Small sample fault diagnosis method based on two-way convolution and closed set domain self-adaption

Abstract

The invention discloses a small sample fault diagnosis method based on two-way convolution and closed set domain self-adaption, vibration signals are preprocessed through maximum and minimum normalization and FFT, preprocessed frequency domain data are used as input by DPFC-FFABNet, and useful features can be fully extracted through a two-way full convolution structure. And group normalization and layer normalization are introduced, so that the robustness of the model is enhanced. A global-local feature fusion attention mechanism is utilized to consider extraction of local and global information of a feature sequence. In order to solve the problem of small sample fault diagnosis generalization, the method provided by the invention has excellent performance under different rotating mechanical parts, different rotating speed conditions and different noise interference conditions, and has good application value. And finally, on the basis of the method provided by the invention, multi-core maximum mean difference MKMMD is combined with class confusion minimization MCC, so that the fault diagnosis generalization capability of variable rotating speed and variable load is further enhanced.

Description

Technical Field

[0001] The present invention relates to the field of fault diagnosis of key mechanical components, and in particular to a small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation. Background Art

[0002] Rotating machinery is widely used in agriculture and industry. However, these machines often operate in harsh and complex environments, such as high temperature, high pressure, and impact corrosion. Failure can lead to unpredictable economic losses. Therefore, fault diagnosis research on key rotating machinery components is crucial for improving the safety and reliability of equipment operation.

[0003] The premise for traditional deep learning methods to achieve good performance is to have a large amount of high-quality training data and to satisfy the assumption that the training set and the test set meet the data distribution. However, in the field of industrial fault diagnosis, mechanical equipment has a long normal operation cycle, rarely fails, and the equipment often changes its operating conditions to achieve specified tasks, resulting in a decrease in the diagnostic accuracy of traditional deep learning methods.

[0004] Industrial equipment operates normally most of the time, and fault samples are scarce. Traditional deep networks, when faced with small-sample fault diagnosis tasks, suffer from issues such as insufficient feature extraction, weak model robustness, and low generalization ability. Summary of the Invention

[0005] In response to the problems of insufficient feature extraction, weak model robustness and low generalization ability reflected by traditional deep networks when facing small sample fault diagnosis tasks, the present invention provides a small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A small sample fault diagnosis method based on two-way convolution and closed set domain adaptation, the method comprising the following steps:

[0008] 1) By adopting a dual-path full convolution structure, more detailed features can be extracted;

[0009] 2) Using global-local feature fusion attention to extract and fuse local and global information of feature sequences;

[0010] 3) Use the bidirectional structure of BiGRU to model the relationship between the front and back of the feature sequence to perform feature enhancement;

[0011] 4) Group normalization and layer normalization are introduced after convolution and BiGRU respectively to make the model performance more robust;

[0012] 5) Combine multi-core maximum mean difference with class confusion minimization to achieve small sample closed set domain adaptive fault diagnosis.

[0013] Compared with the prior art, the present invention has the following technical effects:

[0014] 1. The performance of the proposed algorithm was verified on three datasets: Case Western Reserve University (CWRU) bearing data, Huazhong University of Science and Technology (HUST) bearing data, and Beijing Jiaotong University (BJU) gear data. Experiments demonstrated that the proposed method exhibits superior performance in small-sample fault diagnosis, including noise immunity and variable operating condition fault diagnosis. For small-sample closed-set domain adaptive diagnosis, the average variable operating condition diagnostic accuracy achieved across eight tasks was 95.38%.

[0015] 2. The present invention proposes a small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation, which simultaneously solves the small sample problem and the closed set domain adaptive fault diagnosis problem under variable working conditions.

[0016] 3. The present invention proposes a small sample fault diagnosis network based on the attention mechanism, which is a combination of dual-path full convolution and BiGRU, namely DPFC-FFABNet, to solve the problem of small sample fault diagnosis. The vibration signal is preprocessed using maximum and minimum normalization and FFT. DPFC-FFABNet uses the preprocessed frequency domain data as input. The dual-path full convolution structure can fully extract useful features; the introduction of group normalization and layer normalization enhances the robustness of the model. In terms of the generalization problem of small sample fault diagnosis, the proposed method can perform well under different rotating mechanical components, different speed conditions, and different noise interference conditions, and has great application value. Finally, on the basis of the method proposed in the present invention, the multi-core maximum mean difference MKMMD is combined with the class confusion minimization MCC to further enhance the generalization ability of fault diagnosis with variable speed and load. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Attention map for global-local feature fusion;

[0018] Figure 2 Attention flow chart for global-local feature fusion;

[0019] Figure 3 This is the BiGRU structure diagram;

[0020] Figure 4 is the normalized graph;

[0021] Figure 5 This is the DPFC-FFABNet network structure diagram;

[0022] Figure 6This is a comparison chart of the input effects in the time domain and frequency domain;

[0023] Figure 7 is the time domain diagram;

[0024] Figure 8 is the frequency domain diagram;

[0025] Figure 9 This is a small sample fault diagnosis flow chart;

[0026] Figure 10 This is a comparison chart of the normalized effect curve;

[0027] Figure 11 This is a graph comparing experimental results on the Case Western Reserve University bearing dataset;

[0028] Figure 12 This is the result of the comparative experiment on the bearing dataset of Huazhong University of Science and Technology;

[0029] Figure 13 This is a graph showing the experimental results of the gear dataset comparison of Beijing Jiaotong University;

[0030] Figure 14 This is the result of the noise reduction experiment on the Case Western Reserve University bearing dataset.

[0031] Figure 15 This is the anti-noise experimental result of the bearing dataset of Huazhong University of Science and Technology;

[0032] Figure 16 This is the anti-noise experimental result of the gear dataset of Beijing Jiaotong University;

[0033] Figure 17 Visualize the confusion matrix;

[0034] Figure 18 This is the confusion matrix diagram of the experimental results of task G;

[0035] Figure 19 This is the T-SNE visualization of the experimental results for Task G. DETAILED DESCRIPTION

[0036] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0037] A small sample fault diagnosis method based on two-way convolution and closed set domain adaptation, the method comprising the following steps:

[0038] 1. Fault diagnosis network model based on dual-path convolution

[0039] 1.1 Global-local feature fusion attention mechanism

[0040] Global-Local Feature Fusion Attention (GLFFA), its structure and process are as follows Figure 1 and Figure 2 As shown in the figure, the overall structure of channel attention and local attention is designed in parallel. The design concept of GLFFA is derived from MLCA. First, GLFFA performs local average pooling (LAP) on the input C×L feature map in the L dimension. In the channel attention module, the obtained C×ks feature map is subjected to global average pooling (GAP) in the channel C dimension to compress the features of each channel into a single eigenvalue. Then, convolution is used to obtain C×1 eigenvalues, and anti-global average pooling (anti-GAP) is used to restore it to C×ks resolution. In the local attention module, the C×ks feature tensor is flattened into one dimension, and then convolution and reshape are used to restore it to the original C×ks size. The output of the channel attention module is added to the output eigenvalues ​​of the local attention module. The result is multiplied by the original input after anti-LAP to obtain the attention-weighted feature map.

[0041] In terms of structure and functionality, SE and ECA are limited to channel-level attention and lack the ability to extract features in the spatial dimension. CBAM has high structural and computational complexity, while CA calculates attention weights for each position in the input feature map, resulting in high information redundancy. GLFFA combines the channel-level global attention of SE and ECA while also taking into account local attention at specific positions. In terms of computational efficiency, as shown in the comparison results in Table 1, GLFFA is more lightweight than CA and CBAM in terms of parameters and FLOPs, with lower computational complexity and higher efficiency.

[0042] Table 1 Comparison of parameters and calculation amount

[0043] Table 1 Comparison of parameter quantity and calculation amount

[0044]

[0045] 1.2 Dual-branch Fully Convolutional Structure

[0046] Compared with the DCABiGRU of Zhang et al., the improvement of the dual-path convolutional structure of the DPFC-FFABNet network of the present invention is that, considering that the pooling operation will cause information loss in small-sample fault diagnosis, the maximum pooling of the short branch is replaced by convolution, and the maximum pooling of the long branch is discarded, constructing a dual-path full convolutional structure to extract more detailed features.

[0047] Currently, group normalization (GN) is rarely used in the field of small sample fault diagnosis. Its calculation formula is as follows:

[0048]

[0049] In the formula, subscripts b, c, and l represent batch dimension, channel dimension, and signal feature length, and B, C, L, and G represent batch size, number of feature channels, feature length, and number of channel groups. x is the feature to be processed, μ, σ 2 represents the mean and variance, γ and β are learnable scaling and offset parameters.

[0050] The BN and GN calculation processes described above can be divided into three steps: mean and variance calculation, normalization, and the use of γ. BN normalizes each channel of a batch of samples, while GN normalizes each sample in a batch by channel group. BN normalizes in the batch dimension, which relies on a sufficiently large batch size to calculate accurate mean and variance. However, in the small-batch training scenario used in small-sample fault diagnosis, the mean and variance calculations are inaccurate, leading to unstable network training and large fluctuations in the model's test performance. GN, on the other hand, operates in the channel dimension, grouping all channels for each sample and calculating the mean and variance within each group of channels. Its advantages are that it is independent of batch size and is more stable when trained in small batches, making it more suitable for fault diagnosis under small-sample conditions.

[0051] 1.3 Bidirectional Gated Recurrent Unit

[0052] The bidirectional GRU structure is used in DPFC-FFABNet. Due to the reduced number of parameters and computational complexity, it can effectively avoid the overfitting of deep networks. Compared with the unidirectional GRU, the bidirectional GRU can not only update the current state information based on the previous state information, but also consider the relationship between the next state and the current state. The bidirectional GRU is used to serialize the input features forward and backward, so that each feature can take into account the information of the previous and next feature components, thereby improving the global dependency of the features. Its structure is as follows Figure 3 As shown, it is composed of two layers of GRU with opposite directions superimposed, and the final output is h of the two layers of GRU n In the nth state, the hidden state of each layer is The final hidden state output is yn , the calculation process is as follows:

[0053]

[0054]

[0055] The calculation formula for layer normalization (LN) is as follows:

[0056]

[0057] Where the subscripts b, c, and l represent the batch dimension, channel dimension, and signal feature length, C and L represent the number of feature channels and feature length, x is the feature to be processed, μ and σ2 represent the mean and variance, and γ and β are learnable scaling and offset parameters.

[0058] like Figure 4 As shown in Figure 1, LN normalizes all channels of each sample in a batch. While both LN and GN normalize along the channel dimension, LN normalizes the mean and variance of all channels of each sample. This approach is independent of batch size and is more stable when trained with small batches. Unlike GN, LN is primarily used in variants such as recurrent neural networks (RNNs) and Transformers that process sequential data.

[0059] 1.4 Construction of fault diagnosis network model

[0060] The small sample network of the present invention adopts a structure combining CNN and BiGRU in series, such as Figure 5 CNNs have a clear advantage in extracting local information from input signals, while BiGRU's strong time series modeling capabilities make it suitable for situations where the length of vibration sequences obtained by sliding window sampling is limited, further enabling the full extraction of preceding and following features of the sequence. The vibration signal, after undergoing maximum and minimum normalization and FFT, is used as the network input. The parameter settings after overall network tuning are shown in Table 2.

[0061] The first half of DPFC-FFABNet is based on CNN and adopts a parallel design structure with two fully convolutional branches. One branch has four convolutional layers and the other has three convolutional layers. GN and SiLU activation are introduced after each convolution. The output features of the two branches are fused using the weighting factor β. The fusion method is as follows:

[0062] f=(1-β)×p1+β×p2(1.12)

[0063] In the formula, p1 and p2 represent the output features of the two branches, respectively. The gradient of β is set to True, becoming part of the overall network and a trainable parameter. Its size is adaptively adjusted through loss calculation and network backpropagation. GLFFA can reweight different channels or positions, further enhancing the network's feature expression capabilities by balancing the extraction of global and local information and feature fusion. In the latter half, the fusion of the forward and backward information flows of BiGRU is utilized to capture long-range dependencies in the sequence. The BiGRU structure adopts a two-layer bidirectional structure, followed by LN and SiLU activations. Finally, post-processing is performed using a combination of GAP, a fully connected layer (FC), and a Softmax layer to output the fault status result.

[0064] Table 2 DPFC-FFABNet network parameters

[0065] Table 2 The parameters of the DPFC-FFABNet network

[0066]

[0067]

[0068] 2. Small sample fault diagnosis method considering closed set domain adaptation

[0069] 2.1 Input feature comparison and data preprocessing

[0070] All experiments were conducted on a computer running Windows 10, a 64-bit operating system, an Intel(R) Core(TM) i5-8265U CPU (8-core processor), an NVIDIA GeForce MX150 graphics card with 2GB of video memory, Python version 3.8.18, the deep learning framework Pytorch 1.12.0+cu113, the scientific computing library NumPy 1.19.2, and the data visualization library Matplotlib 3.5.2.

[0071] In terms of network hyperparameter settings, the number of input batch samples (Batch Size) is 8, the network model iterative training (Training Epoch) steps 180, the Adam optimizer is used to optimize the network trainable parameters, the learning rate (LeaningRate) is set to 0.0025, the number of BiGRU layers is 2, the dropout rate (Dropout Rate) is 0.01, and the cross entropy loss function is used. Figure 1The ks parameter of the adaptive average pooling is 31. To reduce the impact of random initialization of network training parameters on fault diagnosis results during each training, all the following experimental results are repeated 7 times, and then the maximum and minimum values ​​are removed. The average of the remaining 5 experimental results is taken as the final accuracy.

[0072] By converting the original time domain signal into frequency domain samples, the DPFC-FFABNet was verified by comparing it with the Support Vector Machine (SVM), Random Forests (RF), WDCNN, CLFormer, and DCABiGRU networks on the 0Hp bearing load data from Case Western Reserve University, the 65Hz bearing speed data from Huazhong University of Science and Technology, and the 35Hz gear speed data from Beijing Jiaotong University, with 7 samples in each category. Figure 6 It shows that frequency domain data input can better improve the accuracy of small sample fault diagnosis.

[0073] The original vibration signal is preprocessed using Min-Max Normalization and Fast Fourier Transform (FFT). Min-Max Normalization linearly maps the vibration signal to the interval between 0 and 1, avoiding the model's bias towards high-amplitude features due to large input amplitude differences. In addition, the model is more sensitive to the normalized data and converges faster, which has obvious advantages. For FFT, Figure 7 and Figure 8 These are time domain and DC-depleted frequency domain images of rolling element, inner race, outer race, and inner and outer race composite faults at a bearing speed of 65Hz from Huazhong University of Science and Technology. Compared to abstract time-frequency images, using one-dimensional frequency domain data for training can save computational overhead and reduce model complexity to avoid overfitting. Compared to time-domain vibration data, the transformed bilateral spectrum can better highlight fault-related features, making the model easier to understand for feature extraction. This reduces the structural complexity of the network itself. Frequency domain data can smooth high-frequency noise, highlight low-frequency fault information, and has noise resistance. The bilateral spectrum is also more suitable for fault diagnosis of symmetrical bearings and gear components. The simplicity of frequency domain data and the prominence of fault features help improve network training efficiency and generalization capabilities in small-sample fault diagnosis.

[0074] 2.2 Objective function design

[0075] The small sample fault diagnosis method of the present invention is based on the cross entropy loss function L ce , a batch of samples is recorded as The optimization target is L, and the loss obtained by forward propagation is calculated as follows:

[0076]

[0077]

[0078] Among them, B represents a batch size, M represents the number of categories, and x i represents the input sample, y i Represents x i The corresponding label, p(·) is the Softmax output of DPFC-FFABNet, 1{y i =j} is when x i The corresponding y i If it is equal to category j, its value is 1, otherwise it is 0.

[0079] Based on the proposed small sample method, the Multi-Kernel Maximum Mean Discrepancy (MKMMD) and Minimum Class Confusion (MCC) methods are combined to achieve small sample closed set domain adaptation. The source domain is denoted as s and the target domain is denoted as t. Cross-entropy loss is used for labeled samples in the source domain for supervised learning; MCC is used for unlabeled target domain samples; MKMMD is used to align the features of source and target domain samples. The target optimization function is shown below, where α is the weight parameter, which is set to 0.001 in the present invention.

[0080]

[0081] ① Multi-core maximum mean difference MKMMD

[0082] Suppose that after the source domain and target domain samples are globally averaged pooled in DPFC-FFABNet, the extracted feature vector is denoted as f s and f t , then the maximum mean difference MMD is calculated as follows:

[0083]

[0084] In the formula, ||·|| H represents the Reproducing Kernel Hilbert Space (RKHS), N s and N t denote the number of samples in the source domain and the target domain respectively, and k(·,·) denotes the kernel function, which is calculated as follows:

[0085]

[0086] Where, 〈,〉 is the inner product operator, k(,) is the feature kernel associated with the feature map φ in RKHS, and the present invention adopts the Gaussian kernel

[0087] ,Right now The kernel function of MKMMD is composed of multiple Gaussian kernels with different bandwidths, as shown in the following formula:

[0088]

[0089] Where N k represents the number of kernel functions. In this paper, it is set to 5. The bandwidths of the five Gaussian kernels are σ, 2σ, 4σ, 8σ, and 16σ, respectively. σ is calculated from the characteristic L2 distance between the source domain and the target domain. K represents the set of multiple Gaussian kernels. β u For each kernel function k u The weight coefficient of the distribution is set to equal weight addition, that is, β u =1. Therefore, the measurement formula of MKMMD is as follows:

[0090]

[0091]

[0092] ②Class confusion minimization MCC

[0093] Assume a batch of unlabeled target domain samples Input into DPFC-FFABNet, the output of the fully connected layer is recorded as Z t ∈R B×C , and then use the temperature coefficient T scaling method for the Softmax function

[0094] To reduce the adverse effects of overconfident predictions, the probability that the i-th sample in a batch belongs to the j-th class is

[0095] As shown in the following formula:

[0096]

[0097] In particular, when T is 1, it becomes a Softmax function, and the present invention sets it to 2.1 for scaling. The correlation between categories is calculated as shown in the following formula:

[0098]

[0099] Where, p· j and p. j′ is the probability that each batch of B samples belongs to the jth and j′th classes respectively.

[0100] Information entropy is used to measure distribution uncertainty, which is calculated as follows:

[0101]

[0102] Smoothing technology is introduced, and the weight calculation formula is as follows:

[0103]

[0104] Class confusion is calculated as follows:

[0105]

[0106] Class confusion is defined based on small batches of samples, so class imbalance may occur in each batch. Therefore, class normalization technology is used. The normalized class confusion can be written as follows:

[0107]

[0108] The constraint objective function formula based on prediction class confusion is:

[0109]

[0110] Minimizing the above objective means maximizing the intra-class confusion, i.e., ideally no target domain samples are ambiguously classified into two classes at the same time.

[0111] 2.3 Complete process of fault diagnosis algorithm

[0112] The small sample fault diagnosis process based on DPFC-FFABNet can be divided into three parts: data preprocessing, model training and offline testing. Figure 9 The specific steps are as follows:

[0113] Step 1: In the data preprocessing stage, vibration signals are first collected through an accelerometer, and samples are cut using a non-overlapping slice sampling algorithm. Each sample is then subjected to maximum and minimum normalization processing. The sample signal is then converted from the time domain to the frequency domain using FFT, and a training set and a test set are constructed according to a certain ratio.

[0114] Step 2: During the model training phase, the training set is used for model training using the cross-entropy loss function. Backpropagation is then used to iteratively optimize the network structure parameters. Model performance is reflected in the state recognition accuracy. Specifically, when the training and test set samples come from different operating conditions, the DPFC-FFABNet is trained through backpropagation based on the aforementioned method, combining minimizing class confusion (MCC) with multi-kernel maximum mean difference (MKMMD). This enables variable operating condition fault diagnosis with small sample sizes in both the source and target domains.

[0115] Step 3: In the offline testing phase, the same data preprocessing as in the training phase is used to input the unlabeled test samples into the trained network model for feature extraction, and then the Softmax classifier is used to obtain the corresponding recognition results.

[0116] 3. Experimental verification and result analysis

[0117] 3.1 Experimental Setup

[0118] The concept of small sample size is difficult to unify and accurately define, as it is related to data complexity and diagnostic model complexity. In their experimental setup, Fang et al. set the size of each class in the training set to 250 and a ratio of 5:6. Chen et al., Luo et al., and Zhang et al. set the size of each class in the training set and the ratio of the training set to the test set to 20 and a ratio of 1:9 in extreme cases. Liang et al. set the size of each class to 20 and a ratio of 1:2. Xue et al. set the size of each class to 10 and a ratio of 1:10. In terms of experimental data preparation, the present invention uses a non-overlapping slice sampling method to intercept the original signal with a length of 1024 points per sample. The 80 samples obtained from the front to the back are used, and the last 40 samples are used as a fixed test set. From the first 40 samples, 8%, 13%, 18%, 23%, 28%, and 33% of the samples from the back to the front are obtained as training sets, respectively. This ensures that the number of training samples is smaller than the number of test samples, and the maximum difference between the two is approximately 1:13. The number and ratio of samples available for network training are far smaller than those set in the above literature.

[0119] 3.2 Ablation Experiment

[0120] DPFC-FFABNet was tested on data from Case Western Reserve University, Huazhong University of Science and Technology, and Beijing Jiaotong University, with 9 samples per state class in the training set. The experimental results are shown in Tables 3, 4, and 5.

[0121] Without GLFFA, DPFC-FFABNet achieves higher recognition accuracy than its predecessors without attention. Under the four CWRU load conditions, GLFFA improves average accuracy by 0.50%, with corresponding improvements across all loads. At a HUST bearing speed of 70 Hz, the improvement is 1.16%, with an average accuracy increase of 0.93% across all four speeds. Under the three BJU speeds, GLFFA improves accuracy by an average of 0.87%, with a 2.20% improvement at 35 Hz. Compared to SE, ECA, CBAM, and CA, GLFFA demonstrates significant improvement in average accuracy, particularly on the BJU gear dataset.

[0122] From the comparison of the attention mechanism effects, SE, ECA, CBAM and CA are beneficial to improving the fault state recognition accuracy, but GLFFA is more effective. The reason is that SE and ECA belong to channel-level attention and can only extract global features at the channel level, while CBAM first extracts channel features and then extracts fine-grained spatial features. The commonality with CA is that the extracted information has more redundancy, which is not conducive to the utilization of effective features and interferes with the recognition results. In addition, the addition of the attention mechanism leads to a decrease in diagnostic accuracy. For example, in Table 3, the diagnostic rate of CA is reduced by 0.60% at a load of 1Hp, in Table 4, the diagnostic rate of SE is reduced by 0.94% at a speed of 80Hz, and in Table 5, the diagnostic rates of ECA and CBAM are reduced by 2.90% and 2.10% at speeds of 45Hz and 40Hz respectively. The reason may be that SE, ECA, CBAM and CA rely on a large amount of data to learn the weight distribution and are prone to overfitting in the case of small samples. However, the GLFFA of the present invention does not show a decrease in diagnostic accuracy in the table, which indirectly shows that it has certain advantages in improving the diagnostic accuracy of small samples.

[0123] "w BN" uses batch normalization BN in DPFC-FFABNet, while "w GLFFA" uses group normalization GN after convolution and layer normalization after BiGRU. In terms of diagnostic accuracy, GN and LN are generally better than BN. In addition, Figure 10 From the perspective of the model's prediction process of the fault state, since BN uses inaccurate mean and standard deviation under small sample training, it cannot represent the overall data distribution, resulting in unstable model fault prediction and large fluctuations in the test curve. Finally, "First-Path" and "Second-Path" represent Figure 5 For the upper and lower branches in the dual-path convolution structure, the “First-Path” branch is only 0.3% higher than the dual branch on the 45Hz BJU gear speed data. In other cases, the dual-path convolution structure using DPFC-FFABNet has obvious advantages in improving the accuracy of small sample fault diagnosis.

[0124] Table 3 CWRU ablation experimental results (%)

[0125] Table 3The results of the CWRU ablation experiment(%)

[0126]

[0127]

[0128] Table 4 HUST ablation experimental results (%)

[0129] Table 4 The results of the HUST ablation experiment(%)

[0130]

[0131] Table 5 BJU ablation experimental results (%)

[0132] Table 5 The results of the BJU ablation experiment(%)

[0133]

[0134] 3.3 Comparative Experiment

[0135] The following methods are used for comparative experiments on small sample fault diagnosis:

[0136] 1) Support vector machine (SVM) constructs the optimal classification hyperplane by replacing empirical risk minimization with structural risk minimization. Its maximum margin classification feature can effectively avoid overfitting, and uses kernel functions instead of dot products for calculations. Through kernel techniques, low-dimensional nonlinear input vectors are mapped to high-dimensional space, realizing the use of linear thinking to solve nonlinear problems, and can better solve small sample classification problems.

[0137] 2) Random Forest (RF) is an ensemble learning algorithm that consists of multiple independent decision trees. By constructing multiple decision trees for voting and making comprehensive decisions on the classification results, the probability of overfitting can be reduced.

[0138] 3) WDCNN is a deep convolutional neural network structure with a wide convolution kernel in the first layer. Its structural feature is the large 64×1 convolution kernel in the first layer, which can learn features that are beneficial to fault diagnosis under noise interference and has a certain noise resistance. The convolution kernel size of the remaining convolution layers is 3×1. Multiple convolution layers with small convolution kernels enhance the feature extraction capability of the neural network.

[0139] 4) CLFormer is a lightweight transformer structure based on convolutional embedding and linear self-attention. It uses a one-dimensional convolutional embedding module instead of a multi-layer perceptron-based embedding module and a positional encoding module, reducing the number of parameters and computation. At the same time, the convolution operation enhances the inductive bias and reduces the model's dependence on the amount of data. The linear self-attention module further reduces model complexity and effectively avoids overfitting in small-sample training.

[0140] 5) DCABiGRU is a dual-path convolutional neural network structure based on the attention mechanism and bidirectional gated recurrent unit. It extracts and fuses spatial features through the dual-path convolution module and the attention mechanism, and uses Bi-GRU to achieve spatiotemporal feature fusion, thus realizing small sample fault diagnosis.

[0141] The error bar graph is used to show the comparative test results. The center point represents the mean of the accuracy results of the five experiments, and the line segment extending from the center point represents the standard deviation. The longer the error bar, the worse the model robustness. Figure 11 、 12 As shown in Figures 13 and 23, the proposed DPFC-FFABNet performs best overall. First, under different operating conditions within the same dataset, DPFC-FFABNet demonstrates high diagnostic accuracy. Second, across different datasets, DPFC-FFABNet demonstrates superior fault diagnosis capabilities for bearings and gears, generalizing to fault diagnosis of various rotating machinery components. Finally, while the accuracy of SVM and RF is generally lower than that of deep networks, their test results are highly stable. This is because deep networks train on random batches of samples and randomly initialize network weights, leading to fluctuations in results. DPFC-FFABNet generally exhibits lower variance than other deep networks, indicating greater stability. Overall, DPFC-FFABNet demonstrates strong small-sample fault diagnosis capabilities and generalization across diverse operating conditions.

[0142] The experimental results on the bearing dataset are as follows Figure 11 、 12As shown. Due to its advantage in small sample classification, SVM performs significantly better than RF when the number of samples per class is 3. However, when the number of samples per class increases to more than 9, taking a load of 1Hp as an example, RF surpasses SVM in diagnostic accuracy due to its voting mechanism of multiple decision trees and its comprehensive decision-making ability for state recognition. WDCNN exhibits high performance with its feature extraction structure of a first-layer large convolution kernel and multiple small convolution kernels connected in series. On the CWRU bearing dataset and the HUST bearing dataset, WDCNN's diagnostic accuracy can reach 99.90% and 98.22% respectively. CLFormer is a lightweight transformer structure. The linear self-attention mechanism reduces the number of network parameters to reduce the risk of overfitting. Its global feature extraction capability can enhance the network's feature extraction capabilities. On the two bearing datasets, its accuracy is as high as 100.00% and 97.94%. The DCABiGRU uses convolution and bidirectional gated recurrent units as its feature extraction architecture. Its convolutional neural network combines convolution and pooling, accelerating network training. It achieved accuracy rates of 99.30% and 98.50% on two datasets, respectively. Compared to these three deep network architectures, the DPFC-FFABNet combines the local feature extraction capabilities of convolution with the global feature extraction capabilities of bidirectional gated recurrent units. Its convolutional architecture uses a two-branch full convolutional architecture, with each branch consisting of a large first-layer convolution kernel and multiple smaller kernels in series, resulting in more compact local feature extraction. Its global-local feature fusion attention mechanism enables more efficient feature extraction, while also being more lightweight. On the CWRU bearing dataset, its performance demonstrated significant superiority under four different load conditions and with varying sample sizes. Its diagnostic accuracy on CWRU was no less than 98.15% when loaded at 0 hp and with three samples per class. In particular, under load conditions of 2Hp and 3Hp, the accuracy reached 100.00% when the number of samples per class was at least 7. On the HUST bearing dataset, the maximum accuracy reached over 92.00% with 3 samples per class, and 99.11% with 13 samples per class. In particular, on the HUST dataset, at a speed of 65Hz and 9 samples per class, CLFormer outperformed DPFC-FFABNet by 0.39%. At a speed of 70Hz, with 3 samples per class, WDCNN outperformed by 0.23%, and with 7 samples per class, DCABiGRU outperformed by 0.56%. This demonstrates that DPFC-FFABNet has significant advantages over the aforementioned comparison models in terms of model prediction stability and diagnostic accuracy.

[0143] The above DPFC-FFABNet shows strong performance on the bearing dataset. The experimental results on the gear dataset are as follows: Figure 13As shown in the figure, on the BJU dataset, with 3 samples per class, DPFC-FFABNet achieved an accuracy of 81.90%, 20.00% higher than the 61.90% maximum accuracy of the other comparison methods. As the number of training samples increased, the gap between the maximum accuracy of DPFC-FFABNet and the other methods narrowed, but still remained 0.9% higher. At 40Hz, with 13 samples per class, DPFC-FFABNet achieved a maximum accuracy of 97.60%. In particular, at 45Hz, with 13 samples per class, CLFormer achieved a 0.30% higher accuracy. In all other cases, DPFC-FFABNet achieved superior diagnostic accuracy to the other models.

[0144] In summary, the above experimental results further demonstrate that DPFC-FFABNet has high diagnostic accuracy not only under different load and speed conditions of bearings, but also under different speed conditions of gears, and can be applied to fault diagnosis of different mechanical components.

[0145] 3.4 Noise immunity experiment

[0146] In the small sample noise immunity experiment, the signal-to-noise ratio is calculated as follows:

[0147]

[0148] Where, P signal is the original signal power, P noise is the noise power, which is the Gaussian noise of the natural random disturbance scene.

[0149] In the 0Hp load data of CWRU, 65Hz speed data of HUST and 40Hz speed data of BJU, experiments were conducted under different training set sizes and different signal-to-noise ratios. The results are as follows: Figure 14 、 15 and 16. Under different signal-to-noise ratio conditions on the three datasets, the accuracy of SVM and RF is lower than that of deep models due to their lack of noise-resistance mechanisms. WDCNN uses large convolution kernels in the first layer to extract features, which act as filters and have noise-resistance capabilities. Subsequently, multiple small convolution kernels are used to extract local detail features, enhancing feature extraction capabilities while also being noise-resistant. The convolutional inductive bias capability of CLFormer and the global feature extraction capability of the linear self-attention mechanism ensure robustness to noise and high accuracy under limited sample sizes. Overall, DCABiGRU performs better than SVM and RF in the presence of noise, but worse than WDCNN and CLFormer.

[0150] On two bearing datasets, the experimental results are as follows Figure 14 and 15As shown in Figure 2, DPFC-FFABNet has a higher small sample fault diagnosis accuracy than other models under different noise conditions. Figure 14 As shown in the figure, on the CWRU bearing dataset, DPFC-FFABNet's noise resistance is far superior to other methods overall. When the signal-to-noise ratio is 0 and the number of samples per class is not less than 7, the accuracy of DPFC-FFABNet is not less than 95.00%; when the number of samples per class is 13, its accuracy is not less than 98.55% under various signal-to-noise ratio conditions. Figure 15 As shown in the figure, on the HUST bearing dataset, except when the signal-to-noise ratio is 2 and there are 5 samples per class, the diagnostic accuracy of WDCNN is 2.61% higher than that of DPFC-FFABNet. When the signal-to-noise ratio is 8 and the number of samples per class is 11 and 13 respectively, the diagnostic accuracy of CLFormer is 0.11% and 0.22% higher than that of DPFC-FFABNet respectively. Under other conditions, the diagnostic accuracy of DPFC-FFABNet is significantly higher than that of other models.

[0151] The above anti-noise experimental results under different signal-to-noise ratio conditions on the bearing dataset show that DPFC-FFABNet has a stronger anti-noise diagnosis accuracy than other networks. Figure 1 As shown in Figure 16, using the same SNR range as the HUST bearing dataset on the BJU gear dataset, the DPFC-FFABNet achieved similar accuracy results to those on the bearing dataset, significantly exceeding the other networks in diagnostic accuracy. When the SNR was 2 and the number of samples per class was 7, the accuracy of the other networks did not exceed 60.00%, while the DPFC-FFABNet achieved 72.70%. When the SNR was 8, the DPFC-FFABNet achieved an accuracy of at least 87%, and especially when the number of samples was at least 9, the accuracy was at least 93.50%. In particular, when the number of samples reached 13, the accuracy reached 96.00%, an improvement of at least 3.30% over the other models.

[0152] In summary, on bearings and gears, under different signal-to-noise ratios, DPFC-FFABNet has higher diagnostic accuracy than the comparison model under small sample conditions.

[0153] 3.5 Confusion Matrix Visualization Analysis

[0154] The experiments conducted above on various bearing and gear data sets are the average values ​​of all state diagnosis accuracies. The average value does not show the comparison of the recognition accuracy of various states on bearings or gears between DPFC-FFABNet and other models. Its disadvantage is that the average value will blur the performance differences of the model in different states, such as low recognition in a certain state, but high recognition in other states, resulting in superior overall performance. In addition, a single average accuracy lacks fine-grained information on the recognition effect of each state and lacks interpretability. Confusion matrix visualization can solve the above problems. The HUST dataset is selected. Compared with the CWRU dataset, it contains multiple composite faults with different fault degrees, which is more difficult to identify; compared with the BJU dataset, it has more fault state categories. In the HUST experimental results Figure 12 In (d), the number of samples per category is selected as 13. The reason is that the average test accuracy of different deep networks is high and very similar. Confusion matrix visualization helps to reveal the hidden differences between different models in the recognition of different state categories. The visualization of the confusion matrix only shows the effects of WDCNN, CLFormer, DCABiGRU and DPFC-FFABNet. The average accuracy of SVM and RF is lower than that of deep networks, and the gap is obvious, which may have obvious defects in the recognition of some state categories.

[0155] The experimental results are as follows Figure 17 As shown, it can be seen Figure 17 (d) DPFC-FFABNet misidentifies one of the 40 "O" bearing inner ring serious fault samples in the test set as "H" healthy state, with an identification accuracy of 97.50%. The recognition rates of other bearing states are all 100.00%. WDCNN, CLFormer and DPFC-FFABNet all have a recognition rate of 97.50% for "O". However, WDCNN and CLFormer have more misidentifications when it comes to the composite serious fault state "C", with recognition rates of 92.50% and 95.00% respectively. In addition, WDCNN N misidentified four samples as normal in the identification of rolling element severe fault "B", while CLFormer misidentified one sample as outer ring severe fault in both the composite mild fault "C_0.5X" and the outer ring mild fault "O_0.5X". DCABiGRU had a 100.00% diagnosis rate for the outer ring severe fault "O", but had large misidentification rates for the outer ring mild fault "O_0.5X", the rolling element severe fault "B" and the composite severe fault state "C". In particular, the accuracy rate for the rolling element severe fault "B" was 87.50%, with multiple samples misidentified as various other states.

[0156] 3.6 Closed-domain Adaptive Generalization Experiment

[0157] This closed-set domain adaptation generalization experiment conducts variable operating condition diagnosis experiments under variable speed and load conditions. Eight tasks are set to verify the effectiveness of the proposed method for variable operating condition diagnosis after adding the domain adaptation module. The experimental task settings are shown in Table 6. The training and test sets of the CWRU dataset use different load data. The training set uses labeled 0-Hp load data as the source domain, and the test set uses unlabeled 1-Hp, 2-Hp, and 3-Hp data as the target domains, respectively. The corresponding experimental tasks are set as A, B, and C. In the HUST dataset, 65-Hz speed data is used as the source domain, and 70-Hz, 75-Hz, and 80-Hz data are used as the target domains, respectively. The corresponding experimental tasks are set as D, E, and F. In the BJU dataset, 35-Hz data is used as the source domain for the training set, and 40-Hz and 45-Hz data are used as the target domains for the test set, respectively. The corresponding experimental tasks are set as G and H. Each state class in the training set contains 12 samples, and each state class in the test set contains 40 samples.

[0158] Table 6 Experimental settings for variable operating conditions

[0159] Table 6 Variable working condition experiment setup

[0160]

[0161] Based on the proposed DPFC-FFABNet small-sample method, the source and target domain training sets are set to have the same sample size and are small. Combining the multi-kernel maximum mean difference (MKMMD) with the minimized class confusion loss (MCC), hereinafter referred to as MKMCC, achieves effective small-sample variable-condition fault diagnosis. Comparative experiments with DANN, MMD, CORAL, and MKMMD demonstrate the superiority of MKMCC for closed-set domain adaptive diagnosis under small-sample conditions. The experimental results are shown in Table 7. MMD performs better than CORAL under small-sample conditions. This is because high-order statistical features based on covariance can be affected by sample size, and small samples lead to inaccurate covariance estimates. MMD, on the other hand, only considers mean differences, making it less susceptible to small-sample effects and more stable. MMD uses a fixed single-kernel function, while MKMMD uses a multi-kernel MMD. The diversity measure of multiple different kernel functions can capture the complex characteristics of the data distribution, resulting in better experimental results for MKMMD. All of the above are based on statistical function metrics, but DANN generally performs worse than other domain adaptation methods. This may be because the domain discriminator is essentially a neural network, requiring a large number of samples to fully train the game between the generator and the discriminator. Insufficient samples make it difficult to learn robust features, which can easily lead to overfitting and performance degradation. Compared with DANN, MMD, and CORAL, MKMMD has higher accuracy, but the statistical metric method of its multiple kernel functions may over-align the global distribution of features and ignore the local structural characteristics of the category. From the perspective of MKMMC's combination of feature space and output space constraints, MKMMD uses multiple Gaussian kernels to more flexibly represent cross-domain distribution differences. This can alleviate the distribution estimation differences caused by insufficient samples and reduce the risk of overfitting. Combined with MCC, it strengthens the classification confidence of target domain samples by minimizing class confusion and further enhances class discrimination. Experiments show that this method performs better with small samples.

[0162] Table 7 Small sample variable operating condition diagnosis test results

[0163] Table 7 Experimental results of small sample variable working condition diagnosis

[0164]

[0165] Take task G as an example, Figure 18The confusion matrix of DANN shows that its recognition rate is 100.00% only in the gear tooth breakage "B", and there are misidentification phenomena in other states. Compared with the original DPFC-FFABNet, MMD has improved the recognition effect of other states except that one sample in the gear tooth missing "MT" state is misidentified as the gear wear "W" state. Compared with the original DPFC-FFABNet, CORAL and MKMMD are similar to MMD. MKMMD is better in the recognition of broken tooth "B", normal "H", tooth root crack "RC" and wear "W" states, but for the recognition of gear tooth missing "MT", MMD is 95.00%, CORAL is 92.50%, and MKMMD is 90.00%. Figure 18 In (f), MKMCC only misidentified one gear tooth breakage "B" sample as a gear tooth missing, and misidentified two gear tooth missing "MT" samples as gear wear. The recognition accuracy of other state samples was 100.00%. Compared with other methods, the recognition accuracy in each state was the best. T-SNE (T-Distributed Stochastic Neighbor Embedding) is an algorithm for dimensionality reduction and visualization of high-dimensional data. It can compress the high-dimensional feature vector extracted by the input signal through the neural network into 2 dimensions to reveal the potential pattern and distribution of the data. It is suitable for visualizing the alignment effect of the source domain and target domain samples with inconsistent data distribution due to variable working conditions after using the closed set domain adaptation method. Figure 19 As shown in the T-SNE visualization results, Figure 18 The confusion matrix of Figure 19 (f) MKMCC has better alignment effect on state sample features between source domain and target domain than other methods, such as Figure 19 (e) MKMMD and MKMCC are more compact, especially in the feature alignment of samples in the healthy and gear wear categories. Overall, compared with other domain adaptation methods, MKMCC has higher state recognition accuracy for each category in the target domain and better feature alignment of corresponding category samples in the source and target domains.

[0166] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A small sample fault diagnosis method based on two-way convolution and closed set domain adaptation, characterized in that: The method comprises the steps of: 1) By adopting a dual-path full convolution structure, more detailed features can be extracted; 2) Using global-local feature fusion attention to extract and fuse local and global information of feature sequences; 3) Use the bidirectional structure of BiGRU to model the relationship between the front and back of the feature sequence to perform feature enhancement; 4) Group normalization and layer normalization are introduced after convolution and BiGRU respectively to make the model performance more robust; 5) Combine multi-core maximum mean difference with class confusion minimization to achieve small sample closed set domain adaptive fault diagnosis.

2. The small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation according to claim 1, characterized in that: In step 2), global-local feature fusion attention is used, and the overall channel attention and local attention parallel structure design is adopted: 2.1) GLFFA performs local average pooling (LAP) on the input C×L feature map in the L dimension. In the channel attention module, the obtained C×ks feature map is subjected to global average pooling (GAP) in the channel C dimension to compress the features of each channel into a single feature value. 2.2) Use convolution to obtain C×1 eigenvalues, and use anti-global average pooling (anti-GAP) to restore to C×ks resolution; in the local attention module, flatten the C×ks feature tensor into one dimension; 2.3) Use convolution operation and reshape to restore to the original size C×ks, add the output of the channel attention module and the output feature value of the local attention module accordingly, and multiply the result with the original input after anti-local average pooling (anti-LAP) to obtain the attention-weighted feature map.

3. The small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation according to claim 1, characterized in that: In step 1), considering that the pooling operation will cause information loss in small sample fault diagnosis, the maximum pooling of the short branch is replaced by convolution, and the maximum pooling of the long branch is discarded to construct a dual-path full convolution structure to extract more detailed features.

4. The small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation according to claim 1, characterized in that: In step 4), group normalization and layer normalization are introduced after the dual-branch full convolution. The group normalization calculation formula is as follows: Where, subscripts b, c, and l represent batch dimension, channel dimension, and signal feature length; B, C, L, and G represent batch size, number of feature channels, feature length, and number of channel groups; x is the feature to be processed, μ, σ 2 represents the mean and variance, γ and β are learnable scaling and offset parameters.

5. The small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation according to claim 4 is characterized in that: The calculation process of BN and GN can be divided into three steps, namely mean and variance calculation, normalization, and translation and scaling using γ and β parameters. BN normalizes each channel of a batch of samples, and GN performs channel group normalization on each sample in a batch. BN normalization is performed in the batch dimension, which relies on a sufficiently large batch size to calculate accurate mean and variance. However, in the small batch training scenario of small sample fault diagnosis, the calculation of mean and variance is inaccurate, resulting in unstable network training process and large fluctuations in the test performance of the model. GN is performed in the channel dimension, grouping all channels of each sample and calculating the mean and variance in each group of channels. Its advantage is that it does not depend on batch size and is more stable when trained in small batches, making it more suitable for fault diagnosis under small sample conditions.

6. The small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation according to claim 1, characterized in that: After step 4) BiGRU, group normalization and layer normalization are introduced. In DPFC-FFABNet, a bidirectional GRU structure is used to perform forward and backward serialization of input features, so that each feature can take into account the information of the previous and next feature components, thereby improving the global dependency of features. In the nth state, the hidden state of each layer is The final hidden state output is y n , the calculation process is as follows: The calculation formula for layer normalization (LN) is as follows: Where, subscripts b, c, and l represent batch dimension, channel dimension, and signal feature length, C and L represent the number of feature channels and feature length, x is the feature to be processed, μ, σ 2 represents the mean and variance, γ and β are learnable scaling and offset parameters. LN normalizes all channels of each sample in a batch. Both LN and GN normalize in the Channel dimension. LN normalizes the mean and variance of all channels of each sample, which is independent of the batch size and more stable when trained in small batches.

7. The small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation according to claim 1, characterized in that: In step 4), the fault diagnosis network model is constructed. The small sample network uses a CNN and BiGRU in series. CNN has obvious advantages in extracting local information of the input signal, while BiGRU has strong time series modeling capabilities. It is suitable for situations where the vibration sequence obtained by sliding window sampling is of limited length and can further fully extract the front and back features of the sequence. The vibration signal is used as the network input after maximum and minimum normalization and FFT. The first half of DPFC-FFABNet is based on CNN and adopts a parallel design structure with two fully convolutional branches. One branch has four convolutional layers and the other has three convolutional layers. GN and SiLU activation are introduced after each convolution. The output features of the two branches are fused using the weighting factor β. The fusion method is as follows: f=(1-β)×p1+β×p2(1.12) In the formula, p1 and p2 represent the output features of the two branches respectively. The gradient of β is set to True, which becomes part of the overall network and is a trainable parameter. It adaptively adjusts its size through the calculation of the loss value and the back propagation of the network. In the second half, the fusion of BiGRU’s forward and backward information flows is used to capture the long-range dependencies of the sequence; In the BiGRU structure, a two-layer bidirectional structure is adopted, and then LN and SiLU activation are introduced; finally, GAP, fully connected layer FC and Softmax layer are combined for post-processing to achieve fault status result output.

8. The small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation according to claim 1, characterized in that: In step 5), the original time domain signal is converted into frequency domain samples; min-max normalization and fast Fourier transform (FFT) are used to preprocess the original vibration signal. Min-max normalization linearly maps the vibration signal to the interval between 0 and 1, avoiding the model's bias towards high-amplitude features due to large input amplitude differences. In addition, the model is more sensitive to the normalized data and converges faster, which has obvious advantages.

9. The small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation according to claim 1, characterized in that: In step 5), the small sample fault diagnosis method is based on the cross entropy loss function L ce , a batch of samples is recorded as The optimization target is L, and the loss obtained by forward propagation is calculated as follows: Among them, B represents a batch size, M represents the number of categories, and x i represents the input sample, y i Represents x i The corresponding label, p(·) is the Softmax output of DPFC-FFABNet, 1{y i =j} is when x i The corresponding y i When it is equal to category j, its value is 1, otherwise it is 0; Based on the proposed small sample method, the Multi-Kernel Maximum Mean Discrepancy (MKMMD) and Minimum Class Confusion (MCC) methods are combined to achieve small sample closed set domain adaptation. The source domain is denoted as s and the target domain is denoted as t. Cross entropy loss is used for supervised learning of labeled samples in the source domain; MCC is used for unlabeled target domain samples. MKMMD is used to align the features of source and target domain samples. The objective optimization function is as follows, where α is the weight parameter, set to 0.

001. ① Multi-core maximum mean difference MKMMD Suppose that after the source domain and target domain samples are globally averaged pooled in DPFC-FFABNet, the extracted feature vector is denoted as f s and f t , then the maximum mean difference MMD is calculated as follows: In the formula, ||·|| H represents the Reproducing Kernel Hilbert Space (RKHS), N s and N t denote the number of samples in the source domain and the target domain respectively, and k(·,·) denotes the kernel function, which is calculated as follows: Where 〈,〉 is the inner product operator, k(,) is the feature kernel associated with the feature map φ in RKHS, and the Gaussian kernel is used, that is, The kernel function of MKMMD is composed of multiple Gaussian kernels with different bandwidths, as shown in the following formula: Where Nk represents the number of kernel functions, which is set to 5. The bandwidths of the five Gaussian kernels are σ, 2σ, 4σ, 8σ, and 16σ, respectively. σ is the characteristic L2 distance between the source domain and the target domain. K represents the set of multiple Gaussian kernels. β u For each kernel function k u The weight coefficient of the distribution is set to equal weight addition, that is, β u =1; therefore, the metric formula of MKMMD is as follows: ②Class confusion minimization MCC Assume a batch of unlabeled target domain samples Input into DPFC-FFABNet, the output of the fully connected layer is recorded as Z t ∈R B×C , and then the temperature coefficient T scaling method is used for the Softmax function to reduce the adverse effects of overconfident predictions. Thus, the probability that the i-th sample in a batch belongs to the j-th class is as follows: In particular, when T is 1, it becomes a Softmax function and is set to 2.1 for scaling; the correlation between categories is calculated as shown in the following formula: Where, p· j and p. j ′ For each batch of B samples, they belong to the jth and jth ′ class probability; Information entropy is used to measure distribution uncertainty, which is calculated as follows: Smoothing technology is introduced, and the weight calculation formula is as follows: Class confusion is calculated as follows: Class confusion is defined based on small batches of samples, so class imbalance may occur in each batch. Therefore, class normalization technology is used. The normalized class confusion can be written as follows: The constraint objective function formula based on prediction class confusion is: Minimizing the above objective means maximizing the intra-class confusion, i.e., ideally no target domain samples are ambiguously classified into two classes at the same time.

10. The small sample fault diagnosis method based on dual-path convolution and closed set domain adaptation according to claim 1, characterized in that: In step 5), the small sample fault diagnosis process based on DPFC-FFABNet can be divided into three parts: data preprocessing, model training, and offline testing. The specific steps are as follows: Step 1: In the data preprocessing stage, vibration signals are first collected through the accelerometer and samples are cut using the non-overlapping slice sampling algorithm. Each sample is then subjected to maximum and minimum normalization. The sample signal is then converted from the time domain to the frequency domain using FFT, and training and test sets are constructed. Step 2: During the model training phase, the training set is used for model training using the cross-entropy loss function. The network structure parameters are iteratively optimized through back-propagation. Model performance is reflected in the state recognition accuracy. Back-propagation training of DPFC-FFABNet is performed by combining minimizing class confusion (MCC) and multi-core maximum mean difference (MKMMD) to achieve variable operating condition fault diagnosis under small sample conditions in the source and target domains. Step 3: In the offline testing phase, the same data preprocessing as in the training phase is used to input the unlabeled test samples into the trained network model for feature extraction, and then the Softmax classifier is used to obtain the corresponding recognition results.

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