Depth joint distribution alignment-based aero-engine residual life prediction transfer learning method
By employing a transfer learning method based on deep joint distribution alignment, and utilizing VAE and distribution alignment modules to align edges and conditional distributions, the problem of insufficient labeled data and inadequate transfer learning in the prediction of remaining life of aero-engines is solved, achieving high-precision unsupervised prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-18
- Publication Date
- 2026-03-24
AI Technical Summary
Existing technologies rely on target domain labeled data that are difficult to obtain in predicting the remaining life of aero-engines. Transfer learning methods are mostly designed for classification tasks and are difficult to apply directly to regression tasks. Furthermore, they fail to effectively align marginal distributions and conditional distributions, resulting in insufficient knowledge transfer.
We employ variational autoencoders (VAEs) to generate latent variables, discretize continuous remaining lifetime labels using reparameterization techniques, align margins and conditional distributions by combining multi-kernel maximum mean difference (MK-MMD) and local maximum mean difference (LMMD), and generate pseudo-labels using an auxiliary stage classifier to achieve unsupervised transfer learning.
It enables cross-domain RUL prediction without requiring real labels in the target domain, improving prediction accuracy and generalization ability. It is suitable for real-world industrial scenarios, and the framework is flexible and scalable.
Smart Images
Figure CN121724099A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of industrial equipment health management technology, specifically relating to a transfer learning method for predicting the remaining life of aero-engines based on deep joint distribution alignment. Background Technology
[0002] As industrial systems evolve towards intelligence and high reliability, Prognostics and Health Management (PHM) is increasingly becoming a core technology for ensuring the safe and stable operation of critical equipment. Remaining Useful Life (RUL) prediction, as an important component of PHM, aims to estimate the remaining time from the current moment to the occurrence of a failure by monitoring and analyzing the equipment's operating status. This provides a basis for decision-making regarding Condition-Based Maintenance (CBM), preventing economic losses and safety accidents caused by sudden failures.
[0003] Traditional RUL prediction methods can be broadly categorized into model-driven and data-driven methods. Model-driven methods establish mathematical models based on physical failure mechanisms, such as the Weibull distribution and degradation trajectory models. While possessing clear physical interpretability, they rely on expert knowledge and face difficulties in modeling complex systems, particularly in multi-failure-mode and nonlinear degradation processes, where their applicability is limited. Data-driven methods, on the other hand, utilize historical monitoring data and automatically learn equipment degradation patterns through machine learning or deep learning models, avoiding complex mechanism modeling and gradually becoming the mainstream research approach. For example, recurrent neural networks (RNNs), long short-term memory networks (LSTMs), and gated recurrent units (GRUs) can effectively capture temporal dependencies; convolutional neural networks (CNNs) and temporal convolutional networks (TCNs) can extract local features; and the Transformer structure captures long-range dependencies through a self-attention mechanism.
[0004] However, data-driven methods heavily rely on large amounts of labeled data for supervised training. In real-world industrial scenarios, target equipment is often in an unknown state or operates in a variable environment, resulting in a lack of authentic RUL labels in the monitoring data. Furthermore, the data distribution varies significantly across different devices and operating conditions. Directly applying a model trained on the source device to the target device leads to a significant performance degradation, known as the domain bias problem.
[0005] To address this problem, transfer learning has been introduced into the field of RUL prediction, aiming to leverage abundant labeled data from the source domain to assist unsupervised or weakly supervised learning in the target domain. Existing methods mainly include: (1) Adversarial training-based methods: such as Domain Adversarial Neural Networks (DANN), which encourage the model to extract domain-invariant features through adversarial learning between the domain discriminator and the feature extractor, but are mostly used for classification tasks and are not well adapted to regression tasks; (2) Methods based on metric learning: such as maximum mean difference (MMD) and its multi-kernel extension (MK-MMD), which achieve distribution alignment by minimizing the distance between the source domain and the target domain in the regenerating kernel Hilbert space, but most works only focus on the alignment of marginal distributions and ignore the influence of conditional distributions; (3) Subdomain adaptation-based methods: such as Deep Subdomain Adaptation Network (DSAN), which introduces Local MMD (LMMD) alignment class conditional distribution, but usually assumes that the label is a discrete category, which is difficult to apply directly to continuous RUL prediction tasks.
[0006] Although the above methods alleviate the domain offset problem to some extent, they still face the following challenges in regression tasks: 1. The continuity of RUL labels makes it difficult to directly measure the conditional distribution; 2. The marginal distribution and conditional distribution are not jointly optimized, resulting in insufficient alignment; 3. The quality of pseudo-labels is unstable, affecting the accuracy of subdomain partitioning.
[0007] Therefore, there is an urgent need for a transfer learning method that can effectively align marginal distributions and conditional distributions and is applicable to continuous label regression tasks, so as to improve the generalization ability of RUL prediction models in unlabeled target domains. To this end, this invention proposes a transfer learning method for predicting the remaining life of aero-engines based on deep joint distribution alignment. Summary of the Invention
[0008] The purpose of this invention is to provide a transfer learning method for predicting the remaining service life of aero-engines based on deep joint distribution alignment, aiming to solve the following problems existing in the prior art for predicting the remaining service life of aero-engines: Traditional supervision methods heavily rely on labeled target domain data, which is difficult to obtain in real-world industrial scenarios; existing transfer learning methods are mostly designed for classification tasks and are difficult to apply directly to regression tasks such as RUL prediction; most domain adaptation methods only focus on a single alignment in marginal or conditional distributions, ignoring the importance of joint distribution alignment, resulting in insufficient knowledge transfer. The continuous and infinite RUL labels pose a significant challenge to subdomain partitioning and conditional distribution measurement.
[0009] The core objective of this invention is to provide an unsupervised transfer learning framework that does not require real labels in the target domain and can effectively align edge distributions and conditional distributions simultaneously, so as to achieve accurate remaining life prediction across different operating conditions or engines.
[0010] The specific technical solution adopted by this invention is as follows: Step 1: Use a variational autoencoder (VAE) to encode the input data in the source and target domains to generate latent variables. The input data is in the following format:
[0011] in, Refers to the first Time step, is a positive integer, representing the time resolution coefficient. The smaller the value, the higher the time resolution; in this invention ; The length of the time window. This refers to the length of the equipment's entire lifecycle; The output data format is , referring to the The remaining lifespan of the device at the time step; Step 2: Sample from the Gaussian distribution using reparameterization techniques to generate latent variables; Step 3: Introduce an auxiliary stage classifier to discretize the continuous remaining lifetime labels into equipment operation stages, generating source domain stage labels and target domain pseudo stage labels; Step 4: Align the edge distributions of the source and target domains using multi-kernel maximum mean difference; Step 5: Align the conditional distributions of the source and target domains using local maximum mean differences; Step 6: Jointly optimize the parameters of the encoder, decoder, stage classifier, and reparameterized network using the total loss function; Step 7: During network training, a warm-up strategy is adopted. In the early stage, only the basic VAE structure is trained: VAE reconstruction loss, KL divergence loss, and stage classification loss. In the later stage, distribution alignment loss is introduced: MK-MMD loss and LMMD loss.
[0012] The technical effects achieved by this invention are as follows: This invention achieves true unsupervised cross-domain RUL prediction: knowledge transfer can be achieved solely based on source domain labels without requiring any real labels from the target domain, greatly improving the applicability of the method in real industrial scenarios.
[0013] This invention solves the distribution alignment problem in regression tasks: by introducing an auxiliary stage classifier to discretize continuous labels, the regression problem is cleverly transformed into a class-conditional distribution alignment problem with pseudo-labels, providing a new approach to domain adaptation in regression tasks.
[0014] This invention improves transfer performance by combining distribution alignment: it considers the alignment of marginal and conditional distributions simultaneously, which can more comprehensively reduce inter-domain differences than methods that only align a single distribution, making the learned feature representation more domain-invariant, thereby significantly improving prediction accuracy and generalization ability.
[0015] The framework of this invention is flexible and robust: the VAE encoder can be replaced with various sequence models (LSTM, GRU, TCN), and the modular design makes the method highly scalable and adaptable. Extensive ablation experiments and visualization analyses demonstrate the effectiveness and necessity of each module.
[0016] Superior Empirical Performance: Extensive experiments on the internationally recognized C-MAPSS dataset demonstrate that this invention significantly outperforms existing mainstream transfer learning methods in multiple evaluation metrics such as MAE, RMSE, and Score, validating its effectiveness and advancement. Attached Figure Description
[0017] Figure 1 This is a diagram of the architecture of a regression prediction model based on VAE; Figure 2 This is a schematic diagram illustrating the conversion of continuous remaining lifetime tags into stage tags in this invention; Figure 3 This is a diagram of the main structure of the present invention; Figure 4 This is a comparison chart of the transfer prediction performance of this invention on six target domain example engines on the C-MAPSS dataset and training only on the source domain. Figure 5 This is a t-SNE visualization result of the target domain and source domain features on the C-MAPSS dataset according to the present invention. Detailed Implementation
[0018] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.
[0019] like Figures 1-5 As shown, a transfer learning method for predicting the remaining life of aero-engines based on deep joint distribution alignment includes the following steps: Step 1: Use a variational autoencoder (VAE) to encode the input data in the source and target domains to generate latent variables. The input data is in the following format:
[0020] in, Refers to the first Time step, is a positive integer, representing the time resolution coefficient. The smaller the value, the higher the time resolution; in this invention ; The length of the time window. This refers to the length of the equipment's entire lifecycle; The output data format is , referring to the The remaining lifespan of the device at the time step; In step 1, the datasets for the source domain and the target domain are constructed as follows:
[0021] in, , refer to Source domain input and output data at each time step refer to The target domain input data at any given time is unlabeled, meaning there is no actual remaining predicted lifespan of the device to refer to. and These refer to the number of samples in the source domain and the target domain, respectively. The VAE model was derived using standard variational inference (VI), and the KL divergence loss and reconstruction loss (MSE loss) of the model were obtained.
[0022] in A label representing the actual remaining lifespan. This refers to the weight hyperparameters of the KL divergence loss. The predicted remaining lifetime generated by the VAE model. Represents the total number of samples in the dataset; It is to estimate the prior distribution. For encoder parameters, For the prior distribution of the latent variables, This refers to the calculation of KL divergence. To estimate the mean of the prior distribution, To estimate the standard deviation of the prior distribution.
[0023] Step 2: Sample from the Gaussian distribution using reparameterization techniques to generate latent variables; In step 2, in order to calculate the gradient during model training, a reparameterization technique is used to sample the Gaussian distribution.
[0024] in Indicates a standard Gaussian distribution; It represents the Hadamardi (or Hadama) stack; In the above formula and In fact, it is calculated using two separate fully connected networks (FCNs) based on their network parameters, and the parameters are automatically updated using a loss function.
[0025] Step 3: Introduce an Auxiliary Stage Classifier (ASC) to discretize the continuous remaining lifetime labels into equipment operation stages, generating source domain stage labels and target domain pseudo-stage labels; for example... Figure 2 As shown, In step 3, the stage label is calculated as follows:
[0026] in, Refers to the first Stage label of each sample, This represents the floor function. This refers to the maximum remaining lifespan of the equipment. This indicates the total number of equipment stages in the division; The above formula can be used to discretize the continuous remaining lifetime labels into equipment stage labels. The auxiliary stage classifier is actually composed of a two-layer fully connected network and is trained using the cross-entropy loss function.
[0027] Step 4: Align the edge distributions of the source and target domains using multi-kernel maximum mean difference (MK-MMD); In step 4, multi-kernel maximum mean difference (MK-MMD) is used to align the edge distributions of the source and target domains.
[0028] in, and This represents the latent space features of the source and target domains after encoding by the encoder. This indicates that kernel functions are calculated for latent space features. , This represents the inner product operation. This represents mapping variables from the input space to the regenerated Hilbert space. The feature mapping function; therefore, It can be used as a metric for the marginal distance between two distributions. This refers to the MK-MMD loss function; the kernel function here... It is multi-core, that is:
[0029] in This refers to the weight of each core; the multi-core function is composed of... It is composed of Gaussian kernels.
[0030] Step 5: Align the conditional distributions of the source and target domains using Local Maximum Mean Difference (LMMD);
[0031] in and It refers to the first The dynamic weights of the source and target domains during the class phase are calculated using the following formula:
[0032] in, Refers to the first The one-hot encoding of the stage label of the source domain sample is the first One element; It refers to the first The one-hot encoding of the pseudo-stage label of the target domain sample. One element; It can be used as a measure of conditional distribution distance between two distributions. This is the MK-MMD loss function.
[0033] Step 6: Jointly optimize the parameters of the encoder, decoder, stage classifier, and reparameterized network using the total loss function; In step 6, the encoder uses sequence models such as Long Short-Term Memory Network (LSTM), Gated Unit (GRU), and Temporal Convolutional Network (TCN) to encode the input data; The total loss function includes: VAE reconstruction loss, KL divergence loss, MK-MMD loss, LMMD loss, and stage classification loss.
[0034] Step 7: During network training, a warm-up strategy is adopted. In the early stage, only the basic VAE structure is trained: VAE reconstruction loss, KL divergence loss, and stage classification loss. In the later stage, distribution alignment loss is introduced: MK-MMD loss and LMMD loss.
[0035] This invention proposes a transfer learning network based on deep joint distribution alignment. The network uses a variational autoencoder (VAE) as its basic architecture and introduces a distribution alignment metric module (MK-MMD, LMMD) and an auxiliary stage classifier (ASC) to collaboratively optimize the alignment of marginal and conditional distributions. The overall technical solution is as follows: Figure 3 As shown, it mainly includes the following components. Data preprocessing and input module The raw sensor time-series data from the source and target domains are preprocessed, including: removing constant sensor variables, performing data denoising using exponential smoothing, and scaling the data to the [0,1] interval using Min-Max normalization. The processed data is then cut into fixed-length time-series sample blocks, which serve as the input to the network.
[0036] Variational Autoencoder (VAE) Feature Extraction and Reconstruction Module Encoder: Employs a sequence model (such as LSTM, GRU, TCN) as the encoder, mapping high-dimensional input data to a low-dimensional latent space and outputting the mean of the latent variables. and variance .
[0037] Reparameterization: Employing reparameterization techniques to transform Gaussian distributions... Mid-sampling to obtain latent variables This solves the problem of non-differentiability in the sampling process and enables backpropagation of the gradient.
[0038] Decoder: Employs a multilayer perceptron (MLP) as the decoder to process the sampled latent variables. Mapping and reconstructing to remaining lifetime predictions .
[0039] Auxiliary Stage Classifier To address the continuity issue of RUL tags, this invention designs an auxiliary stage classifier. This classifier is a fully connected network (FCN), and its function is: Based on the true RUL value of the source domain and the pseudo RUL value predicted by the target domain, the RUL value is discretized into several device health stages according to preset rules (piecewise linear function), such as "early", "mid", and "late", and stage labels are generated using one-hot encoding.
[0040] By minimizing the cross-entropy loss predicted in the source domain stage, we learn feature representations that can distinguish different degradation stages and provide reliable pseudo-labels for conditional distribution alignment.
[0041] Joint distribution alignment module The core innovation of this invention lies in simultaneously aligning edge distributions and conditional distributions to approximately achieve joint distribution alignment.
[0042] Marginal Distribution Alignment: This method uses Multi-Kernel Maximum Mean Difference (MK-MMD) to measure and minimize the overall distribution distance between the latent variables z in the source and target domains. MK-MMD combines multiple Gaussian kernel functions to more flexibly and accurately measure the difference between two distributions.
[0043] Conditional Distribution Alignment (LDA): This method uses Local Maximum Mean Difference (LMMD) to measure and minimize the feature distribution distance between two domains at the same device stage. LMMD uses the source domain's true stage label and the target domain's pseudo stage label provided by the auxiliary stage classifier as weights to calculate a weighted distribution distance, thereby achieving class-conditional alignment.
[0044] Joint optimization and training strategy The overall loss function of the model consists of five parts:
[0045] in: Mean squared error loss measures the difference between the predicted and actual RUL values in the source domain and dominates the VAE reconstruction process.
[0046] KL divergence loss constrains the approximate posterior distribution to approximate the standard prior distribution, ensuring the regularity of the latent space.
[0047] Cross-entropy loss for stage classification, used to optimize the auxiliary classifier.
[0048] MK-MMD loss is used for aligning the edge distributions of the source and target domains.
[0049] LMMD loss is used for aligning the conditional distributions of the source and target domains.
[0050] , , , These are the weight hyperparameters for each loss term.
[0051] Training employs a warm-up strategy: during the initial training phase, the distribution alignment loss is not activated. and Only optimize the VAE reconstruction loss. KL divergence loss and stage classification loss This allows the model to initially learn basic feature representations and pseudo-label generation capabilities. In subsequent stages, distribution alignment loss is introduced for joint optimization to gradually narrow the distribution between the source and target domains.
[0052] In actual operation, the present invention is illustrated in the following embodiments: S1. Data Preparation and Preprocessing Data source: The C-MAPSS dataset provided by NASA Ames Research Center is used, comprising four subsets (FD001, FD002, FD003, FD004). Each subset contains operational cycle data for multiple engines, including three operating parameters and 21 sensor measurements. See Table 1 for details.
[0053] Data cleaning: Remove 6 constant sensors (sensor numbers: 1, 5, 6, 10, 16, 18, 19), and retain 14 valid sensor variables.
[0054] Data smoothing: Exponential smoothing (ES) is used to denoise the sensor data, preserving trend information and reducing high-frequency noise.
[0055] Data normalization: Min-Max normalization is used to scale all input data to the [0,1] interval to accelerate model convergence and improve stability.
[0056] Tag Discretization: According to formula (5), the continuous remaining life tags are discretized into equipment operation stage tags (unique hot coding), with a total number of stages. Set to 20. Set it to 125.
[0057] S2, Network Architecture Setup The network architecture of this invention consists of the following modules: Encoder: Employs one of LSTM, GRU, or TCN as the encoder, with an input dimension of 14 (number of sensors), a hidden layer dimension of 256, and outputs hidden features. and .
[0058] The reparameterization module (Representation module) consists of two fully connected layers (FCNs), which predict the mean of the latent variables. Sum of logarithmic variance .
[0059] Decoder: Consists of a three-layer fully connected network (FCN) that processes the sampled latent variables. and Mapped to remaining lifetime prediction and .
[0060] Auxiliary Stage Classifier (ASC): Consists of two fully connected layers, with hidden features as input. and The output is the one-hot encoding of the stage label.
[0061] Distribution alignment modules: MK-MMD module – used for edge distribution alignment, using 5 Gaussian kernel functions; LMMD module – used for conditional distribution alignment, relying on stage labels provided by ASC.
[0062] S3, Training Process The training process uses a warm-up strategy, and the specific steps are as follows: initialization: Initialize encoder decoder Auxiliary stage classifier Mean predictor Log-variance predictor The parameters. Setting hyperparameters: learning rate. Batch size The Warm-up rounds are 10, and the total training rounds are 200. Loss weights are set as follows: , , , .
[0063] Forward propagation: 1. Input source domain data and target domain data .
[0064] 2. Encoder extracts hidden features
[0065] 3. Auxiliary stage classifier predicts stage labels
[0066] 4. Latent variables for reparameterization
[0067] 5. Decoder predicts source domain lifetime prediction
[0068] Loss Calculation: MSE loss KL divergence loss Stage-based classification loss MK-MMD loss LMMD loss ; Total loss
[0069] Backpropagation and parameter update: If the total loss is less than or equal to the current round number and the number of Warm-up rounds, then let... , ; Otherwise, update all parameters using the Adam optimizer:
[0070] in, , , , These are the parameters for the auxiliary stage classifier, decoder, encoder, and reparameterization module, respectively.
[0071] S4, Prediction Phase The trained model is used to perform forward propagation on the target domain data to obtain the predicted remaining lifetime value of the target domain data. .
[0072] S5, Evaluation Indicators Use the following three metrics to evaluate model performance: MAE (Mean Absolute Error)
[0073] RMSE (Root Mean Square Error)
[0074] Score (a weighted scoring function that imposes a greater penalty for overestimating RUL)
[0075] in, This represents the actual remaining lifespan. This represents the predicted remaining lifespan. This indicates the total number of test samples.
[0076] As shown in Table 2
[0077] This invention uses the target domain test dataset and performs complete performance tests on 12 transfer tasks using three different encoders (LSTM, GRU, TCN). The experiments demonstrate the high robustness of the framework of this invention.
[0078] like Figure 4 As shown, this invention uses the target domain test dataset and compares the transfer prediction performance on six target domain example engines on the C-MAPSS dataset with the prediction performance of engines trained only in the source domain. Figure 4 (a) shows the result of migrating from source domain FD001 to engine number 99 in target domain FD002. Figure 4 (b) shows the result of migrating from source domain FD002 to target domain FD003 using engine number 9. Figure 4 (c) shows the result of migrating from source domain FD002 to target domain FD004 using engine number 12. Figure 4 (d) shows the result of migrating from source domain FD003 to target domain FD002 using engine number 24. Figure 4 (e) shows the result of migrating from source domain FD001 to target domain FD004 using engine number 25. Figure 4 (f) shows the result of migrating from source domain FD001 to target domain FD004 using engine number 24. Compared to training only from the source domain to the target domain, the remaining lifetime prediction curve of this invention is closer to the actual lifetime curve of the device. Experiments demonstrate that this invention achieves better migration results even when the target domain is unlabeled.
[0079] S6. Visualization and Analysis like Figure 5 The image shows the visualization results of t-SNE feature dimensionality reduction on the C-MAPSS dataset, based on this invention. The source domain is the FD001 subset, and the target domain is the FD003 subset. Figure 5 (a) Figure 5 (d) Represents the t-SNE visualization results of the source and target domain features classified by data source and actual remaining lifetime value before training; Figure 5 (b) Figure 5 (e) Represents the t-SNE visualization results of source domain and target domain features trained only in the source domain, classified by data source and actual remaining lifetime value, respectively; Figure 5 (c) Figure 5 (f) shows the t-SNE visualization results of the source and target domain features classified by data source and actual remaining lifetime value, respectively. The t-SNE visualization results show that after the training process of this invention, the source and target domain features are well aligned, achieving good transfer learning results.
[0080] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.
Claims
1. A transfer learning method for predicting the remaining life of aero-engines based on deep joint distribution alignment, characterized in that: Includes the following steps: Step 1: Use a variational autoencoder to encode the input data in the source and target domains to generate latent variables. The input data is in the following format: ； in, Refers to the first Time step, is a positive integer, representing the time resolution coefficient. The smaller the value, the higher the time resolution; in this invention ; The length of the time window. This refers to the length of the equipment's entire lifecycle; The output data format is , referring to the The remaining lifespan of the device at the time step; Step 2: Sample from the Gaussian distribution using reparameterization techniques to generate latent variables; Step 3: Introduce an auxiliary stage classifier to discretize the continuous remaining lifetime labels into equipment operation stages, generating source domain stage labels and target domain pseudo stage labels; Step 4: Align the edge distributions of the source and target domains using multi-kernel maximum mean difference; Step 5: Align the conditional distributions of the source and target domains using local maximum mean differences; Step 6: Jointly optimize the parameters of the encoder, decoder, stage classifier, and reparameterized network using the total loss function; Step 7: During network training, a warm-up strategy is adopted. In the early stage, only the basic VAE structure is trained: VAE reconstruction loss, KL divergence loss, and stage classification loss. In the later stage, distribution alignment loss is introduced: MK-MMD loss and LMMD loss.
2. The transfer learning method for predicting the remaining life of aero-engines based on deep joint distribution alignment as described in claim 1, characterized in that: In step 1, the datasets for the source domain and the target domain are constructed as follows: ； in, , refer to Source domain input and output data at each time step refer to The target domain input data at any given time is unlabeled, meaning there is no actual remaining predicted lifespan of the device to refer to. and These refer to the number of samples in the source domain and the target domain, respectively. The VAE model was derived using standard variational inference (VI), and the KL divergence loss and reconstruction loss (MSE loss) of the model were obtained. ； in A label representing the actual remaining lifespan. This refers to the weight hyperparameters of the KL divergence loss. The predicted remaining lifetime generated by the VAE model. Represents the total number of samples in the dataset; It is to estimate the prior distribution. For encoder parameters, For the prior distribution of the latent variables, This refers to the calculation of KL divergence. To estimate the mean of the prior distribution, To estimate the standard deviation of the prior distribution.
3. The transfer learning method for predicting the remaining life of aero-engines based on deep joint distribution alignment according to claim 2, characterized in that: In step 2, the Gaussian distribution is sampled using a reparameterization technique. ； in Indicates a standard Gaussian distribution; It represents the Hadamardi (or Hadama) stack; In the above formula and In fact, it is calculated using two separate fully connected networks (FCNs) based on their network parameters, and the parameters are automatically updated using a loss function.
4. The transfer learning method for predicting the remaining life of aero-engines based on deep joint distribution alignment according to claim 3, characterized in that: In step 3, the stage label is calculated as follows: ； in, Refers to the first Stage label of each sample, This represents the floor function. This refers to the maximum remaining lifespan of the equipment. This indicates the total number of equipment stages in the division; The above formula can be used to discretize the continuous remaining lifetime labels into equipment stage labels. The auxiliary stage classifier is actually composed of a two-layer fully connected network and is trained using the cross-entropy loss function.
5. The transfer learning method for predicting the remaining life of aero-engines based on deep joint distribution alignment according to claim 4, characterized in that: In step 4, the edge distributions of the source and target domains are aligned using the multi-kernel maximum mean difference. ； in, and This represents the latent space features of the source and target domains after encoding by the encoder. This indicates that kernel functions are calculated for latent space features. , This represents the inner product operation. This represents mapping variables from the input space to the regenerated Hilbert space. The feature mapping function; therefore, It can be used as a metric for the marginal distance between two distributions. This refers to the MK-MMD loss function; the kernel function here... It is multi-core, that is: ； in This refers to the weight of each core; the multi-core function is composed of... It is composed of Gaussian kernels.
6. The transfer learning method for predicting the remaining life of aero-engines based on deep joint distribution alignment according to claim 5, characterized in that: In step 5, the conditional distributions of the source and target domains are aligned using the local maximum mean difference. ； in and It refers to the first The dynamic weights of the source and target domains during the class phase are calculated using the following formula: ； in, Refers to the first The one-hot encoding of the stage label of the source domain sample is the first One element; It refers to the first The one-hot encoding of the pseudo-stage label of the target domain sample. One element; It can be used as a measure of conditional distribution distance between two distributions. This is the MK-MMD loss function.
7. The transfer learning method for predicting the remaining life of aero-engines based on deep joint distribution alignment according to claim 6, characterized in that: In step 6, the encoder uses a sequence model: a long short-term memory network, a gating unit, and a temporal convolutional network to encode the input data. The total loss function includes: VAE reconstruction loss, KL divergence loss, MK-MMD loss, LMMD loss, and stage classification loss.