Single pile bearing capacity prediction method based on XGBoost machine learning algorithm

Abstract

The invention provides a single pile bearing capacity prediction method based on an XGBoost machine learning algorithm, comprising the following steps: (1) acquiring and preprocessing test data including soil layer input parameters, pile parameters and construction parameters, and dividing the preprocessed test data into a test set and a training set; (2) constructing a machine learning model in a pile foundation design stage according to the soil layer input parameters and the pile parameters, constructing a machine learning model in a pile foundation construction stage according to the soil layer input parameters, the pile parameters and the construction parameters, and respectively optimizing the two machine learning models by adopting a Bayesian optimization algorithm; and (3) the two optimized machine learning models are used for calculating the single-pile bearing capacity in the pile foundation design stage and the single-pile bearing capacity in the construction stage according to needs. According to the method, influence factors of all stages are comprehensively considered, algorithm learning is carried out on the influence factors, the bearing capacity of the reinforced concrete prefabricated pipe pile can be rapidly and effectively predicted, and the method can be used for optimizing the pile length design, reducing the pile material cost and improving the construction quality.

Description

Technical Field

[0001] This invention relates to the field of pile foundation construction, specifically a method for predicting the bearing capacity of a single pile based on the XGBoost machine learning algorithm. Background Technology

[0002] Precast reinforced concrete pipe piles, as a commonly used type of pile foundation construction, are widely used in engineering construction due to their high degree of industrialization, fast pile formation speed, relatively low cost, and good construction quality. The single pile bearing capacity is a crucial parameter for assessing whether a pile foundation meets construction quality requirements, and its accurate prediction is of great significance. During the pile foundation design phase, design institutes often conservatively design the single pile bearing capacity of precast reinforced concrete pipe piles based on standard formulas and building load requirements, resulting in overly long pile lengths. This necessitates pile cutting during construction, leading to material waste and increased construction costs. During pile foundation construction, excessively long piles make it difficult to drive them to the design elevation. Repeated hammering makes it impossible to estimate whether the single pile bearing capacity meets design requirements, easily breaking the pile head and causing a decline in construction quality. After pile foundation construction is completed, current national standards require testing the single pile bearing capacity of some pile foundations. However, in practice, pile foundations with low actual single pile bearing capacity are easily overlooked, making testing difficult. The problems mentioned above in the design and construction stages of pile foundations are restricting the construction quality of pile foundation projects, and further accurate prediction of the bearing capacity of single piles is needed.

[0003] With the explosive growth of artificial intelligence technology, a large number of machine learning algorithms have emerged, providing technical support for the prediction of single pile bearing capacity. Many algorithms are simple and convenient, but they consider few influencing factors, include many meaningless correction coefficients, and have poor reliability, which greatly limits their practical application. Summary of the Invention

[0004] To address the shortcomings of the existing technologies, this invention provides a method for predicting the bearing capacity of a single pile based on the XGBoost machine learning algorithm. This method comprehensively considers various influencing factors and parameters in the exploration, design, construction, and testing stages, and learns from them to quickly and in real time effectively predict the bearing capacity of a single reinforced concrete precast pipe pile. This method can be used to optimize pile length design, reduce pile material costs, and improve construction quality.

[0005] The technical solution provided by this invention is a method for predicting the bearing capacity of a single pile based on the XGBoost machine learning algorithm, comprising the following steps:

[0006] (1) Acquire test data and preprocess it. The test data includes soil layer input parameters, pile parameters and construction parameters. Divide the preprocessed test data into training set and test set.

[0007] (2) Using soil layer input parameters and pile parameters as input parameters for the pile foundation design stage, and the actual vertical bearing capacity of the pile foundation as the target parameter, a machine learning model for the pile foundation design stage is constructed. Using soil layer input parameters, pile parameters and construction parameters as input parameters for the pile foundation construction stage, and the actual vertical bearing capacity of the pile foundation as the target parameter, a machine learning model for the pile foundation construction stage is constructed. The two machine learning models are then optimized using the Bayesian optimization algorithm.

[0008] (3) Calculate the single pile bearing capacity during the design and construction stages of the pile foundation using the two optimized machine learning models as needed.

[0009] Furthermore, the soil layer input parameters include the thickness of each soil layer penetrated by the pile during actual construction, the characteristic value of soil bearing capacity fak, the standard value of the number of hammer blows in the standard penetration test Nk, and the compression modulus Es1-2. The pile parameters are the pile diameter and the construction parameters include the penetration depth, the average hammer drop height per meter, the average number of hammer blows per meter, the pile inclination, and the penetration depth.

[0010] Furthermore, the thickness of each soil layer penetrated by the pile during actual construction is determined by superimposing the pile foundation construction plan and the borehole plan, identifying the borehole closest to the pile foundation, and determining the thickness of each soil layer penetrated by the pile foundation in the actual construction based on the soil layer penetration situation of the pile foundation in the borehole profile.

[0011] Furthermore, the experimental data preprocessing in step (1) includes standardization processing, which involves unifying the dimensions of different characteristic parameters.

[0012] Furthermore, in step (2), based on the gradient boosting decision tree algorithm, XGBoost calculates the predicted value by minimizing the objective function to the desired range, as shown in formula (1):

[0013] (1)

[0014] In formula (1): This is a predicted value; For input variables; This is a mean sample; For the first A weak evaluation function; The number of samples; For the set of all classification and regression trees, the XGBoost objective function is defined and calculated as shown in formula (2):

[0015] (2)

[0016] In the formula: The loss function measures the degree of fit between the model and the data. for The regularization term is used to limit the number of leaf nodes. Convert to the number of remaining nodes. The item represents the node weight. and The regularization coefficient is used.

[0017] Minimum objective function:

[0018] (3)

[0019] Expand equation (3) using Taylor second order:

[0020] (4)

[0021] (5)

[0022] (6)

[0023] The first derivative, The objective function is determined by equations (5) and (6), and the constant term is removed. The objective function is shown in equation (7).

[0024] (7)

[0025] The optimal solution to the objective function is finally obtained as shown in equation (8):

[0026] (8)

[0027] In the formula: The structure is a tree. For the number of iterations, Next is the leaf. A set of instances.

[0028] Furthermore, in step (2), a Bayesian optimization algorithm is used to optimize the hyperparameters of the training set.

[0029] Bayes' theorem is shown in formula (9):

[0030] (9)

[0031] In the formula: f is the unknown objective function; D i =(x1,y1), (x2,y2), ..., (x n ,y n p(D) represents the observed set; i |f) is D i The likelihood distribution of f; p(f) is the prior probability distribution of f; p(D ip(f|D) represents the marginal likelihood distribution; i Let f be the posterior probability distribution of f;

[0032] The specific steps of the Bayesian optimization algorithm are as follows:

[0033] ① Define the hyperparameter search space

[0034] Mapping XGBoost key hyperparameters to mathematical vectors:

[0035] (10)

[0036] Where x i The corresponding parameters are learning_rate, max_depth, n_estimators, and subsample;

[0037] ② Construct a Gaussian process surrogate model

[0038] The relationship between hyperparameters and model error is modeled using radial basis kernel functions:

[0039] (11)

[0040] In formula (11), l is the adaptive length scale parameter;

[0041] ③ Design acquisition functions to guide sampling

[0042] Using expected improvements to balance exploration and utilization:

[0043] (12)

[0044] in , , , It is the standard normal distribution function;

[0045] Find the optimal candidate point:

[0046] (13)

[0047] ④ Iterative optimization and early stopping mechanism

[0048] The specific steps are: repeatedly train the model → update the surrogate model → generate new candidate points until the conditions are met;

[0049] or (14)

[0050] For the error threshold, This represents the maximum number of iterations.

[0051] Furthermore, in step (3), test sets are input for prediction during the design and construction phases, and the prediction results of the Xgboost model are evaluated for error. The error between the predicted data of the test set and the actual data is calculated, and the error rate is used as the evaluation index.

[0052] The beneficial effects of this invention are:

[0053] (1) This invention integrates the geometric dimensions of the pile, the stratum parameters and unique construction parameters (hammering data, inclination) to capture the factors affecting the bearing capacity more comprehensively. Through the XGBoost machine learning algorithm, the single pile bearing capacity of the reinforced concrete precast pipe pile in the pile foundation design stage and the construction stage can be effectively predicted. The XGBoost algorithm effectively handles complex nonlinear relationships and the prediction accuracy is better than the traditional empirical formula, which is convenient and fast.

[0054] (2) The present invention uses Bayesian optimization algorithm to tune hyperparameters. Hyperparameter tuning is a key step to improve model performance. By optimizing parameter combinations, the best model configuration can be found, which improves the prediction accuracy of the model. Attached Figure Description

[0055] Figure 1 This is a diagram of the XGBoost tree structure of the present invention;

[0056] Figure 2 This is a schematic diagram illustrating the prediction principle of the pile foundation design stage of this invention;

[0057] Figure 3 This is a schematic diagram illustrating the prediction principle of the pile foundation construction stage of the present invention;

[0058] Figure 4 This is a schematic diagram of the thickness of the soil layer through which the pile foundation of this invention penetrates. Detailed Implementation

[0059] To make the objectives, features, and advantages of this invention more apparent and understandable, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, this invention is not limited to the following embodiments, and specific implementation methods can be determined according to the technical solutions of this invention and actual circumstances. To avoid obscuring the essence of this invention, well-known methods, processes, and procedures are not described in detail.

[0060] During the design phase, the vertical bearing capacity value is mainly based on the load values ​​of the superstructure. According to the empirical formulas in the national standard "Technical Code for Building Pile Foundations", the formulas mainly involve the thickness of each soil layer penetrated by the pile, the pile depth perimeter, the pile side resistance value, the pile end resistance value, and the pile cross-sectional area. Among them, the pile depth perimeter and the pile cross-sectional area are related to the pile diameter, so the diameter is used as the pile parameter. The characteristic value of soil bearing capacity, fak, refers to the maximum uniformly distributed pressure value that the foundation soil can withstand within the allowable deformation range. It reflects the safe load capacity that the foundation soil can withstand without excessive settlement or shear failure. For end-bearing piles, the magnitude of the pile end resistance value is directly affected by the bearing capacity of the soil layer at the pile end, and this capacity is usually characterized by the characteristic value of soil bearing capacity. The magnitude of the pile side resistance value depends on the properties of the soil layer beside the pile, including soil type, density, cohesion, etc., and these factors also affect the value of the characteristic value of soil bearing capacity. Furthermore, the interaction between the pile and the soil is one of the important factors affecting the bearing capacity of the pile foundation. Other factors affecting the bearing capacity of the pile foundation should also be considered. Among them, the standard penetration test blow count (Nk) is a widely used in-situ test parameter in geotechnical engineering. It reflects the soil layer's resistance to penetration and indirectly reflects the soil's compactness and strength characteristics. The soil's compression modulus (Es1-2) is a key parameter for measuring the soil's ability to resist compressive deformation under vertical loads and is of great significance in assessing the vertical bearing capacity of pile foundations. In summary, the thickness of each soil layer penetrated by the pile, the characteristic value of the soil layer's bearing capacity (fak), the standard penetration test blow count (Nk), and the compression modulus (Es1-2) are used as soil layer parameters. The actual vertical bearing capacity of the pile foundation is used as the target parameter. The parameters of the training model during the design phase are shown in Table 1.

[0061] Table 1 Model parameters during the design phase

[0062] During the design phase, for completed pile foundation projects in a specific area, the actual pile parameters, soil parameters, and actual vertical bearing capacity of the piles should be obtained. A predictive model for the vertical bearing capacity of the piles during the design phase should then be constructed using the XGBoost machine learning algorithm. A model trained based on actual parameters is more likely to meet the accuracy requirements for predicting the vertical bearing capacity of the piles during the design phase. The specific principle is as follows: Figure 2 As shown.

[0063] During the construction phase, the hammer-driven pile driving method is commonly used. This method utilizes the repeated impact force of various pile hammers (commonly including diesel hammers and hydraulic hammers) and the self-weight of the pile to overcome the sidewall friction of the pile and the resistance of the soil at the pile tip, driving the pile to the design elevation. The average drop height per meter refers to the height of the hammer when it strikes the pile; the higher the height, the greater the energy transferred to the pile tip. The average number of blows per meter is the number of blows required per meter under the action of the pile hammer, reflecting the amount of energy used for pile driving. Because hammer-driven pile driving is fast, it is not convenient to statistically analyze the drop height and number of blows for each advance; therefore, based on engineering experience, the average drop height per meter and the average number of blows per meter are used. The penetration depth is used to determine the hammering position and can be combined with the number of blows to assess the resistance of the rock and soil layers encountered at different pile driving depths. The pile inclination has a significant impact on the pile's bearing capacity and stability. Excessive inclination can cause cracks or damage during construction, reducing the pile foundation's bearing capacity. When the pile penetrates the bearing stratum, on-site personnel need to record the pile penetration depth, focusing on the last three penetration values. These penetration values ​​can be used to determine the hardness of the foundation soil, thus confirming whether the pile foundation or foundation soil's bearing capacity meets requirements. In summary, during the construction phase, the following parameters are added as input parameters: penetration depth, average hammer drop height per meter, average number of hammer blows per meter, pile inclination, and penetration depth. The actual vertical bearing capacity of the pile foundation is used as the target parameter. The training model parameters for the construction phase are shown in Table 2.

[0064] Table 2 Model parameters during construction phase

[0065] Similar to the design phase, model training is performed based on the newly added construction parameters to further improve the accuracy of predicting the vertical bearing capacity of pile foundations. The specific principle is as follows: Figure 3 As shown.

[0066] XGBoost (eXtreme Gradient Boosting) is a synthetic algorithm that combines basis functions and weights to achieve a better fit to data. Unlike traditional Gradient Boosting Decision Trees (GBDT), XGBoost adds a regularization term to the loss function. Furthermore, since some loss functions are difficult to compute their derivatives, XGBoost uses the second-order Taylor expansion of the loss function as the fit. XGBoost is more efficient when handling large datasets and complex models, and also excels in preventing overfitting and improving generalization ability. The principle is as follows: Figure 1 As shown.

[0067] Based on the gradient boosting decision tree algorithm, XGBoost calculates the predicted value by minimizing the objective function to the desired range, as shown in formula (1):

[0068] (1)

[0069] In formula (1): This is a predicted value; For input variables; This is a mean sample; For the first A weak evaluation function; The number of samples; For the set of all classification and regression trees, the XGBoost objective function is defined and calculated as shown in formula (2):

[0070] (2)

[0071] In the formula: The loss function measures the degree of fit between the model and the data. for The regularization term is used to limit the number of leaf nodes. The remaining number of nodes increases the risk of overfitting. The item represents the node weight. and Here are the regularization coefficients; minimum objective function:

[0072] (3)

[0073] Expand equation (3) using Taylor second order:

[0074] (4)

[0075] (5)

[0076] (6)

[0077] The first derivative, The objective function is determined by equations (5) and (6), and the constant term is removed. The objective function is shown in equation (7).

[0078] (7)

[0079] The optimal solution to the objective function is finally obtained as shown in equation (8):

[0080] (8)

[0081] In the formula: The structure is a tree. For the number of iterations, Next is the leaf. The instance set. The processing flow of this invention:

[0082] 1. Perform data preprocessing and data segmentation.

[0083] Data preprocessing consists of two parts: input feature parameter confirmation and standardization.

[0084] (1) Data preprocessing

[0085] 1) Confirm input feature parameters

[0086] In Tables 1 and 2, the input parameters such as soil bearing capacity characteristic value, standard penetration test blow count standard value, compression modulus, pile diameter, penetration depth, average drop height per meter, average blow count per meter, pile inclination, and penetration depth are all characteristic parameters that can be directly obtained from design and construction data. However, the parameter of the thickness of each soil layer penetrated by the pile in actual construction cannot be directly obtained. Instead, it is determined by overlaying the pile foundation construction plan and the borehole plan to identify the nearest borehole to the pile foundation. Based on the soil layer penetration situation of the pile foundation in the borehole profile, the thickness of each soil layer penetrated by the pile in actual construction is confirmed. Figure 4 As shown:

[0087] 2) Standardization Processing

[0088] Standardization is a process that unifies the dimensions of different feature parameters to improve model training performance, as shown in Table 3.

[0089] Table 3. Dimensional Table of Characteristic Units

[0090] (2) Data partitioning

[0091] The dataset can be divided into a training dataset and a validation dataset. Considering that different divisions of the dataset can significantly impact model training and testing, the random states of the dataset are initialized to fixed values, and the dataset is divided in an 8:2 ratio, with 80% of the dataset used as the training set and 20% as the validation set. The validation set data is used only for algorithm performance evaluation and not for the algorithm itself.

[0092] 2. Model Building and Training

[0093] (1) Define the learning objective function of the XGBoost model

[0094] The objective function of the XGBoost model is shown in the following equation:

[0095]

[0096] (2) Model training to determine the optimal hyperparameters

[0097] Hyperparameter tuning is a crucial step in improving model performance. By optimizing parameter combinations, the optimal model configuration can be found. Appropriate hyperparameter selection can enhance the model's generalization ability, avoid overfitting and underfitting, and ensure good model performance on the validation set. Considering that the problem in this paper is non-convex, a Bayesian optimization algorithm is used to optimize hyperparameters on the training set.

[0098] Bayes' theorem is shown in formula (9):

[0099] (9)

[0100] In the formula: f is the unknown objective function; D i =(x1,y1), (x2,y2), ..., (x n ,y n p(D) represents the observed set; i |f) is D i The likelihood distribution of f; p(f) is the prior probability distribution of f; p(D i p(f|D) represents the marginal likelihood distribution; i Let f be the posterior probability distribution of f.

[0101] The specific steps of the Bayesian optimization algorithm are as follows:

[0102] ① Define the hyperparameter search space

[0103] Mapping XGBoost key hyperparameters to mathematical vectors:

[0104] (10)

[0105] Where x i The corresponding parameters are learning_rate, max_depth, n_estimators, and subsample.

[0106] ② Construct a Gaussian process surrogate model

[0107] The relationship between hyperparameters and model error is modeled using the radial basis function (RBF):

[0108] (11)

[0109] In formula (11), l is the adaptive length scale parameter.

[0110] ③ Design acquisition functions to guide sampling

[0111] Balance exploration and exploitation using Expected Improvement (EI):

[0112] (12)

[0113] That , , , It is the standard normal distribution function.

[0114] Find the optimal candidate point:

[0115] (13)

[0116] ④ Iterative optimization and early stopping mechanism

[0117] The specific steps are: repeatedly train the model → update the surrogate model → generate new candidate points until the conditions are met.

[0118] or (14)

[0119] For the error threshold, This represents the maximum number of iterations.

[0120] The training sets for the design and construction phases were input into the XGBoost model for training, and the parameter tuning results are shown in Table 4.

[0121] Table 4 Optimal Hyperparameter Table

[0122] 3. Model Prediction and Evaluation

[0123] A prediction model for the vertical bearing capacity of pile foundations based on XGBoost is formed using the input and output feature parameters of the training dataset. The model is then used to predict the vertical bearing capacity of pile foundations by inputting the validation dataset during the design and construction phases.

[0124] Error evaluation of the Xgboost model prediction results is performed by comparing the predicted data of the validation dataset with the actual data and using the error rate as the evaluation metric.

[0125] Application Examples

[0126] A steel production base is currently undergoing pile foundation construction. During the construction phase, it was discovered that some piles were excessively long, causing difficulties in pile driving and insufficient bearing capacity. To optimize pile length and control the quality of pile foundation construction, this patented technology was used to establish a predictive model for the vertical bearing capacity of 60 completed pile foundation sets. The process is as follows:

[0127] 1. Perform data preprocessing and data segmentation.

[0128] (1) Data preprocessing

[0129] In the training models during the design and construction phases, the characteristic parameters of "soil bearing capacity characteristic value", "standard penetration test hammer blow count standard value", "compression modulus", "pile diameter" and "thickness of each soil layer penetrated by the pile in actual construction" are the same. Based on the deviation between the designed pile length and the actual construction, the geometric position of the actual pile in the adjacent borehole stratum is calculated, and the characteristic parameter value of "thickness of each soil layer penetrated by the pile in actual construction" is obtained.

[0130] In the training model during the construction phase, data such as "penetration depth," "average hammer drop height per meter," "average number of blows per meter," "pile inclination," and "penetration depth" can be manually entered or automatically collected by sensor equipment. Among them, "average hammer drop height per meter" and "average number of blows per meter" are combined with "penetration depth" respectively, which facilitates on-site statistics. The pile foundation data is shown in Table 5.

[0131] Table 5. Dimensional Table of Characteristic Units

[0132]

[0133] (2) Data partitioning

[0134] In the design and construction phases, the training model selected 48 sets of pile foundations from the pile foundation dataset as the training set and 12 sets of pile foundations as the validation set.

[0135] 2. Model Building and Training

[0136] The input and output parameters of the 48 sets of training data are generated into a JSON format file based on the code tags in Table 3. This file is then input into the training model, and the model is trained according to the optimal hyperparameters in Table 4 to obtain the training model for the design phase and the training model for the construction phase.

[0137] 3. Model Prediction and Evaluation

[0138] The 12 sets of validation set data input parameters were used to generate JSON format files based on the code tags in Table 3. These files were then input into the training models for the design phase and the construction phase, respectively, to obtain the predicted actual bearing capacity values.

[0139] The relationship between the actual bearing capacity and the predicted value during the design and construction phases is shown in Table 6.

[0140] Table 6. Dimensional Table of Characteristic Single Quantities

[0141] The data above shows that the prediction error rate for the vertical bearing capacity of the pile foundation is less than 6% in both the construction and design stages, which meets the requirements in actual engineering applications.

[0142] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications and substitutions should be covered within the scope of the claims of the present invention. Technical aspects, shapes, and structures not described in detail in this invention are all well-known technologies.

Claims

1. A method for predicting the bearing capacity of a single pile based on the XGBoost machine learning algorithm, characterized in that, Includes the following steps: (1) Acquire test data and preprocess it. The test data includes soil layer input parameters, pile parameters and construction parameters. Divide the preprocessed test data into training set and test set. (2) Using soil layer input parameters and pile parameters as input parameters for the pile foundation design stage, and the actual vertical bearing capacity of the pile foundation as the target parameter, a machine learning model for the pile foundation design stage is constructed. Using soil layer input parameters, pile parameters and construction parameters as input parameters for the pile foundation construction stage, and the actual vertical bearing capacity of the pile foundation as the target parameter, a machine learning model for the pile foundation construction stage is constructed. The two machine learning models are then optimized using the Bayesian optimization algorithm. (3) Calculate the single pile bearing capacity during the design and construction stages of the pile foundation using the two optimized machine learning models as needed.

2. The method for predicting the bearing capacity of a single pile based on the XGBoost machine learning algorithm according to claim 1, characterized in that, The soil layer input parameters include the thickness of each soil layer penetrated by the pile during actual construction, the characteristic value of soil bearing capacity fak, the standard value of the number of hammer blows in the standard penetration test Nk, and the compression modulus Es1-2. The pile parameter is the pile diameter. The construction parameters include the penetration depth, the average hammer drop height per meter, the average number of hammer blows per meter, the pile inclination, and the penetration depth.

3. The method for predicting the bearing capacity of a single pile based on the XGBoost machine learning algorithm according to claim 2, characterized in that, The thickness of each soil layer penetrated by the pile during actual construction is determined by superimposing the pile foundation construction plan and the borehole plan, identifying the borehole closest to the pile foundation, and then determining the thickness of each soil layer penetrated by the pile foundation in the actual construction based on the soil layer penetration situation of the pile foundation in the borehole profile.

4. The method for predicting the bearing capacity of a single pile based on the XGBoost machine learning algorithm according to claim 2, characterized in that, The experimental data preprocessing in step (1) includes standardization processing, which unifies the dimensions of different characteristic parameters.

5. The method for predicting the bearing capacity of a single pile based on the XGBoost machine learning algorithm according to claim 1, characterized in that, In step (2), based on the gradient boosting decision tree algorithm, XGBoost minimizes the objective function to the desired range, and the predicted value is calculated as shown in formula (1): （1） In formula (1): This is a predicted value; For input variables; This is a mean sample; For the first A weak evaluation function; The number of samples; For the set of all classification and regression trees, the XGBoost objective function is defined and calculated as shown in formula (2): （2） In the formula: The loss function measures the degree of fit between the model and the data. for The regularization term is used to limit the number of leaf nodes. Convert to the number of remaining nodes. The item represents the node weight. and The regularization coefficient is used. Minimum objective function: （3） Expand equation (3) using Taylor second order: （4） （5） （6） The first derivative, The objective function is determined by equations (5) and (6), and the constant term is removed. The objective function is shown in equation (7). （7） The optimal solution to the objective function is finally obtained as shown in equation (8): （8） In the formula: The structure is a tree. For the number of iterations, Next is the leaf. A set of instances.

6. The method for predicting the bearing capacity of a single pile based on the XGBoost machine learning algorithm according to claim 1, characterized in that, In step (2), the Bayesian optimization algorithm is used to optimize the hyperparameters of the training set. Bayes' theorem is shown in formula (9): （9） In the formula: f is the unknown objective function; D i =(x1,y1), (x2,y2), ..., (x n ,y n p(D) represents the observed set; i |f) is D i The likelihood distribution of f; p(f) is the prior probability distribution of f; p(D i p(f|D) represents the marginal likelihood distribution; i Let f be the posterior probability distribution of f; The specific steps of the Bayesian optimization algorithm are as follows: ① Define the hyperparameter search space Mapping XGBoost key hyperparameters to mathematical vectors: （10） Where x i The corresponding parameters are learning_rate, max_depth, n_estimators, and subsample; ② Construct a Gaussian process surrogate model The relationship between hyperparameters and model error is modeled using radial basis kernel functions: （11） In formula (11), l is the adaptive length scale parameter; ③ Design acquisition functions to guide sampling Using expected improvements to balance exploration and utilization: （12） in , , , It is the standard normal distribution function; Find the optimal candidate point: （13） ④ Iterative optimization and early stopping mechanism The specific steps are: repeatedly train the model → update the surrogate model → generate new candidate points until the conditions are met; or (14) For the error threshold, This represents the maximum number of iterations.

7. The method for predicting the bearing capacity of a single pile based on the XGBoost machine learning algorithm according to claim 1, characterized in that, In step (3), test sets are input for prediction during the design and construction phases, and the prediction results of the Xgboost model are evaluated for error. The error between the predicted data of the test set and the actual data is calculated, and the error rate is used as the evaluation index.

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