Multi-stable stochastic resonance bearing fault diagnosis method combined with multi-scroll chaos

Abstract

The invention relates to the technical field of mechanical fault diagnosis, in particular to a multistable stochastic resonance bearing fault diagnosis method combined with multi-scroll chaos, which comprises the following steps of: constructing a multi-scroll chaos system expression; determining parameters of the multistable stochastic resonance system according to a stability condition and a balance point existence condition, and determining the multistable stochastic resonance system; inputting a bearing vibration acceleration signal into the multistable stochastic resonance system determined in the step 2; inputting a multistable stochastic resonance system of a bearing vibration acceleration signal for discretization iteration, and obtaining a spectrogram from a discretized sequence by using a fast Fourier transform algorithm; and according to the frequency spectrogram obtained in the step 4 corresponding to the fault characteristic frequency, the bearing fault type is determined according to the frequency corresponding to the spectral peak in the frequency spectrogram. According to the method, the multi-scroll chaotic system is transferred to the multi-stable stochastic resonance system, so that the fault characteristics can be effectively highlighted, and the problem that the bearing fault is difficult to diagnose under the strong noise background is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical fault diagnosis, and in particular to a multi-stable stochastic resonance bearing fault diagnosis method combined with multi-scroll chaos. Background Art

[0002] Bearings are used to transmit force and motion in mechanical equipment and are widely used in industries such as wind turbines, aero-engines, and high-speed railway EMUs. As one of the key basic components of major equipment, bearings are called the "joints of industry". However, major equipment operates in harsh working conditions and environments, and bearings are extremely prone to failure, resulting in a decrease in the operating accuracy of the equipment and huge economic losses in severe cases. On the one hand, regularly replacing bearings will cause components that have not reached their service life to be prematurely eliminated, resulting in huge waste. On the other hand, if the bearing fault warning is not timely, it will pose a huge safety hazard. Therefore, an accurate and efficient bearing fault diagnosis method is of great significance for the safe and stable operation of major equipment.

[0003] Traditional signal processing methods based on decomposition or filtering often aim to suppress noise components. Although they can better solve the problem of mechanical fault feature extraction to a certain extent, in the actual engineering environment, the noise frequency often overlaps or is aliased with the signal frequency, and it is inevitable to weaken the features of weak signals while filtering out noise, resulting in the loss of useful information in weak signals and being unfavorable for the analysis and processing of target weak signals. Although the classical Duffing stochastic resonance system can enhance weak signals to a certain extent, the determination of the number of system steady states and the adjustable parameters are limited.

[0004] Therefore, the disadvantages of the current existing technologies are as follows: Traditional signal processing methods based on decomposition or filtering will weaken the features of mechanical fault weak signals while suppressing noise components, resulting in the loss of useful information in weak signals and being unfavorable for the analysis and processing of target weak signals; in the classical Duffing stochastic resonance system, the determination of the number of system steady states and the adjustable parameters are limited. Summary of the Invention

[0005] Aiming at the above technical problems in the existing technologies, that is, weakening the features of mechanical fault weak signals while suppressing noise components, resulting in the loss of useful information in weak signals, and the determination of the number of system steady states and the adjustable parameters in the classical Duffing stochastic resonance system are limited.

[0006] Technical idea: Starting from the problems of the existing technology, this application provides a multi-stable stochastic resonance bearing fault diagnosis method combined with multi-scroll chaos. The stochastic resonance system combined with multi-scroll chaos can convert the energy of the noise part into the energy of the characteristic signal, so as to achieve the purpose of enhancing the signal characteristics. And by combining the characteristics of the multi-stable stochastic resonance system combined with multi-scroll chaos that the steady-state parameters and the number are flexibly adjustable, it can effectively solve the problems of unclear bearing fault characteristics and difficult fault diagnosis under strong noise background.

[0007] To achieve the above technical idea, the technical solutions adopted by the present invention are as follows:

[0008] A multi-stable stochastic resonance bearing fault diagnosis method combined with multi-scroll chaos, comprising the following steps:

[0009] Step 1: Construct the expression of the multi-scroll chaos system;

[0010] Step 2: On the basis of Step 1, determine the parameters of the multi-stable stochastic resonance system through the stability condition and the existence condition of the equilibrium point, and then determine the multi-stable stochastic resonance system;

[0011] Step 3: Input the bearing vibration acceleration signal into the multi-stable stochastic resonance system constructed in Step 2;

[0012] Step 4: Discretize and iterate the multi-stable stochastic resonance system after inputting the bearing vibration acceleration signal, and obtain the spectrogram by using the fast Fourier transform algorithm for the discretized sequence;

[0013] Step 5: According to the spectrogram obtained in Step 4 corresponding to the fault characteristic frequency, determine the bearing fault type through the frequency corresponding to the spectral peak in the spectrogram.

[0014] Furthermore, the mathematical expression of the multi-scroll chaos system constructed in Step 1 is:

[0015]

[0016] In the formula, x, y, z are the state variables of the multi-scroll chaos system, represents the derivative of the state variables x, y, z of the multi-scroll chaos system with respect to time, f(x) is a non-linear switching function, sgn(·) is a sign function, a, b, c, d, e, l, j, k i , p i are the parameters of the multi-scroll chaos system, i = 1, 2,... N, where the parameter N is an integer.

[0017] Even further, the method for determining the parameters of the multi-stable stochastic resonance system in Step 2 is:

[0018] Step 2.1: Let ki > k i-1 > 0, i = 1, 2, ... N, where the parameter N is an integer used to control the number of steady states of the stochastic resonance system. Then the mathematical expression of f(x) in step 1 is recorded as:

[0019]

[0020] Step 2.2: According to step 2.1, the Jacobian matrix J of the multi-stable stochastic resonance system is:

[0021]

[0022] Calculate the characteristic equation H(λ) of the multi-stable stochastic resonance system from the Jacobian matrix:

[0023] H(λ) = |λE - J| = λ 3 +(c + ajl)λ 2 +(acjl - ab + de)λ + adejl.

[0024] Step 2.3: Obtain the stability condition of the multi-stable stochastic resonance system from the Routh-Hurwitz criterion and the characteristic equation of the multi-stable stochastic resonance system as:

[0025]

[0026] Where a, b, c, d, e, l, j are parameters of the multi-stable stochastic resonance system.

[0027] Step 2.4: From the mathematical equation of the multi-scroll chaotic system in step 1, obtain the expression at the equilibrium point of the multi-stable stochastic resonance system as:

[0028]

[0029] Step 2.5: Combine step 2.4 and step 2.3 to obtain:

[0030]

[0031] Where sign(·) is the sign function, x, z are state variables of the multi-stable stochastic resonance system, k i , p i , b, d, j are parameters of the multi-stable stochastic resonance system.

[0032] Step 2.6: When the number of equilibrium points of the multi-stable stochastic resonance system reaches the maximum, i.e., NE max = 2N + 1, N = 1, 2, 3..., k i and p i The existence conditions of the equilibrium points that should be satisfied are:

[0033]

[0034] The maximum number of steady states \(N_E\) of the multi-stable stochastic resonance system max The relationship with the parameter \(N\) is \(N_E\) max = 2N + 1.

[0035] In step 3, the bearing vibration acceleration signal \(S\) f (t)sgn(S f (t)) is input into the multi-stable stochastic resonance system as follows:

[0036]

[0037] where sgn(·) is the sign function.

[0038] Furthermore, in step 4, the fourth-order Runge-Kutta algorithm is adopted;

[0039] Step 4.1: Discretize and iterate the multi-stable stochastic resonance system after inputting the bearing vibration acceleration signal \(S\) f (t)sgn(S f (t)). The specific expression is:

[0040]

[0041] where \(V(t)=S\) f (t)sgn(S f (t));

[0042]

[0043] In the formula, \(k_{x}\) 1 , \(k_{y}\) 1 , \(k_{z}\) 1 , \(k_{x}\) 2 , \(k_{y}\) 2 , \(k_{z2}\), \(k_{x}\) 3 , \(k_{y}\) 3 , \(k_{z}\) 3 , \(k_{x}\) 4 , \(k_{y}\) 4 , \(k_{z}\) 4 are the fourth-order Runge-Kutta intermediate variables, \(h\) is the solution step size of the fourth-order Runge-Kutta algorithm, \(x\) n , \(y\) n , \(z\) n are the values of \(x\), \(y\), \(z\) at the \(n\)th solution, \(f(x\) n ) refers to the value of the non-linear switching function \(f(x)\) after inputting \(x\) n , and \(V(t)=S\) f (t)sgn(S f(t)) is the bearing vibration acceleration signal, and a, b, c, d, e are the parameters of the multi-stable stochastic resonance system.

[0044] Step 4.2: Obtain the sequence {x0, x1, x2... x n , x n+1} through the fourth-order Runge-Kutta method, and x n+1 Use the fast Fourier transform algorithm to obtain the spectrogram.

[0045] Furthermore, the rolling bearing fault types determined in step 5 include the inner race fault characteristic frequency, the outer race fault characteristic frequency, the rolling element fault characteristic frequency, and the cage fault characteristic frequency;

[0046] Step 5.1: Among them, the expression for solving the inner race fault characteristic frequency is:

[0047]

[0048] The expression for solving the outer race fault characteristic frequency is:

[0049]

[0050] The expression for solving the rolling element fault characteristic frequency is:

[0051]

[0052] The expression for solving the cage fault characteristic frequency is:

[0053]

[0054] In the formula, d is the ball diameter (mm), D is the bearing pitch diameter (mm), N is the number of balls, α is the contact angle, and r is the rotational speed (rpm);

[0055] Step 5.2: When the frequency corresponding to the spectral peak in the spectrogram of step 4 is consistent with the fault characteristic frequency in step 5.1, the corresponding fault can be determined.

[0056] Compared with the prior art, the beneficial effects of the present invention are:

[0057] By combining the stability condition and the existence condition of the equilibrium point of the multi-stable stochastic resonance system, this application adjusts the parameter N of the multi-stable stochastic resonance system, enabling the system to transfer from the multi-scroll chaotic state to the multi-stable stochastic resonance state. The signal energy after being processed by the multi-stable stochastic resonance system is increased. By comparing the spectrograms after being processed by the five-stable stochastic resonance system, it can be seen that the bearing fault characteristics are significantly enhanced. The stochastic resonance system transfers the signal noise energy to the fault characteristic signal, enabling the bearing fault diagnosis under low signal-to-noise ratio conditions. The number of steady states of the multi-stable stochastic resonance system is flexibly adjustable, and the signal processing effect can be adjusted only by modifying the system parameters, making the signal processing effect easy to adjust, and effectively solving the problems of unclear bearing fault characteristics and difficult fault diagnosis under strong noise backgrounds. Description of the Drawings

[0058] The drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation to the present invention.

[0059] Figure 1 It is a flowchart of the method of the present invention;

[0060] Figure 2 It is the x-y phase diagram when in five-stable scroll chaos;

[0061] Figure 3 It is the iteration diagram of the bearing outer race fault through the five-stable stochastic resonance system;

[0062] Figure 4 It is the iteration diagram of the rolling element fault through the five-stable stochastic resonance system;

[0063] Figure 5 It is the vibration signal spectrum of the bearing outer race fault;

[0064] Figure 6 It is the vibration signal spectrum of the rolling element fault;

[0065] Figure 7 It is the spectrum of the bearing outer race fault signal after being processed by the five-stable stochastic resonance system;

[0066] Figure 8 It is the spectrum of the rolling element fault signal after being processed by the five-stable stochastic resonance system. Detailed Embodiments

[0067] The following describes the preferred embodiments of the present invention with reference to the drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention and are not used to limit the present invention.

[0068] Embodiment

[0069] A multi-stable stochastic resonance bearing fault diagnosis method combining multi-scroll chaos, comprising the following steps: as Figure 1 shown;

[0070] Step 1: Construct the expression of the multi-scroll chaos system;

[0071] Furthermore, the mathematical expression of the multi-scroll chaos system constructed in Step 1 is:

[0072]

[0073] where x, y, z in the formula are the state variables of the multi-scroll chaos system; denotes the derivative of the state variables x, y, z of the multi-scroll chaos system with respect to time,

[0074]

[0075] where sgn(·) is the sign function, a, b, c, d, e, l, j, k i , p i are the parameters of the multi-scroll chaos system, i = 1, 2,... N, where the parameter N is an integer.

[0076] When the system parameters are N = 2, a = 8, b = c = d = 2, e = 10, j = 0.5, l = 0.5, p1 = 0.5, k1 = 1, p2 = 1, k2 = 3, the system is in a five-stable scroll chaos state, and the x-y phase diagram of the system is as Figure 2 shown.

[0077] Step 2: On the basis of Step 1, determine the parameters of the multi-stable stochastic resonance system through the stability condition and the existence condition of the equilibrium point, and then determine the multi-stable stochastic resonance system;

[0078] Among them, the method for determining the parameters of the multi-stable stochastic resonance system in Step 2 is:

[0079] Step 2.1: Let k i > k i-1 > 0, i = 1, 2,... N, the parameter N is an integer, used to control the number of steady states of the stochastic resonance system, then the mathematical expression of f(x) in Step 1 is recorded as:

[0080]

[0081] Step 2.2: According to Step 2.1, the Jacobian matrix J of the multi-stable stochastic resonance system is:

[0082]

[0083] The characteristic equation \(H(\lambda)\) of the multi-stable stochastic resonance system is calculated from the Jacobian matrix:

[0084] \(H(\lambda)=|\lambda E - J|=\lambda\) 3 +(c + ajl)\(\lambda\) 2 +(acjl - ab + de)\(\lambda\)+adejl;

[0085] Step 2.3: According to the Routh-Hurwitz criterion and the characteristic equation of the multi-stable stochastic resonance system, the stability condition of the multi-stable stochastic resonance system is:

[0086]

[0087] Step 2.4: The expression at the equilibrium point of the multi-stable stochastic resonance system can be calculated from the mathematical equation of the multi-scroll chaotic system in Step 1:

[0088]

[0089] Step 2.5: Combining Step 2.4 and Step 2.3 gives:

[0090]

[0091] Step 2.6: When the number of equilibrium points of the multi-stable stochastic resonance system reaches the maximum, i.e., \(N_E\) max = 2N + 1, N = 1, 2, 3…, k i and \(p\) i The existence condition of the equilibrium point that should be satisfied is:

[0092]

[0093] The maximum number of steady states \(N_E\) of the multi-stable stochastic resonance system max The relationship with the parameter \(N\) is \(N_E\) max = 2N + 1. Adjusting the parameter \(N\) can transfer from the multi-scroll chaotic state to the multi-stable stochastic resonance state.

[0094] As an example, the system parameters for the system to transfer from the five-stable scroll chaotic state to the five-stable stochastic resonance system are determined as \(a = 2\), \(b = 8\), \(c = 8\), \(d = 1.8\), \(e = 10\), \(l = 0.2\), \(j = 0.5\), \(h = 0.1\), \(p1 = 0.5\), \(k1 = 1\), \(p2 = 1\), \(k2 = 3\).

[0095] Step 3: Input the bearing vibration acceleration signal \(S\) f (t)sgn(S f (t)) into the multi-stable stochastic resonance system constructed in Step 2;

[0096] Specifically, in Step 3, such as Figure 3 andFigure 4 The collected bearing outer ring and rolling element fault vibration signal S f (t)sgn(S f (t)) is input into the multi-stable stochastic resonance system according to the following formula to enhance the fault characteristics;

[0097] Input into the multi-stable stochastic resonance system according to the following formula:

[0098]

[0099] where sgn(·) is the sign function.

[0100] Specifically, the bearing vibration acceleration signal contains the bearing outer ring and rolling element fault vibration signals. The bearing outer ring fault vibration acceleration signal and the rolling element fault vibration acceleration signal both belong to the bearing vibration acceleration signal.

[0101] where the spectra of the bearing outer ring and rolling element fault vibration signals are respectively as Figure 5 and Figure 6 shown;

[0102] In detail, for the outer ring fault bearing, the ball diameter d = 6.75 mm, the bearing pitch diameter D = 28.50 mm, the number of balls N = 8, the contact angle α = 0°, the rotational speed r = 1730 rpm, the outer ring fault is 0.53 mm, and the vibration signal sampling frequency is 12 KHz;

[0103] For the rolling element fault bearing, the ball diameter d = 7.94 mm, the bearing pitch diameter D = 39.04 mm, the number of balls N = 9, the contact angle α = 0°, the rotational speed r = 1772 rpm, the rolling element fault size is 0.71 mm, and the vibration signal sampling frequency is 12 KHz.

[0104] Step 4: Discretize and iterate the multi-stable stochastic resonance system after inputting the bearing vibration acceleration signal in Step 3;

[0105] Furthermore, in Step 4, the fourth-order Runge-Kutta algorithm is adopted;

[0106] Step 4.1: The expression for discretizing and iterating the multi-stable stochastic resonance system after inputting the bearing vibration acceleration signal in Step 3 is:

[0107]

[0108]

[0109] where V(t) = S f (t)sgn(S f (t));

[0110] Step 4.2: Obtain the sequence {x0, x1, x2... x n , x n+1} by using the fourth-order Runge-Kutta method, and obtain the spectrogram by using the fast Fourier transform algorithm for x n+1 .

[0111] Step 5: Determine the bearing fault type according to the correspondence between the spectrogram obtained in Step 4 and the fault characteristic frequency, and determine the bearing fault type through the frequency corresponding to the spectral peak in the spectrogram.

[0112] Furthermore, the rolling bearing fault types determined in Step 5 include the inner ring fault characteristic frequency, the outer ring fault characteristic frequency, the rolling element fault characteristic frequency, and the cage fault characteristic frequency;

[0113] Step 5.1: Among them, the solution expression for the inner ring fault characteristic frequency is:

[0114]

[0115] The solution expression for the outer ring fault characteristic frequency is:

[0116]

[0117] The solution expression for the rolling element fault characteristic frequency is:

[0118]

[0119] The solution expression for the cage fault characteristic frequency is:

[0120]

[0121] In the formula, d is the ball diameter (mm), D is the bearing pitch diameter (mm), N is the number of balls, α is the contact angle, and r is the rotational speed (rpm).

[0122] Step 5.2: When the frequency corresponding to the spectral peak in the spectrogram of Step 4 is consistent with the fault characteristic frequency in Step 5.1, the corresponding fault can be determined.

[0123] The envelope spectra of the x-dimensional output signals after iteration of the outer ring and rolling element faults of the bearing shown in Figure 3 and Figure 4 are respectively shown in Figure 7 and Figure 8 . The corresponding fault characteristic frequencies can be calculated according to the outer ring and rolling element fault bearings as follows:

[0124] Outer ring fault characteristic frequency:

[0125] Rolling element fault characteristic frequency:

[0126] Simulation experiment

[0127] Figure 3 and Figure 4 are respectively the time-domain waveform diagrams of the measured vibration acceleration signals of the bearing outer ring and the rolling element faults. The spectra of the vibration acceleration signals of the bearing outer ring and the rolling element faults after fast Fourier transform are respectively as Figure 5 and Figure 6 shown.

[0128] As Figure 7 and Figure 8 shown, the frequencies corresponding to the peaks indicated in the power spectrum diagrams of the bearing outer ring fault and the rolling element fault are 88.0 Hz and 140.0 Hz respectively. The theoretical fault characteristic frequencies of the bearing outer ring and the rolling element corresponding to this frequency are 88.0 Hz and 139.2 Hz respectively. Therefore, the above two faults are caused by the outer ring fault and the rolling element fault respectively.

[0129] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A multi-stable stochastic resonance bearing fault diagnosis method combined with multi-scroll chaos, characterized in that, Including the following steps: Step 1: Construct the expression of the multi-scroll chaotic system; Step 2: Based on Step 1, determine the parameters of the multi-stable stochastic resonance system through the stability condition and the existence condition of the equilibrium point, and then determine the multi-stable stochastic resonance system; Step 3: Input the bearing vibration acceleration signal into the multi-stable stochastic resonance system determined in Step 2; Step 4: Discretize and iterate the multi-stable stochastic resonance system after inputting the bearing vibration acceleration signal, and obtain the spectrogram by using the fast Fourier transform algorithm for the discretized sequence; Step 5: According to the correspondence between the spectrogram obtained in Step 4 and the fault characteristic frequency, determine the bearing fault type through the frequency corresponding to the spectral peak in the spectrogram.

2. A multi - stable stochastic resonance bearing fault diagnosis method combining multi - scroll chaos according to claim 1, characterized in that: The mathematical expression of the multi-scroll chaotic system constructed in Step 1 is: where x, y, and z are the state variables of the multi-scroll chaotic system, denote the derivatives of the state variables x, y, and z of the multi-scroll chaotic system with respect to time, f(x) is a nonlinear switching function, sgn(·) is a sign function, a, b, c, d, e, l, j, k i , p i are all parameters of the multi-scroll chaotic system, i = 1, 2,... N, and the parameter N is an integer.

3. A multi-stable stochastic resonance bearing fault diagnosis method combined with multi-scroll chaos according to claim 2, characterized in that: The method for determining the parameters of the multi-stable stochastic resonance system in Step 2 is: Step 2.1: Let k i > k i-1 > 0, i = 1, 2, ... N, where the parameter N is an integer. Then the mathematical expression of f(x) in Step 1 is recorded as: Step 2.2: According to Step 2.1, the Jacobian matrix J of the multi-stable stochastic resonance system is: Calculate the characteristic equation H(λ) of the multi-stable stochastic resonance system from the Jacobian matrix; H(λ) = |λE - J| = λ 3 +(c + ajl)λ 2 +(acjl - ab + de)λ + adejl; Wherein, H(λ) is a function of λ; Step 2.3: Obtain the stability condition of the multi-stable stochastic resonance system from the Routh-Hurwitz criterion and the characteristic equation of the multi-stable stochastic resonance system as: Where a, b, c, d, e, l, j are the parameters of the multi-stable stochastic resonance system; Step 2.4: Based on the mathematical equation of the multi-scroll chaotic system in Step 1, obtain the expression at the equilibrium point of the multi-stable stochastic resonance system as: Step 2.5: Combine Step 2.4 and Step 2.3 to obtain: where sign(·) is the sign function, x and z are the state variables of the multi-stable stochastic resonance system, and k i , p i , b, d, and j are the parameters of the multi-stable stochastic resonance system; Step 2.6: When the number of equilibrium points of the multi-stable stochastic resonance system reaches the maximum, i.e., NE max = 2N + 1, N = 1, 2, 3…, k i and p i The existence conditions of the equilibrium points satisfied are: The maximum number of steady states NE of the multistable stochastic resonance system max The relationship with the parameter N is NE max = 2N + 1.

4. A multi - stable stochastic resonance bearing fault diagnosis method combining multi - scroll chaos according to claim 3, characterized in that: In step 3, the bearing vibration acceleration signal S f (t)sgn(S f (t)) is input into the multi-stable stochastic resonance system as follows: Wherein, sgn(·) is the sign function.

5. A multi-stable stochastic resonance bearing fault diagnosis method combined with multi-scroll chaos according to claim 4, characterized in that: In Step 4, the fourth-order Runge-Kutta algorithm is adopted; Step 4.1: Discretize and iterate the multi-stable stochastic resonance system after inputting the bearing vibration acceleration signal S f (t)sgn(S f (t)), and the specific expression is as follows: where, V(t) = S f (t)sgn(S f (t)); where \(k_x\) 1 , \(k_y\) 1 , \(k_z\) 1 , \(k_x\) 2 , \(k_y\) 2 , \(k_z\) 2 , \(k_x\) 3 , \(k_y\) 3 , \(k_z\) 3 , \(k_x\) 4 , \(k_y\) 4 , \(k_z\) 4 are the fourth-order Runge-Kutta intermediate variables, \(h\) is the solution step size of the fourth-order Runge-Kutta algorithm, \(x\) n , \(y\) n , \(z\) n are the values of \(x\), \(y\), \(z\) at the \(n\)-th solution, \(f(x\) n ) refers to the value of the non-linear switching function \(f(x)\) after \(x\) n is input, \(V(t)=S\) f (t)\(\text{sgn}(S\) f (t)) is the bearing vibration acceleration signal, and \(a\), \(b\), \(c\), \(d\), \(e\) are the parameters of the multi-stable stochastic resonance system; Step 4.2: Obtain the sequence {x0, x1, x2... x n , x n+1} by using the fourth-order Runge-Kutta method, and obtain the spectrogram by using the fast Fourier transform algorithm for x n+1 .

6. A multi-stable stochastic resonance bearing fault diagnosis method combining multi-scroll chaos according to claim 5, characterized in that: The rolling bearing fault types determined in Step 5 include the inner ring fault characteristic frequency, the outer ring fault characteristic frequency, the rolling element fault characteristic frequency, and the cage fault characteristic frequency; Step 5.1: Among them, the expression for solving the inner ring fault characteristic frequency is: The expression for solving the outer ring fault characteristic frequency is: The expression for solving the rolling element fault characteristic frequency is: The expression for solving the cage fault characteristic frequency is: Where d is the ball diameter (mm), D is the bearing pitch diameter (mm), N is the number of balls, α is the contact angle, and r is the rotational speed (rpm); Step 5.2: When the frequency corresponding to the spectral peak in the spectrogram of Step 4 is consistent with the fault characteristic frequency in Step 5.1, the corresponding fault can be determined.

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