Rolling bearing fault diagnosis method based on novel asymmetric multistable coupling stochastic resonance

Abstract

The invention provides a rolling bearing fault diagnosis method based on novel asymmetric multistable coupling stochastic resonance. The rolling bearing fault diagnosis method comprises the following steps: establishing a novel asymmetric multistable situation function model; establishing a novel asymmetric multistable situation coupling function model; forming a novel linear coupling asymmetric multistable stochastic resonance model by two independent asymmetric multistable systems in a linear coupling mode; signal acquisition and signal preprocessing; calculating the fault characteristic frequency of the rolling bearing; stochastic resonance calculation based on novel asymmetric coupling multistable states; and comparing the output result with the actual fault characteristic frequency. According to the rolling bearing fault diagnosis method based on novel asymmetric multistable coupling stochastic resonance provided by the invention, the problems that potential function symmetry is difficult to maintain in an actual physical model and mutual coupling influence of all parts of equipment is difficult to detect by a single system in an actual working condition are effectively solved; and the fault characteristic frequency can be better highlighted.

Description

Technical Field

[0001] The present invention relates to the field of rolling bearing weak fault feature diagnosis, and in particular to a rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupling random resonance. Background Art

[0002] Vibration signal analysis is an easy-to-implement and reliable method widely used in mechanical equipment fault diagnosis. In mechanical equipment, each moving part has a specific natural vibration frequency. Sensors installed on the equipment collect the vibration signals of the equipment during operation. Analyzing these signals can determine whether the mechanical equipment has a fault and then identify the type of fault.

[0003] However, traditional methods treat noise as "waste". The essence of the method is to deal with noise, which will inevitably process signals that are beneficial to us. In this technology, a random resonance method is proposed. The essence of this method is to use noise to convert the energy of noise into the energy of characteristic signals, so as to extract the fault characteristic frequency and determine the fault characteristic type. In actual working conditions, due to the mutual influence of various equipment components during the operation of mechanical equipment, there are problems such as difficult fault diagnosis and difficult fault feature extraction when conducting fault diagnosis.

[0004] Therefore, it is necessary to provide a rolling bearing fault diagnosis method based on a new asymmetric multi-stable coupled stochastic resonance to solve the above technical problems. Summary of the Invention

[0005] The present invention provides a rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance, which solves the saturation problem of the classical bistable stochastic resonance model and the problem of being unable to detect the characteristic frequency of large parameters of rotating machinery.

[0006] To solve the above technical problems, the present invention provides a rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance, comprising:

[0007] S1. Establish a new asymmetric multi-stable state function model: solve the steady-state solution curve, analyze the dynamic response and build the model;

[0008] S2. Establish a new asymmetric multistable state coupling function model: Two independent asymmetric multistable systems are linearly coupled to form a new linearly coupled asymmetric multistable stochastic resonance model;

[0009] S3, signal acquisition and signal preprocessing: signal acquisition and signal preprocessing;

[0010] S4. Calculation of characteristic frequency of rolling bearing faults;

[0011] S5. Stochastic resonance calculation based on novel asymmetric coupled multistability;

[0012] S6. Compare the output results with the actual fault characteristic frequency.

[0013] Preferably, the function expression corresponding to the novel asymmetric multi-stable state function model in S1 is:

[0014]

[0015] Where a, b, c and r are the system parameters of the potential function, is the asymmetric term of the potential function.

[0016] Preferably, the S3 includes adopting a common variable scaling method to collect large parameter signals to meet the small parameter requirements of stochastic resonance.

[0017] Preferably, the step S4 includes using an existing formula to calculate theoretical fault characteristic frequencies of outer rings, inner rings, and rolling elements of different bearings according to different bearing sizes.

[0018] Preferably, the steady-state solution curve of the asymmetric multistable system is solved in S1, the dynamic response of the system is analyzed based on the steady-state solution curve, and the two are combined to analyze the process of the asymmetric multistable system realizing particle transition, and then a new symmetric multistable potential function model is established.

[0019] Preferably, the novel asymmetric multistable state coupling function model is established in S2, and two independent asymmetric multistable systems are linearly coupled to form a novel linearly coupled asymmetric multistable stochastic resonance model, and the Langevin equation is described as follows:

[0020]

[0021] Where a, a1, b, b1, c, c1, r, r1 are the adjustable system parameters of two independent asymmetric multistable systems, k is the coupling coefficient, -ax+(1+a) / bx 3 -cx 5 +rx 2 is the controlled system, and the control system is -a1y+(1+a1) / b1y 3 -c1y 5 +r1y 2 , and their corresponding output variables are x and y respectively.

[0022] Preferably, the signal preprocessing in S3 is performed by combining the ordinary variable scaling method with the novel asymmetric multi-stable state function model, which can be expressed as:

[0023]

[0024] Where a, b, c, mA and f are all large parameters, forming a large-parameter multistable general variable-scale stochastic resonance model.

[0025] Preferably, the stochastic resonance calculation of S5 is based on a novel asymmetric coupled multistable state; the stochastic resonance calculation of the Langevin equation of the novel asymmetric multistable state is solved by a fourth-order Runge-Kutta algorithm, and its discrete formula is as follows:

[0026]

[0027] Where: n = 1, 2, ..., N, z is the input signal, h is the Runge-Kutta calculation step size, a, b, c and r are system parameters, and x is the system output.

[0028] Preferably, the output result in S6 is compared with the actual fault characteristic frequency, and the output result obtained by random resonance calculation is Fourier transformed to obtain a frequency domain result. The identified fault characteristic frequency is compared with the theoretical fault characteristic frequency calculated previously to determine whether the rolling bearing has a fault and the type of fault. If the identified fault characteristic frequency is close to the theoretical fault characteristic frequency and is within the allowable error range, it can be determined that the bearing has a corresponding fault. If the difference between the two is large, it is necessary to further check the signal processing process or re-analyze and calculate.

[0029] Compared with related technologies, the present invention provides a new type of asymmetric multi-stable coupled stochastic resonance rolling bearing fault diagnosis method with the following beneficial effects:

[0030] The present invention provides a rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance method. Compared with the difficulty in maintaining the symmetry of the potential function in actual physical models and the difficulty in detecting the mutual coupling effects of various equipment components by a single system in actual working conditions, this method effectively solves the above problems, can better highlight the fault characteristic frequency, improve the signal-to-noise ratio, and reduce the sideband interference near the fault characteristic frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A schematic structural diagram of a preferred embodiment of a rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance method provided by the present invention;

[0032] Figure 2 Schematic diagram of the graphical method for solving the equations of the asymmetric multistable system;

[0033] Figure 3 The system output signal is a dynamic response map of the multistable system equation;

[0034] Figure 4 It is the steady-state solution curve of the dynamic response mapping diagram of the multi-stable system equation;

[0035] Figure 5 It is the time domain and frequency domain diagram of the simulated sin signal;

[0036] Figure 6 The time domain and frequency domain diagrams of the outer ring experimental signal of the Case Western Reserve University laboratory;

[0037] Figure 7 6205-2RSJEM SKF bearing parameters;

[0038] Figure 8 The time domain and frequency domain diagrams of the outer ring experimental signal of the self-built platform laboratory;

[0039] Figure 9 The time domain and frequency domain diagrams of the inner circle experimental signal of the self-built platform laboratory are obtained using this method;

[0040] Figure 10 Schematic diagram of fault feature identification error. DETAILED DESCRIPTION

[0041] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0042] Please refer to Figure 1 、 Figure 2 、 Figure 3 、 Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 、 Figure 8 、 Figure 9 and Figure 10 ,in, Figure 1 A schematic structural diagram of a preferred embodiment of a rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance method provided by the present invention; Figure 2 Schematic diagram of the graphical method for solving the equations of the asymmetric multistable system; Figure 3 The system output signal is a dynamic response map of the multistable system equation; Figure 4 It is the steady-state solution curve of the dynamic response mapping diagram of the multi-stable system equation; Figure 5 It is the time domain and frequency domain diagram of the simulated sin signal; Figure 6 The time domain and frequency domain diagrams of the outer ring experimental signal of the Case Western Reserve University laboratory; Figure 7 6205-2RSJEM SKF bearing parameters; Figure 8 The time domain and frequency domain diagrams of the outer ring experimental signal of the self-built platform laboratory; Figure 9 The time domain and frequency domain diagrams of the inner circle experimental signal of the self-built platform laboratory are obtained using this method; Figure 10 A rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance method includes:

[0043] S1. Establish a new asymmetric multi-stable state function model: solve the steady-state solution curve, analyze the dynamic response and build the model;

[0044] S2. Establish a new asymmetric multistable state coupling function model: Two independent asymmetric multistable systems are linearly coupled to form a new linearly coupled asymmetric multistable stochastic resonance model;

[0045] S3, signal acquisition and signal preprocessing: signal acquisition and signal preprocessing;

[0046] S4. Calculation of characteristic frequency of rolling bearing faults;

[0047] S5. Stochastic resonance calculation based on a novel asymmetric coupled multistability;

[0048] S6. Compare the output results with the actual fault characteristic frequency.

[0049] Please refer to Figure 1 It is known that S1 inputs the collected vibration signal and Gaussian white noise into the new asymmetric multistable coupling system.

[0050] S2. Let the input signal undergo Hilbert transform, because the spectrum of the signal after Hilbert transform analysis has only positive frequency bands, and the amplitude is twice the original.

[0051] S3. The signal modulated by the Hilbert transform is passed through a high-pass filter. Before processing the fault signal, a mathematical formula is used to calculate the theoretical location of the fault. The high-pass filter can filter out interference signals before the theoretically calculated fault point to avoid interference.

[0052] S4. Select the variable scale parameter and scale parameter. Check whether the system output meets the stochastic resonance theory and whether the fault location is found.

[0053] S5. Spectrum analysis: Perform Fourier transform on the output time series results to obtain frequency domain results. Compare the identified fault characteristic frequency with the theoretical fault characteristic frequency to determine whether a fault has occurred.

[0054] The function expression corresponding to the novel asymmetric multistable state function model in S1 is:

[0055]

[0056] Where a, b, c and r are the system parameters of the potential function, is the asymmetric term of the potential function.

[0057] The S3 includes adopting a common variable scale method to collect large parameter signals to meet the small parameter requirements of stochastic resonance.

[0058] The S4 includes using existing formulas to calculate theoretical fault characteristic frequencies of outer rings, inner rings, and rolling elements of different bearings according to different bearing sizes.

[0059] The steady-state solution curve of the asymmetric multistable system is solved in S1, and the dynamic response of the system is analyzed based on the steady-state solution curve. The two are combined to analyze the process of particle transition of the asymmetric multistable system, and then a new symmetric multistable potential function model is established.

[0060] The novel asymmetric multistable state coupling function model is established in S2, and two independent asymmetric multistable systems are linearly coupled to form a novel linearly coupled asymmetric multistable stochastic resonance model, and its Langevin equation is described as follows:

[0061]

[0062] Where a, a1, b, b1, c, c1, r, r1 are the adjustable system parameters of two independent asymmetric multistable systems, k is the coupling coefficient, -ax+(1+a) / bx 3 -cx 5 +rx 2 is the controlled system, and the control system is -a1y+(1+a1) / b1y 3 -c1y 5 +r1y 2 , and their corresponding output variables are x and y respectively.

[0063] The signal preprocessing in S3 is a combination of the ordinary variable scaling method and the new asymmetric multi-stable state function model, which can be expressed as:

[0064]

[0065] Where a, b, c, mA and f are all large parameters, forming a large-parameter multistable general variable-scale stochastic resonance model.

[0066] The stochastic resonance calculation of S5 is based on the novel asymmetric coupled multistable state; the stochastic resonance calculation of the Langevin equation of the novel asymmetric multistable state is solved using the fourth-order Runge-Kutta algorithm, and its discrete formula is as follows:

[0067]

[0068] Where: n = 1, 2, ..., N, z is the input signal, h is the Runge-Kutta calculation step size, a, b, c and r are system parameters, and x is the system output.

[0069] The output result in S6 is compared with the actual fault characteristic frequency. The output result obtained by random resonance calculation is Fourier transformed to obtain a frequency domain result. The identified fault characteristic frequency is compared with the theoretical fault characteristic frequency calculated previously to determine whether the rolling bearing has a fault and the type of fault. If the identified fault characteristic frequency is close to the theoretical fault characteristic frequency and is within the allowable error range, it can be determined that the bearing has a corresponding fault. If the difference between the two is large, it is necessary to further check the signal processing process or re-analyze and calculate.

[0070] From the perspective of Brownian particle motion, a multistable system model is constructed and analyzed. Considering the macroscopic equation of Brownian particle motion of a unit mass, it is:

[0071]

[0072] Where k is the damping coefficient, U(x) is the potential function of the potential field in which the particle is located, and the periodic driving force is expressed as s(t) = Asin(2πf0 + φ). The noise intensity is D The standard Gaussian white noise, x(t) represents the output displacement function of the Brownian particle of unit mass under the combined action of damping force, potential field force, periodic driving force and noise excitation.

[0073] From the above, the Brownian particle motion equation under the asymmetric multistable potential field is obtained as follows:

[0074]

[0075] To study the dynamic response of the multistable system, we first consider the case of steady-state input and set the right side of the equation to be a constant z, thus obtaining the asymmetric multistable system equation with steady-state excitation:

[0076]

[0077] Rewrite it into the form of the dynamic equation in state space:

[0078]

[0079] From the perspective of Brownian particle motion, the steady-state response means that the velocity and acceleration of the Brownian particle are both 0, that is:

[0080]

[0081] is equivalent to:

[0082]

[0083] Since the system parameters are determined, the first equation in the above formula can be solved to obtain x as a constant, and the second equation in the equation is obviously valid. Then the first equation in the equation is the implicit expression of the steady-state solution of the asymmetric multistable system equation.

[0084] Due to the existence of high-price terms in the equation, it is difficult to obtain an explicit expression for x from the above formula, so we consider using a graphical method to solve it, and define the curve as follows:

[0085]

[0086] In the formula, a=0.1,b=0.48,c=0.06,r=0.15,z=0.01, draw two curves. Figure 2 As shown, it is easy to know that the derivative of g1 is equal to the potential function U(x), and the abscissa values of the five intersection points with the abscissa axis correspond to the positions of the five extreme points of the potential function. This multistable potential function has a total of five solutions. In the enlarged figure, the two intersection points close to the outside where g1 intersects with the abscissa axis correspond to the unstable equilibrium points of the potential function, and the middle intersection point corresponds to the stable point of the potential function at the origin of the coordinate system. In addition to the multiple intersection points in the enlarged figure, in the overall figure, the two outermost intersection points where the curve intersects with the abscissa axis correspond to the two stable points on the outside of the asymmetric multistable state.

[0087] Based on the above analysis, the curve g1(x) can be defined as the steady-state solution curve of the asymmetric multistable system equation, and the system output response is equal to a certain stable intersection point of g1(x) and the input quantity curve g2=z.

[0088] To ensure that the system model always remains an asymmetric multistable model during the debugging of system parameters, it can be seen from the steady-state solution curve of the asymmetric multistable system equation that when the number of intersection points of the curves g1 and g2 is 5, it means that the system equation has 5 solutions at this time, that is, the system is a multistable system at this time; when the number of intersection points of the two curves is 4 or 3, it means that the system equation has 4 or 3 solutions at this time, that is, the system is a bistable system at this time; when the number of intersection points of the two curves is 2 or 1, it means that the system equation has 2 or 1 solutions at this time, that is, the system is a monostable system at this time. Therefore, to ensure that the system model is always an asymmetric multistable model, the maximum amplitude of the system input cannot be greater than the minimum critical amplitude of the system model.

[0089] If only harmonic signal input is considered, the asymmetric multistable system equation is:

[0090]

[0091] From the above formula, we can see that the system input s(t) changes with time t If f0 is small, the system input is a slowly changing and continuous harmonic signal. Therefore, at any t=t pThe output response of the system is always stable at the stable solution of the system, that is, the input curve g2=s(t p ) and a stable point of g1(x), so the countless steady-state solutions x s By time t By combining the order of s -t curve, which is the output response solution of the asymmetric multistable system equation.

[0092] In the above formula, set a = 0.5, b = 3.0, c = 0.06, r = 0.15, A = 0.1, characteristic frequency f0 = 0.01Hz, Signal sampling frequency f s =5Hz, the number of sampling points N = 5000, the 4th order Runge-Kutta algorithm is used to numerically solve the equation, and the initial value of the signal is set The solution of the asymmetric multistable system can be solved by the graphical method. The critical amplitude of the system can be obtained from the extreme point of the original potential function in the corresponding equation. When the amplitude of the system input signal is less than the critical amplitude of the system, the input signal and output response of the system are as shown in the attached figure. Figure 3 As shown in (a) and (b), the two can be analyzed by the steady-state solution curve g1(x) of the system. The g1(x) curve is shown in the attached figure. Figure 4 As shown, g1(x) establishes a one-to-one correspondence with the input signal and the output response.

[0093] System input signal attached Figure 3 The horizontal axis of each point in (a) represents the time Figure 4 The curve g2 in the figure shows that the system output is at the steady-state solution x = 0 at the initial moment. In the first quarter cycle, as time t increases, the system input gradually increases, which is equivalent to the additional Figure 4 The curve g2 in the equation gradually shifts to the right. The horizontal coordinate of the intersection of the two curves is the steady-state solution. The solution gradually increases along the curve g1(x), so the system output also gradually increases until it reaches the maximum when g2=A. Similarly, in the second and third quarter cycles, as time t increases, the system input gradually decreases, which is equivalent to the following: Figure 4 The curve g2 in the equation gradually shifts to the left. During this process, the steady-state solution gradually decreases along the curve g1(x), and the system output gradually decreases until it reaches a minimum when g2=-A. In the fourth quarter cycle, the system input begins to increase, and the system output also gradually increases until the system output value is consistent with the initial moment. In this way, a cycle is completed and continues. The system output is limited between the two extreme positions of the intersection of the g1 and g2 curves, and a small periodic oscillation is achieved in the middle potential well, and its oscillation period is consistent with the signal period.

[0094] The following experimental signals from our laboratory are used to test the method of the present invention:

[0095] The sin signal is used as the input signal with characteristic information, where the signal amplitude A = 0.1, the signal frequency f = 0.01 Hz, the number of sampling points N = 10000, and the sampling frequency f s =5Hz, input Gaussian white noise, noise intensity D = 0.35, system parameters are a = a1 = 1.0, b = b1 = 4.8, c = c1 = 0.6, r = 1.5 and coupling coefficient k = 0.2, the time domain and frequency domain diagrams of the system output results are shown in the attached Figure 5 As shown, (a) group of images are the time domain waveform and spectrum diagram of the sin signal, and the amplitude at the characteristic frequency is 0.096mV; (b) group of images are the time domain waveform and spectrum diagram of the noisy input signal, and the amplitude at the characteristic frequency of the noisy signal is consistent with the amplitude at the characteristic frequency of the pure signal; (c) group of images are the time domain waveform and spectrum diagram of the system output signal, and the amplitude at the characteristic frequency is 0.496mV. Compared with the first two groups, the amplitude of the characteristic signal after processing by the asymmetric multistable coupled stochastic resonance system increases by more than 4 times. Therefore, it can be concluded that the proposed method effectively identifies and amplifies the fault characteristic frequency, and this method can be applied to actual working conditions.

[0096] In order to verify the effectiveness of this method under complex working conditions, this experiment used the bearing fault data provided by the Case Western Reserve University Laboratory for verification. The bearing used in this experiment is a deep groove ball bearing of model 6205-2RS JEM SKF. Under the condition of known bearing speed and other related parameters, the theoretical fault frequency can be calculated. By comparing the theoretically calculated fault frequency with the actual collected signal, the bearing fault type can be determined through signal processing analysis. The sampling frequency of the experiment is 12000Hz, the number of sampling points is 12000, the speed of the drive shaft is set to 1797r / min, and the fault diameter is 0.2794mm. The theoretical calculation results show that the characteristic frequencies of the outer ring and inner ring faults are 107.304Hz and 162.18Hz respectively. Although there are some cases in the experimental signal that are not completely consistent with the theoretical frequency, these deviations are mainly due to factors such as measurement error, sensor offset or current fluctuation. Through the random resonance method, the resonance of the signal is not limited to a single frequency, but covers a frequency band, which effectively reduces the difference between the theoretical frequency and the actual frequency. Figure 6The application process of this method in bearing fault diagnosis is demonstrated, including time domain and frequency domain diagrams: (a) The group of diagrams shows the original acquired signal, in which the fault frequency is drowned by noise and difficult to identify; (b) The group of diagrams shows the input signal after noise is added to the system. Although the signal is improved after processing, the fault frequency is still difficult to extract; (c) The group of diagrams shows the signal after high-pass filtering, which successfully removes the frequency components below 100Hz, but there is still strong noise interference; (d) The group of diagrams shows the signal after final processing by the asymmetric multistable coupled stochastic resonance system, the time domain of the signal The waveform becomes noticeably regular, and the outer ring fault frequency of 107.666Hz in the frequency domain diagram is significantly amplified. Compared with the original signal, the fault frequency is amplified 400 times, and other interference frequencies are effectively suppressed. During signal processing, the input signal enters the stochastic resonance module after Hilbert transform and high-pass filtering. Since the input signal is a large-parameter signal, the ordinary variable scaling method is used to adjust the signal to meet the requirements of the small-parameter stochastic resonance theory. The scaling coefficient is set to 6000. After system parameter optimization, the fault characteristic frequency is finally amplified, making it more prominent in the spectrum diagram.

[0097] The simulation signal and the bearing vibration data from Western Reserve University show that the method proposed in this chapter has high feasibility. The fault diagnosis test is now completed using the bearing data of the rotating machinery fault signal acquisition experimental platform. The specific steps for obtaining the rotating machinery fault signal on the fault signal acquisition platform are as follows: First, the speed of the Mitsubishi HG-SRJ servo motor is controlled by a dual-motor speed control center with a range of 0-3000r / min; the force is transmitted to the faulty bearing through a coupling through a bevel gear reducer with a reduction ratio of 1:2.5, and then through a planetary gearbox with a reduction ratio of 1:5; finally, the torque is transmitted to the TR-3S speed torque power acquisition instrument by the ZJ-500A torque speed sensor. The above steps can obtain the speed, torque and other information of the rotating machinery. Based on the above process, the YD-186 acceleration sensor is installed at the 12 o'clock position of the faulty bearing, and the collected vibration signal is converted into a digital signal by the Ut3408FRS-ICP 24-bit acquisition device. Finally, the vibration waveform is displayed and the data is stored on the computer using the UTek control test system uTekAcqu V2.0.

[0098] The fault experiment was completed using SKF deep groove ball bearing model 6205JEM, and the bearing fault frequency was calculated theoretically. The bearing parameters are shown in the attached figure. Figure 7As shown, the speed is set to 1000r / min. Since the bevel gear reducer will decelerate at a speed 2.5 times the original speed, the speed of the given motor speed control system is 2500r / min. At this time, the TR-3S speed torque power acquisition instrument shows that the speed after the planetary gearbox is decelerated again is 200.2r / min. The theoretical fault frequency of the outer ring of the rolling bearing is 71.4Hz, and the theoretical fault frequency of the inner ring is 108.3Hz. Set the sampling frequency f s =10240Hz, number of sampling points N=10240.

[0099] As attached Figure 8 As shown in the figure, the whole process of signal processing of the outer ring of the rolling bearing in the laboratory and its corresponding time domain and frequency domain diagrams are shown: (a) The group of figures is the time domain waveform and spectrum diagram of the original signal of the bearing collected. In the spectrum, the theoretical fault frequency is submerged by significant noise and is difficult to identify; (b) The group of figures shows the noisy signal after the noise is added. The spectrum has changed, but the fault frequency cannot be clearly identified; (c) The group of figures is the time domain waveform and spectrum diagram of the noisy signal after Hilbert transform and high-pass filtering. The theoretical fault frequency is 71.4Hz, so the stop band of the high-pass filter is set to 60Hz. After filtering, the signal appears The fault frequency multiplication signal is obtained; (d) The figure shows the final result after system processing. When the variable scale coefficient m = 6000, the system parameters a = 1.1, b = 4.09, c = 0.4, a1 = 0.7, b1 = 3.9, c1 = 0.4, the asymmetry coefficient r = 1.55, and the coupling coefficient k = 0.005, the theoretically calculated fault frequency is 71.4Hz, and the actual fault characteristic frequency is 71.875Hz. Compared with the fault frequency amplitude in the original signal, the characteristic frequency amplitude after the stochastic resonance system processing is increased by 18.5 times, and the multiplication interference is effectively suppressed. Similarly, the attached Figure 9The processing process of the inner ring signal of the laboratory rolling bearing and its corresponding time domain and frequency domain diagrams are shown: (a) The group of figures is the time domain waveform and spectrum diagram of the collected original bearing signal. In the spectrum, fault characteristic information appears near the theoretical fault frequency. Although the signal is not submerged by the noise, the interference is relatively serious, and it is impossible to clearly determine whether the frequency is a real fault signal; (b) The group of figures shows the noisy signal after the noise is added. The characteristic information at the theoretical fault frequency is completely covered by the noise; (c) The group of figures is the time domain waveform and spectrum diagram of the noisy signal after Hilbert transform and high-pass filtering. The theoretical frequency of the inner ring fault is 108.3Hz. The stop band of the high-pass filter is set to 100Hz for filtering. However, there is still noise in the signal at this time. Due to a large amount of interference, the fault signal cannot be accurately identified and further processing is required; (d) The figure shows the final results after system processing. The variable scaling coefficient m = 6500, the system parameters a = 0.8, b = 4.9, c = 0.6, a1 = 1.0, b1 = 4.8, c1 = 0.6, the asymmetry coefficient r = 1.75, and the coupling coefficient k = 0.25 are set. The system successfully suppresses the interference signal and significantly enhances the bearing inner ring fault characteristic signal. The actual fault frequency finally extracted is 108.75 Hz. Compared with the characteristic frequency amplitude in the original signal, the fault characteristic frequency amplitude after processing by the asymmetric multistable coupling system is amplified 75 times. The experimental results successfully identify and amplify the fault characteristics.

[0100] Traditional fault diagnosis time-frequency domain analysis methods include Fourier transform, Hilbert transform, etc. During the experiment, it was found that using only these signal processing methods alone may not be able to accurately find the fault characteristic frequency. The signal is input into the stochastic resonance system and the output result is compared with the former. The fault characteristics output by the stochastic resonance system are more recognizable and the fault amplification effect is better. Figure 10 The absolute identification error between the theoretical and actual characteristic frequencies is given. In experiments conducted at Case Western Reserve University and in self-tests, the absolute identification error was less than a frequency resolution (1 Hz), meeting the requirements for fault diagnosis accuracy. Combined with these experiments, it was found that stochastic resonance occurs in bearing signals at different fault characteristic frequencies. This method can accurately identify fault signatures and amplify characteristic frequencies, demonstrating the feasibility and accuracy of fault diagnosis.

[0101] Compared with related technologies, the present invention provides a new type of asymmetric multi-stable coupled stochastic resonance rolling bearing fault diagnosis method with the following beneficial effects:

[0102] The present invention provides a rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance method. Compared with the difficulty in maintaining the symmetry of the potential function in actual physical models and the difficulty in detecting the mutual coupling effects of various equipment components by a single system in actual working conditions, this method effectively solves the above problems, can better highlight the fault characteristic frequency, improve the signal-to-noise ratio, and reduce the sideband interference near the fault characteristic frequency.

[0103] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance, characterized in that: include: S1. Establish a new asymmetric multi-stable state function model: solve the steady-state solution curve, analyze the dynamic response and build the model; S2. Establish a new asymmetric multistable state coupling function model: Two independent asymmetric multistable systems are linearly coupled to form a new linearly coupled asymmetric multistable stochastic resonance model; S3, signal acquisition and signal preprocessing: signal acquisition and signal preprocessing; S4. Calculation of characteristic frequency of rolling bearing faults; S5. Stochastic resonance calculation based on a novel asymmetric coupled multistability; S6. Compare the output results with the actual fault characteristic frequency.

2. The rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance according to claim 1 is characterized in that: The function expression corresponding to the novel asymmetric multistable state function model in S1 is: Where a, b, c and r are the system parameters of the potential function, is the asymmetric term of the potential function.

3. The rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance according to claim 1 is characterized in that: The S3 includes adopting a common variable scale method to collect large parameter signals to meet the small parameter requirements of stochastic resonance.

4. The rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance according to claim 1 is characterized in that: The S4 includes using existing formulas to calculate theoretical fault characteristic frequencies of outer rings, inner rings, and rolling elements of different bearings according to different bearing sizes.

5. The rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance according to claim 1 is characterized in that: The steady-state solution curve of the asymmetric multistable system is solved in S1, and the dynamic response of the system is analyzed based on the steady-state solution curve. The two are combined to analyze the process of particle transition of the asymmetric multistable system, and then a new symmetric multistable potential function model is established.

6. The rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance according to claim 1 is characterized in that: The novel asymmetric multistable state coupling function model is established in S2, and two independent asymmetric multistable systems are linearly coupled to form a novel linearly coupled asymmetric multistable stochastic resonance model, and its Langevin equation is described as follows: Where a, a1, b, b1, c, c1, r, r1 are the adjustable system parameters of two independent asymmetric multistable systems, k is the coupling coefficient, -ax+(1+a) / bx 3 -cx 5 +rx 2 is the controlled system, and the control system is -a1y+(1+a1) / b1y 3 -c1y 5 +r1y 2 , and their corresponding output variables are x and y respectively.

7. The rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance according to claim 1 is characterized in that: The signal preprocessing in S3 is a combination of the ordinary variable scaling method and the new asymmetric multi-stable state function model, which can be expressed as: Where a, b, c, mA and f are all large parameters, forming a large-parameter multistable general variable-scale stochastic resonance model.

8. The rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance according to claim 1 is characterized in that: The stochastic resonance calculation of S5 is based on the novel asymmetric coupled multistable state; the stochastic resonance calculation of the Langevin equation of the novel asymmetric multistable state is solved using the fourth-order Runge-Kutta algorithm, and its discrete formula is as follows: Where: n = 1, 2, ..., N, z is the input signal, h is the Runge-Kutta calculation step size, a, b, c and r are system parameters, and x is the system output.

9. The rolling bearing fault diagnosis method based on a novel asymmetric multi-stable coupled stochastic resonance according to claim 1 is characterized in that: The output result in S6 is compared with the actual fault characteristic frequency. The output result obtained by random resonance calculation is Fourier transformed to obtain a frequency domain result. The identified fault characteristic frequency is compared with the theoretical fault characteristic frequency calculated previously to determine whether the rolling bearing has a fault and the type of fault. If the identified fault characteristic frequency is close to the theoretical fault characteristic frequency and is within the allowable error range, it can be determined that the bearing has a corresponding fault. If the difference between the two is large, it is necessary to further check the signal processing process or re-analyze and calculate.

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