A self-adaptive stochastic resonance weak fault detection method based on kurtosis optimization

Abstract

The application provides a kind of self-adapting random resonance weak fault detection method based on kurtosis optimization, belongs to the technical field of fault detection, including: collecting transient signal on cable line and preprocessing;Constructing bistable random resonance model;With the kurtosis of output signal as fitness function, the potential well parameters of bistable random resonance model are optimized based on particle swarm optimization algorithm;The optimized potential well parameters are substituted into the bistable random resonance model, and the preprocessed transient signal is processed to obtain the enhanced output signal for fault detection.The beneficial effect is: based on the classical bistable model to construct the random resonance system, the kurtosis of output signal is used as the fitness function of particle swarm optimization algorithm, the potential well parameters are adaptively optimized, the potential well parameters are automatically converged to the optimal state, the high impedance grounding fault traveling wave signal can be extracted and enhanced from strong noise background, and the detection sensitivity and reliability are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fault detection, and in particular to a self-adaptive random resonance weak fault detection method based on kurtosis optimization. BACKGROUND

[0002] High-impedance fault (HIF) is a common but difficult-to-detect fault type in the operation and maintenance of high-voltage cable lines. This type of fault is usually caused by slight damage, aging of cable line insulation, or transient bridging of external objects (such as tree branches, pollutants), and its grounding transition resistance can be as high as several thousand ohms, resulting in extremely small fault current and weak fault energy.

[0003] When a high-impedance ground fault occurs, a traveling wave signal propagates bidirectionally along the cable line. However, due to the weak fault energy, the initial amplitude of this traveling wave signal is extremely low, and it is easily disturbed by the characteristics of the line itself and various electromagnetic environmental noises during propagation, resulting in the signal being completely submerged in strong background noise when it reaches the detection end, with an extremely low signal-to-noise ratio (SNR).

[0004] Currently, existing fault detection methods, such as those based on current jump variables, wavelet transforms, or Fourier analysis, have obvious shortcomings when dealing with such extremely low SNR weak signals. Traditional threshold detection methods have difficulty setting a suitable threshold in a strong noise background, as they need to reliably detect weak fault signals while avoiding false positives due to noise interference, resulting in insufficient detection sensitivity. Because it is difficult to effectively separate the fault signal from the noise, conventional methods often misjudge weak fault traveling wave signals as normal environmental noise, leading to fault omission and increasing the omission rate. In addition, fault omission can prevent the triggering of fault location devices, making it impossible to promptly remove the fault point. Persistent high-impedance ground faults may further develop into permanent and more destructive short-circuit faults, causing serious damage to power equipment and even posing a significant threat to the personal safety of those around, creating a significant safety hazard. SUMMARY

[0005] To solve the above technical problems, the present application provides a self-adaptive random resonance weak fault detection method based on kurtosis optimization, which aims to solve the problem of weak traveling wave signals, extremely low SNR, and difficulty in detection caused by high-impedance ground faults in high-voltage cables.

[0006] The technical problem solved by the present application can be realized by the following technical scheme: a self-adaptive random resonance weak fault detection method based on kurtosis optimization, comprising: step S1, collecting transient signals on a cable line, and pre-processing the transient signals to obtain pre-processed transient signals; step S2, constructing a bistable random resonance model based on the Langevin equation, and using a fourth-order Runge-Kutta algorithm to numerically solve the Langevin equation to obtain an output signal; step S3, taking the kurtosis of the output signal as a fitness function, and optimizing the potential well parameters of the bistable random resonance model based on a particle swarm optimization algorithm to obtain optimized potential well parameters; step S4, substituting the optimized potential well parameters into the bistable random resonance model to process the pre-processed transient signals to obtain an enhanced output signal; and step S5, performing fault detection according to the enhanced output signal to determine whether a fault has occurred.

[0007] Preferably, in the step S1, the preprocessing includes normalization preprocessing, and the normalization preprocessing uses the following formula:

[0008]

[0009] wherein, represents a transient signal; n represents a discrete time point; represents the minimum value of the transient signal in a sliding data window; represents the maximum value of the transient signal in a sliding data window; represents a pre-processed transient signal.

[0010] Preferably, in the step S2, the differential form of the Langevin equation is:

[0011]

[0012] wherein, x represents an output signal of a random resonance system; a , b respectively represent potential well parameters of a bistable random resonance model; represents a pre-processed transient signal; represents a differential form of the Langevin equation.

[0013] Preferably, in the step S2, the output signal is:

[0014]

[0015] wherein, , respectively represent output signals, n, n +1 represents a discrete time point; a, b respectively represent the potential well parameters of the bistable stochastic resonance model; represents the preprocessed transient signal; h represents the calculation step.

[0016] Preferably, the step S3 comprises: a step S31 of initializing a particle swarm; a step S32 of, for each particle, substituting the particle into the bistable stochastic resonance model to obtain an output signal numerically solved for the preprocessed transient signal, taking the kurtosis of the output signal as the fitness value of the particle; a step S33 of updating the individual optimum and the global optimum according to the fitness value of the particle; a step S34 of updating the particle velocity and position; and a step S35 of repeating the steps S32-S34 until the particle swarm converges or a preset iteration number is reached, and outputting the optimized potential well parameters.

[0017] Preferably, the step S33 comprises: comparing the fitness value of the particle with the historical best fitness value of the corresponding particle, and if the fitness value of the particle exceeds the historical best fitness value, updating the historical best fitness value to the fitness value of the particle and recording the corresponding position; and comparing the fitness value of the particle with the global best fitness value, and if the fitness value of the particle exceeds the global best fitness value, updating the global best fitness value to the fitness value of the particle and recording the corresponding position.

[0018] Preferably, in the step S34, the particle velocity and position are updated by the following formula:

[0019]

[0020]

[0021] wherein, represents the inertia weight; represents the particle velocity before updating; represents the particle velocity after updating; , respectively represent the learning factor; , respectively represent a random number between 0 and 1; represents the individual best position; represents the particle position before updating; represents the global best position; represents the particle position after updating, subscript i represents the particle index, d represents the dimension of the potential well parameters, t, t +1 respectively represent the iteration number.

[0022] Preferably, the step S5 comprises: comparing the enhanced output signal with a preset threshold; when the absolute value of the enhanced output signal exceeds the preset threshold, determining that a fault occurs, and recording fault occurrence timestamp information.

[0023] Preferably, the step of comparing the enhanced output signal with a preset threshold further comprises: setting the preset threshold according to the optimized potential well parameter.

[0024] Preferably, the preset threshold is:

[0025]

[0026] wherein, represents a safety factor; , respectively represent the optimized potential well parameter; represents the preset threshold.

[0027] The technical scheme of the present application has the advantages or beneficial effects that: the present application constructs a random resonance system based on a classical bistable model, and adopts a particle swarm optimization algorithm to perform adaptive optimization on key parameters of the system, especially uses the kurtosis of the system output signal as the fitness function of the particle swarm optimization algorithm to drive the system parameters to automatically converge to the optimal state, so that the high-impedance grounding fault traveling wave signal can be effectively extracted and enhanced from a strong noise background, thereby improving the sensitivity and reliability of detection. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 For the preferred embodiment of the present application, the flowchart of the adaptive random resonance weak fault detection method based on kurtosis optimization is shown in the figure;

[0029] Figure 2 For the preferred embodiment of the present application, the flowchart of the particle swarm optimization algorithm is shown in the figure. DETAILED DESCRIPTION

[0030] The technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0031] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0032] The present application will be further described below with reference to the drawings and specific embodiments, but not as a limitation of the present application.

[0033] In the preferred embodiment of the present application, based on the above-mentioned problems existing in the prior art, a self-adaptive random resonance weak fault detection method based on kurtosis optimization is provided, the core idea of which is to construct a random resonance system based on a classical bistable model, and to use a particle swarm optimization (PSO) algorithm to adaptively optimize the key parameters of the system. In particular, the present application takes the kurtosis value of the output signal of the random resonance (SR) system as the fitness function of the particle swarm optimization (PSO) algorithm, so as to drive the system parameters to automatically converge to the optimal state, thereby maximizing the enhancement of the transient traveling wave fault signal submerged in strong noise.

[0034] As shown in Figure 1 , the method comprises the following steps: step S1, collecting a transient signal on a cable line, and pre-processing the transient signal to obtain a pre-processed transient signal; specifically, the transient signal can be obtained by a signal collection module. The signal collection module is electrically connected with a high-frequency current transformer (HFCT) or a coupling capacitor sensor installed at the first and last ends or a designated monitoring point of the cable line.

[0035] The signal collection module collects the transient signal on the cable line at a high sampling rate (for example, ≥10MHz). The transient signal is a discrete digital signal sequence, denoted as .

[0036] Since the random resonance system has certain requirements for the amplitude of the input signal, generally speaking, in order to meet the small parameter condition, it is usually required that the signal amplitude be less than 1. Therefore, for the collected original signal, normalization preprocessing is needed.

[0037] Specifically, in step S1, the preprocessing includes normalization preprocessing, which uses the following formula:

[0038]

[0039] wherein, represents the transient signal; n represents a discrete time point; represents the minimum value of the transient signal in the sliding data window; represents the maximum value of the transient signal in the sliding data window; represents the pre-processed transient signal.

[0040] The linear normalization method is adopted in the embodiment of the present application, which scales the input transient signal to the interval [-1, 1], thereby obtaining the pre-processed transient signal .

[0041] Step S2, a bistable stochastic resonance model is constructed based on Langevin equation, and the fourth-order Runge-Kutta algorithm is used to solve the Langevin equation to obtain an output signal;

[0042] Specifically, the embodiment of the present application adopts a classical bistable Langevin equation as a mathematical model of a stochastic resonance (SR) system. The model describes the motion of a Brownian particle in a double potential well, and the kinetic equation thereof is:

[0043]

[0044] wherein, represents a differential form of the Langevin equation;

[0045] x represents an output signal of the stochastic resonance system, is a function of time t , and is denoted as , which represents displacement of the particle;

[0046] represents a preprocessed transient signal sequence, and contains a weak fault traveling wave signal and background noise;

[0047] a , b respectively represent potential well parameters of the bistable stochastic resonance model, ; the two parameters jointly determine the shape of the potential well, including depth and width, and are the key to the performance of the stochastic resonance system and the objects to be adaptively optimized in the present application.

[0048] For a discrete signal, the above differential equation can be solved by using the fourth-order Runge-Kutta method to obtain an output signal :

[0049]

[0050] wherein, , respectively represent the output signal, n, n +1 represents a discrete time point; a , b respectively represent potential well parameters of the bistable stochastic resonance model; represents the preprocessed transient signal; h represents a calculation step, which is usually the inverse of a sampling period, i.e. , is a sampling frequency.

[0051] Step S3, based on the particle swarm optimization (PSO) algorithm, the potential well parameters of the bistable stochastic resonance model are optimized with the kurtosis of the output signal as the fitness function, and the optimized potential well parameters are obtained; specifically, in order to make the stochastic resonance (SR) system achieve the best signal enhancement effect, the optimal parameter combination must be found , wherein respectively represent the potential well parameters a , b and the optimized values.

[0052] The present application proposes a parameter self-adaptive optimization based on kurtosis optimization, uses the particle swarm optimization (PSO) algorithm, and uses the kurtosis of the output signal as the fitness function.

[0053] The kurtosis is a dimensionless parameter for measuring the steepness or flatness of the probability density distribution curve of the signal, and is very sensitive to the impact component in the signal. Its calculation formula is:

[0054]

[0055] wherein, represents the output signal of the stochastic resonance (SR) system; represents the sequence length; represents the mean value of the output signal sequence.

[0056] When the potential well parameters of the stochastic resonance (SR) system do not match, the output signal sequence is mainly driven by noise, and presents a Gaussian distribution, and the kurtosis value K is close to 3.

[0057] When the potential well parameters of the stochastic resonance (SR) system are adjusted to the optimum, the weak fault traveling wave pulse can obtain sufficient energy to drive the particles (system state) to realize synchronization and dramatic transition between the two potential wells, so that the output signal sequence presents an impact pulse form with large amplitude and sharp waveform, and the kurtosis value K will be much larger than 3, and reaches the maximum at this moment.

[0058] Therefore, maximizing the kurtosis value K of the output signal is equivalent to finding the potential well parameters that make the stochastic resonance (SR) system have the best enhancement effect on the transient impact signal .

[0059] As shown in Figure 2 , the particle swarm optimization (PSO) algorithm in step S3 includes:

[0060] Step S31, initializing the particle swarm;

[0061] Setting the particle swarm size For example, .

[0062] In a preset parameter search space, randomly initialize the positions and velocities of a plurality of particles, where represents a particle index, , represents the number of particles participating in the optimization. Set the inertia weight

[0063] , learning factor and maximum iteration number of a particle swarm optimization (PSO) algorithm. .

[0064] Step S32, for each particle , substitute the particle into the bistable stochastic resonance model in step S2, input the preprocessed transient signal into the bistable stochastic resonance model, and obtain the output signal for the preprocessed transient signal by numerical solution, calculate the kurtosis of the output signal , and take the kurtosis of the output signal as the current fitness value of the th particle. Step S33, update the individual optimum and the global optimum according to the fitness values of the particles; the individual optimum refers to the optimum state reached by each particle in its own history, and the global optimum refers to the optimum state reached by the entire particle swarm in its own history. Specifically, step S33 includes: comparing the current fitness value of each particle with the historical best fitness value

[0065] of the corresponding particle, if the fitness value of the particle exceeds the historical best fitness value, i.e. , update the historical best fitness value to the fitness value of the particle, i.e. , and record the corresponding position; at this time, the current position is the historical best position thereof. Compare the fitness values of all particles with the global best fitness value

[0066] , if the fitness value of the particle exceeds the global best fitness value, i.e. , update the global best fitness value to the fitness value of the particle, i.e. , and record the corresponding position; at this time, the current position is the historical best position thereof. ​For global optimal position .

[0067] Step S34, updating particle velocity and position; the particle velocity and position are updated by using the following formula:

[0068]

[0069]

[0070] wherein, indicates an inertia weight, used to balance the global search and local search capabilities of the particle, and the inertia weight gradually decreases with the increase of the iteration number, so that the particle can better converge to the optimal solution;

[0071] indicates the particle velocity before updating;

[0072] indicates the particle velocity after updating;

[0073] , respectively indicate learning factors;

[0074] , respectively indicate random numbers between 0 and 1;

[0075] indicates the individual optimal position;

[0076] indicates the particle position before updating;

[0077] indicates the global optimal position;

[0078] indicates the particle position after updating, and the subscript i indicates the particle index, d indicates the potential well parameter dimension, i.e. the above-mentioned parameter or , t, t +1 respectively indicate the iteration number.

[0079] Step S35, repeating steps S32-S34 until the particle swarm converges or reaches a preset iteration number, and outputting the optimized potential well parameters.

[0080] Specifically, it is judged whether the termination condition is reached, and the termination condition is that the particle swarm converges, i.e. the global optimal fitness value has no significant change for consecutive generations, or reaches a preset iteration number, i.e. the above-mentioned maximum iteration number . When any of the termination conditions is met, the iteration ends.

[0081] The global optimal position obtained after iteration The optimized potential well parameter .

[0082] In step S4, the optimized potential well parameter is substituted into the bistable stochastic resonance model to process the preprocessed transient signal, and an enhanced output signal is obtained; specifically, the optimized potential well parameter obtained by searching in step S3 is substituted into the bistable stochastic resonance model to process the preprocessed transient signal, and an enhanced output signal is obtained. The stochastic resonance (SR) system is configured.

[0083] Then, the real-time collected and preprocessed transient signal stream is continuously input into the optimized stochastic resonance (SR) system, and an enhanced output signal is obtained .

[0084] In step S5, fault detection is performed according to the enhanced output signal to determine whether a fault occurs.

[0085] Under the condition that the stochastic resonance (SR) system is in the most advantageous well parameter, when the equipment is in a fault-free running state, the enhanced output signal fluctuates slightly within a certain potential well range. The potential well range mentioned here can be an interval corresponding to a positive value, or an interval corresponding to a negative value.

[0086] When a weak fault traveling wave signal arrives, it will trigger a clear and large amplitude transition phenomenon of the system state once or multiple times, that is, the enhanced output signal jumps from one stable state (such as ) to another stable state (such as ), wherein .

[0087] Based on the change characteristics of the system state when a fault occurs, the embodiment of the application converts the originally complex fault detection problem into a simple threshold comparison problem. The threshold comparison method is used to realize fault judgment. Step S5 includes the following steps:

[0088] According to the optimized potential well parameter, a preset threshold is set; for example, the preset threshold is set by using the following formula:

[0089]

[0090] wherein, represents a safety factor, <1, such as ; , respectively represent the optimized potential well parameter; represents a preset threshold value.

[0091] the enhanced output signal is compared with the preset threshold value .

[0092] When the absolute value of the enhanced output signal exceeds the preset threshold value , it is determined that a fault occurs, and a fault occurrence timestamp information is recorded.

[0093] Specifically, in the actual fault detection process, the transient signal on the cable line is continuously monitored and sent into the bistable stochastic resonance model optimized and configured, to obtain the enhanced output signal When the absolute value of the enhanced output signal first crosses the preset threshold value , it is determined that a fault occurs, and the timestamp at this moment is recorded as the arrival time of the fault traveling wave. The time information can be directly used to trigger the subsequent fault location device, so that the specific position of the fault occurrence can be quickly and accurately determined.

[0094] The embodiment of the application utilizes the random resonance (SR) mechanism to transfer part of the noise energy to the weak fault signal, so as to realize amplification and enhancement of the weak fault signal.

[0095] The application introduces an adaptive optimization strategy based on output signal Kurtosis maximization, so that the random resonance (SR) system can automatically optimize to the best parameters without manual intervention and prior knowledge of the signal, and is suitable for detecting non-periodic, transient impact type traveling wave signals.

[0096] Based on the above system characteristics, the weak amplitude detection problem is converted into a clear and reliable system state transition detection problem. In the fault-free state, the system is in a stable state, and the output signal fluctuates little; when a fault occurs, the system state will have obvious transition. By detecting this transition phenomenon, the sensitivity and accuracy of detection can be greatly improved, the false alarm rate is reduced, and reliable triggering basis is provided for subsequent fault location, so that the fault location device can be started in time and accurately, and a foundation is laid for rapid elimination of faults.

[0097] The working process of the application is described in detail below through a specific embodiment of an application scenario.

[0098] Application scenario: a 10kV XLPE cable line with a total length of 5km, a high-frequency current transformer and a signal acquisition module are installed at the head end of the cable line, the sampling frequency of the signal acquisition module is f s =20MHz.

[0099] Suppose that a high impedance grounding fault occurs at a distance of 3 km from the head end of the cable line at a certain moment. The weak traveling wave signal generated by the fault will propagate along the line to the head end. The fault detection specific implementation steps are as follows:

[0100] First, signal acquisition and preprocessing are performed. The signal acquisition module acquires the current signal on the cable line in real time. When a slight fluctuation in signal energy is detected, a transient signal containing a data window of 1024 sampling points is intercepted . Since the amplitude of the fault traveling wave signal is extremely small, it is completely submerged in strong background noise, and the existence of the fault traveling wave signal cannot be distinguished with the naked eye.

[0101] In order to facilitate subsequent processing and analysis, the transient signal in the data window is normalized and preprocessed, the amplitude of the transient signal is adjusted to [-1, 1], and the preprocessed transient signal is obtained.

[0102] Next, the particle swarm optimization (PSO) algorithm based on kurtosis optimization is started, and parameter adaptive optimization is performed. First, the particle swarm is initialized, including the particle swarm size ; the parameter search range , ; the inertia weight linearly decreases from 0.9 to 0.4; the learning factor ; the maximum number of iterations . The iteration optimization process is as follows:

[0103] The algorithm randomly generates 20 particles, such as ;

[0104] For particle , its parameters and the preprocessed transient signal are substituted into the bistable stochastic resonance model, and the fourth-order Runge-Kutta algorithm is used with a step size to calculate the output signal of the particle.

[0105] The kurtosis value of the output signal is calculated.

[0106] This process is repeated for all 20 particles to obtain their respective kurtosis values.

[0107] According to the kurtosis value, the individual optimum of each particle and the global optimum of the population are updated.

[0108] According to the particle swarm optimization formula, the speed and position of all particles are updated.

[0109] Repeat 50 times, after the end of the iteration, assuming the algorithm converges, the global optimal parameters are , at this time the corresponding maximum kurtosis value is .

[0110] Finally, signal enhancement and fault judgment. First, using the optimal parameters to construct the final stochastic resonance system; then, the preprocessed transient signal is input into the optimal stochastic resonance system again, and the enhanced output signal is obtained.

[0111] In the original signal, the weak traveling wave pulse is submerged in noise and difficult to identify. In the enhanced output signal , these weak traveling wave pulses are converted into a sharp transition from negative stable state to positive stable state. The impact characteristics of the signal are greatly enhanced, and the background noise is effectively suppressed near the two stable states.

[0112] In the fault judgment process, first calculate the criterion threshold . Then continuously monitor the enhanced output signal , when the absolute value of the enhanced output signal is greater than 0.67 for the first time, it is judged that a high impedance grounding fault occurs, and the time corresponding to the point is recorded. Send this trigger signal to the fault location system.

[0113] Through the above embodiment, the present application successfully converts the extremely weak signal detection problem with a signal-to-noise ratio of possibly negative decibels into a threshold judgment problem of a bistable signal with high signal-to-noise ratio and obvious characteristics, thereby realizing reliable and sensitive detection of high impedance grounding faults.

[0114] Compared with the prior art, the present application has the following remarkable beneficial effects:

[0115] (1) The present application utilizes the principle of stochastic resonance to convert the inherent noise in the environment from an interference factor into a beneficial energy source, which can effectively amplify the fault signal submerged in strong noise with extremely low amplitude, and the detection sensitivity is much higher than that of traditional methods.

[0116] (2) The present application introduces a particle swarm optimization (PSO) adaptive optimization mechanism based on kurtosis maximization, without any prior knowledge about the signal and noise, such as signal frequency, amplitude, statistical distribution, etc. information, which can automatically find the best working parameters, and has good adaptability and robustness for high impedance grounding faults under different lines, different working conditions and different noise levels.

[0117] (3) The algorithm involved in the present application, such as particle swarm optimization (PSO) algorithm and fourth-order Runge-Kutta algorithm, is a mature algorithm, the calculation complexity is moderate, can be realized on a general digital signal processing (Digital Signal Process, DSP), field programmable gate array (Field-Programmable Gate Array, FPGA) or industrial computer, the hardware cost is low, easy to upgrade or integrate on the existing monitoring equipment, and has high engineering application value.

[0118] The above merely describes the preferred embodiments of the present application, and does not limit the embodiments and protection scope of the present application. It should be understood by those skilled in the art that any equivalent replacement and obvious change made according to the content of the present application should be included in the protection scope of the present application.

Claims

1. An adaptive stochastic resonance weak fault detection method based on kurtosis optimization, characterized in that, include: Step S1: Acquire transient signals on the cable line and preprocess the transient signals to obtain preprocessed transient signals; Step S2: Construct a bistable stochastic resonance model based on the Langevin equation, and use the fourth-order Runge-Kutta algorithm to numerically solve the Langevin equation to obtain the output signal; Step S3: Using the kurtosis of the output signal as the fitness function, the potential well parameters of the bistable stochastic resonance model are optimized based on the particle swarm optimization algorithm to obtain the optimized potential well parameters. Step S4: Substitute the optimized potential well parameters into the bistable stochastic resonance model to process the preprocessed transient signal and obtain the enhanced output signal. Step S5: Perform fault detection based on the enhanced output signal to determine whether a fault has occurred; When the absolute value of the enhanced output signal exceeds a preset threshold, a fault is determined to have occurred, and the fault occurrence timestamp information is recorded. The preset threshold is set based on the optimized potential well parameters, and the preset threshold is: ； in, Indicates the safety factor; , These represent the optimized potential well parameters; This indicates a preset threshold.

2. The adaptive stochastic resonance weak fault detection method based on kurtosis optimization according to claim 1, characterized in that, In step S1, the preprocessing includes normalization preprocessing, which uses the following formula: ； in, Indicates a transient signal; n Represents discrete time points; This represents the minimum value of the transient signal within the sliding data window; This represents the maximum value of the transient signal within the sliding data window; This represents the preprocessed transient signal.

3. The adaptive stochastic resonance weak fault detection method based on kurtosis optimization according to claim 1, characterized in that, In step S2, the differential form of the Langevin equation is: ； in, x This represents the output signal of a random resonance system; a , b ... This represents the preprocessed transient signal; This represents the differential form of the Langevin equation.

4. The adaptive stochastic resonance weak fault detection method based on kurtosis optimization according to claim 1, characterized in that, In step S2, the output signal is: ； in, , These represent the output signals, n、n +1 represents a discrete time point; a , b ... This represents the preprocessed transient signal; h This indicates the calculation step size.

5. The adaptive stochastic resonance weak fault detection method based on kurtosis optimization according to claim 1, characterized in that, Step S3 includes: Step S31, initialize the particle swarm; Step S32: For each particle, substitute the particle into the bistable stochastic resonance model to obtain the output signal obtained by numerical solution of the preprocessed transient signal, and use the kurtosis of the output signal as the fitness value of the particle. Step S33: Update the individual optimal and global optimal values ​​based on the fitness values ​​of the particles; Step S34: Update particle velocity and position; Step S35: Repeat steps S32-S34 until the particle swarm converges or the preset number of iterations is reached, and output the optimized potential well parameters.

6. The adaptive stochastic resonance weak fault detection method based on kurtosis optimization according to claim 5, characterized in that, Step S33 includes: The fitness value of the particle is compared with the historical best fitness value of the corresponding particle. If the fitness value of the particle exceeds the historical best fitness value, the historical best fitness value is updated to the fitness value of the particle, and the corresponding position is recorded. The fitness value of the particle is compared with the global best fitness value. If the fitness value of the particle exceeds the global best fitness value, the global best fitness value is updated to the fitness value of the particle, and the corresponding position is recorded.

7. The adaptive stochastic resonance weak fault detection method based on kurtosis optimization according to claim 5, characterized in that, In step S34, the particle velocity and position are updated using the following formula: ； ； in, Indicates inertia weight; This indicates the particle velocity before the update; This indicates the updated particle velocity; , These represent learning factors; , These represent random numbers between [0, 1]. Indicates the optimal position for an individual; Indicates the particle position before the update; Indicates the globally optimal position; Indicates the updated particle position, subscript i Indicates particle index, d Indicates the dimension of the potential well parameters. t、t +1 represents the number of iterations.

8. The adaptive stochastic resonance weak fault detection method based on kurtosis optimization according to claim 1, characterized in that, Step S5 includes: The enhanced output signal is compared with a preset threshold. When the absolute value of the enhanced output signal exceeds the preset threshold, a fault is determined to have occurred, and the fault occurrence timestamp information is recorded.

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