Method for machine learning assisted establishment of rock joint peak shear strength prediction model

Abstract

The present application relates to a method for machine learning aided establishment of rock joint peak shear strength prediction model, first, through feature screening, three-dimensional roughness parameter, normal pressure, basic friction angle and tensile strength of material are selected as representative parameters as input parameters of machine learning model; Based on support vector machine (SVM), genetic algorithm improved BP neural network (GA-BPNN) and random forest (RF), three commonly used machine learning algorithms are used to establish joint peak shear strength regression prediction model, and 10-fold cross-validation is used to test the prediction performance of each model; Then the sensitivity of the parameters in the machine learning model is analyzed, and the generalization performance of the established model is evaluated; Finally, the peak shear strength model obtained by machine learning is compared with four traditional peak shear strength models, and it is found that the machine learning model significantly improves the prediction performance, and has greater performance improvement in improving the prediction accuracy, reducing the root mean square error and the average absolute error.

Description

Technical Field

[0001] This invention relates to the field of rock joint peak shear strength prediction models, specifically a method for establishing rock joint peak shear strength prediction models with machine learning assistance. Background Technology

[0002] Natural rock masses contain numerous randomly distributed joints. Compared to intact rock masses, the presence of joints reduces the strength and stability of the rock mass to some extent. In the design of rock slopes or underground engineering projects, the shear strength of joints is an important parameter to consider. Therefore, accurately assessing and predicting the shear strength of joints has always been a hot topic in geotechnical engineering. Over the past few decades, researchers have proposed numerous theoretical models or empirical formulas for joint shear strength based on shear tests. However, the shear strength of joint surfaces is influenced by multiple factors, and the parameters used to describe the shear strength of joint surfaces vary from person to person. Researchers studying from different perspectives may use different parameters, thus deriving different shear strength models. Due to the uncertainty and complexity of geotechnical materials, and with the continuous improvement of computer computing efficiency, more and more researchers tend to use machine learning algorithms to solve problems influenced by multiple factors. Machine learning algorithms can learn from raw data without prior assumptions, capture potential correlations between information, discover hidden patterns between data, and thus predict unknown data. Compared with traditional empirical models, machine learning algorithms, due to their powerful nonlinear mapping capabilities, can generally improve prediction accuracy.

[0003] In predicting the peak shear strength of joint surfaces, traditional shear strength models are based on specific experimental datasets, and their expressions are mostly derived from the analysis and fitting of experimental data. While more accurate shear strength prediction models may exist in unknown forms, the large number of parameters involved in current models and the influence of multiple factors make in-depth analysis of experimental data increasingly difficult. Therefore, considering that the description of the complex nonlinear relationship between joint surface shear strength and multiple parameters is currently limited to traditional empirical formulas, there are few reports on joint peak shear strength prediction models based on machine learning algorithms. This paper employs three common machine learning algorithms—Support Vector Machine (SVM), Genetic Algorithm-Improved Backpropagation Neural Network (GA-BPNN), and Random Forest (RF)—combined with a larger shear test dataset, to construct a nonlinear mapping relationship between the peak shear strength of joint surfaces and related parameters, and establish a machine learning regression prediction model for joint peak shear strength. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the prior art by providing a method for using machine learning to assist in establishing a prediction model for the peak shear strength of rock joints.

[0005] This invention provides a method for establishing a machine learning-assisted model for predicting the peak shear strength of rock joints, comprising the following steps:

[0006] S1. By statistically analyzing the parameters used in the traditional rock joint peak shear strength model, parameters related to rock joint peak shear strength are initially selected, and a rock joint peak shear strength database for machine learning is established.

[0007] S2. Perform feature selection, further process and analyze the selected feature parameters, eliminate or merge redundant parameters, select the most suitable features and determine the final input parameters.

[0008] S3. Use a scaling method of standardization or min-max normalization to scale the values ​​of the final selected feature parameters. At the same time, divide the processed dataset into a training set and a test set according to a certain ratio. The training set will be used to train the machine learning model, and the trained model will be used to make predictions on the test set.

[0009] S4. Establishing a machine learning model for the peak shear strength of rock joints and evaluating the model accuracy. Three machine learning algorithms were selected to establish regression analysis models to predict the peak shear strength of joints: Support Vector Machine (SVM), Genetic Algorithm-Improved Backpropagation Neural Network (GA-BPNN), and Random Forest (RF). The three machine learning models were trained on the training set and used for prediction on the test set. The performance of the models was evaluated using the following three metrics: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination (R²). 2 The calculation formula is as follows:

[0010]

[0011]

[0012]

[0013] In the formula, y i It is the actual value. These are model predictions. The average of the true values, i.e. n is the total number of data points.

[0014] R 2 The value of R reflects the goodness of fit of the regression model; the closer to 1, the better the fit, and the closer to 0, the worse the fit. MAE calculates the mean of the absolute error between the actual and predicted values, reflecting the actual error situation. RMSE, on the other hand, calculates the root mean square of the deviation between the actual and predicted values, and is more sensitive to larger error values ​​(outliers). Both have dimensions consistent with the actual values. Generally speaking, R...2 The larger the value, the smaller the MAE and RMSE, indicating a higher accuracy of the trained model.

[0015] In the process of building machine learning models, it is necessary to optimize hyperparameters based on the characteristics of the parameters involved in each model and select the optimal model hyperparameters, including the kernel function, regularization coefficient C, and kernel parameter g in the support vector machine model; the number of hidden layers and neurons in the neural network model; the maximum number of generations, population size, crossover probability, and mutation probability in the optimization part of the genetic algorithm; and the minimum number of leaves and the number of trees in the random forest model.

[0016] At the same time, 10-fold cross-validation is performed, which means that the training set is further subdivided into 10 subsets without repetition. Nine subsets are used as training subsets and the remaining one is used as validation subset. This process is repeated 10 times to obtain 10 trained models and corresponding model performance evaluations.

[0017] S5. Analyze the parameter sensitivity of the established rock joint peak shear strength prediction model and perform predictions and evaluations on a new dataset. To determine the range and control variables of the new dataset, the process of establishing the new dataset involves using the minimum and maximum values ​​of each input parameter in the original dataset as the upper and lower bounds for that parameter, generating 1000 new data points with equally spaced variations. When performing sensitivity analysis on a certain parameter in the model, only that parameter is allowed to vary continuously, while the other parameters remain unchanged, and the values ​​of the other parameters are the mean values ​​of the corresponding parameters in the original dataset. Finally, evaluate the generalization performance of the established machine learning models and select the one with the best performance.

[0018] Compared with the prior art, the beneficial effects of the present invention are:

[0019] 1. Compared to traditional models, the peak shear strength model of joints established by machine learning does not rely on prior assumptions or require a predetermined expression. It directly constructs the complex nonlinear mapping between the peak shear strength of the joint surface and multiple parameters. Therefore, the peak shear strength prediction model established by machine learning has higher accuracy and precision. 2. Machine learning models are built on larger shear datasets, exhibiting stronger generalization ability and better applicability. 3. The peak shear strength model of joints established by machine learning has greater scalability. As the shear test database continues to expand, the peak shear strength prediction model of joints can be continuously improved and optimized. Because more data can be used to train the machine learning model, the accuracy, robustness, and generalization ability of the model in predicting shear strength will be further enhanced. Attached Figure Description

[0020] Figure 1 It is a statistical chart showing the frequency of use of key parameters in the traditional joint peak shear strength model;

[0021] Figure 2 It is a shear strength distribution map in the established peak shear strength database;

[0022] Figure 3 These are frequency histograms and cumulative percentage graphs of the four selected input parameters;

[0023] Figure 4 This is a diagram illustrating the division of the training and test sets;

[0024] Figure 5 This is a comparison graph of the predicted values ​​and actual values ​​of three machine learning models in the training and test sets;

[0025] Figure 6 This is a performance comparison chart of three machine learning models using 10-fold cross-validation;

[0026] Figure 7 In the 10-fold cross-validation of three machine learning models, R... 2 A comparison chart of the average values ​​of RMSE and MAE;

[0027] Figure 8 This is a graph showing the results of a sensitivity analysis of the parameters of three trained machine learning models.

[0028] Figure 9 This is a comparison chart of the peak shear strength predictions and actual experimental values ​​of four empirical models across the entire dataset;

[0029] Figure 10 This is a comparison chart of the peak shear strength predictions and actual experimental values ​​of three machine learning models on the entire dataset. Detailed Implementation

[0030] 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.

[0031] Step 1: Feature parameter selection and database establishment:

[0032] Statistical analysis was conducted on the parameters used in traditional rock joint peak shear strength models, and a total of 24 traditional joint peak shear strength models were collected, as shown in Table 1:

[0033] Table 1:

[0034]

[0035]

[0036] The frequency of use of each parameter in the main parameters used in the model listed in this paper is obtained by statistical analysis. Figure 1 As shown. By analyzing and comparing the parameters used in the traditional model ( Figure 1 ), except for the normal pressure σ n The basic friction angle φ of the joint surface b In addition, three-dimensional roughness related parameters Material tensile strength σ t JCS is used frequently. Further analysis shows that the three-dimensional roughness parameter in the model is mainly related to the tensile strength σ. t They are used together, such as models (11), (12), (14), (15), (19), while the parameter JCS is mainly used for the JRC-JCS model and its improved models, such as (4), (8), (16), (21).

[0037] Among numerous models and parameters, models based on Grasselli 3D roughness and their improved versions are more widely studied, with relatively consistent parameters. The preliminary selection of characteristic parameters related to the peak shear strength of rock joints is: normal pressure σ. n Basic friction angle φ b 3D morphological parameters of joint surfaces A0, C, and the tensile strength σ of the material t Based on the selected characteristic parameters, a database was established by statistically analyzing 127 sets of research data from different literature. The peak shear strength distribution in the database is as follows: Figure 2 As shown.

[0038] Step 2, Feature Selection:

[0039] Grasselli uses The form is used as an evaluation index for three-dimensional roughness and as an input parameter of its model. Tatone et al. used Grasselli's expression for describing the three-dimensional roughness of jointed surfaces in the range of 0 to 1. Integrating the curve yields the area under the curve, leading to a more widely applicable roughness parameter:

[0040]

[0041] Therefore, in order to reduce the data dimensionality, this paper will Combined with C into a single input parameter

[0042] Yang et al., Liu et al., and Tian et al. conducted statistical analysis on the parameter A0, finding that it is generally distributed within a small range of 0.45 to 0.55, with a mean around 0.5. Therefore, they concluded that A0 is not a suitable parameter for describing the three-dimensional roughness of joint surfaces. Liu et al. further assumed A0 to be a constant of 0.5 and substituted A0 = 0.5 into the Grasselli model, finding that the correlation coefficient between the calculated value and the original Grasselli model value reached over 99%, suggesting that the influence of small-range variations in A0 can be ignored. To further reduce the dimensionality of the features, this paper also assumes A0 to be a constant, i.e., ignores the influence of parameter A0, and does not use A0 as an input parameter for model training.

[0043] Ultimately, this paper selects four features: σ n φ b , and σ t Using these as input parameters, a machine learning regression prediction model is established between the four input parameters and the shear strength. The frequency histogram and cumulative percentage of the input parameters are as follows: Figure 3 As shown in Table 2, the input parameters and statistical values ​​of shear strength are as follows.

[0044] Table 2:

[0045]

[0046] Step 3: Data scaling and dataset partitioning:

[0047] The min-max normalization method is used to scale each column of features so that all features lie in the interval [0,1], which facilitates the training and prediction of machine learning models. The value of each sample point after scaling can be calculated using the following formula:

[0048]

[0049] In the formula, x norm This is the scaled value, where x is a sample point. min and x max These represent the minimum and maximum values ​​in the sample data set, respectively.

[0050] The processed dataset was divided into a training set and a test set in a 7:3 ratio. The training set contained 89 data sets, and the test set contained 38 data sets. A diagram illustrating the dataset partitioning is shown below. Figure 4 As shown. The training set will be used to train the machine learning model, and the trained model will make predictions on the test set.

[0051] Step 4: Establish a machine learning prediction model for the peak shear strength of rock joints:

[0052] Three machine learning algorithms were selected to build regression analysis models for predicting the peak shear strength of joints: Support Vector Machine (SVM), Genetic Algorithm-Improved Backpropagation Neural Network (GA-BPNN), and Random Forest (RF). Each machine learning model was trained on a training set and used for prediction on a test set. The performance of each model was evaluated using three metrics: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination (R²). 2 The calculation formula is as follows:

[0053]

[0054]

[0055]

[0056] In the formula, y i It is the actual value. These are model predictions. The average of the true values, i.e. n is the total number of data points.

[0057] In the process of building machine learning models, it is necessary to optimize hyperparameters based on the characteristics of the parameters involved in each model, and select the most suitable model hyperparameters. Through hyperparameter optimization, the kernel function in the support vector machine model is selected as a Gaussian kernel function, and the regularization coefficient C = 2. 5.2 The parameter g=2 of the kernel function -2.4 The neural network model was configured with 1 hidden layer, 5 hidden layer neurons, a maximum number of generations of the genetic algorithm optimization, a population size of 30, a crossover probability of 0.3, and a mutation probability of 0.1. The random forest model had a minimum of 2 leaves and 100 trees.

[0058] Three machine learning models were trained on the same training set and validated on the same test set, with the following results: Figure 5 As shown in the figure, on the training set, the prediction accuracy of all three machine learning models reached over 97%, with root mean square errors (RMSEs) ranging from 0.3 to 0.4 MPa, among which the RF model had the highest accuracy. On the test set, the prediction accuracy of all three machine learning models was over 96%, with RMS errors ranging from 0.3 to 0.44 MPa, among which the SVM model had the highest accuracy, reaching 98.3%. The similar accuracy and RMS error of the three machine learning models on the training and test sets indicate that the models optimized by hyperparameters did not exhibit overfitting.

[0059] Meanwhile, 10-fold cross-validation was performed during model training. This involved further subdividing the training set into 10 subsets without repetition, with 9 subsets used as training subsets and the remaining subset as validation subsets. This process was repeated 10 times to obtain 10 trained models and corresponding model performance evaluations. Figure 6 As shown. Statistical analysis of three performance metrics R in 10-fold cross-validation. 2 The average values ​​of RMSE and MAE are as follows: Figure 7 As shown. From Figure 7 It can be seen that on both the training and test sets, the SVM model outperforms the other two models in all three metrics; the GA-BPNN model outperforms the RF model in all three metrics on the training set.

[0060] Step 5: Perform predictions on the new dataset, analyze the parameter sensitivity of the established rock joint peak shear strength prediction model, and evaluate its generalization performance:

[0061] To determine the scope and control variables of the new dataset, the process of creating the new dataset involves using the minimum and maximum values ​​of each input parameter in the original dataset as the upper and lower bounds for that parameter, generating 1000 new data points with equally spaced variations. When performing sensitivity analysis on a specific parameter in the model, only that parameter is allowed to vary continuously, while the other parameters remain constant, with their values ​​equal to the mean of the corresponding parameters in the original dataset. For example, analyzing parameters... When the value changes, its minimum value of 5.13 and maximum value of 16.95 in the dataset are used as the upper and lower bounds of this parameter, and 1000 equally spaced data points are generated within this range. Meanwhile, the other three parameters remain unchanged, and the mean of the original dataset, φ, is used. b =35.8°, σ t =3.73MPa, σ n =1.57MPa. Figure 8 The machine learning model predicts the peak shear strength when four input parameters vary. Figure 8 It can be seen that the shear stress τ predicted by the SVM model and the GA-BPNN model... p The existence of a continuous and smooth functional relationship with continuously changing input parameters indicates that its generalization ability is good; while the RF model is similar to the SVM model and GA-BPNN model in terms of trend, the shear stress predicted by the RF model is smaller than the above two models, the curve is not smooth enough in a step shape, and the generalization performance is poor.

[0062] Comparative Example

[0063] To further illustrate the superior performance of the model of this invention in predicting the peak shear strength of joints, predictions were made using the four empirical models (Tian et al. model, Tatone model, Xia et al. model, Tang and Wong model) listed in Table 1 of the first step, along with the model of this invention, on the entire original dataset for further comparison and verification. The distribution of the predicted and experimental values ​​of the peak shear strength of the empirical models is shown below. Figure 9 As shown, the distribution of the predicted and experimental peak shear strength values ​​of the model of this invention is as follows: Figure 10 As shown in the table, the shear stress predicted by the machine learning model generally does not fluctuate much, with only a few predictions showing larger errors, and the accuracy of the predictions is above 97%. However, when the shear stress experimental value exceeds 3 MPa, the predicted values ​​calculated by the empirical model fluctuate greatly and cannot be accurately predicted. Furthermore, to provide a more quantitative comparison, Table 3 summarizes the performance of the machine learning model and the empirical model on three evaluation metrics, as well as the performance improvement of the machine learning model over the empirical model on these metrics. Compared to the empirical model, the machine learning model shows a 5%–12% improvement in prediction accuracy, a 38%–60% improvement in reducing the root mean square error, and a 47%–70% improvement in reducing the mean absolute error.

[0064]

[0065] Note: The three numbers in the performance improvement percentage represent the SVM model. ① GA-BPNN model ② and RF model ③ Performance improvement compared to empirical models.

[0066] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for establishing a prediction model for the peak shear strength of rock joints based on machine learning algorithms, characterized in that, Includes the following steps: S1. By statistically analyzing and comparing the parameters used in the traditional empirical model of peak shear strength of joints, we analyze the high-frequency parameters related to peak shear strength of rock joints and establish a database of peak shear strength of rock joints for machine learning based on a large amount of experimental data. In S1, the input parameters related to the peak shear strength of rock joints used for machine learning training are determined by statistically analyzing the frequency of parameters used in a large number of traditional empirical models of peak shear strength of rock joints. The selection process is reasonable and the selection results are more conducive to machine learning training. S2. Perform feature selection to reduce feature dimensionality and determine the most frequently used 3D roughness parameters. / (C+1), Normal pressure Basic friction angle and the tensile strength of the material As input parameters to the final machine learning model; three-dimensional morphology parameters of the joint surface , C and the tensile strength of the material ; In step S2, the parameters initially selected in S1 need to be further analyzed to eliminate or merge redundant parameters, reduce the number of input parameters used for machine learning, and finally determine the three-dimensional roughness parameters that are used most frequently. / (C+1), Normal pressure Basic friction angle and the tensile strength of the material Four parameters are used as input parameters for the machine learning model; S3. Scale the values ​​of the four selected feature parameters and divide the processed dataset into a training set and a test set in a 7:3 ratio. The training set will be used to train the machine learning model, and the trained model will be used to make predictions on the test set. The model will be compared and analyzed with the traditional empirical model of peak shear strength of rock joints to evaluate the performance of the prediction model. S4. The trained rock joint peak shear strength machine learning prediction model is used to analyze the parameter sensitivity of the model. A new dataset with a reasonable parameter range is constructed to predict and evaluate the model. The model with better performance is selected to evaluate the generalization ability of the model. In S3, three machine learning algorithms were selected to build regression analysis models to predict the peak shear strength of joints, including Support Vector Machine (SVM), Genetic Algorithm-Improved Backpropagation Neural Network (GA-BPNN), and Random Forest (RF). The obtained optimal weights and thresholds were then assigned to the BP neural network for training. For the GA-BPNN model with only 4 input parameters, a hidden layer was set with 5 neurons. In the Random Forest model, the minimum number of leaves was 2 and the number of trees was 100. The three machine learning models were trained on the training set and predicted on the test set, and their model performance was mainly evaluated using three metrics.

2. The method for establishing a rock joint peak shear strength prediction model based on machine learning algorithm according to claim 1, characterized in that, The three evaluation metrics are as follows: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination (R²). 2 The calculation formula is as follows: ； ； ； In the formula, It is the actual value. These are model predictions. The average of the true values, i.e. n is the total number of data points; the machine learning prediction model for peak shear strength of rock joints after training is compared and analyzed with the traditional empirical model for peak shear strength of rock joints to further verify the performance of the machine learning model.

3. The method for establishing a rock joint peak shear strength prediction model based on machine learning algorithm according to claim 1, characterized in that, In S4, the parameter analysis of the rock joint peak shear strength machine learning model is performed on a new dataset. The new dataset was not used for the training and validation of the machine learning model. It was artificially generated based on the range of parameter features of the original dataset, in order to further validate and compare the generalization performance of each machine learning model.

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