Adaptive fractional order stochastic resonance based bearing fault diagnosis method

Abstract

The present application relates to the technical field of bearing fault signal detection, and particularly relates to a bearing fault diagnosis method based on adaptive fractional order stochastic resonance, which introduces a time delay feedback term into a fractional order stochastic resonance system in a stochastic resonance detection method, finds the structural optimal parameters of the stochastic resonance system by improving a cuckoo algorithm, substitutes the structural optimal parameters into a time delay fractional order biased nonlinear overdamped stochastic resonance system, and finally extracts rolling bearing fault features and detects fault feature frequencies through time-frequency domain analysis on the signal processed by the stochastic resonance system, so that bearing fault diagnosis is realized through comparison. Compared with existing diagnosis methods based on stochastic resonance systems, the present application has a simple model, fewer algorithm parameters, fast convergence speed, and can accurately and efficiently detect bearing fault signals.

Description

Technical Field

[0001] This invention relates to the field of bearing fault signal detection technology, and specifically to a bearing fault diagnosis method based on adaptive fractional-order random resonance. Background Technology

[0002] Rotating equipment is common in industrial settings. Current challenges in diagnosing faults in rotating equipment include the difficulty in collecting a large number of abnormal samples in actual working environments; measurement data is significantly affected by environmental interference and noise; and early faults are difficult to identify. Stochastic resonance methods based on nonlinear systems are important for extracting vibration characteristic information; however, current research mainly focuses on nonlinear system potential models and noise-driven approaches, with limited research on adaptive stochastic resonance methods with time-delay feedback terms.

[0003] Stochastic resonance (SR) is a signal processing method developed based on nonlinear dynamics and statistical physics, which enhances weak feature information by utilizing noise energy. Instead of direct noise reduction, SR achieves optimal system output through the best matching of the signal, nonlinear system, and noise, converting noise energy into signal energy to enhance or identify weak feature information in a noisy environment. However, traditional SR methods suffer from drawbacks such as difficulty in parameter selection and limited applicability. Summary of the Invention

[0004] The purpose of this invention is to provide a bearing fault diagnosis method based on adaptive fractional-order stochastic resonance, which aims to solve the technical problems of existing bearing fault diagnosis methods based on stochastic resonance, such as complex models, large number of parameters, and slow convergence speed.

[0005] To achieve the above objectives, this invention provides a bearing fault diagnosis method based on adaptive fractional-order stochastic resonance, comprising the following steps:

[0006] Collect a dataset of fault vibration signals from rolling bearings;

[0007] Data preprocessing to obtain the envelope signal;

[0008] The envelope signal is frequency compressed using frequency shift scaling transformation, and the recovered signal is a variable-scale demodulated signal.

[0009] Processing of time-delay fractional-order biased nonlinear overdamped stochastic resonance systems;

[0010] When using the improved Cuckoo Algorithm RACS to optimize the parameters of the delayed fractional-order biased nonlinear overdamped stochastic resonance system;

[0011] The optimized parameter combination is substituted into the time-delay fractional-order biased nonlinear overdamped stochastic resonance system.

[0012] The variable-scale demodulated signal is input into the constructed time-delay fractional-order biased nonlinear overdamped stochastic resonance system to obtain the output signal;

[0013] Process the output signal to obtain the characteristic frequency;

[0014] By comparing the characteristic frequency with the theoretical failure frequency of the rolling bearing, the failure state of the inner ring of the rolling bearing is determined.

[0015] The fault vibration signal dataset of the rolling bearing is a data sample set of the same working condition of the rolling bearing. Specifically, it is the bearing vibration data of the same model, rotational frequency and sampling frequency under the working condition of inner ring failure of the rolling bearing collected by a vibration acceleration sensor.

[0016] Specifically, the data preprocessing process involves demodulating the original signal using the Hilbert transform algorithm.

[0017] In the process of frequency compression and recovery of the envelope signal using frequency-shift scaling transformation to obtain a variable-scale demodulated signal, the envelope signal is first frequency-shifted, causing the signal bandwidth to shift to the left, thereby shifting the characteristic frequency components of the signal into the low-frequency region. Then, the frequency-shifted signal is linearly compressed so that the characteristic frequency of the signal meets the small parameter requirements of random resonance. Next, classical random resonance is performed on the signal to enhance the frequency components in the transformed signal that correspond to the characteristic frequency components. Finally, the frequency of the random resonance output signal is recovered to obtain the variable-scale demodulated signal with enhanced characteristic frequency components.

[0018] The time-delay fractional-order biased nonlinear overdamped stochastic resonance system is a long-memory system formed by introducing a time-delay feedback term into the stochastic resonance system. By introducing the time-delay term, historical information is introduced to modulate the system.

[0019] The improved Cuckoo Algorithm RACS modifies the global search equation of the traditional Cuckoo Algorithm, adopts a sorting-based vector selection method, and uses a combined crossover strategy with parameter adaptation based on the random walking mode in the Levy flight of the traditional Cuckoo Algorithm CS.

[0020] The improved Cuckoo Algorithm RACS also proposes a replacement strategy that updates unimproved solutions at predetermined intervals by utilizing useful information from discarded solutions stored in external archives.

[0021] Specifically, the process of processing the output signal and obtaining the characteristic frequency involves performing a Fourier transform on the output signal to obtain the corresponding spectrum, capturing the frequency components with obvious peaks in the spectrum, and obtaining the characteristic frequency.

[0022] The fault states of the inner ring of the rolling bearing include two states: normal operation and fault existence.

[0023] This invention provides a bearing fault diagnosis method based on adaptive fractional-order stochastic resonance. It introduces a time-delay feedback term into the fractional-order stochastic resonance system in the stochastic resonance detection method. An improved cuckoo algorithm is used to find the optimal structural parameters of the stochastic resonance system, which are then substituted into the time-delay fractional-order biased nonlinear overdamped stochastic resonance system. Finally, the processed signal from the stochastic resonance system is analyzed in the time-frequency domain to extract rolling bearing fault features, detect the fault characteristic frequencies, and achieve bearing fault diagnosis through comparison. Compared with existing stochastic resonance system-based diagnostic methods, this invention has a simpler model, fewer algorithm parameters, faster convergence speed, and can accurately and efficiently detect bearing fault signals. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a flowchart illustrating a bearing fault diagnosis method based on adaptive fractional-order stochastic resonance according to the present invention.

[0026] Figure 2 This is a flowchart of the improved Cuckoo Optimization Algorithm RACS of the present invention.

[0027] Figure 3 This is a time-domain waveform diagram of the original signal of the inner ring of the faulty bearing on the MFS-MG test bench, according to an embodiment of the present invention.

[0028] Figure 4 This is a spectrum diagram of the original signal of the inner ring of the faulty bearing on the MFS-MG test bench, according to an embodiment of the present invention.

[0029] Figure 5 This is a time-domain plot of the random resonance extraction results of the inner ring fault in an embodiment of the present invention.

[0030] Figure 6 This is a spectrum of the random resonance extraction result of the inner ring fault in an embodiment of the present invention. Detailed Implementation

[0031] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0032] Please see Figure 1 This invention provides a bearing fault diagnosis method based on adaptive fractional-order stochastic resonance, comprising the following steps:

[0033] S1: Collect the fault vibration signal dataset of rolling bearings;

[0034] S2: Data preprocessing to obtain the envelope signal;

[0035] S3: The envelope signal is frequency compressed using frequency shift scaling transformation, and the recovered signal is obtained as a variable-scale demodulated signal.

[0036] S4: Processing of time-delay fractional-order biased nonlinear overdamped stochastic resonance systems;

[0037] S5: Parameters of the fractional-order biased nonlinear overdamped stochastic resonance system when optimized using the improved Cuckoo Algorithm RACS;

[0038] S6: Substitute the optimized parameter combination into the time-delay fractional-order biased nonlinear overdamped stochastic resonance system;

[0039] S7: Input the variable-scale demodulated signal into the constructed time-delay fractional-order biased nonlinear overdamped stochastic resonance system to obtain the output signal;

[0040] S8: Process the output signal to obtain the characteristic frequency;

[0041] S9: Compare the characteristic frequency with the theoretical failure frequency of the rolling bearing to determine the failure state of the inner ring of the rolling bearing.

[0042] Specifically, in step S1, during the acquisition of the rolling bearing fault vibration signal dataset, sensors are positioned at the required locations on the target bearing to collect vibration signals. The rolling bearing fault vibration signal dataset is a data sample set of rolling bearings under the same operating condition; firstly, vibration acceleration sensors are used to collect bearing vibration data under the same operating condition of inner ring fault in rolling bearings of the same model, rotational frequency, and sampling frequency. That is, the raw vibration signals of the bearing are collected and stored in the computer.

[0043] The formula for the characteristic frequency of a rolling bearing is as follows:

[0044]

[0045] Where z represents the number of rolling elements, d represents the diameter of the rolling elements, D represents the pitch circle diameter, θ represents the contact angle, and f r Indicates frequency conversion, f 内圈 The inner circle characteristic frequency.

[0046] Step S2: Data Preprocessing

[0047] The Hilbert transform algorithm is used to demodulate the original signal to obtain the envelope signal.

[0048] Step S3: The envelope signal is frequency compressed using frequency shift scaling transformation, and the recovered signal is obtained by scaling demodulation.

[0049] By performing variable-scale frequency transformation on the envelope signal, it is made to meet the adiabatic approximation theoretical requirements of a stochastic resonance system. A suitable modulation frequency fc and compression ratio R are determined based on the theoretical fault characteristic frequencies of the imported rolling bearing fault signal datasets.

[0050] The envelope signal demodulated by the Hilbert transform algorithm described in step S2 is frequency-shifted, causing the overall signal bandwidth to shift to the left, thereby shifting the characteristic frequency components of the signal into the low-frequency region. Then, the frequency-shifted signal is linearly compressed (compression ratio R) to ensure that the signal's characteristic frequencies meet the small parameter requirements of stochastic resonance. Next, classical stochastic resonance is applied to the signal to enhance the frequency components corresponding to the characteristic frequency components in the transformed signal. Finally, frequency recovery (scale transformation recovery and frequency shift recovery) is performed on the stochastic resonance output signal to obtain the scaled demodulated signal with enhanced characteristic frequency components.

[0051] Step S4: Processing of time-delay fractional-order biased nonlinear overdamped stochastic resonance systems;

[0052] The output of the classical stochastic resonance model is determined by the previous output. By adding a long memory term to the negative feedback loop of the stochastic resonance, the system output is determined by multiple preceding outputs, thereby enhancing weak signals. Introducing a time-delay feedback term into the fractional-order stochastic resonance equation, the potential function model equation and Langevin equation for the time-delay fractional-order biased nonlinear overdamped stochastic resonance system (TFODF) are as follows.

[0053]

[0054]

[0055] In the formula, U(x) is the potential function of the stochastic resonance model; x(t) is the system output; c and b are system parameters, both of which are positive real numbers, and α is a fractional-order value. Among the parameters introduced in the time delay feedback term, β represents the feedback strength; τ represents the time delay; s(t) is a periodic signal; and ε(t) is Gaussian white noise.

[0056] Classical stochastic resonance systems are short-memory systems, where the current output depends only on the previous historical output. To address the limitation of traditional stochastic resonance systems that do not consider the influence of historical information, some researchers have introduced a time-delay feedback term into the stochastic resonance system, proposing a long-memory system. The time-delay feedback stochastic resonance system incorporates historical information by introducing a time delay term, modulating the system and improving its detection performance to some extent. The time-delay feedback stochastic resonance system can effectively remember historical information and react accordingly.

[0057] Step S5: Optimize the parameters of the fractional-order biased nonlinear overdamped stochastic resonance system using the improved Cuckoo Algorithm RACS;

[0058] The flowchart of the improved Cuckoo Optimization Algorithm RACS is as follows: Figure 2 As shown, the specific principle is as follows:

[0059] Generally, in nature, good species or individuals always contain good information, making them more likely to guide other individuals. This indicates that the probability of an individual being selected is proportional to its ranking in terms of the amount of useful information it contains. Based on this principle, the improved cuckoo algorithm introduces a novel ranking-based mutation strategy into the traditional cuckoo algorithm. This ranking-based mutation strategy modifies the global search equation of the traditional cuckoo algorithm and employs a ranking-based vector selection method to make the most efficient use of the useful information of the entire population. Instead of selecting vectors with equal probability, some parent vectors in the global search equation are selected proportionally based on their ranking in the current population. The higher the ranking of a parent vector, the greater the chance of generating new solutions. In this case, the parameter-finding ability of the cuckoo algorithm can be significantly improved without reducing its search capability.

[0060] Furthermore, building upon the random walk approach in the Lévy flight of the traditional Cuckoo Algorithm (CS), RACS employs a parameter-adaptive assemblage crossover strategy. This strategy preserves some good elements of the current solution, with the assemblage rate generated independently according to a Gaussian distribution, which helps maintain population diversity.

[0061] Furthermore, the improved Cuckoo Algorithm RACS proposes a replacement strategy that utilizes useful information from discarded solutions stored in an external archive to update unimproved solutions at predetermined intervals. This replacement strategy is easy to implement and can effectively accelerate the algorithm's convergence speed in the later stages without sacrificing population diversity in the early stages.

[0062] Based on these advantages, the proposed improved Cuckoo Algorithm RACS achieves a good balance between the exploration and development levels, thereby improving solution quality, accelerating convergence speed, and enhancing robustness to different optimization problems. Furthermore, the improved Cuckoo Algorithm RACS does not significantly increase the overall complexity of the traditional Cuckoo Algorithm CS.

[0063] An adaptive stochastic resonance system based on an improved cuckoo algorithm is proposed, which involves the improved cuckoo algorithm to adaptively adjust parameters α and c.

[0064] (1) Initialize parameters: set the number of bird nests, search dimension, probability of bird nests being found, range of values ​​for parameters α and c, and termination condition for maximum number of iterations.

[0065] (2) NP number of bird nests are randomly generated. The two search dimensions corresponding to the bird nests represent the optimization parameters α and c, respectively.

[0066] Calculate the fitness value of the initial nest, update the optimal nest location and the optimal solution through a sorting mutation strategy, and select the nest with the best fitness [c, α].

[0067] (3) Update the nest positions using the improved global search equation of the improved cuckoo algorithm. The best nest is retained, and the cuckoo uses formula (3) to update the non-best nests. The nests with poor fitness before the replacement position update are compared, and after obtaining the latest set of nests, the cuckoo eggs are placed in them.

[0068] The three randomly selected individuals, Xr1, Xr2, and Xr3, are chosen using a sorting-based vector selection method. The selection is based on a proportional distribution of their rank within the current population, with higher-ranked solutions having a greater chance of being selected.

[0069] The improved global search equation is as follows.

[0070]

[0071] In the formula, It represents the position of the i-th bird's nest in generation t. It is the tth generation. A new interpretation. This represents randomly selecting the top 100% of individuals from the current population. ω is a uniformly generated random number in the range [0,1]. r1, r2, r3 represent three distinct integers randomly selected from [1,NP]. NP represents the population size. α0 is a constant. φ is a random number extracted from a normal distribution with a mean of 0 and a standard deviation of 1. μ and v are two random numbers generated from a normal distribution, i.e. in, λ is a fixed parameter for Levi's flight.

[0072] The Improved Cuckoo Algorithm (RACS) improves the global search equation compared to the traditional Cuckoo Algorithm (CS) by using three randomly selected individuals. An update equation is introduced to enable the algorithm to explore more within the entire search space while maintaining population diversity.

[0073] (4) Perform a local search by combining crossover operations and replacement strategies.

[0074] During the iterative update phase of the local search, after the location of the new generation of nests is updated, a random number R is generated to represent the host bird's discovery of the cuckoo egg. This number is then used based on the set discovery probability P. a =0.25, using a randomly generated value R that follows a uniform distribution of 0-1 and the probability P that the bird's nest owner found it. a In comparison, if the cuckoo's egg is discovered by the host (R>P) a The cuckoo uses equation (4) to search for a new nest, obtains the latest set of nest locations, and records the current best nest. If R < P a If the nest position does not change, the nest with the highest fitness [c, α] is obtained for subsequent comparison. If the requirement is met, proceed to the next step; otherwise, return to the previous step (3) for updating.

[0075] The formula for the random walk in local search is as follows (4).

[0076]

[0077] In the formula, Based on the current individual A new solution is obtained; r1 and r2 are two positions randomly generated from [1, NP]; r and ∈ are two random numbers uniformly distributed in the range [0, 1]; H represents the Heaviside function; P a This indicates the probability that the cuckoo's egg will be found by the nest's owner.

[0078] To address the problem of traditional Cuckoo Algorithm CS getting trapped in local optima, the improved Cuckoo Algorithm RACS employs a parameter-adaptive combined crossover operation to avoid solutions being attracted to non-optimal solutions (i.e., those solutions with higher rankings but far from the global optimum), thus effectively maintaining good solution values. The formula is as follows.

[0079]

[0080] It is the j-th part of the i-th solution of the improved global search equation formula (3); This is the next test vector; j rand Let represent an integer randomly selected from [1, D], where D is the dimension of the population search. This ensures that at least one part of the trial vector is derived from the mutation vector. Inheritance in formula (6); Represents the crossover rate, and is based on the average value μ. CR It is generated independently of a Gaussian distribution with a standard deviation of 0.1.

[0081]

[0082] The value is restricted to the range [0,1], and if it exceeds [0,1], it is truncated to 0 or 1. All successful crossover probabilities are stored in the set S. CR The average value μ CR It is initialized to 0.5 and updated by formulas (7) and (8).

[0083] μ CR =w·μ CR +(1-w)·mean A (S CR (7)

[0084] w = 0.8 + 0.2 * r(0,1) (8)

[0085] In the formula, w is a weighting factor randomly generated in [0.8,1], and mean A (·) represents the arithmetic mean.

[0086] The Improved Cuckoo Algorithm (RACS) proposes a replacement strategy compared to the traditional Cuckoo Algorithm (CS). This strategy utilizes useful information from discarded solutions stored in an external archive to update unimproved solutions at predetermined intervals. Specifically, if the cuckoo cannot find a better nest within the predetermined interval, the current nest is discarded and replaced by the best discarded nest stored in the external archive. When implementing the replacement strategy, the stall number for each individual is recorded, denoted as trial(i) (i = 1, 2, ..., NP). Furthermore, worse solutions, denoted as A, are stored in the external archive. The archive is initially empty and then updated by adding solutions that failed in the selection operation. If the archive size exceeds a predefined value, some solutions are randomly deleted from the archive.

[0087] (5) Iterate through the process (3)-(4) to find the best-fit nest location. The signal-to-noise ratio (SNR) is used as the fitness function.

[0088] The signal-to-noise ratio (SNR) is defined by the following formula.

[0089]

[0090] In the formula, f is the fault characteristic frequency; P S (f) represents the power at frequency f; P T (f) represents the local total power; k represents the position of frequency f in the power spectrum; X(k) represents the discrete Fourier transform of the time series; j is the value for calculating the local power P. T The selected signal length.

[0091] (6) Determine if the termination condition is met: If the iteration termination condition is met, then terminate the loop.

[0092] (7) The iteration terminates, and the parameter combination c and α corresponding to the optimal bird's nest position are output.

[0093] Step S6: Substitute the optimized parameter combination into the time-delay fractional-order biased nonlinear overdamped stochastic resonance system; the numerical solution algorithm of the Langevin equation for the time-delay fractional-order biased nonlinear overdamped stochastic resonance system is shown in formula (10).

[0094]

[0095] Where h is the sampling step size. y i It is the output signal, x i It is the input signal.

[0096] Step S7: Input the variable-scale demodulated signal obtained in step S3 into the constructed time-delay fractional-order biased nonlinear overdamped stochastic resonance system to obtain the output signal.

[0097] In step S8, a Fourier transform is performed on the output signal to obtain its spectrum, and the frequency components with obvious peaks in the spectrum are captured to obtain the characteristic frequencies.

[0098] Step S9: By comparing the characteristic frequency with the theoretical fault frequency of the rolling bearing, the fault status of the inner ring of the rolling bearing is finally determined, including two states: normal operation and fault existence.

[0099] Furthermore, the present invention provides specific embodiments for further explanation:

[0100] The dataset used in this embodiment is a rolling bearing feature dataset, which was collected using the Mechanical Comprehensive Fault Simulation Experiment Platform (MFS-MG) manufactured by Spectra Quest Corporation, USA. The bearing vibration data under inner ring fault conditions were collected at a sampling frequency of 12.8 kHz. Figure 3 and Figure 4 The images show the time-domain waveform and spectrum of the noisy input signal of the inner ring of the faulty bearing on the MFS-MG experimental platform.

[0101] In this example, the LW149536 piezoelectric accelerometer is used. The performance specifications of this accelerometer are shown in Table 1.

[0102] Table 1. Characteristic Parameters of LW149536 Piezoelectric Accelerometer

[0103]

[0104] The bearing specifications used in this example are shown in Table 2. The bearings used are all bearings with inner ring failures, and their vibration signals and spectra are as follows: Figure 3 and Figure 4 As shown.

[0105] Table 2 Specifications of ER-12K Bearings

[0106]

[0107] Based on the above parameters and formulas, the characteristic frequency of the inner ring of the rolling bearing is 147.8 Hz.

[0108] The characteristic frequency is obtained after processing through the execution steps of this invention. Figure 5 and Figure 6 The images show the time-domain waveform and spectrum of the noisy output signal of the inner ring of the faulty bearing on the MFS-MG experimental platform after processing by the time-delay fractional-order biased nonlinear overdamped adaptive stochastic resonance system.

[0109] Collect vibration signals from inner ring faults, such as... Figure 3 and Figure 4As shown, the motor speed is 1797 r / min, the sampling frequency is 12 kHz, and the theoretical fault characteristic frequency fo can be calculated to be 147.8 Hz based on the bearing parameters. Due to the influence of noise, the impact component is submerged in the noise and is difficult to identify directly. Traditional FFT spectrum and Hibernate envelope spectrum are difficult to extract fault characteristic frequency information, which brings difficulties to fault identification.

[0110] The method of this invention is used to extract weak fault features, and the steps are as follows:

[0111] The collected inner ring fault vibration signal S(x) is demodulated using the Hilbert transform algorithm to obtain the envelope signal S'(x).

[0112] Based on the inner ring fault signal, the frequency scaling coefficient R is set as needed. Frequency compression of the envelope signal S(x) is then performed using frequency shift scaling. If the signal sampling frequency is fs, then the compressed sampling frequency is: To identify weak periodic signals, the actual sampling frequency fs should be more than 50 times the signal frequency f. In this embodiment, the frequency scaling coefficient is set to R = 150 and the modulation frequency fc = 147.78 Hz, so that Δf = fo - fc = 147.8 - 147.78 = 0.02 Hz satisfies the small parameter constraint condition of random resonance.

[0113] The frequency-compressed signal is fed into the time-delay fractional-order bias nonlinear overdamped stochastic resonance system optimized by the improved Cuckoo Algorithm RACS with signal-to-noise ratio as the fitness function. When the stochastic resonance state is reached, the system output signal after small parameter transformation needs to be frequency restored to obtain the variable-scale demodulated signal.

[0114] Let the frequency of the peak value of the output signal spectrum of the random resonance system be fa, then the recovered frequency satisfies the following equation:

[0115] f = R * fa

[0116] according to Figure 6 To obtain the spectrum of the noisy output signal of the inner ring of the faulty bearing on the MFS-MG test bench after processing by the time-delay fractional-order biased nonlinear overdamped adaptive stochastic resonance system, the frequency corresponding to the maximum signal-to-noise ratio of the output is found, and compared with the theoretical fault frequency of the rolling bearing to determine the fault state of the inner ring of the rolling bearing.

[0117] The above description discloses only one preferred embodiment of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A bearing fault diagnosis method based on adaptive fractional-order stochastic resonance, characterized in that, Includes the following steps: Collect a dataset of fault vibration signals from rolling bearings; Data preprocessing to obtain the envelope signal; The envelope signal is frequency compressed using frequency shift scaling transformation, and the recovered signal is a variable-scale demodulated signal. Processing of time-delay fractional-order biased nonlinear overdamped stochastic resonance systems; By introducing a time-delay feedback term into the fractional-order stochastic resonance equation, the potential function model equation and the Langevin equation for the time-delayed fractional-order biased nonlinear overdamped stochastic resonance system are as follows: In the formula, It is the potential function of the stochastic resonance model; This is system output; , These are system parameters, and both are positive real numbers. For fractional-order values; parameters introduced into the time delay feedback term, Indicates the intensity of feedback; Indicates the duration; It is a periodic signal; It is Gaussian white noise; The parameters of the time-delay fractional-order biased nonlinear overdamped stochastic resonance system were optimized using the improved Cuckoo Algorithm RACS. The optimized parameter combination is substituted into the time-delay fractional-order biased nonlinear overdamped stochastic resonance system. The variable-scale demodulated signal is input into the constructed time-delay fractional-order biased nonlinear overdamped stochastic resonance system to obtain the output signal; Process the output signal to obtain the characteristic frequency; By comparing the characteristic frequency with the theoretical failure frequency of the rolling bearing, the failure state of the inner ring of the rolling bearing is determined.

2. The bearing fault diagnosis method based on adaptive fractional-order stochastic resonance as described in claim 1, characterized in that, The fault vibration signal dataset of the rolling bearing is a data sample set of the same working condition of the rolling bearing. Specifically, it is the bearing vibration data of the same model, rotation frequency and sampling frequency under the working condition of inner ring failure of the rolling bearing collected by vibration acceleration sensor.

3. The bearing fault diagnosis method based on adaptive fractional-order stochastic resonance as described in claim 1, characterized in that, The data preprocessing process specifically involves demodulating the original signal using the Hilbert transform algorithm.

4. The bearing fault diagnosis method based on adaptive fractional-order stochastic resonance as described in claim 1, characterized in that, In the process of frequency compression and recovery of the envelope signal using frequency-shift scaling transformation to obtain a variable-scale demodulated signal, the envelope signal is first frequency-shifted, causing the signal bandwidth to shift to the left, thereby shifting the characteristic frequency components of the signal into the low-frequency region. Then, the frequency-shifted signal is linearly compressed so that the characteristic frequency of the signal meets the small parameter requirements of random resonance. Next, classical random resonance is applied to the signal to enhance the frequency components in the transformed signal that correspond to the characteristic frequency components. Finally, the frequency of the random resonance output signal is restored to obtain the variable-scale demodulated signal with enhanced characteristic frequency components.

5. The bearing fault diagnosis method based on adaptive fractional-order stochastic resonance as described in claim 1, characterized in that, The time-delay fractional-order biased nonlinear overdamped stochastic resonance system is a long-memory system formed by introducing a time-delay feedback term into the stochastic resonance system. By introducing the time-delay term, historical information is introduced to modulate the system.

6. The bearing fault diagnosis method based on adaptive fractional-order stochastic resonance as described in claim 1, characterized in that, The improved Cuckoo Algorithm RACS modifies the global search equation of the traditional Cuckoo Algorithm, adopts a sorting-based vector selection method, and uses a combined crossover strategy with parameter adaptation based on the random walking mode in the Levy flight of the traditional Cuckoo Algorithm CS.

7. The bearing fault diagnosis method based on adaptive fractional-order stochastic resonance as described in claim 6, characterized in that, The improved Cuckoo Algorithm RACS also proposes a replacement strategy that updates unimproved solutions at predetermined intervals by utilizing useful information from discarded solutions stored in external archives.

8. The bearing fault diagnosis method based on adaptive fractional-order stochastic resonance as described in claim 1, characterized in that, The process of processing the output signal and obtaining the characteristic frequency specifically involves performing a Fourier transform on the output signal to obtain the corresponding spectrum, capturing the frequency components with obvious peaks in the spectrum, and obtaining the characteristic frequency.

9. The bearing fault diagnosis method based on adaptive fractional-order stochastic resonance as described in claim 1, characterized in that, The fault states of the inner ring of the rolling bearing include two states: normal operation and fault existence.

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