Weighted multi-source domain transfer learning method for bearing remaining life prediction

Abstract

The present invention provides a weighted multi-source domain transfer learning method for bearing remaining life prediction, comprising: obtaining vibration signals over the entire bearing life cycle to determine a bearing degradation dataset; dividing the bearing degradation dataset into a source domain and a target domain, and dividing the target domain into a target domain training portion and a target domain test portion, thereby constructing a multi-source domain transfer learning task dataset; training a source prediction model based on the source domain; fine-tuning the source prediction model based on the target domain training portion to obtain a bearing target prediction model; and obtaining a final bearing remaining life prediction, final prediction uncertainty, and root mean square error based on the target domain test portion and the bearing target prediction model. Taking into account the data scarcity of the target domain, the present invention incorporates a calibration term into the loss function to calibrate the prediction uncertainty during model training. This calibration term can be used to identify negative transfer and quantify the contribution of different prediction models to the target domain prediction task, thereby achieving better remaining life prediction.

Description

Technical Field

[0001] The present invention belongs to the technical field of remaining life prediction, and in particular relates to a weighted multi-source domain transfer learning method for bearing remaining life prediction. Background Art

[0002] Remaining life prediction (RLI) is a crucial component of prognostic and health management systems, used to predict the time until equipment failure. Accurate RLI prediction enables decision makers to assess the health of equipment and plan future maintenance activities. Among the numerous RLI prediction methods, deep learning-based approaches have made significant progress in recent years, thanks to their powerful feature extraction capabilities and growing computational power. Numerous deep learning models, including convolutional neural networks and recurrent neural networks, have been used for RLI prediction and achieved good prediction accuracy. However, their success relies on a large amount of labeled training data; otherwise, their performance degrades significantly. However, in many practical situations, obtaining sufficient labeled data to train sufficiently accurate RLI prediction models is impractical. One reason is that labeling degradation data through full lifecycle experiments is expensive and time-consuming. To train robust RLI prediction models in the target domain when data is insufficient, a feasible approach is to collect labeled degradation data from related but different equipment or operating conditions (i.e., the source domain) and use this data to assist in the prediction task in the target domain. For example, accelerated degradation experiments can be conducted on similar equipment in a controlled laboratory environment, which can significantly reduce experimental time and cost. Therefore, more labeled degradation data can be obtained from the source domain than from the target domain, which is especially applicable when there are multiple source domains. These labeled degradation data contain some similar degradation information and share relevant prediction knowledge with the equipment in the target domain. Therefore, it is feasible to use these labeled degradation data from the source domain to further support the prediction of the target domain. However, it should be noted that due to different mechanical structures, signal measurement settings and working conditions, data from different domains have different distributions. To this end, transfer learning has been proposed by researchers, which can transfer knowledge learned from the source domain to the target domain to assist the prediction task of the target domain.

[0003] A large body of research has applied transfer learning techniques to deep learning-based RLS prediction. In real-world scenarios, labeled degradation data can often be collected from multiple different devices under different operating conditions, constituting multiple distinct source domains. These domains not only have different distributions from the target domain data but may also have different distributions from each other. To fully leverage labeled degradation data from multiple source domains with different distributions and extract more knowledge applicable to the target domain, multi-source domain transfer learning methods are needed. While multi-source domain transfer learning has been applied to fault diagnosis, it has rarely been applied to RLS prediction. Furthermore, existing multi-source domain transfer learning methods for RLS prediction do not fully consider the distinct differences between different source and target domains. Different source domains may have different similarities with the target domain, resulting in different contributions to the target domain prediction. Simply averaging the prediction results from all source domains can reduce the accuracy of target domain predictions, especially when the contributions of different source domains to the target domain prediction vary significantly. Conversely, weighted combination of source domain predictions can increase the focus on higher-performing source domain predictions, thereby improving the accuracy of target domain RLS predictions. However, how to measure the contributions of individual source domain predictions and assign weights to them remains a critical issue. Furthermore, if some source domains differ significantly from the target domain, transferring from them may even be detrimental to the target domain prediction task, resulting in negative transfer. Although negative transfer is a common phenomenon, identifying negative transfer remains challenging. In multi-source transfer learning, negative transfer can lead to inaccurate predictions, and existing deep learning-based multi-source transfer learning methods can only produce overconfident point estimates. Therefore, it is urgent and necessary to measure the contribution of each prediction model to the target domain prediction task by its prediction uncertainty on the target domain data. A weighted multi-source transfer learning method for bearing RLS prediction is therefore needed to accurately quantify prediction uncertainty and identify negative transfer in multi-source transfer learning. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the present invention proposes a weighted multi-source domain transfer learning method for bearing remaining life prediction. The method includes obtaining the full life cycle vibration signal of the bearing and determining the bearing degradation dataset; dividing the bearing degradation dataset into a source domain and a target domain, and dividing the target domain into a target domain training part and a target domain test part, to construct a multi-source domain transfer learning task dataset; training a source prediction model based on the source domain; fine-tuning the source prediction model based on the target domain training part to obtain a bearing target prediction model; and obtaining the final remaining life prediction of the bearing, the final prediction uncertainty, and the root mean square error based on the target domain test part and the bearing target prediction model. The bearing remaining life prediction of the present invention takes the full life cycle vibration signal of the bearing as input, and detects the time when the bearing begins to degrade by the root mean square of the vibration signal. The vibration signal is extracted through a convolutional neural network, and the bearing degradation percentage is used as the prediction target. The full life cycle vibration signal of the bearing obtained under various working conditions is divided into multiple different domains, and the proposed method is then applied. Taking into account the data scarcity of the target domain, the present invention adds a calibration term to the loss function to calibrate the prediction uncertainty during the model training process. After calibration, it can be used to identify negative transfer and quantify the contribution of different prediction models to the target domain prediction task, thereby achieving better remaining life prediction.

[0005] The present invention provides a weighted multi-source domain transfer learning method for bearing remaining life prediction, which includes the following steps:

[0006] S1. Obtain the full life cycle vibration signal of the bearing and determine the bearing degradation data set: Use an accelerometer to obtain the full life cycle vibration signal of the bearing, obtain the first prediction time FPT by root mean square, calculate the remaining life label using degradation percentage, and determine the bearing degradation data set;

[0007] S2. Based on the bearing degradation dataset, construct a multi-source domain transfer learning task dataset: divide the bearing degradation dataset into a source domain and a target domain, divide the target domain into a target domain training part and a target domain test part, combine the source domain and target domain training parts as training data, and use the target domain test part as test data. The training data and test data construct a multi-source domain transfer learning task dataset; the input data of the bearing degradation dataset is divided into a first bearing degradation data matrix, a second bearing degradation data matrix, and a third bearing degradation data matrix; the output data of the bearing degradation dataset is divided into a first remaining life label, a second remaining life label, and a third remaining life label;

[0008] S3. Based on the source domain, train the source prediction model: For all source domains, train the corresponding source prediction model, denoted as in, represents the j-th source domain s jThe corresponding source prediction model, j is the first constant and ranges from 1 to N, N represents the number of source domains; the source prediction model includes M integrated members and is expressed as in, represents the j-th source domain s j The corresponding m-th ensemble member, m is a second constant and ranges from 1 to M; the M ensemble members are provided with different initialization parameters, and different batches of samples are randomly sampled from the source domain to update the parameters of the ensemble members; the ensemble members are convolutional neural networks with the same structure;

[0009] For a new input data X, the j-th source domain s j Corresponding source prediction model Remaining life prediction Expression (1) and prediction uncertainty The calculations of expression (2) are:

[0010]

[0011]

[0012] S4. Based on the target domain training part, fine-tune the source prediction model to obtain the bearing target prediction model: for the source prediction model corresponding to all source domains Fine-tune the target domain separately to obtain the bearing target prediction model Among them, F j represents the j-th source domain s j The corresponding bearing target prediction model;

[0013] S5. Based on the target domain test part and the bearing target prediction model, obtain the final remaining life prediction of the bearing, the final prediction uncertainty and the root mean square error;

[0014] S51. For the target domain test part, based on all bearing target prediction models, the j-th source domain s is obtained according to expressions (1) and (2). j The corresponding bearing target prediction model F j Remaining life prediction and prediction uncertainty u j ;

[0015] S52. Considering the differences between different source domains, the final remaining life prediction of the bearing is obtained by weighting and prediction uncertainty u;

[0016] S53, prediction of the final remaining life of the bearing based on the target domain test portion Use root mean square calculation to obtain the root mean square error RMSE:

[0017]

[0018] Among them, n test Indicates the number of bearing samples in the test data; i test is the fifth constant and ranges from 1 to n test ; Indicates the i-th test The label of the bearing sample, that is, the i-th label of the third remaining life label test values.

[0019] Furthermore, step S1 specifically includes the following steps:

[0020] S11. Obtain a vibration signal of the bearing in the horizontal direction by means of an accelerometer, and perform multiple sampling on the vibration signal as a vibration signal of the bearing throughout its life cycle;

[0021] S12, the vibration signal x obtained by sampling the i-th vibration signal of the bearing throughout its life cycle i , calculate x i Root mean square RMS i :

[0022]

[0023] Where n0 represents the vibration signal x obtained by sampling the bearing's full life cycle vibration signal for the i-th time. i The number of vibration signal data points; x i，k represents the vibration signal x obtained by sampling the ith time in the full life cycle of the bearing i The kth vibration signal data point, k is the sixth constant and ranges from 1 to n0;

[0024] S13, calculate the vibration signal x obtained by each sampling i Root mean square RMS i , RMS i The kth one that exceeds the predetermined threshold p The time corresponding to the sampling is taken as the first prediction time FPT, k p is the seventh constant; the predetermined threshold is selected by the 3 sigma rule as:

[0025] Predetermined threshold = μ + 3σ (5)

[0026] Where μ and σ represent the mean and standard deviation of the root mean square value of the bearing in the early normal state, respectively;

[0027] S14, determining bearing degradation data and remaining life label: the bearing degradation data is the vibration signal obtained by each sampling after the first prediction time FPT of the bearing full life cycle vibration signal; based on the first prediction time FPT of the bearing and the total life T of the bearing, the vibration signal x obtained by the i-th sampling in the bearing full life cycle vibration signal i The remaining lifetime label is calculated with the help of degradation percentage as:

[0028]

[0029] S15. Preprocess the bearing degradation data in the bearing degradation data set by short-time Fourier transform, and obtain the vibration signal x obtained by each sampling after the first prediction time FPT. i is converted into the vibration signal feature matrix X i , as the input of the bearing degradation dataset; the remaining life label is the output of the bearing degradation dataset.

[0030] Preferably, the source domains in step S2 are provided with multiple and mutually different ones, which are represented as in, represents the j-th source domain s j Number of bearing samples in ; represents the j-th source domain s j No. i s The input of bearing samples, that is, the i-th in the first bearing degradation data matrix divided s value, i s is the third constant and takes represents the j-th source domain s j No. i s The label of the bearing sample, that is, the i-th of the first remaining life labels divided s The target domain training part is expressed as Among them, n t represents the number of bearing samples in the target domain; Indicates the i t The input of bearing samples, that is, the i-th in the second bearing degradation data matrix t value, i t is the fourth constant and ranges from 1 to n t ; Indicates the i t The label of the bearing sample, that is, the i-th label of the second remaining life t The target domain test part is expressed as in, Indicates the i testThe input of bearing samples, that is, the i-th in the divided third bearing degradation data matrix test values.

[0031] Preferably, step S4 specifically includes the following steps:

[0032] S41. Set the second loss function to minimize the prediction error of bearing samples in all target domain training parts, expressed as

[0033]

[0034] Among them, l f represents the batch size of the batch samples used for fine-tuning, i f is the ninth constant and ranges from 1 to l f ; Indicates that The j-th source domain s j The corresponding bearing target prediction model F j Remaining life prediction;

[0035] S42. Considering the scarcity of data in the target domain, randomly sample data of size n from the target domain. f Fine-tune the batch of samples and set the calibration items for each batch of samples for:

[0036]

[0037] in, It represents the calculated value for The j-th source domain s j The corresponding bearing target prediction model F j uncertainty in forecasts; Indicates that The j-th source domain s j The corresponding bearing target prediction model F j The prediction error of

[0038] S43. Based on the calibration item, update the second loss function to

[0039]

[0040] Here, λ represents a hyperparameter that controls the influence of the calibration term.

[0041] Preferably, step S52 specifically includes the following steps:

[0042] S521. Considering that the quantitative prediction uncertainty is the variance of the prediction results of a set of ensemble members, the precision weight, i.e. the inverse of the variance, is used to quantify the bearing target prediction model F of different source domains. j The contribution of the j-th source domain s j The corresponding bearing target prediction model F j The normalized weight ω of the prediction uncertainty j Calculated as:

[0043]

[0044] S522: Prediction of the final remaining life of the bearing in the target domain test portion Calculated as:

[0045]

[0046] S523. Use the squared error of the prediction to quantify the final prediction uncertainty u:

[0047]

[0048] S524, considering the quantized j-th source domain s j The corresponding bearing target prediction model F j The prediction uncertainty u j is calibrated to the jth source domain s j The corresponding bearing target prediction model F j The prediction error The final prediction uncertainty u is approximately calculated as:

[0049]

[0050] S525. To ensure the non-negativity of the quantified prediction uncertainty, the final prediction uncertainty u is calculated as:

[0051]

[0052] Preferably, step S5 further includes identifying negative transfer in multi-source domain transfer learning, specifically including the following steps:

[0053] S541, based only on the target domain training part, train the source prediction model with M set members in step S3, and obtain the original prediction model and Indicates that, represents the original prediction model of the mth set member;

[0054] S542: Based on the original prediction model, obtain a second remaining life prediction and the second prediction uncertainty u0:

[0055]

[0056]

[0057] in, represents the remaining life prediction of the original prediction model of the mth set member;

[0058] S543、If the mean of the final forecast uncertainty Greater than the mean of the second prediction uncertainty Right now:

[0059]

[0060] It is determined that negative transfer of multi-source domain transfer learning occurs.

[0061] Preferably, in step S3, for the j-th source domain s j , set the first loss function with mean square error Train the jth source domain s j The corresponding source prediction model The mth member of the integration To minimize the mean square error of each batch of samples, the first loss function Expressed as:

[0062]

[0063] Among them, l e Represents the batch size of the batch samples used for training the ensemble members, that is, a batch of samples for one training contains l e bearing samples, i e is the eighth constant and ranges from 1 to l e ; Indicates that The j-th source domain s j Corresponding source prediction model The mth member of the integration Remaining life prediction.

[0064] Preferably, the convolutional neural network in step S3 includes a first convolutional unit, a second convolutional unit, a third unit and a fourth unit, the first convolutional unit and the second convolutional unit both include a 2-dimensional convolutional layer, a batch normalization layer and a first activation function, the third unit includes a 2-dimensional pooling layer and a flattening layer, and the fourth unit includes a first fully connected layer and a second fully connected layer; the number of neurons in the first fully connected layer is 32 and is provided with a first activation function, the number of neurons in the second fully connected layer is 1 and is provided with a second activation function; the output kernel of the 2-dimensional convolutional layer of the first convolutional unit is 8 and the kernel size is (4, 8), the output kernel of the 2-dimensional convolutional layer of the second convolutional unit is 4 and the kernel size is (2, 4); the kernel size of the 2-dimensional pooling layer is (2, 4); the first activation function is the leaky rectifier linear unit LeakyReLU, and the second activation function is the S-shaped function Sigmoid.

[0065] Preferably, the hyperparameter λ controlling the influence of the calibration term in step S43 is initialized to a value and gradually changes to:

[0066] λ=exp(a*e)-b (19)

[0067] Where e represents the number of rounds of current fine-tuning; a and b represent the first and second hyperparameters that control the range of λ, respectively.

[0068] Compared with the prior art, the technical effects of the present invention are:

[0069] 1. The present invention proposes a method for predicting the remaining life of bearings. This method addresses the problem that existing transfer learning or multi-source domain transfer learning methods may lead to overconfidence in their prediction results because they do not consider the quantification and calibration of prediction uncertainty. Taking into account the data scarcity of the target domain, the proposed method adds a calibration term to the loss function, so that the prediction uncertainty can be calibrated during the model training process without the need for an independent calibration set. In addition, the calibrated prediction uncertainty can be used to identify negative transfer in multi-source domain transfer learning.

[0070] 2. The present invention proposes a method for predicting the remaining life of bearings. The method calculates the weight of the prediction model based on the uncertainty of the prediction of the target domain data, and uses the ability of the prediction uncertainty to detect samples outside the distribution to quantify the contribution of different prediction models to the target domain prediction task. This can better predict the remaining life. Even if some source domains differ too much from the target domain, the prediction accuracy of the target domain data can be guaranteed. It can also serve as a new weighted multi-source domain transfer learning approach to solve regression tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Other features, objects and advantages of the present application will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings.

[0072] Figure 1 This is a flow chart of the weighted multi-source domain transfer learning method for bearing remaining life prediction of the present invention;

[0073] Figure 2 is a schematic diagram of the weighted multi-source domain transfer learning method of the present invention;

[0074] Figure 3 This is a comparison curve of the remaining life prediction results of a bearing in the transfer learning task 1 of a specific embodiment of the present invention;

[0075] Figure 4 This is a comparison chart of the relationship between RMV and RMSE curves with and without calibration in transfer learning task 1, a specific embodiment of the present invention. DETAILED DESCRIPTION

[0076] The present application will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the relevant invention and are not intended to limit the invention. It should also be noted that, for ease of description, only portions relevant to the relevant invention are shown in the accompanying drawings.

[0077] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0078] Figure 1 and Figure 2 The present invention demonstrates a weighted multi-source domain transfer learning method for predicting the remaining life of bearings. Bearings, as crucial components in mechanical equipment, not only support rotating bodies but also reduce friction during movement, enabling better rotation of the equipment. The present invention predicts and analyzes the service life of bearings to ensure their proper operation. The present invention's method for predicting the remaining life of bearings specifically includes the following steps:

[0079] S1. Obtain the vibration signal of the bearing throughout its life cycle and determine the bearing degradation dataset: Use an accelerometer to obtain the vibration signal of the bearing throughout its life cycle. Obtain the first prediction time (FPT) by taking the root mean square (RMS) calculation. Calculate the remaining life label using the degradation percentage to determine the bearing degradation dataset.

[0080] S11. Obtain the vibration signal of the bearing in the horizontal direction by means of an accelerometer, and perform multiple sampling on the vibration signal as the full life cycle vibration signal of the bearing.

[0081] Bearings are in a normal state early in their operating life, but only begin to degrade after a period of time. Remaining life prediction is only necessary after degradation begins. Therefore, it is necessary to detect the time at which degradation begins, also known as the first prediction time (FPT). Remaining life prediction begins after the FPT.

[0082] S12, the vibration signal x obtained by sampling the i-th vibration signal of the bearing throughout its life cycle i , calculate x i Root mean square RMS i :

[0083]

[0084] Where n0 represents the vibration signal x obtained by sampling the bearing's full life cycle vibration signal for the i-th time. i The number of vibration signal data points; x i，k represents the vibration signal x obtained by sampling the ith time in the full life cycle of the bearing i The kth vibration signal data point, k is the sixth constant and ranges from 1 to n0; RMS i The value will gradually increase with degradation.

[0085] S13, calculate the vibration signal x obtained by each sampling i Root mean square RMS i , RMS i The kth one that exceeds the predetermined threshold p The time corresponding to the sampling is taken as the first prediction time FPT, k p is the seventh constant; the predetermined threshold is selected by the 3 sigma rule as:

[0086] Predetermined threshold = μ + 3σ (5)

[0087] where μ and σ represent the mean and standard deviation of the root mean square value of the bearing in its early normal state, respectively.

[0088] S14. Determine bearing degradation data and remaining life label: The bearing degradation data is the vibration signal obtained by each sampling after the first prediction time FPT in the full life cycle vibration signal of the bearing. The life of different bearings under different operating conditions varies greatly, which makes it difficult to obtain a good prediction effect using an absolute remaining life value. For each bearing, the present invention is based on the first prediction time FPT and the total life T of the bearing, and the vibration signal x obtained by the i-th sampling in the full life cycle vibration signal of the bearing. i The remaining lifetime label is calculated with the help of degradation percentage as:

[0089]

[0090] In order to help the prediction model better learn the degradation information of vibration signals from the time domain and frequency domain, a classic time-frequency analysis method, short-time Fourier transform (STFT), is used to analyze the vibration signal x obtained by each sampling of the bearing's full life cycle vibration signal. i Perform preprocessing.

[0091] S15. Preprocess the bearing degradation data in the bearing degradation data set by short-time Fourier transform, and obtain the vibration signal x obtained by each sampling after the first prediction time FPT. i is converted into the vibration signal feature matrix X i , as the input of the bearing degradation dataset; the remaining life label is the output of the bearing degradation dataset.

[0092] In a specific embodiment, two available bearing degradation datasets are used, namely a first bearing dataset, referred to as IEEE12, and a second bearing dataset, referred to as XJTU.

[0093] IEEE12 data is collected from a platform. Two accelerometers are mounted horizontally and vertically on the bearings, sampling and recording the horizontal and vertical vibration signals every 10 seconds. According to relevant research, horizontal vibration signals provide more degradation information than vertical vibration signals. In this example, only horizontal vibration signals are used to reduce noise interference.

[0094] 2560 vibration signal data points are collected in each sampling, denoted as x i ∈R 1×2560 , i takes 1, 2, 3, .... IEEE12 collected the full life cycle vibration signals of 17 bearings under three different working conditions. The specific information is shown in Table 1.

[0095]

[0096] Table 1

[0097] XJTU is collected from the accelerated degradation test bench and records the vibration signals in the horizontal and vertical directions. In this embodiment, only the horizontal vibration signal is used. XJTU collects the full life cycle vibration signals of 15 bearings under three different working conditions. Each sampling contains 2560 vibration signal data points, which are expressed as x i ∈R 1×2560 , i takes 1, 2, 3, ..., and the specific information of the three working conditions is shown in Table 2.

[0098]

[0099] Table 2

[0100] After short-time Fourier transform (STFT), the vibration signal x obtained by each sampling in the bearing's full life cycle vibration signal is i is converted into the vibration signal feature matrix X i ∈R 11×257 , the vibration signal feature matrix is ​​the input of the bearing sample.

[0101] x i Root mean square RMS i Calculated as:

[0102]

[0103] The root mean square RMS i The kth one that exceeds the predetermined threshold p The moment corresponding to the sampling is taken as the first prediction time FPT. Assuming that a bearing has 200 samples in its entire life cycle, the first prediction time FPT is the moment corresponding to the 50th sampling. The vibration signal of the last 150 samples is used as the bearing degradation data. The remaining life label corresponding to the 80th sample in the vibration signal of the bearing throughout its life cycle is 1-(80-50) / (200-50)=0.8.

[0104] S2. Based on the bearing degradation dataset, a multi-source domain transfer learning task dataset is constructed: the bearing degradation dataset is divided into the source domain and the target domain, and the target domain is divided into the target domain training part and the target domain test part. The source domain and the target domain training part are combined as training data, and the target domain test part is used as test data. The training data and the test data construct a multi-source domain transfer learning task dataset; the input data of the bearing degradation dataset is divided into the first bearing degradation data matrix, the second bearing degradation data matrix and the third bearing degradation data matrix, and the output data of the bearing degradation dataset is divided into the first remaining life label, the second remaining life label and the third remaining life label.

[0105] The data of the source domain and the target domain follow different distributions. Multi-source domain transfer learning aims to learn from samples in the training part of the source domain and the target domain to predict the labels of samples from the test part of the target domain.

[0106] There are several different source domains, represented by Where N represents the number of source domains; represents the j-th source domain s j The number of bearing samples in , j is the first constant and ranges from 1 to N; represents the j-th source domain s j No. i s The input of bearing samples is the i-th bearing degradation data matrix in the first partition. s value, i s is the third constant and takes represents the j-th source domain s j No. i s The label of the bearing sample, that is, the i-th label of the first remaining life s values.

[0107] The target domain training part is expressed as Among them, n t represents the number of bearing samples in the target domain; Indicates the i t The input of bearing samples is the i-th bearing degradation data matrix in the second bearing degradation data matrix. t value, i t is the fourth constant and ranges from 1 to n t ; Indicates the i t The label of the bearing sample, that is, the i-th label of the second remaining life t values.

[0108] The target domain test part is expressed as Among them, n test Indicates the number of bearing samples in the test data; i test is the fifth constant and ranges from 1 to n test ; Indicates the i test The input of bearing samples is the i-th bearing degradation data matrix in the third bearing degradation data matrix. test values; Indicates the i-th test The label of the bearing sample, that is, the i-th label of the third remaining life test values.

[0109] In one specific example, the degradation phases of bearings B4_4, B5_4, and B6_2 in XJTU were very short, exhibiting distinct degradation processes. This made predictions for other bearings impossible, and they were therefore discarded. Three multi-source transfer learning task datasets were developed based on vibration signal data points from 29 other bearings in IEEE12 and XJTU. Each multi-source transfer learning task dataset consisted of five source domains and one target domain. The bearing numbers corresponding to the training and test datasets are detailed in Table 3.

[0110]

[0111] Table 3

[0112] S3. Based on the source domain, train the source prediction model: for all source domains Train the corresponding source prediction models respectively, denoted as in, represents the j-th source domain s j The corresponding source prediction model. The health status of a bearing is often characterized by the pulses in its vibration signal. A convolutional neural network, which can effectively focus on the local information of the input data, is used to extract degradation information from the vibration signal and use it for remaining life prediction.

[0113] The source prediction model includes M ensemble members and is represented as in, represents the j-th source domain s j The corresponding m-th ensemble member, m is the second constant and ranges from 1 to M; the M ensemble members are set with different initialization parameters, and different batch samples are randomly sampled from the source domain to update the parameters of the ensemble members to ensure the diversity of the ensemble members and quantify the prediction uncertainty.

[0114] The integrated members are convolutional neural networks with the same structure; the convolutional neural network includes a first convolutional unit, a second convolutional unit, a third unit and a fourth unit. The first convolutional unit and the second convolutional unit both include a 2D convolutional layer, a batch normalization layer and a first activation function. The third unit includes a 2D pooling layer and a flattening layer. The fourth unit includes a first fully connected layer and a second fully connected layer. The number of neurons in the first fully connected layer is 32 and is provided with a first activation function. The number of neurons in the second fully connected layer is 1 and is provided with a second activation function. The output kernel of the 2D convolutional layer of the first convolutional unit is 8 and the kernel size is (4, 8). The output kernel of the 2D convolutional layer of the second convolutional unit is 4 and the kernel size is (2, 4). The kernel size of the 2D pooling layer is (2, 4). The first activation function is the leaky rectified linear unit LeakyReLU, and the second activation function is the S-shaped function Sigmoid.

[0115] For the j-th source domain s j , set the first loss function with mean square error Train the jth source domain s j Corresponding source prediction model The mth integrated member To minimize the mean square error of each batch of samples, the first loss function Expressed as:

[0116]

[0117] Among them, l e Indicates the batch size of the batch samples used for ensemble member training, that is, a batch of samples for training contains l e bearing samples, i e is the eighth constant and ranges from 1 to l e ; Indicates that The j-th source domain sj Corresponding source prediction model The mth integrated member Remaining life prediction.

[0118] In a specific embodiment, the hyperparameter settings for source prediction model training are shown in Table 4.

[0119]

[0120] Table 4

[0121] For a new input data X, the j-th source domain s j Corresponding source prediction model Remaining life prediction Expression (1) and prediction uncertainty The calculations of expression (2) are:

[0122]

[0123]

[0124] S4. Based on the target domain training part, fine-tune the source prediction model to obtain the bearing target prediction model: for the source prediction model corresponding to all source domains Fine-tune the target domain separately to obtain the bearing target prediction model Among them, F j represents the j-th source domain s j The corresponding bearing target prediction model.

[0125] S41, after training N source prediction models from N source domains, based on the target domain The N source prediction models are fine-tuned to adapt to the prediction task of the target domain. The second loss function is set to minimize the prediction error of all bearing samples in the target domain, which is expressed as

[0126]

[0127] Among them, l f represents the batch size of samples used for fine-tuning, i f is the ninth constant and ranges from 1 to l f ; Indicates that The j-th source domain s j The corresponding bearing target prediction model F j Remaining life prediction.

[0128] S42. Considering the scarcity of data in the target domain, calibration is required in the fine-tuning stage, and it is not possible to calibrate after fine-tuning based on an independent calibration set. A calibration term is added to the second loss function to ensure that the quantified prediction uncertainty can reflect the prediction error. Randomly sample n from the target domain. f Fine-tune the batch of samples and set the calibration items for each batch of samples for:

[0129]

[0130] in, It represents the calculated value for The j-th source domain s j The corresponding bearing target prediction model F j uncertainty in forecasts; Indicates that The j-th source domain s j The corresponding bearing target prediction model F j The prediction error is quantified by the proposed calibration term, which can accurately approximate the prediction error. This means that the prediction uncertainty is calibrated.

[0131] S43. Based on the calibration item, update the second loss function to

[0132]

[0133] Here, λ represents a hyperparameter that controls the influence of the calibration term.

[0134] In the present invention, the hyperparameter λ that controls the influence of the calibration term is initialized to a small value and gradually changes to:

[0135] λ=exp(a*e)-b (19)

[0136] Where e represents the number of rounds of current fine-tuning; a and b represent the first and second hyperparameters that control the range of λ, respectively.

[0137] In a specific embodiment, the hyperparameter settings for bearing target prediction model training are shown in Table 5.

[0138]

[0139]

[0140] Table 5

[0141] The dynamic λ enables the model to adapt to the target domain as quickly as possible at the beginning of fine-tuning and reduce the prediction error on the target domain. It then makes the quantified prediction uncertainty close to the prediction error, that is, it ensures prediction accuracy while performing calibration.

[0142] S5. Based on the target domain test part and the bearing target prediction model, the final remaining life prediction of the bearing, the final prediction uncertainty and the root mean square error are obtained.

[0143] S51. For the target domain test part, based on all bearing target prediction models, the following equations (1) and (2) are used to obtain the target domain prediction models: The j-th source domain s j The corresponding bearing target prediction model F j Remaining life prediction and forecast uncertainty

[0144] S52. Considering the differences between different source domains, the final remaining life prediction of the bearing is obtained by weighting and forecast uncertainty

[0145] For multi-source domain transfer learning tasks, the greater the difference between the target domain samples and samples from a particular source domain, the greater the prediction uncertainty of the prediction model for the target domain test portion. Therefore, prediction uncertainty can be used to quantify the similarity between the source and target domains, thereby determining the contribution of the source domain to the prediction task of the target domain test portion.

[0146] S521. Considering that the quantitative prediction uncertainty is the variance of the prediction results of a set of ensemble members, the precision weight, i.e. the inverse of the variance, is used to quantify the bearing target prediction model F of different source domains. j The contribution of the j-th source domain s j The corresponding bearing target prediction model F j The normalized weight of the forecast uncertainty Calculated as:

[0147]

[0148] S522, target domain testing part is aimed at Prediction of the ultimate remaining life of bearings Calculated as:

[0149]

[0150] S523, using the squared error of the prediction to quantify the uncertainty of the final prediction (For clarity, the symbols are omitted in the formula ):

[0151]

[0152] S524、Taking into account the quantitative The j-th source domain s j The corresponding bearing target prediction model F j Prediction uncertainty Calibrated for The j-th source domain s j The corresponding bearing target prediction model F j The prediction error approximation, the final prediction uncertainty The approximate calculation is (for clarity, the symbols are omitted in the formula ):

[0153]

[0154] S525, in order to ensure the non-negativity of the quantitative prediction uncertainty, the final prediction uncertainty Calculated as (for clarity, the symbols are omitted in the formula ):

[0155]

[0156] S53, based on the target domain test part for Prediction of the ultimate remaining life of bearings Use root mean square calculation to obtain the root mean square error RMSE:

[0157]

[0158] Among them, n test Indicates the number of bearing samples in the test data; i test is the fifth constant and ranges from 1 to n test ; Indicates the i-th test The label of the bearing sample, that is, the i-th label of the third remaining life test values.

[0159] Based on uncertainty quantification and calibration, we propose to identify negative transfer in multi-source domain transfer learning based on the final prediction uncertainty of the calibration. Negative transfer occurs when the expected prediction error of the target domain test sample obtained by the transferred model is greater than the expected prediction error obtained by the original model without transfer.

[0160] S54. Identifying negative transfer in multi-source domain transfer learning.

[0161] S541, based only on the target domain training part, train the source prediction model with M set members in step S3, and obtain the original prediction model and Indicates that, represents the original prediction model of the mth set member.

[0162] S542, based on the original prediction model, Get a second remaining life expectancy prediction and second forecast uncertainty

[0163]

[0164]

[0165] in, Indicates that The remaining life prediction of the original prediction model for the mth ensemble member.

[0166] S543, using the average value of the second prediction uncertainty to approximate the expectation of the prediction error of the target domain test part, if for all target domain test parts n test Input of bearing samples The mean of the final prediction uncertainty Greater than the mean of the second prediction uncertainty Right now:

[0167]

[0168] It is determined that negative transfer of multi-source domain transfer learning occurs.

[0169] In a specific embodiment, based on three multi-source domain transfer learning task datasets set by the IEEE12 and XJTU datasets, multi-source domain transfer learning tasks including steps S3 to S5 are performed respectively. Table 6 lists the root mean square error RMSE, mean square prediction error MSE (square of the root mean square error RMSE), and the mean of the final prediction uncertainty of the three multi-source domain transfer learning tasks. And the mean of the mean squared prediction error MSE and the final prediction uncertainty The absolute error The results show that through calibration, the quantified final prediction uncertainty is close to the corresponding root mean square error. Taking the remaining life prediction result of bearing B4_2 in transfer learning task 1 as an example, Figure 3 The area between the thin solid lines represents the final prediction uncertainty of each point, and its width is It can be seen that the quantified final prediction uncertainty can reflect the corresponding root mean square error at most points.

[0170]

[0171] Table 6

[0172] The quality of the quantified final prediction uncertainty can be evaluated by the reliability plot. For a well-calibrated final prediction uncertainty, the root mean square variance (RMV) and the root mean square error (RMSE) of each variance interval should be roughly equal, that is, the reliability plot should be close to an identity function with a slope of 1. For comparison, the calibration term proposed in the second loss function for fine-tuning in step S42 is removed as if no calibration was performed. The relationship between the root mean square variance (RMV) and the root mean square error (RMSE) of each variance interval with and without calibration is plotted, as shown in Figure 2. Figure 4 It can be observed that the final prediction uncertainty quantified by the proposed method is more calibrated, verifying the effectiveness of the proposed calibration method.

[0173] To identify negative transfer, an original prediction model is trained based on the target domain training portion. Negative transfer can then be identified based on the calibrated final prediction uncertainty. Specifically, the root mean square error (RMSE) and prediction uncertainty of the bearing target prediction models trained on the five source domains and the original prediction model in Task 2 are shown in Table 7. It can be seen that using only source domain 2 or (and) source domain 3 as the source domain results in a larger RMS error for the transferred bearing target prediction model than the original prediction model without transfer, indicating that negative transfer has occurred. As expected, the corresponding prediction uncertainty is greater than that of the original model. Therefore, it is demonstrated that the calibrated prediction uncertainty can effectively identify negative transfer, which is of great significance in practical applications. Furthermore, when using prediction models trained on all five source domains, the proposed weighted multi-source domain transfer learning method can reduce the negative impact of poor prediction models by assigning small weights to them. Consequently, more accurate prediction results can be obtained than those of the original prediction model.

[0174]

[0175] Table 7

[0176] In order to verify the effectiveness and superiority of the proposed weighted multi-source domain transfer learning method, three baseline methods and two classic multi-source domain transfer learning methods were used for comparison. The first baseline method is to train an original prediction model using only the bearing samples of the target domain training part. The second baseline method is called the averaging method, which averages the prediction results of the source prediction models trained in the five source domains to obtain the final prediction results. Compared with the proposed method, the third baseline method is called calibration-free, that is, the calibration term in the fine-tuning second loss function is removed. The two classic multi-source domain transfer learning methods are the multi-layer feature space adaptation network MFSAN and the cocktail network DCTN. For fairness, the same model structure and hyperparameters for training as the proposed method are used in these five methods. Table 8 summarizes the root mean square error of these methods.

[0177]

[0178] Table 8

[0179] The experimental results show that the original prediction model achieves the highest root mean squared error (RMSE) across all three tasks, demonstrating that learning from the source domain does benefit prediction tasks in the target domain. The averaging method achieves a lower RMS error than the original prediction model, but its RMS error is higher than that of the proposed method, particularly when some source domains differ significantly from the target domain, such as in Task 2. This suggests that it is necessary to weight the prediction results of source prediction models from different source domains rather than simply averaging them. The uncalibrated method performs poorly because the quantified prediction uncertainty is not well calibrated, resulting in inappropriate weighting. This validates the effectiveness of the proposed calibration term in the second loss function used for fine-tuning. The performance of MFSAN and DCTN depends on high-quality data. Specifically, MFSAN requires adapting both the distribution of features extracted from different domain data and the outputs of source prediction models from different source domains. DCTN uses an additional adversarial module to measure the contribution of source prediction models from different source domains to the target domain prediction task, resulting in a more complex model structure and training process. Therefore, the proposed method achieves the best prediction performance by assigning different weights to source prediction models from different source domains based on calibrated prediction uncertainty.

[0180] The weighted multi-source domain transfer learning method for bearing remaining life prediction disclosed in this invention takes the bearing's full life cycle vibration signal as input and detects the time when the bearing begins to degrade using the root mean square (RMS) of the vibration signal. A convolutional neural network is then used to extract features from the vibration signal, using the bearing degradation percentage as the prediction target. The full life cycle vibration signal obtained under various operating conditions is divided into multiple domains, and the proposed method is then applied. Compared to existing transfer learning or multi-source domain transfer learning methods, which fail to consider the quantification and calibration of prediction uncertainty and may potentially adversely affect their prediction results, the present bearing remaining life prediction method takes into account the data scarcity of the target domain and incorporates a calibration term into the loss function, allowing prediction uncertainty to be calibrated during the model training process without the need for a separate calibration set. In addition, the calibrated prediction uncertainty can be used to identify negative transfer in multi-source domain transfer learning. The weight of the prediction model is calculated based on the uncertainty of the prediction of the target domain data. The ability of the prediction uncertainty to detect out-of-distribution samples is used to quantify the contribution of different prediction models to the target domain prediction task, which can better predict the remaining life of bearings. Even if some source domains are too different from the target domain, the prediction accuracy of the target domain data can be significantly improved. It can also serve as a new weighted multi-source domain transfer learning approach to solve regression tasks.

[0181] Finally, it should be noted that the above embodiments are only intended to illustrate rather than limit the technical solutions of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the present invention can still be modified or replaced by equivalents. Any modification or partial replacement that does not depart from the spirit and scope of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A weighted multi-source domain transfer learning method for bearing remaining life prediction, characterized in that: It includes the following steps: S1. Obtain the full life cycle vibration signal of the bearing and determine the bearing degradation data set: Use an accelerometer to obtain the full life cycle vibration signal of the bearing, obtain the first prediction time FPT by root mean square, calculate the remaining life label using degradation percentage, and determine the bearing degradation data set; S2. Based on the bearing degradation dataset, construct a multi-source domain transfer learning task dataset: divide the bearing degradation dataset into a source domain and a target domain, divide the target domain into a target domain training part and a target domain test part, combine the source domain and target domain training parts as training data, and use the target domain test part as test data. The training data and test data construct a multi-source domain transfer learning task dataset; the input data of the bearing degradation dataset is divided into a first bearing degradation data matrix, a second bearing degradation data matrix, and a third bearing degradation data matrix; the output data of the bearing degradation dataset is divided into a first remaining life label, a second remaining life label, and a third remaining life label; The source domains are provided with several different ones, which are expressed as in, represents the j-th source domain s j Number of bearing samples in ; represents the j-th source domain s j No. i s The input of bearing samples, that is, the i-th in the first bearing degradation data matrix divided s value, i s is the third constant and takes represents the j-th source domain s j No. i s The label of the bearing sample, that is, the i-th of the first remaining life labels divided s The target domain training part is expressed as Among them, n t represents the number of bearing samples in the target domain; Indicates the i t The input of bearing samples, that is, the i-th in the second bearing degradation data matrix t value, i t is the fourth constant and ranges from 1 to n t ; Indicates the i t The label of the bearing sample, that is, the i-th label of the second remaining life t The target domain test part is expressed as in, Indicates the i test The input of bearing samples, that is, the i-th in the divided third bearing degradation data matrix test values; S3. Based on the source domain, train the source prediction model: For all source domains, train the corresponding source prediction model, denoted as in, represents the j-th source domain s j The corresponding source prediction model, j is the first constant and ranges from 1 to N, N represents the number of source domains; the source prediction model includes M integrated members and is expressed as in, represents the j-th source domain s j The corresponding m-th ensemble member, m is a second constant and ranges from 1 to M; the M ensemble members are provided with different initialization parameters, and different batches of samples are randomly sampled from the source domain to update the parameters of the ensemble members; the ensemble members are convolutional neural networks with the same structure; For a new input data X, the j-th source domain s j Corresponding source prediction model Remaining life prediction Expression (1) and prediction uncertainty The calculations of expression (2) are: S4. Based on the target domain training part, fine-tune the source prediction model to obtain the bearing target prediction model: for the source prediction model corresponding to all source domains Fine-tune the target domain separately to obtain the bearing target prediction model Among them, F j represents the j-th source domain s j The corresponding bearing target prediction model; S5. Based on the target domain test part and the bearing target prediction model, obtain the final remaining life prediction of the bearing, the final prediction uncertainty and the root mean square error; S51. For the target domain test part, based on all bearing target prediction models, the j-th source domain s is obtained according to expressions (1) and (2). j The corresponding bearing target prediction model F j Remaining life prediction and prediction uncertainty u j ; S52. Considering the differences between different source domains, the final remaining life prediction of the bearing is obtained by weighting and prediction uncertainty u; S53, prediction of the final remaining life of the bearing based on the target domain test portion Use root mean square calculation to obtain the root mean square error RMSE: Among them, n test Indicates the number of bearing samples in the test data; i test is the fifth constant and ranges from 1 to n test ; Indicates the i-th test The label of the bearing sample, that is, the i-th label of the third remaining life label test values.

2. The weighted multi-source domain transfer learning method for bearing remaining life prediction according to claim 1 is characterized in that: Step S1 specifically includes the following steps: S11. Obtain a vibration signal of the bearing in the horizontal direction by means of an accelerometer, and perform multiple sampling on the vibration signal as a vibration signal of the bearing throughout its life cycle; S12, the vibration signal x obtained by sampling the i-th vibration signal of the bearing throughout its life cycle i , calculate x i Root mean square RMS i : Where n0 represents the vibration signal x obtained by sampling the bearing's full life cycle vibration signal for the i-th time. i The number of vibration signal data points; x i,k represents the vibration signal x obtained by sampling the ith time in the full life cycle of the bearing i The kth vibration signal data point, k is the sixth constant and ranges from 1 to n0; S13, calculate the vibration signal x obtained by each sampling i Root mean square RMS i , RMS i The kth one that exceeds the predetermined threshold p The time corresponding to the sampling is taken as the first prediction time FPT, k p is the seventh constant; the predetermined threshold is selected by the 3 sigma rule as: Predetermined threshold = μ + 3σ (5) Where μ and σ represent the mean and standard deviation of the root mean square value of the bearing in the early normal state, respectively; S14, determining bearing degradation data and remaining life label: the bearing degradation data is the vibration signal obtained by each sampling after the first prediction time FPT of the bearing full life cycle vibration signal; based on the first prediction time FPT of the bearing and the total life T of the bearing, the vibration signal x obtained by the i-th sampling in the bearing full life cycle vibration signal i The remaining lifetime label is calculated with the help of degradation percentage as: S15. Preprocess the bearing degradation data in the bearing degradation data set by short-time Fourier transform, and obtain the vibration signal x obtained by each sampling after the first prediction time FPT. i is converted into the vibration signal feature matrix X i , as the input of the bearing degradation dataset; the remaining life label is the output of the bearing degradation dataset.

3. The weighted multi-source domain transfer learning method for bearing remaining life prediction according to claim 1 is characterized in that: The step S4 specifically includes the following steps: S41. Set the second loss function to minimize the prediction error of bearing samples in all target domain training parts, expressed as Among them, l f represents the batch size of the batch samples used for fine-tuning, i f is the ninth constant and ranges from 1 to l f ; Indicates that The j-th source domain s j The corresponding bearing target prediction model F j Remaining life prediction; S42. Considering the scarcity of data in the target domain, randomly sample data of size n from the target domain. f Fine-tune the batch of samples and set the calibration items for each batch of samples for: in, It represents the calculated value for The j-th source domain s j The corresponding bearing target prediction model F j uncertainty in forecasts; Indicates that The j-th source domain s j The corresponding bearing target prediction model F j The prediction error of S43. Based on the calibration item, update the second loss function to Here, λ represents a hyperparameter that controls the influence of the calibration term.

4. The weighted multi-source domain transfer learning method for bearing remaining life prediction according to claim 1, characterized in that: Step S52 specifically includes the following steps: S521. Considering that the quantitative prediction uncertainty is the variance of the prediction results of a set of ensemble members, the precision weight, i.e. the inverse of the variance, is used to quantify the bearing target prediction model F of different source domains. j The contribution of the j-th source domain s j The corresponding bearing target prediction model F j The normalized weight ω of the prediction uncertainty j Calculated as: S522: Prediction of the final remaining life of the bearing in the target domain test portion Calculated as: S523. Use the squared error of the prediction to quantify the final prediction uncertainty u: S524, considering the quantized j-th source domain s j The corresponding bearing target prediction model F j The prediction uncertainty u j is calibrated to the jth source domain s j The corresponding bearing target prediction model F j The prediction error The final prediction uncertainty u is approximately calculated as: S525. To ensure the non-negativity of the quantified prediction uncertainty, the final prediction uncertainty u is calculated as:

5. The weighted multi-source domain transfer learning method for bearing remaining life prediction according to claim 1, characterized in that: Step S5 also includes identifying negative transfer in multi-source domain transfer learning, which specifically includes the following steps: S541, based only on the target domain training part, train the source prediction model with M set members in step S3, and obtain the original prediction model and Indicates that, represents the original prediction model of the mth set member; S542: Based on the original prediction model, obtain a second remaining life prediction and the second prediction uncertainty u0: in, represents the remaining life prediction of the original prediction model of the mth set member; S543、If the mean of the final forecast uncertainty Greater than the mean of the second prediction uncertainty Right now: It is determined that negative transfer of multi-source domain transfer learning occurs.

6. The weighted multi-source domain transfer learning method for bearing remaining life prediction according to claim 1, characterized in that: In step S3, for the j-th source domain s j , set the first loss function with mean square error Train the jth source domain s j The corresponding source prediction model The mth member of the integration To minimize the mean square error of each batch of samples, the first loss function Expressed as: Among them, l e Represents the batch size of the batch samples used for training the ensemble members, that is, a batch of samples for one training contains l e bearing samples, i e is the eighth constant and ranges from 1 to l e ; Indicates that The j-th source domain s j Corresponding source prediction model The mth member of the integration Remaining life prediction.

7. The weighted multi-source domain transfer learning method for bearing remaining life prediction according to claim 1, characterized in that: The convolutional neural network in step S3 includes a first convolution unit, a second convolution unit, a third unit and a fourth unit, wherein the first convolution unit and the second convolution unit both include a 2-dimensional convolution layer, a batch normalization layer and a first activation function, the third unit includes a 2-dimensional pooling layer and a flattening layer, and the fourth unit includes a first fully connected layer and a second fully connected layer; the number of neurons in the first fully connected layer is 32 and is provided with a first activation function, the number of neurons in the second fully connected layer is 1 and is provided with a second activation function; the output kernel of the 2-dimensional convolution layer of the first convolution unit is 8 and the kernel size is (4,8), the output kernel of the 2-dimensional convolution layer of the second convolution unit is 4 and the kernel size is (2,4); the kernel size of the 2-dimensional pooling layer is (2,4); the first activation function is the leaky rectifier linear unit LeakyReLU, and the second activation function is the S-shaped function Sigmoid.

8. The weighted multi-source domain transfer learning method for bearing remaining life prediction according to claim 3, characterized in that: The hyperparameter λ controlling the influence of the calibration term in step S43 is initialized to a value and gradually changes to: λ=exp(a*e)-b (19) Where e represents the number of rounds of current fine-tuning; a and b represent the first and second hyperparameters that control the range of λ, respectively.

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