Aero-engine life prediction method based on causal learning and physical fusion graph neural network

Abstract

The invention discloses a causal learning and physical law deep fusion graph neural network-based aero-engine remaining service life prediction method. The method specifically comprises the steps of constructing a sensor data initial causal graph through time sequence causal discovery; physically refining the causal diagram based on the thermodynamics / fluid mechanics principle; designing a physically embedded message transmission mechanism; and utilizing a graph neural network to extract degradation features and predict residual life. The invention provides a novel deep physical embedded life prediction method, provides a high-precision and high-robustness residual life prediction result by encoding a physical law to a message function of a graph neural network, solves the problems that a data-driven model in an actual scene lacks physical interpretability and is insufficient in generalization ability under working condition change, and improves the reliability of the data-driven model. And a causal structure is utilized to guide physical constraints, so that prediction errors are reduced, and the accuracy of a key fault stage is remarkably improved. In practical engineering application, especially in predictive maintenance of aero-engines with multiple working conditions and multiple fault modes, the method has wide application.

Description

Technical Field

[0001] The invention belongs to the field of predictive maintenance technology for aero-engines, and in particular relates to a method for predicting remaining service life by combining causal learning and physical information graph neural networks. Background Technology

[0002] As the core power system of modern aircraft, aero engines operate under harsh conditions, and their reliability is crucial to flight safety and economic efficiency. Therefore, accurately predicting the remaining service life (RUL) of aero engines is of key significance for effectively preventing potential failures and significantly optimizing maintenance strategies. This not only improves operational efficiency but also reduces maintenance costs and downtime.

[0003] For a long time, the prediction of RUL (Recovery Duration and Liability) of aero-engines has mainly relied on physics-based failure models and traditional statistical methods. While physics-based models have a clear mechanistic basis, they are difficult to construct and cannot fully cover all complex operating conditions and potential failure modes. Conversely, traditional statistical methods are inadequate when dealing with increasingly high-dimensional, nonlinear, and time-varying sensor data.

[0004] In recent years, with the rapid development of sensor networks, data acquisition, and storage technologies, the research paradigm for Residual Ultraviolet (RUL) prediction has significantly shifted towards data-driven approaches. Deep learning technology, in particular, has emerged as a revolutionary force in RUL prediction due to its powerful ability to automatically learn complex degradation patterns from massive amounts of monitoring data. For example, recurrent neural networks (RNNs) and their variants LSTM and GR, convolutional neural networks (TCNs), and Transformer models based on self-attention mechanisms have all demonstrated superior performance in processing high-dimensional, nonlinear time-series data, effectively capturing time-dependent features and extracting hierarchical degradation characteristics. Furthermore, considering the physical interactions between sensors, graph neural networks (GNNs) have also been introduced, providing new perspectives and tools for RUL prediction by explicitly modeling the interactions between sensors. Although data-driven deep learning models have made significant progress in RUL prediction accuracy, these models often operate as black boxes, lacking transparency in their internal decision-making processes. This makes understanding their predictive basis extremely difficult, and in industries with extremely high reliability and safety requirements, such as aviation, it is difficult to fully trust their results. Additionally, the performance of purely data-driven models is highly dependent on large-scale, high-quality, and representative training data. When encountering new operating conditions or environmental factors that differ from the distribution of training data, the model's generalization ability often decreases significantly, highlighting its lack of robustness.

[0005] To overcome the shortcomings of traditional data-driven models in terms of insufficient physical interpretability and poor robustness, researchers in this field have begun to explore the integration of physical knowledge into machine learning. However, existing physical information machine learning methods typically treat physical knowledge as external constraints or shallow priors, failing to deeply embed it into the core mechanisms of the model. This makes it difficult to achieve predictions that truly follow physical principles, thus their generalization ability and reliability remain challenging in complex dynamic systems. Furthermore, when modeling system degradation processes, understanding the underlying causal mechanisms is crucial for achieving robust remaining lifetime predictions. However, existing causal inference methods often rely on predefined assumptions or indirect inferences, which may introduce inaccurate or spurious associations, affecting the accuracy and reliability of the model. The aforementioned techniques and their limitations are widely recognized by those skilled in the art, and a large body of literature discusses them. Summary of the Invention

[0006] The purpose of this invention is to address the problems of insufficient physical interpretability, inadequate robustness, and insufficient physical information embedding depth in existing aero-engine remaining service life prediction models. This invention proposes an engine life prediction method based on causal learning and physical fusion graph neural networks.

[0007] The technical solution of this invention is: an engine life prediction method based on causal learning and physical fusion graph neural network, comprising the following steps:

[0008] A. Acquire sensor data and operating condition data of aero-engines, and combine the PCMCI+ time series causal discovery algorithm with physical principles and formal physical rules in the field of aero-engines based on thermodynamics, fluid mechanics, mechanical motion and control principles to construct a physically refined causal graph;

[0009] B. Using the physical refined causal graph obtained in step A as its structural prior, a graph neural network is constructed, and the basic physical laws are deeply embedded into the message passing operation of the graph neural network by constructing a dual-path physical information message passing mechanism.

[0010] C. Optimize and train the physical information graph neural network obtained in step B to learn degradation feature representations from complex, high-dimensional time-series data;

[0011] D. Use the physical information graph neural network trained in step C to predict the remaining service life of actual aero-engine signals.

[0012] 2. The method as described in claim 1, wherein step A comprises the following sub-steps:

[0013] A1. Based on the sensor data and operating condition data of the aero-engine, a preliminary causal graph of potential causal links between variables is initially constructed using the PCMCI+ time series causal discovery algorithm;

[0014] A2. Physically refine the preliminary cause-effect graph, wherein the refinement operation is based on a predefined set of physical rules for the aero-engine domain, the set of rules including:

[0015] a. Pruning operations for systematically removing false or contradictory connections that do not conform to the fundamental physical laws of aero-engines, the pruning operations including the removal of connections that violate energy / mass conservation or contradict the direction of physical flow / signal;

[0016] b. Forced operation to supplement physically known critical connections that are essential to engine degradation, the forced operation including the forced addition of strong coupling relationships between core components or the direct effects of control loops;

[0017] c. A direction checking operation is used to correct causal edge directions that do not conform to the physical causal direction. The direction checking operation includes, but is not limited to, correcting the causal edge directions according to the physical flow or the causal hierarchy in the control system, thereby obtaining a refined causal graph.

[0018] 3. The method as described in claim 1, wherein in step B, the dual-path physical information message passing mechanism includes a dual-path physical information message passing function, the dual-path physical information message passing function including:

[0019] B1. Data-driven paths, which capture general patterns and nonlinear relationships in data through learnable parameters that can be specific to edge types;

[0020] B2. Physical information path, which employs learnable physical coefficients and a projection layer to combine the physically relevant signals in the hidden state with predefined physical heuristics. These physical heuristics, based on edge type, include:

[0021] a. Operating conditions to sensor response sensitivity function, used to simulate how operating conditions affect sensor readings;

[0022] b. Temperature-dependent heat transfer function, used to model the temperature signal gradient to reflect heat transfer and thermodynamic coupling, the function may include a term reflecting the temperature difference;

[0023] c. Pressure / flow / velocity related fluid dynamics or mechanical motion functions to capture relationships such as pressure drop, flow resistance, or rotational speed effects. These functions may include quadratic terms to simulate nonlinear physical relationships, such as dynamic pressure or energy dissipation.

[0024] d. Other general mechanical coupling functions for capturing complex mechanical couplings and general interactions not covered in the above categories; all of these physical heuristics are parameterized with learnable scalar coefficients and projection layers to simulate physical relationships such as heat transfer, fluid dynamics, or mechanical motion, thereby achieving a deep fusion of physics and data during message passing.

[0025] 4. The method as described in claim 1, wherein in step C, the optimization training includes: extracting feature representations of nodes at each layer through multi-layer physical information message passing operations and node state updates of the physical information graph neural network, and integrating the feature representations through global average pooling to obtain graph-level feature representations; and inputting the graph-level feature representations into a multi-layer perceptron regression model, and performing end-to-end optimization by minimizing the mean squared error loss function between the predicted value and the true value.

[0026] 5. The method as described in claim 1, wherein step D comprises: using the preprocessed actual aero-engine signal as input to the trained physical information graph neural network model to predict the remaining service life of the aero-engine.

[0027] The beneficial effects of this invention are as follows: This invention proposes a novel deep physical embedding method for predicting remaining useful life (RUL). By deeply fusing physical-guided causal learning with physical laws into a graph neural network, it can provide high-precision, robust, and inherently physically interpretable RUL results. This solves the problems of traditional data-driven models lacking physical interpretability and having insufficient generalization ability under changing operating conditions. Furthermore, by capturing deep causal degradation paths, it significantly reduces prediction errors and significantly improves the accuracy of critical failure stages. Experimental results show that this invention exhibits significant advantages over existing RUL prediction methods in terms of prediction accuracy, robustness under different operating conditions, and interpretability of physical consistency. In practical engineering applications, especially in predictive maintenance of aero-engines with multiple operating conditions and multiple failure modes, this invention has broad application prospects. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the overall process of an engine life prediction method based on causal learning and physical fusion graph neural network according to the present invention.

[0029] Figure 2 This is a schematic diagram of the internal structure of the core message passing function of the physical information graph neural network in this invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0031] like Figure 1 The diagram shown illustrates the overall process of a method for predicting the remaining service life of an aero-engine based on a deep fusion graph neural network of causal learning and physical laws, according to the present invention. The method includes the following steps:

[0032] A. Acquire sensor data and operating condition data of aero-engines, combine the data-driven causal discovery PCMCI+ algorithm with the physical principles and formal physical rules of the aero-engine field, and construct and physically refine a causal graph with high physical consistency.

[0033] A1. First, acquire multivariate time-series sensor data and operating condition data generated during the operation of the aero-engine. After data acquisition, perform necessary data preprocessing, including but not limited to data cleaning, missing value imputation, and normalization. Global scaling can be used for single-condition data, while cluster-based segmented normalization can be used for multi-condition data.

[0034] A2. Based on the preprocessed time-series sensor data and operating condition data, the PCMCI+ time-series causal discovery algorithm is used to initially identify potential causal links between variables and construct a preliminary causal graph.

[0035] A3. Physically refine the preliminary cause-effect graph. This refinement operation is based on a predefined set of physical rules in the aero-engine domain. This set of rules is extracted and formalized from thermodynamics, fluid mechanics, mechanical motion, and control principles, and includes:

[0036] a. Pruning operation: Used to systematically remove false or contradictory connections that do not conform to the fundamental physical laws of aero-engines. The pruning operation includes, but is not limited to, removing connections based on judgments of the following: connections that violate the law of conservation of energy / mass, or connections that contradict the direction of physical flow or signaling.

[0037] b. Forced Operations: Used to supplement physically known critical connections that are essential to engine degradation. Forced operations include, but are not limited to, forcibly adding the following connections: strong couplings between core components, or direct effects of control loops.

[0038] c. Direction Check Operation: Used to correct causal edge directions that do not conform to the physical causal direction. The direction check operation includes correcting the causal edge directions based on the physical flow or the causal hierarchy in the control system. Through the above physical refinement, a statistically significant and physically reasonable refined causal graph is obtained.

[0039] B. Using the physically refined causal graph obtained in step A as its structural prior, construct a novel graph neural network, such as... Figure 2 As shown, fundamental physical laws are deeply embedded into the message passing mechanism of the graph neural network, achieving a deep integration of data and physics.

[0040] In each layer of the graph neural network, a two-path physical information message passing function is designed and applied. Specifically, the two-path physical information message passing function is as follows:

[0041] B1. Data-driven approach: Capturing implicit general patterns and nonlinear relationships in data through learnable parameters. For example... Figure 2 As shown on the left, this path captures the general patterns and relationships for each type of interaction implicitly learned in the data. Specifically, it extracts these patterns from the node's hidden state through linear transformation and the ReLU activation function. Extract the data-driven terms. The specific expression is:

[0042] (1)

[0043] in, and It is for different edge types Learnable parameters are used to capture prevalent, non-linear patterns and relationships in the data.

[0044] B2. Physical information path: such as Figure 2 As shown on the right, this path extracts physically relevant signals from the abstract hidden state and combines them with a predefined physical heuristic function to model the physically meaningful interaction between the source node j and the target node i. In the specific implementation, a small linear projection layer is used. We learn to extract low-dimensional physical signals from high-dimensional abstract hidden states h, and then substitute these signals into a physical heuristic function. This is a linear projection layer used to map high-dimensional hidden states to a low-dimensional feature space related to specific physical quantities. These functions typically contain learnable physical coefficients to adjust the intensity of physical relationships. For the data type of aero-engines, this invention designs the following four types of physical heuristic functions, whose specific expressions are shown below:

[0045] a. Operating conditions to sensor response sensitivity function :

[0046] (2)

[0047] This function is used to simulate how operating conditions affect sensor readings. It is a multilayer perceptron used to map input signals to sensor response sensitivities. It is a learnable scalar coefficient used to scale the spliced ​​operating conditions and sensor state information. These are learnable scalar coefficients used to adjust the intensity of sensitivity; It is a learnable bias term that provides a baseline offset for the effect of operating conditions on sensor readings. The activation function ensures that the output is between 0 and 1, reflecting sensitivity. Concat represents the concatenation operation.

[0048] b. Temperature-dependent heat transfer function :

[0049] (3)

[0050] This function is used to model how the temperature signal gradient reflects heat transfer and thermodynamic coupling. It is a multilayer perceptron used to map heat transfer-related hidden signals to the output. It is a learnable scalar coefficient that controls the scaling of the gradient term; It is a learnable scalar coefficient used to adjust the intensity of the heat transfer effect; It is a learnable bias term that provides a baseline offset for the output of the heat transfer effect. This represents the difference in temperature-related signals extracted from the hidden state of a node through the projection layer, simulating the temperature gradient. Activation functions help capture negative and positive heat transfer relationships.

[0051] c. Pressure / flow / velocity related fluid dynamics or mechanical kinematic functions :

[0052] (4)

[0053] This function is used to capture fluid dynamics or mechanical motion relationships such as pressure drop, flow resistance, or rotational speed effects. It is a multilayer perceptron used to map fluid / mechanically related hidden signals to the output. It is a learnable scalar coefficient used to scale squared terms; It is a learnable scalar coefficient used to adjust the intensity of fluid / mechanical effects; It is a learnable bias term that provides a baseline offset for the output of pressure / flow / velocity related effects. It explicitly includes square terms to simulate nonlinear physical relationships, such as dynamic pressure or energy dissipation. The activation function ensures non-negativity.

[0054] d. Other general mechanical coupling functions :

[0055] (5)

[0056] This function is used to capture complex mechanical couplings and general interactions that are not covered in the categories mentioned above. It is a multilayer perceptron used to map other mechanically coupled hidden signals to the output. It is a learnable scalar coefficient used to adjust the overall influence strength of other complex mechanical couplings and general interactions; These are learnable scalar coefficients used to adjust the overall influence strength of other complex mechanical couplings and general interactions. It is a learnable bias term that provides a baseline offset for the output of other complex mechanical coupling effects. Activation functions are used to introduce nonlinearity. This represents the Hadamard product, used to simulate the interaction of hidden signals between two nodes.

[0057] General MLP structure description: All of the above Typically, a fully connected network structure with at least one hidden layer is used, and the number of layers, the number of neurons per layer, and the type of activation function can be adjusted according to specific task requirements to ensure that the model has sufficient expressive power to capture complex nonlinear relationships.

[0058] B3. After the data-driven part and physical information have been calculated separately, message aggregation is required. The aggregation of messages received by node i from all its neighbors is completed through average aggregation, the specific expression of which is:

[0059] (6)

[0060] in, It is the total message vector aggregated from all neighbors in the l-th layer of the graph neural network with node i.

[0061] C. Perform efficient optimization training on the physical information graph neural network obtained in step B, so that it can learn physically consistent degradation feature representations from complex, high-dimensional time-series data.

[0062] C1. By using multi-layer physical information message passing operations and node state updates in a physical information graph neural network, physically consistent and hierarchical graph-level feature representations are gradually extracted from the input data, capturing the key physical mechanisms of the engine at different degradation stages.

[0063] C2. The graph-level feature representation is input into the multilayer perceptron regression model. End-to-end optimization is performed by minimizing the mean squared error loss function between the predicted and true values, and stabilization strategies such as gradient pruning are employed. Simultaneously, a cosine annealing learning rate scheduling strategy is used to dynamically adjust the learning rate, ensuring the model's training convergence and stability when handling complex and imbalanced degenerate data. During training, the AdamW optimizer can be used, with an initial learning rate of 0.001, a weight decay coefficient of 5e-4, and a batch size of 256, etc.

[0064] D. Use the physical information graph neural network trained in step C to predict the remaining service life of actual aero-engine signals.

[0065] This process corresponds to Figure 1 The "Actual Remaining Service Prediction" module in the system works as follows: Preprocessed actual aero-engine signals are used as input to a trained Physical Information Graph (PIG) ​​neural network model. This model receives the input data, performs feature extraction and inference through its internal physical information message passing mechanism, and finally outputs the predicted remaining service life of the aero-engine via a regression head.

[0066] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for predicting the remaining service life of an aero-engine, characterized in that, The method includes the following steps: A. Acquire sensor data and operating condition data of aero-engines, and integrate the PCMCI+ time-series causal discovery algorithm with physical principles and formal physical rules in the field of aero-engines based on thermodynamics, fluid mechanics, mechanical motion and control principles to construct a physically refined causal graph; B. Using the physical refined causal graph obtained in step A as its structural prior, a graph neural network is constructed, and the basic physical laws are deeply embedded into the message passing operation of the graph neural network by constructing a dual-path physical information message passing mechanism. C. Optimize and train the physical information graph neural network obtained in step B to learn degradation feature representations from complex, high-dimensional time-series data; D. Use the physical information graph neural network trained in step C to predict the remaining service life of actual aero-engine signals.

2. The method as described in claim 1, characterized in that, Step A includes the following sub-steps: A1. Based on the sensor data and operating condition data of the aero-engine, a preliminary causal graph of potential causal links between variables is initially constructed using the PCMCI+ time series causal discovery algorithm; A2. Physically refine the preliminary cause-effect graph, wherein the refinement operation is based on a predefined set of physical rules for the aero-engine domain, the set of rules including: a. Pruning operations for systematically removing false or contradictory connections that do not conform to the fundamental physical laws of aero-engines, the pruning operations including the removal of connections that violate energy / mass conservation or contradict the direction of physical flow / signal; b. Forced operation to supplement physically known critical connections that are essential to engine degradation, the forced operation including the forced addition of strong coupling relationships between core components or the direct effects of control loops; c. A direction checking operation is used to correct causal edge directions that do not conform to the physical causal direction. The direction checking operation includes, but is not limited to, correcting the causal edge directions according to the physical flow or the causal hierarchy in the control system, thereby obtaining a refined causal graph.

3. The method as described in claim 1, characterized in that, In step B, the dual-path physical information message passing mechanism includes a dual-path physical information message passing function, which includes: B1. Data-driven paths, which capture general patterns and nonlinear relationships in data through learnable parameters that can be specific to edge types; B2. Physical information path, which employs learnable physical coefficients and a projection layer to combine the physically relevant signals in the hidden state with predefined physical heuristics. These physical heuristics, based on edge type, include: a. Operating conditions to sensor response sensitivity function, used to simulate how operating conditions affect sensor readings; b. Temperature-dependent heat transfer function, used to model the temperature signal gradient to reflect heat transfer and thermodynamic coupling, the function may include a term reflecting the temperature difference; c. Pressure / flow / velocity related fluid dynamics or mechanical motion functions to capture relationships such as pressure drop, flow resistance, or rotational speed effects. These functions may include quadratic terms to simulate nonlinear physical relationships, such as dynamic pressure or energy dissipation. d. Other general mechanical coupling functions, used to capture complex mechanical couplings and general interactions not covered in the categories above; All the physical heuristic functions are parameterized with learnable scalar coefficients and projection layers to simulate physical relationships such as heat transfer, fluid dynamics, or mechanical motion, thereby achieving a deep fusion of physics and data during message passing.

4. The method as described in claim 1, characterized in that, In step C, the optimization training includes: extracting feature representations of nodes at each layer through multi-layer physical information message passing operations and node state updates of the physical information graph neural network, and integrating the feature representations through global average pooling to obtain graph-level feature representations; and inputting the graph-level feature representations into the multi-layer perceptron regression model and minimizing the mean squared error loss function between the predicted value and the true value for end-to-end optimization.

5. The method as described in claim 1, characterized in that, Step D includes: using the preprocessed actual aero-engine signal as input to the trained physical information graph neural network model to predict the remaining service life of the aero-engine.

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