A Method for Predicting Remaining Service Life of Aero-engines Based on Domain Knowledge-Enhanced Dual-Flow Graph Joint Learning Network

Abstract

This invention discloses a method for predicting the remaining service life (RUL) of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network, belonging to the field of engine life prediction technology. This invention addresses the problem that existing aero-engine RUL prediction methods do not comprehensively capture the complex degradation features of engines, thus affecting prediction accuracy. The method includes: first, constructing a static correlation graph representing the macroscopic physical topology between components, and simultaneously constructing a dynamic correlation graph of sensor parameters that evolves with the engine state; second, proposing a dual-flow graph joint learning network, consisting of a multi-hop graph attention network for static graph feature extraction and a gated graph-temporal attention network for dynamic graph feature extraction, efficiently extracting aero-engine degradation features from the heterogeneous static and dynamic graphs respectively; finally, employing a self-attention-enhanced feature alignment module to adaptively fuse the degradation features extracted from the two branches. This invention achieves more accurate and robust prediction of engine RUL.

Description

Technical Field

[0001] This invention relates to a method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network, belonging to the field of engine life prediction technology. Background Technology

[0002] As a core power component of an aircraft, the health of an aero-engine directly affects the safety and reliability of flight. Remaining useful life (RUL) prediction aims to provide valuable information about the health status of aero-engines based on collected monitoring data, effectively helping decision-makers to formulate reasonable usage and maintenance plans in advance, avoiding catastrophic failures and reducing operating costs. Therefore, accurately estimating the RUL of aero-engines and providing early warnings is of great significance.

[0003] Currently, many deep learning models, such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Long Short-Term Memory Networks (LSTMs), and Transformers, are widely used to automatically model potential correlations and causal relationships in collected engine monitoring data, thereby achieving accurate prediction of the RUL (Range Limit Up) of aero-engines. However, the performance of deep learning-based RUL prediction methods is highly dependent on massive amounts of high-quality engine operation monitoring data, ignoring the actual physical mechanisms behind engine performance degradation. This may lead the model to learn some spurious statistical correlations instead of true causal degradation patterns, thus affecting the model's generalization ability and robustness. More importantly, deep learning models are often considered "black boxes," lacking transparency and interpretability in their decision-making process, which is unacceptable in high-risk fields such as aviation safety.

[0004] Domain knowledge augmentation methods inject knowledge from fields such as physical laws and expert experience as additional knowledge into deep learning models for RUL prediction of complex industrial equipment, thus addressing the aforementioned shortcomings of data-driven approaches. It can improve prediction accuracy, robustness, and interpretability even with limited data.

[0005] In the RUL prediction scenario for aero-engines, commonly used domain knowledge is mainly divided into two categories: macroscopic degradation mechanism knowledge and correlation knowledge between sensor monitoring quantities. Current research on knowledge enhancement methods based on soft embedding focuses on how to accurately characterize the complex correlations between sensor monitoring variables and effectively integrate them into deep learning-based RUL prediction modeling to achieve effective injection of domain knowledge.

[0006] Graph Neural Network (GNN)-based methods transform multivariate monitoring data of aero-engines into a graph structure with sensor monitoring quantities as nodes and the relationships between these quantities as edges. This not only accurately and structurally represents the complex relationships between sensor monitoring quantities but also enables deep extraction and reasoning of these relationships through its core neighborhood aggregation mechanism. Currently, the following technical challenges urgently need to be addressed regarding the physical fidelity and depth of knowledge representation in domain knowledge graph construction:

[0007] 1) The graph structure's association construction lacks in-depth mechanistic support, easily introducing spurious associations. Existing domain knowledge enhancement methods based on GNNs mainly use statistical methods or simplified mechanistic relationship analysis to mine the associations between different sensor monitoring quantities. The associations revealed are more statistical correlations at the data level than essential dependencies at the mechanistic level. In aero-engines, the associations between sensor monitoring quantities originate from their working mechanisms. For example, high-temperature, high-pressure gas expands and does work in the high-pressure turbine, then transfers it to the low-pressure turbine, where it expands and does work, thereby driving the low-pressure compressor to rotate. This means that there is a necessary mechanistic correlation between parameters such as the speed and temperature of the low-pressure turbine and parameters such as the outlet temperature and pressure of the high-pressure turbine. However, current methods only infer these associations by analyzing monitoring data. On the one hand, sensor data is usually severely interfered with by multiple factors such as operating conditions and environmental noise. Relying solely on statistical analysis easily extracts false "spurious associations," thereby reducing the stability and reliability of the graph structure. On the other hand, the essential dependencies between sensors at the aero-engine working mechanism level are ignored, resulting in a graph structure that only reflects the apparent phenomena but fails to reveal the underlying causal mechanisms.

[0008] 2) Existing graph structure modeling methods lack explicit representation of component-level physical topological logic. Current GNN-based domain knowledge enhancement methods focus only on mining fine-grained relationships at the sensor level when constructing graph structures, generally neglecting higher-level physical relationships between components. Specifically, aero-engines consist of core components such as compressors, combustion chambers, and turbines. These components form fixed physical connections through mechanical transmission and gas flow paths, constituting the engine's structural backbone. In other words, the physical topology between components is itself macroscopic domain knowledge of physical relationships, providing an intuitive perspective with structural constraints for understanding the overall engine degradation behavior. Therefore, in addition to the mechanistic relationships between sensor-monitored quantities, the physical relationships between components are also important knowledge worth utilizing. Summary of the Invention

[0009] To address the problem that existing methods for predicting the remaining service life of aero-engines do not fully capture the complex degradation characteristics of engines, thus affecting prediction accuracy, this invention provides a method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network.

[0010] The present invention provides a method for predicting the remaining service life of an aero-engine based on a domain knowledge-enhanced dual-flow graph joint learning network, comprising: collecting time series of sensor monitoring data of various engine components, and dividing them into multiple data windows in chronological order, wherein the number of time steps for each data window is w;

[0011] Obtaining static graph features: For the current data window, a one-dimensional convolutional network is used to extract features from the sensor monitoring data of each component to obtain the state features of each component; based on the structural characteristics of the aero-engine, a component relationship graph is established with components as nodes and physical connection relationships or airflow relationships between components as edges, and the component relationship adjacency matrix is ​​obtained; then, based on establishing connections between all nodes, a jump step number k is selected to obtain an adjacency matrix with a jump step number of k; a GAT network is used to extract features from the state features of all components and the adjacency matrix with a jump step number of k to obtain static graph features;

[0012] To obtain dynamic graph features: Based on the working mechanism of aero-engines, a qualitative relationship graph of sensor parameters is established with sensors as nodes and the mechanistic relationships between sensors as edges; simultaneously, a quantitative relationship graph of sensor parameters is established with sensors as nodes and the statistical correlation of sensor parameters in the current data window as edges; the qualitative and quantitative relationship graphs of sensor parameters corresponding to the current data window are adaptively fused to obtain a fused relationship graph and a sensor parameter relationship adjacency matrix; w gated graph attention units are configured, and the first gated graph attention unit is used to extract features from the sensor parameter relationship adjacency matrix and the sensor monitoring data of the first time step in the current data window to obtain the first time step features; each subsequent gated graph attention unit extracts features from the adjacent previous time step features, the sensor parameter relationship adjacency matrix, and the sensor monitoring data of the corresponding time step to obtain the corresponding time step features; the attention weights of the features of the first w-1 time steps and the w-th time step features are calculated, and the features of the first w-1 time steps are weighted and fused, and then combined with the w-th time step features to obtain dynamic graph features;

[0013] Feature Adaptive Fusion and RUL Prediction: A feature alignment network is used to map dynamic graph features and static graph features to the same feature space and then concatenate them; a self-attention module is then used to fuse the mapped and concatenated features to obtain fused features; a one-layer fully connected network is used to obtain the RUL prediction result of the aero-engine based on the fused features.

[0014] The beneficial effects of this invention are as follows: The method of this invention enhances the ability of GNN to represent and extract complex degradation mechanisms by coupling modeling of multi-level domain knowledge of aero-engines and joint learning of dual-flow graphs, thereby achieving higher RUL prediction accuracy. First, based on the structural characteristics of the aero-engine, the physical relationships between different components are obtained, and a static relationship graph representing the macroscopic physical topology between components is constructed. Similarly, based on the relationship between parameters obtained by fusing aero-engine working mechanisms and data statistics, a dynamic relationship graph of sensor parameters evolving with the engine state is constructed. Second, a joint learning network of dual-flow graphs is proposed, consisting of a multi-hop graph attention network for static graph feature extraction and a gated graph-temporal attention network for dynamic graph feature extraction, efficiently extracting aero-engine degradation features from heterogeneous static and dynamic graphs respectively. Finally, a self-attention enhanced feature alignment module is used to adaptively fuse the degradation features extracted from the two branches, achieving more accurate and robust prediction of engine RUL.

[0015] This invention designs a two-level domain knowledge-enhanced RUL prediction framework for aero-engines. It explicitly models aero-engine domain knowledge at two levels: "component-level static physical topology" and "sensor parameter-level essential mechanism correlation," achieving accurate RUL prediction guided by domain knowledge. A dynamic and static dual-graph construction strategy is designed to achieve high-fidelity embedding of multi-level domain knowledge, embedding domain knowledge at both the aero-engine component structure and sensor parameter levels. On one hand, based on the engine's physical topology, a static graph is constructed with components as nodes and physical correlations between components as edges to capture macroscopic and stable causal paths of performance degradation propagation. On the other hand, combining the engine's actual operating mechanism and time-series monitoring data, a dynamic evolution graph of sensor parameters is constructed with sensor parameters as nodes and correlations between sensor parameters integrated into the mechanism as edges to reflect local, time-varying parameter correlations, effectively avoiding the risk of "spurious correlations" introduced by existing methods. A dual-flow graph joint learning network is proposed to extract spatiotemporal degradation features of the engine's gas path. To effectively extract engine degradation information from specific dynamic and static graphs, a targeted feature extraction and adaptive fusion model was constructed. Specifically, a multi-hop graph attention network captures component-level features sensitive to performance limits (RUL) from the static component association graph using a multi-hop attention mechanism, reflecting the impact of component degradation on the RUL of aero-engines. A gated graph-temporal attention network combines the characteristics of gating networks, graph attention, and temporal attention, while also considering the spatial coupling and temporal evolution of sensor data. This enables the extraction of sensor-level RUL-sensitive features from dynamic sensor graphs, reflecting the impact of coupled changes in engine airflow operating characteristic parameters on RUL. Furthermore, a self-attention-enhanced feature alignment module is used to adaptively fuse two types of key degradation features, obtaining more comprehensive and representative multi-level engine degradation features, significantly improving the accuracy and robustness of RUL prediction. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall structure and sensor measurement point arrangement of a typical dual-rotor turbofan engine; Figure 2 It consists of a component relationship diagram and a component relationship adjacency matrix; Figure 3 This is a qualitative relationship diagram of the FAN inlet / outlet cross-sectional parameters; Figure 4 This is a qualitative relationship diagram of the LPC / HPC outlet section parameters; Figure 5 This is a qualitative relationship diagram of the CC outlet section parameters; Figure 6 This is a qualitative relationship diagram of the HPT inlet / outlet cross-sectional parameters; Figure 7 This is a qualitative relationship diagram of LPT inlet / outlet cross-sectional parameters; Figure 8 It is a qualitative relationship diagram of shaft system parameters; Figure 9 It is a qualitative relationship diagram of sensor parameters based on the working mechanism of aero-engines; Figure 10 It is an adjacency matrix representing the qualitative relationship of sensor parameters; Figure 11 This is a schematic diagram of component-level association feature extraction in a multi-hop graph attention network; Figure 12 This is a schematic diagram of sensor parameter-level degradation feature extraction based on gated graph-temporal attention network; Figure 13 This is a schematic diagram of the GGAT unit structure; Figure 14 This is a schematic diagram of the self-attention enhanced feature alignment module; Figure 15 This is a schematic diagram of sliding window sampling; Figure 16 This is a schematic diagram of the RUL prediction results of the domain knowledge-enhanced dual-flow graph joint learning network on the C-MPASS dataset; Figure 17 This is a box plot of the prediction error distribution for four subsets of data. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Specific Implementation Method 1: Combination Figures 1 to 17 As shown, the present invention provides a method for predicting the remaining service life of an aero-engine based on a domain knowledge-enhanced dual-flow graph joint learning network, including collecting time series of sensor monitoring data of various engine components and dividing them into multiple data windows in chronological order, with each data window having a time step of w;

[0019] Obtaining static graph features: For the current data window, a one-dimensional convolutional network is used to extract features from the sensor monitoring data of each component to obtain the state features of each component; based on the structural characteristics of the aero-engine, a component relationship graph is established with components as nodes and physical connection relationships or airflow relationships between components as edges, and the component relationship adjacency matrix is ​​obtained; then, based on establishing connections between all nodes, a jump step number k is selected to obtain an adjacency matrix with a jump step number of k; a GAT network is used to extract features from the state features of all components and the adjacency matrix with a jump step number of k to obtain static graph features;

[0020] To obtain dynamic graph features: Based on the working mechanism of aero-engines, a qualitative relationship graph of sensor parameters is established with sensors as nodes and the mechanistic relationships between sensors as edges; simultaneously, a quantitative relationship graph of sensor parameters is established with sensors as nodes and the statistical correlation of sensor parameters in the current data window as edges; the qualitative and quantitative relationship graphs of sensor parameters corresponding to the current data window are adaptively fused to obtain a fused relationship graph and a sensor parameter relationship adjacency matrix; w gated graph attention units are configured, and the first gated graph attention unit is used to extract features from the sensor parameter relationship adjacency matrix and the sensor monitoring data of the first time step in the current data window to obtain the first time step features; each subsequent gated graph attention unit extracts features from the adjacent previous time step features, the sensor parameter relationship adjacency matrix, and the sensor monitoring data of the corresponding time step to obtain the corresponding time step features; the attention weights of the features of the first w-1 time steps and the w-th time step features are calculated, and the features of the first w-1 time steps are weighted and fused, and then combined with the w-th time step features to obtain dynamic graph features;

[0021] Feature Adaptive Fusion and RUL Prediction: A feature alignment network is used to map dynamic graph features and static graph features to the same feature space and then concatenate them; a self-attention module is then used to fuse the mapped and concatenated features to obtain fused features; a one-layer fully connected network is used to obtain the RUL prediction result of the aero-engine based on the fused features.

[0022] This implementation mainly comprises three parts: data preprocessing, dynamic and static graph construction based on two-level domain knowledge embedding, and comprehensive extraction of degradation features and RUL prediction based on a dual-flow graph joint learning network. Data preprocessing includes data normalization and time window sampling. The dynamic and static graph construction based on two-level domain knowledge embedding aims to decouple and perform high-fidelity representation of multi-layered domain knowledge of aero-engines. In the component static correlation graph construction, fixed physical correlations between various components are analyzed and qualitatively extracted based on the structural characteristics of the aero-engine. On this basis, a static graph is constructed with engine components as nodes and physical correlations between components as edges, macroscopically depicting the physical topology of the aero-engine at the component level and providing system-level, stable causal path constraints for degradation propagation. In the sensor parameter dynamic graph construction, based on qualitative analysis of the aero-engine's working mechanism and quantitative analysis of sensor data, through in-depth mining at both the qualitative (engine working mechanism) and quantitative (data correlation) levels, a dynamic graph is constructed with sensor parameters as nodes and correlations between parameters as edges, describing the dynamic evolution characteristics of sensor parameter relationships with the aero-engine's operating state. Specifically, at the qualitative level, based on the mass flow rate, pressure, and temperature transmission relationships of gas parameters at various cross-sections of the aero-engine during operation, and the sensor placement within the engine, the essential mechanistic relationships between sensor parameters are qualitatively revealed. Based on this, a sensor parameter graph is constructed, with sensor parameters as nodes and the essential mechanistic relationships between them as edges. At the quantitative level, statistical methods are used to deeply mine sensor data, quantitatively revealing the dynamic correlations between sensor parameters. Similarly, a sensor parameter graph is constructed, with sensor parameters as nodes and statistical correlations between them as edges. Finally, the qualitative and quantitative sensor parameter relationship graphs are adaptively fused to obtain the final dynamic graph of sensor parameter relationships. In the comprehensive extraction of multi-layer degradation features and RUL prediction steps based on the dual-flow graph joint learning network, a dual-flow graph joint learning network is designed according to the characteristics of the constructed dynamic graph and static graph. It consists of two parallel-connected improved graph attention sub-networks (i.e., multi-hop graph attention network and gated graph-temporal attention network) cascaded with a self-attention enhanced feature alignment module. It attempts to achieve parallel extraction and adaptive fusion of static and dynamic graph features in order to obtain more comprehensive and accurate engine degradation features, thereby achieving accurate prediction of the remaining service life of aero-engines.

[0023] Design of a Domain Knowledge-Enhanced Dual-Flow Graph Joint Learning Network Framework: Based on a dynamic-static graph construction strategy using two-layer domain knowledge embedding, the relationships between aero-engine components and between sensor monitoring parameters contain key information about the engine degradation process from different levels. Therefore, a static graph incorporating the physical relationships between engine components and a dynamic graph incorporating the mechanistic relationships between sensor parameters are constructed to accurately represent the actual relationships between engine components and sensor parameters, thereby correctly guiding the deep model in learning degradation features.

[0024] This embodiment combines Figure 1 As shown, the engine components include a fan (FAN), a low-pressure compressor (LPC), a high-pressure compressor (HPC), a high-pressure turbine (HPT), a low-pressure turbine (LPT), and a combustion chamber (CC). In the figure, 2 represents the FAN inlet section, 22 represents the FAN outlet section, 25 represents the LPC outlet section parameter, 3 represents the HPC outlet section parameter, 4 represents the CC outlet section parameter, 45 represents the HPT outlet section parameter, and 5 represents the LPT outlet section parameter.

[0025] In the component relationship diagram, the fan is connected to the low-pressure compressor, the low-pressure compressor is connected to the low-pressure turbine, the low-pressure turbine is connected to the high-pressure turbine, the high-pressure turbine is connected to the high-pressure compressor, and the high-pressure compressor is connected to the low-pressure compressor; the combustion chamber is connected to both the high-pressure compressor and the high-pressure turbine; the component relationship adjacency matrix is ​​as follows. The two-dimensional adjacency matrix is ​​used to assign values ​​to the elements in the component relationship adjacency matrix based on whether there are connections between the nodes in the component relationship graph. Elements corresponding to nodes with connections are assigned a value of 1, and elements corresponding to nodes without connections are assigned a value of 0.

[0026] Combination Figure 1 As shown, the engine can be described based on the physical connections between its components according to its overall structure: There are physical connections between the FAN, LPC, and LPT, and also between the HPC and HPT. Air drawn into the FAN is pressurized by the LPC and then flows directly into the HPC for further pressurization. Therefore, there is a direct physical connection between the LPC and HPC. After being pressurized by the high-pressure compressor, a portion of the gas flows into the CC to mix and burn with fuel. In other words, there is a direct airflow transmission relationship between the HPC and CC. The high-temperature, high-pressure gas flowing out of the CC flows directly into the HPT for expansion and work, thus there is also a direct physical connection between the CC and HPT. The gas flowing out of the HPT continues to flow into the LPT to do work, thus there is a direct physical connection between the HPT and LPT. Based on the physical connections between engine components, a component relationship diagram can be constructed, with components as nodes and physical connections or airflow relationships as edges, such as... Figure 2As shown. Figure 2 The adjacency characteristic means that the edges are fixed at the design level and will not change over time or under operating conditions. To transform this inherent connection logic into a numerical representation that can be learned by the model, a static adjacency matrix reflecting node associations needs to be constructed. First, each node is ordered and denoted as . , build Two-dimensional adjacency matrix Based on whether there is a connection between nodes, the corresponding elements in the matrix are assigned values. If node i and node j are related (i.e., an edge exists), then... =1, if no association exists. =0. Furthermore... =1, that is, considering the autocorrelation of nodes, we obtain the adjacency matrix that represents the knowledge of component association. This transforms the physical essence of the relationship between aero-engine components into a static graph that can be understood by the model. Then, the model learns from the design graph to accurately model and extract the dependencies between components.

[0027] Component-level spatial association feature extraction based on multi-hop graph attention network: Figure 12 This diagram illustrates the principle of component-level static graph feature extraction using a multi-hop graph attention network. First, sensor parameters are grouped according to component operating characteristics, and features are extracted from the grouped sensor monitoring data using a one-dimensional convolutional neural network (1DCNN) to obtain the state feature representation of each component. Then, an adjacency matrix representing multi-hop paths is constructed based on the component node connectivity relationships reflected in the static graph, capturing the global relationships between neighboring nodes. Finally, graph attention is used to filter key paths or nodes, achieving deep feature extraction from the static graph. The detailed process is described below.

[0028] Static graph component information embedding: In the described component-level static relationship graph, each component is represented by a name. Considering that each component contains multiple sensors to express its performance, each node in the component-level static graph can be represented by the multi-sensor parameter data contained in the corresponding component, as shown in Table 1. To ensure that all node vectors have the same dimension, one-dimensional convolution is used to map the multi-sensor data contained in each component to the same-dimensional embedding space.

[0029] ,in, This represents the multi-sensor data corresponding to the q-th component. Indicates the number of sensors. Let q represent the feature vector of the compressed component q. This represents a one-dimensional convolution. By extracting features from the sensor data of each component, a feature set of engine components is obtained. ,in, This refers to the number of components.

[0030]

[0031] Static Graph Feature Extraction Based on Multi-hop Graph Attention Network: The various components of an aero-engine are closely interconnected, with each component influenced by others to varying degrees. Therefore, a multi-hop graph attention network is designed to capture the dependencies between global nodes in the static graph and employs an attention mechanism to dynamically filter critical paths or neighbors. The structure of the multi-hop graph attention network is as follows: Figure 11 As shown, the specific feature extraction process is described in detail below:

[0032] First, the adjacency matrix of the static graph Defined as an adjacency matrix with 1 jump step The adjacency matrix representation of multi-hop paths is obtained by using matrix exponentiation.

[0033] The method for determining the number of jump steps k is as follows: the adjacency matrix of component relationships is defined as the adjacency matrix with a jump step of 1. Then the adjacency matrix of the jump step number k for: Starting from k=2, values ​​are taken sequentially and the calculation is performed iteratively. ,until Given that all elements in the set are non-zero, determine the number of jump steps k. The adjacency matrix representing the number of jump steps k. The (i,j)th element represents the number of paths from node i to node j with a length less than or equal to k. The value of k is chosen based on whether all nodes are connected. There are no elements in the array that are zero.

[0034] Furthermore, the GAT network is used to extract features from the state features of all components and the adjacency matrix with k jump steps to obtain static graph features. The method is as follows: a graph convolutional network is used to extract the state features of all components and the basic association features of the adjacency matrix with k jump steps; a difference operation is performed on the adjacency matrix with k jump steps based on a multi-head attention mechanism to obtain the new path for each hop; a linear transformation is performed on the concatenated features of the new path for each hop and the corresponding start and end nodes, and the LeakReLU activation function is used to obtain the path importance score; the path importance score is normalized to obtain the path attention weight; all path attention weights are concatenated and processed by the Tanh activation function and pooling layer to obtain the static graph features.

[0035] The attention weights of each path from node i to its neighbor node j within k hops are calculated using a graph attention mechanism, thereby enabling the model to focus on more important node path relationships. The calculation process is as follows:

[0036] ,

[0037] in, This represents the path attention weight from node i to its neighbor node j. Let K represent the feature vector of component i, K represent the number of hops when all nodes are connected, and N represent the total number of nodes. It is an all-zero matrix. Then, multi-head attention is combined to capture the feature interactions between nodes from different perspectives. By splicing the outputs of multiple heads, the expressive power of the feature space is enriched.

[0038] ,

[0039] Where M is the total number of attention heads, It is the path attention weight captured by the m-th attention head from node i to its neighbor node j within k hops. It is the linear transformation weight of the m-th attention head.

[0040] Finally, a fully connected layer is used to perform dimensionality transformation on the attention-weighted features to obtain the final component-level associated features. ,in, This represents the weighted characteristics of each node. This represents the feature vector extracted by MGAT. This indicates the computation process of the fully connected layer.

[0041] In summary, by increasing the number of hop steps, long-distance interactions between nodes that are not directly connected can be ensured, thus enabling the reception of information from important multi-hop nodes. Furthermore, through an adaptive hop count decay factor and cumulative effect, nodes with smaller spans or higher importance receive higher attention weights. Multi-hop graph attention networks effectively overcome the dependence of traditional graph models on local neighborhoods, achieving efficient modeling of long-distance dependencies and complex relationships in graph structures.

[0042] Construction of a Dynamic Sensor Parameter Graph Based on Sensor Parameter-Level Association Knowledge Embedding: During aero-engine operation, the dependencies between sensor parameters are affected by factors such as changes in operating conditions and component degradation, exhibiting certain dynamic time-varying characteristics. To accurately capture this characteristic, a dynamic graph is used to represent it. Through detailed analysis of engine operating characteristics, the essential mechanistic relationships between sensor parameters are qualitatively revealed, representing the mechanistic constraints that sensor parameters must follow. Simultaneously, based on the changing trends of sensor-collected data over time, cosine similarity is used to measure the dynamic correlation between sensor parameters in different time periods, representing the dynamic evolution of the relationships between sensor parameters as the engine degrades. Finally, the sensor parameter relationships obtained from qualitative and quantitative analyses are adaptively fused to obtain a domain-knowledge-enhanced dynamic sensor parameter graph that both adheres to the basic principles of engine operation and accurately represents the dynamic evolution of the relationships between monitoring parameters during engine degradation.

[0043] In the qualitative relationship diagram of sensor parameters, the mechanism relationship between sensors is constructed based on the mass flow rate, pressure and temperature transmission relationship of gas parameters at various cross sections of the aero-engine during operation, combined with the sensor's placement position in the engine. In the quantitative relationship diagram of sensor parameters, cosine similarity is used to measure the statistical correlation of correlated sensor parameters, which is used to characterize the dynamic evolution of the correlation between sensor parameters as the engine degrades.

[0044] Figure 1 The sensor measurement point layout of a typical twin-rotor turbofan engine is described, with vertical dashed lines indicating the location and number of the inlet and outlet cross-sections of each component. In the qualitative analysis of the mechanistic relationship between the sensor measurement points at each cross-section, the following assumptions are made: the gas is a complete gas, the flow is one-dimensional and steady, and the airflow has its own isobaric specific heat capacity, isovolumetric specific heat capacity, and specific heat ratio as it flows through the inlet, fan, compressor, turbine, and exhaust nozzle. Furthermore, to better reflect real-world applications, the segmented isobaric specific heat calculation process of a mixed-exhaust turbofan engine is selected for analysis.

[0045] FAN outlet section parameters: Ambient air is drawn into the engine through the intake duct by the FAN, which is an adiabatic isentropic deceleration and pressurization process. The fan does work on the drawn-in air, increasing the airflow pressure and temperature, which is an adiabatic isentropic pressurization process. Therefore, the calculation process for the total temperature and total pressure of each section of the FAN, LPC, and HPC can be expressed as follows:

[0046] , , , ;in, , These represent the gas temperature and pressure at the inlet outlet section, respectively. , These represent atmospheric static pressure and static temperature, respectively, which can be calculated based on flight altitude. , These represent the FAN outlet temperature and outlet pressure, respectively. The total pressure recovery coefficient of the air intake is determined by the flight Mach number M. k represents the adiabatic index of the air. This indicates the adiabatic efficiency of the FAN. This indicates the boost ratio of the fan, and its magnitude is related to the fan speed. Positive correlation. Based on the above derivation process, a qualitative relationship diagram of the fan inlet and outlet cross-sectional parameters can be constructed, such as... Figure 3 As shown.

[0047] LPC / HPC outlet section parameters: The function of the compressor is to further pressurize the air drawn in through the FAN component to obtain high-pressure gas. Compressors include LPC and HPC. The pressurization of gas by the compressor is also an adiabatic isentropic compression process. The total temperature and total pressure of each section of the LPC and HPC can be expressed by the following functional relationship:

[0048] , , , ,

[0049] in, , These represent the temperature and pressure at the outlet of the low-pressure compressor, respectively. , These represent the temperature and pressure at the HPC outlet, respectively. , These represent the efficiencies of LPC and HPC, respectively. , These represent the boost ratios of LPC and HPC, respectively, and their magnitudes are related to the spindle speed (rotor speed). Positive correlation. Based on the derivation process of LPC and HPC parameters, a relationship diagram can be constructed as shown in Figure 4.

[0050] CC outlet cross-sectional parameters: Most (approximately 70%-80%) of the high-pressure gas directly enters the CC and mixes with the fuel for combustion, forming high-temperature, high-pressure gas at the CC outlet. The combustion process can be considered an isentropic, isobaric combustion process. Based on the CC energy balance relationship, we can obtain: ,in, Indicates the CC outlet temperature. This indicates the mass flow rate of the gas exiting the compressor. This indicates the fuel mass flow rate. , These are the specific heat capacities at constant pressure for fuel gas and air, respectively. For CC combustion efficiency, This indicates the lower calorific value of the fuel. The total temperature and total pressure at the CC outlet can be deduced as follows:

[0051] , ;

[0052] in, Represents a mathematical function. This indicates the oil-to-gas ratio. This indicates export pressure on CC. This represents the pressure recovery coefficient of CC. From this, a qualitative relationship diagram regarding the parameters of the CC outlet section can be constructed, such as... Figure 5 As shown.

[0053] HPT inlet / outlet cross-sectional parameters: The high-temperature, high-pressure gas flowing out of the CC outlet directly enters the HPT for expansion and work, converting the thermal and pressure energy of the gas into mechanical energy to drive the operation of components such as the HPC. Based on the energy balance relationship before and after mixing of the high-temperature gas and cooling gas in the HPT, and the power balance relationship of the high-pressure rotor, we can obtain:

[0054] , ,

[0055] in, This indicates the temperature of the mixed gas inside the HPT. This indicates the HPT outlet temperature. This indicates the mass flow rate of the gas discharged from CC. Indicates the mass flow rate of the mixed gas. This represents the relative cooling air volume of the HPT. Therefore, the total temperature at the HPT outlet can be calculated: ;

[0056] The total pressure at the HPT outlet can be obtained from the relationship between temperature and pressure changes during the isentropic expansion process:

[0057] ;

[0058] in, Represents the gas constant. This indicates HPT export pressure. .

[0059] Therefore, a qualitative relationship diagram regarding the inlet / outlet cross-sectional parameters of the HPT can be constructed, such as... Figure 6 As shown.

[0060] LPT inlet / outlet cross-sectional parameters: Similar to the HPT calculation process, the total LPT outlet temperature can be obtained based on the energy conservation of the mixed gas and the power balance of the low-pressure rotor.

[0061] , ,

[0062] in, This indicates the temperature of the mixed gas inside the LPT. This represents the gas mass flow rate at the HPT outlet section. This indicates the mass flow rate of the mixed gas inside the HPT. This indicates the relative amount of cooling air in the LPT. This represents the LPT outlet temperature. Further derivation can be made as follows: .

[0063] Similarly, the total pressure at the LPT outlet can be obtained from the relationship between temperature and pressure changes during the isentropic expansion of the gas:

[0064] , ;in, This represents the LPT outlet pressure. Based on the above process, the relationship between the LPT inlet / outlet cross-sectional parameters can be obtained, as shown in the diagram. Figure 7 As shown.

[0065] Rotor parameters: For low-pressure rotors, the required speed Physical speed and correction speed All of these are implemented by the controller. Using the actual speed as the reference point, we can conclude that: ;in, Adjust FAN speed to meet demand. This represents a mathematical function. Similarly, for a high-voltage rotor, its physical velocity... It can also be expressed as correction speed. Functions: Therefore, a diagram showing the relationship between the operating characteristics of the high-pressure rotor and the low-pressure rotor can be constructed, such as... Figure 8 As shown.

[0066] Based on the above analysis, the mechanistic relationships between the gas parameters at the inlet / outlet sections of each component were extracted. To more clearly describe the mechanistic relationships between different sensor parameters, a system was constructed as follows: Figure 9 The diagram showing the relationship between sensor parameters also includes an adjacency matrix that reflects the essential relationship between the sensor parameters. ,like Figure 10 As shown. It is worth noting that, It remains constant throughout the degradation process of aero-engines, providing constraints on the working mechanism of aero-engines for monitoring the evolution of the correlation between parameters.

[0067] Construction of Sensor Parameter Maps Based on Quantitative Analysis: Time-series data acquired by sensors directly reflects the engine's operational health status; therefore, it is necessary to quantitatively analyze the correlations between sensor parameters at the data level. As engine health deteriorates, the monitoring data acquired by sensors also changes, resulting in the connections or dependencies between variables in the time-series data not being fixed but changing over time. Furthermore, aero-engine degradation is a slow and long-term process, meaning that the dependencies between sensor variables change smoothly rather than drastically over time. In other words, similar or identical variable dependencies exist between adjacent time steps.

[0068] To accurately capture this dynamic correlation, it is assumed that the correlation of variables remains constant within a time period, but evolves between adjacent time periods. Based on this assumption, multivariate time series data collected by sensors can be grouped according to sliding time windows. Then, the statistical correlation between different variables within each subsequence can be analyzed, and a corresponding quantitative relationship graph structure of sensor parameters can be constructed. Therefore, real-time changes in monitoring data can be reflected in the dynamic updates between sensor parameters in real time. For a given multivariate time series... Where T represents the total length of the time series and M represents the number of variables, the specific process of constructing the quantitative relationship diagram of sensor parameters is as follows.

[0069] First, using a time sliding window of size l and a movement step of 1, The sequence is divided into several subsequences according to time order. The l-th subsequence is represented as... Secondly, the statistical correlation between variables within each subsequence is calculated. The cosine distance, which is more sensitive to the trend of time series changes, is chosen to measure the statistical correlation between different variables in each subsequence. The i-th sensor parameter sequence in the l-th subsequence is defined as... (in (This shows the value of the i-th sensor parameter at time step t). Then, the cosine similarity between any two sensor parameter sequences is calculated: ,in, These represent the time series corresponding to the i-th and j-th sensor parameters in the n-th subsequence, respectively. The cosine distance between the i-th and j-th sensor variables in the n-th subsequence is used to characterize their statistical correlation.

[0070] Finally, for each subsequence, using sensor variables as nodes and the statistical correlations between variables as edges, a quantitative relationship graph of sensor parameters is obtained. The adjacency matrix corresponding to the l-th time window is shown below. It can be represented as:

[0071] , ,

[0072] in, This represents the adjacency matrix corresponding to the graph structure of the nth subsequence. This represents the edge between the i-th and j-th variables in the n-th subsequence, i.e., statistical correlation.

[0073] Adaptive fusion of qualitative and quantitative sensor parameter graphs: The method for obtaining the fused relationship graph is as follows: using a learnable matrix. The complement of the learnable matrix Dynamic weights are assigned to the qualitative and quantitative relationship graphs of sensor parameters respectively, and then weighted summation is performed. The result of the weighted summation is normalized to obtain the fused relationship graph. The sensor parameter relationship adjacency matrix is ​​obtained based on the fused relationship graph.

[0074] The sensor parameter map based on qualitative analysis (qualitative map) reflects the mechanistic correlation of sensor parameters, while the sensor parameter map based on quantitative analysis (quantitative map) reflects the dynamic evolution of the correlation between monitored variables as the engine state changes. To organically combine the advantages of both, an adaptive fusion mechanism is designed to fuse the qualitative and quantitative relationship maps of sensor parameters, and to perform mechanistic consistency calibration and enhancement on the statistical correlation in the quantitative map. This ensures that the dynamic evolution of the correlation of sensor parameters strictly follows the working mechanism characteristics of the engine, effectively suppresses spurious correlations that may be introduced by data noise, and thus achieves dynamic synergy and complementary enhancement of mechanistic knowledge and data characteristics. The calculation process of the adaptive fusion mechanism is as follows.

[0075] ,

[0076] in, This represents the final sensor parameter association adjacency matrix corresponding to the parameters in time window n. Adjacency matrix reflecting the essential relationship between sensor parameters and mechanisms. Let represent the statistical correlation adjacency matrix corresponding to the parameters in the time window n. Represents a learnable matrix for dynamic adjustment. and The fusion weight, This indicates 0-1 normalization. This indicates the Hadamard product calculation, which is the multiplication of elements in the same position of a matrix.

[0077] Sensor Parameter-Level Degradation Feature Extraction Based on Self-Attention Enhanced Feature Alignment Module: The topology of dynamic graphs changes over time, reflecting the dynamic evolution of the spatial dependence of sensor parameters during aero-engine degradation. Therefore, a gated graph-temporal attention network is designed to process the dynamic graph, such as... Figure 12 As shown in the diagram, each node in the dynamic graph represents a sensor parameter, and the feature vector of each node is the time-series data collected by that sensor. The Gated Graph-Temporal Attention Network mainly consists of two parts: Gated Graph Attention (GGAT) and Temporal Attention (TAM). On the one hand, GGAT achieves accurate capture of both the spatial and temporal dependencies of sensor parameters by fusing graph attention mechanisms with gated recurrent units. On the other hand, by introducing a temporal attention mechanism, it focuses on timestamps containing key degradation information while suppressing unimportant timestamps.

[0078] like Figure 13 As shown, GGAT implements time-series data processing through a chain-like connection structure. Each unit processes data corresponding to a single timestamp, and multiple units are chained together in chronological order to construct a time-dimensional information transmission channel. Forget gates and reset gates are used to transmit and update key information between time steps, thereby capturing the temporal dependencies of node vectors in the dynamic graph. Given a sequence of dynamic graphs... ,in, This represents the data sampled in the l-th time window. This indicates the total number of time windows for sampling. Let represent the value of the i-th sensor at time j, M represent the total number of sensors, and w represent the length of the time window. Let represent the adjacency matrix of the dynamic graph corresponding to the l-th time window. The detailed process of feature extraction using a gated graph-temporal attention network is described below.

[0079] The method for obtaining the features of the w-th time step by the w-th gated graph attention unit is as follows: extract the spatial correlation features of the sensor parameter relationship adjacency matrix and the sensor monitoring data of the w-th time step through the graph attention network, and simultaneously extract the spatial correlation features of the features of the (w-1)-th time step and the sensor parameter relationship adjacency matrix through the graph attention network. After weighted summation by the corresponding reset gate weight matrix, a linear transformation and Sigmoid activation are performed to obtain the reset gate.

[0080] The graph attention network extracts the spatial correlation features of the sensor monitoring data at the w-th time step and the adjacency matrix of the sensor parameters. At the same time, the graph attention network extracts the spatial correlation features of the features at the (w-1)-th time step and the adjacency matrix of the sensor parameters. After weighted summation by the corresponding update gate weight matrix, a linear transformation and sigmoid activation are performed to obtain the update gate.

[0081] The spatial correlation features of the sensor monitoring data at the w-th time step are extracted using a graph attention network. Simultaneously, the spatial correlation features of the sensor parameter adjacency matrix, the features at the (w-1)-th time step, and the Hadamard product of the reset gate are also extracted using the graph attention network. These are then weighted and summed using the corresponding hidden state weight matrix, and a nonlinear transformation is performed using the tanh activation function to obtain the w-th hidden state. Finally, the w-th time step feature is obtained by adding the Hadamard product of the update gate and the features at the (w-1)-th time step, and the Hadamard product of the complement of the update gate and the w-th hidden state.

[0082] First, use GGAT to... Spatiotemporal features are extracted from each time step within the data. For the graph data sampled in the l-th time window... It needs to be divided into w subgraphs according to the time step order (these subgraphs share the same adjacency matrix). These subgraphs are then sequentially input into the corresponding GGAT units for processing. The subgraph at time t consists of the multi-sensor readings and adjacency matrix at time t. Composition. That is, the input of the GGAT unit corresponding to the t-th time step includes multi-sensor readings. Adjacency matrix and the output characteristics of the previous unit The specific calculation process for the reset and update gates of the GGAT unit is as follows.

[0083] , ,

[0084] in, , These represent the outputs of resetting and updating the gate at time t, respectively. This illustrates the computational process of a graph attention network. and It is the weight matrix for resetting and updating gates. This indicates resetting the door's offset. Current hidden state. The calculation is as follows:

[0085] , ,

[0086] in, This represents the original hidden state at time t, without incorporating historical time information. Let represent the final hidden state at time t. and It is the weight matrix of the hidden state. It can be found that after GGAT processing, the spatiotemporal features corresponding to each time point within the l-th time window can be obtained.

[0087] The attention weights of the features at the first w-1 time steps relative to the feature at the w-th time step are calculated using a temporal attention mechanism. The features at the first w-1 time steps are then weighted and fused to obtain the fused features at the first w-1 time steps. The fused features at the first w-1 time steps are then concatenated with the feature at the w-th time step, and after linear transformation and Softmax activation, the dynamic graph features are obtained.

[0088] A temporal attention mechanism is used to adaptively adjust the importance of features extracted by GGAT at each time step. Specifically, the temporal attention mechanism automatically assigns higher weights to time step features that have a significant impact on RUL, while assigning lower weights to time step features that have a less significant impact on RUL. This allows the model to automatically focus on extracting features containing key degradation information, such as... Figure 12 As shown in the figure. The specific calculation process of the temporal attention mechanism is as follows.

[0089] , , ,

[0090] in, express Hiding the state at all times is important Temporal attention weights that hide the state at all times. Let be a linear transformation matrix. Indicates weighted The hidden state at all times Let be a linear transformation matrix. This represents the feature vector extracted by the gated graph-temporal attention network. This represents a fully connected layer network. The above steps enable the comprehensive extraction of dynamic features from the sensor image.

[0091] Comprehensive Extraction of Aero-engine Degradation Features and RUL Prediction Based on Dual-Stream Graph Joint Learning Network:

[0092] To efficiently extract and fuse multi-scale degradation features from heterogeneous static and dynamic graphs, a dual-flow graph joint learning network uses component-level static graphs and sensor parameter-level dynamic graphs as dual inputs to achieve parallel extraction and adaptive fusion of graph features at different levels. The constructed dual-flow graph joint learning network consists of two parallel-connected improved graph attention sub-networks (i.e., a multi-hop graph attention network and a gated graph-temporal attention network) cascaded with a self-attention-enhanced feature alignment module. The multi-hop graph attention network branch processes component-level static graphs, aiming to capture the macroscopic dependencies between components determined by physical topology. The gated graph-temporal attention network branch processes dynamic sensor graph sequences, aiming to simultaneously consider the spatial coupling and temporal evolution of parameters. Finally, the feature representations extracted by the two branches are fed into the self-attention-enhanced feature alignment module for adaptive fusion to obtain a more comprehensive and physically meaningful degradation feature representation for RUL prediction.

[0093] Static graph features extracted using a multi-hop graph attention network and a gated graph-temporal attention network. and dynamic graph features Focusing on different levels of aero-engine degradation information, these two types of features exhibit significant heterogeneity. Direct feature fusion can lead to confusion in the physical meaning of the original information and distortion of important details. Therefore, to effectively fuse the rich degradation information contained in these two types of features to obtain more comprehensive and representative degradation features, a feature alignment method is employed. This method uses a self-attention-enhanced feature alignment module to achieve adaptive fusion and RUL prediction of static and dynamic graph features. This module comprises two parts: a feature alignment network and a self-attention network. Figure 14 As shown. The feature adaptive fusion and RUL prediction process based on the self-attention enhanced feature alignment module is described below:

[0094] The method for obtaining the mapped spliced ​​features using the feature alignment network is as follows: two fully connected networks with shared parameters and identical structures are used to map dynamic graph features and static graph features to the same feature space, and then spliced ​​together to obtain the mapped spliced ​​features. By mapping two types of features to the same space sensitive to aero-engine degradation information through the feature alignment network, the heterogeneity of features originating from different mechanistic levels is eliminated. The feature alignment network consists of two fully connected networks with shared parameters and identical structures. ,in, This represents the computation process of the fully connected layer. This indicates feature splicing.

[0095] Finally, by leveraging the self-attention mechanism to enhance the core value information related to aero-engine degradation in the enhanced features, the feature components related to aero-engine degradation can be dynamically strengthened while suppressing irrelevant noise or redundant information. The self-attention module uses a linear transformation function of the query vector to map the mapped concatenated features into the query vector required by the attention mechanism. A linear transformation function for key vectors is used to map the concatenated features after mapping to the key vectors required by the attention mechanism. A linear transformation function of value vectors is used to map the concatenated features after mapping into the value vectors required by the attention mechanism. ;

[0096] ,

[0097] The fusion features are represented as : ,

[0098] In the formula Key vector The dimension; Its purpose is to prevent gradient explosion.

[0099] The RUL prediction results for aero-engines are expressed as... : ,

[0100] In the formula It is a fully connected layer network. This is the Sigmoid activation function.

[0101] Validation Experiment: The effectiveness and superiority of the domain knowledge-enhanced dual-flow graph joint learning network were validated using the publicly available C-MAPSS turbofan engine degradation dataset provided by NASA. The C-MAPSS dataset accurately reflects the degradation characteristics of aero-engines under various degradation modes and has been used in several studies to validate methods for predicting remaining useful life (RUL). As shown in Table 2, the C-MAPSS dataset contains four subsets: FD001, FD002, FD003, and FD004. Each subset consists of a training set and a test set. The training set records monitoring data corresponding to the complete lifecycle of an aero-engine, i.e., the engine from normal operation to the end of its life. The test set records many instances of incomplete data where the engine ended before a failure, i.e., the engine started from normal operation and ended at some point before the failure; their RUL is unknown.

[0102]

[0103] Data Preprocessing: Data Normalization and Target RUL Label Standard: The original dataset is normalized according to the operating conditions. First, density-based clustering is used to cluster data corresponding to the same operating condition together. Then, z-score normalization is applied to normalize the data in each class. Finally, the normalized data in each class are rearranged according to the original operating condition order to obtain the normalized dataset. Furthermore, to better simulate the change of RUL over time, a common piecewise linear function is used to construct the RUL labels, as shown below:

[0104] Where R represents the total runtime of the faulty instance, and t represents the current time. The initial RUL representing the faulty running instance is set to 125.

[0105] Time window sampling: A time window of fixed length w is used to slide the sensor data with a step size of 1, so that each sample contains information of the current time step and the previous w-1 time steps. Figure 15 The time window processing operation is shown. Table 1 shows the time window length for each subset, which is beneficial for RUL prediction on the C-MAPSS dataset.

[0106] Evaluation metrics: Two common metrics (i.e., score and root mean square error (RMSE)) were used to evaluate the prediction performance of the domain knowledge-enhanced dual-flow graph joint learning network on the C-MAPSS dataset, and their calculation formulas are as follows.

[0107] , ,

[0108] Where M is the number of test samples. Let be the prediction error for the i-th sample.

[0109] Hyperparameter settings: Different hyperparameter settings affect the feature learning ability and RUL prediction performance of the domain knowledge-enhanced dual-flow graph joint learning network. Therefore, a grid search method is used to determine the key hyperparameters, and the core hyperparameters related to the model architecture are shown in Table 3. Hyperparameters related to optimization are used to define the training process and are briefly described below. The learning rate is 0.005 in the first epoch and then decays with a coefficient of 0.95 every 5 epochs to quickly converge to the optimal solution. Dropout regularization is used to reduce overfitting and improve test performance. The batch size is set to 512, and the training epochs are set to 100. Finally, all hyperparameters of the domain knowledge-enhanced dual-flow graph joint learning network are fed into the Adam optimizer for updating. Furthermore, an early stopping strategy is designed to improve training efficiency; training is terminated once the number of training epochs reaches 100, or if the validation loss does not decrease within the next 10 epochs. The number of aero-engines in the training set of each subset is divided into a training sample set and a validation sample set in an 8:2 ratio. The test sample set is constructed from the test engines in each subset, as shown in Table 2. The training sample set is used to train the domain knowledge-enhanced dual-flow graph joint learning network, the validation sample set is used to select the optimal hyperparameters, and the test sample set is used to evaluate the prognostic performance of the trained domain knowledge-enhanced dual-flow graph joint learning network.

[0110] Table 3 Hyperparameter settings for domain knowledge-enhanced dual-flow graph joint learning network

[0111]

[0112] Experimental Results and Analysis:

[0113] RUL prediction results for the C-MAPSS dataset: Figure 16This paper presents a comparison between the predicted RUL and the actual RUL obtained by the domain knowledge-enhanced dual-flow graph joint learning network for each subset of datasets. It can be observed that the developed domain knowledge-enhanced dual-flow graph joint learning network exhibits high prediction accuracy and excellent prediction performance. Specifically, for FD001 and FD003, within the allowable upper and lower limits, the predicted RUL is highly consistent with the actual RUL, with very small prediction errors. For FD002 and FD004, there are certain differences between the predicted and actual RUL for a few engines, leading to significant local fluctuations in the predicted RUL, especially in FD004. The main reason is that FD002 and FD004 contain multiple operating conditions, making the collected monitoring data more complex. In this case, some degradation characteristics are easily overwhelmed by non-stationary operating conditions, thus reducing the prediction results. Furthermore, it can be observed that the prediction error in the early operating phase of an aero-engine is generally greater than the error in the later operating phase, meaning that predicting the RUL of an aero-engine in the early stages is much more difficult, especially when the aero-engine is in its initial health state. The main possible reason is that the health status of aircraft engines tends to remain almost unchanged in the early stages of operation, making it difficult and unnecessary to accurately predict RUL at this stage.

[0114] Figure 17 Box plots showing the error distribution between predicted and actual RULs on four subsets are presented. It can be seen that the median and mean of the prediction errors for the four subsets are essentially zero. Except for a few outliers, the box plots are relatively short, indicating a more concentrated error distribution with a smaller range. Therefore, the experimental results again demonstrate that the domain knowledge-enhanced dual-flow graph joint learning network has good RUL prediction accuracy and generalization ability. Due to the influence of non-stationary conditions, there are some outliers in the error distributions of FD002 and FD004, but the overall prediction results remain relatively stable.

[0115] Comparative Experiment Analysis: To further demonstrate the superior performance of the domain knowledge-enhanced dual-flow graph joint learning network model, it is compared with eight state-of-the-art RUL prediction methods to comprehensively evaluate its superiority and effectiveness. The eight RUL prediction methods can be broadly categorized into the following three types:

[0116] 1) Three mainstream deep learning-based prediction methods: DDCN, LSTM and Transformer.

[0117] 2) Two methods based on graph neural networks and their variants: GCN and GGCN.

[0118] 3) Three prediction methods based on domain knowledge enhancement: KGHM, KDnet-RUL and NSD-TGTN.

[0119] Table 4 compares the prediction results of the domain knowledge-enhanced dual-flow graph joint learning network with eight other state-of-the-art (SOTA) methods on both RMSE and Score. Double underlines represent the best prediction results, and underlines represent the second-best results. It can be observed that the domain knowledge-enhanced dual-flow graph joint learning network achieves best or second-best results on all four datasets, indicating a significant advantage over the nine prognostic methods. Compared to the other eight prognostic methods, the domain knowledge-enhanced dual-flow graph joint learning network significantly reduces the RMSE score on all four datasets, particularly on FD002 and FD004. For example, the domain knowledge-enhanced dual-flow graph joint learning network achieved RMSE scores of 11.67, 12.93, 11.90, and 13.57 on FD001, FD002, FD003, and FD004, respectively. Specifically, these scores were 0.15 (1.27%), 0.32 (2.42%), 0.11 (0.92%), and 2.39 (14.97%) lower than the best scores obtained by the eight comparative methods. This indicates that the domain knowledge-enhanced dual-flow graph joint learning network has good RUL prediction ability. Regarding the score, the domain knowledge-enhanced dual-flow graph joint learning network significantly outperformed other comparative methods on FD002 and FD004. Compared with the second-best methods, the domain knowledge-enhanced dual-flow graph joint learning network reduced its score by 184.45 (19.85%) and 342.05 (25.25%). On FD001 and FD003, the Score achieved sub-optimal prediction results among the nine methods, with only a small gap compared to the best method. The lower score indicates a lower proportion of delayed predictions, meaning the developed domain-knowledge-enhanced dual-flow graph joint learning network is beneficial in addressing delayed prediction problems. This is crucial for RUL prediction of aero-engines, as delayed predictions often have more severe consequences than early predictions. It's worth noting that FD002 and FD004 involve various operating conditions, leading to significant local fluctuations in sensor parameter trends, making it more difficult to capture engine degradation characteristics. In this situation, due to the influence of non-steady-state operating conditions, many RUL prediction methods fail to effectively capture valid degradation characteristics, resulting in poor prediction performance. In contrast, the domain-knowledge-enhanced dual-flow graph joint learning network combines engine domain knowledge with dynamic and static graph features, effectively capturing aero-engine degradation trend information and representative features, enabling it to still achieve very good prediction results on FD002 and FD004. Therefore, the experimental results show that, compared with other methods, the domain knowledge-enhanced dual-flow graph joint learning network exhibits better robustness, and its prediction performance is almost unaffected by non-steady-state operating conditions, making it more suitable for RUL prediction in practical engineering.

[0120] Table 4 Comparison of prediction results of various methods on the C-MPASS dataset

[0121]

[0122] This invention enhances the dual-flow graph joint learning network with domain knowledge, allowing for the introduction and full utilization of aero-engine domain knowledge. It guides the extraction of degradation features through both dynamic and static dimensions, making the learned high-level degradation features more representative and interpretable. Specifically, firstly, based on an in-depth analysis of the aero-engine's overall structure and operating mechanism, the inherent physical relationships between different components and the mechanistic relationships between different sensor parameters are uncovered. Then, based on the uncovered domain knowledge at the component and parameter levels, static graphs reflecting the causal paths and physical topology of engine components and dynamic graphs reflecting the dynamic relationships of sensor parameters are constructed, respectively, achieving high-fidelity embedding of multi-level domain knowledge of the engine. Finally, based on the constructed dual-flow graph joint learning network, rich aero-engine degradation features are extracted simultaneously from both the static and dynamic graphs. A self-attention-enhanced feature alignment module is used to achieve multi-level feature aggregation, thereby enabling accurate prediction of RUL (Regression Limiting Parameter).

[0123] A series of comparative experiments on the C-MAPSS dataset verified the effectiveness and superiority of the proposed method. Experimental results show that the domain knowledge-enhanced dual-flow graph joint learning network achieved best or near-best prediction performance on four subsets of the dataset, compared to eight state-of-the-art prediction methods. More importantly, the domain knowledge-enhanced dual-flow graph joint learning network significantly improved prediction performance under various degradation modes and unsteady operating conditions. This indicates that the combination of domain knowledge and the dual-flow graph joint learning network enables it to effectively capture degradation information reflecting the actual degradation state of the engine in harsh operating environments, thereby enhancing its robustness and anti-interference capabilities.

[0124] Improving the RUL prediction performance of aero-engines has been a long-standing challenge. While the developed domain-knowledge-enhanced dual-flow-graph joint learning network has shown promising results on the C-MAPSS dataset, its limitations must be considered: the C-MAPSS dataset may not be able to replicate all variables and extreme cases encountered in real-world applications. Real-world data may include additional unknown and unmodeled factors that significantly impact aero-engine RUL prediction. Therefore, future research should focus on collecting more real-world aero-engine operational data under more complex operating conditions and failure modes to further validate the effectiveness of the domain-knowledge-enhanced dual-flow-graph joint learning network.

Claims

1. A method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network, characterized in that... include, Collect time series of sensor monitoring data for various engine components, and divide them into multiple data windows in chronological order, with w being the number of time steps for each data window; Obtain static graph features: For the current data window, a one-dimensional convolutional network is used to extract features from the sensor monitoring data of each component to obtain the state features of each component; Based on the structural characteristics of aero-engines, a component relationship graph is established with components as nodes and physical connections or airflow relationships between components as edges, and a component relationship adjacency matrix is ​​obtained. Then, based on establishing connections between all nodes, a jump step number k is selected to obtain an adjacency matrix with a jump step number of k. The GAT network is used to extract features from the state features of all components and the adjacency matrix with a jump step number of k to obtain static graph features. Obtain dynamic graph features: Based on the working mechanism of aero-engines, establish a qualitative relationship graph of sensor parameters with sensors as nodes and the mechanistic relationship between sensors as edges; at the same time, establish a quantitative relationship graph of sensor parameters with sensors as nodes and the statistical correlation of sensor parameters in the current data window as edges. The qualitative and quantitative relationship graphs of sensor parameters corresponding to the current data window are adaptively fused to obtain a fused relationship graph and a sensor parameter relationship adjacency matrix. w gated graph attention units are configured. The first gated graph attention unit extracts features from the sensor parameter relationship adjacency matrix and the sensor monitoring data of the first time step in the current data window to obtain the first time step features. Subsequently, each gated graph attention unit extracts features from the features of the adjacent previous time step, the sensor parameter relationship adjacency matrix, and the sensor monitoring data of the corresponding time step to obtain the corresponding time step features. Calculate the attention weights of the features at the first w-1 time steps and the features at the wth time step, then perform weighted fusion on the features at the first w-1 time steps, and finally combine them with the features at the wth time step to obtain the dynamic graph features. Feature Adaptive Fusion and RUL Prediction: A feature alignment network is used to map dynamic graph features and static graph features to the same feature space and then concatenate them; a self-attention module is then used to fuse the mapped and concatenated features to obtain fused features; A single fully connected network is used to obtain the RUL prediction results of aero-engines based on fusion features.

2. The method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network according to claim 1, characterized in that, The engine components include a fan, a low-pressure compressor, a high-pressure compressor, a high-pressure turbine, a low-pressure turbine, and a combustion chamber. In the component relationship diagram, the fan is connected to the low-pressure compressor, the low-pressure compressor is connected to the low-pressure turbine, the low-pressure turbine is connected to the high-pressure turbine, the high-pressure turbine is connected to the high-pressure compressor, and the high-pressure compressor is connected to the low-pressure compressor; the combustion chamber is connected to both the high-pressure compressor and the high-pressure turbine. The adjacency matrix of component relationships is The two-dimensional adjacency matrix is ​​used to assign values ​​to the elements in the component relationship adjacency matrix based on whether there are connections between the nodes in the component relationship graph. Elements corresponding to nodes with connections are assigned a value of 1, and elements corresponding to nodes without connections are assigned a value of 0.

3. The method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network according to claim 2, characterized in that, The method for determining the number of jump steps k is as follows: Define the adjacency matrix of component relationships as an adjacency matrix with a jump step of 1. Then the adjacency matrix of the jump step number k for: ， Starting from k=2, values ​​are taken sequentially, and the calculation is performed iteratively. ,until If all elements in the value are not 0, determine the number of jump steps k.

4. The method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network according to claim 3, characterized in that, The method for extracting static graph features by using a GAT network to extract features from the state features of all components and the adjacency matrix with k jump steps is as follows: A graph convolutional network is used to extract the state features of all components and the basic association features of the adjacency matrix with a jump step of k. Based on the multi-head attention mechanism, the adjacency matrix with k jump steps is subjected to difference operation to obtain the new path for each jump; the concatenation features of the new path for each jump and the corresponding start and end nodes of the new path are linearly transformed, and the LeakReLU activation function is used to obtain the path importance score; the path importance score is normalized to obtain the path attention weight. After concatenating all path attention weights, the static graph features are obtained by processing them with the Tanh activation function and pooling layer.

5. The method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network according to claim 1, characterized in that, In the qualitative relationship diagram of sensor parameters, based on the transmission relationship of mass flow rate, pressure and temperature of gas parameters at various cross sections of the aero-engine during operation, and combined with the sensor's placement in the engine, the mechanistic relationship between sensors is constructed. In the quantitative relationship diagram of sensor parameters, cosine similarity is used to measure the statistical correlation of correlated sensor parameters, in order to characterize the dynamic evolution of the correlation between sensor parameters as the engine degrades.

6. The method for predicting the remaining service life of an aero-engine based on a domain knowledge-enhanced dual-flow graph joint learning network according to claim 5, wherein the method for obtaining the fused relationship graph is as follows: Learnable matrices The complement of the learnable matrix Dynamic weights are assigned to the qualitative and quantitative relationship graphs of sensor parameters respectively, and then the weighted sums are performed. The result of the weighted sums is normalized to obtain the fused relationship graph. The adjacency matrix of sensor parameter relationships is obtained based on the fused relationship graph.

7. The method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network according to claim 6, characterized in that, The method for obtaining the feature at time step w by the attention unit of the w-th gated graph is as follows: The spatial correlation features of the sensor monitoring data at the w-th time step are extracted by the adjacency matrix of sensor parameters using a graph attention network. At the same time, the spatial correlation features of the (w-1)-th time step features and the adjacency matrix of sensor parameters are extracted by the graph attention network. After weighted summation by the corresponding reset gate weight matrix, a linear transformation and Sigmoid activation are performed to obtain the reset gate. The graph attention network extracts the spatial correlation features of the sensor monitoring data at the w-th time step and the adjacency matrix of the sensor parameters. At the same time, the graph attention network extracts the spatial correlation features of the features at the (w-1)-th time step and the adjacency matrix of the sensor parameters. After weighted summation by the corresponding update gate weight matrix, a linear transformation and sigmoid activation are performed to obtain the update gate. The spatial correlation features of the sensor parameter relationship adjacency matrix and the sensor monitoring data at the w-th time step are extracted by the graph attention network. At the same time, the spatial correlation features of the sensor parameter relationship adjacency matrix and the features at the (w-1)-th time step and the Hadamard product of the reset gate are extracted by the graph attention network. After weighted summation by the corresponding hidden state weight matrix, the w-th hidden state is obtained by nonlinear transformation through the tanh activation function. The w-th time step feature is obtained by adding the Hadamard product of the update gate and the feature of the (w-1)-th time step, and the Hadamard product of the complement of the update gate and the w-th hidden state.

8. The method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network according to claim 7, characterized in that, The attention weights of the features at the first w-1 time steps relative to the feature at the w-th time step are calculated using a temporal attention mechanism. Then, the features at the first w-1 time steps are weighted and fused to obtain the fused features of the features at the first w-1 time steps. The fused features of the first w-1 time steps are then concatenated with the features of the w-th time step, and after linear transformation and Softmax activation, dynamic graph features are obtained.

9. The method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network according to claim 8, characterized in that, The method for obtaining the mapped concatenated features using a feature alignment network is as follows: Two fully connected networks with shared parameters and identical structures are used to map dynamic graph features and static graph features to the same feature space, and then concatenated to obtain the mapped concatenated features.

10. The method for predicting the remaining service life of aero-engines based on a domain knowledge-enhanced dual-flow graph joint learning network according to claim 9, characterized in that, The self-attention module uses a linear transformation function of the query vector to map the mapped concatenated features into the query vector required by the attention mechanism. A linear transformation function for key vectors is used to map the concatenated features after mapping to the key vectors required by the attention mechanism. A linear transformation function of value vectors is used to map the concatenated features after mapping into the value vectors required by the attention mechanism. ; The fusion features are represented as : ， In the formula Key vector The dimension; The RUL prediction results for aero-engines are expressed as... : ， In the formula It is a fully connected layer network. This is the Sigmoid activation function.

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