A Method for Predicting the Fatigue Strength of Steel Using a Graph Convolutional Network Integrated with a Feature Pyramid

Abstract

The present invention discloses a method for predicting the fatigue strength of steel by using a graph convolutional network integrating a feature pyramid, which includes: processing the steel fatigue strength data, and constructing the fatigue strength sequence data of the steel material into graph data by using a dynamic graph construction method; effectively integrating the feature pyramid and the graph convolutional network to construct a model for predicting the fatigue strength of steel and predicting the fatigue strength of steel. The present invention innovatively constructs the fatigue strength series data of the steel material into graph data through a graph construction method, and for the first time innovatively combines the feature pyramid and the graph convolutional neural network for the prediction of the fatigue strength of the steel material, makes use of the complementary advantages of the graph convolutional neural network and the feature pyramid, reasonably solves the problems existing in the two algorithms themselves, and achieves remarkable results in solving the prediction problem of the fatigue strength of the steel material.

Description

Technical Field

[0001] The present invention relates to the field of material property research in chemical material engineering, and particularly to a method for predicting the fatigue strength of steel by a graph convolutional network integrating a feature pyramid. Background Art

[0002] The mechanical properties of materials affect their state when subjected to loads. The elastic modulus of a material affects the degree of deformation when it is subjected to a load, while the strength of the material determines the load it can withstand before failure. The ductility of a material also plays an important role in determining when the material will break when it exceeds its elastic limit. Since every mechanical system is subjected to loads during operation, it is very important to understand the behavior of the materials that make up these mechanical systems. There are many parameters that affect mechanical properties, such as microstructure, heat treatment, process method, composition, etc. Traditionally, when studying the mechanical properties of materials, the properties of materials are often measured and analyzed through a large number of manual experiments. This method has a long R & D cycle, wastes a large amount of resources, and there are often large errors due to manual intervention during operation, and the experimental expectations cannot be achieved, which is disadvantageous in terms of time and money.

[0003] In the past two decades, impressive progress has been made in the fields of material characterization equipment and physics-based multiscale material modeling tools, which has initiated the big data era of materials science and engineering. With the emergence of big data, it has been recognized that advanced statistical data and modern data analysis will have to play an important role in the future work processes of developing new materials or improving materials. The ability of data science in generating data has far exceeded the ability to understand and analyze data in almost all scientific fields, and materials science is no exception. This has led to the emergence of the fourth paradigm of science, which is data-driven science and discovery, and is based on developing prediction and discovery-based data mining methods for big data in a comprehensive manner. The fourth paradigm complements the three traditional scientific progress models of mathematical modeling, experiments, and computer simulations. In fact, the state-of-the-art technologies in this field come from computer science, high-performance computing, machine learning, and data mining algorithms, and predictive data mining has played a key role in the commercial field, climate science, bioinformatics, astronomy / cosmology, intrusion detection, network analysis, and many other fields through application forms, and has been effectively used for decision-making related to significant benefits and related results in these fields.

[0004] Among the many factors that affect the mechanical properties of materials, the fatigue strength of machinery is an important parameter. It can reflect the mechanical properties of materials to a certain extent in many engineering applications. In the past, some physical and data-driven methods have been used to predict the various properties of alloys and the correlations between their compositions and manufacturing process parameters. However, the current state-of-the-art physics-based models have serious limitations. Nowadays, machine learning methods have been proven to be successful in predicting a large number of material properties. However, there is still no standardized protocol to systematically explore this method in many potential applications. Therefore, establishing the composition-process-structure-property relationship for the material property prediction task remains a daunting task.

[0005] The relevant research results show that some advanced data analysis techniques, such as neural networks, decision trees, and multivariate polynomial regression, have demonstrated the practicality of these data mining methods in ranking the potential of predicting the fatigue strength of steel for composition and process parameters. However, there is still room for innovation in the material mechanical property prediction method, and there is still a large room for improvement in the prediction accuracy. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for predicting the fatigue strength of steel by a graph convolutional network integrating a feature pyramid in view of the above problems. The feature pyramid and the graph convolutional neural network are combined for predicting the fatigue strength of steel materials, and the advantages of the graph convolutional neural network and the feature pyramid are complemented to reasonably solve the problems existing in the two algorithms themselves, and remarkable results are achieved in solving the problem of predicting the fatigue strength of steel materials.

[0007] The technical solution of the present invention is as follows:

[0008] A method for predicting the fatigue strength of steel by a graph convolutional network integrating a feature pyramid of the present invention includes: processing the steel fatigue strength data, and constructing the steel material fatigue strength sequence data into graph data by using a dynamic graph construction method; effectively integrating the feature pyramid and the graph convolutional network to construct a model for predicting the steel fatigue strength and predicting the steel fatigue strength.

[0009] Preferably, the method for predicting the fatigue strength of steel by a graph convolutional network integrating a feature pyramid specifically includes the following steps:

[0010] Step 1: Collect a steel fatigue data set, perform data cleaning, and obtain the attribute features that affect the steel fatigue strength;

[0011] Step 2: Preprocess the original data to ensure consistency, process the attribute features using a similarity matrix, remove redundant data and features in the steel fatigue data, and perform feature engineering and standardization processing on the processed data to obtain the required data set;

[0012] Step 3: Use the dynamic graph creation method to construct a graph structure from the data;

[0013] Step 4: Extract a sparse graph from the learned fully-connected graph and use the similarity matrix between different features as the adjacency matrix;

[0014] Step 5: Effectively fuse the feature pyramid and the graph convolutional network to construct a model for predicting the fatigue strength of steel;

[0015] Step 6: Use the constructed model to train the data after graph embedding, and adjust and optimize the model;

[0016] Step 7: Use the model to predict the fatigue strength of steel.

[0017] Preferably, the steel fatigue data set in Step 1 is sequence data and each data contains attribute features: chemical composition, upstream processing details, heat treatment conditions, and mechanical properties.

[0018] Preferably, the similarity calculation formula between fatigue strength attribute features in Step 2 is:

[0019]

[0020] where Sim x，Y is the correlation coefficient between attribute feature X and attribute feature Y, cov(X, Y) = E[(X - μ x )(Y - μ Y ) is the covariance between attribute feature X and attribute feature Y, σ X , σ Y are the standard deviations of attribute feature X and attribute feature Y respectively, and μ X , μ Y are the means of attribute feature X and attribute feature Y respectively.

[0021] Preferably, the dynamic graph creation method in Step 3 includes: measuring the similarity between nodes through a structure-aware attention mechanism that learns pairwise node similarity, and using the following formula to calculate and construct the graph structure, as shown in the formula:

[0022]

[0023] where represents the similarity between connected nodes i and j in the l-th layer of the graph neural network layer; represents the embedding vector of node i, represents the embedding vector of the edge connecting nodes i and j, represents the embedding vector of node i in the l-th layer of the graph neural network layer, and are trainable weight vectors and weight matrices respectively.

[0024] Preferably, the method for extracting the sparse graph in step four includes: using a graph sparsification component, through knn-style sparse operation, obtaining a sparse adjacency matrix from the node similarity matrix calculated by the similarity metric learning function. The sparse adjacency matrix is calculated as follows:

[0025]

[0026] Among them, for the topK function, represents the similarity matrix for node i. Each node only retains K nearest neighbors (including itself) and the relevant similarity scores, and the remaining similarity scores will be ignored, finally obtaining the sparse matrix of this node

[0027] Preferably, the model for predicting the fatigue strength of steel in step five includes: 5 levels of image pyramids, which are two groups of convolutional layers, pooling layers, fully connected layers, dropout layers, fully connected and activation layers; each level is a three-layer structure of context layer - hierarchy layer - context layer; the context layer only uses context edges, and the context edges are used to propagate context information within the same level, and to propagate context information within the same level; while the hierarchy layer only uses pruned hierarchy edges, and the hierarchy edges are used to bridge the semantic gap between different levels.

[0028] Preferably, the method for constructing the model for predicting the fatigue strength of steel in step five:

[0029] In the architecture of the model, use the GCblock to duplicate and increase the input data into three parts, denoted as data X i , data X j , data X k ; data X i After feature extraction by a 1*1 convolutional kernel, it is activated by the Softmax function; then the result of multiplying it with data X j is put into a 1*1 convolutional kernel; the result after convolution is put into an LN layer (layer normalization) and then activated by the ReLU function, and the obtained result is put into a 1*1 convolutional kernel again; finally, the obtained result is fused with the X k data and output; the GC block is expressed as:

[0030]

[0031] Among them, is the weight of the global attention pooling layer, and δ(·) = W v2 ReLU(LN(W v1 (·))) is expressed as BoTNet.

[0032] Preferably, in step six, the steel fatigue strength dataset is divided into a training set and a test set. After the dataset is divided, the ratio of the training set to the test set is 4:1, and the number of iterations for model training is 100. The constructed model is used to train the graph-embedded data, and the performance of the model is observed through the results of the test set, and the hyperparameters in the model are adjusted to improve the model.

[0033] Preferably, after step seven, cross-validation is used to evaluate the prediction accuracy of the prediction results; specific evaluation method: the standard for using R to evaluate the prediction performance of the model is the correlation coefficient between the actual value and the predicted value.

[0034]

[0035] The formula MAE calculates the mean absolute error.

[0036] The formula RMSE calculates the root mean square error.

[0037] The formula SDE calculates the standard deviation error.

[0038] Among them, y is the actual fatigue strength value. is the predicted fatigue strength value, N is the number of instances in the dataset, and R 2 represents the variance explanation model, which is used to evaluate the accuracy of the regression prediction model. The score mean absolute error MAE represents the error rate.

[0039] In summary, due to the adoption of the above technical solutions, the beneficial effects of the present invention are as follows:

[0040] 1. The present invention realizes the accurate prediction of the mechanical properties of materials. By combining the feature pyramid and the graph convolutional neural network for the prediction of the fatigue strength of steel materials, the advantages of the graph convolutional neural network and the feature pyramid are complementary to each other, reasonably solving the problems existing in the two algorithms themselves, and achieving remarkable results in solving the prediction problem of the fatigue strength of steel materials.

[0041] 2. The present invention preprocesses the fatigue data of steel materials through the consistency description of data and relevant domain knowledge; establishes the best attribute subset of the given material attributes through feature selection of attribute correlation; through the graph similarity metric learning component, learns an adjacency matrix according to the similarity of each pair of nodes in the embedding space, and constructs a graph structure for the steel serialization data through the dynamic graph creation method; through the graph sparsification component, extracts a sparse graph from the learned fully connected graph, and uses the similarity matrix between different features as the adjacency matrix.

[0042] 3. Based on data mining technology and graph convolutional neural network, the present invention effectively fuses the feature pyramid, and utilizes the characteristics of aggregating neighbor node information in the graph convolutional network and residual connection in the graph convolutional network to improve the gradient dispersion problem in backpropagation; combines the upsampling and downsampling of the graph convolutional network, the multi-scale features of the feature pyramid, and models the global context information, and conducts relevant modeling for the fatigue strength data of steel materials.

[0043] 4. For the fatigue strength prediction task of steel materials, the present invention uses a series of advanced data analysis techniques to establish a highly reliable causal relationship between the chemical composition of steel and its fatigue strength, uses a series of deep learning and data analysis methods to model the problem of predicting the fatigue strength of steel using composition and process parameters, and conducts strict evaluations.

[0044] 5. By constructing a graph structure of the steel fatigue strength sequence data, based on the feature pyramid network and the graph convolutional network, the present invention effectively fuses the two to construct a model for predicting the fatigue strength of steel, and realizes the prediction of the fatigue strength of steel materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate other features and related technical solutions of the present invention, the following will briefly introduce the drawings required in the present invention. By reading the detailed description of the non-limiting embodiments with reference to the following drawings, the features, purposes, and advantages of the present invention can be more clearly illustrated.

[0046] Figure 1 It is a flowchart of the method for predicting the fatigue strength of steel by the graph convolutional network integrating the feature pyramid in the embodiment of the present invention.

[0047] Figure 2 It is an architecture diagram of the model for predicting the fatigue strength of steel in the embodiment of the present invention.

[0048] Figure 3 It is an internal structure diagram of the GC Block module in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] All features disclosed in this specification, or all steps in the disclosed methods or processes, except for mutually exclusive features and / or steps, can be combined in any manner.

[0050] Any feature disclosed in this specification (including any additional claims, abstract) can be replaced by other equivalent or similar-purpose alternative features unless specifically stated. That is, unless specifically stated, each feature is only an example of a series of equivalent or similar features.

[0051] The following further describes the features and performance of the present invention in detail in conjunction with embodiments.

[0052] Fatigue life prediction is very important in both the fields of materials science and mechanical engineering. There are very few studies to address the problem of predicting extreme properties (such as fatigue strength) using a large number of heat treatment process parameters and compositions. The use of advanced data analysis techniques and deep learning methods may lead this research direction. Therefore, the object of the present invention is to provide a method to solve the problems in this field and provide preliminary guidance for prospective researchers in this field. The present invention includes a series of data analysis methods and deep learning methods applied to the problem of predicting the fatigue strength of steel using compositions and process parameters.

[0053] The present invention processes the steel fatigue strength data, constructs sequence data into graph data using a dynamic graph construction method, and effectively combines a feature pyramid network and a graph convolutional neural network for predicting the fatigue strength of steel materials.

[0054] The application principle of the present invention will be described in detail below with reference to the accompanying drawings.

[0055] As Figure 1 shown, a method for predicting the fatigue strength of steel materials by a graph convolutional network effectively integrating a feature pyramid according to an embodiment of the present invention includes the following steps:

[0056] Step 1: Collect the steel fatigue data set of the National Institute for Materials Science (NIMS) in the United States. This database is one of the largest databases in the world and contains detailed compositions, mill product (upstream) characteristics, and subsequent processing (heat treatment) parameters. Perform data cleaning to obtain the characteristics affecting the steel fatigue strength;

[0057] Each steel fatigue data includes the following types of attribute characteristics: chemical composition (such as the content of elements such as carbon, silicon, and manganese), upstream processing details (ingot size, reduction ratio, non-metallic inclusions, etc.), heat treatment conditions (temperature, time, and other process conditions of normalizing, overall quenching, carburizing quenching, and tempering processes), mechanical properties (maximum tensile strength, hardness, Charpy impact value, fatigue strength, etc.).

[0058] Step 2: Use domain knowledge to preprocess the original data to ensure consistency, process the attribute characteristics using a similarity matrix, remove redundant data and characteristics in the steel fatigue data, and perform feature engineering and normalization processing on the processed data to obtain the required data set. This data has 437 instances, 25 features (compositions and processing parameters), and 1 target attribute (fatigue strength). The 437 data instances include 371 types of carbon steel and low alloy steel, 48 types of carburized steel, and 18 types of spring steel. This data is applicable to various heats and different processing conditions of each steel type.

[0059] The dataset used in the research consists of multiple steel grades. In some of the data, some heat treatment steps are absent. To introduce structure into the database, we included all the key processes (carburizing, quenching, and tempering) for data normalization.

[0060] Step 3: Use a graph similarity metric learning component to learn an adjacency matrix based on the similarity of each pair of nodes in the embedding space, and dynamically construct the graph structure of these serialized data; calculate and construct the graph structure using the following formula:

[0061]

[0062] where, represents the embedding vector of node i, represents the embedding vector of the edge connecting nodes i and j, represents the embedding vector of node i in the l-th layer of the graph neural network layer, and are the trainable weight vector and weight matrix respectively.

[0063] Step 4: Use a graph sparsification component to extract a sparse graph from the learned fully connected graph.

[0064] The specific description of obtaining the sparse graph using the graph sparsification component is as follows:

[0065] Apply the knn-style sparse operation to obtain a sparse adjacency matrix from the node similarity matrix calculated by the similarity metric learning function. The calculation formula is as follows:

[0066]

[0067] where, for the topK function, represents the similarity matrix for node i. Each node only retains the K nearest neighbor nodes (including itself) and the relevant similarity scores, and the remaining similarity scores will be ignored. Finally, the sparse matrix of the node can be obtained

[0068] In the graph structure constructed after Steps 3 and 4, each node represents a feature. We use the similarity matrix between different features as the adjacency matrix.

[0069] Step 5: Given attribute data such as composition and process parameters, effectively fuse the feature pyramid and the graph convolutional network for the data using the prediction modeling method proposed in the present invention to construct a model for predicting the fatigue strength of steel.

[0070] In this example, the constructed model is as Figure 2As shown. After the data is input into the model, multi-scale features are extracted. The first layer of each scale will pass through a context layer, which extracts the node features of the same layer and the associated features between them. We constructed an image pyramid with 5 levels, which consists of two sets of convolutional layers, pooling layers, fully connected layers, dropout layers, fully connected and activation layers. Each level is a three-layer structure of context layer - level layer - context layer. The context layer only uses context edges, while the level layer only uses pruned level edges (context edges are used to propagate context information within the same level, and level edges are used to bridge the semantic gap between different levels). Although the context layer and the hierarchical structure layer use different edges, the GNN operations in these two types of layers are exactly the same. These two types of layers share the same spatial and channel attention mechanisms. Given node i and its neighborhood N i set, the spatial attention updates the features as shown below:

[0071]

[0072] where M is single-head self-attention, is the set of feature vectors collected from the neighbors of node i, and are the feature vectors of node i before and after update, respectively.

[0073] In the architecture of the model, we use the Global Context Block (GCblock) to duplicate the input data into three copies, denoted as data X i , data X j , data X k . Data X i is activated by the Softmax function after feature extraction through a 1*1 convolutional kernel; then the result of multiplying it with data X j is put into a 1*1 convolutional kernel; in order to reduce the optimization difficulty and improve the generalization ability as a regularization, the result after convolution is put into a LN layer (layer normalization) and activated by the ReLU function, and the obtained result is put into a 1*1 convolutional kernel again; finally, the obtained result is fused with X k data and output. The GC block is expressed as:

[0074]

[0075] where, is the weight of the global attention pooling layer, δ(·) = W v2 ReLU(LN(W v1 (·))) is expressed as Bottleneck Transformer (BoTNet).

[0076] Step 6: Divide the steel fatigue strength dataset into a training set and a test set at a ratio of 4:1. Use the embedded data to train the model. Observe the model performance through the results of the test set and adjust the hyperparameters in the model to improve the model.

[0077] Step 7: Use 10-fold cross-validation for the prediction results of the proposed method and evaluate them using the R 2 , MAE, RMSE, and SDE metric indicators. The R 2 of the model reaches 97.8%, the MAE is 19.37, the RMSE is 18.71, and the SDE is 19.68.

[0078]

[0079]

[0080]

[0081]

[0082] The standard of R for evaluating the model prediction performance is the correlation coefficient between the actual value and the predicted value. The formula for MAE calculates the mean absolute error, the formula for RMSE calculates the root mean square error, and the formula for SDE calculates the standard deviation error. Among them, y is the actual fatigue strength value (MPa), is the predicted fatigue strength value (MPa), N is the number of instances in the dataset, and R 2 represents the variance explanation model (the higher the better), which is considered the most important indicator to evaluate the accuracy of the regression prediction model; another useful metric is the fractional mean absolute error MAE, which represents the error rate (the lower the better).

[0083] The existing mechanical property prediction methods for steel materials fail to fully utilize the internal connections between material properties. Instead of using the method of graph neural network to solve the problem, they only stay at using simple machine learning methods or some common deep learning methods for modeling. In this embodiment, for the steel material fatigue strength prediction task, a series of advanced data analysis techniques are used to establish a highly reliable causal relationship between the chemical composition of steel and the fatigue strength. Using features such as attribute correlation, a graph structure is constructed for the steel serialized data using the dynamic graph creation method, effectively fusing the feature pyramid and the graph convolutional network, and a model for predicting the steel fatigue strength is constructed. By constructing the graph structure of the steel fatigue strength sequence data, based on the feature pyramid network and the graph convolutional network, the two are effectively fused, improving and innovating on the mechanical property prediction method of materials, and making this embodiment better describe a fatigue strength prediction method applicable to steel materials.

[0084] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for predicting the fatigue strength of steel using a graph convolutional network integrating a feature pyramid, characterized in that, Including: Process the steel fatigue strength data, and use the dynamic graph construction method to construct the fatigue strength sequence data of steel materials into graph data; Effectively fuse the feature pyramid and the graph convolutional network to construct a model for predicting the steel fatigue strength and predict the steel fatigue strength; Specifically, it includes the following steps: Step 1: Collect the steel fatigue data set, perform data cleaning, and obtain the attribute features affecting the steel fatigue strength; Step 2: Preprocess the originally collected steel fatigue data set, use the similarity matrix to process the attribute features, remove the redundant data and features in the steel fatigue data, and perform feature engineering and standardization processing on the processed data to obtain the required data set; Step 3: Use the dynamic graph creation method to construct a graph structure from the data; Step 4: Extract a sparse graph from the learned fully connected graph, and use the similarity matrix between different features as the adjacency matrix; Step 5: Fuse the feature pyramid and the graph convolutional network to construct a model for predicting the steel fatigue strength; Step 6: Use the constructed model to train the graph-embedded data, and adjust and optimize the model; Step 7: Use the model to predict the steel fatigue strength; The dynamic graph creation method in Step 3 includes: measuring the similarity between nodes through a structure-aware attention mechanism that learns pairwise node similarity, and using the following formula to calculate and construct the graph structure, as shown in the formula: Among them, represents the connection node and in the similarity of the graph neural network layer at the represents the embedding vector of the node ; represents the embedding vector of the edge connecting the nodes and ; represents the embedding vector of the node in the graph neural network layer at the and are the trainable weight vector and weight matrix respectively; The model for predicting the steel fatigue strength in Step 5 includes: a 5-level image pyramid, which is two sets of convolutional layers, pooling layers, fully connected layers, dropout layers, fully connected and activation layers; each level is a three-layer structure of a context layer - a hierarchical layer - a context layer; the context layer only uses context edges, and the context edges are used to propagate context information within the same level, and propagate context information within the same level; while the hierarchical layer only uses pruned hierarchical edges, and the hierarchical edges are used to bridge the semantic gap between different levels; The method for constructing the model for predicting the steel fatigue strength in Step 5: In the architecture of the model, the input data is replicated three times using the GC block, denoted as data , data , data ; data After feature extraction through a 1*1 convolutional kernel, it is activated by the Softmax function; then the result of multiplying it with data is put into a 1*1 convolutional kernel; the result after convolution is put into an LN layer and then activated by the ReLU function, and the obtained result is put into a 1*1 convolutional kernel again; finally, the obtained result is fused with data and output; the GC block is represented as: Among them, is the weight of the global attention pooling layer, Represented as BoTNet.

2. The method for predicting the fatigue strength of steel by means of the graph convolutional network integrating the feature pyramid according to claim 1, characterized in that, The steel fatigue data set in Step 1 is sequence data, and each piece of data contains attribute features: chemical composition, upstream processing details, heat treatment conditions, and mechanical properties.

3. The method for predicting the fatigue strength of steel by using the graph convolutional network integrating the feature pyramid according to claim 1, characterized in that The similarity calculation formula between attribute features in Step 2: Among them, is the correlation coefficient between attribute feature and attribute feature is the covariance between attribute feature and attribute feature , are respectively the standard deviations of attribute feature and attribute feature , are respectively the means of attribute feature and attribute feature 4. The method for predicting the fatigue strength of steel by a graph convolutional network integrating a feature pyramid according to claim 1, characterized in that The method for extracting the sparse graph in Step 4: Use a graph sparsification component, and through knn-style sparse operation, obtain a sparse adjacency matrix from the node similarity matrix calculated by the similarity metric learning function. The sparse adjacency matrix is calculated as follows: Among them, for function, represents the similarity matrix for node . For each node, only the K nearest neighbor nodes including itself and the relevant similarity scores are retained, and the remaining similarity scores are ignored, finally obtaining the sparse matrix of this node .

5. The method for predicting the fatigue strength of steel by using the graph convolutional network integrating the feature pyramid according to claim 1, wherein, In Step 6, divide the steel fatigue strength data set into a training set and a test set. After the data set is divided, the ratio of the training set to the test set is 4:1, and the number of iterations for model training is 100; use the constructed model to train the graph-embedded data, observe the model performance through the results of the test set, and adjust the hyperparameters in the model to improve the model.

6. The method for predicting the fatigue strength of steel by using the graph convolutional network integrating the feature pyramid according to claim 1, wherein After Step 7, the prediction accuracy is evaluated for the prediction results using cross-validation; specific evaluation method: use The standard for evaluating the prediction performance of the model is the correlation coefficient between the actual value and the predicted value, ; Formula Calculate the mean absolute error, ; Formula Calculate the root mean square error, ; Formula Calculate the standard error of the mean, ; Among them, is the actual fatigue strength value, is the predicted fatigue strength value, is the number of instances in the dataset, represents the variance explanation model, which is used to evaluate the accuracy of the regression prediction model, and the score is the mean absolute error , representing the error rate.

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