A remaining useful life prediction method based on dynamic distribution adaptation multi-source domain migration learning

Abstract

The application discloses a kind of based on dynamic distribution self-adapting multi-source domain migration learning's remaining useful life prediction method, comprising the following steps: 1) given existing source domain and target domain degradation data;2) pre-processing is carried out to degradation data;3) the degradation characteristic representation of source domain and target domain degradation data is extracted;4) align the degradation characteristic distribution of each source domain and target domain, obtain the RUL label of multiple degradation characteristic representation of target domain;5) the RUL label obtained by each specific field predictor is fused as the final RUL prediction label, and the RUL label is fused target domain multiple degradation characteristics. Migration learning can utilize the similarity between data, tasks or models, apply the model and knowledge learned in the old field to the new field. The RUL prediction method based on migration learning trains the prediction model using the existing degradation dataset, and applies the learned knowledge to different working condition datasets to realize cross-domain RUL prediction.

Description

Technical Field

[0001] This invention relates to the field of fault handling technology, and in particular to a method for predicting remaining useful life based on dynamic distribution adaptive multi-source domain transfer learning. Background Technology

[0002] With the rapid development of the intelligent industrial era, artificial intelligence technology has been widely applied in the field of fault and predictive management (PHM) for machinery and equipment. This has significantly improved the reliability of machinery and equipment operation while reducing manpower and material resources. As a key technology of PHM, remaining useful life (RUL) prediction utilizes equipment condition monitoring data and failure mechanisms to establish degradation models, analyze equipment degradation trends, and predict equipment failure time, showing broad prospects in manufacturing and aerospace fields. The development of this technology aims to provide early warnings of impending equipment failure, preventing sudden equipment failures from causing huge losses and safety problems, reducing maintenance costs, and improving equipment reliability. However, the accuracy of RUL prediction is easily affected by various factors, such as working conditions, operating environment, and uncertainties in monitoring data. Therefore, RUL prediction for machinery and equipment has always been a challenging task.

[0003] In recent years, many Remaining Useful Life (RUL) prediction methods have been proposed, which can be divided into three categories: model-based methods, data-driven methods, and hybrid methods. Model-based methods predict the RUL of mechanical components by establishing mathematical or physical degradation models based on system failure mechanisms. Data-driven methods use a large amount of historical data to extract degradation characteristics of the equipment, establish a mapping relationship between degradation characteristics and remaining useful life, and fit a degradation curve to predict RUL. Hybrid methods simultaneously utilize historical operating data and failure mechanisms of the equipment, fully combining the advantages of both methods for RUL prediction. Because model-based methods require a large amount of prior knowledge, and establishing corresponding degradation models for complex equipment is very difficult, data-driven methods have always been a research hotspot in RUL prediction. Deep learning, with its powerful feature extraction and accurate regression analysis capabilities, has made significant progress in the field of remaining useful life prediction, but a key problem remains. In most equipment RUL predictions, it is usually assumed that the test set and training set come from the same operating conditions and follow the same distribution; therefore, the model can only produce accurate predictions under the same operating conditions. However, in actual operation, most devices operate under different conditions, and the distribution of sensor-collected data varies, leading to a sharp decline in the accuracy of RUL prediction. Summary of the Invention

[0004] To address the problems existing in the prior art, the purpose of this invention is to provide a method for predicting remaining lifetime based on dynamic distribution adaptive multi-source domain transfer learning.

[0005] To solve the above problems, the present invention adopts the following technical solution.

[0006] A method for predicting remaining lifetime based on dynamically distributed adaptive multi-source domain transfer learning includes the following steps:

[0007] 1) Given existing source and target domain degraded data;

[0008] 2) Preprocess the degraded data;

[0009] 3) Extract degradation feature representations from the source and target domain degraded data;

[0010] 4) Align the degradation feature distributions of each source domain and target domain to obtain multiple degradation feature representations of the target domain;

[0011] 5) The RUL labels obtained by fusing multiple degradation features of the target domain through various domain-specific predictors are used as the final RUL prediction labels.

[0012] As a further improvement of the present invention

[0013] In step 1), the source and target domain degraded data:

[0014] Given existing multi-sensor degradation data {X} s×b As shown in formula (1).

[0015]

[0016] The degradation data is represented in matrix form, where s represents the number of sensors that can monitor the degradation state, and n is the length of the degradation data, which is generally characterized by time periods to represent the lifespan of the device.

[0017] As a further improvement of the present invention

[0018] In step 2), since the magnitude and size of the monitoring data from multiple sensors vary greatly, normalization is required before applying them to the model. The degraded data is preprocessed using the maximum-minimum normalization method, and the calculation formula is shown in (2).

[0019]

[0020] Where max(x) i ) and min(x i ) represents the i-th feature signal x in the data sample x. iThe maximum and minimum values ​​in the data, and the normalized data x' i ∈[0,1]. Then, the sliding time window method was used to convert the degraded data into a time series input. The size of the input time window is T. w The time step is t d The input data can be represented as:

[0021]

[0022] As a further improvement of the present invention, steps 3) to 5) include three modules: a degradation feature extraction module, a dynamic distribution adaptive module, and a regression prediction module.

[0023] Degradation Feature Extraction Module: This module consists of two parts: a common feature extractor and a domain-specific feature extractor. It is used to extract degradation feature representations of degraded data in the source and target domains.

[0024] Common Feature Extractor: This part primarily extracts low-level feature representations from both the source and target domains. It's a shared feature extractor, consisting of four convolutional blocks used to extract low-level feature representations from both the source and target domains. Convolutional Neural Networks (CNNs) are deep learning structures that utilize convolution operations. They allow neural networks to reduce feature space, effectively filter inputs, and prevent overfitting. Furthermore, CNNs can effectively filter noise from time series data through convolution operations, enabling the generation of robust features that do not include outliers. The convolutional layers use two-dimensional convolution operations, and the kernel size can be represented as (kernel_size, 1), ensuring that the convolutional layers only perform convolution operations along the feature dimension, without disrupting temporal dependencies in the time dimension.

[0025] Domain-Specific Feature Extractor: This part is mainly used to extract features unique to a specific domain. The low-level feature representations of each source and target domain obtained from the previous module are then passed through the domain-specific feature extractor to obtain high-level feature representations, which serve as the final degenerate features. The domain-specific feature extractor consists of four layers of GRU units. The low-level feature representations are passed through this part to obtain high-level feature representations of the source and target domains. GRU is a variant of recurrent neural networks that introduces the concepts of reset gate and update gate to modify the calculation method of hidden states in recurrent neural networks. It solves the problem that gradients are prone to decay or explosion in recurrent neural networks and can better capture the large time step distance dependencies in degenerate data as time series.

[0026] Dynamic Distribution Adaptation Module: This module is used to dynamically adjust the impact of marginal and conditional distribution differences, aligning the degradation feature distributions of each source and target domain to obtain multiple degradation feature representations of the target domain. The dynamic distribution adaptation method proposes that marginal and conditional distribution adaptation are not equally important; this method can adaptively adjust the importance of marginal and conditional distributions during the distribution adaptation process based on the actual distribution of the degradation data. Dynamic distribution adaptation uses a balancing factor μ to dynamically adjust the distance between two distributions.

[0027] D(D s D t )≈(1-μ)D(p s (x,p t (x+μD(p s (y|x,p t (y|x(4)

[0028] Where μ∈[0,1], when μ is close to 0, it indicates that there is a large difference between the degraded data in the source domain and the target domain, and the marginal distribution adaptation is more important; when μ is close to 1, it indicates that the datasets in the source domain and the target domain have a high degree of similarity, and the conditional distribution adaptation is more important.

[0029] This invention employs the multi-core maximum mean difference (MK-MMD) method to measure the difference in data edge distribution D(p) between the source and target domains. s (x,p t (x, edge distribution is adaptive by minimizing MK-MMD, and the calculation method of MK-MMD is shown in (5).

[0030]

[0031] Where, x s This indicates that the source domain exhibits a p-distribution-based degradation characteristic, x t The target domain degradation characteristics are represented by a q-distribution. φ(·) is a mapping function that maps the degraded data to a regenerable Hilbert space (RKHS) for measurement. However, due to the difficulty in selecting φ(·), it is not explicitly defined. Instead, a kernel function is introduced to calculate the inner product of φ(·), indirectly calculating the MMD. This invention uses a Gaussian kernel function, and the calculation formula is shown in (6).

[0032]

[0033] Where σ is the width of the kernel function. In MK-MMD, multiple kernel matrices are calculated using various values ​​of σ, and then summed to obtain the final Gaussian kernel matrix.

[0034] For conditional distribution differences D(p) s (y|),p tIn the specific implementation of (y|)), this invention designs a conditional maximum mean difference (CMMD) based on MK-MMD. First, the RUL labels of the degraded data samples are divided into four categories, and the label classification method is shown in (7).

[0035]

[0036] Among them, y cls and y RUL Let Y represent the classification label and RUL label respectively, and Y be the maximum lifespan. This classification method treats the deterioration data samples in the healthy state as one class. The data samples in the deterioration stage are divided into three stages, with the degree of deterioration gradually increasing from front to back. Since the deterioration data in the target domain is unlabeled, during the training process, the model first uses the source domain pre-trained label classifier, and then the target domain data obtains classification pseudo-labels through the classifier. With iterative training, the accuracy of the classifier gradually improves, thereby obtaining accurate classification labels. This invention uses the cross-entropy loss function to calculate the label classification loss of the source domain, as shown in (8).

[0037]

[0038] Where, N s c represents the number of samples in the source domain. i and Let represent the true label and classification label of the i-th source domain sample, respectively. Based on the classification results of the source and target domains, the CMMD calculation method is shown in (9).

[0039]

[0040] Where C = {c|0,1,2,3} represents the category of degraded data samples. and These represent degenerate data samples belonging to category c in the source and target domains, respectively.

[0041] During the training process of the model, the calculation method of the dynamic distribution adaptive factor μ is shown in (10).

[0042]

[0043] Where, d A (X s ,X t d represents a measure of the feature difference between degraded data samples in the source and target domains. It can measure the alignment of the edge distributions of features in the source and target domains during training. A (X s(c) ,X t(c)) represents a measure of the feature difference between degraded data samples belonging to category c in the source and target domains. It can measure the alignment of the conditional distributions of features in the source and target domains during training. ε represents the error of a binary classifier based on support vectors in distinguishing data samples in the source and target domains.

[0044] From equations (5), (9), and (10), the objective function of the dynamically distributed adaptive module can be obtained as:

[0045]

[0046] By minimizing the objective function, the degenerate features of each source and target domain are mapped to the same feature space, reducing the differences in feature distribution, and finally, multiple degenerate feature representations can be obtained.

[0047] Regression prediction module: First, the degradation features of the source and target domains obtained by the dynamic distribution adaptive module are used to obtain the RUL prediction labels of the source and target domains through a specific domain regression predictor. This invention uses the RMSE performance evaluation index as the prediction loss function, as shown in (13).

[0048]

[0049] Finally, the module integrates multiple degradation features of the target domain and the RUL labels obtained by each specific domain predictor as the final RUL prediction labels. The mean fusion method is used to ensure that the decision boundaries of each domain pair are aligned. The same target sample predicted by different regressors should get the same prediction. Therefore, the model needs to minimize the difference between all specific domain regressors. The objective function for aligning the prediction results of each regressor is shown in (14).

[0050]

[0051] Among them, S and N s These represent the number of source domains and the number of samples in each source domain, respectively. and Let m and n represent the prediction results of the i-th data sample of the regressors, respectively.

[0052] Joint Loss Function: The joint loss function of the MDDAN model consists of four parts: regression prediction loss and error. Label classification loss error Dynamically distributed adaptive objective function Objective function aligned with prediction results Therefore, the joint loss function of this model can be expressed as:

[0053]

[0054] Where λ is the trade-off coefficient used for control. and The proportion of the loss. β=2 / (1+e -10×(i+1) / )-1 is a time-varying coefficient that changes with each training iteration, i is the current iteration number, and epochs is the total number of iterations.

[0055] In summary, shallow feature representations are extracted from multi-source domain data and target domain data through a common feature extractor. Then, different source and target domains are processed by domain-specific feature extractors to obtain source domain degradation features and target domain degradation features. The dynamic distribution difference of degradation features is calculated in the dynamic distribution adaptive module. Then, the degradation features are used for regression prediction to obtain prediction results for each source and target domain, and the error is calculated. The average of multiple prediction results for the target domain is taken to obtain the final RUL prediction label. Finally, the model calculates the joint loss error, uses stochastic gradient descent for backpropagation, optimizes the model parameters, aligns the degradation features of each domain pair, and enables the target domain to obtain multiple degradation feature representations, thereby improving the accuracy and generalization ability of the prediction model.

[0056] Beneficial effects of the present invention

[0057] Compared with the prior art, the advantages of this invention are:

[0058] To improve the accuracy of cross-condition RUL prediction, most existing techniques use single-source domain transfer learning methods. However, single-source domain transfer learning extracts only a single cross-domain invariant feature. If the data distributions of the source and target domains differ significantly, there is a risk of negative transfer. This invention uses training datasets from multiple different operating conditions as the source domain, leveraging the diverse distribution advantages of multiple datasets to avoid negative transfer caused by excessive differences in data distribution between a single source and target domain. Simultaneously, it extracts multiple degradation features from the target domain to fully represent the complex degradation data, thereby improving the accuracy of cross-condition RUL prediction. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the process of the present invention.

[0060] Figure 2 This is a diagram of the convolution block structure of the present invention.

[0061] Figure 3 This is a structural diagram of the GRU unit of the present invention.

[0062] Figure 4 This is a flowchart of the MDDAN model operation of the present invention. Detailed Implementation

[0063] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0064] 1. Degraded data in source and target domains

[0065] Given existing multi-sensor degradation data {X} s×n As shown in formula (1).

[0066]

[0067] The degradation data is represented in matrix form, where s represents the number of sensors that can monitor the degradation state, and n is the length of the degradation data, which is generally characterized by time periods to represent the lifespan of the device.

[0068] 2. Data Preprocessing Strategy

[0069] First, since the monitoring data from multiple sensors vary greatly in magnitude and size, normalization is required before applying them to the model. This invention employs a max-min normalization method to preprocess the degraded data, and the calculation formula is shown in (2).

[0070]

[0071] Where max(x) i ) and min(x i ) represents the i-th feature signal x in the data sample x. i The maximum and minimum values ​​in the data, and the normalized data x' i ∈[0,1]. Then, the sliding time window method was used to convert the degraded data into a time series input. The size of the input time window is T. W The time step is t d The input data can be represented as:

[0072]

[0073] 3. Transfer learning prediction model based on multi-source dynamic distribution adaptation

[0074] This invention proposes a dynamic distribution adaptive multi-source domain transfer learning model for RUL prediction, abbreviated as MDDAN. The model mainly consists of three modules: a degradation feature extraction module, a dynamic distribution adaptive module, and a regression prediction module.

[0075] (1) Degradation feature extraction module: This module consists of two parts: a common feature extractor and a domain-specific feature extractor, which are used to extract degradation feature representations of degraded data in the source domain and the target domain.

[0076] a. Common Feature Extractor: This part primarily extracts low-level feature representations from both the source and target domains; it's a shared feature extractor. The common feature extractor consists of four convolutional blocks used to extract low-level feature representations from both the source and target domains. Convolutional Neural Networks (CNNs) are deep learning structures that utilize convolutional operations, allowing neural networks to reduce feature space, effectively filter inputs, and prevent overfitting. Furthermore, CNNs can effectively filter noise from time series data through convolutional operations, enabling the generation of a series of robust features that do not include outliers. It's important to note that, as... Figure 2 As shown, a typical convolutional block consists of a convolutional layer, a batch normalization layer, and a pooling layer. However, the convolutional blocks used by the common feature extractor do not include pooling layers. This is because pooling loses the positional information of time-series data, making it meaningless to use GRU with convolutional blocks that have undergone pooling. The convolutional layers use two-dimensional convolution operations, and the kernel size can be represented as (kernel_size, 1), ensuring that the convolutional layers only perform convolution operations along the feature dimension, without disrupting the temporal dependencies along the time dimension.

[0077] b. Domain-Specific Feature Extractor: This part is mainly used to extract features unique to a specific domain. The low-level feature representations of each source and target domain, obtained from the previous module, are then processed by the domain-specific feature extractor to obtain high-level feature representations, which serve as the final degenerate features. The domain-specific feature extractor consists of two layers of GRU units. The low-level feature representations are processed by this part to obtain high-level feature representations of the source and target domains. GRU is a variant of recurrent neural networks that introduces the concepts of a reset gate and an update gate, modifying the calculation method of hidden states in recurrent neural networks. This solves the problem of gradient decay or explosion in recurrent neural networks and can better capture the large time-step dependencies in degenerate data as time series. Figure 3 As shown, it can control the flow of information through learnable gates.

[0078] (2) Dynamic Distribution Adaptation Module: This module is used to dynamically adjust the effects of marginal distribution differences and conditional distribution differences, aligning the degradation feature distributions of each source and target domain to obtain multiple degradation feature representations of the target domain. The dynamic distribution adaptation method proposes that marginal distribution adaptation and conditional distribution adaptation are not equally important. This method can adaptively adjust the importance of marginal and conditional distributions during the distribution adaptation process based on the actual distribution of the degradation data. More precisely, dynamic distribution adaptation dynamically adjusts the distance between two distributions by using a balancing factor μ:

[0079] D(D s D t )≈(1-μ)D(p s (x,p t (x+μD(p s (y|x,p t (y|x(4)

[0080] Where μ∈[0,1], when μ is close to 0, it indicates that there is a large difference between the degraded data in the source domain and the target domain, and the marginal distribution adaptation is more important; when μ is close to 1, it indicates that the datasets in the source domain and the target domain have a high degree of similarity, and the conditional distribution adaptation is more important.

[0081] This invention employs the multi-core maximum mean difference (MK-MMD) method to measure the difference in data edge distribution D(p) between the source and target domains. s (x,p t (x, edge distribution is adaptive by minimizing MK-MMD, and the calculation method of MK-MMD is shown in (5).

[0082]

[0083] by

[0084] Where, x s This indicates that the source domain exhibits a p-distribution-based degradation characteristic, x t The target domain degradation characteristics are represented by a q-distribution. φ(·) is a mapping function that maps the degraded data to a regenerable Hilbert space (RKHS) for measurement. However, φ(·) is not explicitly defined due to the difficulty in selection. Instead, a kernel function is introduced to calculate the inner product of φ(·), indirectly calculating the MMD. This invention uses the Gaussian kernel function (RBF kernel), and the calculation formula is shown in (6).

[0085]

[0086] Where σ is the width of the kernel function. In MK-MMD, multiple kernel matrices are calculated using various values ​​of σ, and then summed to obtain the final Gaussian kernel matrix.

[0087] For conditional distribution differences D(p) s (y|),p t In the specific implementation of (y|)), this invention designs a conditional maximum mean difference (CMMD) based on MK-MMD. First, the RUL labels of the degraded data samples are divided into four categories, and the label classification method is shown in (7).

[0088]

[0089] Among them, y cls and y RUL Let Y represent the classification label and RUL label, respectively, and Y be the maximum lifespan. This classification method treats the deterioration data samples in the healthy state as one class, and the data samples in the deterioration stage are divided into three stages, with the degree of deterioration gradually increasing from the beginning to the end. Since the deterioration data in the target domain is unlabeled, during the training process, the model first uses the source domain pre-trained label classifier, and then the target domain data obtains classification pseudo-labels through the classifier. With iterative training, the accuracy of the classifier gradually improves, thereby obtaining accurate classification labels. This invention uses the cross-entropy loss function to calculate the label classification loss of the source domain, as shown in (8).

[0090]

[0091] Where, N s c represents the number of samples in the source domain. i and Let represent the true label and classification label of the i-th source domain sample, respectively. Based on the classification results of the source and target domains, the CMMD calculation method is shown in (9).

[0092]

[0093] Where C = {c|0,1,2,3} represents the category of degraded data samples. and These represent degenerate data samples belonging to category c in the source and target domains, respectively.

[0094] During the training process of the model, the calculation method of the dynamic distribution adaptive factor μ is shown in (10).

[0095]

[0096] d A (X s ,X t )=2(1-2ε(X s ,X t ))(11)

[0097] Where, d A (X s ,Xt This represents a measure of the feature differences between degraded data samples in the source and target domains, and can measure the alignment of the edge distributions of features in the source and target domains during training. A (X s(c) ,X t(c) The ) represents a measure of the feature difference between degraded data samples belonging to category c in the source and target domains. It can measure the alignment of the conditional distributions of features in the source and target domains during training. ε represents the error of the support vector-based binary classifier in distinguishing between data samples in the source and target domains.

[0098] From equations (5), (9), and (10), the objective function of the dynamically distributed adaptive module can be obtained as:

[0099]

[0100] By minimizing the objective function, the degenerate features of each source and target domain are mapped to the same feature space, reducing the differences in feature distribution, and finally, multiple degenerate feature representations can be obtained.

[0101] (3) Regression Prediction Module: First, the degradation features of the source and target domains obtained by the dynamic distribution adaptive module are used to obtain the RUL prediction labels of the source and target domains through a specific domain regression predictor. This invention uses the RMSE performance evaluation index as the prediction loss function, as shown in (13).

[0102]

[0103] Finally, this module integrates multiple degradation features of the target domain with RUL labels obtained from each specific domain predictor as the final RUL prediction label. This invention employs a mean fusion method to ensure that the decision boundaries of each domain pair are aligned, and that the same target sample predicted by different regressors should receive the same prediction. Therefore, the model needs to minimize the differences between all specific domain regressors. The objective function for aligning the prediction results of each regressor is shown in (14).

[0104]

[0105] Among them, S and N s These represent the number of source domains and the number of samples in each source domain, respectively. and Let m and n represent the prediction results of the i-th data sample of the regressors, respectively.

[0106] 4. Joint Loss Function

[0107] The joint loss function of the MDDAN model consists of four parts: regression prediction loss error. Label classification loss error Dynamically distributed adaptive objective function Objective function aligned with prediction results Therefore, the joint loss function of this model can be expressed as:

[0108]

[0109] Where λ is the trade-off coefficient used for control. and The proportion of the loss. β=2 / (1+

[0110] e -10×(i+1) / )-1 is a time-varying coefficient that changes with each training iteration, i is the current iteration number, and epochs is the total number of iterations.

[0111] 5. RUL Prediction Process

[0112] The overall operation flow of the MDDAN model proposed in this invention is as follows: Figure 4 As shown, multi-source domain data and target domain data are processed by a common feature extractor to extract shallow feature representations. Then, different source and target domains are processed by domain-specific feature extractors to obtain source domain degradation features and target domain degradation features. A dynamic distribution adaptive module calculates the dynamic distribution differences of the degradation features. Next, the degradation features are used for regression prediction to obtain prediction results for each source and target domain, and the error is calculated. The average of multiple prediction results for the target domain is taken to obtain the final RUL prediction label. Finally, the model calculates the joint loss error, uses stochastic gradient descent for backpropagation, optimizes the model parameters, aligns the degradation features of each domain pair, and provides multiple degradation feature representations for the target domain, improving the accuracy and generalization ability of the prediction model.

[0113] In summary, the above description represents only a preferred embodiment of the present invention; however, the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and its improved concepts, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting remaining lifetime based on dynamically distributed adaptive multi-source domain transfer learning, characterized in that, Includes the following steps: 1) Given existing source and target domain degraded data; 2) Preprocess the degraded data; 3) Extract degradation feature representations from the source and target domain degraded data; 4) Align the degradation feature distributions of each source domain and target domain to obtain multiple degradation feature representations of the target domain; 5) The RUL labels obtained by fusing multiple degradation features of the target domain through various domain-specific predictors are used as the final RUL prediction labels; In step 1), the source domain and target domain degraded data: Given existing multi-sensor degradation data As shown in formula (1), The degradation data is represented in matrix form, where This represents the number of sensors that can monitor degradation. The length of the degradation data, characterized by a time period, represents the lifespan of the device. Steps 3) to 5) include three modules: a degradation feature extraction module, a dynamic distribution adaptive module, and a regression prediction module. Degradation Feature Extraction Module: This module consists of two parts: a common feature extractor and a domain-specific feature extractor. It is used to extract degradation feature representations from degradation data in the source and target domains. Common Feature Extractor: This part extracts low-level feature representations from both the source and target domains. It is a shared feature extractor, consisting of four convolutional blocks used to extract low-level feature representations from both the source and target domains. Domain-Specific Feature Extractor: This part is used to extract unique features specific to a particular domain. The low-level feature representations of each source and target domain, obtained from the previous module, are then processed by the domain-specific feature extractor to obtain high-level feature representations, which serve as the final degenerate features. The domain-specific feature extractor consists of four layers of GRU units. The low-level feature representations are processed by this part to obtain high-level feature representations of the source and target domains. Dynamic distribution adaptation module: This module is used to dynamically adjust the impact of marginal and conditional distribution differences, aligning the degradation feature distributions of each source and target domain to obtain multiple degradation feature representations of the target domain. The dynamic distribution adaptation method proposes that marginal and conditional distribution adaptation are not equally important. This method can adaptively adjust the importance of marginal and conditional distributions during the distribution adaptation process based on the actual distribution of degradation data. Dynamic distribution adaptation employs a balancing factor. To dynamically adjust the distance between two distributions: in, , When the value is close to 0, it indicates that there is a significant difference between the degraded data in the source and target domains, and edge distribution adaptation becomes more important. A value close to 1 indicates a high degree of similarity between the source and target domain datasets, making conditional distribution adaptation more important. The multi-core maximum mean difference (MK-MMD) method is used to measure the difference in the data margin distribution between the source and target domains. The edge distribution is adaptively achieved by minimizing MK-MMD. The calculation method of MK-MMD is shown in (5). in, This indicates that the source domain exhibits a p-distribution-based degradation characteristic. This indicates that the target domain exhibits degradation characteristics following a q-distribution. It is a mapping function that maps degraded data to a regenerable Hilbert space (RKHS) for measurement, but... Due to the difficulty in selection, it will not be explicitly defined, but will instead be calculated using a kernel function. The inner product is used to indirectly calculate MMD. This invention uses the Gaussian kernel function, and the calculation formula is shown in (6). in, To determine the width of the kernel function, in MK-MMD, various kernel matrices are calculated using different σ values, and then summed to obtain the final Gaussian kernel matrix. For conditional distribution differences In a specific implementation, a Conditional Maximum Mean Difference (CMMD) based on MK-MMD was designed. First, the RUL labels of the degraded data samples were divided into four categories, and the label classification method is shown in (7). in, and Let Y represent the classification label and RUL label respectively, and Y be the maximum lifespan. This classification method treats the deterioration data samples of the healthy state as one class. The data samples of the deterioration stage are divided into three stages, with the degree of deterioration gradually increasing from front to back. Since the deterioration data in the target domain is unlabeled, during the training process, the model first uses the source domain pre-trained label classifier, and then the target domain data obtains classification pseudo-labels through the classifier. With iterative training, the accuracy of the classifier gradually improves, thereby obtaining accurate classification labels. This invention uses the cross-entropy loss function to calculate the label classification loss of the source domain, as shown in (8). in, Indicates the number of samples in the source domain. and Let represent the true label and classification label of the i-th source domain sample, respectively. Based on the classification results of the source and target domains, the CMMD calculation method is as shown in (9): in, Indicates the category of degraded data samples. and Let represent the degenerate data samples belonging to category c in the source and target domains, respectively. During the model training process, the dynamically distributed adaptive factor The calculation method is shown in (10). in, A metric representing the feature differences between degraded data samples in the source and target domains; it can measure the alignment of the edge distributions of features in the source and target domains during training. This measure represents the feature difference between degraded data samples belonging to category c in the source and target domains. It can measure the alignment of the conditional distributions of features in the source and target domains during training. This represents the error of a support vector-based binary classifier in distinguishing between data samples from the source and target domains. From equations (5), (9), and (10), we can obtain the objective function of the dynamically distributed adaptive module as follows: By minimizing this objective function, the degenerate features of each source and target domain are mapped to the same feature space, reducing the difference in feature distribution. Finally, the target domain can obtain multiple degenerate feature representations. Regression prediction module: First, the degradation features of the source and target domains obtained by the dynamic distribution adaptive module are used to obtain the RUL prediction labels of the source and target domains through a specific domain regression predictor. This invention uses the RMSE performance evaluation index as the prediction loss function, as shown in (13). Finally, this module integrates multiple degradation features of the target domain with the RUL labels obtained from each specific domain predictor as the final RUL prediction labels. This module uses the mean fusion method to ensure that the decision boundaries of each domain pair are aligned. The same target sample predicted by different regressors should receive the same prediction. Therefore, the model needs to minimize the differences between all specific domain regressors. The objective function for aligning the prediction results of each regressor is shown in (14). Among them, S and These represent the number of source domains and the number of samples in each source domain, respectively. and Let m and n represent the prediction results of the regressors for the i-th data sample, respectively. Joint Loss Function: The joint loss function of the MDDAN model consists of four parts: regression prediction loss and error. Label classification loss error Dynamically distributed adaptive objective function Objective function aligned with prediction results Therefore, the joint loss function of this model can be expressed as: in, These are trade-off coefficients used for control. The proportion of losses, , is a time-varying coefficient that changes with each training iteration, i is the current iteration number, and epochs is the total number of iterations.

2. The remaining lifetime prediction method based on dynamic distribution adaptive multi-source domain transfer learning according to claim 1, characterized in that: In step 2), since the monitoring data from multiple sensors vary greatly in magnitude and size, normalization is required before applying them to the model. The degraded data is preprocessed using the max-min normalization method, and the calculation formula is shown in (2). in, Represents the i-th feature signal in data sample x The maximum and minimum values ​​in the data, after normalization. Subsequently, the sliding time window method was used to transform the degraded data into a time series input, with the input time window size being [missing value]. The time step is The input data can be represented as: 。

Images