A gearbox fault diagnosis method based on meshing frequency modulation energy entropy

Abstract

The application provides a gearbox fault diagnosis method based on meshing frequency modulation energy entropy, and belongs to the technical field of mechanical intelligent fault diagnosis. The method comprises the following steps: acquiring historical vibration signals of a gearbox and corresponding labels; performing envelope demodulation on the signals, extracting meshing frequencies and sidebands thereof, and constructing meshing frequency modulation energy entropy as an evaluation index; taking the minimization of the entropy as an objective, adopting an improved particle swarm optimization algorithm based on a hybrid strategy to optimize a decomposition modal number and a penalty factor of variational modal decomposition; performing decomposition based on optimal parameters to obtain intrinsic modal components; calculating envelope spectrum modulation entropy of each component, weighting and reconstructing a signal through a double attention mechanism; training a convolutional neural network model by using the reconstructed signal; inputting a signal to be diagnosed into the model after the same processing, and outputting a diagnosis result. The application can adaptively determine decomposition parameters, effectively extract fault features, and significantly improve the accuracy and robustness of gearbox fault diagnosis.

Description

Technical Field

[0001] This invention relates to the field of rotating machinery fault diagnosis technology, and more specifically, to a gearbox fault diagnosis method based on meshing frequency modulation energy entropy. Background Technology

[0002] As a core transmission component in industrial equipment, the health of the gearbox directly determines the continuous operation capability of the production line. Unlike ordinary rotating machinery, gearbox vibration signals exhibit significant multi-source coupling characteristics: the meshing frequency and its harmonics, as well as the modulation sidebands caused by faults, superimpose, resulting in complex signal components. Therefore, effectively extracting fault features from complex vibration signals is crucial for achieving gearbox fault diagnosis.

[0003] In gearbox fault diagnosis, meshing frequency and its sideband energy are important indicators reflecting the fault state. Existing methods mostly use indicators such as sideband energy ratio and sideband energy rate to characterize the severity of the fault. However, these indicators only describe the sideband energy change from a single dimension and fail to comprehensively consider the distribution uncertainty of meshing frequency harmonic energy and the fluctuation characteristics of sideband modulation, making it difficult to fully quantify the fault modulation characteristics.

[0004] Variational mode decomposition (VMD) is an effective signal decomposition method capable of decomposing non-stationary signals into multiple intrinsic mode components. However, its performance is highly dependent on the selection of parameters such as the number of decomposed modes and the penalty factor. Existing methods often use fixed parameters or empirical values, making it difficult to adapt to changes in signal characteristics under different operating conditions. While intelligent optimization algorithms can be used for parameter optimization, existing algorithms have limited ability to balance global exploration and local exploitation, and there is still room for improvement in optimization efficiency and accuracy.

[0005] Furthermore, existing signal reconstruction methods often employ equal weighting or directly select only a portion of the components, failing to fully utilize the differentiated contributions of each component to fault diagnosis. Although attention mechanisms are widely used in deep learning, there is still a lack of mature solutions for applying them to the calculation of reconstruction weights for intrinsic mode components.

[0006] In summary, how to construct a more comprehensive modulation feature evaluation index without human experience, achieve adaptive optimization of variational mode decomposition parameters, and perform intelligent weighted reconstruction based on the feature importance of each component, thereby improving the accuracy and robustness of gearbox fault diagnosis, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] The main objective of this invention is to address the shortcomings of existing technologies and provide a gearbox fault diagnosis method based on meshing frequency modulation energy entropy and adaptive optimization.

[0008] This invention is implemented as follows:

[0009] The technical solution to achieve the purpose of this invention is: a gearbox fault diagnosis method based on meshing frequency modulation energy entropy, comprising the following steps:

[0010] Step 1: Obtain the historical vibration signals of the gearbox and their corresponding tags;

[0011] Step 2: Demodulate the vibration signal by envelope, extract the meshing frequency and its sidebands, and construct the meshing frequency modulation energy entropy as a signal evaluation index.

[0012] Step 3: Using the meshing frequency modulation energy entropy as the optimization objective, an improved particle swarm optimization algorithm based on a hybrid strategy is used to optimize the number of decomposition modes and the penalty factor of variational mode decomposition to obtain the optimal parameter combination;

[0013] Step 4: Perform variational mode decomposition on the vibration signal based on the optimal parameter combination to obtain several intrinsic mode components;

[0014] Step 5: Calculate the envelope spectrum modulation entropy of each intrinsic mode component, calculate the reconstruction weight of each component through a dual attention mechanism, and obtain the reconstructed signal by weighted summation of the components.

[0015] Step Six: Train the neural network model based on the reconstructed signal and its corresponding label;

[0016] Step 7: Obtain the vibration signal of the gearbox to be diagnosed. Based on the optimal parameter combination obtained in Step 3, the reconstructed signal is obtained through Steps 4 and 5. The reconstructed signal is then input into the neural network model constructed in Step 6 for fault diagnosis.

[0017] Furthermore, in step two, the meshing frequency modulation energy entropy is constructed through the following sub-steps:

[0018] Step S21: Perform Hilbert envelope demodulation on the vibration signal to obtain the envelope signal;

[0019] Step S22: Perform a fast Fourier transform on the envelope signal to obtain the envelope spectrum;

[0020] Step S23: Identify the gearbox's meshing frequency and its 2nd to 5th harmonics in the envelope spectrum, and record the energy value of each harmonic;

[0021] Step S24: Calculate the ratio of each harmonic energy to the total energy, and obtain the Shannon entropy of the ratio sequence;

[0022] Step S25: Search for sidebands on both sides of each meshing frequency harmonic, and calculate the ratio of the standard deviation to the mean of the sideband energy as the sideband modulation intensity;

[0023] Step S26: Multiply the Shannon entropy by the sideband modulation intensity to obtain the meshing frequency modulation energy entropy.

[0024] Furthermore, in step three, the improved particle swarm optimization algorithm based on a hybrid strategy is implemented through the following sub-steps:

[0025] Step S31: Initialize the population using the Circle chaotic mapping, where each individual represents a set of parameters to be optimized [number of decomposed modes, penalty factor];

[0026] Step S32: Calculate the meshing frequency modulation energy entropy of each individual as its fitness value, and record the historical best position p of each individual. best,i and the global optimal position g best , where i is the individual ID;

[0027] Step S33: Calculate the dynamic stage discriminant factor φ(t):

[0028] Where t is the current iteration number, T is the maximum iteration number, and k is the steepness coefficient;

[0029] Step S34: When φ(t) > the first threshold, it is determined to be in the global exploration phase, triggering the wide-area scanning mechanism, and the updated formula is:

[0030]

[0031]

[0032] Where D is the adaptive scan step size, b is the spiral shape constant, l is a uniform random number in the range [-1, 1], β is the attenuation coefficient, and x i This represents the position of the i-th individual; Step S35: When φ(t) < the second threshold, it is determined to be in the local development stage, triggering the focused explosion mechanism, and the updated formula is:

[0033]

[0034]

[0035] Among them, A i Let A be the focusing radius of the i-th individual. max For the maximum focusing radius, f(x) i ) represents the fitness value, f min The minimum fitness value is N(0,1), which is a standard normally distributed random number.

[0036] Step S36: When the first threshold ≤ φ(t) ≤ the second threshold, it is determined to be a balanced transition stage. A hybrid driving mechanism is adopted, and the update formula is:

[0037]

[0038]

[0039] Among them, v i (t+1) and v i (t) represents the velocity vector of the i-th particle in generation t+1 and generation t, respectively. For sinusoidal adaptive inertia weights, ω is the mixing coefficient; min and ω max The minimum and maximum inertia weights are preset; c1 and c2 are learning factors, and r1 and r2 are random numbers in [0,1]. Step S37: After each generation update, apply an adaptive perturbation to the 20% of individuals with the worst fitness:

[0040]

[0041] Where, x i mutate σ represents the new individual position vector generated after the perturbation, and σ is the perturbation intensity.

[0042] Step S38: Determine whether the maximum number of iterations has been reached. If so, output the optimal number of decomposition modes and the optimal penalty factor; otherwise, return to step S32.

[0043] Furthermore, in step five, the envelope spectrum modulation entropy is used to perform Hilbert envelope demodulation on each intrinsic mode component to obtain the envelope signal, and Fourier transform is performed on the envelope signal to obtain the envelope spectrum. The Shannon entropy of the energy distribution of each frequency component in the envelope spectrum is calculated as the envelope spectrum modulation entropy of that component.

[0044] Furthermore, in step five, the dual attention mechanism calculates the reconstruction weights of each component through the following sub-steps: Step S41: Calculate the envelope spectrum modulation entropy of each intrinsic mode component; Step S42: Map the envelope spectrum modulation entropy of each component to primary weights using the Sigmoid function; Step S43: Normalize the initial weights using the Softmax function to obtain the final attention weights; Step S44: Perform weighted summation on each intrinsic modal component to reconstruct the vibration signal.

[0045] The beneficial effects of this invention are as follows:

[0046] First, a method for constructing the energy entropy of meshing frequency modulation is proposed. By calculating the Shannon entropy of the meshing frequency harmonic energy proportion sequence, the uncertainty of energy distribution is quantified. The ratio of the standard deviation to the mean of the sideband energy is then used as the modulation intensity, and the two are multiplied to obtain a comprehensive index. This index can comprehensively reflect the energy distribution characteristics of the meshing frequency harmonics and the sideband modulation fluctuation characteristics, exhibiting higher sensitivity and discrimination ability for gearbox modulation faults.

[0047] Second, an improved particle swarm optimization algorithm based on a hybrid strategy is proposed to optimize the number of decomposition modes and the penalty factor in variational mode decomposition. Unlike the standard particle swarm algorithm, this invention introduces a dynamic stage discrimination factor, adaptively switching between three stages—global exploration, equilibrium transition, and local development—according to the iteration process: a spiral wide-area scanning mechanism is used in the global exploration stage to enhance the search breadth; a hybrid driving mechanism is used in the equilibrium transition stage to integrate particle swarm velocity and spiral search; and a focused explosion mechanism is used in the local development stage to achieve fine-grained search. Simultaneously, an adaptive perturbation is applied to the worst-fitting individual in each generation, effectively enhancing the algorithm's ability to escape local optima and significantly improving the efficiency and accuracy of parameter optimization.

[0048] Third, a weighted reconstruction method for intrinsic mode components based on a dual attention mechanism is proposed. Unlike existing technologies that use equal weighting or directly select some components, this invention calculates the envelope spectrum modulation entropy of each intrinsic mode component, and calculates the primary weight and final attention weight sequentially through the Sigmoid function and the Softmax function, thereby enhancing fault-sensitive components and suppressing noise-dominant components, effectively improving the signal-to-noise ratio and fault feature fidelity of the reconstructed signal.

[0049] Fourth, the above methods form a complete gearbox fault diagnosis process. By guiding an improved particle swarm optimization algorithm based on a hybrid strategy using meshing frequency modulation energy entropy, optimal decomposition parameters are obtained, followed by variational mode decomposition. High-quality reconstructed signals are then obtained through dual attention weighted reconstruction, and finally, a convolutional neural network is used for classification and diagnosis. This invention requires no human intervention, can adaptively determine decomposition parameters, effectively extract fault features, and significantly improve the accuracy and robustness of gearbox fault diagnosis. It has significant engineering application value for guiding intelligent operation and maintenance of gearboxes. Attached Figure Description

[0050] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0051] Figure 1 This is a flowchart of a gearbox fault diagnosis method based on meshing frequency modulation energy entropy provided by an embodiment of the present invention;

[0052] Figure 2 This is a detailed flowchart of the improved particle swarm optimization algorithm based on a hybrid strategy provided in the embodiments of the present invention. Detailed Implementation

[0053] First, to address the problem that existing evaluation indicators are insufficient to fully quantify the characteristics of gearbox modulation faults, a method for constructing meshing frequency modulation energy entropy is proposed.

[0054] Secondly, to address the problem of adaptive optimization of variational mode decomposition parameters, a hybrid strategy-based improved particle swarm optimization algorithm (HSI-PSO) is proposed. This algorithm adaptively switches between three stages: global exploration, equilibrium transition, and local exploitation, achieving efficient optimization of the number of decomposition modes and penalty factor in variational mode decomposition (VMD).

[0055] Furthermore, a dual attention weighted reconstruction method is proposed, which calculates the primary weights and final attention weights sequentially using the Sigmoid function and the Softmax function, and then sums the components by weight to obtain the reconstructed signal.

[0056] Finally, a neural network model is trained using the reconstructed signal to achieve gearbox fault diagnosis. This invention deeply integrates meshing frequency modulation energy entropy with an improved particle swarm optimization algorithm based on a hybrid strategy. This enables adaptive determination of decomposition parameters, effective extraction of fault features, and significantly improved accuracy and robustness of gearbox fault diagnosis, providing reliable technical support for intelligent gearbox fault diagnosis.

[0057] The gearbox fault diagnosis method based on meshing frequency modulation energy entropy provided in this embodiment includes the following steps:

[0058] Step 1: Obtain the historical vibration signals of the gearbox and their corresponding tags;

[0059] Step 2: Demodulate the vibration signal by envelope, extract the meshing frequency and its sidebands, and construct the meshing frequency modulation energy entropy as a signal evaluation index.

[0060] Step 3: Using the meshing frequency modulation energy entropy as the optimization objective, an improved particle swarm optimization algorithm based on a hybrid strategy is used to optimize the number of decomposition modes and the penalty factor of variational mode decomposition to obtain the optimal parameter combination;

[0061] Step 4: Perform variational mode decomposition on the vibration signal based on the optimal parameter combination to obtain several intrinsic mode components;

[0062] Step 5: Calculate the envelope spectrum modulation entropy of each intrinsic mode component, calculate the reconstruction weight of each component through a dual attention mechanism, and obtain the reconstructed signal by weighted summation of the components.

[0063] Step Six: Train the neural network model based on the reconstructed signal and its corresponding label;

[0064] Step 7: Obtain the vibration signal of the gearbox to be diagnosed. Based on the optimal parameter combination obtained in Step 3, the reconstructed signal is obtained through Steps 4 and 5. The reconstructed signal is then input into the neural network model constructed in Step 6 for fault diagnosis.

[0065] Furthermore, in step two, the meshing frequency modulation energy entropy is constructed through the following sub-steps:

[0066] Step S21: Perform Hilbert envelope demodulation on the vibration signal to obtain the envelope signal;

[0067] Step S22: Perform a fast Fourier transform on the envelope signal to obtain the envelope spectrum;

[0068] Step S23: Identify the gearbox's meshing frequency and its 2nd to 5th harmonics in the envelope spectrum, and record the energy value of each harmonic;

[0069] Step S24: Calculate the ratio of each harmonic energy to the total energy, and obtain the Shannon entropy of the ratio sequence;

[0070] Step S25: Search for sidebands on both sides of each meshing frequency harmonic, and calculate the ratio of the standard deviation to the mean of the sideband energy as the sideband modulation intensity;

[0071] Step S26: Multiply the Shannon entropy by the sideband modulation intensity to obtain the meshing frequency modulation energy entropy.

[0072] Furthermore, in step three, the improved particle swarm optimization algorithm based on a hybrid strategy is implemented through the following sub-steps:

[0073] Step S31: Initialize the population using the Circle chaotic mapping, where each individual represents a set of parameters to be optimized [number of decomposed modes, penalty factor];

[0074] Step S32: Calculate the meshing frequency modulation energy entropy of each individual as its fitness value, and record the historical best position p of each individual. best,i and the global optimal position g best , where i is the individual ID;

[0075] Step S33: Calculate the dynamic stage discriminant factor φ(t):

[0076] Where t is the current iteration number, T is the maximum iteration number, and k is the steepness coefficient;

[0077] Step S34: When φ(t) > the first threshold, it is determined to be in the global exploration phase, triggering the wide-area scanning mechanism, and the updated formula is:

[0078]

[0079]

[0080] Where D is the adaptive scan step size, b is the spiral shape constant, l is a uniform random number in the range [-1, 1], β is the attenuation coefficient, and x i This represents the position of the i-th individual; Step S35: When φ(t) < the second threshold, it is determined to be in the local development stage, triggering the focused explosion mechanism, and the updated formula is:

[0081]

[0082]

[0083] Among them, A i Let A be the focusing radius of the i-th individual. max For the maximum focusing radius, f(x) i ) represents the fitness value, f min The minimum fitness value is N(0,1), which is a standard normally distributed random number.

[0084] Step S36: When the first threshold ≤ φ(t) ≤ the second threshold, it is determined to be a balanced transition stage. A hybrid driving mechanism is adopted, and the update formula is:

[0085]

[0086]

[0087] Among them, v i (t+1) and v i (t) represents the velocity vector of the i-th particle in generation t+1 and generation t, respectively. For sinusoidal adaptive inertia weights, ω is the mixing coefficient; min and ω max The minimum and maximum inertia weights are preset; c1 and c2 are learning factors, and r1 and r2 are random numbers in [0,1]. Step S37: After each generation update, apply an adaptive perturbation to the 20% of individuals with the worst fitness:

[0088]

[0089] Where, x i mutate σ represents the new individual position vector generated after the perturbation, and σ is the perturbation intensity.

[0090] Step S38: Determine whether the maximum number of iterations has been reached. If so, output the optimal number of decomposition modes and the optimal penalty factor; otherwise, return to step S32.

[0091] Furthermore, in step five, the envelope spectrum modulation entropy is used to perform Hilbert envelope demodulation on each intrinsic mode component to obtain the envelope signal, and Fourier transform is performed on the envelope signal to obtain the envelope spectrum. The Shannon entropy of the energy distribution of each frequency component in the envelope spectrum is calculated as the envelope spectrum modulation entropy of that component.

[0092] Furthermore, in step five, the dual attention mechanism calculates the reconstruction weights of each component through the following sub-steps: Step S41: Calculate the envelope spectrum modulation entropy of each intrinsic mode component; Step S42: Map the envelope spectrum modulation entropy of each component to primary weights using the Sigmoid function; Step S43: Normalize the initial weights using the Softmax function to obtain the final attention weights; Step S44: Perform weighted summation on each intrinsic modal component to reconstruct the vibration signal.

[0093] The method of the present invention will be described below using a specific gearbox fault diagnosis case as an example.

[0094] The specific implementation process is as follows:

[0095] like Figure 1 A gearbox fault diagnosis method based on meshing frequency modulation energy entropy includes the following steps:

[0096] Step 1: Obtain the historical vibration signals of the gearbox and their corresponding tags;

[0097] The experimental data comes from the publicly available gearbox fault diagnosis dataset from Southeast University. The dataset includes five gear states: normal, broken tooth, tooth root crack, tooth surface wear, and missing tooth. Multiple sample files were collected for each state, totaling vibration signals from eight channels. In this embodiment, the sampled signals were denoised and segmented to obtain the final sample set for training and testing. Each sample has 2048 sampling points, encompassing all eight channels, totaling 1024 groups. The dataset is divided into training, validation, and test sets in a 7:1:2 ratio, with a balanced distribution of samples across categories. To simulate the noise environment of a real industrial site, -6dB Gaussian white noise was added to the original signal in this embodiment to verify the robustness of the method under noise conditions.

[0098] Step 2: Demodulate the vibration signal by envelope, extract the meshing frequency and its sidebands, and construct the meshing frequency modulation energy entropy as a signal evaluation index.

[0099] Preferably, the envelope demodulation is achieved using the Hilbert transform method: extracting the envelope signal. Then, a(t) is subjected to a Fast Fourier Transform to obtain the envelope spectrum. Based on the gearbox parameters of this embodiment (32 teeth on the driving gear, 30Hz input shaft frequency), the theoretical meshing frequency is calculated. In the envelope spectrum, the energy of each harmonic is extracted using 960Hz and its 2nd to 5th harmonics as the center frequency; sidebands are searched on both sides of each harmonic at 30Hz intervals, and the sideband modulation intensity is calculated.

[0100] Step 3: Using the meshing frequency modulation energy entropy as the optimization objective, an improved particle swarm optimization algorithm based on a hybrid strategy is used to optimize the number of decomposition modes and the penalty factor of variational mode decomposition to obtain the optimal parameter combination;

[0101] Preferably, N=30, T=100, k=10, b=1, β=0.5, A max =0.5, ω min =0.2, ω max =0.9, c1=c2=1.5, σ=0.1, the first threshold is 0.7, the second threshold is 0.3, the optimization range of the decomposed mode number is [3,10], and the optimization range of the penalty factor is [500,3000].

[0102] Step 4: Perform variational mode decomposition on the vibration signal based on the optimal parameter combination to obtain several intrinsic mode components;

[0103] Step 5: Calculate the envelope spectrum modulation entropy of each intrinsic mode component, calculate the reconstruction weight of each component through a dual attention mechanism, and obtain the reconstructed signal by weighted summation of the components.

[0104] Step Six: Train the neural network model based on the reconstructed signal and its corresponding label;

[0105] Preferably, in this embodiment, the training convolutional neural network (CNN) model has the following structure: input layer; channel rearrangement layer; convolutional layer 1: 64 filters, kernel size 5, ReLU activation, Same padding; batch normalization layer 1; pooling layer 1: max pooling, pooling window 2; dropout layer 1: dropout rate 0.25; convolutional layer 2: 128 filters, kernel size 3, ReLU activation, Same padding; batch normalization layer 2; pooling layer 2: max pooling, pooling window 2; dropout layer 2: dropout rate 0.25; convolutional layer 3: 256 filters, kernel size 3, ReLU activation, Same padding; global average pooling layer; dropout layer 3: dropout rate 0.4; fully connected layer: 128 neurons, ReLU activation; dropout layer 4: dropout rate 0.5; output layer: 5 neurons, Softmax activation.

[0106] Model training parameters: Optimizer: Adam, initial learning rate 0.001; Loss function: sparse classification cross-entropy; Batch size: 64; Maximum training epochs: 100; Early stopping strategy: patience value 10, restore optimal weights; Learning rate decay: decay factor 0.5, patience value 5.

[0107] Step 7: Obtain the vibration signal of the gearbox to be diagnosed. Based on the optimal parameter combination obtained in Step 3, the reconstructed signal is obtained through Steps 4 and 5. The reconstructed signal is then input into the neural network model constructed in Step 6 for fault diagnosis.

[0108] To verify the advantages of the method of the present invention, an ablation experiment was conducted in this embodiment. The experiment compared the method of the present invention with a pure CNN model, a VMD+CNN with fixed parameters, a VMD+attention reconstruction+CNN with fixed parameters (where the VMD decomposition mode number = 8 and the penalty factor = 2000 when the parameters are fixed). The model performance was evaluated by accuracy and F1 score. The evaluation results are shown in Table 1.

[0109] Table 1 Comparison of Model Accuracy and F1 Score

[0110] Model Name accuracy F1 value Raw signal + CNN 91.2% 0.911 Fixed-parameter VMD+CNN 93.3% 0.932 Fixed-parameter VMD + Attention Reconstruction + CNN 94.5% 0.947 Method of the present invention 98.5% 0.984

[0111] As shown in Table 1, the accuracy and F1 value of the method of the present invention have achieved the best results among all models, which fully verifies the advantages of the present invention.

[0112] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A gearbox fault diagnosis method based on meshing frequency modulation energy entropy, characterized in that, Includes the following steps: Step 1: Obtain the historical vibration signals of the gearbox and their corresponding tags; Step 2: Demodulate the vibration signal by envelope, extract the meshing frequency and its sidebands, and construct the meshing frequency modulation energy entropy as a signal evaluation index. Step 3: Using the meshing frequency modulation energy entropy as the optimization objective, an improved particle swarm optimization algorithm based on a hybrid strategy is used to optimize the number of decomposition modes and the penalty factor of variational mode decomposition to obtain the optimal parameter combination; Step 4: Perform variational mode decomposition on the vibration signal based on the optimal parameter combination to obtain several intrinsic mode components; Step 5: Calculate the envelope spectrum modulation entropy of each intrinsic mode component, calculate the reconstruction weight of each component through a dual attention mechanism, and obtain the reconstructed signal by weighted summation of the components. Step Six: Train the neural network model based on the reconstructed signal and its corresponding label; Step 7: Obtain the vibration signal of the gearbox to be diagnosed. Based on the optimal parameter combination obtained in Step 3, the reconstructed signal is obtained through Steps 4 and 5. The reconstructed signal is then input into the neural network model constructed in Step 6 for fault diagnosis.

2. The gearbox fault diagnosis method based on meshing frequency modulation energy entropy as described in claim 1, characterized in that, In step two, the meshing frequency modulation energy entropy is constructed through the following sub-steps: Step S21: Perform Hilbert envelope demodulation on the vibration signal to obtain the envelope signal; Step S22: Perform a fast Fourier transform on the envelope signal to obtain the envelope spectrum; Step S23: Identify the gearbox's meshing frequency and its 2nd to 5th harmonics in the envelope spectrum, and record the energy value of each harmonic; Step S24: Calculate the ratio of each harmonic energy to the total energy, and obtain the Shannon entropy of the ratio sequence; Step S25: Search for sidebands on both sides of each meshing frequency harmonic, and calculate the ratio of the standard deviation to the mean of the sideband energy as the sideband modulation intensity; Step S26: Multiply the Shannon entropy by the sideband modulation intensity to obtain the meshing frequency modulation energy entropy.

3. The gearbox fault diagnosis method based on meshing frequency modulation energy entropy as described in claim 1, characterized in that, In step three, the improved particle swarm optimization algorithm based on a hybrid strategy is implemented through the following sub-steps: Step S31: Initialize the population using the Circle chaotic mapping, where each individual represents a set of parameters to be optimized [number of decomposed modes, penalty factor]; Step S32: Calculate the meshing frequency modulation energy entropy of each individual as its fitness value, and record the historical best position p of each individual. best,i and the global optimal position g best , where i is the individual ID; Step S33: Calculate the dynamic stage discriminant factor φ(t): Where t is the current iteration number, T is the maximum iteration number, and k is the steepness coefficient; Step S34: When φ(t) > the first threshold, it is determined to be in the global exploration phase, triggering the wide-area scanning mechanism, and the updated formula is: Where D is the adaptive scan step size, b is the spiral shape constant, l is a uniform random number in the range [-1, 1], β is the attenuation coefficient, and x i This represents the position of the i-th individual; Step S35: When φ(t) < the second threshold, it is determined to be in the local development stage, triggering the focused explosion mechanism, and the updated formula is: Among them, A i Let A be the focusing radius of the i-th individual. max For the maximum focusing radius, f(x) i ) represents the fitness value, f min The minimum fitness value is N(0,1), which is a standard normally distributed random number. Step S36: When the first threshold ≤ φ(t) ≤ the second threshold, it is determined to be a balanced transition stage. A hybrid driving mechanism is adopted, and the update formula is: Among them, v i (t+1) and v i ω(t) represents the velocity vector of the i-th particle in generation (t+1) and generation t, respectively, where ω(t) = ω min +(ω max -ω min ) ⋅sin(πt / 2T) is the sinusoidal adaptive inertia weight, γ(t)=1-φ(t) is the mixing coefficient; ω min and ω max The minimum and maximum inertia weights are preset; c1 and c2 are learning factors, and r1 and r2 are random numbers in [0,1]. Step S37: After each generation update, apply an adaptive perturbation to the 20% of individuals with the worst fitness: Where, x i mutate σ represents the new individual position vector generated after the perturbation, and σ is the perturbation intensity. Step S38: Determine whether the maximum number of iterations has been reached. If so, output the optimal number of decomposition modes and the optimal penalty factor; otherwise, return to step S32.

4. The gearbox fault diagnosis method based on meshing frequency modulation energy entropy as described in claim 1, characterized in that, In step five, the envelope spectrum modulation entropy is used to perform Hilbert envelope demodulation on each intrinsic mode component to obtain the envelope signal, and Fourier transform is performed on the envelope signal to obtain the envelope spectrum. The Shannon entropy of the energy distribution of each frequency component in the envelope spectrum is calculated as the envelope spectrum modulation entropy of that component.

5. The gearbox fault diagnosis method based on meshing frequency modulation energy entropy as described in claim 1, characterized in that, In step five, the dual attention mechanism calculates the reconstruction weights of each component through the following sub-steps: Step S41: Calculate the envelope spectrum modulation entropy of each intrinsic mode component; Step S42: Map the envelope spectrum modulation entropy of each component to primary weights using the Sigmoid function; Step S43: Normalize the initial weights using the Softmax function to obtain the final attention weights; Step S44: Perform weighted summation on each intrinsic modal component to reconstruct the vibration signal.

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