A cross-domain prediction method for the remaining service life of aero-engines based on graph structure

Abstract

This invention proposes a cross-domain prediction method for the remaining service life (RUL) of aero-engines based on graph structures. The method includes: preprocessing aero-engine sensor subsets in the source and target domains; calculating the correlation between the selected sensor data; constructing an aero-engine graph dataset; designing a domain feature extraction module based on a time-series graph attention model to extract the temporal and spatial topological dependencies of the aero-engine; performing attention-based information aggregation on different sensors in each gated recurrent unit; extracting sensor topological information at each moment during the capture of the entire time-series data; designing a domain feature separation module to separate domain-invariant information from domain-specific information; and using MK-MMD as a metric for domain adaptation to improve transfer performance; finally, updating parameters through backpropagation of the loss calculation to achieve unsupervised cross-domain RUL prediction.

Description

Technical Field

[0001] This invention relates to the field of cross-domain prediction of the remaining service life of aero-engines, and particularly to a cross-domain prediction method for the remaining service life of aero-engines based on a graph structure. Background Technology

[0002] Remaining useful life (RUL) prediction, as a crucial component of Predictive Health Management (PHM), has attracted widespread attention and become a research hotspot in this field. As a critical link in ensuring engine safety, predicting the degradation trend and assessing the health status of complex and precision equipment such as aero engines is extremely challenging. To safeguard national and public safety and property, predicting the RUL of aero engines as early as possible and conducting maintenance and repairs based on the prediction results is of great significance for safe flight and accident prevention.

[0003] With the development and application of deep learning technology in various fields, the health status of aero-engines can be predicted and maintained by analyzing the magnitude and trend of sensor parameters. However, because aero-engines often operate in different working environments and have high operating costs, collecting sensor data samples in actual operating scenarios faces problems such as large distribution differences and difficulty in obtaining labels, which limits the use of traditional deep learning methods.

[0004] This invention is mainly aimed at the cross-domain prediction scenario of RUL for aero-engines. In this scenario, a remaining service life prediction model that can be applied to the target domain is trained by using labeled source domain aero-engine sensor data and unlabeled target domain sensor data.

[0005] In 2021, Li et al. proposed a graph-based scheme for predicting remaining useful life (RUL) in their paper "Hierarchical attention graph convolutional network tofuse multi-sensor signals for remaining useful life prediction". This method constructs an aero-engine graph dataset, utilizes BiLSTM and hierarchical graph representation layers to represent spatiotemporal dependencies, and finally fuses these dependencies into a multi-level RUL. This scheme considers the relationships between multiple sensors and extracts hidden features of the aero-engine from both temporal and spatial perspectives, thus improving its predictive ability. However, to ensure the input of graph-structured data, the proposed scheme extracts temporal dependencies from the input data along the sensor dimension. Furthermore, the graph-based aero-engine feature extraction structure is not applied to cross-domain RUL prediction.

[0006] In 2022, Hu et al. proposed a deep feature disentanglement based transfer learning network for regression tasks to extract domain-invariant features in their paper "Remaining useful life prediction of bearings under different working conditions using a deep feature disentanglement based transfer learning method". This method utilizes a multilayer perceptron (MLP) as the deep feature extractor and simultaneously disentangles the shared domain-invariant representation and the private representation through a pair of jointly learned autoencoders. This method can separate the extracted source and target domain features through decoupling. However, the feature extraction module in this method is a multilayer perceptron, which does not consider the temporal nature of aero-engine degradation data.

[0007] In summary, the current cross-domain RUL prediction methods for aero-engines based on unsupervised domain adaptation methods have the following main defects: (1) The feature extraction methods in existing models only consider the time dependence of aero-engine degradation data, while ignoring the modeling of the data's own structural information, resulting in the lack of representation of multi-sensor structural information in the features extracted by deep networks. Most traditional cross-domain RUL methods for aero-engines use recurrent structures to learn features from the data, while ignoring the relationships between sensor data and spatial topology information. (2) Currently, no research has introduced graph-based feature extraction models into cross-domain RUL prediction for aero-engines. Regarding the modeling of aero-engine topology information, the existing single-domain RUL prediction models based on graph neural networks assume that all neighboring nodes contribute equally to the central node during the information interaction process between sensor nodes, ignoring the influence of the correlation between different sensor nodes on information transmission. (3) In existing unsupervised cross-domain RUL prediction methods for aero-engines, the information transmission process between the source domain and the target domain only considers regression labels and domain labels. These methods only consider how to represent the domain-invariant features between the source and target domains when choosing the transfer method, without taking into account the impact of domain-specific attributes on the transferability of domain-invariant features. Summary of the Invention

[0008] The purpose of this invention is to propose a cross-domain prediction method for the remaining service life of aero-engines based on graph structures, in order to solve the above-mentioned technical problems.

[0009] To achieve the above objectives, the present invention provides the following solution:

[0010] A cross-domain prediction method for the remaining service life of aero-engines based on graph structures, comprising the following steps:

[0011] (1) Data preprocessing:

[0012] This study utilizes the publicly available aero-engine dataset C-MAPSS, which comprises four subsets. Each subset consists of a training dataset, a test dataset, and a set of true RUL labels for the test dataset. First, sensors in the dataset are selected based on their collected data, prioritizing those with a clear degradation trend. Sensors with constant values ​​or no degradation trend are removed to avoid increasing computational costs and impacting training efficiency. The min-max normalization method is then used to normalize the aero-engine sensor signals. To fully utilize the multi-sensor time-series information of the aero-engine, a fixed-length sliding window is used to split the entire dataset's time series data into sub-time data along the time dimension. The piecewise linear degradation model sets a threshold to assign fixed RUL labels for healthy states, while other RUL labels are set to the time interval from the engine's current operating moment to operational failure. This method uses a threshold N to label RUL labels exceeding N as N, while leaving labels less than N unchanged.

[0013] (2) Generate a graph dataset between sensors:

[0014] To obtain the topology of aero-engine sensor data and construct a graph dataset, time-series data from different sensors are treated as graph nodes. The graph structure of each dataset is defined by calculating the correlation between different sensor data. The correlation is calculated using the Pearson correlation coefficient ρ(X, Y) between two sensor nodes, as follows:

[0015]

[0016] Where X and Y represent different samples, and Cov(X, Y) represents the covariance between the two samples; σ X and σ Y These represent the standard deviations of the two samples, μ and μ. X and μ Y represents the mean of the two samples, and E represents the expected value.

[0017] By simply calculating the Pearson coefficients between different sensor samples in the dataset, a sensor graph structure for the subset can be constructed based on a defined threshold. When the correlation between the central node and other sensor nodes exceeds the threshold, the two sensor nodes are considered connected in the graph structure; nodes whose correlation does not meet the condition cannot be added to the set of neighboring nodes of the central node. The method for generating the neighboring node set is as follows:

[0018]

[0019] in Represents sensor node x i The neighbor set of adj(x), where θ represents the threshold for determining whether nodes are connected, and adj(x) represents the neighbor set of adj(x). i x j ) represents the condition ρ(x) when the data from two sensor nodes satisfy the condition. i x j The set of nodes returned when )≥θ j , j≥i}. From this, we can obtain the graph dataset (X, A), where X is the sensor input data, and A is the adjacency matrix corresponding to each subset of the dataset. The adjacency matrix A is based on the set of neighboring nodes of sensor node x. Obtain, when node x i With node x j When a neighbor relationship exists, i.e., x j Existence In the middle, then A ij =1, otherwise A ij =0. In addition, this adjacency matrix contains node self-connections, i.e., A ii =1.

[0020] (3) Deep feature extraction:

[0021] An improved Temporal Graph Attention Network (TGAT) model is used to extract features from the input source and target domain aero-engine sensor data, yielding deep spatiotemporal features of the aero-engine. Specifically, the feature extraction module is composed of the proposed improved temporal graph attention model, and is divided into three parts according to the source and function of the processed features: a shared feature extraction module E... shared Source domain feature extraction module and target domain feature extraction module Shared Feature Extraction Module E shared Simultaneously receiving input data from both the source and target domains, this module learns domain-invariant features unaffected by domain variations across different domains. (Source domain feature extraction module) and target domain feature extraction module These are used to learn specific temporal degradation information from the source and target domain data, respectively; finally, the source and target domain data are processed through three feature extraction modules to obtain source domain-specific features. Target domain-specific features Source domain invariant features Domain-invariant features of the target domain and the unique spatiotemporal characteristics of the source domain Target domain-specific fusion spatiotemporal features Source domain invariant fusion spatiotemporal features Spatiotemporal features of domain invariant fusion with target domain

[0022] The construction process of the improved time-series graph attention model is as follows:

[0023] (3.1) Spatial topological feature extraction

[0024] After obtaining the graph dataset processed in step (2), the source domain data and target domain data are input into the graph attention network (GAT) to update the node features; GAT assigns different weights to different neighbor nodes by calculating the correlation between the center node and different neighbor nodes.

[0025] The correlation between the central node and its different neighboring nodes is calculated as follows:

[0026]

[0027] Where h i It is the central node, h j It is the set of adjacent nodes The neighboring nodes in the graph. W is the shared parameter for calculating the relevant information, which is ultimately mapped to the correlation coefficient through the function a(·). After calculating the correlation coefficients between the central node and all its neighboring nodes, the attention coefficient α assigned to each node can be obtained. ij The details are as follows:

[0028]

[0029] Finally, the features of each node and its first-order neighbors are aggregated using GAT, and the specific structure is defined as follows:

[0030]

[0031] Where σ(·) represents the activation function. Finally, the hidden state of the entire sensor data obtained through aggregation calculation is Z = G(A, X) = [h...]. (1) h (2) , ..., h (i) ]; G(·) represents the GAT node feature aggregation operation, h (i) Let X represent the feature of the i-th node in the graph, A be the adjacency matrix including node self-connections, and X represent the input node features.

[0032] (3.2) Temporal Feature Extraction

[0033] The GRU structure is used to extract time-dependent information from aero-engine data; the GRU model is defined as follows:

[0034] u t =sigmoid(W u ·[X t h t-1 ]+bu )

[0035] r t =sigmoid(W r @[X t h t-1 ]+b r )

[0036] c t =tanh(W c ·[X t , (r t *h t-1 )]+b c )

[0037] h t =u t *h t-1 +(1-u t )*c t

[0038] Where r t and u t Represents the reset gate and update gate, used to update the hidden state h at time t. t ;W u W r W c b u b r b c These are the parameters of the GRU model, and sigmoid(·) and tanh(·) are the activation functions, respectively.

[0039] (3.3) Spatiotemporal Feature Extraction

[0040] To better extract the spatiotemporal features of aero-engine sensor data, an improved time-series graph attention model, TGAT, is designed, which combines the advantages of GAT and GRU.

[0041] First, the graph structure sensor data at each time step is input into the GAT structure to extract spatial topological features. Then, the graph attention layer output at time t and the hidden state of the GRU structure at time t-1 are input into the GRU to extract temporal features. Finally, the extracted features are fused through the attention module to obtain the spatiotemporal features of the aero-engine sensor data; as detailed below:

[0042] u t =sigmoid(W u ·[Z t h t-1 ]+b u )

[0043] r t=sigmoid(W r ·[Z t h t-1 ]+b r )

[0044] c t =tanh(W c ·[Z t , (r t *h t-1 )]+b c )

[0045] h t =u t *h t-1 +(1-u t )*c t

[0046] Z t h represents the spatial topological features obtained by processing sensor data at time t through a GAT structure. t-1 The hidden state represents the output of the GRU structure at the previous time step; ultimately, the spatiotemporal feature H = [h] is obtained. (1) h (2) , ..., h (i) ].

[0047] RUL prediction is performed by fusing spatiotemporal features from all sensors using an attention mechanism. The calculation process is as follows:

[0048] ω i =fc([h (1) h (2) , ..., h (i) ]), i = 1, 2, ... N

[0049]

[0050] Where h (i) ω represents the feature of the i-th sensor node in the graph. i α represents the weight of each of the i sensor features calculated. i Let fc(·) represent the weight coefficients of the i sensor features, and fc(·) represent the mapping process after a fully connected layer. The calculation method for the attention-based fusion spatiotemporal feature F is as follows: (The original text contains some inconsistencies and unclear grammatical structures. A more accurate translation would require the full context.)

[0051]

[0052] (4) Domain feature separation:

[0053] The domain feature separation module consists of a source domain feature difference calculation module, a target domain feature difference calculation module, and a source domain graph reconstruction module Rc.S Target domain graph reconstruction module Rc T The system consists of six parts: a domain difference calculation module, a RUL prediction module, and a domain feature separation module. The domain feature separation module processes the source domain-specific features obtained in step (3). Target domain-specific features Source domain invariant features Domain-invariant features of the target domain Processing and source domain-specific fusion spatiotemporal characteristics. Target domain-specific fusion spatiotemporal features Source domain invariant fusion spatiotemporal features Spatiotemporal features of domain invariant fusion with target domain

[0054] The RUL prediction module calculates the RUL of samples corresponding to source domain features extracted by the model. It uses labeled source domain data to measure the RUL prediction ability of the shared feature extraction module, guiding the prediction of RUL for unlabeled target domain data. The domain difference calculation module uses the MK-MMD metric for domain adaptation, reducing the impact of cross-domain data distribution differences and minimizing the distance between different domains. The source domain feature difference calculation module and the target domain feature difference calculation module guide the shared feature extraction module and the domain-specific feature extraction module to learn different features, thereby distinguishing between domain-invariant and domain-specific features. The source domain graph reconstruction module Rc... s and target domain graph target reconstruction module Rc T These constraints are used to ensure that features extracted from different domains by the feature extraction model retain complete data information; specifically as follows:

[0055] (4.1) RUL Prediction Module

[0056] To minimize the impact of feature extraction module E shared The difference between the predicted RUL obtained from the RUL prediction module and the true label of the source domain RUL; for the obtained source domain domain invariant features after feature fusion. We use a fully connected layer fc(·) to calculate the weights between different sensor features.

[0057]

[0058] This invention uses the root mean square error (RMSE) as a measure of the difference in predicted RUL. The loss function of the RUL prediction module is as follows:

[0059]

[0060] in It is the predicted RUL label, y i It's a genuine RUL label. sIt represents the number of source domain samples in each iteration.

[0061] (4.2) Domain Difference Calculation Module

[0062] The domain difference calculation module uses MK-MMD to define the distance L between different domains. MMD The details are as follows:

[0063]

[0064] in Let be the domain-invariant features of the source domain, and let be the domain-invariant features of the target domain. N S and N T These represent the number of samples in the source and target domains, respectively. As a mapping function, it can map data to the reproducing kernel Hilbert space. Let k denote the regenerated kernel Hilbert space, where k(·,·) is a kernel function defined together by multiple kernels.

[0065] (4.3) Domain Feature Difference Calculation Module

[0066] The domain feature difference calculation module separates the feature differences learned by the domain-specific feature extraction module and the shared feature extraction module as much as possible, so as to explicitly separate domain-specific features when learning domain-invariant features. This module represents the differences between different sensor nodes through orthogonal constraints and guides the domain-specific feature extraction module and the shared feature extraction module to learn different mapping methods in the two domains. Domain feature difference loss L diff The specific calculation method is as follows:

[0067]

[0068] in This represents the source domain feature difference loss calculated from the source domain features. This represents the target domain feature difference loss calculated from the target domain features. It is the square of Frobenius Norm.

[0069] (4.4) Graph Reconstruction Module

[0070] To prevent different feature extraction modules from learning significantly different features during domain feature separation and losing the original and structural information contained in the original data, a graph reconstruction module is introduced to constrain the feature extraction modules in different domains. The graph reconstruction module includes the source domain graph reconstruction module Rc. S and the target domain graph reconstruction module Rc T The inner product is used as a decoder to reconstruct the original adjacency matrix. Specifically as follows:

[0071]

[0072] Where H represents the domain-specific feature H p sum-domain invariant feature H shared The fusion characteristics of H T Let σ(·) represent the transpose of the fused feature matrix, and let σ(·) represent the activation function. The computation process of the graph reconstruction module in the source and target domains can be represented as follows: and [,] represents the operation of merging and concatenating data;

[0073] To ensure that the feature adjacency matrix calculated by the graph reconstruction module is similar to the adjacency matrix of the original data graph structure, the mean-square error (MSE) is used to measure the graph reconstruction loss L between the original graph structure A and the calculated feature adjacency matrix. cons The details are as follows:

[0074]

[0075] in The source domain graph reconstruction loss is represented by the source domain feature computation. This represents the target domain graph reconstruction loss calculated using target domain features. and This represents the connectivity of graph nodes in the adjacency matrix of the source and target domains, and its value is either 0 or 1. and N represents the connectivity between graph nodes in the reconstructed adjacency matrix, with values ​​between [0, 1]. A This represents the number of sensors in the aero-engine, and also the number of nodes in the aero-engine graph dataset.

[0076] We propose an objective function for unsupervised cross-domain RUL prediction:

[0077] The objective function consists of four parts: the RUL prediction loss of the source domain data, and the L... RUL Domain difference loss L MMD Domain feature difference loss L diff and graph reconstruction loss L cons ;

[0078] Combining the four loss functions mentioned above, the overall objective function is expressed as:

[0079] L loss =L RUL +αL MMD +βL diff +γL cons

[0080] Where α, β and γ are all predetermined parameters;

[0081] (5) Evaluation metrics for the proposed RUL cross-domain prediction method:

[0082] The model in this method consists of the computational methods and modules described in steps (1) to (4). After the aero-engine data is processed by steps (1) to (4), the model parameters are updated using the total loss function to train the model. After the model training is completed, cross-domain RUL prediction of the target domain test data is realized. The cross-domain RUL prediction model performance is represented by the root mean square error between the predicted target domain RUL value and the true target domain RUL label, and its formula is as follows:

[0083]

[0084] in and y i These are the predicted RUL and the true RUL labels for the target domain test data, respectively, and N is the total number of sample data in the test set.

[0085] In addition, the Score metric penalizes delayed RUL predictions to indicate the order of predicted RULs and actual RULs, thereby reducing the occurrence of delayed RUL prediction behavior. The Score metric is defined as follows:

[0086]

[0087] in yi and yi are the predicted RUL and true RUL labels of the target domain test data, respectively, and N is the total number of sample data in the test set.

[0088] The beneficial effects of this invention are as follows: By incorporating the spatial topology and temporal dependence information of aero-engine sensor data into the domain adaptation process, this invention can deeply mine hidden information within the sensor data, providing more useful information for domain adaptation. During the domain adaptation process, this invention separates domain-invariant features and domain-specific features based on graph structure information. Simultaneously, graph reconstruction is performed during this separation process to increase the completeness and effectiveness of data information, thereby improving the performance of unsupervised domain adaptation. Attached Figure Description

[0089] Figure 1(a) and Figure 1(b) are schematic diagrams of the unsupervised domain adaptation scenario of aero-engine sensor data according to the present invention. Figure 1(a) shows the data and distribution of the training set, and Figure 1(b) shows the data and distribution of the test set.

[0090] Figure 2 This is a flowchart of the model for a cross-domain prediction method for the remaining service life of an aero-engine based on a graph structure, according to the present invention.

[0091] Figure 3 This is a model structure diagram of the improved time-series graph attention model in this invention. Detailed Implementation

[0092] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0093] A graph-based method for cross-domain prediction of the remaining service life (RUL) of aero-engines is proposed, applied to cross-domain RUL prediction of aero-engines using labeled source domain data and unlabeled target domain data. As shown in Figures 1(a) and 1(b), in real-world industrial scenarios, the distribution of historical sensor data for aero-engines operating under different conditions and failure modes varies, meaning that the training set data and the test set data are often different. Furthermore, to ensure property and life safety, obtaining labels for aero-engines is extremely difficult.

[0094] Therefore, it is necessary to address the domain adaptation problem for data with different distributions under unlabeled conditions in the target domain. Most existing cross-domain prediction methods for aero-engine RUL (Regression Limitation) extract time dependencies from sensor data as features to represent degradation information, and no work has yet incorporated the data structure information of aero-engines into cross-domain RUL prediction. Furthermore, existing methods only consider using regression label information and domain distribution differences during unsupervised domain adaptation for cross-domain RUL transfer, without separating domain-specific features from different domains while extracting domain-invariant features. Therefore, it is necessary to address the limitations of existing cross-domain feature extraction models that do not consider data spatial topology information, and to separate domain-invariant and domain-specific features during global domain adaptation.

[0095] The model structure of this invention is as follows Figure 2 As shown, firstly, the aero-engine sensor subsets in the source and target domains are preprocessed, and the correlation between the selected sensor data is calculated to construct an aero-engine graph dataset. Then, a domain feature extraction module based on a temporal graph attention model is designed to extract the temporal and spatial topological dependencies of the aero-engine data. Its structure is as follows: Figure 3As shown, this model performs attention-based information aggregation on different sensors in each gated recurrent unit, enabling the extraction of sensor topology information at each time step during the capture of the entire time-series data, thus obtaining a more comprehensive feature representation. Finally, a domain feature separation module is designed to separate domain-invariant information from domain-specific information. Specifically, the RUL prediction module maintains the feature representation capability of the feature extraction module during domain adaptation, the domain feature difference calculation module learns both domain-invariant and domain-specific information in the source and target domains, the graph reconstruction module preserves the original information in the data, and the domain difference calculation module uses MK-MMD as a metric function for domain adaptation, avoiding the impact of domain-specific information on transfer learning while learning domain-invariant information, thereby improving transfer performance. Finally, the gradient is backpropagated through the loss function to update the parameters, resulting in a trained model, which is then used to predict unlabeled target domain data.

[0096] The specific steps are as follows:

[0097] A cross-domain prediction method for the remaining service life of aero-engines based on graph structures, comprising the following steps:

[0098] (1) Data preprocessing:

[0099] This study utilizes the publicly available aero-engine dataset C-MAPSS, which comprises four subsets. Each subset consists of a training dataset, a test dataset, and a set of true RUL labels for the test dataset. First, sensors in the dataset are selected based on their collected data, prioritizing those with a clear degradation trend. Sensors with constant values ​​or no degradation trend are removed to avoid increasing computational costs and impacting training efficiency. The min-max normalization method is then used to normalize the aero-engine sensor signals. To fully utilize the multi-sensor time-series information of the aero-engine, a fixed-length sliding window is used to split the entire dataset's time series data into sub-time data along the time dimension. The piecewise linear degradation model sets a threshold to assign fixed RUL labels for healthy states, while other RUL labels are set to the time interval from the engine's current operating moment to operational failure. This method uses a threshold N to label RUL labels exceeding N as N, while leaving labels less than N unchanged.

[0100] (2) Generate a graph dataset between sensors:

[0101] To obtain the topology of aero-engine sensor data and construct a graph dataset, time-series data from different sensors are treated as graph nodes. The graph structure of each dataset is defined by calculating the correlation between different sensor data. The correlation is calculated using the Pearson correlation coefficient ρ(X, Y) between two sensor nodes, as follows:

[0102]

[0103] Where X and Y represent different samples, and Cov(X, Y) represents the covariance between the two samples; σ X and σ Y These represent the standard deviations of the two samples, μ and μ. X and μ Y represents the mean of the two samples, and E represents the expected value.

[0104] By simply calculating the Pearson coefficients between different sensor samples in the dataset, a sensor graph structure for the subset can be constructed based on a defined threshold. When the correlation between the central node and other sensor nodes exceeds the threshold, the two sensor nodes are considered connected in the graph structure; nodes whose correlation does not meet the condition cannot be added to the set of neighboring nodes of the central node. The method for generating the neighboring node set is as follows:

[0105]

[0106] in Represents sensor node x i The neighbor set of adj(x), where θ represents the threshold for determining whether nodes are connected, and adj(x) represents the neighbor set of adj(x). i x j ) represents the condition ρ(x) when the data from two sensor nodes satisfy the condition. i x j The set of nodes returned when )≥θ j (j≥i). This yields a graph dataset (X, A), where X represents the sensor input data, and A is the adjacency matrix corresponding to each subset of the dataset. The adjacency matrix A is based on the set of neighboring nodes of sensor node x. Obtain, when node x i With node x j When a neighbor relationship exists, i.e., x j Existence In the middle, then A ij =1, otherwise A ij =0. In addition, this adjacency matrix contains node self-connections, i.e., A ii =1.

[0107] (3) Deep feature extraction:

[0108] An improved Temporal Graph Attention Network (TGAT) model is used to extract features from the input source and target domain aero-engine sensor data, yielding deep spatiotemporal features of the aero-engine. Specifically, the feature extraction module is composed of the proposed improved temporal graph attention model, and is divided into three parts according to the source and function of the processed features: a shared feature extraction module E... shared Source domain feature extraction module and target domain feature extraction module Shared Feature Extraction Module E shared Simultaneously receiving input data from both the source and target domains, this module learns domain-invariant features unaffected by domain variations across different domains. (Source domain feature extraction module) and target domain feature extraction module These are used to learn specific temporal degradation information from the source and target domain data, respectively; finally, the source and target domain data are processed through three feature extraction modules to obtain source domain-specific features. Target domain-specific features Source domain invariant features Domain-invariant features of the target domain and the unique spatiotemporal characteristics of the source domain Target domain-specific fusion spatiotemporal features Source domain invariant fusion spatiotemporal features Spatiotemporal features of domain invariant fusion with target domain Specifically as follows:

[0109] The construction process of the improved time-series graph attention model is as follows:

[0110] (3.1) Spatial topological feature extraction

[0111] After obtaining the graph dataset processed in step (2), the source domain data and target domain data are input into the graph attention network (GAT) to update the node features; GAT assigns different weights to different neighbor nodes by calculating the correlation between the center node and different neighbor nodes.

[0112] The correlation between the central node and its different neighboring nodes is calculated as follows:

[0113]

[0114] Where h i It is the central node, h j It is the set of adjacent nodes The neighboring nodes in the graph. W is the shared parameter for calculating the relevant information, which is ultimately mapped to the correlation coefficient through the function a(·). After calculating the correlation coefficients between the central node and all its neighboring nodes, the attention coefficient α assigned to each node can be obtained. ij The details are as follows:

[0115]

[0116] Finally, the features of each node and its first-order neighbors are aggregated using GAT, and the specific structure is defined as follows:

[0117]

[0118] Where σ(·) represents the activation function. Finally, the hidden state of the entire sensor data obtained through aggregation calculation is Z = G(A, X) = [h...]. (1) h (2) , ..., h (i) ]; G(·) represents the GAT node feature aggregation operation, h (i) Let X represent the feature of the i-th node in the graph, A be the adjacency matrix including node self-connections, and X represent the input node features.

[0119] (3.2) Temporal Feature Extraction

[0120] The GRU structure is used to extract time-dependent information from aero-engine data; the GRU model is defined as follows:

[0121] u t =sigmoid(W u ·[X t h t-1 ]+b u )

[0122] r t =sigmoid(W r ·[X t h t-1 ]+b r )

[0123] c t =tanh(W c ·[X t , (r t *h t-1 )]+b c )

[0124] h t =u t *h t-1 +(1-u t )*c t

[0125] Where r t and u t Represents the reset gate and update gate, used to update the hidden state h at time t. t ;W u W r W c b u b r b c These are the parameters of the GRU model, and sigmoid(·) and tanh(·) are the activation functions, respectively.

[0126] (3.3) Spatiotemporal Feature Extraction

[0127] To better extract the spatiotemporal features of aero-engine sensor data, an improved time-series graph attention model, TGAT, is designed, which combines the advantages of GAT and GRU.

[0128] First, the graph structure sensor data at each time step is input into the GAT structure to extract spatial topological features. Then, the graph attention layer output at time t and the hidden state of the GRU structure at time t-1 are input into the GRU to extract temporal features. Finally, the extracted features are fused through the attention module to obtain the spatiotemporal features of the aero-engine sensor data; as detailed below:

[0129] u t =sigmoid(W u ·[Z t h t-1 ]+b u )

[0130] r t =sigmoid(W r ·[Z t h t-1 ]+b r )

[0131] c t =tanh(W c ·[Z t , (r t *h t-1 )]+b c )

[0132] h t =u t *h t-1 +(1-u t )*c t

[0133] Z t h represents the spatial topological features obtained by processing sensor data at time t through a GAT structure.t-1 The hidden state represents the output of the GRU structure at the previous time step; ultimately, the spatiotemporal feature H = [h] is obtained. (1) h (2) , ..., h (i) ].

[0134] RUL prediction is performed by fusing spatiotemporal features from all sensors using an attention mechanism. The calculation process is as follows:

[0135] ωi ＝ fc([h (1) h (2) , ..., h (i) ]), i = 1, 2, ... N

[0136]

[0137] Where h (i) ω represents the feature of the i-th sensor node in the graph. i α represents the weight of each of the i sensor features calculated. i Let fc(·) represent the weight coefficients of the i sensor features, and fc(·) represent the mapping process after a fully connected layer. The calculation method for the attention-based fusion spatiotemporal feature F is as follows: (The original text contains some inconsistencies and unclear grammatical structures. A more accurate translation would require the full context.)

[0138]

[0139] (4) Domain feature separation:

[0140] The domain feature separation module consists of a source domain feature difference calculation module, a target domain feature difference calculation module, and a source domain graph reconstruction module Rc. S Target domain graph reconstruction module Rc T The system consists of six parts: a domain difference calculation module, a RUL prediction module, and a domain feature separation module. The domain feature separation module processes the source domain-specific features obtained in step (3). Target domain-specific features Source domain invariant features Domain-invariant features of the target domain Processing and source domain-specific fusion spatiotemporal characteristics. Target domain-specific fusion spatiotemporal features Source domain invariant fusion spatiotemporal features Spatiotemporal features of domain invariant fusion with target domain

[0141] The RUL prediction module calculates the RUL of samples corresponding to source domain features extracted by the model. It uses labeled source domain data to measure the RUL prediction ability of the shared feature extraction module, guiding the prediction of RUL for unlabeled target domain data. The domain difference calculation module uses the MK-MMD metric for domain adaptation, reducing the impact of cross-domain data distribution differences and minimizing the distance between different domains. The source domain feature difference calculation module and the target domain feature difference calculation module guide the shared feature extraction module and the domain-specific feature extraction module to learn different features, thereby distinguishing between domain-invariant and domain-specific features. The source domain graph reconstruction module Rc... S and target domain graph target reconstruction module Rc T These constraints are used to ensure that features extracted from different domains by the feature extraction model retain complete data information; specifically as follows:

[0142] (4.1) RUL Prediction Module

[0143] To minimize the impact of feature extraction module E shared The difference between the predicted RUL obtained from the RUL prediction module and the true label of the source domain RUL; for the obtained source domain domain invariant features after feature fusion. We use a fully connected layer fc(·) to calculate the weights between different sensor features.

[0144]

[0145] This invention uses the root mean square error (RMSE) as a measure of the difference in predicted RUL. The loss function of the RUL prediction module is as follows:

[0146]

[0147] in It is the predicted RUL label, y i It's a genuine RUL label. S It represents the number of source domain samples in each iteration.

[0148] (4.2) Domain Difference Calculation Module

[0149] The domain difference calculation module uses MK-MMD to define the distance L between different domains. MMD The details are as follows:

[0150]

[0151] in Let be the domain-invariant features of the source domain, and let be the domain-invariant features of the target domain. N S and N T These represent the number of samples in the source and target domains, respectively. As a mapping function, it can map data to the reproducing kernel Hilbert space. Let k denote the regenerated kernel Hilbert space, where k(·,·) is a kernel function defined together by multiple kernels.

[0152] (4.3) Domain Feature Difference Calculation Module

[0153] The domain feature difference calculation module separates the feature differences learned by the domain-specific feature extraction module and the shared feature extraction module as much as possible, so as to explicitly separate domain-specific features when learning domain-invariant features. This module represents the differences between different sensor nodes through orthogonal constraints and guides the domain-specific feature extraction module and the shared feature extraction module to learn different mapping methods in the two domains. Domain feature difference loss L diff The specific calculation method is as follows:

[0154]

[0155] in This represents the source domain feature difference loss calculated from the source domain features. This represents the target domain feature difference loss calculated from the target domain features. It is the square of Frobenius Norm.

[0156] (4.4) Graph Reconstruction Module

[0157] To prevent different feature extraction modules from learning significantly different features during domain feature separation and losing the original and structural information contained in the original data, a graph reconstruction module is introduced to constrain the feature extraction modules in different domains. The graph reconstruction module includes the source domain graph reconstruction module Rc. S and the target domain graph reconstruction module Rc T The inner product is used as a decoder to reconstruct the original adjacency matrix. Specifically as follows:

[0158]

[0159] Where H represents the domain-specific feature H p sum-domain invariant feature H shared The fusion characteristics of H T Let σ(·) represent the transpose of the fused feature matrix, and let σ(·) represent the activation function. The computation process of the graph reconstruction module in the source and target domains can be represented as follows: and [,] represents the operation of merging and concatenating data;

[0160] To ensure that the feature adjacency matrix calculated by the graph reconstruction module is similar to the adjacency matrix of the original data graph structure, the mean-square error (MSE) is used to measure the graph reconstruction loss L between the original graph structure A and the calculated feature adjacency matrix. eons The details are as follows:

[0161]

[0162] in The source domain graph reconstruction loss is represented by the source domain feature computation. This represents the target domain graph reconstruction loss calculated using target domain features. and This represents the connectivity of graph nodes in the adjacency matrix of the source and target domains, and its value is either 0 or 1. and N represents the connectivity between graph nodes in the reconstructed adjacency matrix, with values ​​between [0, 1]. A This represents the number of sensors in the aero-engine, and also the number of nodes in the aero-engine graph dataset.

[0163] We propose an objective function for unsupervised cross-domain RUL prediction:

[0164] The objective function consists of four parts: the RUL prediction loss of the source domain data, and the L... RUL Domain difference loss L MMD Domain feature difference loss L diff and graph reconstruction loss L cons ;

[0165] Combining the four loss functions mentioned above, the overall objective function is expressed as:

[0166] L loss =L RUL +αL MMD +βL diff +γL cons

[0167] Where α, β and γ are all predetermined parameters;

[0168] (5) Evaluation metrics for the proposed RUL cross-domain prediction method:

[0169] The model in this method consists of the computational methods and modules described in steps (1) to (4). After the aero-engine data is processed by steps (1) to (4), the model parameters are updated using the total loss function to train the model. After the model training is completed, cross-domain RUL prediction of the target domain test data is realized. The cross-domain RUL prediction model performance is represented by the root mean square error between the predicted target domain RUL value and the true target domain RUL label, and its formula is as follows:

[0170]

[0171] in and y i These are the predicted RUL and the true RUL labels for the target domain test data, respectively, and N is the total number of sample data in the test set.

[0172] In addition, the Score metric penalizes delayed RUL predictions to indicate the order of predicted RULs and actual RULs, thereby reducing the occurrence of delayed RUL prediction behavior. The Score metric is defined as follows:

[0173]

[0174] in Let yi and yi be the predicted and true RUL labels for the target domain test data, respectively, and N be the total number of samples in the test set. In summary:

[0175] This invention proposes a cross-domain prediction method for the remaining service life (RUL) of aero-engines based on graph structures. First, the method preprocesses a subset of aero-engine sensor data from both the source and target domains, calculating the correlation between the selected sensor data to construct an aero-engine graph dataset. Then, a domain feature extraction module based on a temporal graph attention model is designed to extract the temporal and spatial topological dependencies of the aero-engine. This model performs attention-based information aggregation on different sensors in each gated recurrent unit, enabling the extraction of sensor topological information at each moment during the capture of the entire time-series data, thus obtaining a more comprehensive feature representation. Finally, a domain feature separation module is designed to separate domain-invariant information from domain-specific information, and MK-MMD is used as a metric function for domain adaptation. This avoids the influence of domain-specific information on transfer learning while learning domain-invariant information, thereby improving transfer learning performance. Finally, unsupervised cross-domain RUL prediction is achieved by calculating the loss and backpropagating to update the parameters.

Claims

1. A cross-domain prediction method for the remaining service life of an aero-engine based on graph structure, characterized in that, The steps are as follows: (1) Data preprocessing: We utilized the publicly available aero-engine dataset C-MAPSS, which consists of four subsets. Each subset comprises a training dataset, a test dataset, and a set of real RUL labels for the test dataset. First, we selected sensors from the dataset, choosing those with significant degradation trends and removing sensor data with constant values ​​or no degradation trend. Then, we normalized the aero-engine sensor signals using the min-max normalization method. To fully utilize the multi-sensor time-series information of aero-engines, we used a fixed-length sliding window to split the entire dataset's time-series data into sub-time data along the time dimension. The piecewise linear degradation model sets a threshold to a fixed value for the healthy RUL label, and sets the remaining RUL labels to the time interval from the current engine operating time to the operating failure time. RUL labels exceeding the threshold M are marked as N1, while RUL labels less than M remain unchanged. (2) Generate a graph dataset between sensors: To obtain the topology of aero-engine sensor data and construct a graph dataset, time-series data from different sensors are treated as graph nodes. The graph structure of each dataset is defined by calculating the correlation between different sensor data, with the correlation determined by the Pearson correlation coefficient between two sensor nodes. The calculations are as follows: ； in They represent different samples. This represents the covariance between two samples; and These represent the standard deviations of the two samples, and These represent the means of the two samples, respectively. Represents the mathematical expectation; By simply calculating the Pearson coefficients between different sensor samples in the dataset, the sensor graph structure of the subset can be constructed based on a determined threshold. When the correlation between the central node and other sensor nodes is greater than the threshold, the two sensor nodes are considered connected in the graph structure, and nodes whose correlation does not meet the condition cannot be added to the set of neighboring nodes of the central node. The method for generating the neighboring node set is as follows: ； in Represents sensor nodes The neighborhood group, This represents the threshold used to determine whether nodes are connected. This means that when the data from two sensor nodes meet the conditions... The set of nodes returned at that time This yields the graph dataset. ,in Input data to the sensor, The adjacency matrix for each subset of data. According to sensor nodes The set of neighboring nodes Obtain, when node With nodes When a neighborly relationship exists, that is Existence In the middle, then ,otherwise The adjacency matrix contains node self-connections, i.e. ; (3) Deep feature extraction: An improved temporal graph attention model (TGAT) is used to extract features from the input source and target domain aero-engine sensor data, yielding deep spatiotemporal features of the aero-engine. The extraction module consists of the proposed improved temporal graph attention model, and is divided into three parts according to the source and function of the processed features: a shared feature extraction module. Source domain feature extraction module and target domain feature extraction module ; Shared feature extraction module Simultaneously receiving input data from the source domain and the target domain, it is used to learn domain-invariant features between different domains that are unaffected by domain changes; Source domain feature extraction module and target domain feature extraction module These are used to learn specific temporal degradation information from the source and target domain data, respectively; finally, the source and target domain data are processed through three feature extraction modules to obtain source domain-specific features. Target domain-specific features Source domain invariant characteristics Domain-invariant features of the target domain and the unique spatiotemporal characteristics of the source domain. Target domain-specific spatiotemporal characteristics Source domain invariant fusion spatiotemporal features Spatiotemporal features of domain invariant fusion with target domain ; The construction process of the improved time-series graph attention model is as follows: (3.1) Spatial topological feature extraction After obtaining the graph dataset processed in step (2), the obtained source domain data and target domain data are input into the graph attention network GAT to update the node features; GAT assigns different weights to different neighboring nodes by calculating the correlation between the central node and different neighboring nodes; The correlation between the central node and its different neighboring nodes is calculated as follows: ； in It is the central node. It is the set of adjacent nodes Neighboring nodes in; To calculate the relevant shared parameters, the function is ultimately used. The correlation coefficient is mapped to the central node; after calculating the correlation coefficients between the central node and all its neighboring nodes, the attention coefficient assigned to each node is obtained. The details are as follows: ； Finally, the features of each node and its first-order neighbors are aggregated using GAT, and the specific structure is defined as follows: ； in The activation function is represented; finally, the hidden state of the entire sensor data obtained through aggregation calculation is: ; This indicates the feature aggregation operation of GAT nodes. This represents the feature of the i-th node in the graph. It is an adjacency matrix that includes self-connected nodes. Represents the node features of the input; (3.2) Temporal Feature Extraction The GRU structure is used to extract time-dependent information from aero-engine data; the GRU model is defined as follows: ； in and Representing the reset gate and update gate, used to update the hidden state at time t. ;in , , , , , These are the parameters of the GRU model. and These are activation functions; (3.3) Spatiotemporal feature extraction To better extract the spatiotemporal features of aero-engine sensor data, an improved time-series graph attention model, TGAT, is designed, which combines the advantages of GAT and GRU. First, the graph structure sensor data at each time step is input into the GAT structure to extract spatial topological features. Then, the graph attention layer output at time t and the hidden state of the GRU structure at time t-1 are input into the GRU to extract temporal features. Finally, the extracted features are fused through the attention module to obtain the spatiotemporal features of the aero-engine sensor data; as detailed below: ； in The spatial topological features obtained by processing the sensor data at time t through the GAT structure represent the characteristics of the space. The hidden state represents the output of the GRU structure at the previous time step; ultimately, the spatiotemporal features are obtained. ; RUL prediction is performed by fusing the spatiotemporal features of all sensors through an attention mechanism; the calculation process is as follows: ； in This represents the feature of the i-th sensor node in the graph. This represents the weight of each of the i sensor features calculated. This represents the weight coefficient of each of the i sensor features. This indicates that the mapping process has been performed through a fully connected layer; after multiplying the weight coefficients by the corresponding features and summing them, the attention-based fusion spatiotemporal features are obtained. The calculation method is as follows: ； (4) Domain feature separation: The domain feature separation module consists of a source domain feature difference calculation module, a target domain feature difference calculation module, and a source domain graph reconstruction module. Target domain graph reconstruction module Domain Difference Calculation Module and RUL Prediction Module It consists of six parts; the domain feature separation module separates the source domain-specific features obtained in step (3). Target domain-specific features Source domain invariant characteristics Domain-invariant features of the target domain Processing and source domain-specific fusion spatiotemporal characteristics. Target domain-specific spatiotemporal characteristics Source domain invariant fusion spatiotemporal features Spatiotemporal features of domain invariant fusion with target domain ; The RUL prediction module calculates the RUL of samples corresponding to source domain features extracted by the model. It uses labeled source domain data to measure the RUL prediction ability of the shared feature extraction module, guiding the prediction of RUL for unlabeled target domain data. The domain difference calculation module uses the MK-MMD metric for domain adaptation, reducing the impact of cross-domain data distribution differences and minimizing the distance between different domains. The source domain feature difference calculation module and the target domain feature difference calculation module guide the shared feature extraction module and the domain-specific feature extraction module to learn different features, thereby distinguishing between domain-invariant and domain-specific features. The source domain graph reconstruction module... and target domain graph target reconstruction module These constraints are used to ensure that features extracted from different domains by the feature extraction model retain complete data information; specifically as follows: (4.1) RUL Prediction Module To minimize the impact of the feature extraction module The difference between the predicted RUL obtained from the RUL prediction module and the true label of the source domain RUL; for the obtained source domain domain invariant features after feature fusion. Use a fully connected layer Calculate the weights between different sensor features. ； The root mean square error (RMSE) is used as a measure of the difference in predicted RUL values. The loss function for the RUL prediction module is as follows: ； in It is a predicted RUL label. It is a genuine RUL label; It is the number of source domain samples in each iteration; (4.2) Domain Difference Calculation Module The domain difference calculation module uses MK-MMD to define the distance between different domains. The details are as follows: ； in Let be the domain-invariant features of the source domain, and let be the domain-invariant features of the target domain. , and These represent the number of samples in the source and target domains, respectively. The mapping function maps data to the reproducing kernel Hilbert space. Represents the regenerating nucleus Hilbert space. Kernel functions defined together for multiple kernels; (4.3) Domain Feature Difference Calculation Module The domain feature difference calculation module separates the feature differences learned by the domain-specific feature extraction module and the shared feature extraction module, so as to explicitly separate domain-specific features when learning domain-invariant features; this module represents the differences between different sensor nodes through orthogonal constraints and guides the domain-specific feature extraction module and the shared feature extraction module to learn different mapping methods in the two domains; domain feature difference loss. The specific calculation method is as follows: ； in This represents the source domain feature difference loss calculated from the source domain features. This represents the target domain feature difference loss calculated from the target domain features. It is the square of Frobenius Norm; (4.4) Graph Reconstruction Module To prevent different feature extraction modules from learning significantly different features during domain feature separation and losing the original and structural information contained in the original data, a graph reconstruction module is introduced to constrain the feature extraction modules in different domains. The graph reconstruction module includes a source domain graph reconstruction module. and target domain graph reconstruction module The inner product is used as a decoder to reconstruct the original adjacency matrix. The details are as follows: ； in Representation domain-specific features sum-field invariant features The fusion characteristics This represents the transpose of the fused feature matrix. The activation function represents the computation process of the graph reconstruction module for the source and target domains, which is represented as follows: and ,in This represents the operation of merging and concatenating data; To ensure that the feature adjacency matrix calculated by the graph reconstruction module is similar to the adjacency matrix of the original data graph structure, the mean squared error (MSE) is used to measure the graph reconstruction loss between the original graph structure A and the calculated feature adjacency matrix. The details are as follows: ； in The source domain graph reconstruction loss is represented by the source domain feature computation. This represents the target domain graph reconstruction loss calculated using target domain features. and This represents the connectivity of graph nodes in the adjacency matrix of the source and target domains, and its value is either 0 or 1. and The adjacency matrix represents the connectivity between graph nodes, and its value is between [0, 1]. This represents the number of sensors in the aero-engine, and also the number of nodes in the aero-engine graph dataset; We propose an objective function for unsupervised cross-domain RUL prediction: The objective function consists of four parts: the RUL prediction loss of the source domain data. Domain difference loss Domain feature difference loss and graph reconstruction loss ; Combining the four loss functions mentioned above, the overall objective function is expressed as: ； in, , and These are all pre-defined parameters; (5) Evaluation metrics for the performance of the proposed RUL cross-domain prediction method: The model in this method consists of the computational methods and modules described in steps (1) to (4). After the aero-engine data is processed by steps (1) to (4), the model parameters are updated using the total loss function to train the model. After the model training is completed, cross-domain RUL prediction of the target domain test data is realized. The cross-domain RUL prediction model performance is represented by the root mean square error between the predicted target domain RUL value and the true target domain RUL label, as shown in the following formula: ； in and These are the predicted RUL and the true RUL labels of the target domain test data, respectively, and N3 is the total number of sample data in the test set. In addition, the Score metric penalizes delayed RUL predictions to indicate the order of predicted RULs and actual RULs, thereby reducing the occurrence of delayed RUL prediction behavior. The Score metric is defined as follows: ； in and These are the predicted RUL and the true RUL labels for the target domain test data, respectively, and N3 is the total number of sample data in the test set.

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