Fault diagnosis method for rotating machinery based on fractional order stochastic resonance

Abstract

The application discloses a rotating machinery fault diagnosis method based on fractional order stochastic resonance, and belongs to the technical field of mechanical fault diagnosis. The method comprises the following steps: k-neighbor distance and k-neighbor density are calculated by extracting the multi-dimensional features of each data segment of a signal, an abnormality factor of increasing density is constructed, abnormal data segments are screened and removed according to the 3sigma rule, and a vibration signal from which large impact noise has been preliminarily removed is obtained; the Caputo-Fabrizio fractional order derivative is introduced into a second-order classical bistable stochastic resonance model, so that the amplification capacity of the system to weak features is effectively improved; the preprocessed signal is input into the model, a fault characteristic is extracted through a frequency analysis method to realize fault diagnosis, and the extraction result is quantified by using a signal-to-noise ratio. Compared with a traditional signal processing method, the application can achieve more obvious effects and can process a vibration signal seriously polluted by noise.

Description

Technical Field

[0001] This invention relates to the field of mechanical fault diagnosis technology, and in particular to a method for diagnosing rotating machinery faults based on fractional-order random resonance. Background Technology

[0002] Rotating machinery is widely used in various industries and serves as key mechanical equipment or critical components in various fields. With the rapid development of technology, rotating equipment is becoming increasingly larger and more complex; failures can result in severe losses. Therefore, fault monitoring and diagnosis of rotating machinery are of great practical significance for ensuring its safe operation and improving economic productivity.

[0003] To reduce the failure rate of transmission systems, the application of effective and reliable condition monitoring technology is an important means of timely detection of early failures in gears or bearings. Vibration monitoring is widely considered one of the most effective technologies because vibration signals collected from sensors installed near gears or bearings contain fault information.

[0004] Stochastic resonance is a novel theory that utilizes noise to enhance weak signals. It describes a phenomenon in nonlinear systems where, as noise intensity gradually increases, the output signal-to-noise ratio (SNR) rises instead of falling, reaching a peak at a certain intensity where the input signal, noise, and nonlinear system achieve an optimal match. As noise continues to increase, the SNR begins to decline again. In contrast to traditional methods, stochastic resonance works in the opposite direction, transferring some of the noise energy from the noise signal to the weak feature signal. This weakens the noise while simultaneously strengthening the weak feature, enabling effective detection of the weak feature.

[0005] Simply put, random resonance amplifies low-frequency signals by transferring high-frequency noise energy to low frequencies for detection purposes. It can be viewed as a special low-pass filter. As the low-frequency energy increases, weak features previously masked by noise become visible. By utilizing random resonance processing, we can effectively extract the desirable characteristics of these weak features, enabling targeted analysis of low signal-to-noise ratio signals picked up by mechanical equipment, thus facilitating fault diagnosis.

[0006] However, since fault features are often submerged in random background noise, and existing traditional fault diagnosis methods, including random resonance systems based on integer order, are insufficient to effectively amplify weak features, fault diagnosis based on vibration signals is often very difficult. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a fault diagnosis method for rotating machinery based on fractional-order stochastic resonance, which can more effectively amplify weak features in harsh environments. The method involves preprocessing the original signal by constructing an increased density anomaly factor, inputting it into a second-order stochastic resonance model based on the Caputo-Fabrizio fractional derivative to amplify weak features, and using signal-to-noise ratio quantization to determine the output effect.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0009] A fault diagnosis method for rotating machinery based on fractional-order random resonance specifically includes the following steps:

[0010] S1. Construct a density-increasing anomaly factor to preprocess the original signal to eliminate large-impact noise;

[0011] S2. A second-order stochastic resonance model is established based on the Caputo-Fabrizio fractional derivative;

[0012] S3. Substitute the preprocessed signal into the established stochastic resonance model to amplify its weak features for fault diagnosis.

[0013] A further improvement to the technical solution of the present invention is that step S1 specifically includes the following sub-steps:

[0014] S11, Use size w s A rectangular sliding window divides the original signal of length L into N data segments, forming a data segment set:

[0015] S(n) = {s1, s2, ..., s} N}

[0016] Where N = L / w s .

[0017] S12. Perform multi-dimensional feature extraction on each data segment in the data segment set to form a feature set;

[0018] S13. Calculate the distance KD between the monitored objects and their k-nearest neighbors in the feature set, and sort them in ascending order according to their respective k-distances, as follows:

[0019] ADS(s) = {s, p1, p2, ..., p R}

[0020] Where p i ∈N k (s), i = 1, 2, ..., R, where R is the number of k-nearest neighbors for each data segment;

[0021] S14. Calculate the k-nearest neighbor density KND for each data segment;

[0022] S15. Calculate the average density fluctuation (ADF) of each data segment based on the k-nearest neighbor ascending set and k-nearest neighbor density.

[0023] S16. Calculate the upscaling anomaly factor (ADOF) for each data segment, and filter out outliers according to the criteria:

[0024]

[0025] Where j = {j|ADOF(s)} j The process involves finding the value of λ ≥ λ, i = 1, 2, ..., M, M ≤ N, and then obtaining the processed signal.

[0026] x1(t)=S(n)-S o

[0027] Where t = 0, 1, 2, ..., M, M ≤ L.

[0028] A further improvement of the technical solution of the present invention is that the multidimensional feature attributes include 15 time-domain features and 8 frequency-domain statistical features.

[0029] A further improvement of the technical solution of the present invention is that: in step S12, the 15 time-domain features include the mean, maximum, minimum, peak-to-peak value, variance, peak factor, root mean square value, average amplitude, root square amplitude, waveform index, impulse index, margin index, peak value, skewness index, and kurtosis index of the monitoring data; the 8 frequency-domain statistical features are obtained by using "db4" wavelet to perform 3-level orthogonal wavelet packet decomposition on each monitoring data to obtain 8 sub-frequency band data, and calculating the percentage of energy of each frequency band data to the total energy.

[0030] A further improvement to the technical solution of the present invention is that, in step S13, the value of k is 50.

[0031] A further improvement to the technical solution of the present invention is that step S2 specifically includes the following sub-steps:

[0032] S21. Establish a classical second-order stochastic resonance model:

[0033]

[0034] in x(t) is the output signal, and t is the timing parameter. The signal is weakly periodic, and ξ(t) is random noise. The model is transformed into the following form:

[0035]

[0036] in

[0037] S22. Discretize the Caputo-Fabrizio fractional derivative and substitute it into the classical second-order stochastic resonance model:

[0038]

[0039] Where 0 ≤ α ≤ 2, and α is the order; the discrete derivation process is as follows:

[0040] (1) Let

[0041] (2) According to the definition of the Caputo-Fabrizio fractional derivative:

[0042]

[0043] Its discretized form is:

[0044]

[0045]

[0046] Where h is the time step. For a binomial coefficient:

[0047]

[0048] Where Γ(·) is the gamma function and n is the length of the signal sequence.

[0049] (3) Based on Euler's formula, the model expression can be further discretized as follows:

[0050]

[0051] in, This represents the discretized input signal.

[0052] S23. Calculate the discrete solution of the second-order stochastic resonance model based on the Caputo-Fabrizio fractional derivative, i.e., the output response of the model.

[0053] S24. The quantum genetic algorithm is used to optimize the various parameters of the model to obtain the best model performance.

[0054] A further improvement to the technical solution of this invention is that, in step S23, the model's response is:

[0055]

[0056] A further improvement to the technical solution of this invention lies in the following: In step S24, the quantum genetic algorithm optimizes four parameters, namely: fractional order α, potential well width x. m Given the barrier height ΔU and damping ratio γ, the specific steps are as follows:

[0057] (1) Initialize the parent chromosome;

[0058] (2) Measure each chromosome gene locus, i.e., qubit, to obtain a state. Calculate the fitness for each state and record the best individual and its fitness;

[0059] (3) The number of generations set by genetic evolution, in which quantum rotation gates are used to perform genetic mutations on chromosomes in each generation;

[0060] (4) When the termination condition is met, output the best individual and fitness.

[0061] A further improvement to the technical solution of the present invention is that step S3 specifically includes the following sub-steps:

[0062] S31. Input the preprocessed signal into the model;

[0063] S32. Fault characteristics are extracted through frequency analysis to achieve fault diagnosis;

[0064] S33. Quantize the extraction results using the signal-to-noise ratio and evaluate the effect:

[0065]

[0066] Where A d It is the amplitude of the fault characteristic frequency in the frequency spectrum of the output signal. It is the sum of the power of each spectral line in the output spectrum, excluding the fault characteristic frequency.

[0067] The technological advancements achieved by this invention due to the adoption of the above technical solutions are as follows:

[0068] 1. This invention establishes a novel Caputo-Fabrizio fractional derivative second-order stochastic resonance system for fault diagnosis, which achieves more significant results than traditional signal processing methods;

[0069] 2. To eliminate large impulse noise, an increase density anomaly factor was constructed as a method for cleaning raw data. It can not only effectively increase the amplitude of the desired characteristic frequency, but also process vibration signals that are heavily polluted by noise. Attached Figure Description

[0070] Figure 1 This is a flowchart of the rotating machinery fault diagnosis method based on fractional-order random resonance in this invention;

[0071] Figure 2 This is a graph showing the ADOF values ​​in different data segments when k varies within the range of 5 to 95 in this invention.

[0072] Figure 3 This is a schematic diagram of the wind turbine transmission system used in Embodiment 1 of the present invention;

[0073] Figure 4 This is a schematic diagram of the damage to the high-speed shaft gear set of the wind turbine transmission system used in Embodiment 1 of the present invention;

[0074] Figure 5 This is a time-domain waveform diagram of the original vibration signal in Embodiment 1 of the present invention;

[0075] Figure 6 This is the spectrum of the original vibration signal in Embodiment 1 of the present invention;

[0076] Figure 7 This is the envelope spectrum of the original vibration signal in Embodiment 1 of the present invention;

[0077] Figure 8 This is a display diagram of the ADOF values ​​of different data segments of the original vibration signal in Embodiment 1 of the present invention;

[0078] Figure 9 This is a time-domain waveform diagram of the vibration signal processed in Embodiment 1 of the present invention;

[0079] Figure 10 This is the spectrum of the vibration signal after processing in Embodiment 1 of the present invention. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0081] like Figure 1 As shown, this invention provides a method for diagnosing rotating machinery faults based on fractional-order random resonance, specifically including the following steps:

[0082] S1. Construct a density-increasing anomaly factor to preprocess the original signal to eliminate large-impact noise;

[0083] Based on the original signal, the distance KD between the monitored object and its k-nearest neighbor, the k-nearest neighbor density KND, the average density fluctuation ADF, and the density rise anomaly factor ADOF are calculated using the density rise anomaly factor method. The specific steps include the following:

[0084] S11, Use size w s A rectangular sliding window divides the original signal of length L into N data segments s. i This constitutes a data segment set:

[0085] S(n) = {s1, s2, ..., s} N}

[0086] Where N = Lw s ;

[0087] S12. Perform multi-dimensional feature extraction on each data segment in the data segment set to form a feature set;

[0088] The multidimensional feature attributes include 15 time-domain features and 8 frequency-domain statistical features. The 15 time-domain features include the mean, maximum, minimum, peak-to-peak value, variance, peak factor, root mean square value, average amplitude, root square amplitude, waveform index, impulse index, margin index, peak value, skewness index, and kurtosis index of the monitoring data. The 8 frequency-domain statistical features are obtained by using the "db4" wavelet to perform 3-level orthogonal wavelet packet decomposition on each monitoring data to obtain 8 sub-frequency band data and calculating the percentage of energy of each frequency band data to the total energy.

[0089] After feature extraction from the data segments, each data sample is an object described by 23 feature attribute dimensions. The feature set is the set of all feature attributes of the data segments, denoted as set S(n) = {s1, s2, ... sn}. N}, S∈R N × 23 ;

[0090] S13. Calculate the distance KD between the monitored objects and their k-nearest neighbors in the feature set, and sort them in ascending order according to their respective k-distances, as follows:

[0091] ADS(s) = {s, p1, p2, ..., p R}

[0092] Where p i ∈N k (s), i = 1, 2, ..., R, where R is the number of k-nearest neighbors for each data segment;

[0093] The k-distance of a data segment s represents the Euclidean distance from s to its k-th nearest neighbor object. The distance between s and its k-th nearest neighbor in the feature set is the k-distance KD of object s, where k is any positive integer. In the set ADS(s), if object o is a k-nearest neighbor of object s, then the k-distance of the object is:

[0094]

[0095] In the formula, f i (x) represents the i-th feature attribute of the object; from this, we can obtain the k-nearest neighbor set of the object, represented as:

[0096] N k (s)={p|d(s,p)≤KD(s)}

[0097] Where, N k (s) contains all data segment objects whose distance from object point p is less than KD(s).

[0098] S14. Calculate the k-nearest neighbor density KND for each data segment;

[0099] Based on the k-distance KD of each data segment obtained in S13, the k-nearest neighbor density KND of each segment in S(n) is:

[0100]

[0101] The denominator is the median distance from each k-nearest neighbor to s. Therefore, the density distribution of different data segments can be calculated, and N can be used... k (s) eliminates the adverse effects of k-nearest neighbors with the same distance.

[0102] S15. Calculate the average density fluctuation (ADF) of each data segment based on the k-nearest neighbor ascending set and k-nearest neighbor density.

[0103]

[0104] Clearly, the ADF can effectively represent the density difference between S and its neighboring segments, thus allowing closer segments in the ADS to play a more significant role.

[0105] S16. Calculate the upscaling anomaly factor (ADOF) for each data segment, and filter out outliers according to the 3σ criterion:

[0106]

[0107] Where j = {j|ADOF(s)} j The process involves finding the value of λ ≥ λ, i = 1, 2, ..., M, M ≤ N, and then obtaining the processed signal.

[0108] x1(t)=S(n)-S o

[0109] Where t = 0, 1, 2, ..., M, M ≤ L.

[0110] Based on the ADF values ​​obtained in S15, the upscaling anomaly factor (ADOF) for each data segment can be calculated using the following formula:

[0111]

[0112] Clearly, the ADOF value is derived from the density difference between the data segment and its k-nearest neighbors. A larger ADOF indicates that the corresponding data segment is more likely to contain outliers with large impact noise, and its threshold λ is determined by the 3σ criterion. However, the choice of the k value in ADOF is not sensitive to the outlier detection results, such as... Figure 2 As shown, when the k value is between 0 and 95, the ADOF reaches its maximum value in the third data segment for all different k values. Due to statistical fluctuations between different data segments, the ADOF value fluctuates significantly when the k value is less than 5. Therefore, if a k value below 5 is selected, outliers cannot be accurately detected, while other values ​​show no significant difference. In summary, this invention uses k = 50.

[0113] S2. A second-order stochastic resonance model is established based on the Caputo-Fabrizio fractional derivative;

[0114] In this stage, the Caputo-Fabrizio fractional derivative is discretized and substituted into the second-order classical bistable stochastic resonance model to improve the ability of the stochastic resonance system to enhance weak features. Specifically, this includes the following steps:

[0115] S21. Establish a classical second-order stochastic resonance model:

[0116]

[0117] in x(t) is the output signal, and t is the timing parameter. The signal is weakly periodic, and ξ(t) is random noise. The model is transformed into the following form:

[0118]

[0119] in

[0120] S22. Discretize the Caputo-Fabrizio fractional derivative and substitute it into the classical second-order stochastic resonance model:

[0121]

[0122] Where 0 ≤ α ≤ 2, and α is the order; the discrete derivation process is as follows:

[0123] (1) Let

[0124] (2) According to the definition of the Caputo-Fabrizio fractional derivative:

[0125]

[0126] Its discretized form is:

[0127]

[0128]

[0129] Where h is the time step. For a binomial coefficient:

[0130]

[0131] Where Γ(·) is the gamma function and n is the length of the signal sequence.

[0132] (3) Based on Euler's formula, the model expression can be further discretized as follows:

[0133]

[0134] in, This represents the discretized input signal.

[0135] S23. Calculate the discrete solution of the second-order stochastic resonance model based on the Caputo-Fabrizio fractional derivative, i.e., the output response of the model. When the time step h approaches 0, the response of x(t) can be calculated from the discrete equations in S22:

[0136]

[0137] S24. The quantum genetic algorithm is used to optimize the various parameters of the model to obtain the best model performance.

[0138] The quantum genetic algorithm optimizes four parameters: fractional order α, potential well width x. m Given the barrier height ΔU and damping ratio γ, the specific steps are as follows:

[0139] (1) Initialize the parent chromosome;

[0140] (2) Measure each chromosome gene locus, i.e., qubit, to obtain a state. Calculate the fitness for each state and record the best individual and its fitness;

[0141] (3) The number of generations set by genetic evolution, in which quantum rotation gates are used to perform genetic mutations on chromosomes in each generation;

[0142] (4) When the termination condition is met, output the best individual and fitness.

[0143] S3. Substitute the preprocessed signal into the established stochastic resonance model to amplify its weak features for fault diagnosis.

[0144] The preprocessed signal obtained in S1 is substituted into the stochastic resonance model established in S2, and fault characteristic frequencies are extracted using frequency analysis methods to achieve fault diagnosis. The extraction results of weak features are then quantified using the signal-to-noise ratio. Specifically, the process includes the following steps:

[0145] S31. Input the preprocessed signal into the model;

[0146] S32. Fault characteristics are extracted through frequency analysis to achieve fault diagnosis;

[0147] S33. Quantize the extraction results using the signal-to-noise ratio and evaluate the effect:

[0148]

[0149] Where A d It is the amplitude of the fault characteristic frequency in the frequency spectrum of the output signal. It is the sum of the power of each spectral line in the output spectrum, excluding the fault characteristic frequency.

[0150] A higher signal-to-noise ratio indicates a better enhancement effect of the processing method.

[0151] The following is a specific example of the practical application of this method.

[0152] Example 1

[0153] This embodiment uses vibration signals collected from a wind turbine gearbox to verify the proposed system's detection capabilities in harsh environments, such as... Figure 3 As shown, the wind turbine transmission system includes the following structure: wheel axle 1, main bearing 2, main shaft 3, gearbox 4, brake 5, generator shaft 6, generator 7, and base plate 8. After the break-in test, two oil loss incidents caused wear on the pinion of the high-speed stage fixed shaft gear set, as shown in the diagram. Figure 4 As shown. The gearbox has a transmission ratio of 1:81.49 and a rated power of 750kW. The large gear and small gear have 88 and 22 teeth respectively. The high-speed shaft rotates at a frequency of 30Hz, and the gear set meshing frequency is 660Hz. The sampling frequency is 40kHz, and the sampling time is 2s. Figure 5 The original vibration signal of the pinion has the following spectrum in the [500, 800] Hz amplification band: Figure 6 As shown, the envelope spectrum is as follows Figure 7As shown, in the time domain, the repetitive periodic pulses are submerged in heavy noise and difficult to distinguish, with a calculated signal-to-noise ratio of -37.3359 dB. This signal is then processed using a rotating machinery fault diagnosis method based on fractional-order random resonance.

[0154] A fault diagnosis method for rotating machinery based on fractional-order random resonance specifically includes the following steps:

[0155] S1. Construct a density-increasing anomaly factor to preprocess the original signal to eliminate large-impact noise;

[0156] The test results for high-impact noise are as follows: Figure 8 As shown, data segment 25 contains abnormal impact interference that needs to be eliminated.

[0157] S2. A second-order stochastic resonance model is established based on the Caputo-Fabrizio fractional derivative;

[0158] Based on the optimization results of the quantum genetic algorithm, α = 0.08061, ΔU = 5.573, γ = 0.06978, and x... m =69.15.

[0159] S3. Substitute the preprocessed signal into the established stochastic resonance model to amplify its weak features for fault diagnosis.

[0160] like Figure 9 and Figure 10 The image shows the time-domain waveform and spectrum of the vibration signal after amplification of the grid frequency band. It can be seen that the repetitive periodic pulses excited by the faulty gear are evident in the time-domain waveform. Furthermore, the signal-to-noise ratio of the fault characteristic frequency in the processed signal is amplified to -19.2157 dB, significantly higher than the original spectrum, indicating that this method is highly effective for fault diagnosis of wind turbine transmission systems.

[0161] In summary, this invention constructs a novel stochastic resonance system for fault diagnosis based on the Caputo-Fabrizio fractional derivative and the density increase anomaly factor. The core steps of this invention include the construction of the density increase anomaly factor and the establishment of a second-order stochastic resonance model based on the Caputo-Fabrizio fractional derivative. This eliminates large-impact noise, effectively improves the amplitude of the desired characteristic frequency, and the effectiveness is assessed through quantification using the signal-to-noise ratio.

[0162] Finally, it should be noted that the above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for diagnosing rotating machinery faults based on fractional-order random resonance, characterized in that, Includes the following steps: S1. Construct a density increase anomaly factor to preprocess the original vibration signal to eliminate large impact noise; S2. Establish a second-order stochastic resonance model based on the Caputo-Fabrizio fractional derivative; Step S2 specifically includes the following sub-steps: S21. Establish a classical second-order stochastic resonance model: in , The output signal is t, where t is the timing signal. It is a weak periodic signal. For random noise, the model is transformed into the following form: in , ; S22. Discretize the Caputo-Fabrizio fractional derivative and substitute it into the classical second-order stochastic resonance model: in , It is the order; the discrete derivation process is as follows: (1) Let (2) According to the definition of the Caputo-Fabrizio fractional derivative: Its discretized form is: in For time step, For a binomial coefficient: in For gamma function, The length of the signal sequence; (3) Based on Euler's formula, the model expression can be further discretized as follows: in, This represents the discretized input signal; S23. Calculate the discrete solution of the second-order stochastic resonance model based on the Caputo-Fabrizio fractional derivative, i.e., the output response of the model; S24. Optimize the various parameters of the model using a quantum genetic algorithm to obtain the best model performance; S3. Substitute the preprocessed signal into the established stochastic resonance model to amplify its weak features for fault diagnosis.

2. The method for diagnosing rotating machinery faults based on fractional-order random resonance as described in claim 1, characterized in that, Step S1 specifically includes the following sub-steps: S11, Size used is A rectangular sliding window divides the original signal of length L into N data segments. This constitutes a data segment set: in ; S12. Perform multi-dimensional feature extraction on each data segment in the data segment set to form a feature set; S13. Calculate the distance KD between the monitored objects and their k-nearest neighbors in the feature set, and sort them in ascending order according to their respective k-distances, as follows: in , R is the number of k-nearest neighbors for each data segment; S14. Calculate the k-nearest neighbor density KND for each data segment; S15. Calculate the average density fluctuation (ADF) of each data segment based on the k-nearest neighbor ascending set and k-nearest neighbor density. S16. Calculate the upscaling anomaly factor (ADOF) for each data segment, based on... Criteria for filtering and removing outliers: in = Then, the processed signal is obtained: in , .

3. The method for diagnosing rotating machinery faults based on fractional-order random resonance according to claim 2, characterized in that, In step S12, the multidimensional feature attributes include 15 time-domain features and 8 frequency-domain statistical features.

4. The method for diagnosing rotating machinery faults based on fractional-order random resonance according to claim 2, characterized in that, In step S13, the value of k is 50.

5. The method for diagnosing rotating machinery faults based on fractional-order random resonance according to claim 3, characterized in that, The 15 time-domain features include the mean, maximum, minimum, peak-to-peak value, variance, peak factor, root mean square value, average amplitude, root square amplitude, waveform index, impulse index, margin index, peak value, skewness index, and kurtosis index of the monitoring data; the 8 frequency-domain statistical features are obtained by using "db4" wavelet to perform 3-level orthogonal wavelet packet decomposition on each monitoring data to obtain 8 sub-frequency band data, and calculating the percentage of energy of each frequency band data to the total energy.

6. The method for diagnosing rotating machinery faults based on fractional-order random resonance as described in claim 1, characterized in that, In step S23, the model's response is: .

7. The method for diagnosing rotating machinery faults based on fractional-order random resonance as described in claim 1, characterized in that, In step S24, the quantum genetic algorithm optimizes four parameters, namely: fractional order... Potential well width Barrier height Damping ratio The specific steps are as follows: (1) Initialize the parent chromosome; (2) Measure each chromosome gene locus, i.e., quantum bit, to obtain a state, calculate the fitness for each state, and record the best individual and fitness; (3) The number of generations set by genetic evolution, in which quantum rotation gates are used to perform genetic mutations on chromosomes in each generation; (4) When the termination condition is met, output the best individual and fitness.

8. The method for diagnosing rotating machinery faults based on fractional-order random resonance as described in claim 1, characterized in that, Step S3 specifically includes the following sub-steps: S31. Input the preprocessed signal into the model; S32. Fault characteristics are extracted through frequency analysis to achieve fault diagnosis; S33. Quantize the extraction results using the signal-to-noise ratio and evaluate the effect: in It is the amplitude of the fault characteristic frequency in the frequency spectrum of the output signal. It is the sum of the power of each spectral line in the output spectrum, excluding the fault characteristic frequency.

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