description.
FIG. 1 is a flow chart of a gear box compound fault diagnosis method based on inversion editing. The principle of the composite fault diagnosis method based on inversion editing and amplitude level grading is described in detail below with reference to the flow chart.
(1) Bearing fault signal acquisition; measuring a fault bearing experiment table by using an acceleration sensor to obtain a vibration acceleration signal as a signal x (k) to be analyzed;
(2) Performing SAPSO-MCKD noise reduction filtering on the bearing fault vibration signal;
S2.1, initializing a particle swarm, initializing a start-stop temperature T 0,Tl and a cooling speed alpha, and starting annealing; randomly generating M populations;
S2.2, updating the optimal positions of the particles according to a formula (4), calculating a fitness value f (x i), and finding out the current optimal positions p id and the global optimal positions g id of all the particles;
s2.3, judging whether to replace the original particle position with the updated particles according to the formulas (10) and (11), if so, updating the system temperature according to the formula (12); otherwise, the temperature is unchanged;
s2.4 updating the position and the speed of the particles according to formulas (7) to (9), calculating the fitness f (x i) of each particle, and updating p id and g id;
s2.5, judging whether the system reaches the termination temperature; if so, stopping iteration; if not, turning to the step S2.2 to continue iteration;
G id at the end of the S2.6 iteration is the optimal FIR filter f. Which is used for filtering the vibration signal x (t).
(3) 3-Point symmetrical differential energy operator demodulation is carried out on the fault signals after noise reduction and filtering;
(4) And analyzing the extracted characteristics after envelope demodulation to judge the size and the position of the bearing fault.
FIG. 2 is a schematic representation of a simulated fault signal, which is formulated as follows:
x(t)＝b(t)+d(t)+h(t)+n(t)
Wherein: periodic pulse signal b (t) of resonant frequency
Wherein: j is the number of pulses; a j is the amplitude of the j-th pulse; f m is the failure characteristic frequency; f 1 is the resonant frequency; beta 1 is the attenuation parameter; τ r simulates the random slip effect of the rolling elements.
Random pulse signal d (t):
Wherein: m 1 is the number of random pulses; d j denotes the amplitude of the analog jth random pulse; t r (j) represents the time of occurrence of the analog jth random pulse; decay parameter beta 2 is set to 800Hz; the resonance frequency excited by the random pulse f 2 is set to 2000Hz;
discrete harmonic model h (t):
h(t)＝P1sin(2πh1t+θ1)+P2sin(2πh2t+θ2)
Wherein: p 1(P2)、h1(h2)、θ1(θ2) are the amplitude, frequency, and phase of the 1 (2) th harmonic, respectively. Wherein P 1＝P2＝0.6,h1＝40,h2 = 85,
In this case, random pulse M 1 is set to 2; random pulse D j is randomly selected from normal distribution N (0.6,1); the location of the random pulse occurrence is determined by a random function in the MATLAB2019b platform. White noise is also generated from the normal distribution N (0,0.15). The model sampling frequency F s is 12000Hz, and the model fault period T is calculated to be 120 according to a fault period calculation formula.
As can be seen from fig. 2, the periodic pulse signal is buried by heavy noise, and the fault-signature information cannot be determined. The simulation signal is analyzed by the method, the iteration number in the SAPSO algorithm is set to be 50, the population scale is set to be 20, the learning factors c 1 and c 2 are set to be 1.5, the input weight omega max＝0.9,ωmin =0.4, the value range of the position x i is [ -1,1], and in the SAPSO-MCKD, T 0＝200,Tl =10, and alpha=0.9. Setting MCKD displacement M as 7, and when the fault period T is 120 and 122, respectively performing SAPSO-MCKD processing on the simulation signal model, and obtaining a corresponding optimal FIR filter by reaching the maximum value after iteration of the fitness function (maximum correlation kurtosis value) along with the increase of iteration times. Filtering the original signal to obtain a filtered signal, performing envelope demodulation on the filtered signal by using a 3-point symmetrical differential energy operator, and obtaining an envelope spectrum, wherein the envelope spectrum is shown in fig. 3 and 4, and the result shows that the filtering effect robustness of the MCKD algorithm based on the SAPSO is strong, the fault characteristic frequency and the frequency doubling component in the envelope spectrum are obvious, the filtering effect is not reduced along with the continuous increase of the deviation 120 degree of the fault period T input in the MCKD algorithm, the background noise is well suppressed, and the preset fault characteristic frequency and the frequency doubling thereof can be clearly seen.
FIG. 5 is a bearing failure signal as disclosed in the University laboratory of U.S. CASE WESTERN RESERVE. In the experimental set-up, a 1.5KW three-phase induction motor was connected to a torque sensor via a self-calibrating coupling, and finally a fan was driven to run. The load of the motor is regulated by the fan. And vertically fixing the vibration acceleration sensor on a shell above an output shaft supporting bearing of the induction motor for data acquisition. The rolling bearing is a SKF6025-2RS JEM type deep groove ball bearing, single-point faults are machined on the surface of the inner ring by electric spark, the fault size is 0.18mm in diameter, and the depth is 0.28mm. The rotation frequency of the shaft was 29.95Hz (1797 rpm). The characteristic frequency of the inner ring fault is f m＝162.19Hz(5.1452fr). The vibration signal is acquired by an acceleration sensor, and the sensor is installed on the bearing seat by a magnetic seat. The sampling frequency was 12000Hz and the sampling point number was 8192.
FIG. 6 is a time-domain plot and a spectral plot of a bearing failure signature after processing using the method. It can be seen that the periodic fault impact is significantly enhanced. The envelope spectrum obtained by demodulating the Teager energy operator of the filtering signal can find out the characteristic frequency 162.19Hz and the frequency multiplication thereof of the inner ring fault, the frequency conversion is 29.95Hz and the frequency multiplication thereof, and the inner ring fault of the bearing can be judged. In conclusion, the method can diagnose bearing faults.
Claims (2)
1. A bearing fault diagnosis method based on SAPSO-MCKD is characterized in that: the method comprises the steps of collecting bearing fault vibration signals, adopting an annealing particle swarm algorithm to improve MCKD algorithm, and obtaining a good deconvolution effect on bearing fault signals containing random pulses on the premise of non-precise period; the method comprises the steps of firstly adopting a particle swarm algorithm improved by an annealing algorithm to adaptively determine MCKD an optimal filter to realize optimal deconvolution; then solving a Teager energy operator envelope spectrum for the filtered fault signal, so as to judge the specific fault information of the bearing;
S1, annealing particle swarm algorithm:
the annealing particle swarm algorithm SAPSO is a particle swarm algorithm improved by the annealing algorithm; the method comprises the following specific steps:
s1.1 randomly initializing the velocities and positions of all particles,
S1.2, evaluating the fitness of all particles, storing the positions and the fitness values of the particles in an individual extremum P best of the particles, and storing the individual positions and the fitness values of the optimal fitness values in all P best in a global extremum g best;
s1.3, determining an initial temperature;
s1.4, determining the adaptive value of each particle P i at the current temperature according to the following formula:
S1.5, determining a globally optimal substitution value P' i from all P i, and updating the position and the speed of each particle according to the following two formulas;
xi,j(t+1)＝xi,j(t)+vi,j×(t+1),j＝1,2,…,d (2)
Wherein:
S1.6, calculating a particle target value, updating p best and g best, and then performing a temperature-reducing operation;
s1.7, stopping searching and outputting a result when the algorithm reaches a stopping condition, otherwise, returning to S1.4 to continue searching;
S2, a maximum correlation kurtosis deconvolution algorithm:
The filter coefficients of the maximum correlation kurtosis deconvolution algorithm MCKD are iteratively processed by maximizing the correlation kurtosis of the filtered signal; for any signal y (n), its MCKD algorithm objective function is:
wherein: y is an impact signal, and the calculation formula is as follows:
wherein: l is the order of the filter, f= [ f 1,f2,…,fL]T ] is the coefficient of the filter; m is the displacement number; t is a fault period, and the calculation formula is as follows:
T＝Fs/fm
Wherein: f m is the fault signature frequency, F s is the sampling frequency;
s3, 3 point symmetry differential energy operators;
the 3-point symmetrical differential energy operator is developed on the basis of the traditional Teager energy operator, so that the problems of the envelope edge end flying wing phenomenon generated by Hilbert demodulation and the larger demodulation amplitude and demodulation frequency error of the Teager energy operator are effectively solved, and the expression is as follows:
wherein: x (n) is a discrete signal;
S4, a MCKD algorithm improved by SAPSO;
s5, bearing fault diagnosis based on the SAPSO-MCKD.
2. The method for diagnosing bearing faults based on SAPSO-MCKD as claimed in claim 1, wherein: the implementation steps of S5 are as follows:
s5.1, collecting bearing fault signals; measuring a fault bearing experiment table by using an acceleration sensor to obtain a vibration acceleration signal as a signal x (k) to be analyzed;
s5.2, performing SAPSO-MCKD noise reduction filtering on the bearing fault vibration signal;
s5.3, demodulating the fault signal subjected to noise reduction and filtering by using a 3-point symmetrical differential energy operator;
S5.4, analyzing the extracted characteristics after envelope demodulation to judge the size and the position of the bearing fault.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| WO2017128455A1 (en) * | 2016-01-25 | 2017-08-03 | 合肥工业大学 | Analogue circuit fault diagnosis method based on generalized multiple kernel learning-support vector machine |
| CN109101936A (en) * | 2018-08-21 | 2018-12-28 | 北京工业大学 | It is a kind of based on adaptive MED Fault Diagnosis of Rolling Element Bearings method |
| CN111896260A (en) * | 2020-08-01 | 2020-11-06 | 华东交通大学 | NGAs synchronous optimization wavelet filter and MCKD bearing fault diagnosis method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| WO2017128455A1 (en) * | 2016-01-25 | 2017-08-03 | 合肥工业大学 | Analogue circuit fault diagnosis method based on generalized multiple kernel learning-support vector machine |
| CN109101936A (en) * | 2018-08-21 | 2018-12-28 | 北京工业大学 | It is a kind of based on adaptive MED Fault Diagnosis of Rolling Element Bearings method |
| CN111896260A (en) * | 2020-08-01 | 2020-11-06 | 华东交通大学 | NGAs synchronous optimization wavelet filter and MCKD bearing fault diagnosis method |
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