A soil elastic modulus prediction method based on a three-dimensional discrete element model and a convolutional neural network
By combining a three-dimensional discrete element model and a convolutional neural network, the problem of fitting the relationship between soil microstructure and macroscopic mechanical properties was solved, achieving accurate prediction of soil elastic modulus and improving prediction performance and network stability.
Patent Information
- Application Number
- CN202211536718.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-12-02
- Publication Date
- 2026-02-10
- Estimated Expiration
- 2042-12-02
AI Technical Summary
Existing technologies struggle to effectively utilize discrete element models to accurately fit the relationship between the microstructure and macroscopic mechanical properties of soil, especially given the heterogeneity and anisotropy of soil, making it difficult to accurately predict the elastic modulus of soil.
A three-dimensional discrete element model combined with a convolutional neural network is used. Soil structure information is extracted through image segmentation and grayscale preprocessing. A five-layer convolutional neural network is built for training. The model effect is evaluated by mean square error and accuracy, and the soil elastic modulus is predicted.
It achieves elastic modulus prediction that better matches the characteristics of soil structure, improves the accuracy and stability of prediction, reduces redundant information in the model, and enhances the generalization ability of the network.
Smart Images
Figure CN115730501B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geotechnical engineering technology in civil engineering, and in particular to a method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network. Background Technology
[0002] Compared to ideal and artificial materials, soil exhibits heterogeneity and anisotropy, resulting in significant differences in mechanical properties among soils with similar compositions and components, even with varying structures. Therefore, the importance of soil structure should be considered when evaluating its strength and other characteristics. The relationship between soil's mechanical properties and its structure is often complex, influenced by multiple factors, and characterized by high dimensionality, strong randomness, and nonlinearity. Its complex deformation and failure mechanisms are difficult to accurately fit using conventional mathematical formulas. Determining the relationship between soil's microstructure and macroscopic mechanical properties is one of the key concerns in soil mechanics.
[0003] Gong Xiaonan et al. (2000) summarized the influence of clay structure on its compressibility, strength envelope characteristics, stress-strain curve, and consolidation coefficient by incorporating existing research, and classified clay accordingly. He Weichao (2013) analyzed the relationship between the shear strength and microstructure of subgrade soil under freeze-thaw cycles using freeze-thaw tests, triaxial compression tests, and scanning electron microscopy. Xie Wenqiang et al. (2019) predicted the undrained shear strength of cohesive soil based on field test data from pore pressure static cone penetration tests using artificial neural networks. Yan et al. (2020) constructed a two-dimensional model with two significantly different mechanical properties using the finite element method, conducted repeated tests, and then learned from it using a convolutional neural network to predict the stress-strain curve from the model, achieving excellent fitting results.
[0004] However, the following problems still exist: Soil is a product of rock weathering and accumulation, and belongs to granular materials. The discrete element particle model is more in line with the structural characteristics of soil. The structure of the discrete element model is not fixed and cannot be directly converted into a matrix. It can only be regarded as an image, and its structural information extraction is much more difficult than that of the finite element model. Summary of the Invention
[0005] The purpose of this invention is to address the problems raised in the background art by providing a method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network. The method uses a slicing approach to extract the structural information of the discrete element model, and trains the neural network to better reflect the structural characteristics of real soil, thereby achieving prediction of the macroscopic elastic modulus of soil based on particle structure.
[0006] To achieve the above objectives, the present invention provides the following technical solution:
[0007] A method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network, characterized by the following steps:
[0008] Step 1: Construct a three-dimensional discrete element model, conduct a uniaxial compression test simulation, and extract the elastic modulus;
[0009] Step 2: Perform image segmentation on the 3D discrete element model to obtain 2D cross-sectional data, then perform grayscale preprocessing, and finally stack and reconstruct a new 3D data matrix.
[0010] Step 3: Match the three-dimensional data matrix with the elastic modulus from Step 1;
[0011] Step 4: Input a portion of the 3D data matrix into the 3D convolutional neural network for training, and use the mean squared error (MSE) as the loss function to detect its training effect;
[0012] Step 5: Input the remaining three-dimensional data matrix as a test set into the three-dimensional convolutional neural network, and use the accuracy D and mean error rate MER to evaluate the prediction effect of the soil elastic modulus.
[0013] Furthermore, in step 1, the three-dimensional discrete element model is constructed using commercial discrete element software. The material parameters are selected based on the mineral composition of the soil. Repeated uniaxial compression tests are conducted by changing the arrangement of the model particles and the particle size distribution. The stress-strain relationship is recorded and the macroscopic elastic modulus is obtained.
[0014] Furthermore, in step 2, the process of cutting the three-dimensional discrete element model to obtain two-dimensional cross-sectional data is accomplished by using Python to write an automated script under the Windows system to repeatedly run the post-processing module of the commercial discrete element software to obtain the model cross-section including the border, coordinates, and color.
[0015] Furthermore, in step 2, the grayscale preprocessing involves cropping the border and coordinates around the model, and then converting the image to grayscale to discard invalid color information and reduce resolution.
[0016] Furthermore, in step 3, the three-dimensional data and elastic modulus correspond to the three-dimensional data matrix extracted from each three-dimensional discrete element model and the elastic modulus obtained by performing uniaxial compression simulation on the model.
[0017] Furthermore, in step 4, the three-dimensional convolutional neural network is a neural network based on Python language and PyTorch framework, which is built in the VGG model with 5 convolutional layers, 5 activation layers, 5 pooling layers and 2 fully connected layers, used to train the correspondence between the three-dimensional data matrix and the elastic modulus. The learning rate and batch scale need to be set during training.
[0018] Furthermore, in step 4, the mean squared error (MSE) is a loss function used to detect the training effect of the 3D convolutional neural network and optimize the prediction model. Its value converges to a certain range as the training process progresses and no longer fluctuates drastically, indicating that the training is effective. Its expression is:
[0019]
[0020] Where x i The data is in three dimensions, where n is the batch size set during training, and R0 is the data size. i The elastic modulus value is extracted from the uniaxial compression test of the three-dimensional discrete element model. The elastic modulus value is fitted during the training of the 3D convolutional neural network. The five convolutional layers include four equal-width convolutional layers with a kernel size of 3×3×3 and a stride of 1, and one equal-width convolutional layer with a kernel size of 2×2×1 and a stride of 1. This represents the structure in the convolutional neural network that performs a linear weighted summation operation on the image pixel matrix and increases the number of channels. The five activation layers are non-linear activation functions connected after each convolutional layer, representing the structure in the convolutional neural network that improves the non-linear expression capability of the convolution process. The five pooling layers include four max-pooling layers with a kernel size of 2×2×2 and a stride of 2, and one max-pooling layer with a kernel size of 4×4×4 and a stride of 2. The first layer is a structure in a convolutional neural network that removes redundant information, reduces feature map size, and improves generalization ability. The two fully connected layers include one fully connected layer with 50 neurons and one fully connected layer with 10 neurons. These layers integrate the information features extracted after multiple convolutions, activations, and pooling processes and output the target value. This invention uses the dropout method on the fully connected layers to reduce overfitting. The learning rate is a tuning parameter in the optimization algorithm, which determines the step size in each iteration, causing the loss function to converge to its minimum. The batch size is the number of samples input to the neural network in each training batch.
[0021] Preferably, the convolution kernel is the weight used when processing a weighted average of pixels in a portion of the image; the number of channels is the number of feature maps; the stride is the distance the convolution kernel moves on the image each time it slides; the nonlinear activation function used in this invention is the ReLU function, whose equation is:
[0022]
[0023] Preferably, the pooling kernel is a function that filters redundant information and makes features more concentrated; the neuron is an abstraction, simplification and simulation of neurons in human brain tissue, and is a processing unit; the dropout method is that during each training, the neural network randomly discards a given proportion of neurons in the fully connected layer, and only the remaining neurons participate in training. During prediction, all neurons participate together, thereby improving the stability and generalization of the network.
[0024] Furthermore, in step 5, the expression for the accuracy D is:
[0025]
[0026] The expression for the mean error rate (MER) is:
[0027]
[0028] Where N is the number of samples during the test. Y is the arithmetic mean of the elastic modulus extracted from the uniaxial compression test of the three-dimensional discrete element model. i Y is the arithmetic mean of the elastic modulus predicted by the three-dimensional convolutional neural network.
[0029] Compared with existing technologies, this invention provides a method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network, which has certain technical practicality and the following beneficial effects:
[0030] (1) The three-dimensional discrete element model constructed in this invention is more consistent with the structural characteristics of soil.
[0031] (2) This invention enables the extraction of structural information from a three-dimensional discrete element model;
[0032] (3) The three-dimensional convolutional neural network constructed in this invention realizes the prediction of the elastic modulus of soil. Attached Figure Description
[0033] Figure 1 This is a flowchart of the present invention;
[0034] Figure 2 Extracting structural feature maps for the three-dimensional discrete element model of this invention;
[0035] Figure 3 This is a schematic diagram of the three-dimensional convolutional neural network structure of the present invention;
[0036] Figure 4 This is a schematic diagram of the training process of the three-dimensional convolutional neural network of the present invention;
[0037] Figure 5 This is a training effect diagram of the three-dimensional convolutional neural network of the present invention;
[0038] Figure 6 This is a diagram showing the prediction effect of the three-dimensional convolutional neural network of the present invention. Detailed Implementation
[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0040] Example 1
[0041] A method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network, such as... Figure 1 As shown, it includes the following steps:
[0042] Step 1: Construct a three-dimensional discrete element model to perform uniaxial compression simulation and extract the elastic modulus;
[0043] Step 2: Segment the 3D discrete element model to obtain 2D cross-sectional image data, perform grayscale preprocessing, and then stack and reconstruct a new 3D data matrix, such as... Figure 2 As shown;
[0044] Step 3: Match the three-dimensional data matrix with the elastic modulus from Step 1;
[0045] Step 4: Input a portion of the 3D data into the 3D convolutional neural network for training and use the mean squared error (MSE) as the loss function to detect its training effect;
[0046] Step 5: Input the remaining three-dimensional data into the three-dimensional convolutional neural network for testing, and use the accuracy D and mean error rate MER to evaluate its prediction effect on the elastic modulus of soil.
[0047] Step 4: Input a portion of the 3D data matrix into the 3D convolutional neural network for training, and use the mean squared error (MSE) as the loss function to detect its training effect;
[0048] Step 5: Input the remaining three-dimensional data matrix as a test set into the three-dimensional convolutional neural network, and use the accuracy D and mean error rate MER to evaluate the prediction effect of the soil elastic modulus.
[0049] Furthermore, in step 1, the three-dimensional discrete element model of this invention is constructed using MatDEM software with a single quartz sand material. The model material parameters are shown in Table 1. The model is set with 4096 particles, and the particle size is distributed between 0.375mm and 0.675mm. The arrangement of the model particles and the particle size distribution are changed to conduct 3500 sets of repeated uniaxial compression tests, and the stress-strain relationship is recorded to obtain the macroscopic elastic modulus.
[0050] Table 1 Model Material Parameters
[0051]
[0052]
[0053] Furthermore, in step 2, the process of cutting the 3D discrete element model to obtain 2D cross-sectional data is accomplished by using Python to write an automated script under the Windows system to repeatedly run the MatDEM post-processing module to obtain color cross-sectional screenshots of the model, including borders, coordinates, etc. In this invention, each 3D discrete element model is cut into 18 cross-sectional images. The preprocessing involves cropping the borders and coordinates around the model, grayscale conversion to discard invalid color information, and reducing the resolution. In this invention, the resolution is reduced to 72×72.
[0054] Furthermore, in step 3, the three-dimensional data and the elastic modulus correspond one-to-one. The three-dimensional structural data extracted from each three-dimensional discrete element model corresponds to the elastic modulus obtained by performing a uniaxial compression test on the model. In this invention, 3150 sets of three-dimensional data are used as the training set, and another 350 sets of three-dimensional data are used as the test set.
[0055] Furthermore, in step 4, the three-dimensional convolutional neural network is the VGG model referenced in this invention, built using the Python language and PyTorch framework, consisting of 5 convolutional layers, 5 activation layers, 5 pooling layers, and 2 fully connected layers. Figure 3 As shown, the correspondence between three-dimensional data and elastic modulus is used for training, such as... Figure 4 As shown, during training, the learning rate and batch size need to be set. This invention sets the learning rate to 0.1 and the batch sizes to 10(a), 20(b), 32(c), and 64(d), respectively, and increases the training scale to 15 rounds. The training effect is as follows. Figure 5 As shown; the mean squared error (MSE) is the loss function used in this invention to detect the training effect of a 3D convolutional neural network and optimize the prediction model. Its value converges to a certain range as the training process progresses and no longer fluctuates drastically, indicating that the training is effective. Its expression is:
[0056]
[0057] Where x i The data is in three dimensions, where n is the batch size set during training, and R0 is the data size. i The elastic modulus value is extracted from the uniaxial compression test of the three-dimensional discrete element model. The elastic modulus value is fitted during the training of the 3D convolutional neural network. The five convolutional layers include four equal-width convolutional layers with a kernel size of 3×3×3 and a stride of 1, and one equal-width convolutional layer with a kernel size of 2×2×1 and a stride of 1. This represents the structure in the convolutional neural network that performs linear weighted summation on the image pixel matrix and increases the number of channels. The five activation layers are non-linear activation functions connected after each convolutional layer, representing the structure in the convolutional neural network that improves the non-linear expression capability of the convolution process. The five pooling layers include four max-pooling layers with a kernel size of 2×2×2 and a stride of 2, and one max-pooling layer with a kernel size of 4×4×4 and a stride of 2. This represents the structure in the convolutional neural network that removes... The structure aims to reduce redundant information, decrease feature map size, and improve generalization ability. The two fully connected layers include one fully connected layer with 50 neurons and one fully connected layer with 10 neurons. This is a structure in convolutional neural networks that integrates information features extracted after multiple convolutions, activations, and pooling to output the target value. This invention uses the dropout method on the fully connected layers to reduce overfitting. The learning rate is a tuning parameter in the optimization algorithm, which determines the step size in each iteration, causing the loss function to converge to its minimum. The batch size is the number of samples input to the neural network in each training batch. The epoch refers to all samples passing through the neural network once and returning once.
[0058] The convolution kernel is the weight assigned when processing a weighted average of pixels in a portion of the image; the number of channels is the number of feature maps; the stride is the distance the convolution kernel moves on the image each time it slides; the nonlinear activation function used in this invention is the ReLU function, whose equation is:
[0059]
[0060] The pooling kernel is a function that filters redundant information and makes features more concentrated; the neuron is an abstraction, simplification and simulation of neurons in human brain tissue, and is a processing unit; the dropout method is a method in which the neural network randomly discards a given proportion of neurons in the fully connected layer during each training, and only the remaining neurons participate in training. During prediction, all neurons participate together, thereby improving the stability and generalization of the network.
[0061] Furthermore, in step 5, the expression for the accuracy D is:
[0062]
[0063] The expression for the mean error rate (MER) is:
[0064]
[0065] Where N is the number of samples during the test. Y is the arithmetic mean of the elastic modulus extracted from the uniaxial compression test of the three-dimensional discrete element model. i Y is the arithmetic mean of the elastic modulus predicted by the three-dimensional convolutional neural network.
[0066] With a learning rate of 0.1 and batch sizes of 10, 20, 32, and 64, the prediction performance of the 3D convolutional neural network of this invention is as follows: Figure 6 As shown, the accuracy of each batch of scales is less than 5.5%, and the error rate is less than 14%, indicating a good prediction effect and proving the effectiveness of this method in predicting the elastic modulus of soil.
[0067] The method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network provided by this invention uses a slicing method to extract the structural information of the discrete element model, and trains the neural network to better match the structural characteristics of real soil. This method realizes the prediction of the macroscopic elastic modulus of soil based on particle structure and has certain reference value.
[0068] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network, characterized in that, Includes the following steps: Step 1: Construct a three-dimensional discrete element model, conduct a uniaxial compression test simulation, and extract the elastic modulus; Step 2: Perform image segmentation on the 3D discrete element model to obtain 2D cross-sectional data, then perform grayscale preprocessing, and finally stack and reconstruct a new 3D data matrix. Step 3: Match the three-dimensional data matrix with the elastic modulus from Step 1; Step 4: Input a portion of the 3D data matrix into a 3D convolutional neural network for training, and use mean squared error. It serves as a loss function to detect its training effectiveness; Step 5: Input the remaining 3D data matrices as the test set into the 3D convolutional neural network, and use accuracy... With mean error rate Evaluate the predictive effectiveness of soil elastic modulus.
2. The method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network according to claim 1, characterized in that: In step 1, the three-dimensional discrete element model is constructed using commercial discrete element software. The material parameters are selected based on the mineral composition of the soil. Repeated uniaxial compression tests are conducted by changing the arrangement of the model particles and the particle size distribution. The stress-strain relationship is recorded and the macroscopic elastic modulus is obtained.
3. The method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network according to claim 1, characterized in that: In step 2, the process of cutting the three-dimensional discrete element model to obtain two-dimensional cross-sectional data is accomplished by using Python to write an automated script under the Windows system to repeatedly run the post-processing module of the commercial discrete element software to obtain the model cross-section including the border, coordinates, and color.
4. The method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network according to claim 1, characterized in that: In step 2, the grayscale preprocessing involves cropping the border and coordinates around the model, and then converting the image to grayscale to discard invalid color information and reduce resolution.
5. The method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network according to claim 1, characterized in that: In step 3, the three-dimensional data and elastic modulus correspond to the three-dimensional data matrix extracted from each three-dimensional discrete element model and the elastic modulus obtained by performing uniaxial compression simulation on the model.
6. The method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network according to claim 1, characterized in that: In step 4, the three-dimensional convolutional neural network is built on the Python language and PyTorch framework. It consists of 5 convolutional layers, 5 activation layers, 5 pooling layers and 2 fully connected layers in the VGG model. It is used to train the correspondence between the three-dimensional data matrix and the elastic modulus. The learning rate and batch scale need to be set during training.
7. The method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network according to claim 6, characterized in that: In step 4, the mean square error Let $\frac{ ... ， in It is three-dimensional data. The batch scale set during training. The elastic modulus value is extracted from the uniaxial compression test of the three-dimensional discrete element model. The elastic modulus value is fitted during the training of the 3D convolutional neural network. The 5 convolutional layers include four convolutional layers with a kernel size of 3×3×3 and a stride of 1, and one convolutional layer with a kernel size of 2×2×1 and a stride of 1, representing a structure in the convolutional neural network that performs linear weighted summation on the image pixel matrix and increases the number of channels. The 5 activation layers are nonlinear activation functions connected after each convolutional layer, representing a structure in the convolutional neural network that improves the nonlinear expression capability of the convolution process. The 5 pooling layers include four max pooling layers with a kernel size of 2×2×2 and a stride of 2, and one pooling layer with a kernel size of 4... The 4x4 max-pooling layer with a stride of 2 is a structure in convolutional neural networks that removes redundant information, reduces feature map size, and improves generalization ability. The two fully connected layers include one fully connected layer with 50 neurons and one fully connected layer with 10 neurons. This structure integrates the information features extracted after multiple convolutions, activations, and pooling processes and outputs the target value. Dropout is applied to the fully connected layers to reduce overfitting. The learning rate is a tuning parameter in the optimization algorithm, which determines the step size in each iteration, causing the loss function to converge to its minimum. The batch size refers to the number of samples input into the neural network during each batch of training.
8. The method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network according to claim 7, characterized in that: The convolution kernel is the weight assigned when processing a weighted average of pixels in a portion of the image; the number of channels is the number of feature maps; the stride is the distance the convolution kernel moves on the image with each slide; the nonlinear activation function is selected from... Relu The function has the following equation: 。 9. The method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network according to claim 7, characterized in that: The pooling kernel is a function that filters redundant information and makes features more concentrated; the neuron is an abstraction, simplification and simulation of neurons in human brain tissue, and is a processing unit; the dropout method is a method in which the neural network randomly discards a given proportion of neurons in the fully connected layer during each training, and only the remaining neurons participate in training. During prediction, all neurons participate together, thereby improving the stability and generalization of the network.
10. The method for predicting the elastic modulus of soil based on a three-dimensional discrete element model and a convolutional neural network according to claim 1, characterized in that: In step 5, the accuracy The expression is: ， The average error rate The expression is: ， in The number of samples during testing. This represents the arithmetic mean of the elastic modulus extracted from the uniaxial compression test of the three-dimensional discrete element model. To predict the elastic modulus value using a 3D convolutional neural network, The arithmetic mean of the elastic modulus predicted by a three-dimensional convolutional neural network.