Rolling bearing early fault feature extraction method based on chho-vmd

Abstract

The application discloses a CHHO-VMD-based early fault feature extraction method for rolling bearings, and comprises the following steps: obtaining a bearing original vibration signal; identifying an early fault signal in the original vibration signal; applying a CHHO algorithm to adaptively optimize VMD parameters, and generating an optimal parameter combination [K, alpha]; decomposing the fault signal by using the parameter-optimized VMD, and extracting an IMF component thereof; selecting the IMF component based on kurtosis and a correlation coefficient to reconstruct the fault signal; and applying envelope demodulation to extract a fault feature frequency of the rolling bearing. The application has the beneficial effect that the CHHO algorithm is introduced to adaptively determine the optimal parameter combination of the VMD, thereby avoiding the problems of modal component loss and modal aliasing caused by manual parameter selection and incorrect setting; the CHHO and the VMD are combined, the fault feature frequency of the early fault signal of the rolling bearing is effectively extracted, and the accuracy and timeliness of fault detection are high.

Description

TECHNICAL FIELD

[0001] The application relates to a bearing fault detection technology, in particular to a rolling bearing early fault feature extraction method based on CHHO-VMD. BACKGROUND

[0002] The rolling bearing is a basic component of large industrial rotating machinery, and is crucial to improving the efficiency of the mechanical system. Its condition directly affects the stable operation of the equipment. The variational mode decomposition VMD is established on a strict mathematical model, and shows strong noise robustness, and can effectively extract signal components, and is widely used for rolling bearing fault feature extraction. However, VMD is sensitive to parameter selection, especially the modal number K and the penalty factor alpha, and improper selection will lead to over-decomposition or insufficient decomposition. Therefore, many scholars at home and abroad have introduced intelligent optimization algorithms to adaptively search for the optimal values of K and alpha, such as the beetle antenna search (BAS) algorithm, the genetic mutation particle swarm optimization variational mode decomposition (GM-PSO) algorithm and the like.

[0003] Although the traditional intelligent optimization algorithm can effectively optimize the VMD parameters, problems such as long calculation time and difficulty in extracting early fault features still exist. Therefore, there is an urgent need for a technology that can adaptively optimize the VMD parameters and quickly and effectively extract the weak features of the early fault of the rolling bearing, so as to improve the accuracy and timeliness of fault detection. SUMMARY

[0004] The application aims to provide a rolling bearing early fault feature extraction method based on CHHO-VMD, which has the advantages of efficient and accurate fault detection.

[0005] The application achieves the above-mentioned purpose through the following technical solutions.

[0006] The rolling bearing early fault feature extraction method based on CHHO-VMD comprises the following steps:

[0007] S1, acquiring a bearing original vibration signal;

[0008] S2, identifying an early fault signal in the original vibration signal;

[0009] S3, applying the CHHO algorithm to adaptively optimize the VMD parameters to generate an optimal parameter combination [K, alpha];

[0010] S4, decomposing the fault signal by using the parameter-optimized VMD to extract the IMF (intrinsic mode function) component thereof;

[0011] S5, selecting the IMF component to reconstruct the fault signal based on the kurtosis and the correlation coefficient;

[0012] S6, envelope demodulation is applied to extract the fault characteristic frequency of the rolling bearing.

[0013] Further, in the S3 step, the CHHO algorithm introduces a chaotic mapping to generate chaotic values for the initial energy E0, helping the algorithm to break the fixed search pattern in the exploration stage; an exponential decay factor is introduced to dynamically adjust the algorithm parameters, improving the balance between exploration and development; a Gaussian mutation is introduced to increase population diversity and prevent the algorithm from falling into local optima.

[0014] Further, the chaotic mapping is beneficial to the optimization algorithm to maintain population diversity, enabling them to escape from local optima and improve global search performance, and the expression is as follows:

[0015] x n+1 =ux n (1-x n ),u∈[0,4],x n ∈(0,1)

[0016] Where x n represents the proportion of the population at the nth time to the maximum possible population size, x n+1 represents the population proportion at the n+1 time, x is a random number between 0 and 1, and u represents the control parameter, which determines the behavior of the chaotic mapping;

[0017] The exponential decay factor refers to a parameter that gradually decreases in a nonlinear manner during iteration, with the purpose of gradually reducing the global search ability while enhancing the local search ability as iteration proceeds, in order to improve the convergence performance of the algorithm and the quality of the solution;

[0018] The Gaussian mutation is an improvement to the genetic algorithm, aiming to replace the original parameter value with a random number drawn from a normal distribution with mean μ and variance σ 2 The expression is as follows:

[0019] X mutated (t+1)=X(t)(1+N(μ,σ 2 ))

[0020] Where X mutated (t+1) represents the position of the mutated individual, X(t) represents the position of the individual before mutation, and N represents a Gaussian distribution with mean μ and variance σ 2

[0021] Further, in the chaotic mapping to generate chaotic values for the initial energy, the chaotic mapping is used to generate chaotic values for the initial energy E0 of the eagle, giving the algorithm chaos to help break the fixed search pattern in the global search stage, and the update formula of the initial energy is as follows:

[0022] E0=x​n+1 = ux n (1-x n ), x n ∈(0, 1)

[0023] The update formula of escape energy is as follows:

[0024]

[0025] Wherein, sign is a random value of -1 or 1, t represents the current iteration number, and T represents the maximum iteration number.

[0026] Further, the exponential decay factor is used to dynamically adjust the algorithm parameters, improve the balance of the exploration and development stages, and the exponential decay weight is calculated as follows:

[0027] ω i = e -λ·i

[0028] Wherein, ω i is the weight of the i th data point, λ is the decay coefficient, and i is the time interval.

[0029] Further, the Gaussian variation is randomly applied to some individuals to cause slight movement of their positions, enhance the diversity of the population, and avoid falling into local optimum, and the population position update formula is as follows:

[0030]

[0031] Wherein, rand is a random number between 0 and 1, p represents the mutation probability, X(t) represents the current population position, X(t+1) represents the population position after iteration, and f(.) represents the fitness function.

[0032] Further, the S3 step specifically comprises the following steps:

[0033] Step 1, setting the initial parameters of CHHO algorithm;

[0034] Step 2, decomposing early fault signals by VMD;

[0035] Step 3, identifying the optimal individual;

[0036] Step 4, restoring the escape energy of the prey;

[0037] Step 5, judging whether the escape energy is less than or equal to 1, if less than or equal to 1, entering the development stage, and if greater than 1, entering the exploration stage;

[0038] Step 6, judging whether the maximum iteration number is reached;

[0039] Step 7, output K and alpha when the maximum number of iterations is reached, otherwise repeat steps 2 to 6.

[0040] Further, in the S3 step, the average minimum energy entropy is used as the iteration index in the optimization process, and the calculation formula is as follows:

[0041]

[0042] Where, u k is the kth IMF component, H mean (u k ) is the average energy entropy of component u k ; P k represents the proportion of the kth component u k to the total energy, E k is the energy of each component, E is the sum of the energies of the K components, and E i is the energy of the i th component.

[0043] Further, in the S5 step, the kurtosis calculation formula is as follows:

[0044]

[0045] Where, mu and sigma represent the mean and standard deviation of the signal respectively, E(·) is the expected value of the signal, and x represents the value of the signal;

[0046] The calculation formula of the correlation coefficient is as follows:

[0047]

[0048] Where, theta i represents the value of the i th data point in the IMF component, represents the mean of the IMF component, delta i represents the value of the i th data point in the original signal, represents the mean of the original signal.

[0049] The present application has the following advantages:

[0050] 1. The CHHO algorithm is introduced to adaptively determine the optimal parameter combination of VMD, avoiding the loss of modal components and modal aliasing problems caused by manual parameter selection and incorrect settings, and by combining CHHO and VMD, the fault feature frequency of the early fault signal of the rolling bearing is effectively extracted, and the accuracy and timeliness of fault detection are high.

[0051] 2. By introducing chaotic mapping to give the algorithm chaos, help the algorithm break the fixed exploration mode during global exploration, introduce a nonlinear decreasing factor to dynamically adjust the algorithm parameters, improve the balance between exploration and development, and introduce Gaussian variation to effectively prevent the algorithm from falling into local optimum. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 is a flowchart of the present application.

[0053] Figure 2 is a life chart of the outer ring rolling bearing with mean square value as the performance index.

[0054] Figure 3 is a chart of the escape energy E in the process of twice running and 500 iterations of the HHO algorithm.

[0055] Figure 4 is a chart of the escape energy E in the process of twice running and 500 iterations of the CHHO algorithm.

[0056] Figure 5 is a convergence curve of the average energy entropy with respect to the number of iterations in the VMD parameter optimization process.

[0057] Figure 6 is a time domain chart of each IMF component obtained by using the optimal parameter combination obtained after CHHO optimization to perform VMD decomposition on the rolling bearing vibration signal.

[0058] Figure 7 is a frequency spectrum chart of each IMF component obtained by using the optimal parameter combination obtained after CHHO optimization to perform VMD decomposition on the rolling bearing vibration signal.

[0059] Figure 8 is an envelope spectrum chart after IMF1 and IMF2 are reconstructed. DETAILED DESCRIPTION

[0060] To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0061] Therefore, the following detailed description of the embodiments of the application provided in the drawings is not intended to limit the scope of the application claimed, but merely represents selected embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the application.

[0062] It should be noted that the embodiments and features in the embodiments can be combined with each other without conflict.

[0063] It should be noted that: similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0064] In the description of the application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship commonly placed when the product of the application is used, or the orientation or positional relationship commonly understood by those skilled in the art, and are only for the convenience of describing the application and simplifying the description, and do not indicate or imply that the indicated device or element must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the application. In addition, the terms "first", "second" and the like are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0065] In the description of the application, it should also be noted that unless otherwise specified and limited, the terms "set", "mount", "connected", "connected" should be broadly understood, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication inside two elements. For those of ordinary skill in the art, the specific meaning of the above terms in the application can be understood according to the specific circumstances.

[0066] Reference Figures 1-8 An embodiment of the application is shown as follows:

[0067] The CHHO-VMD-based rolling bearing early fault feature extraction method comprises the following steps:

[0068] S1, obtaining the original vibration signal of the bearing.

[0069] The bearing data set of the University of Cincinnati is used in this embodiment, the tested bearing is Rexnord ZA-2115, the sampling frequency is 20 kHz, and the rotation frequency is 33.3 Hz. Table 1 below shows the detailed parameters of the bearing.

[0070] Table 1: Bearing parameters to be tested

[0071] Parameter Value Pitch diameter 71.5 mm Rolling element diameter 8.4 mm Number of rolling elements per row 16 Contact angle 15.17° Static load 26690N

[0072] The formula for calculating the fault characteristic frequency of the inner and outer ring rolling bearing is as follows:

[0073]

[0074] Where N represents the rotation frequency of the bearing, n represents the number of rolling elements, d represents the diameter of the rolling elements, D represents the average diameter of the bearing, and a represents the contact angle of the bearing. Substituting the data in Table 1 into the formula for calculating the fault characteristic frequency of the rolling bearing, the inner ring fault characteristic frequency is 297 Hz, and the outer ring fault characteristic frequency is 236 Hz.

[0075] S2, identify early fault signals in the original vibration signal.

[0076] To identify early fault signals in the original bearing vibration data, the root mean square (RMS) value is used for analysis. 4000 (0.2fs) points of the original vibration signal form a sample, and the root mean square value of each sample is taken as the ordinate, and the sample number is taken as the abscissa. The outer ring rolling bearing life diagram is shown in Figure 2 .

[0077] S3, apply CHHO algorithm to adaptively optimize VMD parameters to produce the best parameter combination [K, a].

[0078] The HHO algorithm divides the hunting behavior of the eagle into three stages: global exploration stage, transition stage from global exploration to local development, and local development stage, during which four distinct hunting strategies are demonstrated. The CHHO algorithm optimizes HHO by introducing chaotic mapping, exponential decay factor and Gaussian variation.

[0079] Global exploration stage: In the HHO algorithm, each Harris hawk is regarded as a candidate solution, and in each iteration, the optimal solution is regarded as the target prey position. Harris eagles randomly perch at different positions and wait to use two different strategies to locate prey. The position update of the Harris eagle at this stage is as follows:

[0080]

[0081] Where X(t+1) represents the position of the Harris eagle after the tth update, X rand (t) represents the position of a random individual in the eagle group, and Xrabbit (t) denotes the position of the current best individual, X m (t) denotes the average energy of the current Harris hawks population, ub and lb denote the upper and lower bounds of the search space, r1, r2, r3, r4 and q are random numbers in the range of (0, 1), r3 is a contraction factor that enhances the randomness of the rules, and r4 is a value that is assumed to be close to 1. When q ≥ 0.5, the hawks randomly perch on tall trees (random positions within the population range), and when q < 0.5, each hawk moves according to the positions of other members and prey.

[0082] Transition phase from global exploration to local exploitation: The HHO algorithm transitions from global exploration to local exploitation based on the escape energy of the prey. When the prey attempts to escape, its energy is significantly depleted. Let E denote the escape energy of the prey, and E0 denote its initial energy state, which varies randomly within the range of (-1, 1). The specific formula describing this phenomenon is as follows:

[0083]

[0084] where t denotes the current iteration number, and T denotes the maximum number of iterations.

[0085] Exploitation phase: In the exploitation phase, the algorithm randomly generates a number between 0 and 1, and the value of r, together with the parameter E, determines the position update mechanism of the Harris hawks. This update process is divided into four different methods, and the update methods are as follows:

[0086] 1) When r ≥ 0.5 and |E| ≥ 0.5, the position update formula for the Harris hawks is:

[0087] X(t+1) = X rabbit (t) - X(t) - E|JX rabbit (t) - X(t)|

[0088] where J is a random number in the interval (0, 2), and X rabbit (t) denotes the position of the current best individual, X(t) denotes the position of the current hawk.

[0089] 2) When r ≥ 0.5 and |E| < 0.5, the position update formula for the Harris hawks is:

[0090] X(t+1) = X rabbit (t) - E|X rabbit -X(t)|

[0091] 3) When r < 0.5 and |E| ≥ 0.5, the position update formula for the Harris hawks is:

[0092]

[0093] where D represents the dimension, S is a D-dimensional random vector, LF is the Levy flight function expression, μ and v are random values in the interval (0, 1), β is a constant with a value of 1.5, F(.) is the fitness function, σ represents the scale factor for controlling the size of the Levy flight step, and Γ(.) represents the gamma function.

[0094] 4) When r < 0.5 and |E| < 0.5, the position update formula of the Harris hawk is:

[0095]

[0096] According to the escape energy E of the prey and the random factors q and r, the HHO algorithm formulates a plurality of position update strategies, and finally finds the optimal solution in the search space by repeatedly adjusting the position of the hawk.

[0097] The HHO mainly changes the escape energy factor through linear decay, which will lead to an imbalance between exploration and development, and cannot accurately represent the actual multi-round hunting and escape process between the hawk and the prey, because |E| must be less than 1 in the later iteration, only local search is performed, so the search is not global, and if the initial population is close to the local optimum, the algorithm may be trapped in the local optimum in the later period and cannot escape. A nonlinear decay method can be used to dynamically adjust the algorithm parameters. Therefore, the initial escape energy E0 is updated by using a chaotic mapping in the present application, which helps the algorithm to break the fixed search pattern in the exploration stage.

[0098] The chaotic mapping is beneficial to the optimization algorithm to maintain population diversity, enable them to escape from the local optimum, and improve the global search performance, and the expression is as follows:

[0099] x n+1 =un n (1-x n ),u∈[0,4],x n ∈(0,1)

[0100] where x n represents the proportion of the population at the nth moment to the maximum possible population size, x n+1 represents the population proportion at the n+1 moment, x is a random number between 0 and 1, and u represents a control parameter that determines the behavior of the chaotic mapping.

[0101] The chaotic mapping is used to generate chaotic values for the initial energy E0 of the hawk, and the algorithm is given with chaos to help break the fixed search pattern in the global search stage, and the update formula of the initial energy is as follows:

[0102] E0=x n+1 =ux n (1-x n), x n ∈(0, 1)

[0103] The update formula of escape energy is as follows:

[0104]

[0105] Wherein, sign is a random value of -1 or 1, t represents the current iteration number, and T represents the maximum iteration number.

[0106] The change of escape energy E with iteration number in two runs of the HHO algorithm is as shown in Figure 1, and the change of escape energy E with iteration number in two runs of the CHHO algorithm is as shown in Figure 2. Figure 3 Figure 4 In the later iteration process of the CHHO algorithm, the value |E| fluctuates around 1, instead of being strictly kept below 1, realizing the balance transition between exploration and development.

[0107] Meanwhile, the present application uses an exponential decay factor for updating, dynamically adjusts the algorithm parameters by introducing an exponential decay factor, improves the balance between exploration and development, and thus ensures sufficient population diversity in the global exploration stage.

[0108] The exponential decay weight is calculated as follows:

[0109] ω i =e -λ·i

[0110] Wherein, ω i is the weight of the i-th data point, λ is the decay coefficient, and i is the time interval.

[0111] Further, the present application also increases population diversity by introducing Gaussian mutation to prevent the algorithm from falling into local optimum.Gaussian mutation is an improvement to genetic algorithm, aiming to replace the original parameter value with a random number drawn from a normal distribution with mean μ and variance σ 2 The expression is as follows:

[0112] X mutated (t+1)=X(t)(1+N(μ,σ2))

[0113] Wherein, X mutated (t+1) represents the position of the mutated individual, X(t) represents the position of the individual before mutation, and N represents a Gaussian distribution with mean μ and variance σ 2

[0114] ​Gaussian variation is randomly applied to some individuals to cause slight movement of their positions, enhance the diversity of the population and avoid falling into local optimum, and the population position updating formula is as follows:

[0115]

[0116] Wherein, rand is a random number between 0 and 1, p represents the mutation probability, X(t) represents the current population position, X(t+1) represents the population position after iteration, and f(.) represents the fitness function.

[0117] In implementation, the process of determining the optimal parameter combination of the mode number and the penalty factor of VMD by applying the CHHO algorithm comprises the following steps:

[0118] Step 1, setting the initial parameters of the CHHO algorithm;

[0119] Step 2, decomposing the early fault signal by VMD;

[0120] Step 3, identifying the optimal individual;

[0121] Step 4, restoring the escape energy of the prey;

[0122] Step 5, judging whether the escape energy is less than or equal to 1, if less than or equal to 1, entering the development stage, and if greater than 1, entering the exploration stage;

[0123] Step 6, judging whether the maximum iteration number is reached;

[0124] Step 7, outputting K and alpha when the maximum iteration number is reached, and repeating steps 2 to 6 when the maximum iteration number is not reached.

[0125] The smaller energy entropy in the bearing signal containing faults indicates that the vibration or impact signal caused by the fault is significant and concentrated, resulting in the enhancement of the periodic signal and making the fault feature more obvious. Therefore, the average minimum energy entropy is adopted as the iteration index in the optimization process, and the calculation formula is as follows:

[0126]

[0127] Wherein, u k is the kth IMF component, H mean (u k ) is the average energy entropy of the component u k ; P k represents the proportion of the kth component u k to the total energy, E k is the energy of each component, E is the sum of the energies of the K components, and E i is the energy of the i th component.

[0128] The CHHO-VMD algorithm is used to extract early fault features from the vibration signal of the outer ring rolling bearing. In the VMD parameter optimization process, the convergence curve of the average energy entropy with respect to the number of iterations is as shown in Figure 5 .

[0129] After CHHO optimization, the optimal parameter combination [k, a] is [3, 400], which makes the minimum value of the average energy entropy 7.4027.

[0130] S4, decompose the fault signal using VMD with parameter optimization and extract its IMF components.

[0131] Using these optimal parameter combinations for VMD decomposition, the time-domain graph and frequency spectrum of the rolling bearing are obtained. The time-domain graph of the rolling bearing vibration signal decomposed by the CHHO-VMD algorithm is as shown in Figure 6 , and the frequency spectrum is as shown in Figure 7 .

[0132] S5, select IMF components to reconstruct the fault signal based on kurtosis and correlation coefficient.

[0133] The kurtosis calculation formula is as follows:

[0134]

[0135] Where μ and σ represent the mean and standard deviation of the signal, E(·) is the expected value of the signal, and x represents the value of the signal.

[0136] The calculation formula of the correlation coefficient is as follows:

[0137]

[0138] Where θ i represents the value of the i-th data point in the IMF component, represents the mean of the IMF component, δ i represents the value of the i-th data point in the original signal, represents the mean value of the original signal.

[0139] The kurtosis and correlation coefficient values of each IMF component are shown in Table 2.

[0140] Table 2: Kurtosis and correlation coefficient values of each IMF component

[0141] IMF component IMF1 IMF2 IMF3 Kurtosis value 2.4627 5.2053 4.0739 Correlation coefficient 0.4261 0.5473 0.7746

[0142] Select IMF with kurtosis value greater than 3 and mutual correlation coefficient greater than 0.45 for signal reconstruction. For the outer ring result, select IMF2 and IMF3 for signal reconstruction. The envelope spectrum of the reconstructed signal is as shown in Figure 8 .

[0143] S6, the envelope demodulation is applied to extract the fault characteristic frequency of the rolling bearing.

[0144] As shown in Figure 8 the characteristic frequency of the outer ring rolling bearing is 230 Hz, which is very close to the theoretical value of 236 Hz, indicating that the envelope spectrum successfully extracts the fault characteristic frequency of the early signal in the outer ring.

[0145] As a comparison, PSO-VMD and ACO-VMD algorithms are respectively used to optimize the VMD parameters, and the time required by different algorithms is shown in Table 3.

[0146] Table 3: Time required for VMD parameter optimization by different optimization algorithms

[0147]

[0148] From Table 3, it can be seen that the CHHO-VMD algorithm of the present application converges faster and more accurately than the PSO-VMD and ACO-VMD algorithms.

[0149] Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions recorded in the foregoing embodiments or make equivalent replacements to some of the technical features, and any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for extracting early fault features of rolling bearings based on CHHO-VMD, characterized in that: The method comprises the following steps: S1, obtaining a bearing original vibration signal; S2, identifying an early fault signal in the original vibration signal; S3, applying a CHHO algorithm to adaptively optimize VMD parameters to generate an optimal parameter combination [K, a]; S4, decomposing the fault signal by using the parameter-optimized VMD to extract an IMF component thereof; S5, selecting the IMF component to reconstruct the fault signal based on kurtosis and a correlation coefficient; S6, applying envelope demodulation to extract a fault characteristic frequency of the rolling bearing; In the S3 step, the CHHO algorithm introduces a chaotic mapping to generate chaotic values for initial energy, introduces an exponential decay factor to dynamically adjust algorithm parameters, and introduces a Gaussian variation to increase population diversity. The chaotic mapping is as follows: x n+1 = ux n (1 - x n ), u e [0, 4], x n e (0, 1) where x n represents the proportion of the population at the nth time to the maximum possible population size, x n+1 represents the population proportion at the n+1th time, u represents the control parameter, and x is a random number between 0 and 1; The Gaussian variation is as follows: X mutated (t+1) = X(t)(1 + N(μ, σ 2 )) where X mutated (t + 1) denotes the position of the mutated individual, X(t) denotes the position of the pre-mutated individual, N denotes a Gaussian distribution with mean μ and variance σ 2 . In the generation of chaotic values for initial energy, the update formula of the initial energy is as follows: E0= x n+1 = ux n (1-x n ), x n ∈(0,1) The update formula of the escape energy is as follows: Wherein, sign is a random value of -1 or 1, t represents the current iteration number, and T represents the maximum iteration number; in the dynamic adjustment of algorithm parameters by the exponential decay factor, the exponential decay weight is calculated as follows: ω i = e -λ·i where ω i is the weight of the i-th data point, λ is the decay coefficient, and i is the time interval. In the S3 step, the average minimum energy entropy is used as an iteration index in the optimization process, and the calculation formula is as follows: wherein u k is the k-th IMF component, H mean (u k ) is the average energy entropy of the component u k ; P k denotes the proportion of the k-th component u k to the total energy, E k is the energy of each component, E is the sum of the energies of the K components, and E i is the energy of the i-th component.

2. The CHHO-VMD based rolling bearing incipient fault feature extraction method according to claim 1, characterized in that: In the Gaussian variation to increase population diversity, the population position update formula is as follows: Wherein, rand is a random number between 0 and 1, p represents a mutation probability, X(t) represents a current population position, X(t+1) represents a population position after iteration, and f(.) represents a fitness function.

3. The CHHO-VMD based rolling bearing incipient fault feature extraction method according to claim 1, characterized in that: The S3 step specifically comprises the following steps: Step 1, setting initial parameters of the CHHO algorithm; Step 2, decomposing the early fault signal by VMD; Step 3, identifying an optimal individual; Step 4, restoring the escape energy of the prey; Step 5, judging whether the escape energy is less than or equal to 1, and if less than or equal to 1, entering the development stage, and if greater than 1, entering the exploration stage; Step 6, judging whether the maximum iteration number is reached; Step 7, outputting K and a when the maximum iteration number is reached, and repeating steps 2 to 6 when the maximum iteration number is not reached.

4. The CHHO-VMD based rolling bearing incipient fault feature extraction method according to claim 1, characterized in that: In the S5 step, the kurtosis calculation formula is as follows: Wherein, μ and σ respectively represent the mean and standard deviation of the signal, E(·) is the expected value of the signal, and x represents the value of the signal; The calculation formula of the correlation coefficient is as follows: where θ i denotes the value of the i-th data point in the IMF component, denotes the mean value of the IMF component, δ i denotes the value of the i-th data point in the original signal, denotes the mean value of the original signal.

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