Prediction method and prediction model for foundation resistance of super-long pile

Abstract

The invention discloses a super-long pile foundation resistance prediction method and model, and the method comprises the steps: firstly, improving the adaptability of the model to complex input and the precise prediction capability of the model to bearing capacity through the strong nonlinear expression capability of a CatBoost algorithm and the characteristics of native support class variables; then six intelligent optimization algorithms are introduced to automatically search hyper-parameters of the model, manual parameter adjustment errors are avoided, the stability and generalization ability of the model are improved, and finally an optimal fusion model is determined for prediction. By constructing the fusion optimization strategy, the multi-optimization algorithm and the CatBoost are deeply fused, the robustness and applicability of the system in the multi-scene and multi-sample environment are improved, and the problems that in the prior art, the resistance prediction precision of the super-long pile foundation is insufficient, and the model stability is poor are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent modeling and machine learning prediction of geotechnical engineering, and more particularly to a method and model for predicting the base resistance of an ultra-long pile. BACKGROUND

[0002] Pile foundations bear the entire load of the superstructure and transmit it to the deep stable soil layer. Accurate prediction of the ultimate bearing capacity (resistance) is the fundamental prerequisite for ensuring that structures such as buildings and bridges do not experience excessive settlement, tilting, or even collapse during long-term use. Pile foundation resistance is a key parameter in geotechnical engineering design. Ultra-long piles are widely used in high-rise buildings, bridges, and large infrastructure projects. The length of the pile foundation affects the safety and stability of the building structure, so fast and accurate prediction of the base resistance of the ultra-long pile becomes an important task in engineering design and construction optimization.

[0003] Traditional prediction methods (such as static load tests, empirical formulas, numerical simulations, etc.) can estimate the base resistance to some extent, but they require a large amount of field test data and are difficult to capture the complex nonlinear mapping between high-dimensional input variables. In particular, they have poor adaptability to special pile types or complex soil conditions, with large errors, high costs, long cycles, and weak generalization ability.

[0004] In recent years, data-driven machine learning methods have been gradually introduced into the field of geotechnical engineering. By constructing high-performance prediction models and combining field test data to model the bearing capacity, the efficiency and accuracy can be significantly improved, and the intelligentization process of foundation engineering can be promoted to become a new means of predicting complex geological parameters. For example, support vector regression (SVR), neural networks (ANN), random forests (RF), and other methods are used to predict the bearing capacity of pile foundations. CN119514350A discloses a method for predicting the vertical bearing capacity of pipe piles based on deep learning, which uses convolutional neural networks and long short-term memory networks for modeling, constructs a pile foundation bearing capacity prediction model, and combines a data set to train the prediction model and optimize the model parameters. The pile foundation bearing capacity prediction model is used in actual pipe pile testing to predict the ultimate bearing capacity of the pipe pile. Although this model improves the prediction accuracy to some extent, the parameter tuning process relies on human experience, which is inefficient, and the model is sensitive to abnormal values and noise, with poor robustness, leading to poor model stability and weak generalization ability.

[0005] To improve the prediction accuracy, mechanisms such as Bayesian are introduced to search and optimize the model parameters, such as the chaos Gaussian Sparrow search algorithm in CN118657043A to optimize the hyperparameters of the sparse Bayesian probability model, multiple fold cross-validation to analyze the potential solutions of the model, root mean square error to select the compromise solution of the Pareto frontier as the optimal hyperparameters, and zero-mean Gaussian explicit prior distribution to select unknown parameters and constrain model preferences. Although this patent introduces optimization algorithms to optimize the model, the pile foundation resistance is affected by many factors, and a single model is difficult to capture the deep relationship between each input variable, and the prediction ability is limited, and in the parameter optimization process, it is easy to fall into local optimum, slow convergence speed and poor robustness, lack of diversity mechanism and adaptive strategy, resulting in unstable final prediction results. SUMMARY

[0006] The main technical problem to be solved by the present application is to provide a super-long pile foundation resistance prediction method and prediction model to solve the problems of insufficient prediction accuracy and poor model stability of existing single models.

[0007] The object of the present application is achieved by the following technical solutions:

[0008] A super-long pile foundation resistance prediction method, comprising the following steps:

[0009] S1. Collecting pile foundation data and pre-processing the data by denoising and standardizing;

[0010] S2. Using a CatBoost regression model to model the nonlinear relationship between the pre-processed pile foundation parameters and the foundation resistance;

[0011] S21. Ordinal target coding is performed on the category features of the pile foundation data, and a function f(x i ) is obtained by predicting the target value y according to the features x i , and the minimum loss function L(θ) is obtained, which is represented as:

[0012]

[0013] Where N is the number of samples; y i is the true value of sample i; f(x i ) is the predicted value of the model for sample i;

[0014] S22. In the iteration process, a new tree h t (x) is added to fit the residual every time the model is updated, and a complete binary tree is used for automatic feature combination, which is represented as:

[0015] f t (x) = f t-1 (x) + ηht (x)

[0016] where f t-1 (x) is the model of the previous t-1 iterations; h t (x) is the prediction result of the tth tree; η is the learning rate;

[0017] S3. Automatically search the hyperparameters of the model using genetic algorithm, whale optimization algorithm, artificial ecosystem optimization algorithm, biogeography-based optimization algorithm, Harris hawk optimization algorithm and adaptive optimization algorithm, respectively;

[0018] The genetic algorithm is based on an adaptive calculation system, and adopts a roulette selection and elite reservation strategy to globally search the learning_rate hyperparameter;

[0019] The whale optimization algorithm adjusts the depth parameter through a spiral bubble net attack mechanism;

[0020] The artificial ecosystem optimization algorithm simulates the producer-consumer energy flow mechanism, and globally optimizes the max-features parameter using a photosynthesis strategy;

[0021] The biogeography-based optimization algorithm is based on a habitat suitability index, and dynamically balances the global exploration and local development of the n-estimators parameter through a species migration model;

[0022] The Harris hawk optimization algorithm uses a prey escape energy model, and combines a diving attack strategy to adaptively adjust the subsample parameter in multiple stages;

[0023] The adaptive optimization algorithm uses a dynamic mutation rate rule to optimize the iterations parameter in real time;

[0024] S4. Calculate the evaluation index of each group of models, and select the optimal fusion model;

[0025] S5. Use the optimal fusion model to predict the pile foundation data.

[0026] Further, the pile foundation data includes one or more of the load point load, the load point settlement, the distance from the load point to the pile end, the axial stiffness, and the standard penetration test value of the foundation soil layer.

[0027] Further, the genetic algorithm (GA) simulates the process of biological evolution, including population initialization, fitness function calculation, selection, crossover, mutation, and termination condition evaluation, wherein the fitness function calculation is represented as:

[0028]

[0029] where g(x) is the original objective function;

[0030] The probability formula of selection is expressed as:

[0031]

[0032] where P i represents the probability of the i-th individual being selected; f(x i ) represents the fitness value of the i-th individual; and N represents the total number of individuals in the population.

[0033] Further, the whale optimization algorithm (WOA) includes a surrounding prey stage, a searching prey stage, and a spiral bubble-net attack stage. The algorithm performs global and local search in the solution space through these behaviors, gradually approaching the optimal solution. In combination with the surrounding behavior and the updating method of the spiral trajectory, the position updating formula is:

[0034]

[0035] where x represents the current position of the individual; x represents the current position of the optimal solution; t represents the current iteration number; b is a constant defining the spiral shape; l is a random number ranging from -1 to 1; and p is a random number ranging from 0 to 1, where a decreases linearly from 2 to 0, and r is a random number ranging from 0 to 1. The algorithm approaches the prey by adjusting the distance vector When the whale surrounds the prey, the spiral trajectory and the surrounding behavior are alternately performed, and the specific behavior is determined by the probability p.

[0036] Further, the artificial ecosystem optimization algorithm (AEO) is based on the behavior patterns of organisms in nature, and promotes the discovery of effective solutions by simulating the attractive effect between individuals, including individual generation, mutual attraction, and position updating, where the expression of mutual attraction is:

[0037]

[0038] where F ij represents the attraction between individuals i and j; A is a constant controlling the strength of attraction; r ij represents the distance between individuals i and j; and β is a parameter controlling distance decay.

[0039] The expression of position updating is:

[0040]

[0041] where x i (t) and x i (t) represent the current position of the i-th individual and the j-th individual, respectively.(t+1) represents the position of individual i in the current and next generation, respectively, v ij is the relative speed between individual i and individual j, and t is the current iteration number.

[0042] Further, the biogeography-based optimization algorithm (BiEO) is an optimization algorithm that combines the principles of biogeography and evolutionary algorithm ideas. It has common features with other biology-based optimization methods. BiEO is an extension of biogeography-based optimization (BBO) that incorporates genetic operations such as crossover and mutation from evolutionary algorithms to enhance global search capabilities and avoid local optimal solutions. It not only draws on the habitat suitability and species migration mechanisms of BBO, but also optimizes the search process through genetic operations to achieve better results in complex optimization problems, including: initializing the population, evaluating suitability, performing migration, genetic operations, and determining termination conditions, where suitability is represented as:

[0043] HSI i = f(x i )

[0044] where HSI i represents the suitability of the i-th habitat; f(x i ) represents the value of the objective function; x i represents the corresponding solution of the i-th habitat;

[0045] Migration is represented as:

[0046]

[0047] where, represents the solution after migration; x i and x j represent the solutions corresponding to habitats i and j, respectively; M ij represents the migration probability, i.e., the probability of migrating from habitat j to habitat i;

[0048] Crossover and mutation operations are introduced in genetic operations, represented as:

[0049]

[0050] Further, the Harris Hawk Optimization Algorithm (HOA) simulates the sudden attack behavior of Harris Hawks during the pursuit process, including surrounding behavior, chasing behavior, and escape behavior, where the surrounding behavior is represented as:

[0051]

[0052] where x i represents the position of the i-th Harris Hawk, x * represents the position of the optimal solution, and r1 is a random number between 0 and 1.

[0053] When the prey is stronger, the eagle will choose to flee. The speed and direction of the escape depend on the escape strategy of the prey:

[0054]

[0055] where r2 is a random factor for simulating the escape behavior. In the pursuit phase, when the prey escapes, the eagle quickly adjusts its position to follow the prey, and the pursuit behavior is expressed as:

[0056]

[0057] where x j represents the position of another eagle; r3 is a random factor representing the strength of the pursuit.

[0058] Further, the adaptive optimization algorithm (SAO) dynamically adjusts the search strategy in real time according to the state of the current solution space and the previously obtained search results, including initializing the population or solution set, evaluating individual fitness, dynamically adjusting algorithm parameters, generating new solutions through mutation, selecting the optimal solution, and stopping iteration according to the predefined termination condition, wherein the expression of mutation is:

[0059]

[0060] where x i is an individual, δ represents the amplitude of mutation; rand is a random number for increasing uncertainty, p mut is the mutation rate.

[0061] The mutation rate p mut is dynamically updated according to the change of fitness during the search process, expressed as:

[0062] p mut = p mut ·(1-α·fitness(x i ))

[0063] where α is a parameter that controls the learning speed, fitness(x i ) is the fitness, and fitness(x) = f(x), f(x) is the objective function.

[0064] Further, according to the cooperation and difference between optimizers, four core hyperparameters in the CatBoost regression model are selectively optimized, and different hyperparameter search ranges are set to effectively enhance the overall search ability and robustness of the model. Specifically, the hyperparameter search ranges of genetic algorithm, whale optimization algorithm, artificial ecosystem optimization algorithm, biogeography-based optimization algorithm, Harris hawk optimization algorithm and adaptive optimization algorithm are:

[0065] Genetic algorithm: iteration number 100-2000, tree depth 3-15, learning rate 0.01-0.3, regularization term 1-10;

[0066] Whale optimization algorithm: iteration number 1000-2000, tree depth 9-10, learning rate 0.1-0.15, regularization term 1-10;

[0067] Artificial ecosystem optimization algorithm: iteration number 1000-2000, tree depth 1-15, learning rate 0.001-0.3, regularization term 1-10;

[0068] Biogeography-based optimization algorithm: iteration number 100-1000, tree depth 9-10, learning rate 0.01-0.3, regularization term 1-10;

[0069] Harris hawk optimization algorithm: iteration number 1000-2000, tree depth 9-10, learning rate 0.1-0.15, regularization term 1-10;

[0070] Adaptive optimization algorithm: iteration number 100-1000, tree depth 3-15, learning rate 0.01-0.5, regularization term 1-10.

[0071] Further, the optimal fitness value is recorded in each iteration, and the convergence of the model is visualized and dynamically monitored. By analyzing the fitness convergence trend of different optimizers at each generation, the optimization progress can be tracked in real time, and the evolution process that does not converge can be terminated in advance.

[0072] A prediction model based on the above super-long pile foundation resistance prediction method, comprising a data preprocessing module, a CatBoost prediction model module, an optimization algorithm fusion module, a model evaluation module and a prediction output module;

[0073] The data preprocessing module reads and cleans the original pile foundation data, performs normalization processing, and then inputs the data into the CatBoost prediction model module;

[0074] The CatBoost prediction model module uses the CatBoost regression model to model the nonlinear relationship between the pile foundation parameters and the foundation resistance;

[0075] The optimization algorithm fusion module includes a genetic algorithm, a whale optimization algorithm, an artificial ecosystem optimization algorithm, a biogeography optimization algorithm, a Harris hawk optimization algorithm and a self-adaptive optimization algorithm, and parameters of a model established in the CatBoost prediction model module are adjusted to form GA-CatBoost, WOA-CatBoost, AEO-CatBoost, BiEO-CatBoost, HOA-CatBoost and SAO-CatBoost hybrid models respectively;

[0076] The model evaluation module evaluates the six hybrid models in the optimization algorithm fusion module, and selects an optimal fusion model based on index feedback;

[0077] The prediction output module inferences to-be-predicted pile foundation data based on the optimal fusion model and outputs a prediction result.

[0078] Compared with the prior art, the beneficial effects are:

[0079] Based on the CatBoost model and the integrated optimization algorithm, the model prediction precision and generalization ability under complex geological conditions are significantly improved through automatic adjustment and integrated learning mechanism.

[0080] The integrated data processing module, model training module, parameter optimization module, performance evaluation module and output module can automatically complete the whole process modeling and reasoning from data preprocessing to foundation resistance prediction, and the precision, stability and automation level of the foundation resistance prediction are significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0081] Figure 1 It is a super-long pile foundation resistance prediction method flow chart;

[0082] Figure 2 It is a CatBoost model principle diagram;

[0083] Figure 3 It is a hybrid model regression diagram;

[0084] Figure 4 It is a hybrid model running time;

[0085] Figure 5 is the average SHAP value of the input feature;

[0086] Figure 6 is the importance ranking of the input feature. DETAILED DESCRIPTION

[0087] The present application is further explained and illustrated with reference to the following examples, which are not intended to limit the application in any way.

[0088] Example 1

[0089] The embodiment provides a super-long pile foundation resistance prediction model, comprising a data preprocessing module, a CatBoost prediction model module, an optimization algorithm fusion module, a model evaluation module and a prediction output module.

[0090] The data preprocessing module reads and cleans the original pile foundation data, performs normalization processing, and then inputs the data to the CatBoost prediction model module;

[0091] The CatBoost prediction model module uses a CatBoost regression model to model the nonlinear relationship between the pile foundation parameters and the foundation resistance;

[0092] The optimization algorithm fusion module includes genetic algorithm (GA), whale optimization algorithm (WOA), artificial ecosystem optimization algorithm (AEO), biogeography optimization algorithm (BiEO), Harris hawk optimization algorithm (HOA) and adaptive optimization algorithm (SAO), which are used to adjust the parameters of the model established in the CatBoost prediction model module, and form GA-CatBoost, WOA-CatBoost, AEO-CatBoost, BiEO-CatBoost, HOA-CatBoost and SAO-CatBoost hybrid models, respectively;

[0093] The model evaluation module evaluates the six hybrid models in the optimization algorithm fusion module and selects the optimal fusion model based on index feedback;

[0094] The prediction output module inferences the to-be-predicted pile foundation data based on the optimal fusion model and outputs the prediction result.

[0095] Example 2

[0096] The embodiment provides a super-long pile foundation resistance prediction method, comprising the following steps:

[0097] S1. Collecting the loading point load, loading point settlement, distance from the loading point to the pile end, axial stiffness and standard penetration test value of the foundation soil layer as input parameters, and performing denoising and standardization preprocessing on the data.

[0098] S2. Using CatBoost regression model to model the nonlinear relationship between the preprocessed pile foundation parameters and the foundation resistance;

[0099] S21. Ordinal target coding is performed on the category features of the pile foundation data, and the function f(x i ) is obtained by predicting the target value y according to the feature x, and the loss function L(θ) is minimized, which is expressed as:

[0100]

[0101] Where N is the number of samples; y i is the true value of sample i; y(x i ) is the predicted value of the model for sample i;

[0102] S22. In the iteration process, a new tree h t (x) is added to fit the residual each time the model is updated, and a complete binary tree is used for automatic feature combination, which is expressed as:

[0103] f t (x) = f t-1 (x) + ηh t (x)

[0104] Where f t-1 (x) is the model of the first t-1 iterations; h t (x) is the prediction result of the tth tree; η is the learning rate;

[0105] S3. Genetic algorithm, whale optimization algorithm, artificial ecosystem optimization algorithm, biogeography-based optimization algorithm, Harris hawk optimization algorithm and adaptive optimization algorithm are used to automatically search the hyperparameters of the model;

[0106] The genetic algorithm is based on the fitness calculation system, and uses wheel selection and elite reservation strategy to search the global learning_rate hyperparameter, including the following steps: population initialization, fitness function calculation, selection, crossover, mutation and termination condition evaluation. In the genetic algorithm, the most critical formulas are usually the fitness function and the selection probability formula, which directly determine the core logic of the algorithm. For the minimization problem, the fitness can be obtained by the following transformation:

[0107]

[0108] Where g(x) is the original objective function. The selection operation determines the probability of an individual being selected by the fitness value, and the calculation formula is as follows:

[0109]

[0110] where P i represents the probability of the i-th individual being selected; f(x i ) represents the fitness value of the i-th individual; N represents the total number of individuals in the population.

[0111] The whale optimization algorithm adjusts the depth parameter through the spiral bubble net attack mechanism, simulates whale behavior through three strategies: surrounding prey, searching for prey (exploration stage), and spiral bubble net attack (development stage). The algorithm performs global and local search in the solution space through these behaviors, gradually approaching the optimal solution. Combined with the surrounding behavior and the updating method of the spiral trajectory, the position updating formula of the whale optimization algorithm is:

[0112]

[0113] where represents the current position of the individual; represents the current position of the optimal solution; t represents the current iteration number; b is a constant that defines the spiral shape; l is a random number with a value range of [-1, 1]; p is a random number with a value range of [0, 1]. and are calculated by the following equation: where a decreases linearly from 2 to 0, and r is a random number with a value range of [0, 1]. The whale optimization algorithm approaches the prey by adjusting the distance vector When the whale surrounds the prey, the spiral trajectory and the surrounding behavior are alternately performed, and the specific behavior is determined by the probability p

[0114] The artificial ecosystem optimization algorithm simulates the producer-consumer energy flow mechanism and uses the photosynthesis strategy to globally optimize the max-features parameter. In this invention, the complexity of the model is indirectly controlled by adjusting the depth or iterations, including the following steps: individual generation, mutual attraction, and position update. In AEO, each solution is regarded as an individual, and the attraction between individuals determines their interaction. The attraction is usually represented by the following formula:

[0115]

[0116] where F ij represents the attraction between individuals i and j; A is a constant that controls the strength of attraction; r ij represents the distance between individuals i and j; β is a parameter that controls the distance decay, usually positive.

[0117] In addition, the displacement update of each individual is realized through the action of attraction. The displacement update formula of individual i can be represented as:

[0118]

[0119] where x i (t) and x i (t+1) represent the position of individual i in the current and next generation, respectively; v ij is the relative velocity between individual i and individual j; t is the current iteration number.

[0120] The biogeography-based optimization algorithm is based on habitat suitability index, dynamically balances the global exploration and local development of n-estimators parameters through species migration model, and integrates genetic operations such as crossover and mutation in evolutionary algorithms to enhance global search ability and avoid local optimal solution. It not only draws on the habitat suitability and species migration mechanism of BBO, but also optimizes the search process through genetic operation to achieve better results in complex optimization problems. The core steps of the algorithm can be summarized as follows: initialization of population, evaluation of suitability, implementation of migration and genetic operation, and determination of termination condition. Habitat suitability (HSI) reflects the quality of the solution, usually measured by the value of the objective function:

[0121] HSI i = f(x i )

[0122] where HSI i represents the suitability of the i-th habitat; f(x i ) represents the value of the objective function; x i represents the corresponding solution of the i-th habitat. Migration operation simulates the process of species migration between habitats, and its formula is:

[0123]

[0124] where x i represents the solution after migration; x j and x ij represent the corresponding solutions of habitats i and j, respectively; M i represents the migration probability, i.e. the probability of migrating from habitat j to habitat i. In addition, crossover and mutation operations are introduced in genetic operation, and their formulas are as follows:

[0125]

[0126] The Harris hawk optimization algorithm employs a prey escape energy model, combined with a dive attack strategy for multi-stage adaptive adjustment of the subsample parameter, which indirectly manages the training process of the model by adjusting iterations and depth. The algorithm mainly consists of two stages to find the optimal solution: the exploration stage and the development stage. The core idea of HOA is to simulate the hunting behavior of Harris hawks, which employ various strategies to capture prey, including surrounding, chasing, and escape behavior. Each "hawk" in HOA represents a candidate solution. During the search process, the hawk group finds the optimal solution by simulating hunting behavior. In the surrounding stage, if the prey is within the hawk's field of view, the hawk will use surrounding behavior to approach the prey:

[0127]

[0128] where x i represents the position of the i * th hawk, x j represents the position of the optimal solution, and r1 is a random number (usually between 0 and 1). In the escape stage, when the prey is strong, the hawk will choose to escape. The speed and direction of escape depend on the escape strategy of the prey:

[0129]

[0130] where r2 is a random factor used to simulate escape behavior. In the pursuit stage, when the prey escapes, the hawk quickly adjusts its position to follow the prey:

[0131]

[0132] where x j represents the position of another hawk; r3 is a random factor used to represent the strength of the pursuit.

[0133] The adaptive optimization algorithm uses a dynamic mutation rate rule to optimize the iterations parameter in real time, including initializing the population or solution set, evaluating individual fitness, dynamically adjusting algorithm parameters, generating new solutions through mutation, selecting the optimal solution, and stopping iteration according to the predefined termination condition. Fitness is an indicator of the quality of an individual. Assuming the objective function is f(x), the fitness of individual x can be evaluated by the value of the objective function:

[0134] fitness(x) = f(x)

[0135] For each individual x i , when mutation occurs, the mutation amplitude Δx i is adaptive. Mutation rate p mut can be used to control the mutation amplitude. The mutation formula is represented as:

[0136]

[0137] where δ represents the magnitude of mutation; rand is a random number for increasing uncertainty. In some variants, the mutation rate p mut It can be dynamically updated according to the change of fitness in the search process:

[0138] p mut = p mut · (1 - a · fitness (x i ))

[0139] where a is a parameter for controlling the learning speed.

[0140] To reflect the synergy and difference between optimizers, each optimization algorithm selectively optimizes the four core hyperparameters in the CatBoost regression model according to its characteristics: iterations, depth, learning_rate and l2_leaf_reg. Different search ranges of hyperparameters are adopted for different optimizers, and this differentiated customization of search space effectively enhances the overall search ability and robustness of the model. Specifically, the search ranges of hyperparameters for each optimization algorithm are as follows:

[0141] Genetic algorithm: iteration number 100-2000, tree depth 3-15, learning rate 0.01-0.3, regularization term 1-10;

[0142] Whale optimization algorithm: iteration number 1000-2000, tree depth 9-10, learning rate 0.1-0.15, regularization term 1-10;

[0143] Artificial ecosystem optimization algorithm: iteration number 1000-2000, tree depth 1-15, learning rate 0.001-0.3, regularization term 1-10;

[0144] Biogeography-based optimization algorithm: iteration number 100-1000, tree depth 9-10, learning rate 0.01-0.3, regularization term 1-10;

[0145] Harris hawk optimization algorithm: iteration number 1000-2000, tree depth 9-10, learning rate 0.1-0.15, regularization term 1-10;

[0146] Adaptive optimization algorithm: iteration number 100-1000, tree depth 3-15, learning rate 0.01-0.5, regularization term 1-10.

[0147] In addition, the optimal fitness value is recorded in each iteration, and the convergence of the model is visualized and dynamically monitored. By analyzing the fitness convergence trend of different optimizers at each generation, the optimization progress can be tracked in real time, and the evolution process that does not converge can be terminated in advance. For the update rule, a new solution can be selected according to the current fitness, and if the fitness of the new solution is better, the current solution is replaced.

[0148] S4. Calculate the coefficient of determination (R 2 ), root mean square error (RMSE) and mean absolute error (MAE) of each group of GA-CatBoost, WOA-CatBoost, AEO-CatBoost, BiEO-CatBoost, HOA-CatBoost and SAO-CatBoost models, use the evaluation index to evaluate the accuracy and error range of the model, and select the model with the best comprehensive performance as the optimal fusion model.

[0149] S5. Use the optimal fusion model to predict the data with the predicted pile foundation.

[0150] Embodiment 3

[0151] The present embodiment provides an application of a method for predicting the resistance of an ultra-long pile foundation. Based on 86 static load test data from 37 actual projects, a total of 1131 groups of data were used, each group of data containing five input features: applied load, settlement of loading point, distance from loading point to pile toe, axial stiffness, and standard penetration test value (SPT) of foundation soil layer; the prediction target is the base resistance of the pile foundation (Qp). To ensure the scientificity of the experiment, after standard normalization processing of the data set, the data set is divided into training set and test set according to the ratio of 80% and 20%. Part of the data is shown as follows:

[0152]

[0153]

[0154]

[0155] In the model construction stage, first, the CatBoost regression model is initialized, and then, through the fusion optimization module, the key hyperparameters (such as learning rate, maximum tree depth and tree number) of the CatBoost model are optimized in parallel by genetic algorithm (GA), whale optimization algorithm (WOA), artificial ecosystem optimization algorithm (AEO), biogeography optimization algorithm (BiEO), Harris hawk optimization algorithm (HOA) and adaptive optimization algorithm (SAO). Each optimization algorithm is independently run, aiming to obtain the smallest prediction error on the validation set, and the obtained optimal parameters are used to train the complete model.

[0156] After the model training is completed, the six optimized versions of the CatBoost model are evaluated on the test set, and the core indicators such as R 2 , RMSE and MAE are calculated, and the unoptimized original CatBoost model is used as a control, and the results are shown in Table 1:

[0157] Table 1

[0158]

[0159] As shown in Table 1 and Figure 3 , compared with the unoptimized original CatBoost model (R 2 = 0.920, RMSE = 0.0363, MAE = 0.0232), the present application has significantly improved in various indicators, with a prediction error reduction of more than 30%. The models optimized by GA and WOA still maintain an R 2 value of more than 0.96 in the test set, while other optimizers such as AEO, BiEO, SAO, etc. also maintain above 0.94. This indicates that different optimization paths can find good hyperparameter combinations, and the model has good generalization ability. Among them, CatBoost-GA achieves a determination coefficient R 2 of 0.965 on the test set, which is 4.5% higher than the unoptimized CatBoost model (R 2 = 0.920); at the same time, the RMSE is reduced from 0.0363 to 0.0242 (↓33.3%), and the MAE is reduced from 0.0232 to 0.0143 (↓38.4%).

[0160] As Figure 4 shown, the models in the present application using different optimizers have differences in running efficiency, among which CatBoost-GA and CatBoost-SAO models have the shortest running time and are suitable for rapid deployment; even the WOA optimized model with the longest running time has an acceptable calculation amount.

[0161] In terms of model explainability, the SHAP (Shapley Additive Explanations) method is used to analyze the variable importance of the final model, as shown in Figures 5-6 As shown in the figure, the load point settlement is the most critical factor affecting the prediction of base resistance, followed by the applied load and the distance from the load point to the pile end, while the axial stiffness and SPT have relatively small influence but complex nonlinear interaction.

[0162] The mixed CatBoost model system has high precision, high stability and strong generalization ability under complex geological conditions, can effectively replace the traditional empirical method or single machine learning model, and is suitable for rapid evaluation and auxiliary design of bearing capacity of various types of pile foundation engineering such as bridge, high-rise building, port terminal, and has obvious practical application value.

[0163] Obviously, the above embodiments of the present application are only examples for clearly illustrating the present application, and are not intended to limit the embodiments of the present application. For ordinary skilled in the art, other different forms of changes or variations can be made on the basis of the above description. Here, it is not necessary and impossible to enumerate all the embodiments. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the claims of the present application.

Claims

1. A method for predicting the foundation resistance of ultra-long piles, characterized in that the steps include... include: S1. Collect pile foundation data and perform noise reduction and standardization preprocessing on the data; S2. Use the CatBoost regression model to model the nonlinear relationship between the pre-processed pile foundation parameters and the foundation resistance; S21. Perform ordered target encoding on the category features of the pile foundation data, and predict the target value y based on feature x to obtain the function f(x). i The loss function L(θ) is minimized, expressed as: Where N is the number of samples; y i It is the true value of sample i; f(x) i ) is the model's predicted value for sample i; S22. During the iteration process, a new tree h is added each time the model is updated. t (x) is used to fit the residuals, and a complete binary tree is used to automate the feature combination, represented as: f t (x)=f t-1 (x)+ηh t (x) Among them, f t-1 (x) is the model for the first t-1 iterations; h t (x) is the prediction result of the t-th tree; η is the learning rate; S3. Genetic algorithm, whale optimization algorithm, artificial ecosystem optimization algorithm, biogeographical optimization algorithm, Harris Eagle optimization algorithm and adaptive optimization algorithm are used respectively to automatically search for the hyperparameters of the model, such as the number of iterations, tree depth, learning rate and regularization term; S4. Calculate the evaluation index for each model group and select the optimal fusion model; S5. Use the optimal fusion model to predict the pile foundation data.

2. The method for predicting the foundation resistance of ultra-long piles according to claim 1, characterized in that, Pile foundation data includes one or more of the following: load at the loading point, settlement at the loading point, distance from the loading point to the pile tip, axial stiffness, and standard penetration test values ​​of the foundation soil layer.

3. The method for predicting the foundation resistance of ultra-long piles according to claim 1, characterized in that, The genetic algorithm includes population initialization, fitness function calculation, selection, crossover, mutation, and termination condition evaluation, wherein the fitness function calculation is expressed as: Where g(x) is the original objective function; The probability formula for selection is expressed as: Among them, P i f(x) represents the probability that the i-th individual is selected; i ) represents the fitness value of the i-th individual; N represents the total number of individuals in the population.

4. The method for predicting the foundation resistance of ultra-long piles according to claim 1, characterized in that, The whale optimization algorithm includes a prey encirclement phase, a prey search phase, and a spiral bubble net attack phase. Its position update formula is as follows: in Indicates the individual's current location; This indicates the current position of the optimal solution; t represents the current iteration number. b is a constant defining the spiral shape; l is a random number ranging from [-1, 1]; p is a random number ranging from [0, 1]. Where a decreases linearly from 2 to 0, and r is a random number taking values ​​in the range [0,1].

5. The method for predicting the foundation resistance of ultra-long piles according to claim 1, characterized in that, The artificial ecosystem optimization algorithm includes: individual generation, mutual attraction, and location update, wherein the expression for mutual attraction is: Among them, F ij Let r represent the attraction between individuals i and j; A is a constant that controls the strength of the attraction; r ij This represents the distance between individuals i and j; β is a parameter that controls distance decay. The expression for position update is: Where, x i (t) and x i (t+1) represent the positions of individual i in the current generation and the next generation, respectively, and v ij t is the relative velocity between individual i and individual j, and t is the current iteration number.

6. The method for predicting the foundation resistance of ultra-long piles according to claim 1, characterized in that, The biogeographic optimization algorithm includes: initializing the population, assessing suitability, performing migration, genetic operations, and determining termination conditions, where suitability is represented as: HSI i =f(x i ) HSI i f(x) represents the suitability of the i-th habitat; i () represents the value of the objective function; x i Let represent the solution corresponding to the i-th habitat; Migration is represented as: in, Indicates the solution after migration; x i and x j M represents the solutions corresponding to habitats i and j, respectively; ij This represents the migration probability, that is, the probability of migrating from habitat j to habitat i; In genetic operations, the crossover and mutation operations are introduced, represented as follows:

7. The method for predicting the foundation resistance of ultra-long piles according to claim 1, characterized in that, The Harris Eagle optimization algorithm includes encirclement behavior, pursuit behavior, and escape behavior, where the encirclement behavior is represented as: Where, x i Let x represent the position of the i-th eagle. * This indicates the position of the optimal solution; r1 is a random number between 0 and 1. The chasing behavior is represented as: Where x j r1 represents the position of the other eagle; r3 is a random factor used to represent the intensity of the chase.

8. The method for predicting the foundation resistance of ultra-long piles according to claim 1, characterized in that, The adaptive optimization algorithm includes initializing the population or solution set, evaluating individual fitness, dynamically adjusting algorithm parameters, generating new solutions through mutation, selecting the optimal solution, and stopping iteration according to a predefined termination condition, wherein the expression for mutation is: Where, x i For an individual, δ represents the magnitude of the mutation; rand is a random number used to increase uncertainty, p mut It is the mutation rate, the mutation rate p mut Dynamically update based on changes in fitness during the search process, represented as: p mut =p mut ·(1-α·fitness(x i )) Where α is a parameter controlling the learning speed, fitness(x) i Let fitness(x) = f(x), where f(x) is the objective function.

9. The method for predicting the foundation resistance of ultra-long piles according to claim 1, characterized in that, The hyperparameter search ranges for genetic algorithms, whale optimization algorithms, artificial ecosystem optimization algorithms, biogeographical optimization algorithms, Harris Eagle optimization algorithms, and adaptive optimization algorithms are as follows: Genetic algorithm: 100-2000 iterations, tree depth 3-15, learning rate 0.01-0.3, regularization term 1-10; Whale optimization algorithm: 1000-2000 iterations, tree depth 9-10, learning rate 0.1-0.15, regularization term 1-10; Artificial ecosystem optimization algorithm: number of iterations 1000-2000, tree depth 1-15, learning rate 0.001-0.3, regularization term 1-10; Biogeographic optimization algorithm: number of iterations 100-1000, tree depth 9-10, learning rate 0.01-0.3, regularization term 1-10; Harris Eagle Optimization Algorithm: 1000-2000 iterations, tree depth 9-10, learning rate 0.1-0.15, regularization term 1-10; Adaptive optimization algorithm: number of iterations 100-1000, tree depth 3-15, learning rate 0.01-0.5, regularization term 1-10.

10. A prediction model based on the prediction method for ultra-long pile foundation resistance according to any one of claims 1 to 9, characterized in that, It includes a data preprocessing module, a CatBoost prediction model module, an optimization algorithm fusion module, a model evaluation module, and a prediction output module; The data preprocessing module reads and cleans the raw pile foundation data, performs normalization processing, and then inputs the data into the CatBoost prediction model module. The CatBoost prediction model module uses the CatBoost regression model to model the nonlinear relationship between pile foundation parameters and foundation resistance. The optimization algorithm fusion module includes genetic algorithm, whale optimization algorithm, artificial ecosystem optimization algorithm, biogeographical optimization algorithm, Harris eagle optimization algorithm and adaptive optimization algorithm. It adjusts the parameters of the model established in the CatBoost prediction model module to form GA-CatBoost, WOA-CatBoost, AEO-CatBoost, BiEO-CatBoost, HOA-CatBoost and SAO-CatBoost hybrid models respectively. The model evaluation module evaluates the six hybrid models in the optimization algorithm fusion module and selects the optimal fusion model based on the indicator feedback. The prediction output module infers the prediction results based on the optimal fusion model using the pile foundation data to be predicted.

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