CN114330417A - Bearing fault diagnosis method based on SAPSO-MCKD - Google Patents

Abstract

The invention discloses a bearing fault diagnosis method based on SAPSO-MCKD, which comprises the steps of firstly adopting an annealing particle swarm algorithm to adaptively determine an optimal FIR filter of the MCKD, applying the optimal FIR filter to carry out filtering and noise reduction on a bearing fault signal, reducing interference frequency components in the signal and realizing deconvolution on the fault signal. Then, the Teager energy operator is used for demodulating the filtered signals, and finally the extraction and diagnosis of the bearing fault signals can be realized. The research result of the simulation signal verifies the effectiveness of the method, and the analysis result of the bearing data of Kaiser Sichu university also shows that the method can effectively realize the accurate diagnosis of the early fault of the bearing.

Description

Bearing fault diagnosis method based on SAPSO-MCKD

Technical Field

The invention relates to a bearing and a fault diagnosis method, in particular to a maximum correlation kurtosis deconvolution bearing fault diagnosis method improved based on an annealing particle group algorithm, and belongs to the technical field of fault diagnosis.

Background

When failures such as pitting, peeling, cracks and the like occur in the inner and outer rings, the rollers and the cage of the rolling bearing, periodic impacts are generated. In the bearing fault diagnosis, the presence, intensity and frequency of the periodic impact signal represent whether a local fault occurs, the degree of the fault and the fault occurring position. However, in actual operating conditions, the shock signal generated by a bearing failure is often swamped by structural vibrations and a significant amount of background noise. It is difficult to obtain useful information directly from the original signal. And (3) carrying out minimum entropy deconvolution MED, taking the kurtosis maximization of an input signal x as an iteration termination condition, and finding an optimal FIR filter to eliminate the transmission path effect so as to recover the pulse signal related to the fault in the signal. And then envelope demodulation is carried out on the filtered signals, the health state of the bearing is diagnosed, and the method is widely applied to the field of bearing diagnosis. However, the robustness of the conventional MED method is poor, a novel MCKD method is provided by McDonald and the like on the basis of the MED, the correlation kurtosis is defined as a novel evaluation index, and continuous pulses submerged in a vibration signal are extracted by using the periodic characteristic of a fault impact signal. The method is applied to gear fault detection, and a good diagnosis effect is obtained.

In the existing fault diagnosis application, the MCKD is often used as a pre-filter to perform noise reduction processing on an original signal, and is combined with other diagnosis methods to be used as a comprehensive diagnosis method. The Teager energy operator provided by Liushankun and the like is combined with an MCKD filtering method, and a maximum correlation kurtosis deconvolution algorithm is adopted to perform noise reduction processing on an original signal and detect a periodic component in the signal by taking the kurtosis of an envelope spectrum as a target. Lie et al effectively highlights the fault signature using MCKD as a noise reduction prefilter to improve IEWT.

The MCKD algorithm is limited by three parameters of FIR filter length L, fault period T and displacement number M. Aiming at the calculation parameters, the MCKD algorithm is improved by researching the adaptivity of the parameters. Tang et al propose a self-adaptive maximum correlation kurtosis deconvolution method, which utilizes the global optimization capability of the Cuckoo algorithm to perform self-adaptive selection on the length L and the displacement number M of the filter, and obtains good diagnosis effect in the composite fault 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 cycle automatic selection program, which can adaptively select a displacement number M and a fault cycle T, apply the displacement number M and the fault cycle T to bearing fault diagnosis, and 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 an inverse filter using a standard particle swarm optimization algorithm. And (5) performing particle optimization on the FIR filter vector by using the maximum kurtosis as an iteration termination condition to obtain the 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 standard particle swarms are easy to fall into local optimal solutions, and meanwhile, the maximum kurtosis index is greatly influenced by random pulse components in fault signals. The method is inspired, the improved MCKD based on the annealing particle swarm optimization algorithm SAPSO is provided, the PSO is improved by utilizing the snap-through characteristic of the simulated annealing algorithm, the PSO is prevented from falling into a local extreme value, the maximum correlation kurtosis is used as an evaluation index of the filtering effect, the vector f of the filter is optimized, the random pulse signal interference is avoided, and the optimal FIR filter is obtained on the premise that the fault period T is inaccurate. And analyzing the fault characteristics obtained by demodulating the filtered signal envelope to realize the accurate diagnosis of the bearing.

Disclosure of Invention

The invention aims to provide an improved maximum correlation kurtosis deconvolution bearing fault diagnosis method based on an annealing particle swarm algorithm, so as to solve the technical problem of the MCKD method in bearing fault diagnosis.

The innovation points of the technology are mainly as follows:

the MCKD algorithm is improved by utilizing the global optimization characteristic of the particle swarm optimization and the snap-through characteristic of the annealing algorithm, so that the local minimum value is avoided from being trapped while the global optimization is carried out, and the FIR filter corresponding to the maximum correlation kurtosis is ensured to be obtained. The phenomenon of failure in fault feature extraction caused by inaccurate fault period T selection of the MCKD algorithm is improved. Compared with the prior art, the method has the advantages that: the method has simple calculation process and high speed; the existing mature signal processing method and diagnosis technology, such as Wavelet Transform (WT), intrinsic mode decomposition (EMD) and the like, are difficult to extract the bearing fault containing random pulse signals, and the method is a method capable of effectively separating the bearing fault signals containing random pulses; in addition, compared with the traditional MCKD method, when the value of the fault period T is inaccurate, the method has a more obvious effect on extracting the fault characteristics of the bearing. The above is the innovation and the advantages of the method.

In order to achieve the 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 a bearing fault vibration signal, and improving the MCKD algorithm by adopting an annealing particle swarm algorithm, so that a good deconvolution effect can be obtained on the bearing fault signal containing random pulses on the premise of a non-precise period. The method comprises the steps of firstly adopting a particle swarm algorithm improved by an annealing algorithm to adaptively determine an optimal filter of the MCKD, and realizing optimal deconvolution. And then, solving the envelope spectrum of the 3-point symmetric difference energy operator for the filtered fault signal, thereby judging the specific fault information of the bearing.

S1 annealing particle swarm optimization:

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 initializes the velocity and position of all particles,

s1.2, evaluating the fitness of all particles, and storing the positions and the fitness values of the particles in the individual extreme values P of the particles_bestIn (1), all P are_bestThe individual position of the optimum adaptive value and the adaptive value are stored in the global extreme value g_bestIn (1).

S1.3 determines the initial temperature.

S1.4 and determining the current temperature of each particle P according to the following formula_iThe adaptive value of (c):

s1.5 from all P_iDetermining, globally optimal replacementSubstitute value P'_iAnd the position and velocity of each particle are updated according to the following two equations.

x_i,j(t+1)＝x_i,j(t)+v_i,j(t+1),j＝1,2,…,d

S1.6 calculating the particle target value and updating p_bestAnd g_bestAnd then performing annealing operation.

And S1.7, when the algorithm reaches the stop condition, stopping searching and outputting the result, otherwise, returning to S1.4 to continue searching.

S2 maximum correlation kurtosis deconvolution algorithm:

the filtering 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), the target function of the MCKD algorithm is as follows:

in the formula: y is an impact signal, and the calculation formula is as follows:

in the formula: l is the order of the filter, f ═ f₁,f₂,…,f_L]^TAre the coefficients of the filter. M is a displacement number; t is a fault period, and the calculation formula is as follows:

T＝F_s/f_m

in the formula: f. of_mIs the fault characteristic frequency, F_sIs the sampling frequency.

S33 point symmetric difference energy operator

The 3-point symmetric differential energy operator is developed on the basis of the traditional Teager energy operator, effectively solves the problems of the enveloping edge-end flying wing phenomenon generated by Hilbert demodulation and the larger errors of demodulation amplitude and demodulation frequency of the Teager energy operator, and has the following expression:

in the formula: x (n) is a discrete signal

The implementation steps of the S4 SAPSO modified MCKD algorithm are as follows:

s4.1 initializing particle swarm, initializing start-stop temperature T₀，T_lAnd the cooling speed alpha, the annealing is started; randomly generating M populations;

s4.2, updating the optimal position of the particle according to the formula (4), and calculating a fitness value f (x)_i) Finding out the current optimal positions p of all particles_idAnd global optimal position g_id；

S4.3, judging whether the original particle position is replaced by the updated particle 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 positions and the speeds of the particles according to the expressions (7) to (9), and calculating the adaptability f (x) of each particle_i) Update p_idAnd g_id；

S4.5, judging whether the system reaches the termination temperature or not; if so, stopping iteration; if not, the step S4.2 is switched to continue iteration;

s4.6 g at the end of iteration_idI.e. the optimal FIR filter f. It is used for filtering the vibration signal x (t).

S5 implementation steps of the bearing fault diagnosis method based on the SAPSO-MCKD:

s5.1, collecting a bearing fault signal; 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, carrying out SAPSO-MCKD noise reduction filtering on the bearing fault vibration signal;

s5.3, carrying out 3-point symmetric difference energy operator demodulation on the fault signal subjected to noise reduction and filtering;

and S5.4, analyzing the extracted features 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 an improved maximum correlation kurtosis deconvolution bearing fault diagnosis method based on an annealing particle swarm algorithm. The method comprises the steps of firstly, adaptively determining an optimal FIR filter of the MCKD by adopting an annealing particle swarm optimization, 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. Then, the Teager energy operator is used for demodulating the filtered signals, and finally the bearing fault signals can be extracted and diagnosed, so that a set of complete bearing fault diagnosis method is formed.

Drawings

FIG. 1 is a flow chart of a bearing fault diagnosis method based on SAPSO-MCKD in the invention.

FIG. 2 is a simulation diagram of a bearing signal of a random pulse signal in the present invention.

Fig. 3 is a time domain graph and a frequency spectrum graph (a fault period T is 120) after the signal shown in fig. 2 is filtered by applying the method in the present invention.

Fig. 4 is a time domain graph and a frequency spectrum graph (the fault period T is 122) after applying the method of the present invention to the signal shown in fig. 2.

FIG. 5 is a failure experimental signal of a bearing inner race of Kaiser university of Sichu in the present invention.

Fig. 6 is a time domain diagram and a frequency spectrum diagram of the signal shown in fig. 5 after filtering by applying the method of the present invention.

Detailed Description

The invention is further described with reference to the following figures and detailed description.

FIG. 1 is a flow chart of a gearbox composite fault diagnosis method based on inversion editing according to the invention. The principle of the composite fault diagnosis method based on inverted editing and amplitude level grading is described in detail below with reference to a flowchart.

(1) Collecting a bearing fault signal; 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) carrying out SAPSO-MCKD noise reduction filtering on the bearing fault vibration signal;

s2.1 initializing particle swarm, initializing start-stop temperature T₀，T_lAnd the cooling speed alpha, the annealing is started; randomly generating M populations;

s2.2, updating the optimal position of the particle according to the formula (4) and calculating a fitness value f (x)_i) Finding out the current optimal positions p of all particles_idAnd global optimal position g_id；

S2.3, judging whether the original particle position is replaced by the updated particle 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 positions and the speeds of the particles according to the expressions (7) to (9), and calculating the adaptability f (x) of each particle_i) Update p_idAnd g_id；

S2.5, judging whether the system reaches a termination temperature or not; if so, stopping iteration; if not, the step S2.2 is switched to continue iteration;

g at the end of S2.6 iteration_idI.e. the optimal FIR filter f. It is used for filtering the vibration signal x (t).

(3) Carrying out 3-point symmetric difference energy operator demodulation on the fault signal subjected to noise reduction and filtering;

(4) and analyzing the extracted features after envelope demodulation to judge the size and the position of the bearing fault.

FIG. 2 is a diagram of a constructed simulated fault signal, which is formulated as follows:

x(t)＝b(t)+d(t)+h(t)+n(t)

in the formula: periodic pulse signal of resonance frequency b (t)

In the formula: j is the number of pulses; a. the_jIs the amplitude of the jth pulse; f. of_mIs the failure signature frequency; f. of₁Is the resonant frequency; beta is a₁Is an attenuation parameter; tau is_rThe random sliding effect of the scrolling unit is simulated.

Random pulse signal d (t):

in the formula: m₁Is the number of random pulses; d_jRepresenting the amplitude of the simulated jth random pulse; t is t_r(j) Representing the occurrence time of the simulated jth random pulse; decay parameter beta₂Set to 800 Hz; from random pulses f₂The resonance frequency of the excitation was set to 2000 Hz;

discrete harmonic model h (t):

h(t)＝P₁sin(2πh₁t+θ₁)+P₂sin(2πh₂t+θ₂)

in the formula: p₁(P₂)、h₁(h₂)、θ₁(θ₂) The amplitude, frequency and phase of the 1 st (2 nd) harmonic, respectively. Wherein P is₁＝P₂＝0.6,h₁＝40,h₂＝85,

In this case, random pulse M₁Is set to 2; random pulse D_jRandomly selecting from normal distribution N (0.6, 1); the position of the occurrence of the random pulse is determined by a random function in the MATLAB2019b platform. Furthermore, white noise is generated from the normal distribution N (0, 0.15). Model sampling frequency F_sAnd taking 12000Hz, and calculating the fault period T of the model to be 120 according to a fault period calculation formula.

As can be seen from FIG. 2, the periodic pulsesThe impulse 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, and the learning factor c is set to be₁And c₂All set to 1.5, input weight omega_max＝0.9，ω_min0.4, position x_iHas a value range of [ -1, 1 [)]In SAPSO-MCKD, T₀＝200，T_l10, α is 0.9. Setting MCKD displacement M to be 7, respectively carrying out SAPSO-MCKD processing on the simulation signal model when the fault period T is 120 and 122, and obtaining a corresponding optimal FIR filter when a fitness function (maximum correlation kurtosis value) reaches a maximum value after iteration along with the increase of iteration times. Filtering the original signal to obtain a filtered signal as shown in fig. 6, performing 3-point symmetric difference energy calculator envelope demodulation on the filtered signal to obtain an envelope spectrum as shown in fig. 3 and fig. 4, and finding out that the filtering effect robustness of the mcpd algorithm based on the SAPSO is strong, the fault characteristic frequency and the frequency multiplication component thereof in the envelope spectrum are obvious, the filtering effect is not reduced along with the continuous increase of the deviation of the fault period T input in the mcpd algorithm from 120 degrees, the background noise is well suppressed, and the preset fault characteristic frequency and the frequency multiplication thereof can be clearly seen.

FIG. 5 is a bearing fault signal disclosed in the American Case Western Reserve University laboratory, in which a 1.5KW three-phase induction motor is connected to a torque sensor through a self-calibrating coupling, and finally drives a fan to operate. The load of the motor is adjusted 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 an SKF6025-2RS JEM type deep groove ball bearing, a single point fault is processed on the surface of an inner ring by electric spark, the fault size is 0.18mm in diameter, and the depth is 0.28 mm. The shaft frequency was 29.95Hz (1797 rpm). Inner ring fault characteristic frequency f_m＝162.19Hz(5.1452f_r). The vibration signal is acquired by an acceleration sensor, and the sensor is arranged on a bearing seat by a magnetic seat. The sampling frequency is 12000Hz, and the number of sampling points is 8192.

FIG. 6 is a time domain graph and a frequency spectrum of a bearing fault signature signal after processing by a method. It can be seen that the periodic fault impact is clearly greatly enhanced. The envelope spectrum obtained by demodulating the filter signal by the Teager energy operator can find that the characteristic frequency of the inner ring fault is 162.19Hz and the frequency multiplication thereof, the frequency conversion is 29.95Hz and the frequency multiplication thereof, the inner ring fault is clear and visible, and the bearing can be judged to have the inner ring fault at the moment. In conclusion, the method can be used for diagnosing the bearing faults.

Claims (3)

1. A bearing fault diagnosis method based on SAPSO-MCKD is characterized in that: the method comprises the steps of collecting a bearing fault vibration signal, and improving the MCKD algorithm by adopting an annealing particle swarm algorithm, so that a better deconvolution effect can be obtained on the bearing fault signal containing random pulses on the premise of a non-precise period; the method comprises the steps of firstly, adaptively determining an optimal filter of the MCKD by adopting a particle swarm algorithm improved by an annealing algorithm to realize optimal deconvolution; then, solving a Teager energy operator envelope spectrum for the filtered fault signal, thereby judging the specific fault information of the bearing;

s1 annealing particle swarm optimization:

the annealing particle swarm algorithm SAPSO is a particle swarm algorithm improved by the annealing algorithm; the method comprises the following specific steps:

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 initializes the velocity and position of all particles,

s1.2, evaluating the fitness of all particles, and storing the positions and the fitness values of the particles in the individual extreme values P of the particles_bestIn (1), all P are_bestThe individual position of the optimum adaptive value and the adaptive value are stored in the global extreme value g_bestPerforming the following steps;

s1.3, determining an initial temperature;

s1.4 and determining the current temperature of each particle P according to the following formula_iThe adaptive value of (c):

s1.5 from all P_iDetermining a global optimal substitute value P'_iAnd updating the position and the speed of each particle according to the following two formulas;

x_i，j(t+1)＝x_i，j(t)+v_i，j(t+1)，j＝1，2，...，d

in the formula:

s1.6 calculating the particle target value and updating p_bestAnd g_bestThen carrying out annealing operation;

s1.7, when the algorithm reaches the stop condition, stopping searching and outputting the result, otherwise, returning to S1.4 to continue searching;

s2 maximum correlation kurtosis deconvolution algorithm:

the filtering coefficient of the maximum correlation kurtosis deconvolution algorithm MCKD is processed in an iteration mode by maximizing the correlation kurtosis of a filtering signal; for any signal y (n), the MCKD algorithm objective function is:

in the formula: y is an impact signal, and the calculation formula is as follows:

in the formula: l is the order of the filter, f ═ f₁，f₂，...，f_L]^TIs the coefficient of the filter;

m is a displacement number; t is a fault period, and the calculation formula is as follows:

T＝F_s/f_m

in the formula: f. of_mIs the fault characteristic frequency, F_sIs the sampling frequency;

s33 point symmetric difference energy operator

The 3-point symmetric differential energy operator is developed on the basis of the traditional Teager energy operator, effectively solves the problems of the enveloping edge-end flying wing phenomenon generated by Hilbert demodulation and the larger errors of demodulation amplitude and demodulation frequency of the Teager energy operator, and has the following expression:

in the formula: x (n) is a discrete signal

S4 SAPSO improved MCKD algorithm

S5 bearing fault diagnosis based on SAPSO-MCKD.

2. The SAPSO-MCKD-based bearing fault diagnosis method according to claim 1, characterized in that: the implementation steps of S4 are as follows:

s4.1 initializing particle swarm, initializing start-stop temperature T₀，T_lAnd the cooling speed alpha, the annealing is started; randomly generating M populations;

s4.2, updating the optimal position of the particle according to the formula (4), and calculating a fitness value f (x)_i) Finding out the current optimal positions p of all particles_idAnd global optimal position g_id；

S4.3, judging whether the original particle position is replaced by the updated particle 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 positions and the speeds of the particles according to the expressions (7) to (9), and calculating the fitness f (x) of each particle_i) Update p_idAnd g_id；

S4.5, judging whether the system reaches the termination temperature or not; if so, stopping iteration; if not, continuing the iteration;

s4.6 g at the end of iteration_idNamely the optimal FIR filter f; it is used for filtering the vibration signal x (t).

3. The SAPSO-MCKD-based bearing fault diagnosis method according to claim 1, characterized in that: the implementation steps of S5 are as follows:

s5.1, collecting a bearing fault signal; 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, carrying out SAPSO-MCKD noise reduction filtering on the bearing fault vibration signal;

s5.3, carrying out 3-point symmetric difference energy operator demodulation on the fault signal subjected to noise reduction and filtering;

and S5.4, analyzing the extracted features after envelope demodulation to judge the size and the position of the bearing fault.

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