A rock burst intensity prediction method, device, medium and product

Abstract

This application discloses a method, device, medium, and product for predicting rockburst intensity, relating to the field of rockburst intensity prediction. The method includes: preprocessing a rock mechanics dataset to generate a preprocessed rock mechanics dataset; extracting the nonlinear interaction structure between the stress concentration coefficient and the elastic energy index using a symbolic regression method to generate a stress-energy coupling index; constructing an enhanced feature vector based on the preprocessed rock mechanics dataset and the stress-energy coupling index; embedding and training a rockburst intensity prediction model to form a gray-box prediction framework; and generating a trained rockburst intensity prediction model by inputting a rock mass sample to be tested into the trained rockburst intensity prediction model and quantifying the uncertainty of the model output using a conformal prediction method based on category conditions to generate a candidate set of rockburst intensity for predicting rockburst intensity. This application improves the physical interpretability of the rockburst intensity prediction model and achieves quantitative characterization of prediction uncertainty.

Description

Technical Field

[0001] This application relates to the field of rockburst intensity prediction, and in particular to a method, equipment, medium, and product for rockburst intensity prediction. Background Technology

[0002] Rockburst is a common dynamic disaster phenomenon during deep underground engineering excavation, and accurate prediction of rockburst intensity is crucial for ensuring engineering safety. While data-driven methods have improved prediction accuracy to some extent, most existing rockburst intensity prediction methods are typical black-box models. They typically use raw physical quantities as input features directly, lacking methods to extract structurally meaningful interactive features from the data. This makes it difficult to explicitly express the inherent nonlinear coupling relationship between stress concentration and elastic energy accumulation during rockburst formation, resulting in poor model physical interpretability. Furthermore, existing rockburst prediction methods often employ deterministic classification outputs, lacking a quantitative description of prediction uncertainty. Under complex geological conditions and when samples are at class boundaries or have high uncertainty, they struggle to provide a reliable basis for engineering decisions. Summary of the Invention

[0003] The purpose of this application is to provide a method, device, medium, and product for predicting rockburst intensity, in order to solve the problems of poor physical interpretability of the model and lack of quantitative description of prediction uncertainty.

[0004] To achieve the above objectives, this application provides the following solution.

[0005] In a first aspect, this application provides a method for predicting rockburst intensity, comprising the following steps.

[0006] Obtain the rock mechanics dataset and preprocess it to generate a preprocessed rock mechanics dataset.

[0007] Based on the preprocessed rock mechanics dataset, the nonlinear interaction structure between stress concentration factor and elastic energy index is extracted using the symbolic regression method to generate the stress-energy coupling index.

[0008] Based on the preprocessed rock mechanics dataset and the stress-energy coupling index, an enhanced feature vector is constructed. The enhanced feature vector is then embedded and used to train the rockburst intensity prediction model, forming a gray box prediction framework and generating a trained rockburst intensity prediction model.

[0009] The rock mass sample to be tested is input into the trained rockburst intensity prediction model, and the uncertainty of the model output is quantified by combining the conformal prediction method based on category conditions to generate a candidate set of rockburst intensity for the rock mass sample to be tested, so as to predict the rockburst intensity.

[0010] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described rockburst intensity prediction method.

[0011] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described rockburst intensity prediction method.

[0012] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described rockburst intensity prediction method.

[0013] According to the specific embodiments provided in this application, this application has the following technical effects: This application employs a symbolic regression method to extract the nonlinear interaction structure between the stress concentration factor and the elastic energy index from a preprocessed rock mechanics dataset, generating a stress-energy coupling index. This index, along with the original physical quantities, is used to construct an enhanced feature vector to train a rockburst intensity prediction model. This stress-energy coupling index explicitly introduces structured features characterizing the synergistic effect of stress and energy, breaking the limitations of traditional black-box models and improving the physical interpretability of the rockburst intensity prediction model. Simultaneously, the rock mass sample to be tested is input into the trained rockburst intensity prediction model, and the uncertainty of the model output is quantified using a conformal prediction method based on category conditions. This generates a candidate set of rockburst intensities for the rock mass sample to be tested, thereby predicting the rockburst intensity. This effectively overcomes the shortcomings of traditional deterministic classification, which is prone to misjudgment under complex geological conditions or when the sample is at the category boundary. It achieves a quantitative characterization of prediction uncertainty, thus significantly improving the reliability, stability, and engineering applicability of the rockburst intensity prediction results. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a flowchart illustrating a rockburst intensity prediction method provided in an embodiment of this application.

[0016] Figure 2 This is a schematic diagram showing the statistical distribution of stress concentration factors under different rockburst intensity levels, provided as an embodiment of this application.

[0017] Figure 3This is a schematic diagram showing the statistical distribution of the brittleness coefficient under different rockburst intensity levels, as provided in an embodiment of this application.

[0018] Figure 4 This is a schematic diagram showing the statistical distribution of the elastic energy index under different rockburst intensity levels, as provided in an embodiment of this application.

[0019] Figure 5 A schematic diagram of the complexity-error distribution and empirical Pareto front of the symbolic regression results provided in one embodiment of this application over 100 independent runs.

[0020] Figure 6 A schematic diagram illustrating the reproducibility of the dominant coupled topology in 100 independent runs of the symbolic regression results provided in an embodiment of this application.

[0021] Figure 7 A schematic diagram showing the frequency of occurrence of the top few summing algebraic forms in 100 independent runs of the symbolic regression results provided in an embodiment of this application.

[0022] Figure 8 This is a schematic diagram of the empirical density distribution of samples and strong impact events provided in an embodiment of this application.

[0023] Figure 9 The coupling index contour map and the rockburst intensity classification diagram are provided for an embodiment of this application.

[0024] Figure 10 This diagram illustrates the ensemble convergence and generalization stability of a random forest model provided in an embodiment of this application.

[0025] Figure 11 A SHAP dependency graph of various categories of SC and EEI is provided for one embodiment of this application; wherein, Figure 11 Used to display category-specific interaction patterns. Figure 11 (a) in the diagram is a schematic diagram of the stress-energy coupling mechanism of L0; Figure 11 (b) in the diagram is a schematic diagram of the stress-energy coupling mechanism of L1; Figure 11 (c) in the diagram is a schematic diagram of the stress-energy coupling mechanism of L2; Figure 11 (d) in the figure is a schematic diagram of the stress-energy coupling mechanism of L3.

[0026] Figure 12 This is a schematic diagram of the confusion matrix of a random forest model deployed on an independent test set, provided in an embodiment of this application.

[0027] Figure 13 This is a schematic diagram illustrating the uncertainty quantification of a category-conditional conformal prediction method; where, Figure 13 (a) in the diagram is a schematic diagram of the distribution of prediction set size (efficiency analysis); Figure 13 (b) in the diagram is a schematic of the empirical coverage under the category condition. Detailed Implementation

[0028] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0029] To make the objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0030] like Figure 1 As shown in the figure, this application provides a method for predicting rockburst intensity, including the following steps.

[0031] S1: Obtain the rock mechanics dataset and preprocess the rock mechanics dataset to generate a preprocessed rock mechanics dataset.

[0032] S2: Based on the preprocessed rock mechanics dataset, the nonlinear interaction structure between the stress concentration factor and the elastic energy index is extracted using the symbolic regression method to generate the stress-energy coupling index.

[0033] S3: Based on the preprocessed rock mechanics dataset and the stress-energy coupling index, construct an enhanced feature vector, embed the enhanced feature vector into and train the rockburst intensity prediction model to form a gray box prediction framework, and generate a trained rockburst intensity prediction model.

[0034] S4: Input the rock mass sample to be tested into the trained rockburst intensity prediction model, and combine the conformal prediction method based on category conditions to quantify the uncertainty of the model output, and generate a candidate set of rockburst intensity for the rock mass sample to be tested, so as to predict the rockburst intensity.

[0035] This application extracts the nonlinear interaction structure between stress concentration factor and elastic energy index from the preprocessed rock mechanics dataset using symbolic regression, generates a physically meaningful stress-energy coupling index, and embeds it into the rockburst intensity prediction model to form a gray box prediction framework. At the same time, it combines a conformal prediction method based on category conditions to realize the quantitative expression of prediction uncertainty, thereby improving the accuracy, interpretability and reliability of rockburst intensity prediction.

[0036] In an exemplary embodiment, step S1 involves preprocessing the rock mechanics dataset to generate a preprocessed rock mechanics dataset, specifically including: S11: Perform a repeatability check on the rock mechanics dataset to determine the checked rock mechanics dataset; the rock mechanics dataset includes the stress concentration factor, brittleness factor, elastic energy index, and rockburst intensity level of multiple rock mass samples.

[0037] S12: Perform physical rationality screening on the inspected rock mechanics dataset to ensure that the stress concentration factor, brittleness factor, and elastic energy index are all positive, and determine the screened rock mechanics dataset.

[0038] S13: Perform global Windsorization on the selected rock mechanics dataset, truncating the stress concentration factor, brittleness factor, and elastic energy index to the range of the 1st to 99th percentile, to generate the preprocessed rock mechanics dataset.

[0039] In practical applications, a rock mechanics dataset containing 761 records was constructed by integrating rockburst case data from publicly available literature and engineering reports. Each record includes the stress concentration coefficient (SC), brittleness coefficient (BC), elastic energy index (EEI), and the corresponding rockburst intensity level. The construction process of the rock mechanics dataset emphasized the traceability and consistency of data sources to ensure the reliability of subsequent modeling processes.

[0040] To ensure data quality, the rock mechanics data in the dataset underwent preprocessing, including: performing duplicate checks on all records to remove duplicate samples; conducting physical plausibility screening to ensure that SC, BC, and EEI are all positive; and performing global Windsoring on SC, BC, and EEI to reduce the impact of extreme measurements while preserving the variability of physical meaning, truncating them to the 1st to 99th percentile. This processing does not delete observations, but only limits the impact of extreme values ​​that may arise from inconsistencies in reporting among independent studies. Given that symbolic regression is sensitive to outliers, this approach helps in the identification of stable structures without altering the class composition or introducing label information.

[0041] Considering the natural class imbalance between rock mass samples at different rockburst intensity levels, in order to maintain the original statistical relationship between stress concentration factor and elastic energy index, no resampling, data augmentation or class equalization processing is performed on the rock mechanics data.

[0042] like Figures 2-4 As shown, SC, BC, and EEI exhibit certain distribution differences and overlapping characteristics under different rockburst intensity levels, illustrating that rockburst intensity is difficult to classify using a single variable threshold.

[0043] Based on the above processing, the rock mechanics dataset retains physical meaning while possessing a stable statistical structure, providing a foundation for subsequent nonlinear interaction structure extraction.

[0044] In an exemplary embodiment, S2 specifically includes: S21: Perform a symbolic regression search in the candidate operator set containing addition, subtraction, multiplication, division and nonlinear transformation functions to determine the optimal expression; S22: Construct the stress-energy coupling index based on the optimal expression, wherein the expression for the stress-energy coupling index is: ;in, The stress-energy coupling index, SC The stress concentration factor is... EEI It is the elastic energy index.

[0045] In practical applications, based on rock mechanics datasets, a symbolic regression method is employed to search the candidate expression space, which consists of basic arithmetic operations and nonlinear transformations, to extract the nonlinear interaction structure between SC and EEI. The goal of the symbolic regression method is not to directly establish new rockburst constitutive criteria, but rather to search for low-complexity mathematical expressions that simultaneously satisfy prediction effectiveness, expression simplicity, and structural stability under the constraint of a given rockburst intensity level.

[0046] Specifically, candidate expressions are evaluated from three aspects: complexity-error tradeoff, number of operators, and structural reproducibility in multiple independent searches. The optimal expression, which is near the empirical Pareto front, has a small number of operators, and appears stably in repeated runs, is selected. The optimal expression obtained in this way serves as a data-consistent structural descriptor to characterize the nonlinear coupling mode between the stable stress concentration factor and the elastic energy exponential accumulation in rockburst case data, i.e., the nonlinear interaction structure.

[0047] The symbolic regression method is performed on a set of candidate operators that include addition, subtraction, multiplication, division and nonlinear transformation functions. The nonlinear transformation functions include at least one of exponential, logarithmic and power functions, or equivalent monotonic nonlinear transformation functions.

[0048] like Figures 5-7 As shown, the candidate expressions in the symbolic regression process exhibit a trade-off between complexity and fitting ability, illustrating the distribution characteristics of candidate expressions in terms of complexity and fitting performance. Among these, Figure 5The out-of-sample mean square error (MSE) is a core metric in regression modeling that measures the prediction accuracy and generalization ability of a model (i.e., a rockburst intensity prediction model): 1. Mean Square Error: Calculated as the average of the squares of the differences between the predicted and actual values. The smaller the value, the smaller the deviation between the model's prediction and the actual value, and the higher the prediction accuracy. 2. Out-of-sample: This refers to the fact that the MSE is calculated on a test set not used during model training. It reflects the model's generalization ability—that is, the model's actual performance on unfamiliar data—and is used to avoid the model performing well only on training data (overfitting). In short, the lower the value on the y-axis, the better the model's prediction performance on new data; the higher the value, the larger the prediction error and the worse the performance. Figure 7 The numerical constants 0.337, -0.080, -0.918, -0.694, and -0.765 are empirical constants automatically generated by the symbolic regression algorithm during the candidate expression search process. They are used to scale, shift, or adjust the values ​​of input variables or intermediate combination terms.

[0049] In the process of candidate expression selection, the following factors are considered to optimize the candidate expression: candidate expression complexity, fitting error level, simplicity of operation structure (few operators), and consistency of structure under different search conditions.

[0050] The expression form with a stable topological structure is preferred to ensure that the extracted nonlinear interaction relationship has good repeatability and structural stability.

[0051] The expression for the Physics-informed Stress-energy Residual Index (PISR) consists of a stress concentration term and an energy surplus term, and the coupling relationship between the two is characterized by a multiplicative interaction. This indicates the difference between energy accumulation and stress consumption.

[0052] To ensure the computability and physical plausibility of the exponent, the permissible domain of PISR satisfies EEI ≥ When EEI approaches When the energy surplus term approaches 0, the PISR decreases accordingly, indicating that under conditions of insufficient release elastic energy, stress concentration alone is insufficient to form high-intensity dynamic instability. For conditions where EEI ≥ The samples can be identified as low-energy residual or boundary transition states, and processed using boundary truncation, zeroing, or uncertainty set output methods.

[0053] like Figures 8-9As shown, PISR exhibits a distribution characteristic corresponding to rockburst intensity level in the characteristic space composed of stress concentration factor and elastic energy index.

[0054] This PISR, as a data-driven structural descriptor, is used to characterize the synergistic effect between stress concentration and elastic energy accumulation during rockburst incubation, and provides structured input features with physical constraints for subsequent random forest model construction.

[0055] It should be noted that the PISR is not used as a new rockburst constitutive relation or deterministic failure criterion, but rather as a structured input feature extracted from rockburst case data. This PISR is used to explicitly expose the nonlinear interaction structure between the stress concentration factor and the elastic energy index to the subsequent machine learning model (i.e., the rockburst intensity prediction model), giving the rockburst intensity prediction model an interpretable physical input structure during data-driven classification.

[0056] In an exemplary embodiment, S3 specifically includes: S31: The stress concentration factor, brittleness factor, elastic energy index, and stress-energy coupling index are combined to form an enhanced feature vector. ;in, To enhance feature vectors SC The stress concentration factor is... The brittleness coefficient, EEI The elastic energy index, The stress-energy coupling index is denoted as .

[0057] S32: The preprocessed rock mechanics dataset is divided into a training set and a validation set using a hierarchical random subsampling method.

[0058] S33: The enhanced feature vector is used as the explanatory variable of the rockburst intensity prediction model. The rockburst intensity prediction model is trained using the training set. Multiple training subsets are generated through bootstrapping sampling. Features are randomly selected for splitting during the construction of each decision tree to generate the trained rockburst intensity prediction model. The rockburst intensity prediction model is a gray box prediction framework based on a random forest model. The gray box prediction framework has structured physical feature constraints.

[0059] In practical applications, an enhanced feature vector for rockburst intensity classification is constructed based on the rock mechanics dataset and the stress-energy coupling index. By fusing the original physical variables (i.e., the preprocessed rock mechanics dataset) with the data-driven extracted coupled structural features (i.e., the stress-energy coupling index), a gray box feature system is formed.

[0060] In the preferred embodiment, the random forest model is selected as the base classifier because it is suitable for heterogeneous tabular rock mechanics data, has low sensitivity to hyperparameters, and can better characterize the nonlinear relationship between SC, BC, EEI, and PISR. During model selection, repeated hierarchical cross-validation can be used to compare models such as random forest, extreme gradient boosting (XGBoost), categorical feature boosting (CatBoost), support vector machine, k-nearest neighbors (KNN), and neural networks using a unified protocol. The macro-average F1 score (F1), equilibrium accuracy, and strong rockburst intensity level recall are used as evaluation indicators, and the model with stable overall performance is selected as the rockburst intensity prediction model.

[0061] This rockburst intensity prediction model uses an enhanced feature vector as input. During model construction, the enhanced feature vector X=[SC, BC, EEI, PISR] is used as input, where PISR, a derived structural feature obtained from symbolic regression, participates in the sample partitioning process of each decision tree in the random forest model along with the original physical variables. The enhancement of this feature vector does not replace the original variables; instead, it explicitly provides stress-energy nonlinear interaction information, i.e., the stress-energy coupling index, based on the original SC, BC, and EEI. This allows the decision trees to avoid implicitly approximating this interaction relationship without relying entirely on multi-level splitting, thus forming a gray-box prediction framework with structural input constraints. Therefore, the rockburst intensity prediction model explicitly includes the coupling relationship between stress and energy in its structure, realizing a random forest model that combines physical information constraints with data-driven modeling. This random forest model, through the ensemble of multiple decision trees, characterizes the nonlinear interaction relationship between input features, improving physical interpretability while retaining the high expressive power of the rockburst intensity prediction model.

[0062] In an exemplary embodiment, S4 specifically includes: S41: Based on the predicted probability of the rock mass sample to be tested belonging to each category calculated from the prediction results of the out-of-bag samples in the trained rockburst intensity prediction model, construct a non-consistency metric function and generate a non-consistency score.

[0063] S42: Based on the non-consistency score, the rock mass samples to be tested are grouped according to the rockburst intensity level, and the distribution of the non-consistency score outside the bag for each category of rock mass samples is statistically analyzed. The quantile threshold of the corresponding category is calculated, and the calibration threshold of each category is generated.

[0064] S43: For the rock mass sample to be tested, determine the predicted probability of belonging to each rockburst intensity level according to the trained rockburst intensity prediction model, and calculate the candidate inconsistency score.

[0065] S44: Based on the candidate non-consistency scores and the calibration thresholds for each category, determine whether to include the candidate rockburst intensity level in the prediction set, and generate a candidate rockburst intensity set for the rock mass sample to be tested, so as to predict the rockburst intensity.

[0066] In one exemplary embodiment, S44 specifically includes: S411: If the candidate non-consistency score is less than or equal to the quantile threshold of the corresponding category, the candidate rockburst intensity level is included in the prediction set to generate a rockburst intensity candidate set for the rock mass sample to be tested; wherein, if the rockburst intensity candidate set contains only one level, a single rockburst intensity prediction is output; if the rockburst intensity candidate set contains multiple rockburst intensity levels, it is output in the form of a multi-level risk set.

[0067] In one exemplary embodiment, after S3, the method further includes: S5: Introduce the SHAP method based on game theory to perform quantitative attribution analysis on the contribution of each input feature in the enhanced feature vector to the rockburst intensity classification process, and generate feature contribution analysis results; S6: Construct a feature dependency analysis model based on the feature contribution analysis results, generate a feature interaction graph, and reveal the main discrimination criteria of the trained rockburst intensity prediction model under different rockburst intensity states.

[0068] In practical applications, during the construction of the rockburst intensity prediction model, a hierarchical cross-validation strategy is employed to divide the rock mechanics data, and out-of-bag (OOB) samples are used for unbiased performance estimation. Simultaneously, the role of each variable in the rockburst intensity prediction model is evaluated through feature contribution assessment.

[0069] Based on the constructed random forest model, the rockburst intensity prediction model is trained and optimized to improve its generalization ability and stability. First, a hierarchical random subsampling method is used to divide the rock mechanics dataset into training and validation sets. Multiple repetitions of this division and training are performed while ensuring consistent distribution across categories, thereby reducing the impact of randomness from a single division. A division ratio of approximately 80% training set to 20% validation set is used, and multiple rounds of independent, repeated experiments are conducted.

[0070] During the training of the rockburst intensity prediction model, the random forest model generates multiple training subsets through bootstrap sampling and randomly selects some features for splitting during the construction of each decision tree, thereby achieving dual randomization of the sample and feature space, effectively reducing model variance and improving generalization performance. As the number of decision trees increases, the rockburst intensity prediction model gradually converges through ensemble learning without relying on optimization methods such as gradient descent.

[0071] To monitor the training process and convergence behavior of the rockburst intensity prediction model, a multi-class logarithmic loss function (Log-Loss) and classification accuracy are introduced as evaluation metrics to track and analyze the model's performance under different numbers of decision trees. Figure 10 As shown, with the increase in the number of base learners, the model performance gradually stabilizes and achieves a better generalization effect within a certain range.

[0072] In terms of parameter optimization, key parameters, including the number of decision trees, maximum tree depth, and minimum number of split samples, are adjusted based on performance on the validation set to determine the optimal parameter combination that balances prediction performance and model complexity. Through the above training and optimization process, a stable and reliable rockburst intensity prediction model is obtained.

[0073] In practical applications, to reveal the internal decision-making mechanism of the model and enhance the physical interpretability of the prediction results, this application introduces the SHapley Additive exPlanations (SHAP) method to perform quantitative attribution analysis on the contribution of each input feature in the enhanced feature vector to the rockburst intensity classification process.

[0074] Specifically, the trained rockburst intensity prediction model is used as the explanatory object, and the enhanced feature vector is selected as the explanatory variable. By constructing a training subset combination and calculating the marginal contribution of each feature to the model output under different combination conditions, the SHAP value of each feature in the prediction of each sample is obtained. This SHAP value represents the degree of positive or negative contribution of the feature relative to the baseline prediction level to the final classification result.

[0075] Based on this, statistical analysis was performed on different rockburst intensity levels (L0–L3) to construct category-specific SHAP distributions. By statistically summarizing and visualizing the SHAP values, the contribution direction and magnitude differences of each input feature under different categories were analyzed, thereby identifying the main discrimination criteria of the trained rockburst intensity prediction model under different rockburst intensity states.

[0076] In the stable level (no shock (L0)), higher SC and EEI usually correspond to negative contributions, reducing the probability of the sample being judged as a stable state; in the mild level (weak shock (L1)) and moderate level (moderate shock (L2)), the contributions of each feature show an alternating positive and negative distribution, reflecting the increased uncertainty in the discrimination of the transition zone between categories; in the strong level (strong shock (L3)), EEI and PISR usually show significant positive contributions, indicating that this feature has a high contribution weight in the model discrimination process.

[0077] Furthermore, to characterize the interaction relationships between features, a feature dependency analysis model was constructed based on SHAP values. SC was used as the principal variable, the corresponding SHAP value as the response variable, and EEI as the interaction variable for encoding, to analyze the coupling contribution patterns between features under different rockburst intensity levels. The analysis results can be visualized using a feature interaction diagram.

[0078] like Figure 11 As shown in (a)-(d), the stress concentration factor and elastic energy index exhibit differentiated characteristic interaction contribution relationships under different rockburst intensity levels, which are used to characterize the coupling influence mode between characteristics.

[0079] Analysis shows that, under steady-state conditions, the combination of high SC and high EEI usually corresponds to a negative contribution; in the transitional levels (weak shock (L1) and moderate shock (L2)), the interaction relationship exhibits a non-monotonic change characteristic; while in the severe level (strong shock (L3)), the combination of high SC and high EEI corresponds to a significant positive contribution, and the contribution magnitude increases, indicating that the coupling effect between features is enhanced under extreme conditions.

[0080] It should be noted that the above SHAP attribution analysis falls under the category of statistical interpretation. Its results are used to reveal the decision-making basis and characteristic response patterns of the model, and do not constitute a physical causal explanation or thermodynamic verification of the rock eruption mechanism.

[0081] Through the above analysis, the predictive behavior of the trained rockburst intensity prediction model (i.e., gray box model) can be transparently expressed, and the statistical contribution patterns of PISR and original rock mass mechanical indices under different intensity levels can be clarified.

[0082] In practical applications, the rock mass sample to be tested is input into the trained rockburst intensity prediction model, which outputs the corresponding rockburst intensity level prediction results and its corresponding prediction set.

[0083] like Figure 12As shown, the horizontal axis represents the predicted category, i.e., the predicted rockburst level, and the vertical axis represents the true category, i.e., the true rockburst level. The cell value represents the number or proportion of samples where the true level Li is predicted as Lj, i,j=0,1,2,3; the main diagonal represents the number of correct classifications, and the off-diagonal represents the number of misclassifications. The confusion matrix is ​​used to evaluate and analyze the model's classification results on independent datasets, which is used to illustrate the model's recognition ability and misclassification distribution characteristics under different rockburst intensity levels.

[0084] To further improve the reliability of the model in engineering applications and avoid the instability that may arise from traditional deterministic classification under complex conditions, this application introduces a category-conditional conformal prediction (CP) method to quantify the uncertainty of the model output.

[0085] First, construct the inconsistent metric function: in, This indicates the OOB prediction results based on the random forest model. Category The predicted probability. Inconsistency score. Used to measure the degree of consistency between model predictions and the true class.

[0086] Considering that strong rockburst intensity levels in rock mass samples typically belong to a minority of categories, using a conventional marginal conformal prediction method might result in overall coverage meeting requirements but insufficient coverage of strong rockburst categories. Therefore, this application employs a category-based conformal prediction method (Mondrian Conformal Prediction, MCP).

[0087] Specifically, the rock mass samples to be tested were grouped according to rockburst intensity levels L0, L1, L2, and L3. The non-consistency score distribution of the out-of-bag samples in each category was statistically analyzed, and then compared at a given significance level. Calculate the quantile threshold for the corresponding category. q L0 、q L1 、q L2 and q L3 Therefore, each rockburst intensity level has an independent calibration threshold, which can alleviate the problem of low coverage of a few high-intensity rock mass samples under category imbalance conditions.

[0088] At a given significance level The quantile thresholds are calculated based on the inconsistent score distributions of out-of-bag samples for each category. The out-of-bag sample probabilities generated during the training of the random forest model are used as an unbiased estimation source, thus eliminating the need for additional independent calibration datasets, avoiding data leakage, and improving data utilization efficiency.

[0089] For a rock mass sample x to be tested, the random forest model outputs the predicted probability p(k|x) of it belonging to each rockburst intensity level k. For each rockburst intensity level k, k = L0, L1, L2 or L3, the candidate inconsistency score is calculated. : like Then the rockburst intensity level k will be included in the prediction set. C ( x The final output C ( x This means that the rock mass sample under test is at a significance level. The candidate set of rockburst intensities is as follows. C ( x If only one level is included, then a single rockburst intensity prediction will be output; if C ( x If a sample contains multiple rockburst intensity levels, it indicates that the sample is located at the category boundary or mechanical transition zone and should be output as a multi-level risk set.

[0090] When the rock mass sample to be tested is located in a high-confidence region of the feature space, the prediction set usually contains only a single category; while when the sample is in a category boundary or uncertain region, the prediction set will contain multiple candidate categories, thereby avoiding over-deterministic judgments on high-risk rockburst events.

[0091] like Figure 13 As shown in (a)-(b), the distribution of the prediction set size and the empirical coverage of each category are used to characterize the uncertainty expression ability of the conformal prediction method, indicating that the present application can provide a small prediction set in most cases, and adaptively expand the prediction range in the uncertain region, while maintaining a coverage ability close to the preset confidence level in each category.

[0092] In summary, by combining the random forest model with a category-based conformal prediction method, this application achieves quantitative characterization of prediction uncertainty while outputting rockburst intensity classification results, thereby improving the reliability and engineering applicability of rockburst intensity prediction results.

[0093] (1) This application extracts PISR from SC and EEI through symbolic regression, so that the model no longer relies solely on the original rock mechanics indicators, but explicitly introduces structural features that can characterize the synergistic effect of stress concentration and elastic energy accumulation.

[0094] (2) In this application, PISR, SC, BC and EEI are used together to form an enhanced feature vector to establish a rockburst intensity prediction model, so that the rockburst intensity prediction model has a clear physical input structure while maintaining nonlinear discrimination capability.

[0095] (3) This application uses out-of-bag prediction probability to construct non-consistent scores and uses a conformal prediction method based on class conditions to calibrate the prediction thresholds for different rockburst intensity levels, which can output a controlled set of rockburst intensity predictions under class imbalance conditions.

[0096] (4) This application can convert deterministic rockburst intensity prediction into a set of single-level or multi-level predictions. When the rock mass sample to be tested is in a stable characteristic zone, a single level is output. When the rock mass sample to be tested is in a transition boundary or a high-risk uncertainty zone, multiple candidate rockburst intensity levels are output, thereby avoiding overly certain single-point judgments on strong rock mass samples.

[0097] (5) This application can interpret the statistical contributions of SC, BC, EEI and PISR through SHAP attribution analysis, providing a basis for engineers to understand model output, identify transitional risk samples and make risk classification decisions.

[0098] In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments. The computer device can be a server or a terminal. The computer device includes a processor, a memory, an input / output interface (I / O), and a communication interface. The processor, memory, and I / O interface are connected via a system bus, and the communication interface is connected to the system bus via the I / O interface. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device stores data to be processed. The I / O interface of the computer device is used for exchanging information between the processor and external devices. The communication interface of the computer device is used for communicating with an external terminal via a network connection. When the computer program is executed by the processor, it implements the above-described methods.

[0099] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0100] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0101] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0102] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by hardware related to computer program instructions. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0103] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0104] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0105] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for predicting rockburst intensity, characterized in that, include: Obtain a rock mechanics dataset and preprocess the rock mechanics dataset to generate a preprocessed rock mechanics dataset; Based on the preprocessed rock mechanics dataset, the nonlinear interaction structure between stress concentration factor and elastic energy index is extracted using the symbolic regression method to generate stress-energy coupling index. Based on the preprocessed rock mechanics dataset and the stress-energy coupling index, an enhanced feature vector is constructed, which is then embedded into and used to train the rockburst intensity prediction model to form a gray box prediction framework and generate a trained rockburst intensity prediction model. The rock mass sample to be tested is input into the trained rockburst intensity prediction model, and the uncertainty of the model output is quantified by combining the conformal prediction method based on category conditions to generate a candidate set of rockburst intensity for the rock mass sample to be tested, so as to predict the rockburst intensity.

2. The rockburst intensity prediction method according to claim 1, characterized in that, The rock mechanics dataset is preprocessed to generate a preprocessed rock mechanics dataset, specifically including: The rock mechanics dataset is subjected to a repeatability check to determine the checked rock mechanics dataset; the rock mechanics dataset includes the stress concentration factor, brittleness factor, elastic energy index, and rockburst intensity level of multiple rock mass samples; The physical rationality of the inspected rock mechanics dataset is screened to ensure that the stress concentration factor, brittleness factor, and elastic energy index are all positive, and the screened rock mechanics dataset is determined. The selected rock mechanics dataset is subjected to global Windsorization, and the stress concentration factor, brittleness factor, and elastic energy index are truncated to the range of the 1st to the 99th percentile to generate the preprocessed rock mechanics dataset.

3. The rockburst intensity prediction method according to claim 1, characterized in that, Based on the preprocessed rock mechanics dataset, the nonlinear interaction structure between stress concentration factor and elastic energy index is extracted using the symbolic regression method to generate a stress-energy coupling index, specifically including: A symbolic regression search is performed on the candidate operator set, which includes addition, subtraction, multiplication, division, and nonlinear transformation functions, to determine the optimal expression; The stress-energy coupling index is constructed based on the optimal expression, and the expression for the stress-energy coupling index is as follows: ;in, The stress-energy coupling index, SC The stress concentration factor is... EEI It is the elastic energy index.

4. The rockburst intensity prediction method according to claim 1, characterized in that, Based on the preprocessed rock mechanics dataset and the stress-energy coupling index, an enhanced feature vector is constructed. This enhanced feature vector is then embedded into and used to train the rockburst intensity prediction model, forming a gray-box prediction framework. The trained rockburst intensity prediction model is then generated, specifically including: The stress concentration factor, brittleness factor, elastic energy index, and stress-energy coupling index are collectively used to construct the enhanced feature vector. ;in, To enhance the feature vector, SC The stress concentration factor is... The brittleness coefficient, EEI The elastic energy index, The stress-energy coupling index; The preprocessed rock mechanics dataset is divided into a training set and a validation set using a hierarchical random subsampling method. The enhanced feature vector is used as the explanatory variable of the rockburst intensity prediction model. The rockburst intensity prediction model is trained using the training set. Multiple training subsets are generated through bootstrapping sampling. During the construction of each decision tree, features are randomly selected for splitting to generate the trained rockburst intensity prediction model. The rockburst intensity prediction model is a gray box prediction framework based on a random forest model. The gray box prediction framework has structured physical feature constraints.

5. The rockburst intensity prediction method according to claim 1, characterized in that, The rock mass sample to be tested is input into the trained rockburst intensity prediction model, and the uncertainty of the model output is quantified by combining the conformal prediction method based on category conditions to generate a candidate set of rockburst intensities for the rock mass sample to be tested, so as to predict the rockburst intensity. Specifically, this includes: Based on the predicted probability of the rock mass sample to be tested belonging to each category calculated from the prediction results of the out-of-bag sample in the trained rockburst intensity prediction model, an inconsistency metric function is constructed to generate an inconsistency score. Based on the inconsistency score, the rock mass samples to be tested are grouped according to the rockburst intensity level. The distribution of the out-of-bag inconsistency score of each category of rock mass samples is statistically analyzed, and the quantile threshold of the corresponding category is calculated to generate the calibration threshold for each category. For the rock mass sample to be tested, the predicted probability of belonging to each rockburst intensity level is determined according to the trained rockburst intensity prediction model, and the candidate inconsistency score is calculated. Based on the candidate inconsistency scores and the calibration thresholds for each category, it is determined whether to include the candidate rockburst intensity level in the prediction set, thereby generating a candidate rockburst intensity set for the rock mass sample to be tested, in order to predict the rockburst intensity.

6. The rockburst intensity prediction method according to claim 5, characterized in that, Based on the candidate inconsistency scores and the calibration thresholds for each category, it is determined whether to include the candidate rockburst intensity level in the prediction set, thereby generating a candidate rockburst intensity set for the rock mass sample to be tested, specifically including: If the candidate non-consistency score is less than or equal to the quantile threshold of the corresponding category, the candidate rockburst intensity level is included in the prediction set to generate a rockburst intensity candidate set for the rock mass sample to be tested; wherein, if the rockburst intensity candidate set contains only one level, a single rockburst intensity prediction is output; if the rockburst intensity candidate set contains multiple rockburst intensity levels, it is output in the form of a multi-level risk set.

7. The rockburst intensity prediction method according to any one of claims 1-6, characterized in that, Based on the preprocessed rock mechanics dataset and the stress-energy coupling index, an enhanced feature vector is constructed. This enhanced feature vector is then embedded into and used to train a rockburst intensity prediction model, forming a gray-box prediction framework. After generating the trained rockburst intensity prediction model, the process further includes: The SHAP method based on game theory is introduced to perform quantitative attribution analysis on the contribution of each input feature in the enhanced feature vector to the rockburst intensity classification process, and generate feature contribution analysis results. Based on the feature contribution analysis results, a feature dependency analysis model is constructed, a feature interaction graph is generated, and the main discrimination criteria of the trained rockburst intensity prediction model under different rockburst intensity states are revealed.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the rockburst intensity prediction method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the rockburst intensity prediction method according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the rockburst intensity prediction method according to any one of claims 1-7.

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