Vertical bearing capacity calculation method and system of rigid-flexible combined bag-bottomed pile

Abstract

The present application belongs to the field of building, especially a kind of rigid-flexible combination bagged pile vertical bearing capacity calculation method and system, the method specifically includes: obtaining the initial parameter set that influences pile vertical bearing capacity, including pile geometry, bag performance, soil mechanical parameters, and the one-dimensional control point vector of bottom expansion form extracted based on point cloud data reconstruction by non-uniform rational B spline, divided into side resistance parameter subset and end resistance parameter subset;Using historical sample training set, construct the hybrid kernel matrix of polynomial kernel and radial basis kernel combination for two subsets respectively, and weight according to the sensitivity difference of parameter to resistance;Mean centering and feature decomposition are carried out to the hybrid kernel matrix, and the principal component is selected according to the cumulative variance contribution rate and parameter correlation coefficient absolute value and threshold value rule, and the core factor of side resistance and end resistance is obtained by decoupling;Gaussian process regression model is established respectively with the two core factors, the side friction resistance and end resistance are predicted, and the sum is obtained to obtain the vertical bearing capacity of pile.

Description

Technical Field

[0001] This application belongs to the field of construction, and in particular relates to a method and system for calculating the vertical bearing capacity of a rigid-flexible composite bag-type expanded-base pile. Background Technology

[0002] Rigid-flexible composite bag-type expanded-base piles, as a type of pile foundation, combine the high strength of rigid piles with the expansion characteristics of flexible bags by installing flexible bags at the pile bottom and grouting them in. They are used in soft soil foundation reinforcement and geological engineering. The vertical bearing mechanism of this type of pile is complex. Its bearing capacity depends not only on the conventional geometric parameters of the pile and the mechanical parameters of the surrounding soil, but also on the performance parameters of the flexible bag itself and the expanded-base shape obtained after grouting. There are correlation effects among multiple parameters, and the mechanisms of side friction and end resistance are different. Semi-empirical and semi-theoretical formulas and conventional numerical simulation methods cannot represent the comprehensive influence of multi-dimensional parameters, resulting in large deviations in calculation results, ambiguous mechanism expressions, and poor engineering applicability when calculating the vertical bearing capacity of rigid-flexible composite bag-type expanded-base piles.

[0003] Applying data-driven and artificial intelligence algorithms to predict the bearing capacity of pile foundations has become a research hotspot in the field. For example, Shi Yongqiang et al. disclosed a method for constructing a regression prediction model based on historical sample data in "Optimized Neural Network Model Based on Principal Component Analysis and Prediction of Ultimate Bearing Capacity of Single Static Pressure Pipe Pile" (Journal of Shenyang Jianzhu University (Natural Science Edition)), 2008. This method combines principal component analysis (PCA) parameter dimensionality reduction technology to compress input variables into low-dimensional features before bearing capacity prediction. Su Guoshao et al. proposed mapping nonlinear inputs to a Gaussian process regression (GPR) machine learning model for bearing capacity prediction in "Gaussian Process Model for Predicting Bearing Capacity of CFG Pile Composite Foundation" (Computer Engineering and Applications), 2011. In addition, for irregular geometries formed by grouting and enlargement, Hou Zhenkun et al. proposed using three-dimensional scanning to obtain point cloud data of the grouting body to quantitatively characterize the three-dimensional geometric features of the enlarged base in "Physical Simulation Experiment Study on Bearing Performance of Drilling Pipe Pile Considering Hole Collapse" (Chinese Journal of Geotechnical Engineering), 2021. Although the aforementioned existing technologies have driven the development of prediction methods, firstly, existing dimensionality reduction methods such as principal component analysis cannot effectively decouple the side resistance parameters affecting side friction from the end resistance parameters affecting end resistance from a mechanical mechanism perspective, resulting in a black box state for the model and unclear mechanism expression; secondly, the kernel functions used in existing dimensionality reduction and prediction models cannot represent the complex nonlinear mapping relationship with high-dimensional and strong coupling under the rigid-flexible combination characteristics of the bag, and are prone to losing key information when extracting kernel space features, resulting in limited generalization ability of the overall prediction model and prediction accuracy that cannot meet the engineering application requirements of rigid-flexible combined bag expanded base piles. Summary of the Invention

[0004] To improve the accuracy and overall computational efficiency of calculating the vertical bearing capacity of rigid-flexible composite bag-type expanded-base piles, one or more embodiments of the present invention provide a method for calculating the vertical bearing capacity of rigid-flexible composite bag-type expanded-base piles, the method comprising: An initial parameter set affecting the vertical bearing capacity of the pile is obtained. The initial parameter set includes pile geometric parameters, bag performance parameters, soil mechanical parameters, and enlarged base morphology parameters. The enlarged base morphology parameters are one-dimensional control point vectors extracted based on point cloud data through non-uniform rational B-spline reconstruction. The obtained initial parameter set affecting the vertical bearing capacity of the pile is divided into a subset of side resistance parameters affecting side friction and a subset of end resistance parameters affecting end resistance. A historical sample training set is obtained, and a hybrid kernel matrix representing the correlation is constructed by dividing the side resistance parameter subset that affects side friction and the end resistance parameter subset that affects end resistance. The hybrid kernel matrix is ​​generated by combining a polynomial kernel function and a radial basis kernel function. According to the difference in the sensitivity of each parameter to resistance within the side resistance parameter subset and the end resistance parameter subset, weights are assigned to different parameters at the kernel space input. The two hybrid kernel matrices are subjected to mean centering and eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors. Principal components are selected according to the cumulative variance contribution rate and the absolute value of the correlation coefficient with the parameter and the rule that it exceeds a preset threshold. The side resistance core factor and the end resistance core factor are decoupled and generated. Gaussian process regression prediction models were established using the decoupled side resistance core factors and end resistance core factors as inputs, respectively. The predicted side friction and the predicted end resistance were calculated, and the vertical bearing capacity of the pile was obtained by summing the predicted side friction and the predicted end resistance.

[0005] One or more embodiments of the present invention also provide a vertical bearing capacity calculation system for a rigid-flexible composite bag-type expanded-base pile, the system comprising: The partitioning module is used to obtain the initial parameter set that affects the vertical bearing capacity of the pile. The initial parameter set includes pile geometric parameters, bag performance parameters, soil mechanical parameters, and enlarged base morphology parameters. The enlarged base morphology parameters are one-dimensional control point vectors extracted based on point cloud data through non-uniform rational B-spline reconstruction. The obtained initial parameter set that affects the vertical bearing capacity of the pile is divided into a subset of side resistance parameters that affect side friction and a subset of end resistance parameters that affect end resistance. The generation module is used to acquire historical sample training sets, construct hybrid kernel matrices representing the correlation between the side resistance parameter subsets that affect side friction and the end resistance parameter subsets that affect end resistance. The hybrid kernel matrices are generated by combining polynomial kernel functions and radial basis kernel functions. Based on the difference in the sensitivity of each parameter to resistance within the side resistance parameter subset and the end resistance parameter subset, weights are assigned to different parameters at the kernel space input. The two hybrid kernel matrices are subjected to mean centering and eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors. Principal components are selected according to the cumulative variance contribution rate and the absolute value of the correlation coefficient with the parameter and the rule that it exceeds a preset threshold. The side resistance core factor and the end resistance core factor are decoupled and generated. The calculation module is used to establish a Gaussian process regression prediction model with the decoupled generated side resistance core factor and end resistance core factor as inputs, respectively, to calculate the predicted side friction and the predicted end resistance, and to sum the predicted side friction and the predicted end resistance to obtain the vertical bearing capacity of the pile.

[0006] This invention reconstructs point cloud data of the expanded-base morphology into a one-dimensional control point vector using non-uniform rational B-splines, and divides multi-source parameters into side resistance and end resistance subsets according to their mechanisms. A hybrid kernel matrix combining polynomials and radial basis functions is constructed, and weights are assigned based on parameter sensitivity differences to detect the correlation between parameters. Principal component optimization is performed by combining cumulative variance contribution rate and parameter correlation, achieving dimensionality reduction and decoupling of the data, retaining core meaning while eliminating redundant information. The decoupled side resistance and end resistance core factors are used to drive Gaussian process regression models for prediction and summation, reducing the model input dimension and computational complexity, and improving the accuracy and overall computational efficiency of calculating the vertical bearing capacity of rigid-flexible composite bag-type expanded-base piles. Attached Figure Description

[0007] Figure 1 A flowchart illustrating the calculation method for the vertical bearing capacity of a rigid-flexible composite bag-shaped expanded-base pile; Figure 2 A schematic diagram of the eigenvalue distribution in principal component analysis; Figure 3 This is a diagram illustrating the comparison of predictive performance. Detailed Implementation

[0008] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0009] In this application, a method for calculating the vertical bearing capacity of a rigid-flexible composite bag-type expanded-base pile is provided, such as... Figure 1As shown, it includes: S1. Obtain the initial parameter set that affects the vertical bearing capacity of the pile. The initial parameter set includes pile geometric parameters, bag performance parameters, soil mechanical parameters, and base expansion morphology parameters. The base expansion morphology parameters are one-dimensional control point vectors extracted based on point cloud data through non-uniform rational B-spline reconstruction. Divide the obtained initial parameter set that affects the vertical bearing capacity of the pile into a subset of side resistance parameters that affect side friction and a subset of end resistance parameters that affect end resistance.

[0010] The geometric parameters of the pile, including pile diameter and length, and the performance parameters of the soil bag, including tensile strength and elastic modulus, were obtained through on-site surveys and geotechnical tests. The soil mechanical parameters, including soil cohesion and internal friction angle, were also obtained. The original point cloud data of the enlarged base section was acquired using a 3D laser scanner. The point cloud data was then read, and a statistical filtering algorithm was used to remove outliers and noise.

[0011] A global surface interpolation algorithm is used to reconstruct the denoised point cloud data using non-uniform rational B-splines, generating a three-dimensional continuous surface model. The control point mesh of the surface model is extracted and flattened in a row-first, column-later order to obtain a one-dimensional control point vector as the base morphology parameter. The DataFrame data structure from the Pandas data analysis library is used. Based on the soil mechanics pile foundation bearing capacity mechanism, pile length, bag tensile strength, and soil cohesion are classified as subsets of side resistance parameters affecting side friction, while pile diameter, bag elastic modulus, soil internal friction angle, and base morphology parameters are classified as subsets of end resistance parameters affecting end resistance.

[0012] In some implementations, the expanded base morphological parameters are one-dimensional control point vectors extracted from point cloud data through non-uniform rational B-spline reconstruction, including: The Gaussian filtering algorithm is used to smooth the original point cloud data and filter out noise points; The smoothed point cloud data is divided into a multi-dimensional basic grid set according to the spatial grid distribution; Construct three-dimensional non-uniform rational B-spline basis functions based on a multidimensional fundamental mesh set; The three-dimensional control point matrix of the non-uniform rational B-spline surface is solved by fitting the basis function of the three-dimensional non-uniform rational B-spline with the smoothed point cloud data using the least squares fitting algorithm. The three-dimensional control point matrix is ​​sequentially connected end to end to perform one-dimensional flattening and dimensionality reduction, generating a one-dimensional control point vector, which is then written into the initial parameter set.

[0013] In the extraction and dimensionality reduction of the bottom morphology parameters, a 3D laser scanning device was used to obtain the original point cloud data coordinate set inside the bottom hole of the bag. A Gaussian filter algorithm with a kernel width standard deviation of 2.0 mm was used to perform spatial convolution weighted smoothing on the original point cloud data within a local 3D window with a length, width, and depth of 10 mm.

[0014] After smoothing, the point cloud data is divided into non-overlapping multidimensional basic mesh sets along the depth axis, radial axis, and circumferential axis of the 3D cylindrical coordinate system, according to resolution thresholds of 50mm intervals in the depth direction, 5mm intervals in the radial direction, and 15° intervals in the circumferential direction. Based on the topological nodes of the multidimensional basic mesh sets, a 3D non-uniform rational B-spline basis function with third-order smoothness is constructed by allocating polynomial node vectors at the bottom layer.

[0015] By using the sum of squared Euclidean distances between the point cloud data coordinates and the mathematical parametric equations of the NURBS surface as the minimization objective function, a least-squares fitting algorithm with a Levenberg-Marquardt step size optimization strategy is used to perform regression fitting operations. The process is iterated until the error converges within a tolerance of 0.1 mm, thereby solving for a three-dimensional control point matrix that can represent the contour of the bladder expansion surface. The matrix is ​​pre-defined with 10 sections in the depth direction, 24 azimuth angles in the circumferential direction, and 3 Euclidean coordinate axes.

[0016] Following the column traversal mechanism prioritizing depth sections, the three-dimensional control point matrix is ​​sequentially connected end to end for one-dimensional flattening and dimensionality reduction, generating a one-dimensional control point vector containing 720 single-precision floating-point elements. This one-dimensional control point vector is then written into the memory region of the initial parameter set containing all set parameters via I / O streams, completing the transformation from geometric shape to parameterized features.

[0017] In some implementations, the initial parameter set affecting the vertical bearing capacity of the pile is divided into a subset of side resistance parameters affecting side skin friction and a subset of end resistance parameters affecting end resistance, including: Iterate through and read the text tag identifier code attached to each parameter in the initial parameter set; By comparing the classification table rules in the preset classification database, extract the parameters corresponding to the fields of pile perimeter soil friction angle, pile outer diameter and bag roughness in the text label identification code, and write them into the memory space to generate a subset of side resistance parameters. Extract the text tag identifier code containing parameters corresponding to the bearing layer compression modulus, enlarged head diameter, pile tip soil cohesion, and one-dimensional control point vector fields, and write them into another memory space to generate a subset of end resistance parameters.

[0018] When separating and classifying the initial parameter set at the data layer, the data scheduling module uses an iterator to traverse by index and read the JSON-formatted text tag identifier code attached to each engineering parameter in the initial parameter set.

[0019] Using the KMP string matching algorithm, the tag identifiers read through the process are compared character by character with the regular expression classification rules stored in the local SQLite relational database. Once a side resistance classification rule is matched, the numerical parameters corresponding to the pile perimeter soil friction angle, pile outer diameter, and bag roughness fields in the text tag identifier are extracted. For example, when the pile outer diameter is detected to be 600mm, the pile perimeter soil friction angle is 25°, and the bag surface roughness coefficient is 0.85, the associated numerical values ​​are serialized, packaged, and allocated to the memory space starting at address 0x00A1 to generate a subset of side resistance parameters.

[0020] Simultaneously, a parallel background retrieval and scheduling thread continues to execute the regular expression comparison program to extract text tag identifiers containing end reaction control parameters corresponding to the bearing layer compression modulus, enlarged head diameter, pile tip soil cohesion, and the deep field of the one-dimensional control point vector. For example, the bearing layer compression modulus value of 20 MPa, the effective diameter of the bottom enlarged head of 1200 mm, the undisturbed pile tip soil cohesion of 30 kPa, and the previously calculated one-dimensional control point vector containing 720 coordinate point values ​​are extracted.

[0021] The extracted parameters are packaged and serialized, and then written to another isolated memory space starting at, for example, 0x00B2, via a bus channel to construct a subset of end-resistance parameters, thus achieving decoupled partitioning of the load-bearing capacity-influencing parameter variable pool. This avoids cross-interference and information aliasing caused by different mechanical parameters in a single high-dimensional complex model, thereby reducing the feature dimension and computational complexity of machine learning algorithm mapping.

[0022] S2, Obtain the historical sample training set, and construct a hybrid kernel matrix representing the correlation between the side resistance parameter subset that affects side friction and the end resistance parameter subset that affects end resistance. The hybrid kernel matrix is ​​generated by combining a polynomial kernel function and a radial basis kernel function. According to the difference in the sensitivity of each parameter to resistance within the side resistance parameter subset and the end resistance parameter subset, weights are assigned to different parameters at the kernel space input end. The two hybrid kernel matrices are subjected to mean centering and eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors. Principal components are selected according to the cumulative variance contribution rate and the absolute value of the correlation coefficient with the parameter and the rule that it exceeds a preset threshold. The side resistance core factor and the end resistance core factor are decoupled and generated.

[0023] The Pandas data analysis library is used to read a CSV file containing historical test data as a historical sample training set. A random forest regressor is used to pre-train the side resistance parameter subset and the end resistance parameter subset respectively. The feature_importances_ attribute is extracted to obtain the importance score of each parameter to the resistance. After normalization, it is used as a weight vector and element-wise multiplied with the corresponding parameter subset to achieve weighting.

[0024] The weighted subset of parameters is input into a polynomial kernel function to calculate the polynomial kernel matrix, and then into a radial basis function to calculate the radial basis function kernel matrix. The polynomial kernel matrix and the radial basis function kernel matrix are linearly weighted and summed using mixing coefficients to generate a side-resistance mixed kernel matrix and an end-resistance mixed kernel matrix. The `KernelCenterer` class from the scikit-learn machine learning library is used to center the two mixed kernel matrices. Eigenvalue decomposition is then performed on the centered mixed kernel matrices to obtain the eigenvalues ​​and their corresponding eigenvectors arranged in descending order.

[0025] The variance contribution rate is obtained by calculating the proportion of each eigenvalue to the total sum of eigenvalues. The cumulative variance contribution rate is obtained by summing the eigenvectors one by one. At the same time, the absolute values ​​of the correlation coefficients between each eigenvector and each parameter in the corresponding parameter subset are calculated and summed. Eigenvectors with a cumulative variance contribution rate greater than 85% and a sum of absolute values ​​of correlation coefficients greater than, for example, 0.6 are selected. The selected eigenvectors are multiplied by the original kernel matrix to obtain the side resistance core factor and the end resistance core factor after dimensionality reduction and decoupling.

[0026] In some implementations, the hybrid kernel matrix is ​​generated by combining a polynomial kernel function and a radial basis function, and weights are assigned to different parameters at the kernel space input based on the differences in drag sensitivity of each parameter within the side drag parameter subset and the end drag parameter subset, including: The correlation coefficient between each parameter in the side resistance parameter subset and end resistance parameter subset of the historical sample training set and the corresponding pile side resistance vector and pile end resistance vector were calculated using the Pearson correlation coefficient formula. Divide the absolute value of the correlation coefficient by the sum of the absolute values ​​of the correlation coefficients of all parameters in the corresponding parameter subset to generate and lock the normalized weight value of the absolute value corresponding to each parameter. At the input of the kernel function, each parameter of the side resistance and end resistance is multiplied by the corresponding absolute value normalized weight value to perform feature weighting. Based on the weighted input vector matrix, the global initial kernel matrix of the polynomial kernel function and the local initial kernel matrix of the radial basis kernel function are calculated respectively. Multiply the global initial kernel matrix by the first constant factor, multiply the local initial kernel matrix by the second constant factor, and add the results of the scalar multiplication to construct the basic hybrid kernel matrix, which serves as the side-resistance hybrid kernel matrix and the end-resistance hybrid kernel matrix, respectively.

[0027] When constructing the hybrid kernel matrix for mapping the detection parameters, a batch of historical sample training sets containing, for example, 200 sets of static load test feedback records of physical pile foundations are loaded, and the statistical Pearson correlation coefficient calculation formula is called to calculate the scalar value of the correlation coefficient between each engineering parameter in the side resistance parameter subset and the end resistance parameter subset and the corresponding resistance vector of the measured record, namely the measured resistance vector of the pile side and the measured resistance vector of the pile end.

[0028] The absolute values ​​of all obtained correlation coefficients are extracted and algebraically summed for each corresponding subset to obtain two independent summation constants of absolute values. The absolute value of the correlation coefficient for each parameter is then divided by the summation constant of its subset to generate the normalized weight value for each parameter. For example, the normalized weight coefficient for the bag roughness in the side resistance parameter is calculated to be 0.45, and the normalized weight coefficient for the enlarged head diameter in the end resistance parameter is 0.38. These values ​​distributed in the 0-1 interval are fixed and locked in the environment initialization parameter configuration table of the subsequent kernel function.

[0029] At the input level of the kernel function model, the original parameter matrix columns from the training set are extracted. The Z-score algorithm (mean-variance standardization) is used to perform zero-mean, unit-variance dedimensionalization on each parameter column, eliminating numerical magnitude differences caused by different physical dimensions such as length, pressure, and angle. The dimensionless standard feature vectors generated after dedimensionalization are then multiplied by the corresponding normalized weight values ​​using a term-by-term Hadamard product, thus completing the feature weighting of the kernel space input. Based on this feature-weighted input vector matrix, the model performs independent calculations on the weighted input vector matrices corresponding to the side drag parameters and the end drag parameters. Specifically, the weighted input vector matrices are input into the equations of the polynomial kernel function to generate the global initial kernel matrix, and simultaneously input into the decay equations of the radial basis function to generate the local initial kernel matrix. In pile foundation engineering, side drag refers to the frictional resistance generated between the pile's side surface and the surrounding soil, while end drag refers to the bearing capacity generated between the pile's bottom face and the underlying foundation.

[0030] According to the specified empirical weighting ratio, all elements within the global initial kernel matrix are multiplied by a first constant factor, for example, 0.4, and all elements within the local initial kernel matrix are multiplied by a second constant factor, for example, 0.6. Then, the corresponding elements of the two scaled same-dimensional symmetric matrices are algebraically added together, thereby independently outputting two basic hybrid kernel matrices that possess both global generalization ability and local mapping accuracy. These are then injected into the next dimensionality reduction operation as the side-resistance hybrid kernel matrix and the end-resistance hybrid kernel matrix, respectively.

[0031] In some implementations, the process of performing mean centering and eigenvalue decomposition on the two generated hybrid kernel matrices to obtain eigenvalues ​​and eigenvectors includes: The two mixed kernel matrices are then subjected to mean-centered subtraction operations sequentially using a global constant-centered matrix to generate the corresponding centered kernel matrices. The Jacobi diagonalization iterative method is applied to perform multiple rotational orthogonal transformations on two centered kernel matrices, gradually eliminating the values ​​of off-diagonal elements in the matrices until the error converges to near zero. A set of orthogonal transformation characteristic matrices that can completely diagonalize the matrices are then calculated. Extract all the values ​​distributed along the main diagonal of the diagonal matrix generated after the orthogonal transformation, and set them as the main feature values ​​required for dimensionality reduction; Each column vector of the orthogonal transformation feature matrix is ​​extracted column by column and used as the spatial feature vector of each corresponding principal eigenvalue mapping.

[0032] When performing feature space projection transformation and decomposition on the hybrid kernel matrix, an N×N dimensional centering operator matrix is ​​constructed based on the sample size. This operator is generated by subtracting a matrix with all values ​​of 1 / N from the identity matrix. This centering operator matrix is ​​then multiplied sequentially by the side resistance and end resistance hybrid kernel matrices, and matrix operations are used to perform mean-centered subtraction, thereby projecting and transforming it to generate a centralized kernel matrix with a row and column mean of zero.

[0033] After obtaining the symmetric positive semi-definite centralized kernel matrix, the underlying algorithm uses the Jacobi iteration method to continuously search for and locate the off-diagonal element with the largest absolute value in both kernel matrices. Based on the row and column coordinates of this element, the rotation angle is calculated, and a Givens rotation orthogonal transformation is applied to the kernel matrix. Each rotation sets the currently selected off-diagonal element with the largest absolute value to zero, making the sum of the squares of all off-diagonal elements monotonically decrease. This process is repeated until the absolute values ​​of all off-diagonal elements in the matrix are less than a preset convergence threshold, such as 0.001.

[0034] After the iteration, the orthogonal transformation feature matrices are multiplied by all the orthogonal rotation matrices to calculate a set of orthogonal transformation feature matrices that can diagonalize the centered kernel matrix. At this point, the system module extracts all the diagonal constant values ​​distributed along the main diagonal from the generated diagonal matrix according to the coordinates, and packages them as the main feature value sequence required for the dimensionality reduction strategy.

[0035] Each N-dimensional column vector inside the orthogonal transformation feature matrix is ​​extracted column by column along the memory slice direction. The column vector is associated with its diagonal elements one by one, and used as the projection space feature vector of the dimension where each corresponding main feature value is located.

[0036] In some implementations, the step of selecting principal components based on the cumulative variance contribution rate and the absolute value of the correlation coefficient with the parameters exceeding a preset threshold, and decoupling the generation of side-resistance core factors and end-resistance core factors, includes: The obtained principal feature values ​​are rearranged according to the descending order and all spatial feature vectors of the accompanying mapping are simultaneously mobilized to complete the equi-order position migration and adjustment. The contribution rate of the step-by-step variance of the single-dimensional feature is obtained by dividing the individual rearranged principal feature value by the sum of all principal feature values. The sum is performed successively along the descending position and truncated at the limit of 85% of the preset accumulation constant. The package includes all the associated spatial feature vectors extracted from the previous position as the initial decoupled principal component basis. Extract the remaining feature vectors that fall outside the boundary truncation segmentation, and perform matrix multiplication between the corresponding centered kernel matrix and the remaining feature vectors to calculate and generate the remaining principal component score vectors; Calculate the Pearson correlation coefficient between each remaining principal component score vector and the feature columns corresponding to each parameter in the corresponding parameter subset. For a one-dimensional control point vector containing multiple elements in the end-resistance parameter subset, calculate the Pearson correlation coefficient between the multiple feature columns formed by expanding the vector in the historical sample training set and the remaining principal component score vector, and take the arithmetic mean as the comprehensive Pearson correlation coefficient of the one-dimensional control point vector. The absolute values ​​of the real numbers of the Pearson correlation coefficients of each parameter are summed. The sum of the absolute values ​​of the real numbers is compared with a rigid fixed threshold parameter. When the comparison and judgment requirements are met, the feature vectors corresponding to the remaining principal components are extracted as the additional feature principal components that need to be retained and filled. The extracted additional feature principal components are combined and appended to the end of the initial decoupled principal component base and then spliced ​​column by column.

[0037] In the principal component truncation and feature supplementation selection mechanism, the controller prioritizes calling the quicksort function to rearrange all obtained principal feature values ​​in descending order according to their scalar values. Simultaneously, based on the memory index addresses after feature value swapping, the underlying controller uses pointers to synchronously move the spatial feature vectors associated with the mapping, ensuring that each column vector in the feature matrix follows its eigenvalues ​​to complete the equivalent position translation and reload migration adjustment.

[0038] The calculator takes the rearranged main feature values ​​as numerators and divides them by the sum of all main feature values ​​as denominators to obtain the single-dimensional feature step-by-step variance contribution rate, which represents the information density of that dimension. The contribution rate percentages of each dimension are then successively added together from left to right in descending order of index. When the total accumulated value reaches or exceeds 85% of the preset accumulation constant, an interrupt command is triggered to perform a truncation and segmentation operation at that point.

[0039] The tensor set, constructed from the K most relevant spatial feature vectors extracted from the position and all preceding positions, is packaged and solidified as the initial decoupled principal component basis of the dimensionality-reduced system. Low-contribution residual feature vectors falling outside the 85% threshold truncation are extracted. The corresponding centered kernel matrix generated in the previous steps is multiplied by each extracted residual feature vector, and the exact residual principal component score vector is calculated through projection mapping. The Pearson correlation coefficient between each residual principal component score vector and the original scalar physical parameter data series in the corresponding initial end / side drag parameter subset is then calculated. Specifically, when processing the end-impedance parameter subset consisting of multiple samples of N×M, such as the aforementioned N×720 matrix dimension one-dimensional control point vector parameter, the slice is traversed along the column direction of the matrix, and the Pearson correlation coefficient between the N×1 residual principal component score vector and each N×1 data column cut from the slice is calculated one by one. The absolute values ​​of these M correlation coefficients are extracted and the arithmetic mean is calculated. This mean is used as the comprehensive correlation coefficient between the one-dimensional control point vector as a whole and the current principal component.

[0040] For a specific residual principal component, the absolute values ​​of its Pearson correlation coefficients (obtained from all parameters, including independent correlation coefficients of scalar parameters and comprehensive correlation coefficients of high-dimensional morphological parameters) are calculated and summed. This sum is then pushed to a configured logical threshold comparator to compare whether it is greater than a preset constant threshold parameter of 0.4. If the comparison criteria are met, the comparator raises a valid flag signal and extracts the low-variance eigenvectors associated with that specific residual principal component as additional feature principal components with latent properties that need to be retained.

[0041] After the decision loop ends, all additional principal components that meet the extraction criteria are appended to the end of the previously packaged initial decoupled principal component base using column expansion instructions. A low-dimensional parametric feature matrix is ​​reconstructed by column-wise concatenation, and the required side-resistance core factor and end-resistance core factor data arrays are decoupled and output. The eigenvalue distribution of principal component analysis is as follows: Figure 2 As shown, the cumulative variance contribution rate of the first 5 principal components has exceeded 85%, and the additional feature principal components supplemented by the correlation coefficient threshold can retain the engineering mechanics information contained in the low variance dimension.

[0042] S3. Using the decoupled core factors of side resistance and end resistance as inputs, a Gaussian process regression prediction model is established to calculate the predicted side friction and the predicted end resistance. The predicted side friction and the predicted end resistance are then summed to obtain the vertical bearing capacity of the pile.

[0043] The GaussianProcessRegressor class is used to instantiate two prediction models for predicting side friction and end resistance, respectively. During instantiation, the kernels module is used to define a composite covariance function consisting of the product of a constant kernel function and a Matrn kernel function, and the optimization algorithm is set to the L-BFGS-B quasi-Newton method to maximize the logarithmic marginal likelihood estimate to optimize the hyperparameters.

[0044] The decoupled lateral resistance core factor is used as input features, and historical lateral skin friction is used as labels, to be fed into the first Gaussian process regression prediction model for fitting and training. Similarly, the decoupled end resistance core factor is used as input features, and historical end resistance is used as labels, to be fed into the second Gaussian process regression prediction model for fitting and training. The lateral resistance core factor and end resistance core factor of the pile to be tested are input respectively, and the predicted lateral skin friction value and predicted end resistance value are calculated and output. The predicted lateral skin friction value and predicted end resistance value are added together to obtain and output the vertical bearing capacity of the pile.

[0045] In some implementations, the step of establishing a Gaussian process regression prediction model using the decoupled side resistance core factor and end resistance core factor as inputs includes: The fixed prior expectation baseline mean function of the initial model for calculating pile side resistance and pile end resistance under specified operating conditions is set as a digital zero vector form, and the expression function with squared exponential internal decay characteristics is assigned as the baseline covariance kernel function. Import the decoupled side resistance core factor and end resistance core factor as the bottom training input sample, and independently match and map the historical actual side friction test record data and the historical actual end resistance test record data as the top training verification true result feedback target of their respective models. By calling the L-BFGS step size to find the optimization operator, the maximum likelihood maximization solution gradient climbing action is continuously carried out on the formula of the target logarithmic marginal probability density corresponding to the set of all training points of the basic model. The length scale parameter and signal variance value in the hyperplane variable of the parameter space that can limit the probability density are deduced and extracted. Replace all intrinsic parameters of the preceding baseline kernel function with the constants of the two spatial hyperplanes that have been solved and anchored, construct a prediction mapping relationship based on the inversion of the kernel matrix, and declare the end of the single model encapsulation and establishment.

[0046] In some implementations, before calculating the predicted resistance value by inputting the side resistance core factor and end resistance core factor of the pile to be tested, the method further includes a step of feature projection mapping of the initial parameters of the pile to be tested, including: Obtain the original subset of side resistance parameters and subset of end resistance parameters of the pile to be tested; The mean, variance, and absolute value normalized weights of the historical sample training set are called, and the original parameter subset of the pile body to be tested is sequentially subjected to dimensionless processing and feature weighting. Calculate the mixed test kernel vector between the weighted subset of parameters of the pile body to be tested and the weighted data of the historical sample training set, and call the centering parameter of the training set to center and correct the mixed test kernel vector to be tested; The centered and corrected hybrid test kernel vector to be tested is multiplied by the decoupled and retained feature projection matrix composed of principal component eigenvectors to generate the side resistance core factor and end resistance core factor of the pile body to be tested.

[0047] When performing unknown pile bearing capacity prediction, the front end first acquires the independent parameters of the pile and automatically splits them into a subset of original side resistance parameters and a subset of original end resistance parameters. The preprocessing module calls the dictionary of mean and standard deviation constants of each parameter stored in local memory during the training phase, performs a strict identically distributed Z-score standardization and dimensionless transformation on the parameters to be tested, and extracts the previously locked absolute value normalized weight values ​​and performs term-by-term Hadamard product with the dimensionless parameters to be tested to complete the feature weighting at the test end.

[0048] After input weighting, the kernel mapping engine calculates the spatial distance and inner product between the weighted sample vector to be tested and the weighted sample matrix of the entire training set. These are substituted into the polynomial and radial basis function, respectively, and then combined and added according to the aforementioned empirical ratio (0.4 and 0.6) to construct a 1×N dimension basic mixed test kernel vector, where N is the number of training samples. To ensure the consistency of the translation of the feature kernel space, the row mean vector of the kernel matrix generated during the centering process of the training set and the global mean scalar are further used as centering parameters. The mixed test kernel vector is then subjected to mean-removing centering correction subtraction to generate a centered test kernel vector.

[0049] The spatial feature projection matrix, constructed by concatenating the initial decoupled principal components and additional feature principal components in the preceding steps, is extracted. This matrix represents the selected set of principal component feature vectors. The centered and corrected test kernel vector is then projected onto this feature projection matrix using linear algebraic dot multiplication. Through this mapping projection, the high-dimensional nonlinear features are effectively folded into a low-dimensional sensitive space. The decoupled output contains arrays of the side resistance core factors and end resistance core factors of the test pile, which are in the same distribution basis dimension as the training set.

[0050] During the stage of building the bearing capacity prediction model, for the decoupled friction resistance solution channel, the modeler allocates memory to instantiate a running Gaussian process regression algorithm model. Through the parameter initialization interface, the prior expected baseline mean function of this initial regression model is specified to be a zero vector distribution.

[0051] Simultaneously, a mathematical expression function with squared exponential decay characteristics is assigned to the model as its underlying baseline covariance kernel function, in which the unknown length scaling parameter is retained. and signal fluctuation variance parameter The model imports a low-dimensional side-resistance core factor matrix or end-resistance core factor array generated by the dimensionality reduction and column-by-column concatenation operation in the previous step at the input port, and deploys it as the coordinates of the feature nodes in the underlying training input sample space for the internal conditional distribution calculation of the model.

[0052] In addition, through the mapping relationship reading module, the aforementioned 200 sets of historical actual side friction test records and historical actual end resistance test records discrete data sequences are matched from the loaded test database and independently mapped to the corresponding input coordinates of the side resistance prediction model and the end resistance prediction model, respectively. This serves as the training and verification of the true results of the continuous feedback numerical target variable at the top of the GPR probability surface.

[0053] After entering the parameter optimization phase, the model calculation module calls the L-BFGS step-size optimization operator program to focus on performing mathematical analysis on the target logarithmic marginal probability density formula set for the entire set of training data points that encompass all the aforementioned factors and measured response results in the basic model. Under this boundary constraint, the operator continuously performs the maximization of partial derivatives of the objective function and multi-dimensional gradient detection within the set learning rate tolerance.

[0054] After multiple optimization iterations, the algorithm model converges and deduces from its gradient space, extracting the parameter combination of the hyperplane variables that causes the joint probability density of the current data samples to reach the limit state. For example, it extracts and calculates the length scale parameter of 1.25 to approximate the local smoothness property, and the signal variance value of 15.6 to fit the confidence interval of the residual noise.

[0055] The modeling engine invokes the overwrite instruction, replacing all unknown, undetermined intrinsic parameter placeholders within the preceding baseline kernel function with two already solved fixed constant values, thus solidifying the covariance benchmark mapping calculation logic. At this point, the background compiler, utilizing matrix multiplication and its internal core matrix inversion operator based on the Cholesky decomposition inversion theorem, constructs the mathematical mapping constraint relationship for the multivariate posterior prediction probability density when any unknown new sample is inserted. Thus, the dual-channel Gaussian process regression prediction analysis model module for side friction and end resistance is encapsulated, compiled, and established.

[0056] The experimental conditions involved collecting 300 sets of complete solid pile foundation static load test and drilling feedback data from a typical engineering site as the total sample set, which was then randomly divided into training and test sets at a ratio of 70% and 30%. The convergence tolerance for iterative optimization operators was set to 10. -5The experiment included a baseline group using traditional single radial basis kernel function and conventional variance-trunculated principal component analysis; an ablation group 1 using only correlation coefficients to supplement additional feature principal components without using a mixed kernel matrix; an ablation group 2 using only a mixed kernel matrix without feature supplementation; and a complete scheme group using an absolute value normalized weighted mixed kernel matrix combined with a feature supplementation mechanism and Gaussian process regression. The predictive performance comparison results of the different schemes are shown below. Figure 3 As shown, the prediction error of the complete protocol group was lower than that of the baseline group and the two ablation groups.

[0057] In the test set verification phase of the total bearing capacity at the pile tip and pile side, the evaluation data showed the gradual change in model accuracy. The baseline group measured a root mean square error (RMSE) of 25.6 kN, a mean absolute error (MAO) of 19.2 kN, and a coefficient of determination (COP) of 0.81. Ablation group one reduced the RMSE to 19.4 kN and increased the COP to 0.88. Ablation group two measured an RMSE of 18.7 kN and achieved a COP of 0.89. The complete scheme group showed the best prediction performance, with its test set RMSE reduced to 12.3 kN, MAO decreased to 9.6 kN, and the COP reached 0.95, indicating that the data results tended to stabilize and converge.

[0058] The complete solution group achieved a root mean square error reduction of over 51% compared to the baseline group. This was achieved by utilizing a hybrid kernel matrix of polynomials and radial basis functions with constant factors of 0.4 and 0.6, which simultaneously ensures both global generalization ability and local feature approximation accuracy in high-dimensional kernel space, surpassing the expression boundary of a single kernel function. Furthermore, by incorporating an additional feature extraction mechanism based on the rule that the absolute value of the Pearson correlation coefficient is greater than 0.4, hidden principal components containing real engineering mechanical fluctuations but falling outside the conventional 85% truncation variance limit were detected. This prevented signal loss during the dimensionality reduction stage, ensuring that the Gaussian process regression model could output reliable load-bearing capacity prediction results.

[0059] In this application, a vertical bearing capacity calculation system for a rigid-flexible composite bag-type expanded-base pile includes: The partitioning module is used to obtain the initial parameter set that affects the vertical bearing capacity of the pile. The initial parameter set includes pile geometric parameters, bag performance parameters, soil mechanical parameters, and enlarged base morphology parameters. The enlarged base morphology parameters are one-dimensional control point vectors extracted based on point cloud data through non-uniform rational B-spline reconstruction. The obtained initial parameter set that affects the vertical bearing capacity of the pile is divided into a subset of side resistance parameters that affect side friction and a subset of end resistance parameters that affect end resistance. The generation module is used to acquire historical sample training sets, construct hybrid kernel matrices representing the correlation between the side resistance parameter subsets that affect side friction and the end resistance parameter subsets that affect end resistance. The hybrid kernel matrices are generated by combining polynomial kernel functions and radial basis kernel functions. Based on the difference in the sensitivity of each parameter to resistance within the side resistance parameter subset and the end resistance parameter subset, weights are assigned to different parameters at the kernel space input. The two hybrid kernel matrices are subjected to mean centering and eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors. Principal components are selected according to the cumulative variance contribution rate and the absolute value of the correlation coefficient with the parameter and the rule that it exceeds a preset threshold. The side resistance core factor and the end resistance core factor are decoupled and generated. The calculation module is used to establish a Gaussian process regression prediction model with the decoupled generated side resistance core factor and end resistance core factor as inputs, respectively, to calculate the predicted side friction and the predicted end resistance, and to sum the predicted side friction and the predicted end resistance to obtain the vertical bearing capacity of the pile.

[0060] In some implementations, the expanded base morphological parameters are one-dimensional control point vectors extracted from point cloud data through non-uniform rational B-spline reconstruction, including: The Gaussian filtering algorithm is used to smooth the original point cloud data and filter out noise points; The smoothed point cloud data is divided into a multi-dimensional basic grid set according to the spatial grid distribution; Construct three-dimensional non-uniform rational B-spline basis functions based on a multidimensional fundamental mesh set; The three-dimensional control point matrix of the non-uniform rational B-spline surface is solved by fitting the basis function of the three-dimensional non-uniform rational B-spline with the smoothed point cloud data using the least squares fitting algorithm. The three-dimensional control point matrix is ​​sequentially connected end to end to perform one-dimensional flattening and dimensionality reduction, generating a one-dimensional control point vector, which is then written into the initial parameter set.

[0061] In some implementations, the initial parameter set affecting the vertical bearing capacity of the pile is divided into a subset of side resistance parameters affecting side skin friction and a subset of end resistance parameters affecting end resistance, including: Iterate through and read the text tag identifier code attached to each parameter in the initial parameter set; By comparing the classification table rules in the preset classification database, extract the parameters corresponding to the fields of pile perimeter soil friction angle, pile outer diameter and bag roughness in the text label identification code, and write them into the memory space to generate a subset of side resistance parameters. Extract the text tag identifier code containing parameters corresponding to the bearing layer compression modulus, enlarged head diameter, pile tip soil cohesion, and one-dimensional control point vector fields, and write them into another memory space to generate a subset of end resistance parameters.

[0062] In some implementations, the hybrid kernel matrix is ​​generated by combining a polynomial kernel function and a radial basis function, and weights are assigned to different parameters at the kernel space input based on the differences in drag sensitivity of each parameter within the side drag parameter subset and the end drag parameter subset, including: The correlation coefficient between each parameter in the side resistance parameter subset and end resistance parameter subset of the historical sample training set and the corresponding pile side resistance vector and pile end resistance vector were calculated using the Pearson correlation coefficient formula. Divide the absolute value of the correlation coefficient by the sum of the absolute values ​​of the correlation coefficients of all parameters in the corresponding parameter subset to generate and lock the normalized weight value of the absolute value corresponding to each parameter. At the input of the kernel function, each parameter of the side resistance and end resistance is multiplied by the corresponding absolute value normalized weight value to perform feature weighting. Based on the weighted input vector matrix, the global initial kernel matrix of the polynomial kernel function and the local initial kernel matrix of the radial basis kernel function are calculated respectively. Multiply the global initial kernel matrix by the first constant factor, multiply the local initial kernel matrix by the second constant factor, and add the results of the scalar multiplication to construct the basic hybrid kernel matrix, which serves as the side-resistance hybrid kernel matrix and the end-resistance hybrid kernel matrix, respectively.

[0063] In some implementations, the process of performing mean centering and eigenvalue decomposition on the two generated hybrid kernel matrices to obtain eigenvalues ​​and eigenvectors includes: The two mixed kernel matrices are then subjected to mean-centered subtraction operations sequentially using a global constant-centered matrix to generate the corresponding centered kernel matrices. The Jacobi diagonalization iterative method is applied to perform multiple rotational orthogonal transformations on two centered kernel matrices, gradually eliminating the values ​​of off-diagonal elements in the matrices until the error converges to near zero. A set of orthogonal transformation characteristic matrices that can completely diagonalize the matrices are then calculated. Extract all the values ​​distributed along the main diagonal of the diagonal matrix generated after the orthogonal transformation, and set them as the main feature values ​​required for dimensionality reduction; Each column vector of the orthogonal transformation feature matrix is ​​extracted column by column and used as the spatial feature vector of each corresponding principal eigenvalue mapping.

[0064] In some implementations, the step of selecting principal components based on the cumulative variance contribution rate and the absolute value of the correlation coefficient with the parameters exceeding a preset threshold, and decoupling the generation of side-resistance core factors and end-resistance core factors, includes: The obtained principal feature values ​​are rearranged according to the descending order and all spatial feature vectors of the accompanying mapping are simultaneously mobilized to complete the equi-order position migration and adjustment. The contribution rate of the step-by-step variance of the single-dimensional feature is obtained by dividing the individual rearranged principal feature value by the sum of all principal feature values. The sum is performed successively along the descending position and truncated at the limit of 85% of the preset accumulation constant. The package includes all the associated spatial feature vectors extracted from the previous position as the initial decoupled principal component basis. Extract the remaining feature vectors that fall outside the boundary truncation segmentation, and perform matrix multiplication between the corresponding centered kernel matrix and the remaining feature vectors to calculate and generate the remaining principal component score vectors; Calculate the Pearson correlation coefficient between each remaining principal component score vector and the feature columns corresponding to each parameter in the corresponding parameter subset. For a one-dimensional control point vector containing multiple elements in the end-resistance parameter subset, calculate the Pearson correlation coefficient between the multiple feature columns formed by expanding the vector in the historical sample training set and the remaining principal component score vector, and take the arithmetic mean as the comprehensive Pearson correlation coefficient of the one-dimensional control point vector. The absolute values ​​of the real numbers of the Pearson correlation coefficients of each parameter are summed. The sum of the absolute values ​​of the real numbers is compared with a rigid fixed threshold parameter. When the comparison and judgment requirements are met, the feature vectors corresponding to the remaining principal components are extracted as the additional feature principal components that need to be retained and filled. The extracted additional feature principal components are combined and appended to the end of the initial decoupled principal component base and then spliced ​​column by column.

[0065] In some implementations, the step of establishing a Gaussian process regression prediction model using the decoupled side resistance core factor and end resistance core factor as inputs includes: The fixed prior expectation baseline mean function of the initial model for calculating pile side resistance and pile end resistance under specified operating conditions is set as a digital zero vector form, and the expression function with squared exponential internal decay characteristics is assigned as the baseline covariance kernel function. Import the decoupled side resistance core factor and end resistance core factor as the bottom training input sample, and independently match and map the historical actual side friction test record data and the historical actual end resistance test record data as the top training verification true result feedback target of their respective models. By calling the L-BFGS step size to find the optimization operator, the maximum likelihood maximization solution gradient climbing action is continuously carried out on the formula of the target logarithmic marginal probability density corresponding to the set of all training points of the basic model. The length scale parameter and signal variance value in the hyperplane variable of the parameter space that can limit the probability density are deduced and extracted. Replace all intrinsic parameters of the preceding baseline kernel function with the constants of the two spatial hyperplanes that have been solved and anchored, construct a prediction mapping relationship based on the inversion of the kernel matrix, and declare the end of the single model encapsulation and establishment.

[0066] In this specification, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise limited, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. In this document, "a," "an," "the," "the," and "its" may also include plural forms unless the context clearly indicates otherwise. "Multiple" refers to at least two, such as 2, 3, 5, or 8, etc. "And / or" includes any and all combinations of the associated listed items.

[0067] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The various embodiments can be combined as needed, and the same or similar parts can be referred to each other.

[0068] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the vertical bearing capacity of a rigid-flexible composite bag-shaped expanded-base pile, characterized in that, Includes the following steps: An initial parameter set affecting the vertical bearing capacity of the pile is obtained. The initial parameter set includes pile geometric parameters, bag performance parameters, soil mechanical parameters, and enlarged base morphology parameters. The enlarged base morphology parameters are one-dimensional control point vectors extracted based on point cloud data through non-uniform rational B-spline reconstruction. The obtained initial parameter set affecting the vertical bearing capacity of the pile is divided into a subset of side resistance parameters affecting side friction and a subset of end resistance parameters affecting end resistance. A historical sample training set is obtained, and a hybrid kernel matrix representing the correlation is constructed by dividing the side resistance parameter subset that affects side friction and the end resistance parameter subset that affects end resistance. The hybrid kernel matrix is ​​generated by combining a polynomial kernel function and a radial basis kernel function. According to the difference in the sensitivity of each parameter to resistance within the side resistance parameter subset and the end resistance parameter subset, weights are assigned to different parameters at the kernel space input. The two hybrid kernel matrices are subjected to mean centering and eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors. Principal components are selected according to the cumulative variance contribution rate and the absolute value of the correlation coefficient with the parameter and the rule that it exceeds a preset threshold. The side resistance core factor and the end resistance core factor are decoupled and generated. Gaussian process regression prediction models were established using the decoupled side resistance core factors and end resistance core factors as inputs, respectively. The predicted side friction and the predicted end resistance were calculated, and the vertical bearing capacity of the pile was obtained by summing the predicted side friction and the predicted end resistance.

2. The method according to claim 1, characterized in that, The expanded base morphology parameters are one-dimensional control point vectors extracted from point cloud data through non-uniform rational B-spline reconstruction, including: The Gaussian filtering algorithm is used to smooth the original point cloud data and filter out noise points; The smoothed point cloud data is divided into a multi-dimensional basic grid set according to the spatial grid distribution; Construct three-dimensional non-uniform rational B-spline basis functions based on a multidimensional fundamental mesh set; The three-dimensional control point matrix of the non-uniform rational B-spline surface is solved by fitting the basis function of the three-dimensional non-uniform rational B-spline with the smoothed point cloud data using the least squares fitting algorithm. The three-dimensional control point matrix is ​​sequentially connected end to end to perform one-dimensional flattening and dimensionality reduction, generating a one-dimensional control point vector, which is then written into the initial parameter set.

3. The method according to claim 1, characterized in that, The initial parameter set affecting the vertical bearing capacity of the pile is divided into a subset of side resistance parameters affecting side skin friction and a subset of end resistance parameters affecting end resistance, including: Iterate through and read the text tag identifier code attached to each parameter in the initial parameter set; By comparing the classification table rules in the preset classification database, extract the parameters corresponding to the fields of pile perimeter soil friction angle, pile outer diameter and bag roughness in the text label identification code, and write them into the memory space to generate a subset of side resistance parameters. Extract the text tag identifier code containing parameters corresponding to the bearing layer compression modulus, enlarged head diameter, pile tip soil cohesion, and one-dimensional control point vector fields, and write them into another memory space to generate a subset of end resistance parameters.

4. The method according to claim 1, characterized in that, The hybrid kernel matrix is ​​generated by combining a polynomial kernel function and a radial basis function. Based on the differences in drag sensitivity of each parameter within the side drag parameter subset and the end drag parameter subset, weights are assigned to different parameters at the kernel space input, including: The correlation coefficient between each parameter in the side resistance parameter subset and end resistance parameter subset of the historical sample training set and the corresponding pile side resistance vector and pile end resistance vector were calculated using the Pearson correlation coefficient formula. Divide the absolute value of the correlation coefficient by the sum of the absolute values ​​of the correlation coefficients of all parameters in the corresponding parameter subset to generate and lock the normalized weight value of the absolute value corresponding to each parameter. At the input of the kernel function, each parameter of the side resistance and end resistance is multiplied by the corresponding absolute value normalized weight value to perform feature weighting. Based on the weighted input vector matrix, the global initial kernel matrix of the polynomial kernel function and the local initial kernel matrix of the radial basis kernel function are calculated respectively. Multiply the global initial kernel matrix by the first constant factor, multiply the local initial kernel matrix by the second constant factor, and add the results of the scalar multiplication to construct the basic hybrid kernel matrix, which serves as the side-resistance hybrid kernel matrix and the end-resistance hybrid kernel matrix, respectively.

5. The method according to claim 1, characterized in that, The process of performing mean centering and eigenvalue decomposition on the two generated hybrid kernel matrices to obtain eigenvalues ​​and eigenvectors includes: The two mixed kernel matrices are then subjected to mean-centered subtraction operations sequentially using a global constant-centered matrix to generate the corresponding centered kernel matrices. The Jacobi diagonalization iterative method is applied to perform multiple rotational orthogonal transformations on two centered kernel matrices, gradually eliminating the values ​​of off-diagonal elements in the matrices until the error converges to near zero. A set of orthogonal transformation characteristic matrices that can completely diagonalize the matrices are then calculated. Extract all the values ​​distributed along the main diagonal of the diagonal matrix generated after the orthogonal transformation, and set them as the main feature values ​​required for dimensionality reduction; Each column vector of the orthogonal transformation feature matrix is ​​extracted column by column and used as the spatial feature vector of each corresponding principal eigenvalue mapping.

6. The method according to claim 1, characterized in that, The step of selecting principal components based on the cumulative variance contribution rate and the absolute value of the correlation coefficient with the parameters, and exceeding a preset threshold, and decoupling to generate side-resistance core factors and end-resistance core factors, includes: The obtained principal feature values ​​are rearranged according to the descending order and all spatial feature vectors of the accompanying mapping are simultaneously mobilized to complete the equi-order position migration and adjustment; The contribution rate of the step-by-step variance of the single-dimensional feature is obtained by dividing the individual rearranged principal feature value by the sum of all principal feature values. The sum is performed successively along the descending position and truncated at the limit of 85% of the preset accumulation constant. The package includes all the associated spatial feature vectors extracted from the previous position as the initial decoupled principal component basis. Extract the remaining feature vectors that fall outside the boundary truncation segmentation, and perform matrix multiplication between the corresponding centered kernel matrix and the remaining feature vectors to calculate and generate the remaining principal component score vectors; Calculate the Pearson correlation coefficient between each remaining principal component score vector and the feature columns corresponding to each parameter in the corresponding parameter subset. For a one-dimensional control point vector containing multiple elements in the end-resistance parameter subset, calculate the Pearson correlation coefficient between the multiple feature columns formed by expanding the vector in the historical sample training set and the remaining principal component score vector, and take the arithmetic mean as the comprehensive Pearson correlation coefficient of the one-dimensional control point vector. The absolute values ​​of the real numbers of the Pearson correlation coefficients of each parameter are summed. The sum of the absolute values ​​of the real numbers is compared with a rigid fixed threshold parameter. When the comparison and judgment requirements are met, the feature vectors corresponding to the remaining principal components are extracted as the additional feature principal components that need to be retained and filled. The extracted additional feature principal components are combined and appended to the end of the initial decoupled principal component base and then spliced ​​column by column.

7. The method according to claim 1, characterized in that, The step of establishing a Gaussian process regression prediction model using the decoupled side resistance core factor and end resistance core factor as inputs includes: The fixed prior expectation baseline mean function of the initial model for calculating pile side resistance and pile end resistance under specified operating conditions is set as a digital zero vector form, and the expression function with squared exponential internal decay characteristics is assigned as the baseline covariance kernel function. Import the decoupled side resistance core factor and end resistance core factor as the bottom training input sample, and independently match and map the historical actual side friction test record data and the historical actual end resistance test record data as the top training verification true result feedback target of their respective models. By calling the L-BFGS step size to find the optimization operator, the maximum likelihood maximization solution gradient climbing action is continuously carried out on the formula of the target logarithmic marginal probability density corresponding to the set of all training points of the basic model. The length scale parameter and signal variance value in the hyperplane variable of the parameter space that can limit the probability density are deduced and extracted. Replace all intrinsic parameters of the preceding baseline kernel function with the constants of the two spatial hyperplanes that have been solved and anchored, construct a prediction mapping relationship based on the inversion of the kernel matrix, and declare the end of the single model encapsulation and establishment.

8. A vertical bearing capacity calculation system for a rigid-flexible composite bag-type expanded-base pile, characterized in that, include: The partitioning module is used to obtain the initial parameter set that affects the vertical bearing capacity of the pile. The initial parameter set includes pile geometric parameters, bag performance parameters, soil mechanical parameters, and enlarged base morphology parameters. The enlarged base morphology parameters are one-dimensional control point vectors extracted based on point cloud data through non-uniform rational B-spline reconstruction. The obtained initial parameter set that affects the vertical bearing capacity of the pile is divided into a subset of side resistance parameters that affect side friction and a subset of end resistance parameters that affect end resistance. The generation module is used to acquire historical sample training sets, construct hybrid kernel matrices representing the correlation between the side resistance parameter subsets that affect side friction and the end resistance parameter subsets that affect end resistance. The hybrid kernel matrices are generated by combining polynomial kernel functions and radial basis kernel functions. Based on the difference in the sensitivity of each parameter to resistance within the side resistance parameter subset and the end resistance parameter subset, weights are assigned to different parameters at the kernel space input. The two hybrid kernel matrices are subjected to mean centering and eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors. Principal components are selected according to the cumulative variance contribution rate and the absolute value of the correlation coefficient with the parameter and the rule that it exceeds a preset threshold. The side resistance core factor and the end resistance core factor are decoupled and generated. The calculation module is used to establish a Gaussian process regression prediction model with the decoupled generated side resistance core factor and end resistance core factor as inputs, respectively, to calculate the predicted side friction and the predicted end resistance, and to sum the predicted side friction and the predicted end resistance to obtain the vertical bearing capacity of the pile.

9. The system according to claim 8, characterized in that, The expanded base morphology parameters are one-dimensional control point vectors extracted from point cloud data through non-uniform rational B-spline reconstruction, including: The Gaussian filtering algorithm is used to smooth the original point cloud data and filter out noise points; The smoothed point cloud data is divided into a multi-dimensional basic grid set according to the spatial grid distribution; Construct three-dimensional non-uniform rational B-spline basis functions based on a multidimensional fundamental mesh set; The three-dimensional control point matrix of the non-uniform rational B-spline surface is solved by fitting the basis function of the three-dimensional non-uniform rational B-spline with the smoothed point cloud data using the least squares fitting algorithm. The three-dimensional control point matrix is ​​sequentially connected end to end to perform one-dimensional flattening and dimensionality reduction, generating a one-dimensional control point vector, which is then written into the initial parameter set.

10. The system according to claim 8, characterized in that, The initial parameter set affecting the vertical bearing capacity of the pile is divided into a subset of side resistance parameters affecting side skin friction and a subset of end resistance parameters affecting end resistance, including: Iterate through and read the text tag identifier code attached to each parameter in the initial parameter set; By comparing the classification table rules in the preset classification database, extract the parameters corresponding to the fields of pile perimeter soil friction angle, pile outer diameter and bag roughness in the text label identification code, and write them into the memory space to generate a subset of side resistance parameters. Extract the text tag identifier code containing parameters corresponding to the bearing layer compression modulus, enlarged head diameter, pile tip soil cohesion, and one-dimensional control point vector fields, and write them into another memory space to generate a subset of end resistance parameters.

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