A pile-soil coupling loss prediction method based on soil layer quantification and neural network

Abstract

The application discloses a pile-soil coupling loss prediction method based on soil layer quantification and a neural network. Firstly, the parameterized finite element-infinite element coupling numerical simulation is used to extract the pile-soil coupling loss quantification index, i.e., the transfer function amplitude ratio. Then, the logistic function or the double logistic function is introduced and combined with the soil layer depth-soil layer shear wave speed normalization coordinate system, and the parameters in the logistic function or the double logistic function are used to represent the soil layer distribution characteristic parameters. Then, the neural network model is constructed, the pile body parameters, the load parameters, the characteristic frequency points and the soil layer distribution characteristic parameters are taken as the inputs, and the transfer function amplitude ratio is taken as the output target for training. Finally, the trained model is used to realize the rapid and accurate prediction of the pile-soil coupling loss. The application innovatively realizes the effective quantification of the spatial distribution of the complex soil layer, and solves the problems of low accuracy and low efficiency of the traditional method in the prediction of the pile-soil dynamic coupling loss.

Description

Technical Field

[0001] This invention relates to the fields of geotechnical engineering and pile foundation dynamics, and in particular to a method for predicting pile-soil coupling loss based on soil layer quantification and neural networks. Background Technology

[0002] As a primary form of deep foundation, pile foundations are widely used in high-rise buildings, long-span bridges, offshore wind power, integrated transportation hubs, and major industrial facilities. Their core function is to effectively transfer the load of the superstructure to deep, stable soil. Under dynamic loads (such as earthquakes, waves, mechanical vibrations, and vehicle impacts), the dynamic interaction between the pile and soil system, i.e., the pile-soil coupling effect, is a key factor determining the dynamic response characteristics of pile foundations. Accurately predicting the energy loss during the pile-soil coupling process (i.e., pile-soil coupling loss) is crucial for assessing the vibration characteristics, bearing capacity, and long-term service performance of pile foundations.

[0003] Currently, the analytical methods for pile-soil coupling effects used in engineering practice and academia can be mainly classified into the following categories: 1. Analytical methods based on simplified theoretical models: These methods are typically based on the Winkler foundation model or elastic half-space theory, simplifying the complex pile-soil continuum interaction into a series of independent spring-damper systems or idealized elastic media. However, these simplified models struggle to accurately reflect the stratification, heterogeneity, and key physical mechanisms of dynamic interactions such as wave propagation and radiation damping in soil. For complex, multi-layered soils commonly encountered in practical engineering, the computational accuracy is often difficult to guarantee, resulting in coarse calculations that fail to meet the needs of refined design.

[0004] 2. Refined analysis methods based on numerical simulation: With the development of computer technology, the finite element method, boundary element method, and finite element-infinite element coupled method have become important tools for studying pile-soil dynamic interactions. Commercial software (such as ABAQUS and PLAXIS) can be used to build detailed three-dimensional numerical models, considering material nonlinearity, contact behavior, and complex boundary conditions. Although these methods offer high computational accuracy, their modeling process is complex, computationally resource-intensive, and computationally intensive. For example, a complete parametric analysis often requires establishing and calculating hundreds or thousands of working conditions, which is unsustainable in the initial stages of engineering design and scheme comparison. This method inherently presents a trade-off between computational efficiency and model accuracy, making rapid prediction and real-time feedback impossible.

[0005] 3. Empirical and Semi-Empirical Formula Methods Based on Experimental Data: Through regression analysis of field or model test data, empirical formulas can be established to predict the dynamic response of pile foundations. These formulas typically depend on specific geological conditions, pile type, and load type, resulting in insufficient universality. When applied to new projects with significantly different experimental conditions, or when dealing with complex layered soils, the reliability of the prediction results decreases significantly. Furthermore, full-scale testing is costly and it is difficult to obtain sufficient sample data to cover various complex working conditions.

[0006] In recent years, machine learning technology has provided a new paradigm for solving complex geotechnical engineering problems. For example, Chinese patent document (CN111209708B) discloses a method for predicting pile-soil interaction by combining numerical simulation and neural networks. This method generates parameter samples through Latin hypercube sampling, uses the Lasso algorithm for sensitivity analysis and dimensionality reduction of input variables, and finally uses a BP neural network to predict the static response of the pile, such as bending moment distribution, settlement, and ultimate bearing capacity.

[0007] Although this technical solution demonstrates the potential of machine learning in pile foundation analysis, its core mechanism and the technical problems it solves are fundamentally different from the concept of this invention, specifically in the following aspects: The fundamental difference lies in the problem domains: the aforementioned existing technologies aim to solve the static bearing capacity and deformation problems of pile foundations. Their output targets are static forces and displacements, falling under the category of quasi-static analysis. In contrast, this invention focuses on the dynamic interaction of the pile-soil system, particularly the energy loss (i.e., coupling loss) generated when stress waves propagate through the pile-soil system under dynamic loads (such as vibration and wave action), which falls under the category of dynamic analysis. The theoretical foundations, physical phenomena they address, and ultimate engineering application goals are all fundamentally different.

[0008] The difference between core mechanisms and quantitative indicators: Due to different problem domains, there are fundamental differences between core technical mechanisms and quantitative indicators. The aforementioned literature directly obtains the static response values ​​of the pile body through numerical simulation as the target of machine learning. In contrast, this invention introduces a frequency domain analysis method, extracting the transfer function amplitude ratio as a quantitative indicator of pile-soil coupling loss by comparing the dynamic responses of the pile field and the free field. This indicator can essentially reflect the scattering and radiation effects of wave field energy by the pile body, and is a core parameter for dynamic coupling analysis.

[0009] A stark difference in methodologies for soil layer information processing: In the crucial step of processing complex soil layer information, this invention takes a completely different technical path from existing technologies. Existing technologies employ statistical methods such as Lasso to perform sensitivity screening and dimensionality reduction on the original soil material parameters. Essentially, this involves selecting key factors affecting the static response from numerous input parameters, but it does not change the properties of the parameters themselves, nor does it solve the problem of effectively characterizing the spatial distribution patterns of soil layers.

[0010] This invention proposes a novel method for parameterized and functionalized soil layer quantification. By establishing a normalized coordinate system and introducing a logistic or double logistic function to fit the distribution of soil shear wave velocity with depth, arbitrarily complex multi-layered soil profiles are abstracted into a set of standardized feature parameters with clear physical meaning (such as asymptotes and inflection points). This method transforms spatial distribution information into low-dimensional feature vectors that are easily processed by neural networks, fundamentally solving the problems of "curse of dimensionality" and difficulty in feature representation faced by traditional methods when dealing with soil layers of varying number and thickness.

[0011] In summary, existing technologies provide a general machine learning framework for static response, while this invention is a specialized technical solution with creative designs for the specific scientific problem of pile-soil dynamic coupling loss, from mechanism modeling (transfer function) to data preprocessing (soil layer quantification). Summary of the Invention

[0012] In view of the problems of poor calculation accuracy, efficiency and adaptability to complex soil layers (especially multi-layered soil) in existing pile-soil coupling loss prediction methods, this invention is proposed.

[0013] Therefore, the problem to be solved by this invention is to address the issues of soil layer quantification, as well as the accuracy and efficiency of calculations in current pile-soil coupling loss prediction methods.

[0014] To solve the above-mentioned technical problems, the present invention provides the following technical solution: The core of this invention lies in establishing a complete "numerical simulation-feature extraction-intelligent prediction" technical framework. It generates training data through parameterized numerical simulation, processes complex soil information through an innovative soil layer normalization method, and finally achieves fast and accurate prediction through neural networks.

[0015] This invention provides a method for predicting pile-soil coupling loss based on soil layer quantization and neural networks, which includes the following steps: S1. Parametric numerical simulation and extraction of pile-soil coupling loss index: Determine the range of pile parameters, load parameters, and soil parameters that affect pile-soil coupling loss, and determine the characteristic frequency points within the observation frequency band; Based on the range and characteristic frequency points of the pile parameters, load parameters, and soil parameters, design multiple analysis conditions; For each condition, perform parametric finite element-infinite element coupled numerical simulation, and extract the pile-soil coupling loss quantification index with the transfer function amplitude ratio as the core by comparing the dynamic response of the pile field and the free field; S2. Parameterization and Quantification of Soil Layer Distribution Characteristics: The distribution information of multiple soil layers in each working condition is transformed into a set of standardized soil layer distribution characteristic parameters through the following sub-steps: S2.1 Establish a depth-normalized coordinate system and a shear wave velocity-normalized coordinate system; S2.2. By introducing a logistic function or a double logistic function, the data points of each soil layer condition in the normalized coordinate system are fitted. The logistic function is: ; in For the parameters of the upper asymptote, For the lower asymptote parameters, For the slope parameter, For the inflection point position parameters, Normalized depth of soil layers The normalized depth of the soil layer is The corresponding normalized shear wave velocity; or the double logistic function: ; in , , For asymptote parameters, , For the slope parameter, , For the inflection point position parameters, Normalized depth of soil layers The normalized depth of the soil layer is The corresponding normalized shear wave velocity; The selected fitting function was fitted using the least squares method, and the goodness of fit was: ; in, This represents the actual normalized shear wave velocity value. The normalized shear wave velocity value is calculated for the fitted function, where m (represents the m-th layer in a soil profile: 1, 2, 3…, counting downwards from the top layer) and n (represents the total number of soil layers in the fitted working condition: 1, 2, 3…). The average value of the normalized shear wave velocity is used as the basis for the fitting process, and the goodness of fit is required. A threshold greater than 0.95 ensures that the fitting function can accurately characterize the distribution of soil shear wave velocity; a threshold of 0.95 is chosen to ensure that the soil parameter fitting has sufficient accuracy, providing reliable input features for the neural network. S2.3 Extract the parameters from the logistic function or double logistic function as the soil layer distribution characteristic parameters. When using the logistic function, the... , , , The soil layer distribution characteristic parameters are defined as follows; when using a double logistic function, the... , , , , , , These are the soil layer distribution characteristic parameters; S3. Construction and training of neural network models: A neural network model is constructed, with the following input features: the pile parameters, load parameters, and feature frequency points obtained in step S1, and the soil layer distribution feature parameters obtained in step S2; the output target is: the transfer function amplitude ratio extracted in step S1; the neural network model is trained using the dataset generated in steps S1 and S2. S4. Pile-soil coupling loss prediction: Input the actual parameters of the target project into the trained neural network model, and output the predicted value of the amplitude ratio of the transfer function, thereby realizing the rapid prediction of pile-soil coupling loss.

[0016] As a preferred embodiment of the pile-soil coupling loss prediction method based on soil layer quantification and neural networks described in this invention, the pile-soil coupling loss quantification index is the transfer function amplitude ratio. It is obtained through the following methods: In the numerical simulation, the time history data of the vertical vibration acceleration at the center point of the pile head is extracted as the response of the pile field; In the same model without piles, the time history data of vertical vibration acceleration at the same location point are extracted as the free field response; Fast Fourier Transform (FFT) was performed on the time history data of the piled field response and the free field response, respectively, to obtain their respective amplitude spectra. and ; The amplitude ratio of the transfer function is calculated as follows: ; The amplitude ratio of the transfer function The amplitude ratio corresponding to each characteristic frequency within the target frequency band is preferably (4-80) Hz in this invention, and is used as the output target of neural network training in step S3.

[0017] As a preferred embodiment of the pile-soil coupling loss prediction method based on soil layer quantization and neural network described in this invention, the pile parameters include pile diameter and pile length, the load parameters include the distance between the excitation source and the receiver, the soil parameters include the shear wave velocity and thickness of each soil layer, and the characteristic frequency points are determined by the sampling frequency and the number of sampling points.

[0018] As a preferred embodiment of the pile-soil coupling loss prediction method based on soil layer quantization and neural networks described in this invention, the preferred variation range of the pile diameter is 0.4m to 1.6m, the preferred variation range of the pile length is 10m to 40m, the preferred variation range of the distance between the excitation source and the receiver is 10m to 50m, the preferred variation range of the soil wave velocity is 150m / s to 800m / s, and in the finite element-infinite element coupling model, the size of the finite element region is long. Width The optimal height is 60m 30m 45m, the dimensions of the infinite dimension region: length Width The optimal height is 90m 60m In the finite element-infinite element coupled model, the global mesh size of the finite element region is preferably 0.2m, and the infinite element boundary corresponding to the finite element boundary is seeded along the edge, preferably with the same number of seeds as the corresponding finite element boundary.

[0019] As a preferred embodiment of the pile-soil coupling loss prediction method based on soil layer quantization and neural network described in this invention, the load in Abaqus modeling is preferably a Ricker wavelet with a center frequency of 50Hz and an analysis time of 0.5s.

[0020] As a preferred embodiment of the pile-soil coupling loss prediction method based on soil layer quantization and neural networks described in this invention, the establishment of a depth-normalized coordinate system and a shear wave velocity-normalized coordinate system includes: Establish a depth-normalized coordinate system, where the normalized depth is the ratio of the depth at the midpoint of the soil layer to the reference depth; Establish a normalized coordinate system for shear wave velocity, where the normalized shear wave velocity is the ratio of the soil layer shear wave velocity to the reference soil layer shear wave velocity. The monotonically increasing wave velocity conforms to the natural weathering and deposition law, that is, the wave velocity of the lower soil layer is greater than or equal to the wave velocity of the upper soil layer. The above working condition design follows the principle that the wave velocity of the lower soil layer is greater than or equal to the wave velocity of the upper soil layer, and this design conforms to the distribution of most soil layers.

[0021] As a preferred embodiment of the pile-soil coupling loss prediction method based on soil layer quantification and neural network described in this invention, it further includes a sensitivity analysis step to determine whether the influence of the soil layer below the pile tip is lower than a preset threshold. Design sensitivity analysis case: Keeping pile body parameters, load parameters, and soil layer parameters within the pile length constant, the thickness of the soil layer below the pile tip (excluding the soil layer where the pile tip is located) is changed systematically and independently. or shear wave velocity , ( This generates a series of analysis cases, starting from the ground and counting vertically from the i-th soil layer (1, 2, 3...). Numerical simulation was performed: Finite element-infinite element coupled numerical simulations were conducted for all the above working conditions, and the quantitative index of pile-soil coupling loss for each working condition was extracted. ( (Indicates the number of operating conditions: 1, 2, 3...). Calculation of the degree of influence: based on the thickest and softest soil layer below the pile tip. As a reference benchmark, calculate the relative rate of change of the amplitude ratio of the transfer function for other operating conditions: ; Determine the threshold: Analyze the relative rate of change The law of variation of soil parameters below the pile tip; preferably, the preset threshold can be 5%; that is, when the rate of change of loss coefficient caused by the change of soil parameters below the pile tip is consistently less than 5%, it is determined that its influence is negligible; otherwise, it is considered that its influence is not negligible. When the influence of the soil layer below the pile tip (excluding the soil layer where the pile tip is located) is lower than the preset threshold, the reference depth is the soil layer from the ground to the pile tip, and the reference soil layer is the soil layer where the pile tip is located. When the influence of the soil layer below the pile tip (excluding the soil layer where the pile tip is located) is not less than the preset threshold, the reference depth is the total soil thickness, and the reference soil layer is the bottommost soil layer.

[0022] As a preferred embodiment of the pile-soil coupling loss prediction method based on soil layer quantization and neural network described in this invention, the dataset consisting of the pile parameters, load parameters, and characteristic frequency points obtained in step S1, the soil layer distribution characteristic parameters obtained in step S2, and the transfer function amplitude ratios that correspond one-to-one with the input features obtained in step S1 is divided into a training set (70%), a validation set (15%), and a test set (15%). A random stratified sampling method is used to ensure the representativeness of the data distribution in each subset and to avoid the impact of data partitioning bias on model performance. The training set is used for parameter training of the neural network model, the validation set is used for performance monitoring and early stopping during the training process, and the test set is used for final model performance evaluation. The neural network model is a feedforward neural network, including an input layer, at least one hidden layer, and an output layer; Input layer design: The number of neurons is strictly consistent with the dimension of the input features; in this invention, the input features include pile diameter, pile length, excitation distance, and feature parameters extracted from soil layer normalization processing, forming a fixed-dimensional input vector; Hidden layer optimization: The number of hidden layers and neurons was determined using a systematic cross-validation method. This method, based on the k-fold cross-validation process mentioned below, ensures that the selected network structure possesses both sufficient expressive power and good generalization performance. The ReLU activation function is used in the hidden layers, and its mathematical expression is: ; The net input to a neuron is represented by the following formula: ; This indicates that the current neuron is related to the previous neuron. Connection weights between neurons; Indicates the previous level. The output value of each neuron; The bias parameters of the current neuron; Output layer configuration: Based on the characteristic that pile-soil coupling loss prediction is a single-valued regression problem, the output layer is configured with a neuron and a linear activation function to ensure that the output value can cover the possible range of the transfer function amplitude ratio in actual engineering.

[0023] As a preferred embodiment of the pile-soil coupling loss prediction method based on soil layer quantization and neural networks described in this invention, the training of the neural network is a systematic iterative optimization process, with each training cycle containing complete forward and backward propagation closed loops: Forward propagation process: Input features start from the input layer and are processed layer by layer through each hidden layer. Each neuron performs weighted summation and applies activation function calculations. The training mean squared error is used as the loss function to quantify the difference between the predicted and the true values: ; in The ratio of the amplitudes of the true transfer functions in the training set. These are the predictions made by the neural network on the training set. (Indicates which condition in the training set: 1, 2, 3...) Given the number of training set samples, this loss function provides an optimization objective for subsequent backpropagation; Backpropagation process: Based on the chain rule, the gradient of the loss function with respect to each parameter in the network is calculated. Starting from the output layer, the error signal is propagated backward layer by layer to clarify the contribution of each parameter to the total error and the adjustment direction. An adaptive moment estimation optimizer is used to update the network parameters. This optimizer maintains an adaptive learning rate for each parameter. During training, continuously monitor the validation mean squared error performance on the validation set: ; in To verify the true transfer function amplitude ratio in the set, The neural network's predictions for the validation set. (Indicates the nth working condition in the verification set: 1, 2, 3...) The number of samples in the validation set; The cross-validation method uses k-fold cross-validation: the training set data is randomly divided into k mutually exclusive subsets; each subset is used as a validation subset, and the remaining k-1 subsets are used as training subsets; each candidate network structure is trained and validated k times; the training of the neural network model uses the training mean squared error. As a loss function (note the case in k-fold validation) The parameters are input as a subset of the training set; the neural network model is validated using the validation mean squared error. As a loss function (note the case in k-fold validation) The input parameters are the validation subset partitioned from the training set. Select k rounds The network structure with the minimum mean square error is the optimal network structure, and this network structure is used in the subsequent training and validation processes of the neural network. The neural network model employs early stopping to prevent overfitting during training, specifically as follows: During training, the mean squared error loss value on the validation set (here, the validation set is the validation set divided from the initial total data, not the validation subset in the k-fold cross-validation mentioned above) is continuously monitored. The mean square error of the validation set is calculated using the actual pile-soil coupling loss coefficient in the validation set; Set patience parameter When the mean square error of the validation set is continuous Early stopping is triggered when the value no longer drops to a new minimum within a training cycle, and the model parameters at the point where the mean square error of the validation set is the lowest are saved throughout the training process. Model Validation and Performance Evaluation: The trained neural network model needs to undergo rigorous performance validation. Final performance evaluation is performed using a test set that was not used during training. Multiple metrics can be used for validation, including the mean squared error. Coefficient of determination Multiple performance indicators: ; in The ratio of the true transfer function amplitude in the test set. This represents the neural network's predictions for the test set. (Indicates the nth operating condition in the test: 1, 2, 3...) This represents the number of samples in the test set. ; in The ratio of the true transfer function amplitude in the test set. This represents the neural network's predictions for the test set. The average value of the amplitude ratio of the true transfer function in the test set. (Indicates the nth operating condition in the test: 1, 2, 3...) This represents the number of samples in the test set. Finally, the trained prediction model is obtained. By inputting the actual working condition parameters, the values ​​corresponding to each characteristic frequency are obtained. The values ​​corresponding to (4-80) Hz can be combined by linear interpolation to form a pile-soil coupling loss prediction curve with frequency as the x-axis and transfer function amplitude ratio as the y-axis. Attached Figure Description

[0024] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 The attached figure is an abstract of a pile-soil coupling loss prediction method based on soil layer quantification and neural networks.

[0025] Figure 1This is a flowchart illustrating the steps of a pile-soil coupling loss prediction method based on soil layer quantization and neural networks.

[0026] Figure 2 This is a flowchart of the neural network in a pile-soil coupling loss prediction method based on soil layer quantification and neural networks. Detailed Implementation

[0027] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0028] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0029] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] The purpose of this invention is to provide a method for predicting pile-soil coupling loss based on soil layer quantification and neural networks. This method enables engineers to quickly and accurately predict pile-soil coupling loss even when dealing with varying soil parameters. To make the above-mentioned objectives, features, and advantages of this invention more apparent and understandable, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Figure 1 As shown in the figure, an embodiment of the present invention provides a pile-soil coupling loss prediction method based on soil layer quantization and neural networks, which includes the following steps: S1. Parametric numerical simulation and extraction of pile-soil coupling loss index: Determine the range of pile parameters, load parameters, and soil parameters that affect pile-soil coupling loss, and determine the characteristic frequency points within the observation frequency band; Based on the range and characteristic frequency points of the pile parameters, load parameters, and soil parameters, design multiple analysis conditions; For each condition, perform parametric finite element-infinite element coupled numerical simulation, and extract the pile-soil coupling loss quantification index with the transfer function amplitude ratio as the core by comparing the dynamic response of the pile field and the free field; S2. Parameterization and Quantification of Soil Layer Distribution Characteristics: The distribution information of multiple soil layers in each working condition is transformed into a set of standardized soil layer distribution characteristic parameters through the following sub-steps: S2.1 Establish a depth-normalized coordinate system and a shear wave velocity-normalized coordinate system; S2.2. By introducing a logistic function or a double logistic function, the data points of each soil layer condition in the normalized coordinate system are fitted, wherein the logistic function is: ; in For the parameters of the upper asymptote, For the lower asymptote parameters, For the slope parameter, For the inflection point position parameters, Normalized depth of soil layers The normalized depth of the soil layer is The corresponding normalized shear wave velocity; or the double logistic function: ; in , , For asymptote parameters, , For the slope parameter, , For the inflection point position parameters, Normalized depth of soil layers The normalized depth of the soil layer is The corresponding normalized shear wave velocity; The selected fitting function was fitted using the least squares method, and the goodness of fit was: ; in, This represents the actual normalized shear wave velocity value. The normalized shear wave velocity value is calculated for the fitted function, where m (represents the m-th layer in a soil profile: 1, 2, 3…, counting downwards from the top layer) and n (represents the total number of soil layers in the fitted working condition: 1, 2, 3…). The average value of the normalized shear wave velocity is used as the basis for the fitting process, and the goodness of fit is required. A threshold greater than 0.95 ensures that the fitting function can accurately characterize the distribution of soil shear wave velocity; a threshold of 0.95 is chosen to ensure that the soil parameter fitting has sufficient accuracy, providing reliable input features for the neural network. S2.3 Extract the parameters from the logistic function or double logistic function as the soil layer distribution characteristic parameters. When using the logistic function, the... , , , The soil layer distribution characteristic parameters are defined as follows; when using a double logistic function, the... , , , , , , These are the soil layer distribution characteristic parameters; S3. Construction and training of neural network models: A neural network model is constructed, with the following input features: the pile parameters, the load parameters, the characteristic frequency points obtained in step S1, and the soil layer distribution characteristic parameters obtained in step S2; the output target is: the transfer function amplitude ratio extracted in step S1. The neural network model is trained using the dataset generated in steps S1 and S2; S4. Pile-soil coupling loss prediction: Input the actual parameters of the target project into the trained neural network model, and output the predicted value of the amplitude ratio of the transfer function, thereby realizing the rapid prediction of pile-soil coupling loss.

[0032] In this embodiment, the quantitative index of pile-soil coupling loss is the transfer function amplitude ratio. It is obtained through the following methods: In the numerical simulation, the time history data of the vertical vibration acceleration at the center point of the pile head is extracted as the response of the pile field; In the same model without piles, the time history data of vertical vibration acceleration at the same location point are extracted as the free field response; Fast Fourier Transform (FFT) was performed on the time history data of the piled field response and the free field response, respectively, to obtain their respective amplitude spectra. and ; The amplitude ratio of the transfer function is calculated as follows: ; The amplitude ratio of the transfer function The amplitude ratio corresponding to each characteristic frequency within the target frequency band is preferably (4-80) Hz in this invention, and is used as the output target of neural network training in step S3.

[0033] In this embodiment, the pile parameters include pile diameter and pile length, the load parameters include the distance between the excitation source and the receiver, the soil parameters include the shear wave velocity and thickness of each soil layer, and the characteristic frequency points are determined by the sampling frequency and the number of sampling points.

[0034] In this embodiment, the sampling frequency is 500Hz, the number of sampling points is 250, the analysis time is 0.5s, and the characteristic frequency points are (4Hz, 6Hz, 8Hz...80Hz).

[0035] In this embodiment, the preferred variation range of the pile diameter is 0.4m to 1.6m, the preferred variation range of the pile length is 10m to 40m, the preferred variation range of the distance between the excitation source and the receiver is 10m to 50m, the preferred variation range of the soil wave velocity is 150m / s to 800m / s, and the size of the finite element region in the finite element-infinite element coupled model is long. Width The optimal height is 60m 30m 45m, the dimensions of the infinite dimension region: length Width The optimal height is 90m 60m In the finite element-infinite element coupled model, the global mesh size of the finite element region is preferably 0.2m, and the infinite element boundary corresponding to the finite element edge is seeded along the edge, preferably with the same number of seeds as the corresponding finite element boundary; in the Abaqus modeling, the load is preferably a Ricker wavelet with a center frequency of 50Hz and an analysis time of 0.5s.

[0036] In this embodiment, soil layers are grouped by the number of layers: single-layer soil is one group, two-layer soil is another group, and so on, designing the working conditions for each group. The normalized fitting curves below use the logistic function or double logistic function, representing a distribution of soil layers from soft to hard from top to bottom, conforming to the natural weathering and deposition law, i.e., the wave velocity of the lower soil layer is greater than or equal to the wave velocity of the upper soil layer. The following working condition design follows the principle that the wave velocity of the lower soil layer is greater than or equal to the wave velocity of the upper soil layer, and this design conforms to the distribution of most soil layers. First, the single-layer soil working condition is designed, keeping a single variable. After the pile length, pile diameter, pile spacing, and soil wave velocity are designed, cross-design begins, with the working conditions varying with the pile length, pile diameter, and pile spacing. The design process incorporates variations in soil wave velocity to explore the coupling loss patterns of pile length, diameter, and spacing under different wave velocities. Then, a two-layer soil design is implemented, following the aforementioned design principles for single-variable working conditions. Here, the wave velocity and thickness of both soil layers can be kept constant. First, working conditions with varying pile length, diameter, and spacing are designed, and then variations in wave velocity and thickness of the two soil layers are interspersed within these working condition designs. The design approach for three- and four-layer soil layers is the same as for the two-layer soil layer. Sensitivity analysis is then conducted, selecting working conditions with varying wave velocity and thickness of the soil layer below the pile tip (excluding the soil layer containing the pile tip) for both two-, three-, and four-layer soil layers. The degree of influence is calculated: for each group, the working conditions with the thickest and softest soil layer below the pile tip are selected. As a reference benchmark, calculate the relative rate of change of the amplitude ratio of the transfer function for each group of operating conditions: ; : Amplitude ratio of transfer function under various operating conditions; =(1, 2, 3…); Determine the threshold: Analyze the relative rate of change The pattern of changes in soil parameters below the pile tip.

[0037] In this embodiment, preferably, the preset threshold can be 5%, and the threshold can be adjusted according to the specific situation; that is, when the rate of change of the loss coefficient caused by the change of soil parameters below the pile tip is continuously less than 5%, it is determined that its influence is negligible; otherwise, it is considered that its influence is not negligible. When the influence of the soil layer below the pile tip (excluding the soil layer where the pile tip is located) is lower than the preset threshold, the following reference depth is from the ground to the soil layer where the pile tip is located, and the reference soil layer is the soil layer where the pile tip is located. When the influence of the soil layer below the pile tip (excluding the soil layer where the pile tip is located) is not less than the preset threshold, the following reference depth is the total soil thickness, and the reference soil layer is the bottommost soil layer.

[0038] In this embodiment, the number of layers used in the above sensitivity analysis is only for reference. If the sensitivity analysis results are unclear, you can decide to select more or fewer layers for analysis.

[0039] In this embodiment, after the sensitivity analysis is completed, more soil layer condition analyses can be performed. When the influence of the soil layer below the pile tip (excluding the soil layer where the pile tip is located) is lower than the preset threshold, the thickness and wave velocity of the soil layer below the pile tip can be fixed, and the condition design of the remaining soil layers can be carried out. The condition design of the remaining soil layers is consistent with the above two-layer soil design concept. When the influence of the soil layer below the pile tip (excluding the soil layer where the pile tip is located) is not lower than the preset threshold, all soil layer condition designs follow the two-layer soil design concept.

[0040] In this embodiment, after completing the above-mentioned soil layer working condition design, a depth-normalized coordinate system and a shear wave velocity-normalized coordinate system are established, including: Establish a depth-normalized coordinate system, where the normalized depth is the ratio of the depth at the midpoint of the soil layer to the reference depth; Establish a normalized coordinate system for shear wave velocity, where the normalized shear wave velocity is the ratio of the soil layer shear wave velocity to the reference soil layer shear wave velocity.

[0041] In this embodiment, the pile parameters, load parameters, characteristic frequency points, and the soil layer distribution characteristic parameters obtained from step S2 are used as inputs, and the transfer function amplitude ratio obtained from step S1 is used as the output.

[0042] In this embodiment, the input features can be [pile length, pile spacing, pile diameter, ...]. , , , [4Hz], the output characteristics are those corresponding to the above parameters. [The value corresponding to 4Hz in the text.]

[0043] In this embodiment, as Figure 2 The dataset consisting of all the above input and output features is divided into a training set (70%), a validation set (15%), and a test set (15%). A random stratified sampling method is used to ensure the representativeness of the data distribution in each subset and to avoid the impact of data partitioning bias on model performance. The training set is used for parameter training of the neural network model, the validation set is used for performance monitoring and early stopping during the training process, and the test set is used for final model performance evaluation. The neural network model is a feedforward neural network, including an input layer, at least one hidden layer, and an output layer; Input layer design: The number of neurons is strictly consistent with the dimension of the input features. In this invention, the input features include pile diameter, pile length, excitation distance, and feature parameters extracted from soil layer normalization processing, forming a fixed-dimensional input vector; Hidden layer optimization: The number of hidden layers and neurons was determined using a systematic cross-validation method. This method, based on the k-fold cross-validation process mentioned below, ensures that the selected network structure possesses both sufficient expressive power and good generalization performance. The ReLU activation function is used in the hidden layers, and its mathematical expression is: ; The net input to a neuron is represented by the following formula: ; This indicates that the current neuron is related to the previous neuron. Connection weights between neurons; Indicates the previous level. The output value of each neuron; The bias parameters of the current neuron; Output layer configuration: Based on the characteristic that pile-soil coupling loss prediction is a single-valued regression problem, the output layer is configured with a neuron and a linear activation function to ensure that the output value can cover the possible range of the transfer function amplitude ratio in actual engineering.

[0044] In this embodiment, the training of the neural network is a systematic iterative optimization process, and each training cycle contains complete forward and backward propagation closed loops: Forward propagation process: Input features start from the input layer and are processed layer by layer through each hidden layer. Each neuron performs weighted summation and applies activation function calculations. The training mean squared error is used as the loss function to quantify the difference between the predicted and the true values: ; in The ratio of the amplitudes of the true transfer functions in the training set. These are the predictions made by the neural network on the training set. (Indicates which condition in the training set: 1, 2, 3...) Given the number of training set samples, this loss function provides an optimization objective for subsequent backpropagation; Backpropagation process: Based on the chain rule, the gradient of the loss function with respect to each parameter in the network is calculated. Starting from the output layer, the error signal is propagated backward layer by layer to clarify the contribution of each parameter to the total error and the adjustment direction. An adaptive moment estimation optimizer is used to update the network parameters. This optimizer maintains an adaptive learning rate for each parameter. During training, continuously monitor the validation mean squared error performance on the validation set: ; in To verify the true transfer function amplitude ratio in the set, The neural network's predictions for the validation set. (Indicates the nth working condition in the verification set: 1, 2, 3...) The number of samples in the validation set; The cross-validation method uses k-fold cross-validation: the training set data is randomly divided into k mutually exclusive subsets; each subset is used as a validation subset, and the remaining k-1 subsets are used as training subsets; each candidate network structure is trained and validated k times; the training of the neural network model uses the training mean squared error. As a loss function (note the case in k-fold validation) The input parameters are a subset of the training set; the neural network model is validated using the validation mean squared error. As a loss function (note the case in k-fold validation) The input parameters are the validation subset partitioned from the training set. Select k rounds The network structure with the minimum mean square error is the optimal network structure, and this network structure is used in the subsequent training and validation processes of the neural network. The neural network model employs early stopping to prevent overfitting during training, specifically as follows: During training, the mean squared error loss value on the validation set (here, the validation set is the validation set divided from the initial total data, not the validation subset in the k-fold cross-validation mentioned above) is continuously monitored. The mean square error of the validation set is calculated using the actual pile-soil coupling loss coefficient in the validation set; Set patience parameter When the mean square error of the validation set is Early stopping is triggered when the value no longer drops to a new minimum within a training cycle, and the model parameters at the point where the mean square error of the validation set is the lowest are saved throughout the training process. Model Validation and Performance Evaluation: The trained neural network model needs to undergo rigorous performance validation. Final performance evaluation is performed using a test set that was not used during training. Multiple metrics can be used for validation, including the mean squared error. Coefficient of determination Multiple performance indicators: ; in The ratio of the true transfer function amplitude in the test set. This represents the neural network's predictions for the test set. (Indicates the nth operating condition in the test: 1, 2, 3...) This represents the number of samples in the test set. ; in The ratio of the true transfer function amplitude in the test set. This represents the neural network's predictions for the test set. The average value of the amplitude ratio of the true transfer function in the test set. (Indicates the nth operating condition in the test: 1, 2, 3...) This represents the number of samples in the test set.

[0045] Finally, the trained prediction model is obtained. By inputting the actual working condition parameters, the values ​​corresponding to each characteristic frequency are obtained. The values ​​corresponding to (4-80) Hz can be combined by linear interpolation to form a pile-soil coupling loss prediction curve with frequency as the x-axis and transfer function amplitude ratio as the y-axis.

Claims

1. A pile-soil coupling loss prediction method based on soil layer quantification and neural networks, characterized by, Includes the following steps: S1. Parametric numerical simulation and extraction of pile-soil coupling loss index: Determine the range of pile parameters, load parameters, and soil parameters that affect pile-soil coupling loss, and determine the characteristic frequency points within the observation frequency band; Based on the range and characteristic frequency points of the pile parameters, load parameters, and soil parameters, design multiple analysis conditions; For each condition, perform parametric finite element-infinite element coupled numerical simulation, and extract the pile-soil coupling loss quantification index with the transfer function amplitude ratio as the core by comparing the dynamic response of the pile field and the free field; S2. Parameterization and Quantification of Soil Layer Distribution Characteristics: The distribution information of multiple soil layers in each working condition is transformed into a set of standardized soil layer distribution characteristic parameters through the following sub-steps: S2.1 Establish a depth-normalized coordinate system and a shear wave velocity-normalized coordinate system; S2.

2. By introducing a logistic function or a double logistic function, the data points of each soil layer condition in the normalized coordinate system are fitted. The logistic function is: ； in For the parameters of the upper asymptote, For the lower asymptote parameters, For the slope parameter, For the inflection point position parameters, Normalized depth of soil layers The normalized depth of the soil layer is The corresponding normalized shear wave velocity; or the double logistic function: ； in , , For asymptote parameters, , For the slope parameter, , For the inflection point position parameters, Normalized depth of soil layers The normalized depth of the soil layer is The corresponding normalized shear wave velocity; The selected fitting function is fitted using the least squares method; S2.3 Extract the parameters from the logistic function or double logistic function as the soil layer distribution characteristic parameters. When using the logistic function, the... , , , The soil layer distribution characteristic parameters are defined as follows; when using the double logistic function, the... , , , , , , These are the soil layer distribution characteristic parameters; S3. Construction and training of neural network models: A neural network model is constructed, with the following input features: the pile parameters, the load parameters, the characteristic frequency points obtained in step S1, and the soil layer distribution characteristic parameters obtained in step S2; the output target is: the transfer function amplitude ratio extracted in step S1. The neural network model is trained using the dataset generated in steps S1 and S2; S4. Pile-soil coupling loss prediction: Input the actual parameters of the target project into the trained neural network model, and output the predicted value of the amplitude ratio of the transfer function, thereby realizing the rapid prediction of pile-soil coupling loss.

2. The method of claim 1, wherein, In step S1, the pile-soil coupling loss quantification index is a transfer function amplitude ratio which is obtained by: In the numerical simulation, the time history data of the vertical vibration acceleration at the center point of the pile head is extracted as the response of the pile field; In the same model without piles, the time history data of vertical vibration acceleration at the same location point are extracted as the free field response; respectively, and then performing fast Fourier transform on the time-history data of the responses of the piling site and the free field respectively to obtain the amplitude spectrum of each and ; The amplitude ratio of the transfer function is calculated as follows: ； The transfer function amplitude ratio The amplitude ratio values corresponding to each characteristic frequency within the target frequency band are taken as the output target of the neural network training in step S3.

3. The method of claim 1, wherein, In step S1, the pile parameters include pile diameter and pile length, the load parameters include the distance between the excitation source and the receiver, the soil parameters include the shear wave velocity and thickness of each soil layer, and the characteristic frequency point is determined by the sampling frequency and the number of sampling points.

4. The method of claim 3, wherein, The preferred range for the pile diameter is 0.4m to 1.6m, the preferred range for the pile length is 10m to 40m, the preferred range for the distance between the excitation source and the receiver is 10m to 50m, the preferred range for the soil wave velocity is 150m / s to 800m / s, and the preferred range for the finite element-infinite element coupled model is the length of the finite element region. Width The optimal range is (50m-70m). (25m-35m) (40m-50m), the dimensions of the infinite elemental region: length Width The optimal depth is (80m-100m). (50m-70m) (60m-70m), in the finite element-infinite element coupled model, the global mesh size of the finite element region is preferably 0.1m-0.3m.

5. The method of claim 1, wherein, The establishment of the depth-normalized coordinate system and the shear wave velocity-normalized coordinate system in step S2.1 includes: Establish a depth-normalized coordinate system, where the normalized depth is the ratio of the depth at the midpoint of the soil layer to the reference depth; Establish a normalized coordinate system for shear wave velocity, where the normalized shear wave velocity is the ratio of the soil layer shear wave velocity to the reference soil layer shear wave velocity.

6. The method of claim 5, wherein, The method also includes a sensitivity analysis step to determine whether the influence of the soil layer below the pile tip is lower than a preset threshold, wherein the soil layer below the pile tip does not include the soil layer where the pile tip is located. When the influence of the soil layer below the pile tip is lower than the preset threshold, the reference depth is the soil layer from the ground to the pile tip, and the reference soil layer is the soil layer where the pile tip is located. When the influence of the soil layer below the pile tip is not less than the preset threshold, the reference depth is the total soil thickness, and the reference soil layer is the bottommost soil layer. The preset threshold is determined through systematic sensitivity analysis, and is preferably 5%.

7. The method of claim 1, wherein, The dataset consisting of the pile parameters, load parameters, and characteristic frequency points obtained in step S1, the soil layer distribution characteristic parameters obtained in step S2, and the transfer function amplitude ratios that correspond one-to-one with the input features obtained in step S1, is divided into a training set, a validation set, and a test set. The training set is used for parameter training of the neural network model, the validation set is used for performance monitoring and early stopping during the training process, and the test set is used for final model performance evaluation. The neural network model is a feedforward neural network, including an input layer, at least one hidden layer, and an output layer; The number of neurons in the input layer is consistent with the dimension of the input features; The output layer contains a neuron for outputting the amplitude ratio of the transfer function; The number of hidden layers and neurons is determined by cross-validation. The hidden layer uses an activation function, whose mathematical expression is ; represents the net input of a neuron, and the calculation formula is: ; represents the connection weight between the current neuron and the th neuron in the previous layer; represents the output value of the th neuron in the previous layer; bias parameter of the current neuron; The output layer uses a linear activation function to ensure that the output value covers the actual range of the transfer function amplitude ratio.

8. The method of claim 7, wherein, The training of the neural network model employs a complete iterative process including forward propagation and back propagation; the forward propagation is used to calculate the network's predicted output, and the back propagation is used to calculate the gradient of the loss function with respect to the network parameters. The cross-validation method uses k-fold cross-validation: the training set data is randomly divided into k mutually exclusive subsets; each subset is used as a validation subset, and the remaining k-1 subsets are used as training subsets; k training and validation cycles are performed for each candidate network structure. The training of the neural network model uses the training mean squared error as the loss function, and its calculation formula is as follows: ； wherein is the true transfer function amplitude ratio in the training subset, is the predicted value of the neural network for the training subset, denotes the number of the operating condition in the training subset: 1, 2, 3, and so on, is the number of samples in the training subset; The validation of the neural network model uses the validation mean squared error as the loss function, and its calculation formula is as follows: ； wherein are the true transfer function amplitude ratios in the validation subset, are the predicted values of the neural network for the validation subset, denotes the i-th operating condition in the validation subset: 1, 2, 3, and so on, is the number of validation set samples; Select k rounds The network structure with the minimum average mean square error is taken as the optimal network structure, and the subsequent neural network training and verification processes use the network structure. The neural network model employs early stopping to prevent overfitting during training, specifically as follows: The mean squared error loss value on the validation set is continuously monitored during the training process Here the validation set is the initial total data split validation set, not the validation subset in the above k-fold cross-validation, and the validation set mean squared error is calculated using the true transfer function amplitude ratio in the validation set; When the mean squared error of the validation set no longer decreases to a new minimum value within several consecutive training cycles, the training process is terminated early, and the model parameters at the point when the mean squared error of the validation set is the lowest are saved. The model is evaluated using a test set, and the final prediction model is obtained.

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