Rolling bearing residual life prediction method based on uncertainty weighted domain generalization
Patent Information
- Application Number
- CN202311236135.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-09-22
- Publication Date
- 2026-09-22
- Estimated Expiration
- 2043-09-22
AI Technical Summary
然而，领域自适应的方法只对指定迁移目标的效果有所提升，无法泛化到任何可能的目标条件，导致模型训练成本提高、实用性差
[0042]本发明通过教师网络和学生网络构建知识蒸馏框架，捕获源域振动数据样本集的域内不变特征，并以每个源域振动数据样本集的域内不变特征在教师网络和学生网络的差异最小为目标构建第一损失函数，指导学生网络捕获源域振动数据样本集的域内不变特征，利用相关性对齐算法约束每个源域振动数据样本集的域间不变特征在学生网络的空间分布，构建第二损失函数，指导学生网络学习源域振动数据样本集的域间不变特征，以学生网络对源域振动数据样本的预测结果和源域振动数据样本的真实标签的差异化最小为目标构建第四损失函数，根据同方差的不确定性对第一损失函数、第二损失函数、第三损失函数和第四损失函数进行加权构建学生网络的损失函数，以学生网络的损失函数最小为优化目标对学生网络进行训练，得到滚动轴承剩余使用寿命预测模型，对未知工况的目标域振动数据样本进行泛化，利用本发明的方法可以将教师网络从源域泛化到多种未知的目标域，降低模型训练成本，增强模型的实用性，提高了轴承寿命预测的精确度与泛化性。
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of mechanical resource prediction technology, and specifically relates to a method for predicting the remaining life of rolling bearings based on uncertainty weighted domain generalization. Background Technology
[0002] As a critical component in rotating machinery, bearings inevitably experience performance degradation such as fatigue damage and stress failure during long-term operation. Therefore, accurately predicting the remaining usable life (RUL) of bearings is of significant practical importance in addressing issues such as safe equipment operation and personnel casualties. In recent years, although scholars both domestically and internationally have conducted extensive research on bearing RUL prediction based on artificial intelligence such as machine learning and deep learning, in actual engineering, the varying operating conditions of each bearing due to factors such as variable speed and load lead to diverse characteristic distributions of vibration data, reducing the prediction accuracy of models and limiting the application of deep learning in bearing life prediction.
[0003] To address the problem of the severe degradation of traditional machine learning methods caused by the inconsistent distribution of training and test samples, many scholars have adopted the Domain Adaptation (DA) method. By learning invariant features between the source and target domains across domains, the difference in feature distribution between the source and target domains is reduced, which improves the accuracy to some extent.
[0004] In the field of bearing life prediction, Xu Juan et al. introduced adversarial domain adaptation into bearing remaining service life prediction, improving the accuracy and generalization of rolling bearing remaining service life prediction. However, domain adaptation methods only improve performance for a specified migration target and cannot generalize to any possible target conditions, leading to increased model training costs and poor practicality. Furthermore, the high cost of data acquisition often prevents access to new target domains, severely limiting their application in real-world situations. Summary of the Invention
[0005] To improve the accuracy and generalization of life prediction under varying operating conditions, this invention proposes a method for predicting the remaining life of rolling bearings based on uncertainty-weighted domain generalization, specifically including the following steps:
[0006] S1: Obtain the target domain vibration data sample and the M source domain vibration data sample sets of the rolling bearing;
[0007] S2: Construct a knowledge distillation framework using teacher and student networks to capture the domain-invariant features of the source domain vibration data sample set; and construct a first loss function with the goal of minimizing the difference between the domain-invariant features of each source domain vibration data sample set in the teacher and student networks.
[0008] S3: Use the correlation alignment algorithm to constrain the inter-domain invariant features of each source domain vibration data sample set in the spatial distribution of the student network, and construct a second loss function;
[0009] S4: A third loss function is constructed by using cosine regularization to maximize the difference between the intra-domain invariant features and inter-domain invariant features of the source domain vibration data sample set;
[0010] S5: Construct a fourth loss function with the objective of minimizing the difference between the student network's prediction results for the source domain vibration data samples and the true labels of the source domain vibration data samples;
[0011] S6: Based on the uncertainty of homoscedasticity, the first loss function, the second loss function, the third loss function and the fourth loss function are weighted to construct the loss function of the student network. The student network is trained with the minimum loss function of the student network as the optimization objective to obtain the rolling bearing remaining service life prediction model.
[0012] S7: Use the rolling bearing remaining service life prediction model to predict the vibration data sample set of the target domain and obtain the remaining service life of the rolling bearings in the target domain.
[0013] Preferably, the step of constructing a knowledge distillation framework using teacher and student networks to guide student networks in capturing the domain-invariant features of the source domain vibration data sample set includes:
[0014] S21: Perform a fast Fourier transform on the source domain vibration data samples to obtain the Fourier phase spectrum of the source domain vibration data samples.
[0015] S22: The teacher network is trained using the Fourier phase spectra of the source domain vibration data samples from the M source domain vibration data sample sets.
[0016] S23: Input the source domain vibration data samples into the trained teacher network, and use the features output by the bottleneck layer of the teacher network as the domain-invariant features of the source domain vibration data samples.
[0017] Preferably, training the teacher network using the Fourier phase spectra of the source domain vibration data samples from the M source domain vibration data sample sets includes:
[0018] The loss function of the teacher network is constructed to update the parameters of the teacher network with the optimization objective of minimizing the difference between the prediction results of the teacher network on the source domain vibration data samples and the true labels of the source domain vibration data samples.
[0019]
[0020]
[0021]
[0022] Among them, L T Describes the loss function of the teacher network. This represents the i-th source domain vibration data sample in the k-th source domain vibration data sample set; N represents the sample Fourier phase transform function; N represents Length; express The Fourier phase spectrum; Indicates teacher network The prediction results; express The true label; and F represents the teacher network feature generator. T (·) parameters, teacher network bottleneck layer B T The parameters of (·) and the teacher network predictor P T The parameter of (·); P tr This represents the sample distribution of the vibration data sample set of the k-th source domain; Expressing expectations; This represents the mean squared error loss function.
[0023] Preferably, the first loss function includes:
[0024]
[0025]
[0026] in, Denotes the first loss function. This represents the i-th source domain vibration data sample in the k-th source domain vibration data sample set. Features of the bottleneck layer output by the student network after inputting into the student network; express Domain-invariant characteristics of student networks express In the inter-domain invariant property of student networks, F S (·) and B S (·) represent the feature generator and bottleneck layer of the student network, respectively; express The Fourier phase spectrum; and These represent the parameters of the student network feature generator and the bottleneck layer, respectively. This represents the mean squared error loss function.
[0027] Preferably, the second loss function includes:
[0028]
[0029]
[0030]
[0031] in, Let C represent the second loss function, k∈{1,2,…,M}; M represents the number of vibration data samples in the source domain; k Let represent the covariance matrix of the k-th source domain vibration data sample set; Represents the Frobenius normal form of a matrix, n k This represents the number of source domain vibration data samples in the k-th source domain vibration data sample set, and 1 represents a column vector where all elements are equal to 1.
[0032] Preferably, the third loss function includes:
[0033]
[0034] in, This represents the third loss function; ||·||2 is the Euclid normal form; ∈ is an infinitesimal; max() represents the maximum value function; This represents the intra-domain invariant and inter-domain invariant features of the k-th source domain data.
[0035] Preferably, the fourth loss function includes:
[0036]
[0037] in, P represents the fourth loss function; S (·) represents the predictor of the student network; Indicates sample The true label; Satisfying distribution p tr ; It is the mean squared error loss.
[0038] Preferably, the loss function for constructing the student network includes:
[0039]
[0040] in, The loss function of the student network; f W (x) represents the network output in the first, second, third, and fourth loss functions; These represent the true labels in the first, second, third, and fourth loss functions, respectively; σ iif ,σ mif ,σ cos ,σ pre These represent the learnable uncertain parameters of the first, second, third, and fourth loss functions, respectively.
[0041] The present invention has at least the following beneficial effects
[0042] This invention constructs a knowledge distillation framework using teacher and student networks to capture the intra-domain invariant features of source domain vibration data sample sets. A first loss function is constructed with the objective of minimizing the difference between the intra-domain invariant features of each source domain vibration data sample set in the teacher and student networks, guiding the student network to capture these features. A second loss function is constructed using a correlation alignment algorithm to constrain the spatial distribution of the inter-domain invariant features of each source domain vibration data sample set within the student network, guiding the student network to learn the inter-domain invariant features of the source domain vibration data sample sets. The prediction results of the student network on the source domain vibration data samples are then compared with the prediction results of the source domain vibration data samples. The fourth loss function is constructed with the goal of minimizing the difference in the true labels of the dynamic data samples. The first, second, third, and fourth loss functions are weighted according to the uncertainty of homoscedasticity to construct the loss function of the student network. The student network is trained with the goal of minimizing the loss function of the student network, resulting in a rolling bearing remaining service life prediction model. This model is then generalized to vibration data samples in the target domain under unknown working conditions. The method of this invention can generalize the teacher network from the source domain to multiple unknown target domains, reducing model training costs, enhancing the practicality of the model, and improving the accuracy and generalization of bearing life prediction. Attached Figure Description
[0043] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation
[0044] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.
[0045] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.
[0046] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.
[0047] Please see Figure 1 This invention provides a method for predicting the remaining life of rolling bearings based on uncertainty-weighted domain generalization, comprising:
[0048] S1: Obtain the target domain vibration data sample and the M source domain vibration data sample sets of the rolling bearing;
[0049] Preferably, an implementation method for acquiring target domain vibration data samples and M source domain vibration data sample sets of a rolling bearing includes:
[0050] Vibration data was collected by installing accelerometers with a sampling frequency of 25.6 kHz in the vertical and horizontal directions on different types of rolling bearings. The sampling interval was set to 10 seconds, and each sampling lasted for 0.1 seconds. The collected vibration data was divided into M source domain vibration data sample sets and target domain vibration data samples. For each source domain vibration data sample set, the source domain vibration data samples were pre-labeled with real information based on prior knowledge.
[0051] S2: Construct a knowledge distillation framework using teacher and student networks to capture the domain-invariant features of the source domain vibration data sample set; and construct a first loss function with the goal of minimizing the difference between the domain-invariant features of each source domain vibration data sample set in the teacher and student networks.
[0052] Preferably, the step of constructing a knowledge distillation framework using teacher and student networks to guide student networks in capturing the domain-invariant features of the source domain vibration data sample set includes:
[0053] S21: Perform a fast Fourier transform on the source domain vibration data samples to obtain the Fourier phase spectrum of the source domain vibration data samples.
[0054] S22: The teacher network is trained using the Fourier phase spectra of the source domain vibration data samples from the M source domain vibration data sample sets.
[0055] Preferably, training the teacher network using the Fourier phase spectra of the source domain vibration data samples from the M source domain vibration data sample sets includes:
[0056] The loss function of the teacher network is constructed to update the parameters of the teacher network with the optimization objective of minimizing the difference between the prediction results of the teacher network on the source domain vibration data samples and the true labels of the source domain vibration data samples.
[0057]
[0058]
[0059]
[0060] in, Describes the loss function of the teacher network. This represents the i-th source domain vibration data sample in the k-th source domain vibration data sample set; N represents the sample Fourier phase transform function; N represents Length; express The Fourier phase spectrum; Indicates teacher network The prediction results; express The true label; and F represents the teacher network feature generator. T (·) parameters, teacher network bottleneck layer B T The parameters of (·) and the teacher network predictor P T The parameter of (·); P tr This represents the sample distribution of the vibration data sample set of the k-th source domain; Expressing expectations; This represents the mean squared error loss function.
[0061] S23: Input the source domain vibration data samples into the trained teacher network, and use the features output by the bottleneck layer of the teacher network as the domain-invariant features of the source domain vibration data samples.
[0062] In this embodiment, the teacher network has a similar structure to the student network, including a feature generator, a bottleneck layer, and a predictor. The feature generator adopts a stacked design of 1D and 2D convolutional layers. The input data first passes through the 1D convolutional layer, then is reconstructed through the 2D convolutional layer, and finally concatenated to enhance the distinguishability of data features. This structure is usually used for feature extraction to help the model better understand the features of the data.
[0063] The bottleneck layers of the teacher network and the student network differ slightly. The bottleneck layer of the teacher network consists of one linear layer (512-dimensional), one Tanh activation function, and one linear layer (128-dimensional). The bottleneck layer of the student network consists of one linear layer (512-dimensional), one Tanh activation function, and one linear layer (64-dimensional).
[0064] The predictor consists of a linear (1-dimensional) layer for predicting remaining lifetime.
[0065] Domain-invariant features are properties that remain unchanged within a specific domain, regardless of the presence or absence of other domains. In essence, domain-invariant features are features that are unaffected by other domains for a given specific domain.
[0066] Inter-domain invariant features are those features whose properties remain unchanged across multiple different domains, even if there are differences or changes between the domains. This means that inter-domain invariant features are shared features across different domains, and their properties remain stable across all domains.
[0067] Preferably, the first loss function includes:
[0068]
[0069]
[0070] in, Denotes the first loss function. This represents the i-th source domain vibration data sample in the k-th source domain vibration data sample set. Features of the bottleneck layer output by the student network after inputting into the student network; express Domain-invariant characteristics of student networks express In the inter-domain invariant property of student networks, F S (·) and B S (·) represent the feature generator and bottleneck layer of the student network, respectively; express The Fourier phase spectrum; and These represent the parameters of the student network feature generator and the bottleneck layer, respectively. This represents the mean squared error loss function.
[0071] S3: Use the correlation alignment algorithm to constrain the inter-domain invariant features of each source domain vibration data sample set in the spatial distribution of the student network, and construct a second loss function;
[0072] Preferably, the second loss function includes:
[0073]
[0074]
[0075]
[0076] in, Let C represent the second loss function, k∈{1,2,…,M}; M represents the number of vibration data samples in the source domain; k Let represent the covariance matrix of the k-th source domain vibration data sample set; Represents the Frobenius normal form of a matrix, n k The expression represents the number of source domain vibration data samples in the k-th source domain vibration data sample set, and 1 indicates a column vector where all elements are equal to 1. Since the internal invariant features of a single domain are insufficient to support effective generalization in a network, this invention constructs a cross-domain knowledge learning task. It utilizes CORAL to align second-order statistics across multiple source domains, thereby obtaining inter-domain invariant features for cross-domain learning.
[0077] S4: A third loss function is constructed using cosine regularization to maximize the difference between intra-domain invariant and inter-domain invariant features of the source domain vibration data sample set. During the learning process, distinguishing between inter-domain invariant and intra-domain invariant features can be challenging for the network due to potential overlap and redundancy. Therefore, to ensure that the network learns as many different domain features as possible, the cosine distance loss function is used to measure the difference between inter-domain invariant and intra-domain invariant features.
[0078] Preferably, the third loss function includes:
[0079]
[0080] in, This represents the third loss function; ||·||2 is the Euclid normal form; ∈ is an infinitesimal; max() represents the maximum value function; This represents the intra-domain invariant and inter-domain invariant features of the k-th source domain data.
[0081] S5: Construct a fourth loss function with the objective of minimizing the difference between the student network's prediction results for the source domain vibration data samples and the true labels of the source domain vibration data samples;
[0082] Preferably, the fourth loss function includes:
[0083]
[0084] in, P represents the fourth loss function; S (·) represents the predictor of the student network; Indicates sample The true label; Satisfying distribution p tr ; It is the mean squared error loss.
[0085] S6: Based on the uncertainty of homoscedasticity, the first loss function, the second loss function, the third loss function and the fourth loss function are weighted to construct the loss function of the student network. The student network is trained with the minimum loss function of the student network as the optimization objective to obtain the rolling bearing remaining service life prediction model.
[0086] Preferably, the loss function for constructing the student network includes:
[0087]
[0088] in, The loss function of the student network; f W (x) represents the network output in the first, second, third, and fourth loss functions; These represent the true labels in the first, second, third, and fourth loss functions, respectively; σ iif ,σ mif ,σ cos ,σ pre These represent the learnable uncertain parameters of the first, second, third, and fourth loss functions, respectively. Manually assigning weights to different loss functions and summing them is a common method for constructing network objective functions, but this weighting method can negatively impact model performance. Therefore, in this invention, the uncertainty of homoscedasticity is used to adaptively weight multiple objective loss functions to achieve optimal model performance. The specific implementation is as follows:
[0089] The following probabilistic model is defined for the variance of the evaluation task:
[0090]
[0091] Among them, fW (x) represents the output value of the model with weights W for input x; The input and label differ for different loss functions; refer to the first to fourth loss functions mentioned above for details. σ represents the observed noise parameter. This is a Gaussian function. When estimating the maximum likelihood, it is converted to a log-likelihood function:
[0092]
[0093] in, To optimize the loss function in this task, logσ serves as a regularization term, preventing σ from continuously increasing during model training and making it difficult to reach the convergence boundary. Based on the above weighting criteria, the optimization objective of the entire network is:
[0094]
[0095] Among them, among them, The loss function of the student network; f W (x) represents the network output in the first, second, third, and fourth loss functions; These represent the true labels in the first, second, third, and fourth loss functions, respectively; σ iif ,σ mif ,σ cos ,σ pre These represent the learnable uncertain parameters of the first, second, third, and fourth loss functions, respectively. The specific inputs and labels are as described in the first, second, third, and fourth loss functions.
[0096] S7: Use the rolling bearing remaining service life prediction model to predict the vibration data samples in the target domain and obtain the remaining service life of the rolling bearings in the target domain.
[0097] To verify the predictive effectiveness of the proposed method for the remaining service life of rolling bearings, an accelerated degradation experiment was first conducted on a PRONOSTIA to collect vibration signals. This dataset consists of three main parts: a rotation module, a degradation generation module, and a data acquisition module. Vibration signals from the bearing's run-in phase were collected under different rotational speeds and radial loads to simulate different operating conditions, as shown in Table 1. Two accelerometers with a sampling frequency of 25.6 kHz were installed in both the vertical and horizontal directions on the experimental platform to collect vibration signals. The sampling interval was 10 s, with each sampling lasting 0.1 s, meaning 2560 data points were collected every 10 s as one data sample.
[0098] Table 1 Dataset Description
[0099]
[0100] To further compare and analyze the effectiveness of the method of the present invention, the present invention is compared and analyzed with a convolutional neural network (CNN) trained only on the source domain as a baseline method.
[0101] This invention uses three commonly used metrics for predicting RUL to evaluate the performance of the model: root mean square error (RMSE), mean absolute error (MAE), and score.
[0102]
[0103]
[0104]
[0105]
[0106]
[0107] Among them, Er i For percentage error; RUL i and These are the actual and predicted values of RUL, respectively. Predictions that are closer to the actual value have smaller errors but higher scores.
[0108] The experimental results are shown in Table 2.
[0109] Table 2 Comparison of bearing remaining life prediction indicators for generalized tasks in different fields
[0110]
[0111] As shown in Table 2, the proposed method is significantly superior to the baseline method in the experimental results, with RMSE and MAE values of 0.1252 and 0.1108, respectively. This demonstrates that the rolling bearing remaining life prediction method based on uncertainty weighted domain generalization can better predict the bearing remaining life in unknown target domains, and greatly improves the accuracy and generalization of life prediction.
[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A method for predicting the remaining life of rolling bearings based on uncertainty-weighted domain generalization, characterized in that, Includes the following steps: S1: Obtain the target domain vibration data sample and the M source domain vibration data sample sets of the rolling bearing; S2: Construct a knowledge distillation framework using teacher and student networks to capture the domain-invariant features of the source domain vibration data sample set; and construct a first loss function with the goal of minimizing the difference between the domain-invariant features of each source domain vibration data sample set in the teacher and student networks. The knowledge distillation framework constructed using teacher and student networks, guiding the student network to capture the domain-invariant features of the source domain vibration data sample set, includes: S21: Perform a fast Fourier transform on the source domain vibration data samples to obtain the Fourier phase spectrum of the source domain vibration data samples. S22: The teacher network is trained using the Fourier phase spectra of the source domain vibration data samples from the M source domain vibration data sample sets. S23: Input the source domain vibration data samples into the trained teacher network, and use the features output by the bottleneck layer of the teacher network as the domain-invariant features of the source domain vibration data samples. The training of the teacher network using the Fourier phase spectra of source domain vibration data samples from a set of M source domain vibration data samples includes: The loss function of the teacher network is constructed to update the parameters of the teacher network with the optimization objective of minimizing the difference between the prediction results of the teacher network on the source domain vibration data samples and the true labels of the source domain vibration data samples. in, Describes the loss function of the teacher network. Indicates the first The first source domain vibration data sample set Vibration data samples from the source domain; Represents the sample Fourier phase-value transform function; express Length; express The Fourier phase spectrum; Indicates teacher network The prediction results; express The true label; , and These represent the teacher network feature generator, respectively. Parameters, teacher network bottleneck layer Parameters and teacher network predictor Parameters; Indicates the first Sample distribution of vibration data sample sets in each source domain; Expressing expectations; This represents the mean squared error loss function; S3: Use the correlation alignment algorithm to constrain the inter-domain invariant features of each source domain vibration data sample set in the spatial distribution of the student network, and construct a second loss function; S4: A third loss function is constructed by using cosine regularization to maximize the difference between the intra-domain invariant features and inter-domain invariant features of the source domain vibration data sample set; S5: Construct a fourth loss function with the objective of minimizing the difference between the student network's prediction results for the source domain vibration data samples and the true labels of the source domain vibration data samples; S6: Based on the uncertainty of homoscedasticity, the first loss function, the second loss function, the third loss function and the fourth loss function are weighted to construct the loss function of the student network. The student network is trained with the minimum loss function of the student network as the optimization objective to obtain the rolling bearing remaining service life prediction model. S7: Use the rolling bearing remaining service life prediction model to predict the vibration data samples in the target domain and obtain the remaining service life of the rolling bearings in the target domain.
2. The method for predicting the remaining life of rolling bearings based on uncertainty-weighted domain generalization according to claim 1, characterized in that, The first loss function includes: in, Denotes the first loss function. Indicates the first The first source domain vibration data sample set Vibration data samples from the source region Features of the bottleneck layer output by the student network after inputting into the student network; express Domain-invariant characteristics of student networks express In the inter-domain invariant characteristics of student networks, and These represent the feature generator and bottleneck layer of the student network, respectively. express The Fourier phase spectrum; and These represent the parameters of the student network feature generator and the bottleneck layer, respectively. This represents the mean squared error loss function.
3. The method for predicting the remaining life of rolling bearings based on uncertainty-weighted domain generalization according to claim 2, characterized in that, The second loss function includes: in, This represents the second loss function. ; Indicates the number of source domain vibration data samples; Indicates the first The covariance matrix of a vibration data sample set from each source domain; Representing the Frobenius normal form of a matrix, Indicates the first The number of source domain vibration data samples in the source domain vibration data sample set, where 1 represents a column vector where all elements are equal to 1.
4. The method for predicting the remaining life of rolling bearings based on uncertainty-weighted domain generalization according to claim 3, characterized in that, The third loss function includes: in, Represents the third loss function; It is the Euclid paradigm; It is an infinitesimal quantity; Represents the maximum value function; , Indicates the first Intra-domain invariant features and inter-domain invariant features of source domain data.
5. The method for predicting the remaining life of rolling bearings based on uncertainty-weighted domain generalization according to claim 4, characterized in that, The fourth loss function includes: in, This represents the fourth loss function; A predictor representing a student network; Indicates sample The true label; Satisfy distribution ; It is the mean squared error loss.
6. The method for predicting the remaining life of rolling bearings based on uncertainty-weighted domain generalization according to claim 5, wherein the loss function for constructing the student network includes: in, The loss function representing the student network; This represents the network output in the first, second, third, and fourth loss functions; These represent the true labels in the first, second, third, and fourth loss functions, respectively. These represent the learnable uncertain parameters of the first, second, third, and fourth loss functions, respectively.