Method for predicting bearing capacity of screw anchor based on machine learning

Abstract

The invention discloses a spiral anchor bearing capacity prediction method based on machine learning, and solves the problems that in the prior art, numerical analysis consumes long time, actuarial precision is limited by precise description of soil constitutive, the operation difficulty is high, and large-scale application is difficult. According to the method, methods of algorithm and database establishment, model training and hyper-parameter optimization, model evaluation, characteristic important analysis and the like are adopted, an ensemble learning algorithm with high popularity is utilized to improve the limit gradient to establish a screw anchor bearing capacity prediction model, and the screw anchor bearing capacity is rapidly and accurately predicted based on a machine learning model.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of spiral anchor bearing capacity prediction method, and particularly relates to a spiral anchor bearing capacity prediction method based on machine learning. BACKGROUND

[0002] The spiral anchor foundation is mainly composed of one or several anchor plates and anchor rods, and is made of steel. By applying a downward pressure and a torque at the top of the anchor rod, the spiral anchor is directly screwed into the soil, which reduces the damage to the original soil and the environment, and the required equipment is relatively light, the installation is rapid, and the noise is relatively small. The spiral anchor plate can also provide significant bearing capacity, and the vertical bearing capacity is significantly better than that of the traditional pile foundation, that is, under the condition of providing the same bearing capacity, the spiral anchor is smaller in size and more convenient to construct. Therefore, the spiral anchor foundation is often used in soft ground in the early stage, such as the Maplin Sands lighthouse.

[0003] The bearing capacity of the spiral anchor is mainly borne by the anchor plate, so that the spiral anchor has excellent performance by flexibly adjusting the number of anchor plates. With the deepening of the understanding of the spiral anchor foundation, it has been applied to the fields of ocean engineering, power transmission lines, wind turbines, photovoltaic industry and the like.

[0004] Domestic and foreign scholars have carried out a large number of experimental and finite element analysis researches on the bearing capacity prediction of the spiral anchor foundation. Ghaly et al. studied the uplift bearing capacity of the spiral anchor in sand through experiments and theoretical analysis, and proposed a prediction model. Merifield et al. proposed a prediction method for the ultimate uplift bearing capacity of the spiral anchor in sand through numerical simulation and experimental research. Li Yiqi et al. analyzed the continuous evolution law and theoretical characterization method of the sliding surface of the soil around the spiral anchor in sand based on numerical simulation, and further studied the uplift mechanical model and unified calculation method of the spiral anchor with multiple anchor plates in sand. Wang Jie et al. carried out curve fitting on the test data through indoor test, analyzed the test data by using regression analysis method, and proposed a calculation method for the ultimate uplift bearing capacity of the spiral anchor. Hao Dongxue et al. carried out indoor model test research on the uplift behavior and ultimate uplift bearing capacity of the single-anchor and multi-anchor spiral anchor in sand, and obtained the influence of the critical buried depth of the single-anchor, the anchor plate spacing and the number of the multi-anchor spiral anchor on the soil failure mode and the ultimate uplift bearing capacity.

[0005] Prior art: The traditional spiral anchor bearing capacity prediction methods mainly include theoretical formula, empirical formula, field test and numerical simulation, although some valuable results and research methods for actual engineering and design are added in the specification, but these methods still have certain limitations. For example, the theoretical formula is usually based on simplified assumptions, which is difficult to fully consider the complex geological conditions and the geometric parameters of the spiral anchor; the empirical formula needs a large amount of experimental data to calibrate the parameters, and the generalization ability is poor; the field test can provide accurate bearing capacity data, but the cost is high, the time is long, and it is difficult to be applied on a large scale. Numerical analysis is time-consuming, and the precision is limited by the accurate description of the soil body, and the operation is difficult. And based on the current research, it is not difficult to find that there are many factors affecting the bearing capacity of the spiral anchor, including soil parameters, anchor plate diameter, anchor plate depth, anchor plate spacing, etc., and there is no comparison between the influence degree of each feature on the bearing capacity, and the core feature affecting the bearing capacity of the spiral anchor cannot be determined.

[0006] In order to solve the above technical problems, a machine learning spiral anchor bearing capacity prediction method is urgently needed. SUMMARY

[0007] In order to solve the above technical problems, the technical scheme provided by the present application is: a machine learning spiral anchor bearing capacity prediction method, comprising the following steps,

[0008] (1) The initial model usually uses a constant model as the initial prediction, which provides a starting point for the subsequent iterative training of the model;

[0009]

[0010] (2) Calculate the residual error after obtaining the initial prediction value The residual error is the difference between the tth real value and the (t-1)th prediction value, that is,

[0011]

[0012] (3) Calculate the first residual error Combine the target function to train a new model, use the residual error as the new target variable during the training process, select the best split point and tree structure by optimizing the target function, and train a new weak learner f t (x), the target function of the model is different from the traditional GBDT, and a regularization term is added, and the target function is defined as follows:

[0013]

[0014] In the formula, is the loss function, Ω(f k ) is the regularization term, the complexity penalty term of the kth tree, which is used to control the complexity of the model to prevent overfitting, and the regularization term is defined as follows:

[0015]

[0016] In the formula: T is the number of leaf nodes, w j is the weight of leaf node j, γ is the penalty coefficient of the number of leaf nodes, λ is the L2 regularization parameter, α is the L1 regularization parameter, the model optimization objective function is approximated by a second-order Taylor expansion, and a greedy algorithm is used to find the best split point. The greedy algorithm is to calculate the objective function gain for each feature by traversing all possible split points, and select the split point with the maximum gain;

[0017]

[0018] In the formula: g i , h i are the first and second derivatives of the loss function, respectively, I L and I R are the sample sets of the left and right child nodes after splitting, I is the sample set before splitting, γ is the regularization coefficient, used to punish the newly added leaf nodes. After finding the best split point by the greedy algorithm, a new weak learner is constructed and the model is updated;

[0019]

[0020] where η is the learning rate, used to control the contribution of each tree and the update amplitude of each step, thereby affecting the model convergence speed and performance. The value of η is usually a positive number between 0 and 1. The larger the value, the fewer the iterations;

[0021] (4) Repeat the above process until the maximum number of iterations is reached or the objective function value no longer decreases. Then output the final model and predict the new sample data in the test set by the trained model to test the generalization ability, accuracy and stability, overfitting and underfitting, and actual application effect of the model. The final model is the weighted sum of multiple weak learners, as shown in the following formula;

[0022]

[0023] In the formula: T is the number of iterations, and η is the learning rate;

[0024] (5) Database establishment, when establishing the data set of the screw anchor bearing capacity prediction model, it is necessary to ensure that the data source is reliable, accurately labeled and balanced in class distribution, support the addition and update of subsequent data, and cover various working conditions and reference ranges and other conditions as much as possible, so as to provide a reliable foundation for subsequent model training and prediction;

[0025] (6) Model training and hyperparameter optimization, after the data set is established, pre-processing is performed, all features (ρ d , c、E、D、H) Select the most relevant features using the correlation coefficient, and divide the data set into a training set (70%), a validation set (20%), and a test set (10%). Use K-fold cross-validation to train the model for single disc anchor pull-up and down bearing capacity, respectively, to obtain the feature importance;

[0026] (7) Model evaluation, comprehensive evaluation of the performance of the model by the coefficient of determination R2, root mean square error MSE, mean absolute error MAE, and mean absolute percentage error MAPE;

[0027]

[0028] wherein: y i is the true value, is the predicted value, is the average value of all true values, and n is the number of calculation samples. The higher the R2, the lower the RMSE, MAE, and MAPE, indicating that the model performance is better, and the difference between the predicted value and the true value is smaller;

[0029] (9) Feature importance analysis, usually using feature importance analysis method for model explanation and analysis.

[0030] Further, the step (6) uses K-fold cross-validation for training set and validation set division and model evaluation, which is randomly and uniformly divided into K similar subsets, each subset maintains the distribution characteristics of the data as much as possible, and each time one subset is selected as the validation set, and the remaining K-1 subsets are used as the training set. This will be trained and verified K times, and the results of K times verification are averaged to obtain a comprehensive evaluation index for measuring the performance of the model.

[0031] The advantages of the present application compared with the prior art are:

[0032] The present application uses the integrated learning algorithm limit gradient boosting to establish a spiral anchor bearing capacity prediction model, and realizes rapid and accurate prediction of the spiral anchor bearing capacity based on a machine learning model. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 is a schematic diagram of the gradient boosting algorithm;

[0034] Figure 2 is a schematic diagram of the Pearson correlation coefficient matrix of input and output variables;

[0035] Figure 3 is a schematic diagram of K-fold cross-validation.

[0036] Figure 4 . is a single disc spiral anchor bearing capacity-depth ratio curve in S4 soil (the upper graph is the pull-up bearing capacity-depth ratio curve, and the lower graph is the down bearing capacity-depth ratio curve);

[0037] Figure 5 This is a comparison chart showing the accuracy of machine learning prediction results. Detailed Implementation

[0038] The present invention will now be described in further detail with reference to the accompanying drawings.

[0039] The present invention will be described in detail with reference to the accompanying drawings.

[0040] This invention provides an efficient gradient boosting algorithm that constructs a strong learner by integrating multiple weak learners (typically CART decision trees). Its core principle is to use the residual between the prediction results of the previous round and the true values ​​of the current round to train the model for the next round, progressively optimizing the model's predictive ability. The weak learners obtained from each round of training are weighted and summed to obtain the final prediction result, such as... Figure 1 As shown, compared to traditional methods, this approach offers greater flexibility, stronger generalization ability, and better interpretability in predicting load-bearing capacity.

[0041] In its specific implementation, this invention provides a machine learning-based method for predicting the bearing capacity of helical anchors, comprising the following steps:

[0042] (1) Initializing the model usually uses a constant model as the initial prediction to provide a starting point for the iterative training of the subsequent model;

[0043]

[0044] (2) Calculate the residuals after obtaining the initial predicted values. The residual is the difference between the t-th true value and the (t-1)-th predicted value, i.e.

[0045]

[0046] (3) Calculate the first residual Then, a new model is trained using the objective function. During training, the residuals are used as the new objective variable. By optimizing the objective function, the optimal split point and tree structure are selected, and a new weak learner ft(x) is trained. The objective function of this model differs from that of the traditional GBDT model by incorporating a regularization term. The objective function is defined as follows:

[0047]

[0048] In the formula: Let Ω(f) be the loss function. k The regularization term () is the complexity penalty term for the k-th tree, used to control the complexity of the model and prevent overfitting. The regularization term is defined as follows:

[0049]

[0050] wherein: T is the number of leaf nodes, wj is the weight of leaf node j, γ is the penalty coefficient of the number of leaf nodes, λ is the L2 regularization parameter, α is the L1 regularization parameter, the model optimization objective function is approximated by a second-order Taylor expansion, and a greedy algorithm is used to find the best split point, the greedy algorithm is to calculate the objective function gain of each feature for all possible split points, and the split point with the maximum gain is selected;

[0051]

[0052]

[0053] wherein: g i , h i are the first and second derivatives of the loss function respectively, I L and I R are the sample set of the left and right child nodes after splitting, I is the sample set before splitting, γ is the regularization coefficient for penalizing the newly added leaf nodes, after finding the best split point by the greedy algorithm, a new weak learner is constructed and the model is updated

[0054]

[0055] η is the learning rate, which is used to control the contribution of each tree and the update amplitude of each step, thereby affecting the model convergence speed and performance, the value of η is usually a positive number between 0 and 1, and the larger the value, the fewer the iteration times;

[0056] (5) Repeat the above process until the maximum iteration number is reached or the objective function value no longer decreases, then output the final model, and input the new sample data in the test set into the trained model for prediction to test the generalization ability, accuracy and stability, overfitting and underfitting, and actual application effect of the model, and the final model is the weighted sum of multiple weak learners, as shown in the following formula;

[0057]

[0058] wherein: T is the number of iterations, and η is the learning rate;

[0059] (6) Database establishment, when establishing the data set of the screw anchor bearing capacity prediction model, it is necessary to ensure that the data source is reliable, accurately labeled and balanced in class distribution, support the addition and update of subsequent data, and cover various working conditions and reference ranges and other conditions as much as possible, thereby providing a reliable foundation for subsequent model training and prediction;

[0060] (7) Model training and hyperparameter optimization, after the data set is established, all features (ρ d, φ, c, E, D, H) the most relevant features are selected using the correlation coefficient, and the data set is divided into a training set (70%), a validation set (20%), and a test set (10%). K-fold cross-validation is used to train the model for single-plate anchor pull-up and push-down bearing capacity, respectively, to obtain the importance of the features;

[0061] (8) Model evaluation: the performance of the model is comprehensively evaluated by the coefficient of determination R2, the root mean square error MSE, the mean absolute error MAE, and the mean absolute percentage error MAPE;

[0062]

[0063] where: y i is the true value, is the predicted value, is the average value of all true values, and n is the number of samples. The higher the R2, the lower the RMSE, MAE, and MAPE, indicating better model performance and smaller difference between predicted and true values;

[0064] (9) Feature importance analysis: feature importance analysis is usually used for model interpretation and analysis.

[0065] Embodiment:

[0066] 1) Training database establishment

[0067] Select ABAQUS, a large finite element analysis software with powerful nonlinear solution function. The software provides two methods to describe the motion of microelements over time: Lagrange method and Euler method. The coupled Euler-Lagrange method (CEL) combines the advantages of both Lagrange and Euler methods, allowing large deformation of materials while maintaining accuracy in material motion analysis. Therefore, the CEL solution method is selected. To ensure the accuracy of the CEL solution, the simulation will be modeled according to the actual size.

[0068] According to the "Standard for Soil Test Methods" (GB 50123-2019), the standard quartz sand triaxial shear strength and strength index (unconsolidated and undrained shear test UU) are obtained as shown in Table 4. The spiral anchor disc diameter D (mm) is taken as 500, 600, 700, 800, 900, and 1000; the buried depth H (mm) is taken as the value of the depth-diameter ratio (H / D = 2-10, 12, 14, 16, 18, 20), and other parameters are shown in Table 4.2. The spiral anchor rod diameter is uniformly taken as 189 mm, and the pitch is uniformly taken as 152 mm. Based on the above data, the target problem (spiral anchor bearing capacity) is modeled.

[0069] Table 4.1 Standard quartz sand triaxial shear strength and strength index (UU)

[0070]

[0071] Note: pd is dry density, σ3 is confining pressure, (σ1-σ3)f is triaxial shear strength, c is cohesion, φ is internal friction angle, E is elastic modulus.

[0072] Table 4.2 Other parameters of spiral anchor

[0073]

[0074] From the numerical analysis results, it can be seen that the uplift and down pressure bearing capacity increases with the increase of the depth-diameter ratio of the anchor plate. Among them, the uplift bearing capacity increases rapidly when the depth-diameter ratio of the anchor plate is less than 5-6, and the uplift bearing capacity is significantly less than the down pressure bearing capacity at this stage; when the depth-diameter ratio is greater than 5-6, the uplift bearing capacity increases slowly, and is basically equivalent to the down pressure bearing capacity, as shown in FIG. 4.1 (taking S4 soil as an example). It is shown that the critical value of the depth-diameter ratio of the shallow buried anchor and the deep buried anchor in sandy soil is 5-6. Figure 4

[0075] 2) Model training

[0076] According to the data set, the model hyperparameters are optimized, and the optimal model hyperparameter values are shown in Table 4.3. According to the calculation, the R2, RMSE, MAE and MAPE of the uplift bearing capacity prediction are 0.9976, 41.174, 30.467 and 4.232%, respectively; the R2, RMSE, MAE and MAPE of the down pressure bearing capacity prediction are 0.9978, 38.838, 28.240 and 2.227%, respectively. The data shows that the model has good comprehensive performance and can meet the research requirements.

[0077] Table 4.3 Optimal model hyperparameter values

[0078]

[0079] 3) Comparative analysis of results

[0080] After the final model is obtained through iterative training of the model data set, the final model is used to predict the uplift and down pressure bearing capacity of the spiral anchor, and the prediction results are compared with the numerical analysis results, as shown in FIG. 4.2. It can be seen from the figure that the machine learning model prediction results are in good agreement with the numerical analysis results, and the error is within ±10%. It is shown that the model is feasible for the bearing capacity prediction of the spiral anchor, and the accuracy meets the requirements. Figure 4

[0081] ​​To ensure the comprehensiveness of the model training features, this study selected internal friction angle, density, initial cohesive force, compression modulus, disk diameter, and embedding depth as features, and extracted the gain, weight, and cover parameters for each feature. Under upward pulling force, the embedding depth had the largest gain value (650), the disk diameter had the largest weight value (520000), and the embedding depth, disk diameter, and internal friction angle had the largest cover values ​​(60). Under downward pressing force, the embedding depth had the largest gain value (450), the disk diameter and internal friction angle had the largest weight values ​​(580000), and the embedding depth, disk diameter, and internal friction angle had the largest cover values ​​(65). In summary, internal friction angle, disk diameter, and embedding depth are the three features that have the most significant impact on bearing capacity.

[0082] As a further explanation of the present invention, when establishing the database and creating the dataset for the helical anchor bearing capacity prediction model, it is necessary to ensure that the data source is reliable, accurately labeled, and has a balanced category distribution, support the addition and updating of subsequent data, and cover various working conditions and reference ranges as much as possible, so as to provide a reliable foundation for subsequent model training and prediction.

[0083] Based on the current application status of helical anchors in China, the bearing capacity of helical anchors can be accurately calculated using the bearing capacity coefficient Nq. However, the bearing capacity coefficient of helical anchors is affected by various factors such as soil parameters, anchor diameter, anchor depth, and load direction. Therefore, soil parameters (dry density ρ) are considered. d The internal friction angle φ, initial cohesion c, compression modulus E, anchor diameter D, and anchor burial depth H are used as features (input variables), and the uplift bearing capacity Tu and download bearing capacity Cu are used as labels (output variables). Based on the experimentally verified numerical model, a large number of parameter analysis results are used as the training database, where the Tu and Cu data are from numerical simulation.

[0084] When designing the helical anchor bearing capacity prediction dataset, it is necessary to examine the interdependencies of sample variables to avoid multicollinearity. The Pearson correlation coefficient matrix for correlation analysis is shown below. Figure 2 As shown in the figure, r is the Pearson correlation coefficient, which ranges from -1 to 1. The closer r is to 1, the stronger the positive correlation between the variables; conversely, the closer r is to -1, the stronger the negative correlation between the variables. Figure 2It can be seen that the input variables D, H have a more significant impact on the spiral anchor Tu, Cu than other features, and there is a complex nonlinear relationship between all features and the spiral anchor Tu, Cu. To avoid the influence of collinearity causing information duplication, methods such as deleting highly correlated features (features with Pearson correlation coefficient higher than 0.8 or 0.9) or adding regularization (L1, L2 regularization) can be used to reduce the collinearity effect. In this study, the method of adding regularization term in the model objective function can effectively avoid the collinearity effect, so that the data set can be used for model training of machine learning.

[0085] As a further elaboration of the present application, 3) model training and hyperparameter optimization After the data set is established, pre-processing is performed, and all features (p d , φ, c, E, D, H) are selected using the correlation coefficient to select the most relevant features, and the data set is divided into a training set (70%), a validation set (20%), and a test set (10%). K-fold cross-validation is used to train the single disc anchor pull-up and push-down bearing capacity, and the feature importance is obtained. K-fold cross-validation is used for division and model evaluation of the training set and the validation set, and is randomly and uniformly divided into K similar subsets, each of which maintains the distribution characteristics of the data as much as possible. Each time one of the subsets is selected as the validation set, and the remaining K-1 subsets are used as the training set, so that K times of training and validation are performed. Finally, the results of K times of validation are averaged to obtain a comprehensive evaluation index for measuring the performance of the model. As shown in Figure 3 Model training and hyperparameter optimization.

[0086] After the data set is established, pre-processing is performed, and all features (p d , φ, c, E, D, H) are selected using the correlation coefficient to select the most relevant features, and the data set is divided into a training set (70%), a validation set (20%), and a test set (10%). K-fold cross-validation is used to train the single disc anchor pull-up and push-down bearing capacity, and the feature importance is obtained. K-fold cross-validation is used for division and model evaluation of the training set and the validation set, and is randomly and uniformly divided into K similar subsets, each of which maintains the distribution characteristics of the data as much as possible. Each time one of the subsets is selected as the validation set, and the remaining K-1 subsets are used as the training set, so that K times of training and validation are performed. Finally, the results of K times of validation are averaged to obtain a comprehensive evaluation index for measuring the performance of the model. As shown in Figure 3 .

[0087] As a further elaboration of the present application, 5) Feature Importance Analysis, in order to reveal the core influence features of the screw anchor bearing capacity, the feature importance analysis method is usually used for model explanation and analysis. Feature importance analysis is an important tool for model explanation, which can help understand how the model uses input features for prediction and understand which features contribute most to the model's prediction results. At the same time, by comparing feature importance with domain knowledge, the rationality of the model can be verified, potential data or model problems can be found, and according to the feature importance results, the feature engineering strategy (such as feature combination, feature transformation) can be adjusted to further improve the model performance. Important features can also be identified to remove redundant or irrelevant features, reduce model complexity, improve training efficiency and generalization ability.

[0088] Feature importance is generally expressed by Gain (gain), Weight (weight) and Cover (coverage) parameter values of each feature. Gain represents the average information gain brought by a certain feature when used as a split node in all trees, and the higher the Gain, the greater the contribution of the feature to the model. Weight represents the total number of times a certain feature is used as a split node in all trees, and the higher the Weight, the more times the feature is used by the model. Cover represents the average value of the number of samples covered when a certain feature is used as a split node in all trees, and the higher the Cover, the more samples the feature affects when splitting.

[0089] The above describes the present application and its embodiments, which are not limiting, and the embodiments shown in the drawings are only one of the embodiments of the present application, and the actual structure is not limited thereto. In summary, if a person skilled in the art is inspired thereby, without departing from the spirit of the present application, without creative design, similar structural modes and embodiments of the technical solutions can be designed, which shall belong to the protection scope of the present application.

Claims

1. A machine learning-based method for predicting the bearing capacity of helical anchors, characterized by: Includes the following steps, (1) Initializing the model usually uses a constant model as the initial prediction to provide a starting point for the iterative training of the subsequent model; (2) Calculate the residual r after obtaining the initial predicted value. i (t) The residual is the difference between the t-th true value and the (t-1)-th predicted value, i.e. (3) Calculate the first residual r i (1) Then, a new model is trained using the objective function. During training, the residuals are used as the new objective variable. By optimizing the objective function, the optimal split point and tree structure are selected, and a new weak learner ft(x) is trained. The objective function of this model differs from that of the traditional GBDT model by incorporating a regularization term. The objective function is defined as follows: In the formula: Let Ω(f) be the loss function. k The regularization term () is the complexity penalty term for the k-th tree, used to control the complexity of the model and prevent overfitting. The regularization term is defined as follows: In the formula: T is the number of leaf nodes, wj is the weight of leaf node j, γ is the penalty coefficient for the number of leaf nodes, λ is the L2 regularization parameter, α is the L1 regularization parameter, the model optimization objective function is approximated by second-order Taylor expansion, and the optimal split point is found by using a greedy algorithm. The greedy algorithm calculates the objective function gain for each feature by traversing all possible split points and selects the split point with the largest gain. In the formula: g i h i These are the first and second derivatives of the loss function, I. L and I R is the set of left and right child nodes after splitting, I is the set of samples before splitting, γ is the regularization coefficient used to penalize newly added leaf nodes. After finding the optimal split point through a greedy algorithm, a new weak learner is constructed and the model is updated. Where η is the learning rate, which controls the contribution of each tree and the update magnitude of each step, thus affecting the model's convergence speed and performance. The value of η is usually a positive number between 0 and 1, and the larger the value, the fewer the number of iterations. (4) Repeat the above process until the maximum number of iterations is reached or the objective function value no longer decreases. Then output the final model and substitute the new sample data in the test set into the trained model for prediction. Test the model's generalization ability, accuracy and stability, overfitting and underfitting, and practical application effect. The final model is a weighted sum of multiple weak learners, as shown in the following formula. In the formula: T is the number of iterations, and η is the learning rate; (5) Database establishment: When establishing the dataset for the helical anchor bearing capacity prediction model, it is necessary to ensure that the data source is reliable, accurately labeled and the category distribution is balanced, support the addition and updating of subsequent data, and cover various working conditions and reference ranges as much as possible, so as to provide a reliable foundation for subsequent model training and prediction. (6) Model training and hyperparameter optimization: After the dataset is established, preprocessing is performed to optimize all features (ρ) d , c, E, D, H) use correlation coefficients to select the most relevant features, and divide the dataset into training set (70%), validation set (20%) and test set (10%). Use K-fold cross-validation to train the model on the single-disc anchor pull-out and pull-down bearing capacity respectively to obtain the feature importance. (7) Model evaluation: The performance of the model is comprehensively evaluated by different evaluation indicators such as coefficient of determination R2, root mean square error MSE, mean absolute error MAE, and mean absolute percentage error MAPE. In the formula: y i For the true value, For predicted values, R² is the average of all true values, and n is the number of samples. The higher the R², the lower the RMSE, MAE, and MAPE, indicating better model performance and a smaller gap between predicted and true values. (8) Feature importance analysis: Feature importance analysis is usually used for model interpretation and analysis.

2. The machine learning-based method for predicting the bearing capacity of a helical anchor according to claim 1, characterized in that: Step (6) uses K-fold cross-validation to divide the training set and validation set and to evaluate the model. The model is randomly and uniformly divided into K subsets of similar size. Each subset maintains the data distribution characteristics as much as possible. Each time, one subset is selected as the validation set and the remaining K-1 subsets are selected as the training set. This will result in K training and validation cycles. Finally, the results of the K validation cycles are averaged to obtain a comprehensive evaluation index to measure the performance of the model.

3. The machine learning-based method for predicting the bearing capacity of a helical anchor according to claim 1, characterized in that: In step (8), the importance of a feature is expressed by the Gain, Weight and Cover parameter values ​​of each feature. Gain represents the average information gain brought by a feature when it is used to split nodes in all trees. The higher the Gain, the greater the contribution of the feature to the model.

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