A 3D printing simulation sand peak strength confirmation method based on an SVR-BPNN model
By employing a hybrid modeling approach based on the SVR-BPNN model, and utilizing 3D printing and a two-stage optimization strategy, the efficiency and accuracy issues in the study of peak strength of sand were addressed, achieving efficient and reliable prediction of sand strength and promoting the data-driven transformation of geotechnical engineering.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- POWERCHINA HUADONG ENG CORP LTD
- Filing Date
- 2026-04-01
- Publication Date
- 2026-07-21
AI Technical Summary
Existing technologies for studying peak strength of sandy soil suffer from problems such as long cycle time, high cost, and low computational efficiency, making it difficult to meet the needs of rapid analysis at the engineering scale. Furthermore, traditional methods are easily affected by sample disturbances, and machine learning models such as BPNN suffer from slow training convergence and overfitting.
A hybrid modeling approach based on the SVR-BPNN model was adopted. Simulated sand particles were prepared by 3D printing. Combined with consolidated drained triaxial shear tests, a high-precision dataset was constructed. A two-stage optimization strategy was used to train the network, which fused the SVR and BPNN models. The SVR model was used to learn the nonlinear mapping relationship, and the BPNN model was used to predict the peak intensity.
It achieves high-precision prediction of peak strength of sandy soil, reduces reliance on traditional methods, provides a computationally efficient and reliable analysis method, and provides efficient parameter identification support for geotechnical engineering.
Smart Images
Figure CN122436069A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of engineering and technological science, and specifically relates to a method for confirming the peak strength of 3D printed simulated sand based on the SVR-BPNN model. Background Technology
[0002] Peak strength of sand is a key parameter in geotechnical engineering design. Its mechanical behavior is influenced by multiple factors, including particle size distribution, morphological characteristics, and confining pressure, exhibiting significant nonlinearity and complexity. Current research mainly relies on two methods: laboratory experiments and numerical simulations. Traditional experimental methods are limited by long cycles, high costs, and susceptibility to sample disturbances. While numerical methods such as discrete element method (DEM) can reveal the microscopic mechanical mechanisms of sand, they suffer from low computational efficiency and complex parameter calibration, making them unsuitable for rapid analysis at the engineering scale.
[0003] In recent years, with the innovation of artificial intelligence technology, machine learning has opened up a new paradigm for the study of the mechanical properties of sand. Compared with traditional methods, data-driven intelligent prediction technology has shown significant advantages in handling multivariate and strongly nonlinear problems, with characteristics such as high prediction efficiency, strong generalization ability, and wide applicability. This study focuses on two typical machine learning models: Backpropagation Neural Network (BPNN), with its powerful nonlinear mapping ability, can effectively simulate the strength characteristics of sand, but it has inherent defects such as being prone to getting trapped in local optima and slow training convergence. Support Vector Regression (SVR), as a machine learning method based on statistical learning theory, performs excellently in small sample modeling and high-dimensional data processing, and can effectively solve the overfitting problem. Summary of the Invention
[0004] The main objective of this invention is to provide a method for confirming the peak strength of 3D printed simulated sand based on the SVR-BPNN model, addressing the aforementioned problems.
[0005] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution:
[0006] A method for confirming the peak strength of 3D printed simulated sand based on the SVR-BPNN model includes the following steps:
[0007] S1. Simulated sand particles with different morphological parameters are prepared by 3D printing to quantify the sphericity, roundness and roughness of the particles;
[0008] S2. Conduct consolidated drained triaxial shear tests on the simulated sand to obtain peak strength data corresponding to different morphological parameters;
[0009] S3. By quantifying the relationship between particle morphology and mechanical properties, a high-precision experimental dataset is established.
[0010] S4. Construct SVR-BPNN hybrid modeling, use the SVR model to learn the nonlinear mapping relationship between morphological parameters and peak intensity, extract the support vectors and Lagrange multipliers of the SVR model, use the normalized support vectors as the initial weight matrix from the input layer to the first hidden layer of the BPNN, and generate the initial value of the bias term according to the multipliers.
[0011] S5. A two-stage optimization strategy combining frozen training and fine-tuning is adopted. First, the initial weight layers are fixed to train the deep network, and then the entire network is unfrozen for joint fine-tuning. Finally, the peak intensity prediction results are output.
[0012] While adopting the above technical solutions, the present invention may also adopt or combine the following technical solutions:
[0013] As a preferred embodiment of the present invention: in step S4, the support vectors of the SVR model are S V ={s v 1,s v 2,...,s v m}, Lagrange multipliers are ( - ).
[0014] As a preferred technical solution of the present invention, the support vector normalization in step S4 specifically includes the following steps:
[0015] S41. Calculate the L2 norm of the support vectors;
[0016] S42. Normalize each support vector: v'=v / ||v|| 2 ;
[0017] S43. Transpose the normalized vector matrix as the initial weight matrix of the BPNN.
[0018] As a preferred embodiment of the present invention: in step S4, the initial weight matrix is W(0)=[s v 1 T / ||s v 1||;s v 2 T / ||s v 2||;...;s v m T / ||s v m||].
[0019] As a preferred embodiment of the present invention: In step S4, the initial value of the bias term is as shown in the following formula:
[0020] b j (0) = 0.01 × Σ( - )×K(s vi ,x j )
[0021] In the formula, ( - ) is a Lagrange multiplier, and K is the RBF kernel function.
[0022] As a preferred technical solution of the present invention: In step S5, the two-stage optimization strategy includes: in the first stage, freezing the weights from the input layer to the first hidden layer and training only the subsequent network layers; in the second stage, unfreezing the frozen state of all network layers and performing joint fine-tuning.
[0023] As a preferred technical solution of the present invention: the SVR model adopts the RBF kernel function, the kernel parameter γ is determined by grid search method, and the penalty factor C is 50.
[0024] As a preferred embodiment of the present invention: the BPNN model contains 3-5 hidden layers, each hidden layer uses the ReLU function as its activation function, and the output layer uses a linear activation function.
[0025] Compared with the prior art, the present invention has the following beneficial effects:
[0026] This invention, based on 3D-printed simulated sand samples, obtains high-quality datasets through systematic indoor experiments and innovatively integrates BPNN and SVR models to achieve high-precision prediction of the peak strength of simulated sand. This invention not only systematically evaluates the applicability and prediction accuracy of different machine learning methods in sand strength prediction, but more importantly, it provides an intelligent analysis method for geotechnical engineering parameter identification that combines computational efficiency and prediction reliability, promoting the transformation of traditional soil mechanics research towards a data-driven paradigm. This invention reduces the reliance of traditional methods on high-cost indoor experiments, providing efficient and reliable technical support for sand strength prediction in geotechnical engineering, geological exploration, and other fields, and has significant engineering application value. Attached Figure Description
[0027] Figure 1 The flowchart shows the method for confirming the peak strength of 3D printed simulated sand based on the SVR-BPNN model provided by this invention. Detailed Implementation
[0028] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.
[0029] like Figure 1 As shown, a method for confirming the peak strength of 3D printed simulated sand based on the SVR-BPNN model specifically includes the following steps:
[0030] S1. Simulated sand particles with different morphological parameters (such as sphericity, roundness, and roughness) are prepared by 3D printing to quantify the sphericity, roundness, and roughness of the particles.
[0031] S2. Conduct consolidated drained triaxial shear tests on the simulated sand to obtain peak strength data corresponding to different morphological parameters;
[0032] S3. By quantifying the relationship between particle morphology and mechanical properties, a high-precision experimental dataset X={S p ,R a ,R p D m ,σ3'}, where S p For sphericity, R a For roundness, R p For roughness, D m σ is the fractal dimension, and σ3' is the effective confining pressure;
[0033] S4. Construct an SVR-BPNN hybrid model, using the SVR model to learn the nonlinear mapping relationship between morphological parameters and peak intensity, and extract the support vectors S of the SVR model. V ={s v 1,s v 2,...,s v m} and Lagrange multipliers ( - The normalized support vectors are used as the initial weight matrix W(0) from the input layer to the first hidden layer of the BPNN. v 1 T / ||s v 1||;s v 2 T / ||s v 2||;...;s v m T / ||s v m||] and the initial value of the bias term is generated according to the multiplier, as shown in the following formula:
[0034] b j (0) = 0.01 × Σ( - )×K(s vi ,x j )
[0035] In the formula, ( - ) are Lagrange multipliers, and K is the RBF kernel function;
[0036] S41. Calculate the L2 norm of the support vectors;
[0037] S42. Normalize each support vector: v'=v / ||v|| 2 ;
[0038] S43. Transpose the normalized vector matrix as the initial weight matrix of the BPNN.
[0039] The SVR model employs the RBF kernel function, with its kernel parameter γ optimized using a grid search method, and a penalty factor C of 50. The BPNN model contains 3-5 hidden layers, each using the ReLU activation function, and the output layer uses a linear activation function. This method effectively solves the training instability problem caused by random initialization in traditional BPNNs, while also overcoming the deficiency of insufficient prediction accuracy of a single SVR model under high confining pressure.
[0040] S5. A two-stage optimization strategy combining frozen training and fine-tuning is adopted. First, the initial weight layers are fixed to train the deep network, and then the entire network is unfrozen for joint fine-tuning. Finally, the peak intensity prediction results are output.
[0041] The two-stage optimization strategy includes: in the first stage, freezing the weights from the input layer to the first hidden layer and training only the subsequent network layers; in the second stage, unfreezing all network layers and performing joint fine-tuning.
[0042] Example
[0043] First, simulated sand samples were prepared using a high-precision LCD photopolymerization printer. By precisely controlling the printing parameters, sand grains with different morphological characteristics were obtained, including key parameters such as sphericity (0.65-0.92), roundness (0.3-0.8), surface roughness (2-15μm), and fractal dimension. After sample preparation, high-resolution microscopes and profilometers were used to precisely quantify each morphological parameter. Sphericity was calculated using the area-to-perimeter ratio method, roundness was obtained through profile curvature analysis, roughness was measured using a white light interferometer, and fractal dimension was determined using the multi-scale box counting method. Mechanical property testing was conducted using a fully automated triaxial testing system. Consolidated drained shear tests were performed under five different confining pressures (50, 100, 200, 300, and 400 kPa), with strict control over the saturation process and shear rate to ensure reliable peak strength data.
[0044] In the data processing stage, the original experimental data was first standardized to construct a dataset containing basic morphological parameters and derived features, which was then divided into training, validation, and test sets in a 7:2:1 ratio. The model construction adopted an SVR-BPNN hybrid architecture. First, the hyperparameters (penalty factor C and kernel parameter γ) of the SVR model were optimized using a grid search method. After training to obtain the initial prediction model, support vectors and Lagrange multipliers were extracted. These support vectors were normalized using the L2 norm and then transposed as the initial weight matrix from the input layer to the first hidden layer of the BP neural network. Simultaneously, initial values for the bias term were calculated based on the multipliers. The BPNN network adopted a 4-layer hidden structure (64-32-16-8 nodes), using the ReLU activation function, with the output layer having linear activation. The model training innovatively adopted a two-stage optimization strategy: the first stage froze the weight layers initialized by SVR, training only subsequent network layers; the second stage unfroze all network layers for joint fine-tuning, with the learning rate and number of training epochs adjusted accordingly. The test set results are shown in Table 1 below. The final model shows excellent prediction performance on the test set, with a mean absolute error of less than 10 kPa and a coefficient of determination R² of more than 0.97, which is significantly better than the traditional single model method.
[0045] Table 1. Test set results using different model methods
[0046]
[0047] The entire implementation process emphasizes the precision of parameter control and the standardization of data processing to ensure the reliability of prediction results and their applicability to engineering projects.
[0048] The technical solution of the present invention has been described in conjunction with the specific experimental procedures shown in the accompanying drawings. However, the scope of protection of the present invention is not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions resulting from such changes or substitutions will all fall within the scope of protection of the present invention.
Claims
1. A method for confirming the peak strength of 3D printed simulated sand based on the SVR-BPNN model, characterized in that, Includes the following steps: S1. Simulated sand particles with different morphological parameters are prepared by 3D printing to quantify the sphericity, roundness and roughness of the particles; S2. Conduct consolidated drained triaxial shear tests on the simulated sand to obtain peak strength data corresponding to different morphological parameters; S3. By quantifying the relationship between particle morphology and mechanical properties, a high-precision experimental dataset is established. S4. Construct SVR-BPNN hybrid modeling, use the SVR model to learn the nonlinear mapping relationship between morphological parameters and peak intensity, extract the support vectors and Lagrange multipliers of the SVR model, use the normalized support vectors as the initial weight matrix from the input layer to the first hidden layer of the BPNN, and generate the initial value of the bias term according to the multipliers. S5. A two-stage optimization strategy combining frozen training and fine-tuning is adopted. First, the initial weight layers are fixed to train the deep network, and then the entire network is unfrozen for joint fine-tuning. Finally, the peak intensity prediction results are output.
2. The method according to claim 1, characterized in that: In step S4, the support vectors of the SVR model are S V ={s v 1,s v 2,...,s v m}, Lagrange multipliers are ( - ).
3. The method according to claim 1, characterized in that: The support vector normalization in step S4 specifically includes the following steps: S41. Calculate the L2 norm of the support vectors; S42. Normalize each support vector: v'=v / ||v|| 2 ; S43. Transpose the normalized vector matrix as the initial weight matrix of the BPNN.
4. The method according to claim 1, characterized in that: In step S4, the initial weight matrix is W(0)=[s v 1 T / ||s v 1||;s v 2 T / ||s v 2||;...;s v m T / ||s v m||].
5. The method according to claim 1, characterized in that: In step S4, the initial value of the bias term is shown in the following formula: b j (0)=0.01×Σ( - )×K(s vi ,x j ) In the formula, ( - ) is a Lagrange multiplier, and K is the RBF kernel function.
6. The method according to claim 1, characterized in that: In step S5, the two-stage optimization strategy includes: in the first stage, freezing the weights from the input layer to the first hidden layer and training only the subsequent network layers; in the second stage, unfreezing all network layers and performing joint fine-tuning.
7. The method according to claim 1, characterized in that: The SVR model uses the RBF kernel function, and its kernel parameter γ is determined by grid search optimization. The penalty factor C is set to 50.
8. The method according to claim 1, characterized in that: The BPNN model contains 3-5 hidden layers, each with the ReLU activation function, and the output layer uses a linear activation function.