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

Abstract

The present invention relates to the technical field of damage detection of complex equipment, and specifically to a damage trend prediction method based on a hierarchical graph structure and Markov residual correction, which is superior to a traditional time series regression model in terms of prediction accuracy and generalization ability. 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, wherein the prediction module converts damage size data obtained from an engine borescope inspection 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 a prediction of edge weights between nodes in the graph, and reveals the intrinsic connection between the damage data; the correction module designs a residual correction method based on a multi-class Markov chain, thereby constructing a Markov chain model to correct the prediction results.

Description

Technical Field

[0001] The present invention relates to the technical field of complex equipment damage detection, and in particular 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 both prediction accuracy and generalization ability. Background Art

[0002] Damage to civil aircraft engines typically begins with minor defects such as localized surface cracks and oxidation ablation pits, gradually evolving into more severe structural failures. With continued aircraft use, engine operating conditions become increasingly complex. Under the interplay of multiple physical and chemical factors, the damage progression of core engine components exhibits significant nonlinearity and uncertainty. While borescope inspections, currently widely used by airlines, can detect damage to core civil aircraft engine components, future damage trends still rely solely on subjective judgment by maintenance personnel based on manufacturer-provided maintenance manuals or their own experience. This damage trend prediction method, primarily based on experience and human judgment, struggles to capture the nonlinear characteristics of damage progression using only the limited data obtained from borescope inspections. This method can easily lead to over- or under-prediction of damage, resulting in potential safety hazards and unnecessary economic losses. With the continuous advancement of artificial intelligence technology, researchers and engineers are exploring more scientific and systematic damage trend prediction methods to reduce the uncertainty of human judgment and improve prediction accuracy. Currently, the main approaches used in industry for damage trend prediction include model-driven and data-driven approaches. Model-driven approaches primarily use experimental simulations or known mechanisms to calculate future damage progression, based on material and modeling information. Data-driven approaches use continuous historical damage development data to train statistical models to predict future damage development. In the field of civil aviation engine health management, the selection of damage trend prediction methods must fully consider the complexity of the engine, the variability of operating conditions, and the availability and discreteness of data.

[0003] Traditional model-driven approaches rely on physical mechanisms and engineering knowledge and are suitable for scenarios lacking extensive historical data. However, the application of model-driven civil aircraft engine damage trend prediction methods faces significant technical barriers for airlines. Due to intellectual property protection, civil aircraft engine manufacturers typically do not provide airlines with core parameters and key design specifications for civil aircraft engine manufacturing materials. This lack of information makes it difficult for airlines to develop damage prediction models with engineering application value when implementing intelligent civil aircraft engine operation and maintenance. Data-driven approaches primarily leverage large-scale monitoring data and intelligent algorithms, offering strong predictive capabilities in data-rich environments. Compared to model-driven approaches, data-driven approaches no longer rely on complex physical environments. Instead, they directly learn underlying patterns of damage evolution from historical data and construct predictive models using statistical learning or deep learning techniques. However, despite widespread adoption in industry, no model or algorithm has yet emerged in the aviation sector that can effectively utilize civil aircraft engine damage data for reliable prediction. Therefore, using traditional data-driven approaches to develop internal damage trend prediction models for civil aircraft engines also struggles to achieve ideal prediction results. Summary of the Invention

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

[0005] The present invention is achieved by the following measures:

[0006] A damage trend prediction method based on a hierarchical graph structure and Markov residual correction is characterized in that a damage trend prediction model based on a hierarchical graph structure and Markov residual correction is established, and the damage trend prediction model based on a hierarchical graph structure and Markov residual correction includes a prediction module and a correction module, wherein the prediction module converts the damage size data obtained by the engine borescope inspection 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 the edge weights between nodes in the graph, and reveals the intrinsic connection between the damage data; the correction module designs a residual correction method based on a multi-class Markov chain, which is used to cluster the engine damage data, convert the size evolution into a transfer relationship between categories, and obtains 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.

[0007] The specific calculation steps of the prediction module in the present invention are as follows:

[0008] Step 1: Define nodes and edges, and define the node set of the damage data graph Each node corresponds to a borescope inspection record, which is characterized by the detected damage size data; then, a directed edge set is defined. For each node, a directed edge set 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, i.e., 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:

[0009] (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):

[0010] (16),

[0011] Where: The elements representing the adjacency matrix, through this construction, can reflect the increasing trend of damage size while also encoding the time interval information into the edge weight;

[0012] Step 2: Filter abnormal nodes. According to the trend of damage evolution, each edge should point from a node with smaller damage size to a node with larger damage size. If the direction of an edge is detected to be opposite to this rule, that is, there is a node with larger damage size pointing to a node with smaller damage size, it indicates that the node pair is abnormal. The abnormal edge and the corresponding node with smaller damage size need to be removed from the graph to clear the erroneous damage records, as shown in formula (17):

[0013] (17), where represents the elements of the adjacency matrix, Representative Node The characteristic value of Representative Node The eigenvalue of;

[0014] Step 3: Fleet graph structure construction, the damage data graph 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 constructed as a subgraph and introduced into the global node The subgraphs 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. The details are as follows: First, the eigenvector of the global node is set to the zero vector, indicating that the engine has not yet incurred any damage and the damage size is 0, as shown in Equation (18): (18), where Represents the characteristics of the global node,

[0015] Next, build the edge connection between the global node and each subgraph node , the direction is fixed from the global node Pointing detection node On this basis, the edge weight is determined according to the number of flight cycles from the engine being put into operation to each borescope inspection operation. The corresponding number of flight cycles recorded is , That is, the cumulative number of flight cycles from the time the engine was put into operation to the time of the borescope inspection, then the global node Pointing detection node The edge weight of is shown in formula (19):

[0016] (19),

[0017] In this way, the adjacency matrix elements of the global edge can be defined as:

[0018] (20),

[0019] Where, represents the elements of the global edge adjacency matrix,

[0020] Finally, the individual graphs constructed for each engine are merged to form a complete fleet graph structure for model training. The fleet graph structure is expressed as:

[0021] (twenty one),

[0022] Where, Represents the total number of civil aviation engines in the fleet, Represents the damage data subgraph structure in the fleet, Represents the index in the fleet civil aviation engines.

[0023] Next, we use graph neural networks to extract features and predict damage data intervals. The prediction module encoder network consists of two sub-networks: a two-layer graph convolutional network for local feature extraction and a graph attention mechanism network for global information fusion. We first perform local feature extraction through a two-layer graph convolution. The initial node embedding is , that is, the original damage size data of each detection record, for each node , double-layer graph convolution for each node The update formula for domain information aggregation is:

[0024] (twenty two),

[0025] (twenty three),

[0026] Where, Represents the learnable weight matrix for the input edge of the first and second layers of the model, Represents the learnable weight matrix for the output edge of the first and second layers of the model, Represents the self-loop transformation matrix of the first and second layers, represents a nonlinear activation function, Represents the node embedding features after processing by the first and second layers of the model. After double-layer graph convolution, the node embedding fully reflects the structural information between local detection records and their second-order neighbors;

[0027] The specific calculation of the prediction module of the present invention also includes global information fusion through the graph attention mechanism. For the acquired local node embedding, the attention score between the global node embedding and the local node embedding is calculated:

[0028] (24), where represents the shared linear transformation matrix, represents the vector used to calculate attention, represents a nonlinear activation function, Represents the global node embedding and local node embedding Attention score;

[0029] Normalize the attention score to obtain the attention coefficient:

[0030] (25), where Represents the set of all local nodes connected to the global node, Represents the global node embedding and local node embedding The attention coefficient,

[0031] Finally, global information fusion is performed on each local node embedding:

[0032] (26), where Transformation matrix representing global node information;

[0033] The prediction module decoder network uses a multi-layer perceptron as the decoder part. The task of the decoder part is to convert the final 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 node has not appeared in the training process, the model realizes the prediction process by capturing its similarity with other nodes. Given two nodes and nodes The final embedding and , the formula for predicting edge weight is shown in formula (27)

[0034] (27),

[0035] Where, Represents multi-layer perceptron computation, consisting of fully connected layers and activation functions.

[0036] 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, using the mean square error (MSE) as the loss function, which is expressed as shown in formula (28):

[0037] (28),

[0038] Where, represents the set of edges that need to be predicted, Represents the edge that needs to be predicted, Nodes representing model predictions i Pointing to a node j The weight of the edge, Represented by the node i Pointing to a node j The true weight of the edge.

[0039] The present invention proposes a multi-class Markov chain residual correction method 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 the eigenvalues ​​of each node, which are 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 node categories, the edge connection relationship between the nodes is redescribed as the conversion relationship between categories, that is, if the features of the two nodes connected by an edge belong to the categories and , then redescribe the edge as The direction of the category conversion relationship should be determined according to the direction of the edge. According to the characteristics of the category conversion, the edges in the graph structure are divided into six types of conversion relationships, namely:

[0040] , , , , , ; Methods for constructing any type of Markov chain include:

[0041] ① State interval division, according to the obtained residual sequence , select a constant value to divide into k states , ,..., , as shown in formulas (29) to (31):

[0042] (29), (30), (31),

[0043] Where, Representative m states, Representative k states, Representative The starting point of the state interval, Representative The end point of a state interval;

[0044] ② The state transfer probability matrix. The calculation of the state transfer probability matrix is ​​mainly calculated by the frequency of transfer. Assume that for the residual sequence, from the state Transfer to state

[0045] The number of observations is ,in , then the one-step transition probability can be calculated from the transition frequency, and its calculation formula is shown in (32):

[0046] (32), where Represents the slave state Transfer to state The one-step transition probability, Represents that in the training data, the residual from the state Transfer to state The number of times,

[0047] Through this calculation, we can get the one-step state transition probability matrix: (33), this matrix reflects the transition law of the residual sequence between different discrete states;

[0048] ③ Markov property test: After obtaining a clear and discretized state sequence through the above steps, the statistical test method is used to verify whether the obtained residual sequence satisfies the Markov property. First, the marginal probability of each state is calculated. Let The marginal probability of a state is the first Column sum and total frequency , that is, the ratio of the number of all transfers, as shown in formula (34):

[0049] (34), where Representation status The marginal probability of Represents all from any state Transfer to state The sum of the times of Represents the total number of transitions in the residual sequence. Subsequently, the test statistic is constructed based on the classic Markov test statistic , here we use the likelihood ratio test form, and its calculation formula is shown in (35):

[0050] (35),

[0051] Where, Representation status The marginal probability of Represents the slave state Transfer to state The one-step transition probability, Represents all from any state Transfer to state The sum of the times of Represents the statistic of Markov test; since it is obtained in the state division stage Taken a state, therefore, at a given significance level Under the condition of , then the sequence is considered to have Markov properties and Markov correction can be applied in the prediction process;

[0052] ④ Modification of the initial predicted value: For this type of known original data, assume that the initial predicted value of a certain edge to be modified is ,in and is the corresponding node in the graph. If the residual corresponding to the edge is discretized into In the Markov chain correction model, first determine the state Next, the prediction interval of the next residual, assuming the state The corresponding residual value interval is , then use the median of the interval As the correction value in this state:

[0053] (36),

[0054] Where, Representation status The upper and lower bounds of the corresponding residual interval are finally added to the preliminary prediction value to obtain the corrected prediction edge weight:

[0055] (37),

[0056] Where, Representative Node To Node The initial predicted edge weights of represents the predicted edge weight after Markov chain correction,

[0057] ⑤Calculation of the probability of the predicted value relative to the residual state, using the one-step state transfer matrix To calculate Step state transfer matrix (in ), thereby realizing the establishment of the dynamic prediction transfer matrix, if the residual state of the observation value before the prediction moment is , then for the Step prediction, specific use Step transfer matrix To predict the state probability distribution of the new node relative to the residual, record it as: (38),

[0058] Where, Representatives passed The state transfer matrix of the step transfer, the probability of the new node in the state is:

[0059] (39),

[0060] Where, Representative Matrix Move from state to state The probability of predicting the residual of the new node in the step is in the state probability;

[0061] ⑥Final correction result, record n The predicted value of the new node in step +1 is k The Markov correction values ​​under the residual state interval are , then the final revised prediction value of the new node is the weighted sum of the preliminary prediction value and the revised values ​​of each state:

[0062] (40), where Represents the new node in The initial predicted edge weights of the step, Representation status The residual correction value under , here is the median of the corresponding interval, Represents the final predicted edge weight after Markov correction.

[0063] The prediction module of the present invention converts the damage size data obtained from engine borescope inspection into a graph structure, constructs a hierarchical graph-structured damage prediction network (HiGDNet) to process the graph structure, and converts the damage trend prediction problem into the prediction of edge weights between nodes in the graph, revealing the intrinsic connection between the damage data; the correction module designs a residual correction method based on multi-class Markov chain (MC-RC), which clusters engine damage data, converts size evolution into transfer relations between categories, and combines the dynamic update characteristics of the graph structure to obtain residual observation sequences, thereby constructing a Markov chain model to correct the prediction results. It is superior to traditional time series regression models in both prediction accuracy and generalization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Attachment Figure 1 It is the overall architecture diagram of the present invention.

[0065] Attachment Figure 2 It is a schematic diagram of converting the damage size into a graph structure in the present invention.

[0066] Attachment Figure 3 This is a schematic diagram of adding a global node to merge subgraphs in the present invention.

[0067] Attachment Figure 4 It is a schematic diagram of the conversion relationship of the redescription of the edge in the present invention.

[0068] Attachment Figure 5 It is a schematic diagram of the residual sequence of the conversion relationship obtained by predicting the next sub-graph after the splitting after the merging operation in the present invention.

[0069] Attachment Figure 611 is a comparison curve of the actual and predicted crack damage development trends of the engine in the embodiment of the present invention.

[0070] Attachment Figure 7 This is a comparison curve of the prediction and correction results of various indicators for the crack damage development trend of the engine numbered 11 in an embodiment of the present invention.

[0071] Attachment Figure 8 It is a comparison curve of prediction performance indicators of various methods in the embodiments of the present invention under the same data set. DETAILED DESCRIPTION

[0072] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0073] Graph Neural Networks (GNNs) are a type of deep learning model specifically designed for processing graph-structured data. By learning the graph's topological structure and node characteristics, they efficiently capture the relationships between nodes, thereby explicitly expressing the internal associations within the data. By directly linking nodes and edges through the graph structure, they can better mine and characterize the complex internal connections within the data.

[0074] Single graph The expression of is shown in formula (1): (1),

[0075] Where, A set of nodes representing a graph, , where the number of nodes is , represents the set of edges in the graph, , represents the edge weight set, , express and The edge weight between

[0076] Here each node Possesses feature representation :

[0077] (2), the feature matrix of all nodes ; Here, the graph structure is represented by an adjacency matrix, whose elements are defined as:

[0078] (3),

[0079] Where, represents the elements in the adjacency matrix,

[0080] At this point, the elements of the adjacency matrix represent the degree of relationship between two nodes or the strength of the connection. It is worth noting that if the constructed graph is a directed graph, Symmetry is not usually satisfied, and this property preserves the directional information of connections between nodes. The core mechanism of GNNs is message passing. By iteratively aggregating information about neighboring nodes on the graph structure, each node gradually incorporates contextual features from its neighbors, thereby continuously updating and optimizing node feature representations and more effectively capturing relationships and interactions in the data. The message passing mechanisms differ for different graph structures:

[0081] I. For undirected graphs, an undirected graph consists of vertices (nodes) and undirected edges (edges connecting two nodes). Each edge represents a bidirectional connection between two nodes, meaning that information can be transmitted in any direction along the edge. Therefore, there is no need to make complex distinctions. The transfer model is expressed as:

[0082] (4),

[0083] Where, represents the input features, Representative Node The set of neighbor nodes of represents a nonlinear activation function, , Represents the learnable parameter matrix and bias term;

[0084] II. Regarding directed graphs, a directed graph consists of vertices (nodes) and directed edges (connections with a clear direction). Each edge only allows information to flow in a specific direction. Therefore, compared to undirected graphs, information propagation in directed graphs is constrained by the direction of the edges and is more hierarchical and structured. When aggregating information in a directed graph, it is necessary to consider both the input and output edges separately.

[0085] Here, set the node The input neighbor set is set to ,node The output neighbor set of At this time, the update of the directed graph node features needs to use both the input neighbor information and the output neighbor information, as shown in the following formula:

[0086] (5),

[0087] Where, represents the input features,

[0088] Representative Node The set of neighbor nodes of represents a nonlinear activation function, , represents the learnable parameter matrix and bias term,

[0089] 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 use the information transmitted by the node from the predecessor (input edge) and the successor (output edge) to achieve a fine modeling of the interaction of directed relationship features, thereby fully capturing the complex causal and temporal relationships within the data.

[0090] The training goal of graph neural networks is still to optimize the parameters of the network by minimizing the loss function. Represents the output of the GNN model, where Representing all learnable parameters in the network, the network loss function can be expressed as:

[0091] (6), where represents the true label (e.g., node classification or target of graph-level tasks), Represents the loss function; during the training process, the model parameters will be updated through back propagation and gradient descent , to obtain the optimal network parameters.

[0092] A Markov model is a mathematical model used to model random processes in which the future state of a system depends only on its current state and is independent of the historical process that led to the current state. This property is known as the Markov property.

[0093] set up Indicates that a system is at time The state of Markov can be expressed mathematically as:

[0094] (7),

[0095] The next state of the system Depends only on the current state , not dependent on past states X t-1 , X t-2 , ....

[0096] Markov Chain is a Markov process in a discrete state space, where the state transition is described by a state transition matrix. Suppose the possible state set of the system is , the probability of state transition is given by the matrix gives:

[0097] (8),

[0098] Where, Represents the system from the state Migrate to state The probability of (9),

[0099] And the normalization conditions are met: (10), for the state distribution, let the initial state distribution be:

[0100] (11),

[0101] Where, Represents the state of the system at the initial moment The probability of After the round transfer, the state distribution of the system is:

[0102] (12), after expansion, we can get: (13)

[0103] when When the system reaches a stable probability distribution ,satisfy:

[0104] , (14), solving this set of equations can obtain the steady-state distribution of the Markov chain.

[0105] Internal damage data from civil aviation engines is affected by the intervals between borescope inspections and the number of borescope inspections, exhibiting characteristics of non-uniform sampling and discontinuity. This study discovered that while engine borescope damage data lacks temporal continuity, it exhibits a clear spatial trajectory, making it amenable to graph modeling. Specifically, if the damage size recorded in each borescope inspection is used as the feature of a node in the graph, the edges between nodes represent their temporal evolutionary relationships, and the edge weights are determined by the number of flight cycle intervals between nodes, the engine damage evolution process can be abstracted as a graph-structured edge weight prediction problem. This approach effectively avoids the reliance of traditional time series methods on equally spaced sampling and reflects the damage evolution path in a more realistic manner. Furthermore, by further combining prediction residual correction methods, it is expected to more accurately extract the potential connections between damage features and enhance the model's ability to perceive complex damage evolution patterns. Therefore, this example will implement the design of a civil aviation engine damage trend prediction method based on this approach.

[0106] This example details the design of various modules of a damage trend prediction method based on a hierarchical graph structure and Markov residual correction. The overall architecture of the model is as follows Figure 1 As shown in the figure, it mainly includes two modules: prediction and correction.

[0107] For the prediction module, the damage size data obtained from the borescope inspection of a single engine is first used as the node, and the number of flight cycles between the data is used as the edge weight between the nodes to establish a single damage data graph structure. That is, the development relationship of the internal damage data of the engine is abstracted as the connection between the nodes and edges in the graph structure; then, a global node is introduced, and the damage data graphs of the same part of the fleet are integrated through the merge graph operation to form a fleet damage data graph; then, the constructed fleet damage data graph is subjected to feature extraction and convolution operations through the graph neural network to explore the deep intrinsic correlation between the damage data; finally, the damage trend prediction problem is transformed into the prediction of the edge weights between nodes to accurately capture the development trend of future damage data.

[0108] For the correction module, this example designs a multi-class Markov chain residual correction prediction method based on the dynamic state update characteristics of the graph structure. Specifically, a clustering method is first used to classify the internal engine damage data into three categories. Subsequently, the evolution of damage size is converted into transition relationships between the categories, re-depicting the edges connecting the nodes in the graph as transitions between categories, totaling six transition relationships. Next, based on the state update characteristics of the graph structure during the merge operation, the merge operation is treated as a time step, and corresponding Markov chain models are established using the residual data obtained from the six different category transitions. For the edge weight between two nodes to be predicted (i.e., the number of flight cycles between the damage sizes), the category transition relationship of the connecting edge is first determined based on the category of the two nodes' features. Then, the corresponding category Markov chain is used to fine-tune the prediction residual, improving the accuracy of damage trend prediction.

[0109] The main task of the prediction module is to predict the future development trend of damage based on the historical development data of damage. In this case, a damage development trend prediction method based on graph neural network is designed.

[0110] First, a single damage graph structure is constructed. Based on the characteristics of damage size data obtained from engine borescope inspections, this example uses a single borescope inspection operation that records damage size as a graph node, and the damage size data obtained from the borescope inspection as the feature of the graph node. Each node is connected by an edge, with the direction of the edge being from the node with a smaller feature value to the node with a larger feature value. The time interval between damage size data is then used as the weight of the connecting 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.

[0111] Next, the fleet damage graph structure is constructed. To further utilize damage size data from the same model and location within the fleet, this method introduces a global node to merge the damage data graphs generated by each engine. The eigenvalue of the global node is set to 0, indicating that the engine has just been put into operation and has not yet incurred any damage. On this basis, edge connections are established between the global node and each inspection node, and the flight cycle interval between the global node and each borescope inspection (node ​​in the graph) that records damage size is calculated. This flight cycle interval serves as the weight of the edge between the global node and each inspection node. Finally, the damage data graphs generated for each engine in the entire fleet are merged to form a complete fleet graph structure.

[0112] Finally, based on the fleet graph structure, this example designs a hierarchical graph-based damage prediction network (HiGDNet) to process the fleet graph. This network employs an encoder-decoder architecture. The encoder consists primarily of a local feature extraction network and a global information fusion network. The local feature extraction network utilizes a two-layer graph convolutional network, which aggregates information from both incoming and outgoing neighbor nodes and preserves node attributes by utilizing self-loop connections to capture local and second-order neighborhood features in borescope inspection data from individual engines. The global information fusion network, based on a graph attention mechanism, adaptively fuses information from global nodes (representing the moment an engine is first put into operation, with zero features) with local node embeddings, leveraging temporal relationships and global reference information between engine data within the fleet. The decoder, composed of a multilayer perceptron, uses the node embedding features obtained by the encoder to predict edge weights between new nodes. This edge weight represents the number of flight cycle intervals between the damage sizes to be predicted. This design fully leverages the topological structure between nodes, allowing information to flow within the graph. This allows each node to learn and integrate information from its neighbors, supporting the prediction of edge weights between new nodes. This structural design also enhances the model's generalization capabilities when predicting new, unlearned graph structures.

[0113] The specific calculation steps of the prediction module are as follows:

[0114] I. Define nodes and edges. For a certain type of damage, first, a borescope inspection of a certain engine that records damage size data is taken as a node, and the damage size of a certain type of damage obtained in the inspection is used as the feature of the node. Then, on the basis of constructing all detection nodes, edges are constructed between the borescope inspection nodes. The edge information consists of three parts: the edge index and the edge weight. The edge index defines the starting point and end point of the edge. In the process of adding edges, it should be set strictly according to the time sequence of the borescope inspection to ensure that the model can pay attention to the increasing trend of damage size over time during training. The edge weight is defined as the number of flight cycles between adjacent borescope inspection nodes, which is used to quantify the flight cycle interval between inspections. As Figure 2 shown.

[0115] It should be noted that the number of flight cycles described here refers to the complete working process of a civil aviation engine in a flight mission: starting - idling - taxiing - takeoff - climb - cruising - descending - approach - reverse thrust - idling - shutdown.

[0116] Here, this example first defines the node set of the damage data graph , each node corresponds to a borescope inspection record, which is characterized by 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 It is the time interval between two borescope inspections, that is, the number of flight cycles.

[0117] Based on the above settings, the directed graph of the borescope inspection data of a single engine is defined as follows:

[0118] (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, on this basis, we can get the adjacency matrix of the graph The definition of is shown in formula (16):

[0119] (16), where: The elements representing the adjacency matrix can reflect the increasing trend of damage size through such a constructed form, and further encode the time interval information into the edge weight.

[0120] II. Filtering abnormal nodes. Considering that there are cases where damage size errors are recorded during borescope inspection, after converting the borescope inspection data of a single civil aviation engine into graph structure data, the node pairs in the graph are checked. Here, a node pair refers to two nodes connected by a directed edge. Under normal circumstances, according to the trend of damage evolution, each edge should point from a node with a smaller damage size to a node with a larger damage size. If the direction of an edge is detected to be opposite to this rule, that is, there is a node from a node with a larger damage size to a node with a smaller damage size, it indicates that the node pair is abnormal. The abnormal edge and the corresponding node with a smaller damage size need to be removed from the graph to clear the erroneous damage record and ensure that the subsequent graph structure and information aggregation process are based only on normal and reasonable detection data, as shown in Equation (17). (17), where represents the elements of the adjacency matrix, Representative Node The characteristic value of Representative Node The eigenvalue of;

[0121] Fleet graph structure construction. Based on the above steps, in order 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 obtained from the first borescope inspection of a single engine with recorded damage data to the last borescope inspection when the damage exceeds the standard as a subgraph. Introducing global nodes The subgraphs 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. The details are as follows:

[0122] First, the eigenvector of the global node is set to the zero vector, indicating that the engine has not yet incurred any damage and the damage size is 0, as shown in Equation (18):

[0123] (18), where Represents the characteristics of the global node,

[0124] Next, build the edge connection between the global node and each subgraph node , the direction is fixed from the global node Pointing detection node On this basis, the edge weight is determined according to the number of flight cycles from the engine being put into operation to each borescope inspection operation (i.e. each node). The corresponding number of flight cycles recorded is , That is, the cumulative number of flight cycles from the time the engine was put into operation to the time of the borescope inspection. Pointing detection node The edge weight of is shown in formula (19). (19),

[0125] In this way, the adjacency matrix elements of the global edge can be defined as:

[0126] (20), where represents the elements of the global edge adjacency matrix,

[0127] Finally, the individual graphs constructed for each engine are merged to form a complete fleet graph structure for model training. The fleet graph structure is expressed as:

[0128] (21), where Represents the total number of civil aviation engines in the fleet, Represents the damage data subgraph structure in the fleet, Represents the index in the fleet civil aviation engines;

[0129] This construction method not only preserves the local time series and numerical relationship of the single engine detection data, but also integrates the time series reference information of the entire fleet through global nodes, providing a rich information foundation for the subsequent use of graph neural networks to extract features and predict damage data intervals (number of flight cycles), as shown in the attached figure. Figure 3 shown.

[0130] i Prediction module encoder network design. The encoder part of the model mainly consists of two sub-networks, namely a two-layer graph convolution network for local feature extraction and a graph attention mechanism network for global information fusion. First, local features are extracted through two-layer graph convolution. Assume that the initial node embedding is , that is, the original damage size data of each detection record. For each node , double-layer graph convolution for each node The update formula for domain information aggregation is:

[0131] (twenty two), (twenty three),

[0132] Where, Represents the learnable weight matrix for the input edge of the first and second layers of the model, Represents the learnable weight matrix for the output edge of the first and second layers of the model, Represents the self-loop transformation matrix of the first and second layers, represents a nonlinear activation function, Represents the node embedding features after being processed by the first and second layers of the model,

[0133] It should be noted that in the above formulas (22) and (23), the first term represents the aggregation of input side information, the second term represents the aggregation of output side information, and the third term represents the aggregation of self-loop information. The purpose of self-loop information is to preserve the node's own characteristics.

[0134] After two layers of graph convolution, the node embedding fully reflects the structural information between local detection records and their second-order neighbors. Next, global information fusion is performed through the graph attention mechanism. The graph attention mechanism mainly adaptively fuses the global node information with the local node embedding to further reflect the temporal relationship of the damage size development. For the obtained local node embedding, the attention score between the global node embedding and the local node embedding is calculated: (twenty four),

[0135] Where, represents the shared linear transformation matrix, represents the vector used to calculate attention, represents a nonlinear activation function, Represents the global node embedding and local node embedding Attention score;

[0136] On this basis, the attention score is normalized to obtain the attention coefficient: (25),

[0137] Where, Represents the set of all local nodes connected to the global node, Represents the global node embedding and local node embedding The attention coefficient,

[0138] Finally, global information fusion is performed on each local node embedding:

[0139] (26),

[0140] Where, The encoder represents the transformation matrix of global node information. By fully integrating global information with local information, the model can more accurately capture fine-grained characteristic trends when the damage size in some borescope inspection records increases significantly, thereby better characterizing the dynamic process of damage size evolution over time.

[0141] ii. Decoder network design for the prediction module. Considering that the decoder's task is to map the high-dimensional node embeddings extracted by the encoder to the target output (edge ​​weight) space and to fully capture the nonlinear characteristics of the damage data development process, this method uses a multi-layer perceptron (MLP) as the decoder.

[0142] The decoder's task is to convert the final fused node representation into edge weight predictions, specifically predicting the flight cycle intervals between damage size data. The model infers possible edge weights between new nodes based on learned parameters. If a new node has not been seen during training, the model predicts its edge weights by capturing its similarity to other nodes.

[0143] Given two nodes and nodes The final embedding and , the formula for predicting edge weight is shown in formula (27) (27),

[0144] Where, Represents multi-layer perceptron computation, consisting of fully connected layers and activation functions;

[0145] Loss function design. Considering that the ultimate goal of the model is to predict the weights between nodes, the model is trained 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 its expression is shown in Equation (28).

[0146] (28), where represents the set of edges that need to be predicted, Represents the edge that needs to be predicted, Nodes representing model predictions i Pointing to a node j The weight of the edge, Represented by the node i Pointing to a node j The true weight of the edge;

[0147] During training, the back-propagation algorithm is used according to the loss function to simultaneously update the double-layer graph convolution module, the global attention fusion module, and all the parameters of the decoder, so that the model is continuously optimized during training.

[0148] Ultimately, the prediction module of this method was formed. Its design fully leverages the topological structure and temporal information between nodes in the graph. It captures fine-grained and second-order neighborhood features between borescope inspection records through local feature extraction, and uses global information fusion to capture overall fleet damage trends. This effectively explores damage evolution patterns and improves the model's generalization ability for predicting new edge weights (flight cycle intervals).

[0149] On the basis of the above-mentioned prediction model construction, considering that the new nodes provided by this method during prediction are unlikely to have sufficient historical data corresponding to them, certain errors will occur when capturing the potential relationships between new nodes for edge weight prediction. Therefore, this example also introduces Markov chain as a supplementary mechanism and proposes a multi-class Markov chain-based residual correction method (Multi-Class Markov Chain-based Residual Correction, MC-RC), which is used to train the model according to the residuals in the edge weight prediction results of the training set, and then to make fine corrections to the prediction results of the new edge weights.

[0150] It should be noted that the Markov model was chosen as the baseline model in the correction module of this example. This was primarily based on an analysis of the dynamic evolution characteristics of the fleet graph structure merging process. This example found that when constructing the complete fleet graph structure, the damage data graphs of individual engines were merged into the current fleet graph structure one by one. Each time a merge was completed, the fleet graph structure underwent a state update. At this point, if the model is trained on the current merged graph structure, its predicted edge weights depend only on the current state (i.e., the current fleet graph structure) and are unaffected by the state of the fleet graph structure before the merge. This conforms to the Markov property that state transitions depend only on the current state. Given this, this method uses a Markov chain as the underlying architecture of its correction module.

[0151] However, Markov chains rely on continuous time series data to accurately calculate state transition probabilities. Because the fleet graph structure studied in this example is composed of multiple subgraphs of damage data from individual engines, each derived from data from a different engine. The nodes between the subgraphs do not form a continuous data sequence. Directly applying Markov chains to correct prediction results would be extremely difficult. To address this, this example proposes a multi-class Markov chain residual correction method. The specific steps are described below.

[0152] First, the KMeans clustering algorithm is used to divide the nodes into three groups according to their characteristic values, which are 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 between the conversions between categories. That is, if the features of the two nodes connected by an edge belong to the categories and , then redescribe the edge as The category conversion relationship, such as Figure 4 As shown in the figure, the direction of category conversion should be determined according to the direction of the edge.

[0153] According to the characteristics of category conversion, the edges in the graph structure can be divided into six types of conversion relationships, namely:

[0154] , , , , , .

[0155] Subsequently, this example constructs corresponding Markov chain models for the six categories of conversion relationships mentioned above. Before construction, it is necessary to clarify the definitions of the time step and 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, this example adopts the method of merging subgraphs one by one. 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 observation data can be obtained. The specific observation value acquisition method is as follows:

[0156] I. Complete a subgraph merge operation. Completing a time step means completing a merging operation on the damage data subgraphs, forming a new fleet graph structure.

[0157] II. Split the next subgraph and redescribe the transformation relationship. For the next single damage data graph to be merged, redescribe the edges of the nodes in the graph based on the transformation relationship between the groups.

[0158] III. Obtain the residual values ​​of the transformation relationships. Train the prediction model on the current fleet graph structure and predict the edge weights of the transformation relationships obtained in II. Calculate the residual between the predicted value and the true value. This residual is the observed value of the Markov chain corresponding to each transformation relationship at the current time step.

[0159] IV. Merge the subgraph into the current fleet graph structure, and repeat the above operation for the damage data subgraph of the next engine until all damage data subgraphs in the fleet are merged. Figure 5 shown.

[0160] After completing the above steps, the predicted residual values ​​of the six transformation relationships can be obtained as the observation sequence data of various Markov chains. Taking the construction method of one type of Markov chain as an example, it is described below. The construction methods of various Markov chains are basically the same.

[0161] State interval division. According to the obtained residual sequence , select a constant value to divide into k states , ,..., , as shown in formulas (29) to (31): (29), (30), (31),

[0162] Where, Representative m states, Representative k states, Representative The starting point of the state interval, Representative The end point of a state interval;

[0163] The number and range of state intervals are mainly based on the number of subgraphs and the range of the relative residual sequence. In order to simplify the analysis and decision-making process and avoid over-refining the state division, which increases the difficulty of model calculation and judgment, resulting in reduced interpretability and overfitting, this example divides the state interval into only three situations: overestimation, reasonableness, and underestimation. The value is 3. The upper and lower limits of each state interval and the number of data included need to be determined according to the actual situation of the prediction object.

[0164] State transition probability matrix. In this example, the calculation of the state transition probability matrix is ​​mainly calculated by the frequency of the transition. Assume that for the residual sequence, from the state Transfer to state The number of observations is (in ). Then the one-step transition probability can be calculated from the transition frequency, and its calculation formula is shown in (32): (32), where Represents the slave state Transfer to state The one-step transition probability, Represents that in the training data, the residual from the state Transfer to state The number of times,

[0165] Through this calculation, we can get the one-step state transition probability matrix:

[0166] (33), this matrix reflects the transition law of the residual sequence between different discrete states;

[0167] Markov property test. After obtaining a 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. Assume The marginal probability of a state is the first Column sum and total frequency (i.e., the number of all transfers), as shown in formula (34): (34), where Representation status The marginal probability of Represents all from any state Transfer to state The sum of the times of Represents the total number of transitions in the residual sequence. Subsequently, the test statistic is constructed based on the classic Markov test statistic , here we use the likelihood ratio test form, and its calculation formula is shown in (35): (35), where Representation status The marginal probability of Represents the slave state Transfer to state The one-step transition probability, Represents all from any state Transfer to state The sum of the times of Represents the statistic of Markov test; since it is obtained in the state division stage Taken a state, therefore, at a given significance level Under the condition of , then the sequence is considered to have Markov properties and Markov correction can be applied in the prediction process.

[0168] IV. Modification of preliminary prediction value. For this type of known original data, suppose the preliminary prediction value of a certain edge to be modified is ,in and is the corresponding node in the graph. If the residual corresponding to the edge is discretized into In the Markov chain correction model, first determine the state Next, the prediction interval of the residual error for the next step. Assuming the state The corresponding residual value interval is , then use the median of the interval As the correction value in this state:

[0169] (36), where Representation status The upper and lower bounds of the corresponding residual interval are finally added to the preliminary prediction value to obtain the corrected prediction edge weight: (37),

[0170] Where, Representative Node To Node The initial predicted edge weights of Represents the predicted edge weight after Markov chain correction, and the calculation of the probability of the predicted value relative to the residual state. Using the one-step state transfer matrix To calculate Step state transfer matrix (in ), thereby realizing the establishment of the dynamic prediction transfer matrix. If the residual state of the observation value before the prediction time is , then for the Step prediction, in this case, can be used Step transfer matrix To predict the state probability distribution of the new node relative to the residual. Note:

[0171] (38), where Representatives passed The state transfer matrix of step transfer;

[0172] V. Then the new node is in state The probability is:

[0173] (39),

[0174] Where, Representative Matrix Middle slave state Transfer to state The probability of Representative prediction The new node residual is in the state probability;

[0175] Final correction result. n The predicted value of the new node in step +1 is k The Markov correction values ​​under the residual state interval are The final revised prediction value of the new node is the weighted sum of the initial prediction value and the revised values ​​of each state:

[0176] (40),

[0177] Where, Represents the new node in The initial predicted edge weights of the step, Representation status The residual correction value under , here is the median of the corresponding interval, Represents the final predicted edge weight after Markov correction.

[0178] The Markov model constructed by the correction module utilizes the dynamic evolution characteristics of the residual sequence and models the respective prediction residuals through multiple types of Markov chains, thereby making fine corrections to the preliminary prediction results and improving the overall prediction accuracy of the method and the robustness of the model.

[0179] The following will elaborate on the experimental verification scheme of this method, including the experimental dataset, environment configuration, evaluation indicators and comparison methods, to comprehensively evaluate the effectiveness and practicality of the proposed model.

[0180] To verify the effectiveness of the proposed algorithm in actual engineering scenarios, this example focuses on the most representative blade crack damage type in borescope inspections of civil aviation engines and conducts experimental verification. Eleven P***00 engines (numbered 1-11) from an airline company were selected, and crack damage data occurring in the same part of their high-pressure turbines were used as the research object. Measurements and statistical analysis were performed based on the borescope inspection results. Detailed statistical data are shown in Tables 1 and 2.

[0181] The engine crack damage development data for case 11 was used as a validation case to evaluate the performance of the proposed method in damage trend prediction. The observed data showed that the crack growth rate exhibited a nonlinear pattern of first accelerating and then slowing down.

[0182] Table 1 Crack damage data used for training

[0183] Table 2 Crack damage data used for verification

[0184]

[0185] The experiments in this example were conducted in a Windows 11 operating system environment. The experimental hardware configuration was an Intel i9-12900K processor and an NVIDIA GeForce RTX 4090 graphics card. All model training and testing were based on the PyTorch 1.13.1 deep learning framework, accelerated by CUDA 11.6.

[0186] The learning rate during model training is 1e-3, full-graph training is used, and the number of training rounds 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 nonlinear modeling ability, gradient propagation continuity, and adaptability to sparse graph structures, so as to improve the stability and generalization ability of the model in the task of civil aviation engine damage trend prediction.

[0187] It should be noted that the graph neural network model used in this study involves multiple structural and training-related hyperparameters. To manage model complexity and maintain computational resource constraints, this initial experiment primarily configured key parameters based on empirical settings and conducted comparative analysis under a unified setup. Future research will further explore the impact of different hyperparameter combinations on the model's prediction accuracy and generalization capabilities.

[0188] To ensure a systematic evaluation of model performance, this example selects a multi-dimensional statistical index system as the evaluation index system. Among them, the mean square error (MSE) reflects the square mean of the prediction error; the root mean square error (RMSE) represents the standard deviation of the error; the mean absolute error (MAE) measures the absolute level of prediction deviation; the mean absolute percentage error (MAPE) provides a relative proportional perspective on the error; 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.

[0189] (41), (42),

[0190] (43), (44),

[0191] (45),

[0192] Where, represents the number of edges to be predicted, Representative The actual weight of the directed edge, Representative The predicted weight of the directed edge, represents the mean of the actual directed edge weights;

[0193] Through the above indicators, a comprehensive evaluation framework from absolute deviation to relative error, from degree of dispersion to goodness of fit was constructed.

[0194] The civil aviation engine damage trend prediction model constructed in this example consists of two parts: a prediction module and a correction module. This example provides a detailed description and analysis of the calculation process and experimental results of these two core components.

[0195] Prediction section

[0196] As the core component of the overall method, the prediction module is responsible for modeling damage development trends and predicting edge weights (number of flight cycles). Its main steps are as follows:

[0197] First, a corresponding graph structure was constructed based on the internal crack damage data of 10 engines of the same model number, generating 10 damage data subgraphs. Subsequently, these 10 subgraphs were merged by introducing global nodes and establishing global edges to form a complete fleet graph. Based on this graph structure, the HiGDNet model was constructed, which integrates local structural information with global temporal information.

[0198] Then, after the model training is completed, this example uses the internal crack damage development data of engine number 11 as an example to predict the number of flight cycles (i.e., edge weight) that the engine needs to experience during the damage evolution process. The model uses the learned graph structure features to predict the edge weights of the subgraph constructed from the internal crack damage development data of engine number 11, that is, to predict the number of flight cycles required for the corresponding damage development. The model prediction results are shown in Table 3 and Figure 6 As shown:

[0199] Table 3 Comparison of actual and predicted development trends of crack damage in engine No. 11

[0200]

[0201] The results show that the flight cycle number predicted by the model is highly consistent with the actual observed data in terms of overall trend, which verifies the effectiveness and good generalization ability of the proposed method in the damage evolution prediction task for directed graph structures.

[0202] Correction

[0203] Based on the initial edge weight (number of flight cycles) predictions completed by the prediction module, the correction component plays a key supplementary optimization role in the overall process. Its core task is to first construct a correction model for modeling prediction errors, thereby improving the ability of the final prediction to fit the actual damage evolution process. The main steps are as follows:

[0204] Clustering and Class Transformation. The K-Means algorithm was used to cluster all crack damage data in the graph (i.e., the eigenvalues ​​of each borescope inspection node), dividing the damage sizes into three classes: Class 1, Class 2, and Class 3. As shown in Table IV, the corresponding damage size ranges for each class are 1.4–2.3, 2.3–3.4, and 3.4–4.2, respectively. Based on the clustering results, the edge connections between nodes in the original damage data graph were redefined as transformation relationships between classes. The direction of the transformation relationship should be the same as the direction of the edge. For example, if an edge connects two nodes belonging to Class 1 and Class 1, respectively, the edge is described as a "1→1" transformation. Similarly, based on the obtained damage size data, five transformation relationships can be defined: "1→2," "2→2," "2→3," and "3→3." Based on this, a separate Markov chain model was constructed for each transformation relationship.

[0205] Table 4 Clustering results of crack damage data

[0206]

[0207] Time step division and observation sequence construction. To construct the fleet graph structure, after introducing the global node, the damage data subgraphs of each individual engine are merged sequentially. Each subgraph merging operation is considered a time step. Based on the existing data, the Markov chain in this example contains a total of 9 time steps. The specific operations are as follows:

[0208] The first step is to split the subgraphs before merging and obtain residuals. At each time step, for the next subgraph to be merged, the damage data within that subgraph is converted into the transformation relationship between corresponding categories based on the clustering results in Table 4. Taking the subgraph constructed from engine crack damage data numbered 3 as an example, the damage data development relationship is re-described in Table 5.

[0209] Table 5 Pairs Figure 3 The crack damage data development relationship is re-described

[0210]

[0211] After completing the merging of the engine subgraphs numbered 1 and 2, 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. This residual is used as the observed value of the corresponding category conversion at the current time step.

[0212] 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 counted into 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.

[0213] 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 aggregated to form the observation sequences of the five Markov chains, as shown in Table 6.

[0214] Table 6 Markov chain observation sequence data of five types of development relationships

[0215]

[0216] 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 the five types of development relationships.

[0217] The third step is to obtain experimental results. Using the crack damage data of civil aviation engine No. 11 as an example, the multi-class Markov chain correction method described above was applied to correct the prediction results of its crack damage development trend. Table 7 shows the prediction and correction results for this engine crack damage data under different category conversion relationships, including the desired predicted crack damage development trend, category conversion relationship, corresponding number of flight cycles, the initially predicted number of flight cycle intervals, and the corrected number of flight cycle intervals.

[0218] Table 7 Comparison of the prediction and correction results of the crack damage development trend of engine No. 11

[0219]

[0220] Table 8 compares the performance indicators of the initial prediction (Predicted) and the revised prediction (Revised), including mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R²), and mean absolute percentage error (MAPE).

[0221] Table 8 Comparison of the predicted and corrected indicators for the crack damage development trend of engine No. 11

[0222]

[0223] From the above results, we can see that after being corrected by the multi-class Markov chain, the prediction model has been significantly improved in all indicators, making the prediction results more consistent with the original data.

[0224] Based on the correction module, this example also uses KNeighbors regression, Lasso regression, linear regression, decision tree regression, random forest regression, MLP regression and SVR regression for comparative experiments. To ensure the consistency of performance evaluation of each method, this example uniformly selects the same data set and evaluation scale for comparative analysis. The evaluation scale uses prediction performance indicators, including mean square error (MSE), mean absolute error (MAE) and determination coefficient (R2 ） .

[0225] At the same time, each method explicitly uses the same pre-training benchmark, which is a uniformly divided training set and test set. Figure 8 The comparison results of the prediction performance indicators of various methods under this unified scale standard and pre-training benchmark are shown.

[0226] Table 9 Comparison of prediction performance indicators of various methods under the same dataset

[0227]

[0228] Overall, the prediction module, by constructing HiGDNet that integrates local structure and global temporal information, effectively mines the topological structure and temporal evolution characteristics of damage detection data, achieving a preliminary prediction of the edge weights (i.e., the number of flight cycles) between nodes, and providing basic support for damage evolution trend modeling. The correction module further utilizes clustering to divide the crack damage data into multiple categories, redefines the edge types between nodes based on the category conversion relationship, constructs a multi-class Markov chain model, models and dynamically learns the prediction residuals under different category conversions, and achieves refined correction of the initial prediction results.

[0229] The above experimental results show that the synergistic effect of the prediction module and 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 task of damage evolution trend prediction.

Claims

1. A damage trend prediction method based on 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 the engine borescope inspection into a graph structure, constructs a damage prediction network with a hierarchical graph structure to process the graph structure, and converts the damage trend prediction problem into the prediction of the edge weights between nodes in the graph, revealing the intrinsic connection between the damage data. The correction module designs a residual correction method based on a multi-class Markov chain to cluster the engine damage data, convert the size evolution into a transfer relationship between categories, and obtains 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. 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 , each node corresponds to a borescope 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, i.e., 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: The elements representing the adjacency matrix, through this construction, can reflect the increasing trend of damage size while also encoding the time interval information into the edge weight; Step 2: Filter abnormal nodes. According to the trend of damage evolution, each edge should point from a node with smaller damage size to a node with larger damage size. If the direction of an edge is detected to be opposite to this rule, that is, there is a node with larger damage size pointing to a node with smaller damage size, it indicates that the node pair is abnormal. The abnormal edge and the corresponding node with smaller damage size need to be removed from the graph to clear the erroneous damage records, as shown in formula (17): (17), where represents the elements of the adjacency matrix, Representative Node The characteristic value of Representative Node The eigenvalue of; Step 3: Fleet graph structure construction, the damage data graph 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 constructed as a subgraph and introduced into the global node The subgraphs 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. The details are as follows: First, the eigenvector of the global node is set to the zero vector, indicating that the engine has not yet incurred any damage and the damage size is 0, as shown in Equation (18): (18), where Represents the characteristics of the global node, Next, build the edge connection between the global node and each subgraph node , the direction is fixed from the global node Pointing detection node On this basis, the edge weight is determined according to the number of flight cycles from the engine being put into operation to each borescope inspection operation. The corresponding number of flight cycles recorded is , That is, the cumulative number of flight cycles from the time the engine was put into operation to the time of the borescope inspection, then the global node Pointing detection node The edge weight of is shown in formula (19): （19）， In this way, the adjacency matrix elements of the global edge can be defined as: （20）， Where, represents the elements 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. The fleet graph structure is expressed as: （21）， Where, Represents the total number of civil aviation engines in the fleet, Represents the damage data subgraph structure in the fleet, Represents the index in the fleet civil aviation engines; Next, the graph neural network is used to extract features and predict damage data intervals. The prediction module encoder network consists of two sub-networks, namely a two-layer graph convolution network for local feature extraction and a graph attention mechanism network for global information fusion. First, local features are extracted through a two-layer graph convolution. The initial node embedding is set to , that is, the original damage size data of each detection record, for each node , double-layer graph convolution for each node The update formula for domain information aggregation is: （22）， （23）， Where, Represents the learnable weight matrix for the input edge of the first and second layers of the model, Represents the learnable weight matrix for the output edge of the first and second layers of the model, Represents the self-loop transformation matrix of the first and second layers, represents a nonlinear activation function, Represents the node embedding features after processing by the first and second layers of the model. After 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 also includes global information fusion through the graph attention mechanism. For the obtained local node embedding, the attention score between the global node embedding and the local node embedding is calculated: (24), where represents the shared linear transformation matrix, represents the vector used to calculate attention, represents a nonlinear activation function, Represents the global node embedding and local node embedding Attention score; Normalize the attention score to obtain the attention coefficient: （25）， Where, Represents the set of all local nodes connected to the global node, Represents the global node embedding and local node embedding The attention coefficient, Finally, global information fusion is performed on each local node embedding: (26), where 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 final 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 node has not appeared in the training process, the model realizes the prediction process by capturing its similarity with other nodes. Given two nodes and nodes The final embedding and , the formula for predicting edge weight is shown in formula (27) （27）， Where, Represents multi-layer perceptron computation, consisting of fully connected layers and activation functions; The model is trained by minimizing the error between the predicted edge weights and the true edge weights, using the mean square error (MSE) as the loss function, which is expressed as follows: （28）， Where, represents the set of edges that need to be predicted, Represents the edge that needs to be predicted, Nodes representing model predictions i Pointing to a node j The weight of the edge, Represented by the node i Pointing to a node j The true weight of the edge; In the correction module, a multi-class Markov chain residual correction method is proposed. The specific steps are described as follows: First, the KMeans clustering algorithm is used to divide the nodes into three groups according to their characteristic values, which are 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 node categories, the edge connection relationship between the nodes is redescribed as the conversion relationship between categories, that is, if the features of the two nodes connected by an edge belong to the categories and , then redescribe the edge as The direction of the category conversion relationship should be determined according to the direction of the edge. According to the characteristics of the category conversion, the edges in the graph structure are divided into six types of conversion relationships, namely: ， ， ， ， ， ； The methods for constructing any type of Markov chain include: ① state interval division, according to the obtained residual sequence , select a constant value to divide into k states , ,..., , as shown in formulas (29) to (31): （29）， （30）， （31）， Where, Representative m states, Representative k states, Representative The starting point of the state interval, Representative The end point of a state interval; ② The state transfer probability matrix. The calculation of the state transfer probability matrix is ​​mainly calculated by the frequency of transfer. Assume that for the residual sequence, from the state Transfer to state The number of observations is ,in , then the one-step transition probability can be calculated from the transition frequency, and its calculation formula is shown in (32): （32）， Where, Represents the slave state Transfer to state The one-step transition probability, Represents that in the training data, the residual from the state Transfer to state The number of times, Through this calculation, we can get the one-step state transition probability matrix: (33), this matrix reflects the transition law of the residual sequence between different discrete states; ③ Markov property test: After obtaining a clear and discretized state sequence through the above steps, the statistical test method is used to verify whether the obtained residual sequence satisfies the Markov property. First, the marginal probability of each state is calculated. Let The marginal probability of a state is the first Column sum and total frequency , that is, the ratio of the number of all transfers, as shown in formula (34): （34）， Where, Representation status The marginal probability of Represents all from any state Transfer to state The sum of the times of Represents the total number of transitions in the residual sequence. Subsequently, the test statistic is constructed based on the classic Markov test statistic , here we use the likelihood ratio test form, and its calculation formula is shown in (35): （35）， Where, Representation status The marginal probability of Represents the slave state Transfer to state The one-step transition probability, Represents all from any state Transfer to state The sum of the times of Represents the statistic of the Markov property test; Since the state division stage Taken a state, therefore, at a given significance level Under the condition of , then the sequence is considered to have Markov properties and Markov correction can be applied in the prediction process; ④ Modification of the initial predicted value: For this type of known original data, assume that the initial predicted value of a certain edge to be modified is ,in and is the corresponding node in the graph. If the residual corresponding to the edge is discretized into In the Markov chain correction model, first determine the state Next, the prediction interval of the next residual, assuming the state The corresponding residual value interval is , then use the median of the interval As the correction value in this state: （36）， Where, Representation status The upper and lower bounds of the corresponding residual interval are finally added to the preliminary prediction value to obtain the corrected prediction edge weight: （37）， Where, Representative Node To Node The initial predicted edge weights of represents the predicted edge weight after Markov chain correction, ⑤Calculation of the probability of the predicted value relative to the residual state, using the one-step state transfer matrix To calculate Step state transfer matrix (in ), thereby realizing the establishment of the dynamic prediction transfer matrix, if the residual state of the observation value before the prediction moment is , then for the Step prediction, specific use Step transfer matrix To predict the state probability distribution of the new node relative to the residual, record it as: （38）， Where, Representatives passed The state transfer matrix of the step transfer, the new node is in state The probability is: （39）， Where, Representative Matrix Middle slave state Transfer to state The probability of Representative prediction The new node residual is in the state probability; ⑥Final correction result, record n The predicted value of the new node in step +1 is k The Markov correction values ​​under the residual state interval are , then the final revised prediction value of the new node is the weighted sum of the preliminary prediction value and the revised values ​​of each state: （40）， Where, Represents the new node in The initial predicted edge weights of the step, Representation status The residual correction value under , here is the median of the corresponding interval, Represents the final predicted edge weight after Markov correction.

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