Adaptive small sample fault diagnosis method based on lightweight one-dimensional residual network

Abstract

The invention discloses a self-adaptive small sample fault diagnosis method based on a lightweight one-dimensional residual network, and belongs to the technical field of mechanical fault diagnosis and intelligent monitoring, and the method comprises the steps: obtaining a one-dimensional vibration signal of a rolling bearing, and dividing the one-dimensional vibration signal into a training set, a verification set and a test set; constructing a lightweight self-adaptive one-dimensional residual error network model containing a multi-scale lightweight residual error network and a self-adaptive training optimization framework, performing feature extraction, fusion and dimension unification on vibration signals in a training set through the multi-scale lightweight residual error network to obtain category probability distribution, and realizing parameter optimization of the model through the self-adaptive training optimization framework; and performing fault diagnosis on verification set signals by using the optimized model to obtain category probability distribution, and finally performing experimental verification by using verification set signal data. The problems of low rolling bearing fault diagnosis precision and poor generalization are solved through dynamic dimension adaptation and multiple optimization strategies with a lightweight structure, and efficient, accurate and stable fault diagnosis is realized.

Description

Technical Field

[0001] This invention belongs to the field of mechanical fault diagnosis and intelligent monitoring technology, and specifically relates to an adaptive small-sample fault diagnosis method based on a lightweight one-dimensional residual network. Background Technology

[0002] As a core supporting component of rotating machinery, the operating state of rolling bearings determines the reliability and safety of mechanical equipment. Timely and accurate diagnosis of the type and extent of their faults is of great engineering significance for avoiding equipment downtime, reducing maintenance costs, and ensuring continuous and stable industrial production. In actual industrial scenarios, rolling bearings are prone to failures such as inner ring cracks, outer ring spalling, and rolling element pitting due to factors such as wear, fatigue, and impact. When such faults occur, the bearing vibration signal will exhibit obvious non-stationary and transient impact characteristics. Intelligent diagnostic methods based on vibration signals have become the mainstream fault diagnosis solution in the current industrial sector.

[0003] However, the dual constraints in practical industrial applications pose a severe challenge to rolling bearing fault diagnosis, becoming a core bottleneck for the implementation of intelligent operation and maintenance technologies. On the one hand, the small sample size problem is prominent: under high-speed operating conditions, the bearing fault evolution cycle is short, and the cost of shutting down to conduct fault simulation tests is high and the operation is complex, making it difficult to collect sufficient labeled fault data. In most scenarios, only a small number of fault samples can be obtained. On the other hand, computing resources are limited: diagnostic systems deployed in industrial sites mostly rely on edge computing nodes. These nodes have limited computing power and scarce storage resources, which imposes strict requirements on the number of parameters and inference latency of diagnostic models, making it difficult to adapt to complex and large deep neural network models.

[0004] To address the aforementioned issues, scholars both domestically and internationally have conducted extensive research, resulting in two main technical approaches. However, both have significant limitations and cannot meet the practical needs of small sample sizes and lightweight design. Early research primarily employed a combination of manual feature extraction and shallow classifiers. This involved extracting low-dimensional features such as time-frequency domain statistics and wavelet packet energy from vibration signals based on expert experience, and then using shallow models like support vector machines and random forests for fault identification. However, these methods rely excessively on expert experience, have poor generalization ability in feature extraction, and struggle to adapt to the diverse fault characteristics in complex industrial scenarios, resulting in limited diagnostic accuracy and practicality.

[0005] With the rise of deep learning technology, one-dimensional convolutional neural networks (1D-CNN) have been widely used in the field of rolling bearing fault diagnosis. They can directly mine the mapping relationship between the original vibration signal and the fault category through end-to-end learning, eliminating the need for manual feature extraction and significantly improving diagnostic accuracy, providing a new technical approach for small-sample fault diagnosis. However, existing deep learning-based fault diagnosis models still have three major problems: First, insufficient model generalization ability. Traditional 1D-CNN convolutional kernels have limited receptive fields, resulting in insufficient feature extraction and a tendency to overfit under small-sample conditions, leading to a significant drop in diagnostic performance in complex real-world scenarios. Second, insufficient model lightweighting. Existing deep diagnostic models (such as ResNet-18 and MobileNetV2) have large parameter counts, high computational complexity, and long inference latency, making them difficult to deploy on edge computing nodes. Third, weak adaptive capability. Most models have not been specifically optimized for the characteristics of one-dimensional time-series vibration signals, failing to adapt to signal inputs of different lengths and features. Furthermore, the lack of effective adaptive optimization mechanisms during training leads to slow model convergence and unstable training, further affecting diagnostic accuracy and efficiency.

[0006] In addition, although some existing models have attempted to improve performance through techniques such as attention mechanisms, data augmentation, and depthwise separable convolution, they have either failed to balance accuracy and lightweight design, or have excessively high computational costs and high engineering difficulty, or have limited effectiveness in alleviating overfitting of small samples. All of these have failed to effectively overcome the dual constraints of sample scarcity and limited computing power.

[0007] In summary, the current field of rolling bearing fault diagnosis still lacks effective solutions for the high-precision, lightweight, and adaptive diagnostic requirements under small sample conditions. Therefore, there is an urgent need to design an intelligent diagnostic model that can adapt to one-dimensional time-series vibration signals, has a small parameter set, high inference efficiency, and effectively suppress overfitting and improve generalization ability under small sample conditions. This would address the practical pain points of fault diagnosis in industrial settings and promote the engineering implementation and application of intelligent rolling bearing fault diagnosis technology. Summary of the Invention

[0008] To address the shortcomings of the existing technologies, the present invention aims to propose an adaptive small-sample fault diagnosis method based on a lightweight one-dimensional residual network. This method acquires one-dimensional vibration signals and divides the dataset, constructs a model containing a multi-scale lightweight residual network and an adaptive training optimization framework, and achieves multi-scale feature fusion and dimension adaptation through a ResNet1D dynamic dimension adaptation module. Combined with a dynamic learning rate scheduling strategy, an intelligent early-stop mechanism, and multiple regularization integration techniques, this lightweight structure enables efficient fault diagnosis of rolling bearings in small-sample scenarios, solving the problem of balancing accuracy and efficiency in fault diagnosis for small-sample, low-complexity equipment.

[0009] The technical solution adopted in this invention: An adaptive few-sample fault diagnosis method based on a lightweight one-dimensional residual network includes the following steps: S1) Obtain the one-dimensional vibration signal of the rolling bearing, wherein the one-dimensional vibration signal is divided into a training set, a validation set, and a test set; S2) Construct a lightweight adaptive one-dimensional residual network model to extract features and predict faults from the one-dimensional vibration signals in the training set. The process of building a lightweight adaptive one-dimensional residual network model is as follows: The one-dimensional vibration signal in the training set is processed by the initial convolutional layer of the multi-scale lightweight residual network for feature extraction, downsampling by the max pooling layer, and then multi-scale feature fusion is achieved by two residual blocks of the ResNet1D dynamic dimension adaptation module. Subsequently, the feature vector is obtained by adaptive average pooling to unify the feature dimension and flattening layer. Finally, the class probability distribution is obtained by two fully connected layers and the Softmax function. The ResNet1D dynamic dimension adaptation module includes a residual block, which includes a residual path and an identity mapping path. The residual path uses a series of convolutional layers, normalization layers, and a ReLU function to calculate the length of the output feature map. After dimension checking by the identity mapping path, if the dimension matches, the identity mapping strategy is directly used for output. If the dimension does not match, dimension adaptation is performed through a downsampling module. Finally, the results of the residual path and the identity mapping path are summed and then processed by the ReLU activation function to obtain the output result. S3) Input the one-dimensional vibration signal from the validation set into the lightweight adaptive one-dimensional residual network model, and train and optimize the lightweight adaptive one-dimensional residual network model through an adaptive training optimization framework. The adaptive training optimization framework includes a dynamic learning rate scheduling strategy, an intelligent early stopping mechanism, and a multi-regularization ensemble mechanism. The dynamic learning rate scheduling strategy balances the convergence speed and optimization accuracy, and then the parameters are updated individually through parameter updates and bias correction. Next, the accuracy of the validation set is monitored through the intelligent early stopping mechanism. Finally, a multi-regularization ensemble mechanism including weight decay, Dropout, and batch normalization is adopted to improve the training stability and generalization performance of the model.

[0010] Preferably, the specific process of the lightweight adaptive one-dimensional residual network model in S2) is as follows: 1) The input one-dimensional vibration signal is Feature extraction is performed through the initial convolutional layer, and the initial convolutional layer result is output. The calculation formula is expressed as:

[0011] in, For batch normalization operations, This is a one-dimensional convolution operation. It has a 7×1 convolution kernel. It is the bias vector; The feature map length of the initial convolutional layer result is from Down to The number of channels has increased to 64; 2) After further downsampling through the max pooling layer, the calculation formula for the max pooling layer result is expressed as:

[0012] In the formula, This is a one-dimensional max pooling operation. The pooling window size is 3. The pooling window slides two positions to the right each time. To pad the input with a zero at both ends; The feature map length of the max pooling layer is reduced to The number of channels remains unchanged; 3) The ResNet1D dynamic dimension adaptation module uses two residual blocks. The first residual block keeps the feature map size unchanged, outputs 64 channels, and keeps the feature map length at 256. The downsampling module uses 1×1 convolution to increase the number of channels. The second residual block halves the feature map length to 128 and increases the number of channels to 128. 4) Through adaptive average pooling, the feature maps of the two residual blocks are processed. The transformation is performed to convert feature maps of different resolutions into vectors of fixed dimensions. The formula for adaptive average pooling is as follows:

[0013] In the formula, This refers to the location index of the feature map in the residual block output. For the first The end position of each interval. For the first The starting position of each interval, Feature map of the residual block output The element values ​​in the text, The average pooling eigenvalue; Among them, the length of the output feature map of adaptive average pooling Setting the number to 9 maps the feature maps output by the residual blocks to a fixed size, dividing them evenly into 9 intervals. The feature values ​​within each interval are averaged, reducing the number of channels to 9 and resulting in a unified output dimension. The average pooling eigenvalues; 5) Flattening is performed through a flattening layer to obtain a 1152-dimensional feature vector; 6) The feature vectors are mapped to the class space through two fully connected layers; where fully connected layer 1 performs feature dimensionality reduction and fully connected layer 2 performs class decision; fully connected layer 1 maps the 1152-dimensional feature vectors to a 500-dimensional hidden layer, and after ReLU activation and Dropout regularization, the 500-dimensional hidden layer features are obtained. Its calculation formula is expressed as:

[0014] In the formula, ReLU is the activation function. This is the weight matrix. It is a 1152-dimensional feature vector. It is the bias vector; The 500-dimensional hidden layer features are then mapped to a 10-dimensional output space through a fully connected layer 2, outputting the corresponding 10 types of fault states; finally, the class probability distribution is obtained through the Softmax function.

[0015] Preferably, in step S2), the specific steps for the residual block are as follows: The result of the max pooling layer is a three-dimensional tensor. , as the input to the residual block, where For batch size, For input channels, As input to the residual block; 1) The residual path consists of two cascaded one-dimensional convolutional layers. The first convolutional layer is followed by a batch normalization layer and a ReLU activation function, and the second convolutional layer is followed by a batch normalization layer. The formula for calculating the output of the first convolutional layer is as follows:

[0016] In the formula, For convolution kernel, For bias; After the first convolutional layer, a batch normalization layer and a ReLU activation function are connected in sequence to obtain intermediate features. ; Let the stride of the first convolutional layer be... The kernel size is , Fill as The length of the output feature map of the first convolutional layer is... for:

[0017] in, For filling, The kernel size is [size]. Step size; Next, As the input to the second convolutional layer, the output of the second convolutional layer is calculated using the following formula:

[0018] In the formula, For convolution kernel, For bias; After the second convolutional layer, batch normalization layers are sequentially connected to obtain intermediate features. ; Length of the output feature map of the second convolutional layer The calculation formula is as follows:

[0019] in, It is the stride of the second convolutional layer. It is the kernel size of the second convolutional layer. It is the padding size of the second convolutional layer; 2) Identity Mapping Path: After passing through the residual path, the input and output of the residual path are matched in terms of dimension. When the input and output dimensions of the residual path are equal and the step size is 1, the identity mapping strategy is adopted, and the identity mapping term is set to... If the input is the direct output of the residual path, then the input is used; otherwise, dimensionality adaptation is performed through a downsampling module. The downsampling module consists of 1×1 convolutions and batch normalization, and its output is... The calculation formula is expressed as:

[0020] 3) After performing dimension matching judgment on the input and output of the residual path, the feature of the output results of the residual path and the identity mapping path are added together; ① When the dimensions of the input and output of the residual path match, a residual block of basic unit is used, and its calculation formula is expressed as:

[0021] In the formula, and These represent the input and output of the residual block, respectively. It is the residual function; ② When the dimensions of the input and output of the residual path do not match, linear projection is used. The dimension of the residual block is adjusted according to the input dimension, and its calculation formula is expressed as follows:

[0022] 4) Obtain the feature maps of the two residual blocks using the ReLU activation function. Its calculation formula is expressed as:

[0023] Preferably, the specific process of S3 is as follows: 1) Use a constant initial learning rate for the first 4 training cycles. The learning rate does not decay, keeping it constant for the first four cycles. The formula for calculating this is:

[0024] in, The initial learning rate, For the first The learning rate for each training cycle; Starting from the 5th training period, a dynamic learning rate scheduling strategy is adopted, and the learning rate decays from the 5th period onwards. This is achieved through a phased learning rate decay strategy. Learning rate per training cycle The calculation formula is:

[0025] In the formula, As the attenuation factor, This is to decay the step size, which is to enable the model to converge stably in the better region during the middle of training; In the later stages of training, the learning rate is drastically reduced to an extremely low level. This ensures that the model converges to a flat region of minimum values. Next, the parameter update uses an adaptive moment estimation optimizer, setting all the weight parameters of the model as parameters. In training steps The gradient at time is Calculate the first moment estimate and second moment estimates The update rule is calculated using the following formula:

[0026] In the formula, All of these are attenuation rate hyperparameters. For the first First-order moment estimate at the nth training step For the first Second-order moment estimate at the next training step; Then, after bias correction, the parameter update amount The calculation formula is:

[0027] In the formula, , All are deviation correction items. It is the numerical stability constant; 2) A smart early stopping mechanism is used to continuously monitor the validation set accuracy. When the validation set performance reaches its optimal level, the model parameters are saved; the validation set accuracy sequence is denoted as... The best accuracy rate is ,when Update the model parameters in real time; 3) By integrating three complementary multiple regularization techniques: weight decay, Dropout, and batch normalization; First, weight decay regularization is used in the adaptive moment estimation optimizer to achieve deep coupling rather than simple superposition. That is, an L2 regularization term is added to the total loss function, and the calculation formula is as follows:

[0028] in, For the total loss function, For cross-entropy loss, The regularization coefficient is set to... , These are the weight parameters of the model.

[0029] Compared with existing technologies, this invention proposes an adaptive small-sample fault diagnosis method based on a lightweight one-dimensional residual network. The advantages of this method are: (1) Lightweight structure and strong deployment applicability: The lightweight one-dimensional residual network is adopted to simplify the network structure, reduce the number of parameters and computation, reduce the hardware computing power requirements, and meet the real-time fault diagnosis needs of low computing power devices such as embedded and edge devices, and adapt to the actual deployment scenarios in industrial sites.

[0030] (2) Efficient and accurate feature extraction: The ResNet1D dynamic dimension adaptation module is designed. By using residual blocks and dimension adaptation strategies, the dimension mismatch problem in one-dimensional vibration signal feature extraction is solved, multi-scale feature fusion is achieved, the deep features of the fault are fully explored, and the feature representation capability under small sample conditions is improved.

[0031] (3) Stable training and excellent generalization: Based on the adaptive training optimization framework, multi-stage learning rate scheduling, adaptive moment estimation optimizer and bias correction are adopted to balance convergence speed and optimization accuracy; combined with intelligent early stopping, weight decay, Dropout and batch normalization multiple regularization, overfitting is effectively suppressed and the generalization performance of the model is greatly improved.

[0032] (4) Adapting to small sample diagnosis scenarios: In response to the pain point of scarce fault samples in industrial scenarios, relying on lightweight networks and adaptive optimization strategies, the diagnostic accuracy can still be guaranteed with a small number of training samples, solving the problem that traditional deep learning fault diagnosis relies on massive data and performs poorly in small sample scenarios. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the overall architecture of the adaptive small-sample fault diagnosis method based on a lightweight one-dimensional residual network of the present invention. Figure 2 This is a schematic diagram of the framework of the dynamic dimension adaptation strategy proposed in this invention; Figure 3 This is a schematic diagram of the bearing experimental platform for an embodiment; Figure 4 The accuracy curve is shown in the example. Figure 5 The loss value curve is shown in the example. Figure 6 A T-SNE visualization of an example; Figure 7 Here is a confusion matrix diagram for an example; Figure 8 The T-SNE visualization is shown in the example. Detailed Implementation

[0034] The technical solutions of the embodiments of this application will be further described clearly and completely below with reference to the accompanying drawings. It should be noted that the described embodiments are only some embodiments of this application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0035] To make the inventive objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be further described in detail below with reference to the accompanying drawings: In order to better understand the above-mentioned objectives, features, and advantages of this invention, the advantages of this invention will be further illustrated below by comparing the embodiments with the accompanying drawings and specific implementation methods.

[0036] This invention proposes an adaptive few-sample fault diagnosis method based on a lightweight one-dimensional residual network. The overall structure of this method is shown in the schematic diagram below. Figure 1 The steps of this method are described in detail below: S1) Obtain the one-dimensional vibration signal of the rolling bearing, wherein the one-dimensional vibration signal is divided into a training set, a validation set, and a test set; S2) Construct a lightweight adaptive one-dimensional residual network model to extract features and predict faults from the one-dimensional vibration signals in the training set. The process of building a lightweight adaptive one-dimensional residual network model is as follows: The one-dimensional vibration signal in the training set is processed by the initial convolutional layer of the multi-scale lightweight residual network for feature extraction, downsampling by the max pooling layer, and then multi-scale feature fusion is achieved by two residual blocks of the ResNet1D dynamic dimension adaptation module. Subsequently, the feature vector is obtained by adaptive average pooling to unify the feature dimension and flattening layer. Finally, the class probability distribution is obtained by two fully connected layers and the Softmax function. The ResNet1D dynamic dimension adaptation module includes a residual block, which includes a residual path and an identity mapping path. The residual path uses a series of convolutional layers, normalization layers, and a ReLU function to calculate the length of the output feature map. After dimension checking by the identity mapping path, if the dimension matches, the identity mapping strategy is directly used for output. If the dimension does not match, dimension adaptation is performed through a downsampling module. Finally, the results of the residual path and the identity mapping path are summed and then processed by the ReLU activation function to obtain the output result. Specifically, the specific steps of the multi-scale lightweight residual network in S2) are as follows: To address the challenges of limited labeled data and computational resources in industrial fault diagnosis scenarios, a lightweight adaptive one-dimensional residual network model employs a shallow and efficient multi-scale lightweight residual network. The core design concept of this network is to combine a minimalist two-layer residual structure with a strictly controlled channel expansion scheme while ensuring feature extraction capabilities. This innovative combination significantly reduces model complexity and integrates a multi-scale feature fusion mechanism into the network architecture to further improve network performance. The multi-scale lightweight residual network adopts an initial convolutional layer and a two-layer residual structure in its structural design. Each layer of the residual structure is equipped with a residual block. The total number of convolutional layers is strictly controlled to be within 5 layers. The total number of convolutional layers includes 1 initial convolutional layer and 4 convolutional layers inside the residual blocks. 1) Input one-dimensional vibration signal is , The batch size is 1024, representing the length of each vibration signal. Feature extraction is performed using an initial convolutional layer with a stride of 2 (the kernel slides two positions to the right each time) and padding of 3 (three zeros are added to both ends of the vibration signal). The convolutional kernel is used to extract local features of the vibration signal, and the initial convolutional layer result is output. The calculation formula is expressed as:

[0037] in, For batch normalization operations, This is a one-dimensional convolution operation. It has a 7×1 convolution kernel. It is the bias vector; The feature map length of the initial convolutional layer result is from Down to The number of channels is increased to 64; while reducing the feature map length, the receptive field is expanded by using a larger convolution kernel size to capture the global pattern of vibration signals. 2) After further downsampling through the max pooling layer, the calculation formula for the max pooling layer result is expressed as:

[0038] In the formula, This is a one-dimensional max pooling operation. The pooling window size is 3. The pooling window slides two positions to the right each time. To pad the input with a zero at both ends; The feature map length of the max pooling layer is reduced to The number of channels remains unchanged; the max pooling layer operation takes the maximum value within the local receptive field to enhance the invariance of features; 3) The ResNet1D dynamic dimension adaptation module uses two residual layer units, each containing only one one-dimensional adaptive residual block. This shallow design avoids the training difficulties caused by overly deep networks. The first residual block keeps the feature map size unchanged, outputs 64 channels, and maintains a feature map length of 256. Through the downsampling module, 1×1 convolutions are used to increase the number of channels, enhancing the network's ability to learn shallow features. The second residual block halves the feature map length to 128 while increasing the number of channels to 128, achieving multi-scale feature fusion. 4) Through adaptive average pooling, the feature maps of the two residual blocks are processed. The transformation is performed to convert feature maps of different resolutions into vectors of fixed dimensions. The formula for adaptive average pooling is as follows:

[0039] In the formula, This refers to the location index of the feature map in the residual block output. For the first The end position of each interval. For the first The starting position of each interval, Feature map of the residual block output The element value in the string represents the first element. The first vibration signal In the first feature channel The element values ​​at each point in time. Let be the average pooling eigenvalue, representing the th eigenvalue. The sample, the first In the first passage, the... The average feature value of each output position; Among them, the length of the output feature map of adaptive average pooling Setting the number to 9 maps the feature maps output by the residual blocks to a fixed size, dividing them evenly into 9 intervals. The feature values ​​within each interval are averaged, reducing the number of channels to 9, thus outputting a uniform dimension. The average pooling eigenvalues; 5) The flattening operation is performed through the flattening layer to obtain a 1152-dimensional feature vector, which is then fed into the classifier for final decision-making; this enables the model to handle input signals of variable length, enhances generalization ability, and significantly reduces the number of parameters in the fully connected layer through dimensionality reduction. 6) The feature vectors are mapped to the class space through two fully connected layers; where fully connected layer 1 performs feature dimensionality reduction and fully connected layer 2 performs class decision; fully connected layer 1 maps the 1152-dimensional feature vectors to a 500-dimensional hidden layer, and after ReLU activation and Dropout regularization, the 500-dimensional hidden layer features are obtained. Its calculation formula is expressed as:

[0040] In the formula, ReLU is the activation function. This is the weight matrix. It is a 1152-dimensional feature vector. It is the bias vector; The 500-dimensional hidden layer features are then mapped to the 10-dimensional output space through the fully connected layer 2, outputting the corresponding 10 fault states. Finally, the class probability distribution is obtained through the Softmax function. In this stage, the fully connected layer achieves intelligent weighted integration of cross-scale features through global linear combination and nonlinear activation, enabling the model to adaptively focus on the scale features most important to the current diagnostic task.

[0041] Specifically, in S2), the specific process of the residual block is as follows: Based on residual learning theory, a ResNet1D dynamic dimension adaptation strategy was designed to migrate the core architecture of traditional two-dimensional residual networks to the field of one-dimensional vibration signal processing. The core idea of ​​ResNet is preserved through operator dimensionality reduction and reconstruction. Specifically, it transforms the residual connections originally used to process spatial information into residual paths that adapt to temporal features. Its key innovation lies in realizing dynamic dimension adaptation between residual paths and identity mappings, thereby effectively improving the model's ability to process one-dimensional temporal data. The result of the max pooling layer is a three-dimensional tensor. , as the input to the residual block, where For batch size, For input channels, As input to the residual block; 1) The residual path consists of two cascaded one-dimensional convolutional layers. The first convolutional layer is followed by a batch normalization (BN) layer and a modified linear unit (ReLU) activation function. The second convolutional layer is followed only by a batch normalization layer. The strategy for dynamically adapting the residual block structure is as follows: Figure 2 As shown; The formula for calculating the output of the first convolutional layer is as follows:

[0042] In the formula, For convolution kernel, For bias; After the first convolutional layer, a batch normalization layer and a ReLU activation function are connected in sequence to obtain intermediate features. ; Let the stride of the first convolutional layer be... The kernel size is , Fill as The length of the output feature map of the first convolutional layer is... for:

[0043] in, For filling, The kernel size is [size]. Step size; Next, As the input to the second convolutional layer, the output of the second convolutional layer is calculated using the following formula:

[0044] In the formula, For convolution kernel, For bias; After the second convolutional layer, batch normalization layers are sequentially connected to obtain intermediate features. ; Length of the output feature map of the second convolutional layer The calculation formula is as follows:

[0045] in, It is the stride of the second convolutional layer. It is the kernel size of the second convolutional layer. It is the padding size of the second convolutional layer; 2) Identity Mapping Path: After passing through the residual path, the input and output of the residual path are matched in terms of dimension. The identity mapping strategy is adopted if and only if the input and output dimensions of the residual path are equal and the step size is 1. If the input is directly output as the residual path, then the dimension is adapted to match the output dimension of the identity mapping term and the residual path for element-wise addition. The downsampling module consists of a 1×1 convolution and batch normalization, and its output is... The calculation formula is expressed as:

[0046] In the formula, For linear projection; This design ensures that the output dimension of the downsampling module remains constant regardless of changes in the number of channels and step size. It perfectly matches the residual path output; 3) After performing dimension matching judgment on the output and input of the residual path, the output results of the residual path and the identity mapping path are summed by feature addition; ① When the dimensions of the output and input of the residual path match, a residual block of basic unit is used, and its calculation formula is expressed as:

[0047] In the formula, and These represent the input and output of the residual block, respectively. The residual function is composed of operations such as convolution and normalization. ② When the dimensions of the input and output of the residual path do not match, linear projection is used. Adjusting the dimensions of the residual blocks of the input dimensions to achieve a dimension identity mapping fit is expressed by the following formula:

[0048] 4) Obtain the feature maps of the two residual blocks using the ReLU activation function. Its calculation formula is expressed as:

[0049] This ResNet1D dynamic dimension adaptation strategy makes the residual block a basic module for building networks with variable depth and width. While balancing efficiency and receptive field range, it not only retains the advantage of residual learning in mitigating gradient vanishing by leveraging the identity mapping mechanism, but also provides greater flexibility for network structure design, thereby improving the model's ability to express features.

[0050] S3) Input the one-dimensional vibration signal from the validation set into the lightweight adaptive one-dimensional residual network model, and train and optimize the lightweight adaptive one-dimensional residual network model through an adaptive training optimization framework. The adaptive training optimization framework includes a dynamic learning rate scheduling strategy, an intelligent early stopping mechanism, and a multi-regularization ensemble mechanism. The dynamic learning rate scheduling strategy balances the convergence speed and optimization accuracy, and then the parameters are updated individually through parameter updates and bias correction. Next, the accuracy of the validation set is monitored through the intelligent early stopping mechanism. Finally, a multi-regularization ensemble mechanism including weight decay, Dropout, and batch normalization is adopted to improve the training stability and generalization performance of the model.

[0051] Specifically, the specific steps of S3 are as follows: To address the issues of model overfitting, training instability, and slow convergence in small-sample industrial fault diagnosis scenarios, an innovative adaptive training optimization framework is proposed. This framework improves the training stability, convergence speed, and generalization performance of lightweight networks under small-sample conditions through dynamic learning rate scheduling strategy, intelligent early stopping mechanism, and multi-regularization integration. 1) Use a constant initial learning rate for the first 4 training cycles. Because the learning rate is high and convergence is rapid in the early stages of training, the learning rate is not decayed, so the learning rate remains unchanged for the first four epochs. The calculation formula is as follows:

[0052] in, The initial learning rate is set to [value]. , For the first The learning rate per training epoch; When the 5th training cycle begins, a dynamic learning rate scheduling strategy is employed to intelligently adjust the learning rate to improve training efficiency. Starting from the 5th cycle, the learning rate decays. Through a phased learning rate decay strategy, a relatively high initial learning rate is maintained in the early stages of training to facilitate rapid convergence. From the 5th training cycle onwards, the learning rate... Learning rate per training cycle The calculation formula is:

[0053] In the formula, The attenuation factor is set to 0.3. The decay step size is set to 5, which means that the model can stably converge in the better region during the middle of training. In the later stages of training (episodes > 20), the learning rate is drastically reduced to an extremely low level. It is used to fine-tune all weight parameters in the network to ensure that the model converges to a flat minimum region.

[0054] Next, the parameter update employs the Adaptive Moment Estimator (Adam), which calculates independent first-order and second-order moment estimates for each weight parameter to achieve personalized learning rate adjustment. All weight parameters of the model are set as parameters. In training steps The gradient at time is Calculate the first moment estimate and second moment estimates The update rule is calculated using the following formula:

[0055] In the formula, All of these are attenuation rate hyperparameters. For the first First-order moment estimate at the nth training step For the first Second-order moment estimate at the next training step; Then, after bias correction, the parameter update amount The calculation formula is:

[0056] In the formula, , All are deviation correction items. This is a numerical stability constant; this multi-stage scheduling strategy enables the model to obtain an appropriate learning rate at different training stages, effectively balancing convergence speed and optimization accuracy. 2) An intelligent early stopping mechanism is used. This mechanism does not rely on a preset early stopping point, but continuously monitors the validation set accuracy throughout the training process. When the validation set performance reaches its optimal value, the model parameters are saved. The validation set accuracy sequence is denoted as... The best accuracy rate is ,when The model parameters are updated in real time. This strategy avoids overfitting the model on the training set and ensures that the model with the best generalization performance is obtained. 3) To prevent overfitting under small sample conditions, a multi-regularization integration technique is used, which integrates three complementary techniques: weight decay, Dropout, and batch normalization. First, in the adaptive moment estimation optimizer (Adam), weight decay regularization is used to achieve deep coupling rather than simple aggregation. That is, an L2 regularization term is added to the total loss function, and the calculation formula is as follows:

[0057] in, For the total loss function, For cross-entropy loss, The regularization coefficient is set to... , These are the weight parameters of the model; By penalizing larger parameter values ​​through weight decay, it is directly incorporated into each step of adaptive moment estimation, prompting the model to learn smoother decision boundaries and improving generalization ability. Next, Dropout is precisely applied to the fully connected layer to match the characteristics of shallow layers of the network, forcing the learning of robust features, and avoiding the information loss and training efficiency reduction caused by Dropout in the already extremely lightweight convolutional layers. Batch normalization is integrated after all convolutional layers. In small-sample training, the noise introduced by the small-batch statistics itself becomes an effective implicit regularization. At the same time, for one-dimensional time-series signals, batch normalization stabilizes the feature distribution of each convolutional layer output, effectively alleviates the covariate shift problem, and ensures the stability and reliability of the training process.

[0058] The specific experiments of this invention are described in detail below with reference to the technical solution and accompanying drawings: 1. Description of the experimental dataset In order to verify the effectiveness of the LA1DRN-FD model, this study uses the rolling bearing dataset published by Case Western Reserve University (CWRU) for experimental verification. The CWRU experimental platform consists of core components such as motor, torque sensor, electronic controller, drive end bearing, fan end bearing and electronic controller

[19] . Figure 3 As shown; This paper selects the DE drive end bearing, model SKF6205 deep groove ball bearing, as the sensor data acquisition object. The vibration signal of the bearing is collected under zero load conditions and the sampling frequency is 12kHz. Faults are artificially added to the rolling bearing by electrical discharge machining, including three types of faults: rolling element faults, inner ring faults, and outer ring faults. Each fault type has three different degrees of damage of 0.1778, 0.3556, and 0.5334 mm, respectively. The detailed experimental data are shown in Table 1. Table 1 Bearing Dataset

[0059] 2. Experimental parameter settings The original signal has 119,808 data points. To adapt to the input requirements of the deep learning model, the bearing dataset is segmented using a sliding window method. The sliding window length is set to 1024, with an overlap rate of 50%, resulting in a sliding step size of 512. For a length of... The number of samples obtainable from the original signal by sliding window segmentation The calculation formula is:

[0060] Each category yields 232 samples, for a total of 2320 samples across 10 categories. Each sample contains 1024 continuous vibration data points. To eliminate the influence of features at different scales on model training, min-max normalization is performed on each sample, calculated as follows:

[0061] in, The original vibration signal value. and These are the minimum and maximum values ​​of the signal sequence, respectively; after normalization, all feature values ​​are mapped to... The interval ensures the weight balance of each feature during model training; The total sample was divided into training, validation, and test sets in a 6:2:2 ratio. The specific division method was as follows: First, all samples were randomly shuffled using a specified seed, ensuring that the specific samples in the training, validation, and test sets were not identical for each experiment. This simulated the uncertainty of data distribution in real-world applications while ensuring a uniform distribution of samples across all categories. Then, the samples were allocated according to a predetermined ratio, resulting in a training set of 1392 samples covering the 10 fault categories, and a validation and test set of 464 samples in total. 3. Experimental Results and Analysis (1) Experimental results of LA1DRN-FD The preprocessed one-dimensional signal sequence was input into the LA1DRN-FD model. The diagnostic performance of the model was evaluated using accuracy, loss value, T-SNE visualization, and confusion matrix. The accuracy and loss values ​​of the LA1DRN-FD model on the training, validation, and test sets are shown below. Figure 4 , Figure 5 As shown, the T-SNE visualization results on the validation set are as follows: Figure 6 As shown, the confusion matrix metrics results on the test set are as follows: Figure 7As shown, the model converges rapidly within about 10 training epochs. The accuracy curves of the training set, validation set, and test set rise rapidly and closely match. The accuracy of the test set is as high as 99.32%, and the corresponding loss curve decreases rapidly and tends to stabilize, effectively avoiding overfitting and ensuring excellent generalization ability. (2) Ablation test To verify the effectiveness of the three key dimensions—dynamic dimension adaptation strategy, multi-scale lightweight residual network, and adaptive intelligent training optimization framework—this experiment conducted a systematic ablation study. Under the same training conditions, the three modules were removed from the table, and fault diagnosis was performed on them. Ablation-1 indicates the removal of the dynamic dimension adaptation strategy; Ablation-2 indicates the removal of the lightweight design; Ablation-3 indicates the removal of the intelligent training optimization mechanism; MSFAN-DFE is the complete model, containing all three modules. Key accuracy metrics are shown in Table 2. Table 2 Ablation Experiment

[0062] Ablation experiments show that the complete LA1DRN-FD model achieves the optimal balance between accuracy and efficiency through multi-module collaborative optimization. The Ablation-1 model, which removes the dynamic dimension adaptation strategy, suffers a drop in test accuracy to 1.17% and a 0.79% increase in the performance difference between training and validation, highlighting its crucial role in ensuring robust feature representation. The Ablation-2 model, which removes the multi-scale lightweight residual network design, severely compromises model efficiency, with parameters surging by 241% to 2.35M, inference time doubling, and accuracy decreasing by 1.89%, demonstrating the key value of this design in achieving extreme lightweighting while maintaining high accuracy. The Ablation-3 model, which removes the adaptive intelligent training optimization framework, results in a significant 56% increase in model convergence period and an increased risk of overfitting, validating its important contribution to accelerating training and improving stability. These results fully demonstrate the necessity of each innovative module design and its synergistic mechanism, collectively forming a high-accuracy, high-efficiency, and strongly generalizable LA1DRN-FD model.

[0063] Compared with other deep learning models, this paper replaces the multi-scale lightweight residual network with the corresponding model, without modifying the original dynamic dimension adaptation strategy and adaptive intelligent training optimization framework. The accuracy results of the comparison experiment with other models are as follows: Figure 8 As shown.

[0064] LA1DRN-FD represents the method proposed in this study. The MobileNetV2 model's input layer uses a one-dimensional convolution with a kernel size of 3 and a stride of 2 for initial downsampling and feature extraction, outputting 16 channels. The main structure consists of six inverted residual blocks cascaded together. The core of each residual block is a depthwise separable convolution, composed of a channel-wise convolution with a kernel size of 3 followed by a pointwise convolution, with a scaling factor of 6. The first layer of ResNet-18 uses a one-dimensional convolution with a kernel size of 7 and a stride of 2, outputting 64 channels, followed by a max-pooling layer with a kernel size of 3 and a stride of 2 for fast downsampling. The feature extraction backbone consists of four layers, containing 2, 2, 2, and 2 standard residual blocks respectively, with output channels of 64, 128, 256, and 512 respectively. ResNet-34 has the same initial convolution and pooling layer settings as ResNet-18. The feature extraction backbone is also divided into four layers, but the number of residual blocks increases to 3, 4, 6, and 3, with output channel numbers of 64, 128, 256, and 512 respectively. The first layer of the 1D-CNN uses a large convolutional kernel (size 7) to obtain the initial receptive field, outputting 16 feature maps. This is followed by two stacked convolutional layers, each with a kernel size of 3, gradually increasing the number of output channels to 32 and 64. Each convolutional layer is followed by batch normalization, ReLU activation, and a max-pooling layer with a kernel size of 2. A random deactivation layer with a dropout rate of 0.5 is added after the last convolutional block to control overfitting. Finally, the flattened feature maps are fed into a fully connected layer containing 128 neurons and ReLU activation, ultimately outputting the classification result through a 10-dimensional output layer.

[0065] Table 3 Model Comparison Experiment

[0066] This study compares the performance of five models, MobileNetV2

[20] , ResNet-18

[21] , ResNet-34

[22] , 1D-CNN and LA1DRN-FD, as shown in Table 3, and verifies the comprehensive advantages of the LA1DRN-FD method in fault diagnosis tasks.

[0067] In terms of diagnostic accuracy, the LA1DRN-FD model outperforms MobileNetV2 and 1D-CNN models with a test accuracy of 99.32%, and is on par with the deepest ResNet-34, demonstrating its excellent feature representation and classification capabilities.

[0068] In terms of lightweight design and efficiency, the model has only 0.69M parameters, a 42.5% reduction compared to MobileNetV2, 13.3% of ResNet-18, and 7.2% of ResNet-34, demonstrating good model compression. Meanwhile, its single-sample inference time is only 0.9ms, a 76.3% improvement over ResNet-18, almost on par with lightweight 1D-CNNs, validating its significant advantage in computational efficiency. Overall, the LA1DRN-FD model achieves an optimal balance between accuracy and lightweight design. With approximately 0.69M parameters and low inference latency, it meets the core requirements of high-precision, low-latency fault diagnosis for industrial edge devices under resource constraints, providing an efficient and reliable solution for engineering deployment.

[0069] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0070] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. An adaptive small-sample fault diagnosis method based on a lightweight one-dimensional residual network, characterized in that, include: S1) Obtain the one-dimensional vibration signal of the rolling bearing, wherein the one-dimensional vibration signal is divided into a training set, a validation set, and a test set; S2) Construct a lightweight adaptive one-dimensional residual network model to extract features and predict faults from the one-dimensional vibration signals in the training set. The process of building a lightweight adaptive one-dimensional residual network model is as follows: The one-dimensional vibration signal in the training set is processed by the initial convolutional layer of the multi-scale lightweight residual network for feature extraction, downsampling by the max pooling layer, and then multi-scale feature fusion is achieved by two residual blocks of the ResNet1D dynamic dimension adaptation module. Subsequently, the feature vector is obtained by adaptive average pooling to unify the feature dimension and flattening layer. Finally, the class probability distribution is obtained by two fully connected layers and the Softmax function. The ResNet1D dynamic dimension adaptation module includes a residual block, which includes a residual path and an identity mapping path. The residual path uses a series of convolutional layers, normalization layers, and a ReLU function to calculate the length of the output feature map. After dimension checking by the identity mapping path, if the dimension matches, the identity mapping strategy is directly used for output. If the dimension does not match, dimension adaptation is performed through a downsampling module. Finally, the results of the residual path and the identity mapping path are summed and then processed by the ReLU activation function to obtain the output result. S3) Input the one-dimensional vibration signal from the validation set into the lightweight adaptive one-dimensional residual network model, and train and optimize the lightweight adaptive one-dimensional residual network model through an adaptive training optimization framework. The adaptive training optimization framework includes a dynamic learning rate scheduling strategy, an intelligent early stopping mechanism, and a multi-regularization ensemble mechanism. The dynamic learning rate scheduling strategy balances the convergence speed and optimization accuracy, and then the parameters are updated individually through parameter updates and bias correction. Next, the accuracy of the validation set is monitored through the intelligent early stopping mechanism. Finally, a multi-regularization ensemble mechanism including weight decay, Dropout, and batch normalization is adopted to improve the training stability and generalization performance of the model.

2. The adaptive small-sample fault diagnosis method based on a lightweight one-dimensional residual network according to claim 1, characterized in that, The specific process of the lightweight adaptive one-dimensional residual network model in S2) is as follows: 1) The input one-dimensional vibration signal is Feature extraction is performed through the initial convolutional layer, and the initial convolutional layer result is output. The calculation formula is expressed as: ； in, For batch normalization operations, This is a one-dimensional convolution operation. It has a 7×1 convolution kernel. It is the bias vector; The feature map length of the initial convolutional layer result is from Down to The number of channels has increased to 64; 2) After further downsampling through the max pooling layer, the calculation formula for the max pooling layer result is expressed as: ; In the formula, This is a one-dimensional max pooling operation. The pooling window size is 3. The pooling window slides two positions to the right each time. To pad the input with a zero at both ends; The feature map length of the max pooling layer is reduced to The number of channels remains unchanged; 3) The ResNet1D dynamic dimension adaptation module uses two residual blocks. The first residual block keeps the feature map size unchanged, outputs 64 channels, and keeps the feature map length at 256. The downsampling module uses 1×1 convolution to increase the number of channels; the second residual block halves the feature map length to 128 while increasing the number of channels to 128. 4) Through adaptive average pooling, the feature maps of the two residual blocks are processed. The transformation is performed to convert feature maps of different resolutions into vectors of fixed dimensions. The formula for adaptive average pooling is as follows: ; In the formula, This refers to the location index of the feature map in the residual block output. For the first The end position of each interval. For the first The starting position of each interval, Feature map of the residual block output The element values ​​in the text, The average pooling eigenvalue; Among them, the length of the output feature map of adaptive average pooling Setting the number to 9 maps the feature maps output by the residual blocks to a fixed size, dividing them evenly into 9 intervals. The feature values ​​within each interval are averaged, reducing the number of channels to 9 and resulting in a unified output dimension. The average pooling eigenvalues; 5) Flattening is performed through a flattening layer to obtain a 1152-dimensional feature vector; 6) The feature vectors are mapped to the class space through two fully connected layers; where fully connected layer 1 performs feature dimensionality reduction and fully connected layer 2 performs class decision; fully connected layer 1 maps the 1152-dimensional feature vectors to a 500-dimensional hidden layer, and after ReLU activation and Dropout regularization, the 500-dimensional hidden layer features are obtained. Its calculation formula is expressed as: ； In the formula, ReLU is the activation function. This is the weight matrix. It is a 1152-dimensional feature vector. It is the bias vector; The 500-dimensional hidden layer features are then mapped to a 10-dimensional output space through a fully connected layer 2, outputting the corresponding 10 types of fault states; finally, the class probability distribution is obtained through the Softmax function.

3. The adaptive small-sample fault diagnosis method based on a lightweight one-dimensional residual network according to claim 1, characterized in that, In step S2), the specific steps of the residual block are as follows: The result of the max pooling layer is a three-dimensional tensor. , as the input to the residual block, where For batch size, For input channels, As input to the residual block; 1) The residual path consists of two cascaded one-dimensional convolutional layers. The first convolutional layer is followed by a batch normalization layer and a ReLU activation function, and the second convolutional layer is followed by a batch normalization layer. The formula for calculating the output of the first convolutional layer is as follows: ； In the formula, , For bias; After the first convolutional layer, a batch normalization layer and a ReLU activation function are connected in sequence to obtain intermediate features. ; Let the stride of the first convolutional layer be... The kernel size is , Fill as The length of the output feature map of the first convolutional layer is... for: ； in, For filling, The kernel size is [size]. Step size; Next, As the input to the second convolutional layer, the output of the second convolutional layer is calculated using the following formula: ； In the formula, For convolution kernel, For bias; After the second convolutional layer, batch normalization layers are sequentially connected to obtain intermediate features. ; Length of the output feature map of the second convolutional layer The calculation formula is as follows: ； in, It is the stride of the second convolutional layer. It is the kernel size of the second convolutional layer. It is the padding size of the second convolutional layer; 2) Identity Mapping Path: After passing through the residual path, the input and output of the residual path are matched in terms of dimension. When the input and output dimensions of the residual path are equal and the step size is 1, the identity mapping strategy is adopted, and the identity mapping term is set to... If the input is the direct output of the residual path, then the input is used; otherwise, dimensionality adaptation is performed through a downsampling module. The downsampling module consists of 1×1 convolutions and batch normalization, and its output is... The calculation formula is expressed as: ； 3) After performing dimension matching judgment on the input and output of the residual path, the feature of the output results of the residual path and the identity mapping path are added together; ① When the dimensions of the input and output of the residual path match, a residual block of basic unit is used, and its calculation formula is expressed as: ; In the formula, and These represent the input and output of the residual block, respectively. It is the residual function; ② When the dimensions of the input and output of the residual path do not match, linear projection is used. The dimension of the residual block is adjusted according to the input dimension, and its calculation formula is expressed as follows: ； 4) Obtain the feature maps of the two residual blocks using the ReLU activation function. Its calculation formula is expressed as: 。 4. The adaptive small-sample fault diagnosis method based on a lightweight one-dimensional residual network according to claim 1, characterized in that, The specific process of S3 is as follows: 1) Use a constant initial learning rate for the first 4 training cycles. The learning rate does not decay, keeping it constant for the first four cycles. The formula for calculating this is: ; in, The initial learning rate, For the first The learning rate for each training cycle; Starting from the 5th training period, a dynamic learning rate scheduling strategy is adopted, and the learning rate decays from the 5th period onwards. This is achieved through a phased learning rate decay strategy. Learning rate per training cycle The calculation formula is: ； In the formula, As the attenuation factor, This is to decay the step size, which is to enable the model to converge stably in the better region during the middle of training; In the later stages of training, the learning rate is drastically reduced to an extremely low level. This ensures that the model converges to a flat region of minimum values. Next, the parameter update uses an adaptive moment estimation optimizer, setting all the weight parameters of the model as parameters. In training steps The gradient at time is Calculate the first moment estimate and second moment estimates The update rule is calculated using the following formula: ； In the formula, , All of these are attenuation rate hyperparameters. For the first First-order moment estimate at the nth training step For the first Second-order moment estimate at the next training step; Then, after bias correction, the parameter update amount The calculation formula is: ; In the formula, , All are deviation correction items. It is the numerical stability constant; 2) A smart early stopping mechanism is used to continuously monitor the validation set accuracy. When the validation set performance reaches its optimal level, the model parameters are saved; the validation set accuracy sequence is denoted as... The best accuracy rate is ,when Update the model parameters in real time; 3) By integrating three complementary multiple regularization techniques: weight decay, Dropout, and batch normalization; First, weight decay regularization is used in the adaptive moment estimation optimizer to achieve deep coupling rather than simple superposition. That is, an L2 regularization term is added to the total loss function, and the calculation formula is as follows: ； in, For the total loss function, For cross-entropy loss, The regularization coefficient is set to... , These are the weight parameters of the model.

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