An enhanced diagnosis method based on feature fusion convolutional neural network and max-min elimination algorithm

Abstract

The application discloses an enhanced diagnosis method based on a feature fusion convolutional neural network and a max-min elimination algorithm, which comprises the following steps: data acquisition and preprocessing based on a max-min elimination algorithm (MMFA), wherein data is divided into different operation categories, and the data is sorted according to amplitude to eliminate noise signals; data enhancement based on fast Fourier transform and wavelet transform, wherein standardization processing is performed and data is output; a preprocessed convolutional neural network (PRE-ENFCNN) is constructed and trained through 5-fold cross-training, feature saliency and feature diversity are learned, and an optimal model is saved; fault diagnosis and testing based on ablation experiments and comparative experiments are performed to verify the effectiveness and superiority of the PRE-ENFCNN method, and enhanced diagnosis of various fault modes of a planetary gear box is completed. The application provides an enhanced diagnosis method using a feature fusion convolutional neural network and a max-min elimination algorithm, which can realize accurate fault diagnosis of the planetary gear box and improve the efficiency and reliability of predictive maintenance.

Description

Technical Field

[0001] This invention relates to the field of aerospace mechanical equipment technology, and in particular to an enhanced diagnostic method based on feature fusion convolutional neural networks and a maximum-minimum elimination algorithm. Background Technology

[0002] With the continuous advancement of industrial automation and intelligence, health monitoring and fault diagnosis of complex aerospace mechanical equipment have become increasingly important. Planetary gearboxes, as transmission devices widely used in various fields, are crucial for production efficiency and equipment lifespan due to their stable operation. However, due to their complex structure and harsh working environment, early fault diagnosis of planetary gearboxes has always been a challenging task. In recent years, the rapid development of deep learning technology has provided new ideas and methods for solving this problem.

[0003] Planetary gearbox failures typically manifest as abnormal vibration, abnormal sound, and elevated temperature. However, due to various factors such as load variations, lubrication conditions, and operating environment, fault characteristics may be masked or become difficult to extract from vibration signals. Traditional frequency and time domain analysis methods struggle to capture the characteristics of complex fault modes, thus requiring more advanced techniques to improve diagnostic accuracy.

[0004] Deep learning technologies, especially convolutional neural networks (CNNs), recurrent neural networks (RNNs), and transformers, have been widely applied to the processing of multimodal sensor data such as vibration signals, sound signals, and images due to their excellent feature extraction and pattern recognition capabilities. In fault diagnosis, traditional feature extraction methods typically rely on domain experts to manually design features; however, such methods may fail to capture crucial information under complex fault modes. Deep learning methods, on the other hand, have the ability to automatically learn features, acquiring higher-level abstract features from raw data to better represent fault characteristics. Feature fusion, as an effective means of improving fault diagnosis accuracy, plays a crucial role in deep learning. In practical applications, information collected from different sensors or data sources is often complementary; by fusing them, a more comprehensive reflection of the equipment's operating status can be achieved. For example, in planetary gearbox fault diagnosis, data from different sensors, such as vibration signals, sound signals, and temperature signals, can provide multifaceted information. Deep learning models can fuse these different modalities of data to better distinguish between normal and abnormal states. Feature fusion not only improves model accuracy but also enhances its robustness, enabling it to maintain good performance under various operating conditions.

[0005] In practical applications, sensor data may contain a large amount of redundant or noisy information, which can interfere with the extraction and diagnosis of fault features. To reduce computational burden and improve model efficiency, feature selection becomes particularly important. MMFA is a commonly used feature selection method that evaluates the contribution of features to the classification task by calculating the maximum and minimum values ​​of features, thereby selecting the most informative features.

[0006] In summary, regarding the enhanced diagnostics of planetary gearboxes, the failure modes of industrial equipment are becoming increasingly complex, and traditional methods often fail to meet the demands for accurate diagnosis. Preliminary analysis of existing data identifies four main challenges: short sample length, lack of time-series features, small differences in vibration signals across different failure modes, and abnormal samples within the dataset. These issues reduce the diagnostic efficiency and limit the model's accuracy. Therefore, optimizing these four aspects is a key focus and challenge of current research. Summary of the Invention

[0007] Objective: This invention provides an enhanced diagnostic method based on a feature fusion convolutional neural network and a maximum-minimum elimination algorithm. The method involves data acquisition and preprocessing, dividing the data into different operation classes and sorting the data according to the original amplitude to eliminate noise signals. Next, data enhancement is performed based on FFT and WT. The original input data is standardized using FFT and WT, and then output. Furthermore, 5x cross-training is used to learn feature saliency and feature diversity, retaining the optimal model. Finally, performance analysis is conducted through two experiments, and comparative experiments verify the effectiveness and superiority of PRE-ENFCNN, successfully completing the enhanced diagnostic process for planetary gearboxes.

[0008] Technical Solution: This invention provides a diagnostic enhancement method based on feature fusion and PRE-ENFCNN, including: data acquisition and preprocessing of raw data, sorting by original amplitude and filtering noise signals; data enhancement process based on FFT and WT for standardization and output of data; feature saliency learning and feature diversity learning based on 5x cross-training to output the optimal model; implementation of comparative experiments to verify the effectiveness and superiority of PRE-ENFCNN, and completion of enhanced diagnosis of planetary gearboxes.

[0009] Specifically, the data preprocessing and data augmentation include:

[0010] To address noise interference in data preprocessing, a max-min elimination algorithm is proposed to remove outliers, achieving data cleaning through data processing. Data augmentation utilizes FFT and WT for data standardization. FFT significantly reduces the number of multiplications required to compute DFT. In particular, the more sample points N to be transformed, the greater the computational savings of the FFT algorithm. The formula for calculating DFT is as follows:

[0011]

[0012] in Dividing the above equation into odd and even parts, the first 2 / N points can be represented by the following formula.

[0013]

[0014]

[0015] Similarly, the last 2 / N points can be represented as:

[0016]

[0017] Continue performing parity decomposition on variables A[k] and B[k] until they become two-point DFTs. This avoids repeated calculations and thus achieves the progress of FFT.

[0018] Traditional Fourier transform is used for time-frequency domain processing and has high accuracy when processing periodically stationary signals. However, when processing non-stationary signals such as pulse signals, the Fourier transform can only reflect the average value of the signal's frequency components and cannot describe the characteristics of a specific segment of the signal. Wavelet transform is a widely used signal processing method. Its basic idea is to consider that different frequency components of the signal have different time-varying characteristics. In other words, high frequencies change rapidly, and low frequencies change slowly.

[0019] If the function ψ(x) satisfies the following formula, then it is defined as an allowed wavelet.

[0020]

[0021] Perform an integral transform on any given function f(x):

[0022]

[0023] This formula is called the continuous wavelet transform of f(x) based on ψ(x). The practical significance of the wavelet transform lies in representing the correlation of a function using a wavelet translation and extension system.

[0024] By fusing the signal features extracted by FFT and WT, combining two different feature extraction methods, the richness and diversity of feature information are enhanced, thereby improving CNN performance. The specific algorithm is as follows:

[0025] Fea = conateted(x1, x2)

[0026] Where x1 is the signal feature vector after FFT processing, x2 is the image feature vector after WT processing, and Fea is the signal feature quantity after data augmentation.

[0027] Specifically, the PRE-ENFCNN includes:

[0028] A one-dimensional CNN is used to extract deep features from the signal after FFT. Simultaneously, a time-spectrum graph is converted from the input original fault signal using a time-weighted array (WT), and a two-dimensional CNN is used to extract deep features from the time-spectrum graph. Finally, the deep and diverse features extracted by the CNN are fused using connection layers. At the end of PRE-ENFCNN, a softmax activation function is used to obtain the classification result for fault diagnosis. Before fusing features from different dimensions, the output data of the 2D-CNN must be flattened to 1D. The flattening principle is as follows:

[0029]

[0030]

[0031] Among them, Q i It is an n×n feature map, where f represents a single feature value of the two-dimensional network, and q i This represents flattened data as a vector.

[0032] Feature diversity fusion is performed in the connection layer. The flattened multi-channel features from the previous one-dimensional CNN and two-dimensional CNN will be fused. The principle of feature fusion is as follows:

[0033]

[0034] Where, p i is the feature value of the one-dimensional network; s is a single feature value of the one-dimensional network. Through flattening and feature diversity fusion, the fused features are sent to a 2FC layer. Finally, the Softmax activation function is used to obtain fault diagnosis results based on heterogeneous fused features. During feature learning, k-fold cross-validation is used to improve the effectiveness of the diagnosis.

[0035] This invention provides a novel method called "PRE-ENFCNN," which combines feature fusion and CNN techniques to achieve a data preprocessing-enhanced diagnostic method. The core objective of this method is to provide more accurate results in the field of fault diagnosis. The specific steps are as follows: First, through data acquisition and preprocessing, the acquired data is divided into different operation categories and sorted according to the original amplitude of the data. This aims to eliminate potential noise signals, thereby improving the quality of subsequent processing. Second, based on the sorted data, data augmentation is performed using FFT and WT algorithms. The original data is input into this process and then standardized using FFT and WT to obtain the processed output data. Next, a 5x cross-training strategy is employed to perform feature saliency learning and feature diversity learning to identify the most salient and diverse features. During training, the model with the best performance is saved. Finally, in two experiments, we compare the experimental results to perform performance analysis, verifying the effectiveness and superiority of the PRE-ENFCNN method.

[0036] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: Effective data partitioning and sorting eliminates noise signals, improving the accuracy of fault feature extraction. Data augmentation based on FFT and WT helps capture hidden patterns, improving data consistency and analysis quality. Five-fold cross-training strengthens feature learning, reduces feature redundancy, and enhances model generalization ability. Finally, performance analysis verifies the effectiveness of the method, contributing to improved diagnostic efficiency and reduced costs. Attached Figure Description

[0037] Figure 1 Here is the overall flowchart of the proposed method;

[0038] Figure 2 A fault diagram of the sun gear for testing and measurement;

[0039] Figure 3 The original signal diagram consists of 250 random samples of class 0;

[0040] Figure 4 A comparison chart of level 0 normal samples and abnormal samples;

[0041] Figure 5 A comparison of the signal before and after cleaning;

[0042] Figure 6 The image shows the results of the ablation experiment at 1500 rpm.

[0043] Figure 7 A graph showing the results of 5x cross-validation and a performance evaluation comparison of the four methods;

[0044] Figure 8A graph comparing diagnostic results with existing epidemiological methods;

[0045] Figure 9 The image shows the results of the ablation experiment at 2700 rpm.

[0046] Figure 10 A graph showing the results of 5x cross-validation and a performance evaluation comparison of the four methods;

[0047] Figure 11 This is a graph comparing diagnostic results with existing popular methods. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0049] See Figure 1 This is a schematic diagram of the planetary gearbox enhanced diagnostic method based on feature fusion convolutional neural network and maximum-minimum elimination algorithm provided by the present invention.

[0050] To illustrate the method of this invention, its effectiveness is verified using the ICPHM2023 data challenge test bench. This test bench includes a drive motor, a two-stage planetary gearbox, a two-stage parallel gearbox, and a magnetic brake. During the experiment, the sun gear exhibits five health states: normal, surface wear, cracks, chips, and missing teeth. The test bench and fault conditions are as follows: Figure 2 As shown. In this case, there are two different operating conditions: a motor speed of 1500 rpm and a load of 10 Nm, and a motor speed of 2700 rpm and a load of 25 Nm. An accelerometer is installed on the second stage of the planetary gearbox to acquire vibration signals. Each vibration signal is recorded in three directions (x, y, z) with a period of 5 minutes and a sampling frequency of 10 kHz. There are 10,000 samples for each fault mode, and a total of 50,000 samples for the five modes of one operating condition. This invention employs... x Data. Detailed information about the data used is shown in Table 1.

[0051] Table 1. Detailed information on the data used.

[0052]

[0053] To address the issue of outliers in the dataset, data cleaning was performed. The original signal, consisting of 250 random samples of class 0, was observed, such as... Figure 3 As shown, it is not difficult to find some abnormal samples, such as Figure 3 As shown in the red circle. Comparing a normal sample with an abnormal sample yields better analysis, such as... Figure 4As shown in the figure; although each individual sample is short, the number of samples is very large, with 10,000 samples for each fault mode. Therefore, based on the small amplitude difference characteristics of vibration signals under different fault modes, this invention proposes a maximum-minimum elimination algorithm that can adaptively eliminate 5% of the samples. This method can effectively and automatically detect and remove abnormal samples. To more intuitively demonstrate the effect of data cleaning, under the operating conditions of 1500rpm-10Nm, the figure shows the signals of 250 random samples under each fault mode, as shown in the figure. Figure 5 As shown.

[0054] To address the three main challenges of short sample length, lack of time-series features, and small differences in vibration signals under different fault modes, which lead to poor generalization ability of trained models, we propose the PRE-ENFCNN method for gearbox fault diagnosis. This method utilizes FFT and WT to enhance the data information, and then constructs two CNNs of different dimensions to extract and fuse features for accurate fault diagnosis.

[0055] Step (1) uses MMFA to preprocess the original vibration signal to prevent the occurrence of abnormal samples.

[0056] This paper describes a data preprocessing procedure to address noise interference. A proposed maximum-minimum elimination algorithm is used to process the raw data, aiming to eliminate outliers. The preprocessing process includes data loading, sorting, segmentation, and further processing. First, the raw data is sorted according to labels, and observation data and labels are extracted. Then, the observation data is divided into multiple subsets. For each subset, the difference between the maximum and minimum values ​​of the data columns is calculated, and columns with smaller differences are removed from the data. This preprocessing reduces noise interference to a certain extent, providing a cleaner data foundation for subsequent analysis and modeling.

[0057] Step (2) involves augmenting the samples using FFT and WT techniques, then standardizing them to ensure data consistency, and finally inputting the samples into the PRE-ENFCNN model.

[0058] By introducing FFT and WT techniques, data augmentation aims to improve data quality by analyzing the frequency domain characteristics and multi-scale information of signals. FFT transforms the signal into a frequency domain signal, revealing frequency information, while WT's scale decomposition reveals the signal's characteristics at different scales. These methods help detect periodicity, resonant frequencies, and trend changes, and can suppress noise, making the signal smoother. Therefore, FFT and WT, as data augmentation tools, can not only enhance signal features but also improve data quality, providing more informative input for subsequent analysis and model training.

[0059] After FFT and WT data augmentation, data standardization was performed to optimize the data before it was input into PRE-ENFCNN. The main goal of this step is to ensure the data has a consistent scale and distribution, eliminating scale differences between different features and thus optimizing the neural network training process. Standardization adjusts the data to a uniform range, which helps improve model stability and convergence, providing more favorable conditions for subsequent feature learning and model training.

[0060] In step (3), a 5x cross-training was performed to train a high-quality model. The optimal model was continuously tracked and saved while using PRE-ENFCNN for feature saliency learning and feature diversity learning.

[0061] To ensure high-quality model training, a 5x cross-training strategy was employed. In this process, the data was divided into five subsets, used for training and validation respectively, to evaluate model performance from multiple perspectives and in diverse ways. While using PRE-ENFCNN for feature saliency learning and feature diversity learning, model performance was continuously monitored, and the best-performing model was tracked and saved during training. This approach aims to maximize the model's learning and generalization abilities, ensuring that the resulting model performs well even when handling unseen data.

[0062] Step (4) involved an in-depth analysis of the performance through two sets of experiments. The comparative experiments clearly demonstrated the effectiveness and superiority of the PRE-ENFCNN method.

[0063] Through in-depth analysis of two sets of experiments, the model performance was comprehensively evaluated. A comparison of these two sets of experiments clearly demonstrates the effectiveness and superiority of the PRE-ENFCNN method. The comparative results reveal the method's outstanding performance in handling data augmentation, feature learning, and model training, providing ample support and validation for its superiority in practical applications.

[0064] (1) Operating conditions of 1500rpm-10Nm

[0065] The model was trained using two experiments under two different working conditions, and then tested using the trained model. The test results are provided as a supplementary .csv file, showing the results based on the training dataset. The seven methods are ENFCNN, PRE-FCNN, FCNN, FFT-1D-CNN, WT-2DCNN, FFT-Cascaded Forest, and FFT-Lightweight GBM.

[0066] The hyperparameters of the model are set as shown in Table 2. The input of 1D-CNN is set to 201×1, and the input of 2D-CNN is set to 32×32. In addition, the learning rate is 0.005, the number of epochs is 200, and the batch size is 64.

[0067] Table 2. Architecture of the proposed method

[0068]

[0069] To verify the effectiveness of the proposed PRE-ENFCNN method, ablation experiments were conducted under operating conditions of 1500 rpm and 10 Nm. ENFCNN, PRE-FCNN, and FCNN were used for comparison in the experiments. To avoid unforeseen consequences, the experiments were repeated three times. Figure 6 The detailed diagnostic accuracy for each method is shown. Furthermore, the mean diagnostic accuracy and standard deviation are shown in Table 3.

[0070] Table 3. Fault diagnosis results and standard deviations of the four methods

[0071]

[0072] As shown in Table 3, the proposed method based on PRE-ENFCNN has the highest average diagnostic accuracy at 92.86%, followed by ENFCNN, PRE-FCNN, and FCNN, with 92.86%, 79.71%, 65.06%, and 33.21%, respectively. Furthermore, the proposed method exhibits the lowest standard deviation of only 0.11, despite having the highest average diagnostic accuracy.

[0073] The comprehensive diagnostic performance of the four methods was analyzed in detail, and the results are as follows: Figure 7 As shown, the proposed method outperforms the other three methods, especially in fault mode 2, achieving a diagnostic accuracy of 91.63%. This is the best among all methods. According to... Figure 7 As shown in (b), the proposed method also has the highest recall and F1 score, both at 0.93. It is worth noting that PRE-FCNN has a precision of 0.66 but an F1 score of 0.65, indicating the instability of the method.

[0074] To demonstrate the superiority of the proposed method, comparative experiments were conducted, using FFT-1D-CNN, WT-2D-CNN, FFT-Cascaded Forest, and FFT-LightGBM as comparison models. The overall results are as follows: Figure 8As shown, the proposed method achieves the highest diagnostic accuracy of 93%, which is 5.32%, 10.38%, 8.08%, and 5.83% higher than FFT-1D-CN, WT-2D-CN, FFT-Cascade Forest, and FFT-Light GBM, respectively. This demonstrates the superiority of the proposed method under operating conditions of 1500 rpm and 10 Nm.

[0075] (2) Operating conditions of 2700rpm-25Nm

[0076] Similarly, the ablation experiment was repeated three times under operating conditions of 2700 rpm and 25 Nm. The detailed accuracy of each method is as follows: Figure 9 As shown in the figure. Furthermore, its average diagnostic accuracy and standard deviation are shown in Table 4.

[0077] Table 4. Fault diagnosis results and standard deviations of the four methods

[0078]

[0079] As shown in Table 4, the proposed method has the highest average diagnostic accuracy of 93.19%, followed by ENFCNN, PRE-FCNN, and FCNN, with 91.56%, 70.36%, and 66.89%, respectively. Furthermore, the proposed method has the lowest standard deviation of 0.17, indicating the best diagnostic stability. The comprehensive diagnostic performance of the four methods is then analyzed in detail, and the results are as follows: Figure 10 As shown. Although ENFCC ranked second in diagnostic accuracy among the four methods, its accuracy for class 4 was 4.83% lower than the proposed method. According to Figure 10 (b) shows that the proposed method has the highest recall and F1 score, both at 0.94. It is noteworthy that PRE-FCNN has a precision of 0.7 but an F1 score of 0.71, indicating the method's instability.

[0080] Similarly, comparative experiments were conducted on FFT-1D-CNN, WT-2D-CNN, FFT-Cascaded Forest, and FFT-Light GBM, with the following results: Figure 11 As shown in the figure, the proposed method has the highest diagnostic accuracy of 93.51%, which is 3.36%, 7.31%, 4.44%, and 4.62% higher than FFT-1D-CN, WT-2D-CN, FFT-Cascade, and FFT-Light GBM, respectively. These results verify the superiority and versatility of the proposed method under these working conditions.

[0081] To address the four key issues mentioned above, this invention proposes an enhanced diagnostic method based on feature fusion and PRE-ENFCNN for diagnosing planetary gearbox faults under two different operating conditions, requiring only a short single sample. The effectiveness and superiority of the proposed method are verified through comparison with existing popular methods. Furthermore, the versatility of the proposed method is demonstrated through two different experiments.

Claims

1. An enhanced diagnostic method based on feature fusion convolutional neural networks and a maximum-minimum elimination algorithm, characterized in that, The method includes the following steps: The Max-Min Elimination Algorithm (MMFA) is used to collect and preprocess triaxial vibration signal data to eliminate outlier samples. The MMFA process includes: calculating the maximum and minimum differences of individual samples in each axis of the vibration signal data, and sorting these maximum and minimum differences; obtaining the maximum and minimum sample difference matrix for the three axes based on a target screening index k; determining a common maximum and minimum sample index matrix based on the common index of the three axes' maximum and minimum sample difference matrices; calculating an elimination matrix based on the common maximum and minimum sample index matrix; and determining the filtered data samples based on the index indicators in the elimination matrix. The samples are enhanced using Fast Fourier Transform (FFT) and Wavelet Transform (WT) and then standardized. Through 5x cross-training, a preprocessed convolutional neural network (PRE-ENFCNN) is used to learn feature saliency and diversity, and the optimal model is saved. The PRE-ENFCNN includes: using a one-dimensional CNN to extract deep features of the signal after FFT, using a two-dimensional CNN to extract deep features of the spectrogram of WT, flattening the data output by the two-dimensional CNN into one-dimensional data, fusing it with the features output by the one-dimensional CNN in the connection layer, sending the fused features to the fully connected layer, and obtaining the fault diagnosis classification result through the Softmax activation function. The effectiveness and superiority of the PRE-ENFCNN method were verified through ablation experiments and comparative experiments, and its performance was analyzed and compared.

2. The enhanced diagnostic method based on feature fusion convolutional neural network and maximum-minimum elimination algorithm according to claim 1, characterized in that, The specific data acquisition and preprocessing based on MMFA are as follows: By observing and analyzing the raw data, comparing normal and abnormal samples, differences in amplitude were identified. Based on the vibration signal characteristics under different fault modes, MMFA was used to eliminate abnormal samples, effectively reducing noise interference and providing a clean data foundation for subsequent analysis and modeling. The MMFA algorithm is as follows: Suppose there are three vibration signal data points X = [x1, x2, ..., x] along different axes. i ..., x n ], Y = [y1, y2, ..., y n ] and Z = [z1, z2, ..., z n ], where n is the number of samples, and for a single sample xi = [x i1 ,x i2 , ..., x il ], where l is the length of a single sample of the original vibration signal data; first, determine the maximum and minimum differences between single sample data: a i =max(x i )-min(x i ) This allows us to obtain the maximum and minimum differences between samples of data from different axes, A = [a1, a2, ..., a...]. i ,....,a n ], and sort the value; Define the target screening index k to obtain the new maximum and minimum sample difference matrix A′. Where f is the index of the difference a' in the original matrix A; thus, for the other two axial data Y and Z, the maximum and minimum sample difference matrices B' and C' are obtained: Similarly, g and h are the indices of the differences b' and c' in the original matrices B and C, respectively; Based on this, the common maximum and minimum sample index matrix U is determined according to the common index of the three matrices: Where p is the spatial length of the common maximum and minimum sample index matrix, and p > k; based on this, the elimination matrix U' is calculated: d j =sort j [min(a″1,b″1,c″1),min(a″2,b″2,c″2),...,,min(a″ p ,b″ p ,c″ p )],j∈[1,k] Finally, based on the index indicator u in the elimination matrix U' j 'Identify the filtered data samples X', Y', and Z': X′=X-X U′ Y′=YY U′ Z′=ZZ U′。 3. The enhanced diagnostic method based on feature fusion convolutional neural network and maximum-minimum elimination algorithm according to claim 1, characterized in that, Data augmentation based on FFT and WT specifically includes: By introducing FFT and WT algorithms as data augmentation steps, feature enhancement is achieved, providing a more accurate and comprehensive feature representation for convolutional neural networks. The feature vectors processed by FFT and WT are combined with the original feature vectors to form a fusion function, thereby optimizing model performance and constructing a more comprehensive feature representation. The specific algorithms for FFT and WT are as follows: The FFT is used to extract signal features, reducing the number of multiplications required for the computer to perform the Discrete Fourier Transform (DFT). Furthermore, the more sample points N to be transformed, the more significant the computational savings of the FFT algorithm. The formula for calculating the DFT is as follows: in Let be the rotation factor; dividing the above equation into odd and even parts, the first N / 2 points can be expressed as the following formula: Similarly, the last N / 2 points can be represented as: Continue performing parity decomposition on variables A[k] and B[k] until they become two-point DFTs, thereby avoiding repeated calculations and realizing FFT; Assuming the function ψ(x) satisfies the wavelet allowance condition, it is defined as an allowable wavelet, as shown in the following formula: By performing an integral transform on any given function f(x), we obtain the continuous wavelet transform Wf(a, b) of f(x) based on ψ(x): By fusing the signal features extracted by FFT and WT, combining two different feature extraction methods, the richness and diversity of feature information are enhanced, thereby improving CNN performance; the specific algorithm is as follows: Fea = concatenated(x1, x2) Where x1 is the signal feature vector after FFT processing, x2 is the image feature vector after WT processing, and Fea is the signal feature quantity after data augmentation.

4. The enhanced diagnostic method based on feature fusion convolutional neural network and maximum-minimum elimination algorithm according to claim 1, characterized in that, The PRE-ENFCNN model was constructed and trained using a 5x cross-training method, specifically as follows: A PRE-ENFCNN model is constructed and trained using a 5x cross-validation method to conduct comprehensive deep model validation and performance evaluation. The dataset is divided into five mutually exclusive subsets, with four used for training and one for validation, ensuring sufficient validation for each subset and thus providing a comprehensive performance evaluation of the model. The PRE-ENFCNN includes: A one-dimensional CNN is used to extract deep features from the signal after FFT; simultaneously, the original input fault signal is converted into a time-spectrum image using WT, and a two-dimensional CNN is used to extract deep features from the time-spectrum image; finally, the deep and diverse features extracted by the CNN are fused using connection layers; at the end of PRE-ENFCNN, the softmax activation function is used to obtain the classification result of fault diagnosis; before fusing features of different dimensions, the data output by the two-dimensional CNN is flattened into one dimension, and the flattening process is as follows: Among them, Q i It is an n×n feature map, where f represents a single feature value of the two-dimensional network, and q i Represents flattened data as a vector; The output features of the one-dimensional CNN and the two-dimensional CNN are passed to the connection layer to obtain the fused feature vector: F i T =Concatenation(p i ,q i )=[S 11 ,...S nn ,f 11 ,...,f nn ] Where, p i is the eigenvalue of a one-dimensional network; s is a single eigenvalue of a one-dimensional network; The fused feature vectors are sent to a fully connected layer, which is then input into a Softmax activation function, outputting the probability of each category. The diagnostic model identifies the category with the highest probability as the final diagnostic result.

Images