Damage trend prediction method based on hierarchical graph structure and Markov residual correction

Abstract

The invention relates to the technical field of complex equipment damage detection, in particular to a damage trend prediction method based on a hierarchical graph structure and Markov residual correction, which is superior to a traditional time sequence regression model in the aspects of prediction precision and generalization ability. According to the method, a damage trend prediction model based on a hierarchical graph structure and Markov residual correction is established, the damage trend prediction model based on the hierarchical graph structure and the Markov residual correction comprises a prediction module and a correction module, and the prediction module converts damage size data obtained through engine borescope inspection into a graph structure; a damage prediction network of a hierarchical graph structure is constructed to process the graph structure, a damage trend prediction problem is converted into prediction of edge weights among nodes in the graph, and internal relations among damage data are revealed; and the correction module designs a residual error correction method based on multiple types of Markov chains so as to construct a Markov chain model to correct a prediction result.

Description

Technical Field

[0001] The present invention relates to the technical field of complex equipment damage detection, and specifically to a damage trend prediction method based on a hierarchical graph structure and Markov residual correction, which is superior to traditional time series regression models in terms of prediction accuracy and generalization ability. Background Art

[0002] The damage of civil aviation engines usually starts from minor defects such as local surface cracks and oxidation ablation points, and gradually evolves into more serious structural failures. With the continuous use of aircraft, the working state of engines becomes more complex. Under the alternating action of various physical and chemical factors, the damage development of the internal core components of engines shows significant nonlinearity and uncertainty. At present, although the borescope inspection widely used by each airline can detect the damage of the internal core components of civil aviation engines, for the future development trend of the damage, it still depends only on maintenance personnel to make subjective judgments based on the maintenance manuals provided by manufacturers or their own experience. This damage development trend prediction method mainly based on experience and manual judgment is difficult to capture the nonlinear characteristics in the damage development process only by the limited data obtained from borescope inspections, and it is extremely easy to cause over-prediction or under-prediction of damage judgments, thus bringing potential safety hazards and unnecessary economic losses. With the continuous development of artificial intelligence technology, researchers and engineers have begun to explore more scientific and systematic damage trend prediction methods to reduce the uncertainty of human judgment and improve prediction accuracy. At present, the methods used in the industry for damage trend prediction mainly include model-driven methods and data-driven methods. Model-driven methods mainly calculate the future development of damage through experimental simulation or known mechanisms under the condition of obtaining material and modeling information. Data-driven methods use continuous historical damage development data to predict the future damage development by training statistical models. In the field of civil aviation engine health management, the selection of damage trend prediction methods needs to fully consider the complexity of engines, the variability of working conditions, as well as the availability and discreteness of data.

[0003] Traditional model-driven methods rely on physical mechanisms and engineering knowledge and are applicable to scenarios lacking a large amount of historical data. However, the application of model-driven civil aviation engine damage trend prediction methods faces extremely high technical barriers for airlines. Generally, due to intellectual property protection, civil aviation engine manufacturers will not provide airlines with core parameters and key design indicators of civil aviation engine manufacturing materials. The lack of this information makes it difficult for airlines to build damage prediction models with engineering application value when carrying out intelligent operation and maintenance of civil aviation engines. Data-driven methods mainly rely on large-scale monitoring data and intelligent algorithms and have strong prediction capabilities under data-rich conditions. Compared with model-driven methods, the data-driven form no longer depends on complex physical environments but directly learns the potential patterns of damage evolution from historical data and uses statistical learning or deep learning techniques to build prediction models. However, although these methods have been widely developed in the industrial field, in the aviation field, there is no model algorithm that can effectively utilize civil aviation engine damage data for reliable prediction. Therefore, it is also difficult to achieve ideal prediction results by using traditional data-driven methods to build a prediction model for the development of internal damage trends of civil aviation engines. Summary of the Invention

[0004] In view of the problem of low accuracy in judging the damage evolution trend relying on manual experience currently, the present invention proposes a damage trend prediction method based on a hierarchical graph structure and Markov residual correction, which is superior to traditional technologies in terms of prediction accuracy and generalization ability.

[0005] The present invention is achieved through the following measures: A damage trend prediction method based on a hierarchical graph structure and Markov residual correction, characterized in that a damage trend prediction model based on a hierarchical graph structure and Markov residual correction is established. The damage trend prediction model based on a hierarchical graph structure and Markov residual correction includes a prediction module and a correction module. The prediction module converts the damage size data obtained from engine borescope inspections into a graph structure, constructs a damage prediction network with a hierarchical graph structure to process the graph structure, converts the damage trend prediction problem into the prediction of edge weights between nodes in the graph, and reveals the internal relationship between damage data. The correction module designs a residual correction method based on multiple Markov chains, which is used to cluster engine damage data, convert size evolution into a transition relationship between categories, and obtain a residual observation sequence in combination with the dynamic update characteristics of the graph structure, thereby constructing a Markov chain model to correct the prediction results.

[0006] The specific calculation steps of the prediction module in the present invention are as follows: Step 1: Define nodes and edges, and define the node set of the damage data graph , each node corresponds to a borescope inspection record, characterized by the detected damage size data; then, a set of directed edges is defined. For each node, a directed edge is established according to the chronological order of each borescope inspection , representing the detection order and the increasing trend of damage; finally, the edge weight is defined , the edge 's weight is the time interval between two borescope inspections, that is, the number of flight cycles. Based on the above settings, for the borescope inspection data of a single engine, a directed graph is constructed and defined as follows: (15), where represents the set of nodes of the graph, , where the number of nodes is , represents the set of directed edges, , represents the set of edge weights, , represents and 's edge weight. On this basis, the adjacency matrix of the graph is defined as shown in Equation (16): (16), where: represents the element of the adjacency matrix. Through this constructed form, while reflecting the increasing trend of damage size, the time interval information is also encoded into the edge weight; Step 2: Filter abnormal nodes. According to the trend of damage evolution, each edge should point from the node with a smaller damage size to the node with a larger damage size. If it is detected that the direction of a certain edge is contrary to this rule, that is, there is an edge pointing from the node with a larger damage size to the node with a smaller damage size, it indicates that there is an abnormality in this node pair, and the abnormal edge and the corresponding node with a smaller damage size need to be removed from the graph to clear the wrong damage record, as shown in Equation (17): (17), where represents the element of the adjacency matrix, represents the eigenvalue of node , represents the eigenvalue of node ; Step 3: Construction of the fleet graph structure. The damage data graph constructed from the damage data obtained from the first borescope inspection that recorded damage data to the last borescope inspection when the damage exceeded the standard for a single engine is used as a subgraph, and a global node is introduced Merge the sub - graphs of the same fleet to improve the model's ability to integrate and generalize damage data. Here, the global node represents the global reference benchmark for the overall damage evolution trend in the fleet, as follows: First, set the feature vector of the global node as a zero vector, indicating that the engine has not suffered any damage and the damage size is 0, as shown in Equation (18): (18), where represents the feature of the global node, Next, construct the edge connections between the global node and the nodes of each sub - graph , and the direction is fixed from the global node to the detection node . On this basis, determine the edge weight according to the number of flight cycles that the engine has experienced from the start of operation to each borescope inspection operation. Let the number of flight cycles recorded by the borescope inspection node be , that is, the cumulative number of flight cycles of the engine from the start of operation to this borescope inspection. Then, the edge weight from the global node to the detection node is shown in Equation (19): (19), Based on this, the elements of the adjacency matrix of the global edge can be defined as: (20), where represents the element of the global edge adjacency matrix, Finally, merge the individual graphs constructed for each engine to form a complete fleet - graph structure for model training. Denote the expression of the fleet - graph structure as: (21), where represents the total number of civil aviation engines in the fleet, represents the damage - data sub - graph structure in the fleet, represents the civil aviation engine with index in the fleet.

[0007] Next, use the graph neural network to extract features and predict the damage - data interval. The prediction - module encoder network consists of two sub - networks, namely, a two - layer graph convolutional network for local feature extraction and a graph attention mechanism network for global information fusion. First, perform local feature extraction through the two - layer graph convolution. Let the initial node embedding be , that is, the original damage - size data of each detection record. For each node , the update formula for aggregating the neighborhood information of each node by the two - layer graph convolution is: (22), (23), Wherein, represents the learnable weight matrix for the input edges of the first and second layers of the model, represents the learnable weight matrix for the output edges of the first and second layers of the model, represents the self-loop transformation matrix of the first and second layers, represents the non-linear activation function, represents the node embedding features after being processed by the first and second layers of the model. After being processed by the double-layer graph convolution, the node embedding fully reflects the structural information between local detection records and their second-order neighbors; The specific calculation of the prediction module of the present invention further includes global information fusion through the graph attention mechanism. For the obtained local node embeddings, calculate the attention scores between the global node embeddings and the local node embeddings: (24), wherein, represents the shared linear transformation matrix, represents the vector for calculating the attention, represents the non-linear activation function, represents the global node embedding and the local node embedding of the attention score; Normalize the attention scores to obtain the attention coefficients: (25), wherein, represents the set of all local nodes connected to the global node, represents the global node embedding and the local node embedding of the attention coefficient, Finally, perform global information fusion on each local node embedding: (26), wherein, represents the transformation matrix of the global node information; The decoder network of the prediction module uses a multi-layer perceptron as the decoder part. The task of the decoder part is to convert the finally fused node representation into edge weight prediction, that is, to predict the flight cycle interval between damage size data. The model infers the possible edge weights between new nodes based on the learned parameters. If the new nodes have not appeared during the training process, the model realizes the prediction process by capturing their similarities with other nodes. Given two nodes and node of the final embedding and , the formula for predicting the edge weight is shown in Equation (27). (27), where, represents the calculation of the multi-layer perceptron, which is composed of a fully connected layer and an activation function.

[0008] The training of the model of the present invention is carried out by minimizing the error between the predicted edge weight and the true edge weight, and the mean square error (MSE) is used as the loss function, and its expression is shown in Equation (28): (28), where, represents the set of edges to be predicted, represents the edge to be predicted, represents the weight of the edge predicted by the model from node i to node j , represents the true weight of the edge from node i to node j .

[0009] The present invention proposes a multi-class Markov chain residual correction method in the correction module, and the specific steps are described as follows: First, the KMeans clustering algorithm is used to divide into three groups according to the eigenvalue of each node, denoted as , and . In the original graph structure, the feature of each node represents the damage size data obtained from a borescope inspection. By labeling the categories of the nodes, the edge connection relationship between the nodes is re-described as the relationship of category conversion, that is, if the features of two nodes connected by an edge belong to categories and respectively, then this edge is re-described as the category conversion relationship of , and the direction of category conversion should be determined according to the direction of the edge. According to the characteristics of category conversion, the edges in the graph structure are divided into six conversion relationships, namely: , , , , , ; The method for constructing any kind of Markov chain includes: ① State interval division. According to the obtained residual sequence , select a constant value to divide into k states , ,..., , as shown in Equations (29) to (31): (29), (30), (31), Wherein, represents the m th state, represents the k th state, represents the starting point of the th state interval, represents the th state interval end point; ② State transition probability matrix. For the calculation of the state transition probability matrix, it is mainly calculated through the frequency of transition. Let for the residual sequence, from state to state

[0010] the number of observations is Among them, Then the one-step transition probability can be calculated from the transition frequency, and its calculation formula is as shown in (32): (32), wherein, represents the one-step transition probability from state to state represents the number of times the residual transitions from state to state in the training data, Through this calculation, the one-step state transition probability matrix can be obtained: (33), this matrix reflects the transition law of the residual sequence between different discrete states; ③ Markov property test. After obtaining the clear and discretized state sequence through the above steps, use statistical test methods to verify whether the obtained residual sequence satisfies the Markov property. First, calculate the marginal probability of each state. Let the marginal probability of the th state be the sum of the th column in the frequency matrix and the total frequency that is, the number of all transitions, ratio, as shown in formula (34): (34), wherein, represents the marginal probability of state represents the sum of the number of times all transitions from any state to state represents the total number of transitions in the residual sequence. Subsequently, construct a test statistic , here the likelihood ratio test form is adopted, and its calculation formula is as shown in (35): (35), Wherein, represents the marginal probability of state ; represents the one-step transition probability from state to state ; represents the sum of the number of times of all transitions from any state to state ; represents the statistic of the Markov property test; since states are obtained in the state partitioning stage, therefore, under the given significance level , if the statistic satisfies , it is considered that the sequence has the Markov property, and the Markov correction can be applied in this prediction process; ④ Preliminary prediction value correction. For this type of known original data, assume that the preliminary prediction value of a to-be-corrected edge is , where and are the corresponding nodes in the graph. Suppose the state of the residual corresponding to this edge after discretization is . In the Markov chain correction model, first determine the prediction interval of the next-step residual under state . Assume that the residual value interval corresponding to state is , then use the interval median as the correction value in this state: (36), Wherein, represents the upper and lower bounds of the residual interval corresponding to state . Finally, add the correction value to the preliminary prediction value to obtain the corrected predicted edge weight: (37), Wherein, represents the preliminary predicted edge weight from node to node , represents the predicted edge weight after Markov chain correction, ⑤ Calculation of the relative residual state probability of the prediction value. Use the one-step state transition matrix to calculate the -step state transition matrix (where ), so as to realize the establishment of the dynamic prediction transition matrix. If the residual states of the previous observation value before the prediction time are in turn , then for the prediction of the th step, specifically using the th step transition matrix to predict the state probability distribution of the new node relative to the residual, denoted as: (38), In the formula, represents the state transition matrix after steps of transition. Then the probability of the new node in the state is: (39), In the formula, represents the probability of transitioning from state to state in the matrix , and represents the probability that the residual of the new node at the th step of prediction is in the state; ⑥ Final correction result. Denote the Markov correction values of the predicted value of the new node at the n + 1th step under the k residual state intervals as in turn. Then the final corrected predicted value of the new node is the weighted sum of the preliminary predicted value and the correction values of each state: (40). In the formula, represents the preliminary predicted edge weight of the new node at the th step, represents the residual correction value under the state , which is the median of the corresponding interval here, represents the final predicted edge weight after Markov correction.

[0011] The prediction module of the present invention converts the damage size data obtained from the engine borescope inspection into a graph structure, constructs a damage prediction network (HiGDNet) with a hierarchical graph structure to process this graph structure, converts the damage trend prediction problem into the prediction of the edge weights between nodes in the graph, and reveals the internal relationship between the damage data; the correction module designs a residual correction method based on multi-class Markov chains (MC-RC). This method clusters the engine damage data, converts the size evolution into the transition relationship between classes, and combines the dynamic update characteristics of the graph structure to obtain the residual observation sequence, thereby constructing a Markov chain model to correct the prediction result, which is superior to the traditional time series regression model in terms of prediction accuracy and generalization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Att Figure 1 is the overall architecture diagram of the present invention.

[0013] AttFigure 2 It is a schematic diagram of converting the damage size into a graph structure in the present invention.

[0014] Attached Figure 3 It is a schematic diagram of adding global nodes to merge subgraphs in the present invention.

[0015] Attached Figure 4 It is a schematic diagram of redescribing the conversion relationship of edges in the present invention.

[0016] Attached Figure 5 It is a schematic diagram of obtaining the residual sequence of the conversion relationship by predicting the next subgraph after splitting after the merging operation in the present invention.

[0017] Attached Figure 6 It is a comparison curve of the actual and predicted development trends of the crack damage of the engine numbered 11 in the embodiment of the present invention.

[0018] Attached Figure 7 It is a comparison curve of the predicted and corrected index results of the development trend of the crack damage of the engine numbered 11 in the embodiment of the present invention.

[0019] Attached Figure 8 It is a comparison curve of the prediction performance indexes of each method under the same data set in the embodiment of the present invention. Detailed implementation manners

[0020] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0021] Graph Neural Networks (GNN) is a class of deep learning models specifically used to process graph-structured data. By learning the topological structure and node features of a graph, it can efficiently capture the relationship information between nodes, thereby explicitly expressing the internal association characteristics of the data. By directly associating nodes and edges through a graph structure, it can better mine and characterize the complex internal connections in the data.

[0022] A single graph is represented as shown in Equation (1): (1), In the formula, represents the set of nodes of the graph, where the number of nodes is , represents the set of edges in the graph, , represents the set of edge weights, , represents the edge weight between and Here, each node has a feature representation : (2), the features of all nodes form a matrix ; Here, the graph structure is represented by an adjacency matrix, and its elements are defined as: (3), In the formula, represents the element in the adjacency matrix, At this time, the elements of the adjacency matrix represent the degree of relationship or the strength of connection between two nodes. It should be noted that if the constructed graph is a directed graph, it usually does not satisfy symmetry, and this characteristic preserves the direction information of the connection between nodes. The core mechanism of GNN is message passing, which iteratively aggregates the information of neighboring nodes on the graph structure, enabling each node to gradually incorporate the context features from neighboring nodes, thereby realizing the continuous update and optimization of node feature representation and being able to capture the relationship and interaction information in the data more effectively. Among them, for different graph structures, their information passing mechanisms also have certain differences: I. For an undirected graph, an undirected graph consists of vertices (nodes) and undirected edges (edges connecting two nodes), where each edge represents a two-way connection between two nodes, that is, information can propagate in either direction along the edge, so no complex distinction is required. Its transfer model expression is: (4), In the formula, represents the input feature, represents the set of neighboring nodes of node , represents the non-linear activation function, , represents the learnable parameter matrix and bias term; II. For a directed graph, a directed graph consists of vertices (nodes) and directed edges (connections with a clear direction), and each edge only allows information to flow in a specific direction. Therefore, compared with an undirected graph, the information propagation in a directed graph is restricted by the direction of the edge and is more hierarchical and structured. When aggregating information in a directed graph, it is necessary to consider the information of input edges and output edges separately.

[0023] Here, it is set that the input neighbor set of node is set as , and the output neighbor set of node is set as . At this time, the update of the directed graph node features needs to utilize both the input neighbor information and the output neighbor information simultaneously, as shown in the following formula: (5), In the formula, represents the input feature, represents the node and its set of neighbor nodes, represents the non - linear activation function, , represents the learnable parameter matrix and bias term, Among them, the first term in Equation (5) represents the information of the input edge, and the second term represents the information of the output edge. The purpose of this design is to be able to utilize the information passed by the node from the predecessors (input edges) and successors (output edges) respectively, to achieve a fine - grained modeling of the directed relationship feature interaction, so as to fully capture the complex causal and temporal relationships within the data.

[0024] The training objective of the graph neural network is still to optimize the network parameters by minimizing the loss function. Assume represents the output of the GNN model. In the formula, represents all the learnable parameters in the network. The loss function of the network can be expressed as: (6), where represents the true label (such as the target of node classification or graph - level tasks), represents the loss function; during the training process, the model parameters will be updated through backpropagation and gradient descent to obtain the optimal network parameters.

[0025] The Markov model is a mathematical model used to model stochastic processes. The future state of its system depends only on the current state and is independent of the historical process of reaching the current state. This property is called the Markov property.

[0026] Let represent the state of a certain system at time , the Markov property can be mathematically expressed as: (7), that is, the next state of the system depends only on the current state and not on the past states X t-1 , X t-2 ,...

[0027] A Markov chain is a Markov process with a discrete state space, and the state transition is described by a transition matrix. Let the set of possible states of the system be , the probability of state transition is given by the matrix as follows: (8), wherein, represents the probability that the system migrates from state to state , (9), and satisfies the normalization condition: (10). For the state distribution, assume the initial state distribution is: (11), wherein, represents the probability that the system is in state at the initial moment. After rounds of transitions, the state distribution of the system is: (12). After expansion, it can be obtained: (13) When , the system may reach a stable probability distribution , satisfying: , (14). Solving this system of equations can obtain the steady-state distribution of the Markov chain.

[0028] The internal damage data of civil aviation engines is affected by the borescope inspection interval and the number of borescope inspections, showing the characteristics of non-uniform sampling and discontinuity. The present invention discovers that although the borescope damage data of the engine does not have continuity in the time dimension, it presents a clear development trajectory in the spatial structure, which enables it to have the potential to be modeled with a graph structure. Specifically, if the damage size recorded in each borescope inspection is used as the feature of a node in the graph, the edges between the nodes represent their evolutionary relationship in time, and the weight of the edge is determined by the number of flight cycle intervals between the nodes, then the damage evolution process of the engine can be abstracted into a prediction problem of the edge weights of a graph structure. In this way, it is possible to effectively avoid the dependence on equally spaced sampling of traditional time series methods and reflect the evolution path of damage in a more realistic manner. At the same time, further combining the prediction residual correction method is expected to more accurately extract the potential connections between damage features and enhance the model's perception ability of complex damage evolution laws. In view of this, this example will implement the design of the civil aviation engine damage trend prediction method according to this idea.

[0029] This example details the design scheme of each module of a damage trend prediction method based on a hierarchical graph structure and Markov residual correction. The overall architecture of the model is as Figure 1 shown, mainly including two modules: prediction and correction.

[0030] For the prediction module, first, using the damage size data obtained from the borescope inspection of a single engine as nodes, and the number of flight cycles between the data as the edge weights between the nodes, a single damage data graph structure is established, that is, the development relationship of the internal engine damage data is abstracted as the connection between nodes and edges in the graph structure; then, a global node is introduced, and the damage data graphs of the same parts of the fleet are integrated through the merge graph operation to form a fleet damage data graph; then, through the graph neural network, feature extraction and convolution operations are performed on the constructed fleet damage data graph to mine the deep internal correlations between the damage data; finally, the damage trend prediction problem is transformed into the prediction of the edge weights between nodes, realizing the accurate capture of the future development trend of the damage data.

[0031] For the correction module, aiming at the dynamic state update characteristic of the graph structure, in this example, a residual correction prediction method based on a multi-class Markov chain is designed. Specifically, first, the internal engine damage data is divided into three categories by using the clustering method; then, the evolution of the damage size is transformed into the conversion relationship between categories, that is, the connecting edges between the nodes in the graph are re-described as the conversions between categories, with a total of six conversion relationships; then, according to the state update characteristic of the graph structure in the merge graph operation, the merge graph operation is regarded as a time step, and corresponding Markov chain models are established respectively by using the residual data obtained from the six different category conversions. For the edge weight between two nodes to be predicted (that is, the number of flight cycles between the damage sizes), first judge which category conversion relationship its connecting edge belongs to according to the categories to which the features of the two nodes belong, and then finely correct the prediction residual through the Markov chain of the corresponding category to improve the accuracy of the damage trend prediction.

[0032] The main work of the prediction module is to predict the future development trend of the damage based on the damage historical development data. In this example, a damage development trend prediction method based on the graph neural network is designed.

[0033] First, a single damage graph structure is constructed. Aiming at the characteristics of the damage size data obtained from the engine borescope inspection, in this example, a single borescope inspection operation that records the damage size once for a single engine is used as a graph node, the damage size data obtained from the borescope inspection is used as the feature of this graph node, each node is connected by an edge, the direction of the edge is from the node with a smaller feature value to the node with a larger feature value, and then the time interval between the damage size data is used as the weight connecting this edge. Finally, the damage size data obtained from the borescope inspection is integrated into a directed graph structure, and the graph structure constructed from the single engine borescope damage data is used as a single damage data graph.

[0034] Next, construct the fleet damage graph structure. To further utilize the damage size data of the same model and the same part in the fleet, this method introduces a global node to merge the damage data graphs formed by each engine. Among them, the eigenvalue of the global node is set to 0, indicating the state where the engine has just been put into operation and no damage has occurred yet. On this basis, establish the edge connection between the global node and each detection node, and calculate the flight cycle interval between the global node and the borescope inspection (the nodes in the figure) that records the damage size each time. This number of flight intervals is the weight of the edge between the global node and each detection node. Finally, merge the damage data graphs constructed by each engine in the entire fleet to form a complete fleet graph structure.

[0035] Finally, on the basis of forming the fleet graph structure, this example designs a damage prediction network based on a hierarchical graph structure (Hierarchical Graph-based Damage Prediction Network, HiGDNet) to process the fleet graph structure. This network adopts an encoder-decoder architecture. The encoder part is mainly composed of a local feature extraction network and a global information fusion network. Among them, the local feature extraction network is designed with a double-layer graph convolutional network. This network aggregates information from in-neighbor nodes and out-neighbor nodes respectively, and considers the self-loop connection mechanism to retain the node's own attributes to capture the local and second-order neighborhood features in the borescope inspection data of a single engine. The global information fusion network is based on the graph attention mechanism to adaptively fuse the information of the global node (representing the moment when the engine has just been put into operation, with a feature of zero) with the local node embeddings to make full use of the temporal relationship and global reference information among the data of each engine in the fleet. The decoder part is composed of a multi-layer perceptron. Through the node embedding features obtained by the encoder part, predict the edge weights between new nodes. This edge weight is the number of flight cycle intervals between the required predicted damage sizes. This design makes full use of the topological structure between nodes, allows information to flow in the graph, enables each node to learn and integrate information from neighbor nodes, and provides support for predicting the edge weights between new nodes. At the same time, this structural design also enhances the generalization ability of the model when predicting new and unlearned graph structures.

[0036] The specific calculation steps of the prediction module are as follows: I. Define nodes and edges. For a certain type of damage, first, take a borescope inspection that records the damage size data of a certain engine at a certain time as a node, and use the damage size of a certain type of damage obtained from this inspection as the feature of this node. Subsequently, on the basis of constructing all the detection nodes, construct edges between the borescope inspection nodes. The edge information consists of three parts: the index of the edge and the weight of the edge. The index of the edge defines the starting point and the ending point of the edge. Among them, during the process of adding edges, it should be strictly set in accordance with the time sequence of the borescope inspections, so as to ensure that the model can pay attention to the increasing trend of the damage size over time during training. The weight of the edge is defined as the number of flight cycles between adjacent borescope inspection nodes, which is used to quantify the flight cycle interval between detections. As Figure 2 shown

[0037] It should be noted that the number of flight cycles described here refers to a complete working process of a civil aviation engine in a flight mission, including startup - idle - taxi - takeoff - climb - cruise - descent - approach - reverse - idle - shutdown.

[0038] Here, in this example, first define the node set of the damage data graph , each node corresponds to a borescope inspection record, and its feature is the detected damage size data; then, define the set of directed edges . For each node, establish a directed edge according to the time sequence of each borescope inspection, indicating the detection sequence and the increasing trend of the damage; finally, define the edge weight . The weight of the edge is the time interval between two borescope inspections, that is, the number of flight cycles.

[0039] Based on the above settings, for the borescope inspection data of a single engine, the definition of a directed graph is constructed as follows: (15), where represents the node set of the graph, , and the number of nodes is , represents the set of directed edges, , represents the set of edge weights, , represents the edge weight between and . On this basis, the definition of the adjacency matrix of the graph is shown in Equation (16): Represents the elements of the adjacency matrix. In this constructed form, while being able to reflect the increasing trend of the damage size, the time interval information is further encoded into the edge weights.

[0040] II. Filter abnormal nodes. Considering that there may be cases of incorrect damage size records during the borescope inspection process, after converting the borescope inspection data of a single civil aviation engine into graph-structured data, the node pairs in the graph are checked. Here, a node pair refers to two nodes connected by a directed edge. Normally, according to the trend of damage evolution, each edge should point from the node with a smaller damage size to the node with a larger damage size. If it is detected that the direction of a certain edge is contrary to this rule, that is, there is an edge pointing from the node with a larger damage size to the node with a smaller damage size, it indicates that this node pair is abnormal, and the abnormal edge and the corresponding node with a smaller damage size need to be removed from the graph to eliminate the incorrect damage records and ensure that the subsequent graph structure and information aggregation process are only based on normal and reasonable inspection data, as shown in Equation (17). (17), where Represents the elements of the adjacency matrix, Represents the node Eigenvalue, Represents the node Eigenvalue; Fleet graph structure construction. On the basis of the above steps, to make full use of the damage data of the same model and the same part in the fleet, this method uses the damage data graph constructed from the damage data obtained from the first borescope inspection that records damage data to the last borescope inspection when the damage exceeds the standard for a single engine as a subgraph. Introduce a global node Merge the subgraphs of the same fleet to improve the model's ability to integrate and generalize damage data. Here, the global node represents the global reference benchmark for the overall damage evolution trend in the fleet. Specifically as follows: First, set the feature vector of the global node to a zero vector, indicating that the engine has not generated any damage and the damage size is 0, as shown in Equation (18): (18), where Represents the feature of the global node, Next, construct the edge connection between the global node and the nodes of each subgraph , and the direction is fixed to point from the global node To the detection node . On this basis, determine the weight of the edge according to the number of flight cycles experienced by the engine from being put into operation to each borescope inspection operation (i.e., each node). Let the number of flight cycles corresponding to the borescope inspection node Recorded be , That is, the cumulative number of flight cycles of the engine from the start of operation to the borescope inspection. Then the global node points to the detection node and the edge weight is shown in Equation (19). (19), Based on this, the elements of the adjacency matrix of the global edge can be defined as: (20), where represents the element of the global edge adjacency matrix, Finally, the individual graphs constructed for each engine are merged to form a complete fleet graph structure for model training. Denote the expression of the fleet graph structure as: (21), where represents the total number of civil aviation engines in the fleet, represents the damaged data sub-graph structure in the fleet, represents the civil aviation engine with index in the fleet; This construction method not only retains the local temporal and numerical relationships of the detection data of a single engine, but also integrates the overall temporal reference information of the fleet through global nodes, providing a rich information basis for subsequent extraction of features using graph neural networks and predicting the damage data interval (flight cycles), as shown in the appendix Figure 3 .

[0041] i Design of the encoder network of the prediction module. The encoder part of the model mainly consists of two sub-networks, namely a two-layer graph convolutional network for local feature extraction and a graph attention mechanism network for global information fusion. First, local feature extraction is performed through a two-layer graph convolution. Let the initial node embedding be , that is, the original damage size data of each detection record. For each node , the update formula for aggregating neighborhood information of each node by the two-layer graph convolution is: (22), (23), where represents the learnable weight matrix for the input edges of the first and second layers of the model, represents the learnable weight matrix for the output edges of the first and second layers of the model, represents the self-loop transformation matrix of the first and second layers, represents the non-linear activation function, represents the node embedding features processed by the first and second layers of the model, It should be noted that in the above formulas (22) and (23), the first term represents the aggregation of input edge information, the second term represents the aggregation of output edge information, and the third term represents the aggregation of self-loop information. The purpose of self-loop information is to retain the characteristics of the node itself.

[0042] After double-layer graph convolution processing, the node embeddings fully reflect the structural information between local detection records and their second-order neighbors. Then, global information fusion is performed through the graph attention mechanism. The graph attention mechanism mainly adaptively fuses the information of global nodes with local node embeddings to further reflect the temporal relationship of the development of damage size. For the obtained local node embeddings, calculate the attention scores between the global node embeddings and the local node embeddings: (24), In the formula, represents the shared linear transformation matrix, represents the vector used to calculate the attention, represents the non-linear activation function, represents the global node embedding and the local node embedding of the attention score; On this basis, normalize the attention scores to obtain the attention coefficients: (25), In the formula, represents the set of all local nodes connected to the global node, represents the global node embedding and the local node embedding of the attention coefficient, Finally, perform global information fusion on each local node embedding: (26), In the formula, represents the transformation matrix of the global node information. Through the full fusion of global information and local information by the encoder, when the damage size in some borescope inspection records grows significantly, the model can capture the fine-grained feature trends more accurately, so as to better characterize the dynamic process of the damage size evolving over time.

[0043] ii Prediction module decoder network design. Considering that the task of the decoder is to map the high-dimensional node embeddings extracted by the encoder to the space of the target output (edge weights) and can fully capture the non-linear features in the development process of the damage data, therefore, this method uses a multi-layer perceptron (MLP) as the decoder part.

[0044] The task of the decoder part is to convert the finally fused node representations into edge weight predictions, that is, to predict the flight cycle intervals between damage size data. The model infers the possible edge weights between new nodes based on the learned parameters. If a new node has not appeared during the training process, the model realizes the prediction process by capturing its similarity with other nodes.

[0045] Given two nodes and node 's final embeddings and , the formula for predicting the edge weight is shown in Equation (27) (27), where, represents the calculation of the multi-layer perceptron, which consists of a fully connected layer and an activation function; Loss function design. Considering that the ultimate goal of the model is to predict the weights between nodes, therefore, the training of the model is carried out by minimizing the error between the predicted edge weights and the true edge weights. The mean squared error (MSE) is used as the loss function, and its expression is shown in Equation (28).

[0046] (28), where, represents the set of edges to be predicted, represents the edge to be predicted, represents the weight of the edge predicted by the model from node i to node j , represents the true weight of the edge from node i to node j ; During training, the backpropagation algorithm is used according to the loss function to update all the parameters of the double-layer graph convolution module, the global attention fusion module, and the decoder simultaneously, so that the model is continuously optimized during training.

[0047] Finally, the prediction module part of this method is formed. The design of the prediction module makes full use of the topological structure and temporal information between the nodes in the graph, captures the fine-grained and second-order neighborhood features between the borescope inspection records through local feature extraction, and uses global information fusion to capture the overall damage development trend of the fleet, which can effectively mine the evolution pattern of damage and improve the generalization ability of the model to predict new edge weights (flight cycle intervals).

[0048] Based on the construction of the above prediction model, considering that it is difficult for the new nodes provided by the method in this example to have sufficient historical data corresponding to them during prediction, certain errors will occur when capturing the potential relationships between new nodes for edge weight prediction. Therefore, this example also introduces a Markov chain as a supplementary mechanism and proposes a Multi-Class Markov Chain-based Residual Correction (MC-RC) method to train the model according to the residuals in the edge weight prediction results of the training set, and then finely correct the prediction results of new edge weights.

[0049] It should be noted that this example selects the Markov model as the benchmark model in the correction module, mainly because it is based on the analysis results of the dynamic evolution characteristics of the fleet graph structure merging process. This example finds that when constructing a complete fleet graph structure, the damage data graphs of single engines are successively merged into the current fleet graph structure one by one. Each time a merger is completed, the state of the fleet graph structure is updated. At this time, if the model is trained on the merged graph structure, the predicted edge weight results only depend on the current state (i.e., the current fleet graph structure) and are not affected by the state of the fleet graph structure before the merger, which conforms to the Markov property that state transitions only depend on the current state. In view of this, this method uses the Markov chain as the basic framework of the correction module of this method.

[0050] However, the Markov chain relies on continuous time series data to calculate accurate state transition probabilities. Since the fleet graph structure studied in this example is composed of multiple subgraphs of single engine damage data merged together, and the nodes between the subgraphs come from the data of different engines, and the nodes do not form a continuous data sequence, it will face great difficulties to directly apply the Markov chain to correct the prediction results. In view of this, this example proposes a multi-class Markov chain residual correction method. The specific steps are described as follows.

[0051] First, use the KMeans clustering algorithm to divide into three groups according to the eigenvalue of each node, denoted as , and . In the original graph structure, the feature of each node represents the damage size data obtained from a borescope inspection. By labeling the categories of nodes, the edge connection relationship between nodes is re-described as the relationship of category conversion. That is, if the features of two nodes connected by an edge belong to categories and respectively, then this edge is re-described as the category conversion relationship of , as shown in Figure 4 . The direction of category conversion should be determined according to the direction of the edge.

[0052] According to the characteristics of category conversion, the edges in the graph structure can be divided into six conversion relationships, namely: , , , , , .

[0053] Subsequently, this example constructs corresponding Markov chain models for the above six category conversion relationships respectively. Before construction, it is necessary to clarify the definitions of the time step and the observation sequence of the Markov chain model in this example. Usually, there are multiple civil aviation engines in the fleet, which means there are multiple damage data subgraphs. Therefore, when constructing the fleet graph structure in this example, the method of merging subgraphs one by one is adopted. In this way, combined with the state update characteristics of the fleet graph structure, the merging operation of the fleet graph structure and the single-engine damage data subgraph can be regarded as a time step, and then the observed value data can be obtained. The specific method for obtaining the observed values is as follows: I. Complete a subgraph merging operation. Completing a time step means completing the merging operation of a damage data subgraph to form a new fleet graph structure.

[0054] II. Split the next subgraph and re-describe the conversion relationship. For the next single damage data graph to be merged, re-describe the edges of the nodes in the graph according to the conversion relationship between groups.

[0055] III. Obtain the residual value of the transformation relationship. Train a prediction model on the current fleet graph structure, predict the edge weights of the conversion relationship obtained in II, and calculate the residual between the predicted value and the true value. This residual is the observed value of the corresponding Markov chain of each conversion relationship at the current time step.

[0056] IV. Merge this subgraph into the current fleet graph structure, and repeat the above operations for the damage data subgraph of the next engine until all the damage data subgraphs in the fleet are merged. As shown in the appendix Figure 5 shown.

[0057] After completing the above steps, the predicted residual values of the six conversion relationships can be obtained as the observed sequence data of each Markov chain. Taking the construction method of one of the Markov chains as an example, the description is as follows. The construction methods of each Markov chain are basically the same.

[0058] State interval division. According to the obtained residual sequence , select constant values to divide it into k states , ,..., , as shown in Eqs. (29) - (31): (29), (30), (31), Wherein, represents the m th state, represents the k th state, represents the starting point of the th state interval, represents the end point of the th state interval; The number and range of state interval divisions are mainly based on the number of sub - graphs and the range of relative residual sequences. To simplify the analysis and decision - making process and avoid over - refining the state division, which increases the computational and judgment difficulty of the model, resulting in reduced interpretability and over - fitting, therefore, in this example, the state intervals are only divided into three cases: over - estimation, reasonable, and under - estimation. That is, the value is taken as 3 in this example. The upper and lower limits of each state interval and the number of data points included need to be determined according to the actual situation of the prediction object.

[0059] State transition probability matrix. In this example, the calculation of the state transition probability matrix is mainly through the frequency of transitions. Let for the residual sequence, the number of observations from state to state be (where ). Then the one - step transition probability can be calculated from the transition frequency, and its calculation formula is as shown in (32): (32), wherein, represents the one - step transition probability from state to state , represents the number of times the residual transitions from state to state in the training data, Through this calculation, the one - step state transition probability matrix can be obtained: (33), this matrix reflects the transition law of the residual sequence between different discrete states; Markov property test. After obtaining the clear and discretized state sequence through the above steps, this example uses statistical test methods to verify whether the obtained residual sequence satisfies the Markov property. First, calculate the marginal probability of each state. Let the marginal probability of the th state be the ratio of the sum of the th column in the frequency matrix to the total frequency (i.e., the number of all transitions), as shown in formula (34): (34), wherein, Marginal probability of , represents the sum of the number of times of all transitions from any state to state ; represents the total number of transitions in the residual sequence. Subsequently, a test statistic is constructed according to the classical Markov property test statistic . Here, the likelihood ratio test form is adopted, and its calculation formula is shown in (35): (35), where represents the marginal probability of state , represents the one-step transition probability from state to state , represents the sum of the number of times of all transitions from any state to state ; represents the test statistic of the Markov property test; since states are obtained during the state partitioning stage, therefore, under the given significance level , if the statistic satisfies , it is considered that the sequence has the Markov property, and the Markov correction can be applied in the prediction process.

[0060] IV. Correction of the preliminary predicted value. For such known original data, assume that the preliminary predicted value of a certain edge to be corrected is , where and are the corresponding nodes in the graph. Suppose the state of the residual corresponding to this edge after discretization is . In the Markov chain correction model, first determine the prediction interval of the next-step residual under state . Assume that the residual value interval corresponding to state is , then use the interval median as the correction value in this state: (36), where represents the upper and lower bounds of the residual interval corresponding to state . Finally, add the correction value to the preliminary predicted value to obtain the corrected predicted edge weight: (37), where represents the preliminary predicted edge weight from node to node , Represents the predicted edge weight after Markov chain correction, and the calculation of the predicted value relative to the residual state probability. Using the one-step state transition matrix to calculate step state transition matrix (where ), thus realizing the establishment of the dynamic prediction transition matrix. If the residual states of the previous observation value before the prediction moment are successively , then for the prediction of the th step, in this example, the step transition matrix can be used to predict the state probability distribution of the new node relative to the residual. Denote as: (38), where represents the state transition matrix after steps of transition; V. Then the probability of the new node in state is: (39), where represents the probability of transitioning from state to state in matrix , represents the probability that the residual of the new node at the predicted th step is in state ; Final correction result. Denote the Markov correction values of the predicted value of the new node at the n +1th step under the k residual state intervals as successively. Then the final corrected predicted value of the new node is the weighted sum of the preliminary predicted value and the correction values of each state: (40), where represents the preliminary predicted edge weight of the new node at the th step, represents the residual correction value under state , which is the median of the corresponding interval here, represents the final predicted edge weight after Markov correction.

[0061] The Markov model constructed by the correction module utilizes the dynamic evolution characteristics of the residual sequence, models the respective predicted residuals through multiple types of Markov chains, thereby finely correcting the preliminary prediction results and improving the overall prediction accuracy of the method and the robustness of the model.

[0062] The experimental verification scheme of this method will be elaborated in detail below, including experimental datasets, environmental configurations, evaluation metrics, and comparison methods, etc., to comprehensively evaluate the effectiveness and practicality of the proposed model.

[0063] To verify the effectiveness of the algorithm proposed in this example in actual engineering scenarios, this example focuses on the most representative blade crack damage type in civil aviation engine borescope inspections and conducts experimental verification. Eleven engines of model P***00 (numbered 1 - 11) from an airline are selected, and the crack damage data occurring at the same part of their high-pressure turbines are used as the research object. Measurement and statistical analysis are carried out based on the borescope inspection results. The specific statistical data are shown in Table 1 and Table 2; Among them, the crack damage development data of the engine numbered 11 are used as the verification case to evaluate the performance of the proposed method in the damage trend prediction task. According to the observed data, the crack propagation rate shows a non-linear change law of accelerating first and then slowing down.

[0064] Table 1 Crack damage data for training

[0065] Table 2 Crack damage data for verification

[0066] The experiments carried out in this example are completed in the Windows 11 operating system environment. The experimental hardware configuration is an Intel i9-12900K processor and an NVIDIA GeForce RTX 4090 graphics card. The training and testing of all models are based on the PyTorch 1.13.1 deep learning framework, and CUDA 11.6 is used for acceleration.

[0067] Among them, the learning rate during the model training process is set to 1e-3, and full-image training is adopted. The number of training epochs is set to 300. In this example, Leaky ReLU is used as the activation function in both the graph convolutional network (GCN) and the multi-layer perceptron (MLP), with the default leakage coefficient α = 0.01. This choice mainly takes into account the non-linear modeling ability, gradient propagation continuity, and adaptability to sparse graph structures to improve the stability and generalization ability of the model in the civil aviation engine damage trend prediction task.

[0068] It should be noted that in this study, the graph neural network model adopted involves multiple structural and training-related hyperparameters. Considering model complexity control and computational resource limitations, in the initial experiments of this example, key parameters were mainly configured based on empirical settings and comparative analysis was carried out under unified settings. This example will further explore the influence of different hyperparameter combinations on the model prediction accuracy and generalization ability in future research.

[0069] To ensure a systematic evaluation of the model performance, this example selects multi-dimensional statistics as the evaluation index system. Among them, the mean squared error (MSE) reflects the average value of the squared prediction errors; the root mean squared error (RMSE) characterizes the standard deviation magnitude of the errors; the mean absolute error (MAE) measures the absolute level of the prediction deviation; the mean absolute percentage error (MAPE) provides a relative proportion perspective of the errors; and the coefficient of determination (R²) is used to evaluate the model's ability to explain data fluctuations. Equations (41) to (45) are the mathematical expressions of the above five indicators.

[0070] (41), (42), (43), (44), (45), In the formula, represents the number of edges to be predicted, represents the actual weight of the th directed edge, represents the predicted weight of the th directed edge, represents the mean of the actual directed edge weights;

[0071] Through the above indicators, a comprehensive evaluation framework from absolute deviation to relative error, from dispersion degree to goodness of fit is constructed.

[0072] Prediction part As the core component of the overall method, the prediction module undertakes the main tasks of modeling the damage development trend and predicting the edge weights (flight cycle numbers). The main steps are as follows: First, based on the internal crack damage data of 10 engines of the same model with the same number, construct the corresponding graph structure and generate 10 damage data subgraphs respectively. Subsequently, by introducing global nodes and establishing global edges, these 10 subgraphs are merged to form a complete fleet graph structure. Based on this graph structure, construct the HiGDNet model that fuses local structure information and global time series information.

[0073] Next, after the model training is completed, in this example, taking the internal crack damage development data of the engine numbered 11 as an example, the number of flight cycles (i.e., edge weights) required by the engine during the damage evolution process is predicted. Through the learned graph structure features, the model realizes the prediction of the edge weights of the subgraph constructed from the internal crack damage development data of the engine numbered 11, that is, predicts the number of flight cycles required for the corresponding damage development. The model prediction results are shown in Table 3 and Figure 6 as follows: Table 3 Comparison of the actual development and prediction results of the crack damage development trend of the engine numbered 11

[0074] It can be seen from the results that the number of flight cycles predicted by the model is highly consistent with the actual observed data in the overall trend, verifying the effectiveness and good generalization ability of the proposed method in the damage evolution prediction task for directed graph structures.

[0075] Correction part On the basis of the preliminary edge weight (number of flight cycles) prediction completed by the prediction module, the correction part plays a key supplementary and optimization role in the overall process. The core task of this part is to first construct a correction model for modeling the prediction error to improve the fitting ability of the final predicted value to the actual damage evolution process. The main steps are as follows: Clustering and class conversion. The KMeans algorithm is used to cluster all crack damage data (i.e., the eigenvalue of each borescope inspection node) in the graph structure, and the damage size is divided into three categories, named Class 1, Class 2, and Class 3 respectively. As shown in Table IV, the corresponding damage size ranges for each category are 1.4 - 2.3, 2.3 - 3.4, and 3.4 - 4.2. Based on the clustering results, the edge connection relationship between nodes in the original damage data graph is redefined as the conversion relationship between categories, and the direction of the conversion relationship should be the same as the direction of the edge. For example, if the two nodes connected by an edge belong to Class 1 and Class 1 respectively, then this edge is described as a "1→1" conversion; similarly, according to the obtained damage size data, five conversion relationships can be defined, namely "1→2", "2→2", "2→3", and "3→3". On this basis, an independent Markov chain model is constructed for each conversion relationship.

[0076] Table 4 Clustering results of crack damage data

[0077] Time step division and observation sequence construction. For the construction of the fleet graph structure, after introducing the global node, the damage data subgraphs of each single engine are merged in sequence. Each subgraph merging operation is regarded as a time step. According to the existing data, the Markov chain in this example contains a total of 9 time steps. Among them, the specific operations are as follows: The first step is to split the subgraphs and obtain the residuals before merging. In each time step, for the next subgraph to be merged, the damage data in the subgraph is converted into the conversion relationship between the corresponding categories according to the clustering results in Table 4. Taking the subgraph constructed by the engine crack damage data numbered 3 as an example, the damage data development relationship is re-described as shown in Table 5.

[0078] Table 5 Pairs Figure 3 The crack damage data development relationship is re-described

[0079] After the merging of the engine subgraphs numbered 1 and 2 is completed, HiGDNet is trained using the currently merged fleet graph structure (which only contains the engine subgraphs numbered 1 and 2). Figure 3 The five category conversion relationships are predicted and the residual between the predicted value and the true edge weight is calculated. The residual is used as the observed value of the corresponding category conversion at the current time step.

[0080] It should be noted here that if a category conversion data is missing in a certain time step, although the merging operation of the damage data subgraph is completed at this time step, this time step is not included in the observation sequence. When this category appears later, this time step will be merged with the previous time step and regarded as a state update at the same time step.

[0081] The second step is to construct the observation sequence. The prediction residuals of each category transition (1→1, 1→2, 2→2, 2→3, 3→3) in all time steps are summarized to form the observation sequences of 5 Markov chains, as shown in Table 6.

[0082] Table 6 Markov chain observation sequence data of five types of development relationships

[0083] Markov chain model construction and prediction correction are performed. According to the Markov model construction method described in the present invention, based on the above observation data, Markov chain models are constructed according to five types of development relationships.

[0084] Step 3: Obtain the experimental results. Taking the crack damage data of a civil aviation engine numbered 11 as an example, the prediction results of the crack damage development trend are corrected using the above multi-class Markov chain correction method. Table 7 shows the prediction and correction results under different category conversion relationships of the crack damage data of this engine, including the required predicted crack damage development trend, category conversion relationship, corresponding flight cycles, initially predicted flight cycle intervals, and corrected flight cycle intervals.

[0085] Table 7 Comparison of prediction and correction results of the crack damage development trend of the engine numbered 11

[0086] Table 8 compares the performance indicators of the initial prediction (Predicted) and the corrected (Revised), including the mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), coefficient of determination (R²), and mean absolute percentage error (MAPE).

[0087] Table 8 Comparison of the results of each index of the prediction and correction of the crack damage development trend of the engine numbered 11

[0088] As can be seen from the above results, after being corrected by the multi-class Markov chain, the prediction model has been significantly improved in each index, making the prediction results more consistent with the original data.

[0089] On the basis of the correction module, in this example, comparative experiments are also carried out using KNeighbors regression, Lasso regression, linear regression, decision tree regression, random forest regression, MLP regression, and SVR regression. To ensure the consistency of the performance evaluation of each method, in this example, the same data set and evaluation scale standard are uniformly selected for comparative analysis, and the evaluation scale standard uses prediction performance indicators, including the mean squared error (MSE), mean absolute error (MAE), and coefficient of determination (R2 ） .

[0090] At the same time, each method clearly uses the same pre-training benchmark, which is the uniformly divided training set and test set. Table 9 and Figure 8 show the comparison results of the prediction performance indicators of each method under this unified scale standard and pre-training benchmark.

[0091] Table 9 Comparison results of the prediction performance indicators of each method under the same data set

[0092] Generally speaking, the prediction module effectively mines the topological structure and temporal evolution features in the damage detection data by constructing HiGDNet that fuses local structure and global time information, realizes the preliminary prediction of the edge weights (i.e., flight cycle numbers) between nodes, and provides basic support for modeling the damage evolution trend. The correction module further uses clustering to divide the crack damage data into multiple categories, redefines the edge types between nodes according to the category conversion relationship, constructs a multi-class Markov chain model, models and dynamically learns the prediction residuals under different category conversions, and realizes the refined correction of the preliminary prediction results.

[0093] The above experimental results show that the collaborative action of the prediction module and the correction module constructed by this method not only significantly reduces the prediction error, but also demonstrates the accuracy and generalization ability of the model in the damage evolution trend prediction task.

Claims

1. A damage trend prediction method based on a hierarchical graph structure and Markov residual correction, characterized in that A damage trend prediction model based on a hierarchical graph structure and Markov residual correction is established. The damage trend prediction model based on the hierarchical graph structure and Markov residual correction includes a prediction module and a correction module. The prediction module converts the damage size data obtained from engine borescope inspections into a graph structure, constructs a damage prediction network with a hierarchical graph structure to process the graph structure, converts the damage trend prediction problem into the prediction of edge weights between nodes in the graph, and reveals the internal relationship between damage data. The correction module designs a residual correction method based on multiple Markov chains, which is used to cluster engine damage data, convert size evolution into a transition relationship between categories, and obtain a residual observation sequence by combining the dynamic update characteristics of the graph structure, thereby constructing a Markov chain model to correct the prediction results.

2. A damage trend prediction method based on a hierarchical graph structure and Markov residual correction according to claim 1, characterized in that The specific calculation steps of the prediction module are as follows: Step 1: Define nodes and edges, and define the node set of the damage data graph , where each node corresponds to an inspection record Its feature is the detected damage size data; then, define the directed edge set For each node, a directed edge is established according to the time sequence of each borescope inspection. , indicating the increasing trend of detection order and damage; finally, define the edge weight ,side Weight is the time interval between two borescope inspections, that is, the number of flight cycles. Based on the above settings, for the borescope inspection data of a single engine, a directed graph is constructed and defined as follows: (15), where A set of nodes representing a graph, , where the number of nodes is , represents a set of directed edges, , represents the edge weight set, , express and The edge weights between them are obtained on this basis. The definition of is shown in formula (16): (16), where: represents the elements of the adjacency matrix. Through this constructed form, while reflecting the increasing trend of damage size, the time interval information can also be encoded into the edge weights; Step 2: Filter abnormal nodes. According to the trend of damage evolution, each edge should point from the node with a smaller damage size to the node with a larger damage size. If it is detected that the direction of a certain edge is opposite to this rule, that is, there is an edge pointing from the node with a larger damage size to the node with a smaller damage size, it indicates that there is an abnormality in this node pair. The abnormal edge and the corresponding node with a smaller damage size need to be removed from the graph to clear the incorrect damage record, as shown in Equation (17): (17), where represents the element of the adjacency matrix, represents the node eigenvalue, represents the node eigenvalue; Step 3: Construction of the fleet diagram structure. The damage data diagram constructed from the damage data obtained from the borescope inspection of a single engine from the first borescope inspection that recorded damage data to the last borescope inspection when the damage exceeded the standard is used as a sub-diagram, and a global node is introduced. The sub-diagrams of the same fleet are merged to improve the model's ability to integrate and generalize damage data. Here, the global node represents the global reference benchmark for the overall damage evolution trend in the fleet, as follows: First, the feature vector of the global node is set to a zero vector, indicating that the engine has not suffered any damage and the damage size is 0, as shown in Equation (18): (18), where represents the feature of the global node. Next, construct the edge connections between the global node and each subgraph node , with the direction fixed from the global node to the detection node . On this basis, determine the edge weight according to the number of flight cycles experienced by the engine from the start of operation to each borescope inspection operation. Let the number of flight cycles corresponding to the borescope inspection node be recorded as , that is, the cumulative number of flight cycles of the engine from the start of operation to this borescope inspection. Then, the edge weight of the global node pointing to the detection node is shown in Equation (19): （19）， Based on this, the elements of the adjacency matrix of the global edge can be defined as: （20）， In the formula, represents the element of the global edge adjacency matrix, Finally, the individual graphs constructed for each engine are merged to form a complete fleet graph structure for model training. Denote the expression of the fleet graph structure as: （21）， In the formula, represents the total number of civil aviation engines in the fleet, represents the damaged data subgraph structure in the fleet, represents the civil aviation engine with index in the fleet; Next, the graph neural network is used to extract features and predict the damage data interval. The prediction module encoder network consists of two sub-networks, namely, a two-layer graph convolutional network for local feature extraction and a graph attention mechanism network for global information fusion. First, local feature extraction is performed through the two-layer graph convolution. Let the initial node embedding be , that is, the original damage size data of each detection record. For each node , the update formula for aggregating the domain information of each node by the two-layer graph convolution is: （22）， (23), where represents the learnable weight matrix for the input edges of the first and second layers of the model, represents the learnable weight matrix for the output edges of the first and second layers of the model, represents the self-loop transformation matrix of the first and second layers, represents the non-linear activation function, represents the node embedding features after being processed by the first and second layers of the model. After being processed by the double-layer graph convolution, the node embedding fully reflects the structural information among the local detection records and their second-order neighbors.

3. The damage trend prediction method based on the hierarchical graph structure and Markov residual correction according to claim 2, characterized in that The specific calculation of the prediction module also includes global information fusion through the graph attention mechanism. For the obtained local node embeddings, calculate the attention scores between the global node embeddings and the local node embeddings: (24), where represents a shared linear transformation matrix, represents a vector for calculating attention, represents a non-linear activation function, represents a global node embedding and the attention score of the local node embedding ; Normalize the attention scores to obtain attention coefficients: (25), where represents the set of all local nodes connected to the global node, represents the global node embedding and the local node embedding of the attention coefficient Finally, global information fusion is performed on each local node embedding: (26), where is the transformation matrix representing global node information; The prediction module decoder network uses a multi-layer perceptron as the decoder part. The task of the decoder part is to convert the finally fused node representation into an edge weight prediction, that is, to predict the flight cycle interval between damage size data. The model infers the possible edge weights between new nodes based on the learned parameters. If a new node has not appeared during the training process, the model realizes the prediction process by capturing its similarity with other nodes. Given two nodes and node 's final embedding and , the formula for predicting the edge weight is shown in Equation (27). （27）， In the formula, represents the calculation of a multi-layer perceptron, which consists of a fully connected layer and an activation function.

4. A damage trend prediction method based on a hierarchical graph structure and Markov residual correction according to claim 3, characterized in that The training of the model is carried out by minimizing the error between the predicted edge weights and the true edge weights. The mean square error MSE is used as the loss function, and the expression is shown in Equation (28): （28）， In the formula, represents the set of edges to be predicted, represents the edge to be predicted, represents the weight of the edge predicted by the model from node i to node j , represents the true weight of the edge from node i to node j .

5. A damage trend prediction method based on a hierarchical graph structure and Markov residual correction according to claim 4, characterized in that, A multi-class Markov chain residual correction method is proposed in the correction module. The specific steps are described as follows: First, the KMeans clustering algorithm is used to divide the nodes into three groups according to their eigenvalue, denoted as , and . In the original graph structure, the feature of each node represents the damage size data obtained from a borescope inspection. By labeling the categories of the nodes, the edge connection relationship between the nodes is re-described as the relationship of category conversion, that is, if the features of two nodes connected by an edge belong to categories and respectively, then the edge is re-described as the category conversion relationship of . The direction of category conversion should be determined according to the direction of the edge. According to the characteristics of category conversion, the edges in the graph structure are divided into six conversion relationships, namely: ， ， ， ， ， ； The method for constructing any type of Markov chain includes: ① State interval division. According to the obtained residual sequence , select a constant value and divide it into k states , ,..., , as shown in formulas (29) to (31): （29）， （30）， （31）， In the formula, represents the m th state, represents the k th state, represents the starting point of the th state interval, represents the ending point of the th state interval; ② State transition probability matrix. The calculation of the state transition probability matrix is mainly carried out through the frequency of transitions. For the residual sequence, let the number of observations from state to state be , where . Then the one-step transition probability can be calculated from the transition frequency, and its calculation formula is shown in (32): （32）， In the formula, represents the one-step transition probability from state to state , represents the number of times that in the training data, the residual transfers from state to state . Through this calculation, the one-step state transition probability matrix can be obtained: (33), which reflects the transition law of the residual sequence between different discrete states; ③ Markov property test. After obtaining the clear and discretized state sequence through the above steps, use statistical test methods to verify whether the obtained residual sequence satisfies the Markov property. First, calculate the marginal probability of each state. Let the marginal probability of the th state be the ratio of the sum of the th column in the frequency matrix to the total frequency , that is, the number of all transitions, as shown in Equation (34): （34）， wherein, represents the marginal probability of the state , represents the sum of the number of times of all transfers from any state to state , represents the total number of transfers in the residual sequence. Subsequently, a test statistic is constructed according to the classical Markov property test statistic. Here, the likelihood ratio test form is adopted, and its calculation formula is shown in (35): （35）， wherein, represents the marginal probability of the state, represents the one-step transition probability from state to state , represents the sum of the number of times of all transitions from any state to state , represents the statistic of the Markov property test; Since a state is obtained in the state partitioning stage, therefore, under the given significance level , if the statistic satisfies under the condition of , it is considered that the sequence has Markov property and Markov correction can be applied in the prediction process; ④ Preliminary prediction value correction. For such known original data, assume that the preliminary prediction value of a side to be corrected is , where and are the corresponding nodes in the figure. Suppose the state of the residual corresponding to this side after discretization is . In the Markov chain correction model, first determine the prediction interval of the next-step residual in state . Assume that the residual value interval corresponding to state is , then use the interval median as the correction value in this state: （36）， In the formula, represents the upper and lower bounds of the residual interval corresponding to the state. Finally, by superimposing the correction value on the preliminary predicted value, the corrected predicted edge weight can be obtained: （37）， In the formula, represents the preliminary predicted edge weight from node to node , and represents the predicted edge weight after being corrected by the Markov chain. ⑤ Calculation of the predicted value relative to the residual state probability, using the one-step state transition matrix to calculate the one-step state transition matrix , where , thus realizing the establishment of the dynamic prediction transition matrix. If the residual states of the previous observation value before the prediction time are successively , then for the prediction of the th step, specifically use the step transition matrix to predict the state probability distribution of the new node relative to the residual, denoted as: （38）， In the formula, represents the state transition matrix after steps of transition. Then the probability of the new node in state is: （39）， In the formula, represents the matrix from state to state probability, represents the predicted step new node residual in state probability; ⑥The final correction result. Denote the predicted value of the new node at the n +(1)-th step in the k Markov correction values under the residual state intervals are successively . Then the final corrected predicted value of the new node is the weighted sum of the preliminary predicted value and the correction values of each state: （40）， In the formula, represents the preliminary predicted edge weight of the new node at the step, represents the residual correction value under the state , which is the median of the corresponding interval here, represents the final predicted edge weight after Markov correction.

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