A method and system for predicting a frictional resistance coefficient

Abstract

The application discloses a kind of friction resistance coefficient prediction method and system, belong to mine ventilation safety technical field.The method first obtains historical sample set, adopts ISMOTE algorithm to carry out data enhancement by Mahalanobis distance, diversity interpolation strategy and uniqueness verification mechanism to train XGBoost model;AGDO algorithm is used again by progressive gradient momentum integral rule, dynamic gradient interaction rule and optimization operator rule to globally optimize model hyperparameter;The point prediction result of the friction resistance coefficient is predicted using the optimized model, and the prediction residual is non-parametrically fitted using kernel density estimation to construct the prediction confidence interval;Finally, the average marginal contribution of each input feature is quantified by SHAP analysis method, and the interpretability analysis is realized.The problem of insufficient model generalization ability, algorithm easily trapped in local optimum and only providing point prediction in the prior art is solved, and the reliability of ventilation network solution is improved.

Description

Technical Field

[0001] This invention belongs to the field of mine ventilation safety technology, specifically relating to a method and system for predicting friction resistance coefficient. Background Technology

[0002] The friction resistance coefficient of mine roadways is a key parameter characterizing the magnitude of frictional resistance between airflow and roadway walls. It is also the basis for calculating mine ventilation networks, adjusting airflow distribution, and analyzing ventilation energy consumption. The accuracy of its value directly affects the reliability of ventilation system design and the economy of its operation.

[0003] A method and system for predicting the friction resistance coefficient of mine ventilation is disclosed in Chinese patent document CN121257406B. The method includes constructing a numerical simulation geometric model and obtaining simulated data of the friction resistance coefficient of mine ventilation using the numerical simulation geometric model; constructing a prediction model of the friction resistance coefficient of the mine ventilation system based on an ensemble learning algorithm and optimizing the hyperparameters of the prediction model of the friction resistance coefficient of the mine ventilation system through an improved swarm intelligence algorithm; training and verifying the optimized prediction model of the friction resistance coefficient of the mine ventilation system based on historical measured data and simulated data; and predicting the friction resistance coefficient of the mine ventilation system using the trained prediction model of the friction resistance coefficient of the mine ventilation system.

[0004] However, the training data for this method mainly relies on numerical simulation. Although this can expand the sample size, the distribution deviation between the simulated data and the actual roadway conditions is difficult to eliminate. When faced with small-scale measured samples, the model's generalization ability is insufficient, making it difficult to guarantee prediction accuracy. Furthermore, the improved swarm intelligence algorithm used in this method is prone to getting stuck in local optima in the later stages of optimization, resulting in hyperparameter configurations that are not globally optimal. In addition, the model only provides point prediction results and fails to reflect the range variation characteristics of the friction resistance coefficient, making it impossible to accurately predict the friction resistance coefficient of mine roadways and reducing the reliability of the ventilation network solution results. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for predicting friction resistance coefficient, so as to solve the technical problem in the prior art that the hyperparameters of the prediction model are prone to getting trapped in local optima, which leads to the inability to accurately predict the friction resistance coefficient and thus reduces the reliability of the ventilation network solution results.

[0006] To achieve the above objectives, the present invention provides a method for predicting the friction resistance coefficient, comprising the following steps: Data processing steps: Obtain historical sample sets and train the XGBoost model based on the historical sample sets; each sample in the historical sample set includes input features and measured values ​​of friction drag coefficient.

[0007] Hyperparameter optimization steps: The AGDO algorithm is used to optimize the hyperparameters of the XGBoost model to obtain the optimized XGBoost model; the AGDO algorithm realizes global optimization of hyperparameters through the asymptotic gradient momentum integral rule, dynamic gradient interaction rule and optimization operator rule.

[0008] Model prediction steps: Use the XGBoost optimization model to predict the sample to be predicted, and obtain the point prediction results of the friction drag coefficient.

[0009] By adopting the above technical solution, this invention obtains a historical sample set containing input features and measured values ​​of friction resistance coefficient and trains an XGBoost model. Then, it uses the AGDO algorithm to optimize the hyperparameters of the XGBoost model. The AGDO algorithm uses the asymptotic gradient momentum integral rule, the dynamic gradient interaction rule, and the optimization operator rule to achieve global optimization of hyperparameters, thereby obtaining the globally optimal hyperparameter configuration. This effectively overcomes the defect of improved swarm intelligence algorithms in the prior art that are prone to getting trapped in local optima in the later stages of optimization. As a result, the optimized XGBoost model can more accurately predict the samples to be predicted, obtain high-precision point prediction results of friction resistance coefficient, and thus improve the reliability of the ventilation network solution results.

[0010] Furthermore, in the hyperparameter optimization step, the AGDO algorithm includes the following steps: Population initialization steps: Within the hyperparameter search space of the XGBoost model, an initial population of N individuals is randomly generated, with each individual corresponding to a set of hyperparameter combinations to be optimized.

[0011] Fitness evaluation steps: Substitute the hyperparameter combination corresponding to each individual into the XGBoost model, train on the training set and calculate the prediction error on the validation set, and use the prediction error as the fitness value of the current individual.

[0012] Global exploration steps: Perturbations are generated through the asymptotic gradient momentum integral rule to update the individual's position and guide the individual to move in the direction that reduces the prediction error within the search space.

[0013] Local development and optimization steps: Nearest neighbor sample interaction is performed through dynamic gradient interaction rules, and Levy flight is introduced through optimization operator rules to perform long and short step jumps, update individual positions, and avoid getting trapped in local optima.

[0014] Optimal solution output steps: After the iteration is completed, select the hyperparameter combination corresponding to the individual with the smallest fitness value as the optimal hyperparameter output.

[0015] By employing the above-mentioned technical solutions, the AGDO algorithm of this invention specifically generates an initial population in the search space through population initialization in the hyperparameter optimization step. It uses the prediction error as the fitness value through fitness evaluation. In the global exploration step, it generates perturbations through the asymptotic gradient momentum integral rule to guide individuals to move in the direction of reducing prediction error. Then, in the local development and optimization steps, it uses the dynamic gradient interaction rule to interact with neighboring samples and the optimization operator rule to introduce Levy flight for long and short steps, thereby effectively avoiding getting trapped in local optima. Finally, after the iteration, it outputs the optimal hyperparameter combination corresponding to the individual with the smallest fitness value. This series of steps work together to enable the AGDO algorithm to effectively jump out of local optima while maintaining convergence accuracy, ensuring the global optimality of hyperparameter configuration and further improving the prediction accuracy of the friction drag coefficient prediction model.

[0016] Furthermore, in the hyperparameter optimization step, In the asymptotic gradient momentum integral rule, the individual position update adopts the following piecewise function form:

[0017]

[0018] In the formula, For individuals In the The position at the next iteration; These are dynamic parameters; For individuals The random phase parameter; For segmented indexes; is the total number of iterations; D is the number of hyperparameters to be optimized; A random number uniformly distributed within the interval [0,1]. For individuals In the The position at the next iteration; In the dynamic gradient interaction rule, the individual position is updated through the pre-utilization phase and the post-utilization phase, as shown in the following formula:

[0019] In the formula, This is the updated position after the pre-use phase; The location will be updated in the later utilization phase; For individuals In the The position at the next iteration; This is the system direction pointer; This is a dynamic scaling factor; Use as a reference point; and For random selection Nearest neighbor samples; In the optimization operator rules, the Levy flight strategy is introduced to update the individual position, as shown in the following formula:

[0020] In the formula, For individuals Position after updating the optimized operator rules; This represents the current optimal individual position. For flight functions; For flight parameters; and It is the attenuation factor; For individuals In the The position at the next iteration; and for Random numbers within a certain range; These are random numbers distributed according to a standard normal distribution. These are the stable distribution parameters.

[0021] By adopting the above technical solutions, the AGDO algorithm of this invention specifically defines the asymptotic gradient momentum integral rule as a piecewise function with dynamic parameter ω in the hyperparameter optimization step. This allows the algorithm to adaptively adjust the individual position update amplitude according to the number of iterations. The dynamic gradient interaction rule updates the individual position and introduces the system direction pointer ξ and dynamic scaling factor a through the pre-utilization and post-utilization stages, respectively. The optimization operator rule introduces the Levy flight strategy for long and short step jumps. These three rules work together in an orderly manner: the asymptotic gradient momentum integral rule provides exploration momentum, the dynamic gradient interaction rule ensures utilization efficiency, and the optimization operator rule compensates for search blind spots. This enables the AGDO algorithm to achieve intelligent optimization within a mathematical framework, ensuring that the algorithm can effectively escape local optima while maintaining convergence accuracy and obtain the globally optimal hyperparameter configuration. This significantly improves the generalization ability and prediction accuracy of the friction drag coefficient prediction model.

[0022] Furthermore, in the data processing step, the ISMOTE algorithm is used to augment the historical sample set, generate an augmented training set, and train the XGBoost model based on the augmented training set. The ISMOTE algorithm augments the data by introducing Mahalanobis distance, diversity interpolation strategy and uniqueness verification mechanism.

[0023] By employing the above-mentioned technical solutions, this invention uses the ISMOTE algorithm to augment the historical sample set in the data processing step. The ISMOTE algorithm enhances the data by introducing Mahalanobis distance, diversity interpolation strategies, and uniqueness verification mechanisms. This effectively overcomes the problems in existing technologies where training data relies on numerical simulation, leading to the difficulty in eliminating the deviation between simulated data and real roadway conditions, and the insufficient generalization ability of the model under small-scale measured samples. By generating a high-quality augmented training set through the ISMOTE algorithm, the XGBoost model trained on the augmented training set can obtain stronger generalization ability in small-sample scenarios, thereby improving the accuracy and robustness of friction resistance coefficient prediction.

[0024] Furthermore, in the data processing steps, The formula for calculating Mahalanobis distance is as follows:

[0025] In the formula, Indicates sample With sample Mahalanobis distance between them The inverse matrix of the covariance matrix of the training set; In the diversity interpolation strategy, the formula for generating new samples is as follows:

[0026] In the formula, For new samples; For the selected minority class samples; To and The nearest neighbor sample in Mahalanobis distance; These are the interpolation coefficients. ,in, The random numbers are uniformly distributed in the range [0,1]. These are random numbers from a standard normal distribution. For diversity adjustment parameters; The uniqueness verification mechanism must meet the following conditions:

[0027] In the formula, For any sample; X For historical sample sets; The preset threshold; This is a new sample.

[0028] By employing the above technical solutions, this invention specifically limits the use of Mahalanobis distance calculation formula for similarity measurement in the ISMOTE algorithm, making nearest neighbor search more physically reasonable and significantly improving the accuracy of sample matching under key working conditions; the diverse interpolation strategy adopts a diversity enhancement strategy that integrates dynamic perturbation and nonlinear interpolation, and the interpolation coefficients are adjusted when generating new samples. It incorporates normally distributed random perturbations, breaking the spatial limitations of traditional linear interpolation; the uniqueness verification mechanism calculates the minimum Euclidean distance between the new sample and the historical sample set and determines whether it is greater than a preset threshold, preventing the redundant generation of duplicate or highly similar samples; the synergistic effect of these three elements enables the ISMOTE algorithm to generate high-quality and diverse synthetic samples, effectively expanding the minority class samples, thereby significantly improving the training effect and prediction stability of the XGBoost model in small sample scenarios.

[0029] Furthermore, it also includes a confidence interval prediction step, which uses kernel density estimation to perform nonparametric fitting on the prediction residuals generated during the prediction process of the XGBoost optimization model, and constructs the prediction confidence interval of the point prediction results.

[0030] Because of the above-mentioned technical solution, this invention also includes a confidence interval prediction step. By using kernel density estimation to perform nonparametric fitting on the prediction residuals generated during the prediction process of the XGBoost optimization model, a prediction confidence interval for the point prediction results is constructed. This effectively overcomes the shortcomings of existing technologies where the model only provides point prediction results and fails to reflect the range variation characteristics of the friction resistance coefficient. Through this confidence interval prediction step, the uncertainty of the prediction results can be quantified, providing probabilistic input parameters for ventilation network solution. This allows ventilation design schemes to be robustly analyzed based on interval boundaries, significantly improving the reliability and engineering applicability of ventilation network solution results.

[0031] Furthermore, in the interval prediction step, the kernel density estimation is calculated using the following formula:

[0032] In the formula, For the residual in numerical The probability density estimate at point ; For kernel functions; For bandwidth parameters; This represents the number of residual samples; For the first One predicted residual.

[0033] Because of the above technical solution, this invention specifically defines the calculation formula for kernel density estimation in the confidence interval prediction step, through the kernel function K( The prediction residuals are nonparametrically fitted using the bandwidth parameter h. Since the distribution of prediction residuals in actual engineering often does not follow a normal distribution, traditional interval estimation methods based on the normality assumption will produce large deviations. However, the kernel density estimation method of this invention does not rely on prior distribution assumptions and directly fits the probability density function of the residual data itself. It can flexibly capture the complex distribution characteristics of the residuals, such as asymmetry and heavy tails, thereby constructing a more accurate and compact prediction confidence interval, providing a reliable uncertainty quantification method for the prediction of friction resistance coefficient.

[0034] Furthermore, it also includes an interpretability analysis step, which uses the SHAP analysis method to analyze each input feature in the historical sample set to obtain the corresponding average marginal contribution, and measures the impact of each input feature on the point prediction result based on the average marginal contribution. The formula for calculating the average marginal contribution is as follows:

[0035] In the formula, For the first The average marginal contribution of each input feature; The input is the complete set of features; This is a subset of input features that does not include input feature i. The point prediction results for the input feature subset S; - Features Marginal contribution under the current feature set S.

[0036] By employing the aforementioned technical solution, this invention uses the SHAP analysis method to analyze each input feature in the historical sample set to obtain the corresponding average marginal contribution. Based on the average marginal contribution, the impact of each input feature on the point prediction result is quantified. Since most models and algorithms exhibit black-box characteristics, lacking correlation analysis between features and mechanistic explanations of the prediction results, engineers find it difficult to understand the model's decision-making basis. This invention, through the SHAP analysis method, can quantify the marginal contribution of each input feature to the friction resistance coefficient, thereby enabling engineers to understand the model's decision-making basis. This analysis result can enhance engineering credibility, guide key feature selection and tunnel design optimization, and improve data utilization efficiency and decision-making scientificity.

[0037] Furthermore, in the data processing step, the input features include roadway attributes, geometric parameters, environmental conditions, and operating condition information.

[0038] By adopting the above technical solution, the present invention limits the input features in the data processing step to include roadway attributes, geometric parameters, environmental conditions and working condition information. These multi-dimensional feature parameters can comprehensively characterize the key factors affecting the roadway friction resistance coefficient, enabling the XGBoost optimization model to learn and predict based on rich physical information, thereby improving the model's adaptability to complex roadway working conditions and its prediction accuracy.

[0039] A friction resistance coefficient prediction system includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the friction resistance coefficient prediction method as described above.

[0040] By employing the above-mentioned technical solution, the friction resistance coefficient prediction system provided by this invention executes a computer program stored in memory through a processor, enabling it to realize all steps of the aforementioned friction resistance coefficient prediction method, including data processing, hyperparameter optimization based on the AGDO algorithm, model prediction, confidence interval prediction, and interpretability analysis. This system inherits all the advantages of the method and can complete the entire process from historical sample set processing to point prediction and interval prediction of friction resistance coefficient. It effectively solves the problems of insufficient model generalization ability, hyperparameters easily getting trapped in local optima, lack of interval prediction and interpretability in the prior art, providing a reliable friction resistance coefficient prediction tool for mine ventilation network calculation.

[0041] Compared with existing technologies, the advantages of this invention are as follows: Addressing the issues of discrepancies between simulated data and real-world operating conditions, and insufficient generalization with small samples, existing technologies employ the ISMOTE algorithm for data augmentation through Mahalanobis distance, diversity interpolation strategies, and uniqueness verification mechanisms, effectively improving the model's generalization ability in small-sample scenarios. To address the problem of hyperparameters easily getting trapped in local optima, the AGDO algorithm is used to achieve global optimization of hyperparameters through asymptotic gradient momentum integral rules, dynamic gradient interaction rules, and optimization operator rules, ensuring the acquisition of globally optimal hyperparameter configurations. Furthermore, a confidence interval prediction step is added, utilizing kernel density estimation to perform nonparametric fitting on the prediction residuals to construct prediction confidence intervals, overcoming the deficiency of only providing point prediction results. Additionally, the SHAP analysis method is used to quantify the average marginal contribution of each input feature, enhancing the model's interpretability, thereby comprehensively improving the prediction accuracy of the friction resistance coefficient and the reliability of the ventilation network solution results.

[0042] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the friction resistance coefficient prediction model provided in an embodiment of the present invention; Figure 2This is a flowchart illustrating the hyperparameter optimization steps provided in an embodiment of the present invention; Figure 3 This is the correlation heatmap of indicators provided by the present invention; Figure 4 This is a comparison chart of R² for different data augmentation experiments provided by this invention; Figure 5 This is the iterative curve of the average fitness function provided by the present invention; Figure 6 This is the optimal box plot provided by the present invention; Figure 7 This is the 5-fold experimental hyperparameter optimization iteration curve provided by the present invention; Figure 8 This is a graph showing the prediction results of the 5-fold experimental test set provided by the present invention; Figure 9 This is the prediction error graph of the 5-fold experimental test set provided by the present invention; Figure 10 This is the Shap interpretability analysis diagram provided by the present invention; Figure 11 This is the KDE interval prediction map provided by the present invention; Figure 12 This is a schematic diagram of the through-running scheme for the North Second No. 1 Auxiliary Transport Main Roadway provided by the present invention. Detailed Implementation

[0044] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following detailed description of the solution according to the present invention is provided in conjunction with the accompanying drawings and specific embodiments.

[0045] The foregoing and other technical contents, features, and effects of the present invention will be clearly presented in the following detailed description of specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, a more in-depth and concrete understanding can be gained of the technical means and effects adopted by the present invention to achieve its intended purpose. However, the accompanying drawings are for reference and illustration only and are not intended to limit the technical solutions of the present invention.

[0046] Example 1 like Figure 1 The diagram shows a flowchart of a friction drag coefficient prediction model provided by an embodiment of the present invention, which mainly includes a data processing step, a hyperparameter optimization step, and a model prediction step. The AGDO algorithm used in the hyperparameter optimization step mainly achieves global optimization of hyperparameters through the asymptotic gradient momentum integral rule, the dynamic gradient interaction rule, and the optimization operator rule.

[0047] Specifically, I. Data processing steps: Obtain historical sample sets and train the XGBoost model based on the historical sample sets; each sample in the historical sample set includes input features and measured values ​​of friction drag coefficient.

[0048] Specifically, through a special measurement of mine ventilation resistance, a historical sample set of multiple roadways in the target mine is obtained. Each sample in the historical sample set includes multiple input features and a measured value of friction resistance coefficient. In this application, the input features include roadway attributes, geometric parameters, environmental conditions, and operating condition information.

[0049] Furthermore, the tunnel attributes include cross-sectional shape and support type; geometric parameters include cross-sectional area, perimeter, length, and equivalent diameter; environmental conditions include temperature, humidity, and wind speed; and operating condition information includes the presence of structures, which here refer to air doors and ventilation windows. In addition, to ensure data quality, after obtaining the historical sample set, this application also performs physical threshold filtering and IQR monitoring on the measured data to remove outliers from the original data, ensuring the reasonableness of the sample.

[0050] In practical engineering, due to the difficulty and high cost of acquiring mine-based measured data, the original measured data obtained is often small in scale, making it difficult to support the training of machine learning models. Therefore, this embodiment employs an improved synthetic minority class oversampling algorithm (ISMOTE algorithm) to augment the historical sample set, generating an augmented training set, and then trains the XGBoost model based on this augmented training set.

[0051] The ISMOTE algorithm in this application augments data by introducing Mahalanobis distance, a diversity interpolation strategy, and a uniqueness verification mechanism, as detailed below: (1) Similarity measurement level To make nearest neighbor search more physically plausible and significantly improve the accuracy of sample matching under key working conditions, such as those involving structures, a minority class sample in the sample dataset that contains a specific working condition is considered. (For samples containing extreme operating conditions such as dampers and windows), calculate its comparison with all other samples of the same type in the set. The Mahalanobis distance between them is calculated using the following formula:

[0052] In the formula, Indicates sample With sample Mahalanobis distance between them The inverse matrix of the covariance matrix of the training set; (2) Sample generation mechanism level A diversity enhancement strategy that integrates dynamic perturbation and nonlinear interpolation is adopted to break through the spatial limitations of traditional linear interpolation. The formula for generating new samples is as follows:

[0053] In the formula, For new samples; For the selected minority class samples; To and The nearest neighbor sample in Mahalanobis distance; These are the interpolation coefficients. ,in, The random numbers are uniformly distributed in the range [0,1]. These are random numbers from a standard normal distribution. For diversity adjustment parameters; (3) Sample quality control level This application establishes a uniqueness verification mechanism to prevent the redundant generation of duplicate or highly similar samples. Each time a new sample is generated... Then, the algorithm will calculate its relationship with the historical sample set. X Find the minimum Euclidean distance among all samples and determine if the following conditions are met:

[0054] In the formula, For any sample; X For historical sample sets; The preset threshold; This is a new sample.

[0055] Finally, after completing all the above operations, the algorithm performs deduplication and random shuffling to achieve seamless integration of the synthetic samples with the original data, forming enhanced training sample data for better training of the XGBoost model.

[0056] II. Hyperparameter Optimization Steps: The AGDO (Adam Gradient Descent Optimizer) algorithm is used to optimize the hyperparameters of the XGBoost model, resulting in an optimized XGBoost model. The AGDO algorithm achieves global optimization of hyperparameters through asymptotic gradient momentum integral rules, dynamic gradient interaction rules, and optimization operator rules.

[0057] The AGDO algorithm in this application is a novel metaheuristic algorithm inspired by the Adam optimizer, such as... Figure 2 As shown, the specific steps include the following: (1) Population initialization steps: Within the hyperparameter search space of the XGBoost model, an initial population of N individuals is randomly generated, with each individual corresponding to a set of hyperparameters to be optimized; the mathematical expression is:

[0058] In the formula, For the first The individual's location; Population size; For dimensions; and These are the upper and lower bounds, respectively; For the first The minimum allowed value for each hyperparameter; (2) Fitness evaluation steps: Substitute the hyperparameter combination corresponding to each individual into the XGBoost model, train on the training set and calculate the prediction error on the validation set, and use the prediction error as the fitness value of the current individual; (3) Global exploration steps: Perturbation is generated by the asymptotic gradient momentum integral rule, the individual position is updated, and the individual is guided to move in the direction of reducing the prediction error within the search space; Specifically, in the asymptotic gradient momentum integral rule, the individual position update adopts the following piecewise function form:

[0059]

[0060] In the formula, For individuals In the The position at the next iteration; These are dynamic parameters; For individuals The random phase parameter; For segmented indexes; is the total number of iterations; D is the number of hyperparameters to be optimized; A random number uniformly distributed within the interval [0,1]. For individuals In the The position at the next iteration; (4) Local development and optimization steps: Nearest neighbor sample interaction is carried out through dynamic gradient interaction rules, and Levy flight is introduced through optimization operator rules to perform long and short step jumps, update individual positions, and avoid getting trapped in local optima; Specifically, in the dynamic gradient interaction rule, the individual position is updated through a pre-utilization phase and a post-utilization phase, as shown in the following formula:

[0061] In the formula, This is the updated position after the pre-use phase; The location will be updated in the later utilization phase; For individuals In the The position at the next iteration; This is the system direction pointer; This is a dynamic scaling factor; Use as a reference point; and For random selection Nearest neighbor samples; In the optimization operator rules, the Levy flight strategy is introduced to update the individual position, as shown in the following formula:

[0062] In the formula, For individuals Position after updating the optimized operator rules; This represents the current optimal individual position. For flight functions; For flight parameters; and It is the attenuation factor; For individuals In the The position at the next iteration; and for Random numbers within a certain range; These are random numbers distributed according to a standard normal distribution. These are the stable distribution parameters.

[0063] (5) Optimal solution output steps: After the iteration is completed, select the hyperparameter combination corresponding to the individual with the smallest fitness value as the optimal hyperparameter output.

[0064] As can be seen from the above, the AGDO algorithm achieves intelligent optimization within a mathematical framework through the orderly collaboration of three layers of rules: the asymptotic gradient momentum integral rule provides the driving force for exploration, the dynamic gradient interaction rule ensures utilization efficiency, and the optimization operator rule compensates for search blind spots; thus ensuring that the algorithm can effectively escape local optima while maintaining convergence accuracy.

[0065] III. Model Prediction Steps: The optimized XGBoost model is used to predict the sample to be predicted, and the point prediction results of the friction resistance coefficient are obtained, which are used as input parameters for the ventilation network solution.

[0066] (1) Feature acquisition of the sample to be predicted First, the multi-dimensional characteristic parameters of the roadway to be predicted are obtained. Based on the characteristic index system constructed according to this invention, the input features of the sample to be predicted include: roadway cross-sectional shape, support type, cross-sectional area, roadway perimeter, roadway length, equivalent diameter, structure type, and ambient temperature. These characteristic parameters can be obtained through on-site measurements, engineering drawings, or actual mine records.

[0067] (2) Prediction recursion of XGBoost model The feature vectors of the samples to be predicted are input into the XGBoost optimized model after optimization by the AGDO algorithm. As an ensemble learning algorithm, XGBoost adopts a stepwise accumulation strategy in its prediction process: the model consists of multiple regression trees, and each tree is modified based on the prediction results of the previous stage.

[0068] Specifically, for any sample ,make Indicates the preceding Tree samples The cumulative predicted value, Indicates the first Tree regression for samples The output value; at the learning rate Under the control of, the first The cumulative prediction value after the next update is:

[0069] During initialization, .go through After the recursion, The total number of regression trees determined after AGDO algorithm optimization, and the final point prediction result of friction drag coefficient. for:

[0070] In the formula, For the sample The predicted results of the friction resistance coefficient; The learning rate is used to control the contribution of each regression tree to the final prediction result. The total number of regression trees; This represents the regression tree index. Shrinking the output of a single tree by adjusting the learning rate can reduce the excessive influence of a single tree on the model results, thereby suppressing overfitting to some extent.

[0071] (3) Objective function of XGBoost optimization model After optimizing the hyperparameters using the AGDO algorithm, the generation of each tree during model training is based on minimizing the following objective function:

[0072] In the formula, For the first The objective function of the trees; N is the total number of training samples; The measured value of the frictional resistance coefficient for the i-th sample; This represents the cumulative predicted value of the i-th sample in the first k-1 trees; For the first The output values ​​of each tree; Let be the input feature vector of the i-th sample; The function for the k-th tree; The loss function; , They are respectively The first and second derivatives; This is a regularization term used to control model complexity.

[0073] The objective function is accelerated to convergence through second-order Taylor expansion and overfitting is avoided through a regularization mechanism, thus ensuring that the XGBoost optimization model can output stable and accurate point prediction results of friction resistance coefficient values ​​during the prediction stage.

[0074] (4) Application of point prediction results in ventilation network solution This invention will predict the point results As a key input parameter for mine ventilation network calculation, the ventilation network calculation is a process of steady-state simulation analysis of the entire mine or a local ventilation network based on the airflow balance law, resistance balance law, and wind resistance law. The frictional resistance coefficient of each roadway directly determines its wind resistance value, thus affecting the airflow distribution of the entire network.

[0075] In traditional methods, the frictional resistance coefficient usually relies on empirical table lookups or rough estimations, leading to significant deviations between the calculated results and actual conditions. This invention utilizes the point prediction results output by the AGDO-XGBoost model and substitutes them into the ventilation network calculation model, which can significantly improve the accuracy of airflow distribution and resistance calculation.

[0076] To overcome the technical shortcomings of existing methods for predicting friction resistance coefficients, which can only output a single value (point prediction result) and cannot quantify the uncertainty of the prediction result, this invention further introduces a confidence interval prediction step based on the above steps.

[0077] Confidence interval prediction steps: Use kernel density estimation to perform nonparametric fitting on the prediction residuals generated during the XGBoost optimization model prediction process to construct the prediction confidence interval of the point prediction result.

[0078] Specifically, the confidence interval prediction steps include the following: (1) Obtain the prediction residual set Using an XGBoost optimized model trained with the AGDO algorithm, predictions are made on the validation sample set, or on samples that did not participate in the current round of training during cross-validation, to obtain the point prediction result for each sample. The measured values ​​of the friction resistance coefficient for the corresponding samples. Point prediction results Subtracting them yields the predicted residuals. The residuals of all samples constitute the residual sample set. .in, This refers to the number of samples used in the residual calculation. Constructing a residual set using out-of-sample prediction residuals from the validation sample set or cross-validation avoids the problem of narrow prediction intervals caused by directly using training set residuals.

[0079] (2) The residual distribution is fitted using kernel density estimation. Since the distribution of predicted residuals in practical engineering often does not follow a normal distribution, traditional interval estimation methods based on the normality assumption will produce significant biases. Therefore, this invention introduces the nonparametric kernel density estimation (KDE) method. Starting from the residual data itself, it does not rely on prior distribution assumptions and directly fits its probability density function, exhibiting high adaptability when dealing with complex data. The basic calculation formula for kernel density estimation is as follows:

[0080] In the formula, For residuals in numerical The probability density estimate at point ; The kernel function, such as the Gaussian kernel or the Epanechnikov kernel, is used to control the shape of the contribution of each residual sample point to the density estimate. The bandwidth parameter determines the smoothness of the density estimation curve; This represents the number of residual samples; For the first Each prediction residual. Bandwidth parameter. Cross-validation or rules of thumb can be used to automatically select the appropriate method to balance fitting accuracy and smoothness.

[0081] (3) Constructing prediction confidence intervals For any sample to be predicted, the point prediction result is: The residual probability density function obtained from the above kernel density estimation. Calculate the residual distribution at a specified confidence level. The lower and upper quantiles are denoted as follows: and .in, and satisfy:

[0082]

[0083] Therefore:

[0084] Since the prediction residual is defined as The confidence interval for predicting the friction resistance coefficient of the roadway to be predicted is: This interval reflects the range at a given confidence level. The range within which the true value of the friction drag coefficient may fall is determined. Assuming the coverage requirement is met, a smaller interval width indicates lower prediction uncertainty and more reliable prediction results.

[0085] Therefore, probabilistic ventilation network analysis can be performed by inputting the point prediction results and their confidence intervals into the ventilation network solution module. Specifically, the lower limit of the interval, the point prediction value, and the upper limit of the interval are used as the friction resistance coefficient of the roadway, and the ventilation network solution is repeated three times to obtain the variation range of air volume, air pressure, and total system resistance of key branches. If this range meets the mine ventilation safety requirements, it indicates that the ventilation design scheme has sufficient robustness; conversely, if the interval boundaries cause safety hazards in the solution results, it suggests that further optimization of the roadway design or enhanced monitoring is needed.

[0086] Furthermore, since most models and algorithms are black-box in nature, lacking correlation analysis between features and mechanistic explanations of the prediction results, engineers find it difficult to understand the basis of the model's decisions, resulting in a lack of credibility and acceptance of the model in engineering practice. Therefore, the friction resistance coefficient prediction method in this embodiment also includes an interpretability analysis step.

[0087] Interpretability analysis steps: Analyze each input feature in the historical sample set using the SHAP analysis method to obtain the corresponding average marginal contribution, and quantify the impact of each input feature on the point prediction results based on the average marginal contribution. The formula for calculating the average marginal contribution is as follows:

[0088] In the formula, For the first The average marginal contribution of each input feature; The input is the complete set of features; This is a subset of input features that does not include input feature i. The point prediction results for the input feature subset S; - Features Marginal contribution under the current feature set S.

[0089] Through interpretability analysis, this application can quantify the marginal contribution of each input feature to the friction resistance coefficient, thereby enabling engineers to understand the basis of model decisions. The analysis results can enhance engineering credibility, guide the selection of key features and the optimization of tunnel design, and improve data utilization efficiency and decision-making scientificity.

[0090] Example 2 A friction resistance coefficient prediction system includes a processor for executing a computer program to implement a friction resistance coefficient prediction classification method as described in Example 1, which will not be repeated here.

[0091] Verification Experiment 1. Dataset Construction To obtain reliable data, a special measurement of underground ventilation resistance was conducted at Shaanxi Coal Huangling No. 2 Coal Mine, strictly adhering to coal mining industry standards. A CZC5A3 digital precision barometer was used to measure static pressure difference, a YJDM1101 laser cross-section analyzer was used to acquire cross-sectional shape and geometric parameters, and a JD7 ultrasonic anemometer was used to simultaneously record environmental indicators such as wind speed, temperature, and humidity. These devices support the barometer point-by-point measurement method, simultaneously collecting key parameters such as roadway cross-sectional shape and support type. Physical threshold filtering and the IQR interquartile range method were used to monitor outliers in the raw data to ensure sample validity. Combined with on-site survey records, the authenticity of samples including structures was manually verified, ultimately resulting in a dataset accurately reflecting the roadway conditions.

[0092] As shown in Table 1, the dataset contains only 34 samples, with very few samples containing structures. The small dataset is insufficient to support the cross-validation requirements of machine learning models. To overcome this limitation, the ISMOTE algorithm was introduced. It adaptively enhances the training set, focusing on expanding the minority class samples containing special working conditions such as dampers and windows, thereby solving the data sparsity problem and providing solid support for high-precision prediction models.

[0093] Table 1. Ventilation resistance measurement data of Huangling No. 2 Well Table 1 Measurement Data of Ventilation Resistance in Huangling No. 2Well serial number Cross-sectional shape Support type <![CDATA[Section / m 2 > Circumference / m Length / m Equivalent diameter / m Structures … <![CDATA[Frictional resistance coefficient / (N·s² m -4 )]]> 1 semicircular arch Masonry arch 16.25 20.45 20.00 3.18 none … 21.50 2 semicircular arch Masonry arch 16.18 20.38 199.50 3.18 none … 18.25 3 semicircular arch Masonry arch 17.20 21.06 2707.50 3.27 none … 30.41 4 semicircular arch Anchor spray 18.67 18.56 103.00 4.02 none … 28.86 5 semicircular arch Anchor spray 19.73 16.48 1446.50 4.79 none … 28.15 … … … … … … … … … … 30 semicircular arch Anchor spray 24.88 17.29 273.13 5.76 Air damper, air window … 987.87 31 semicircular arch Anchor spray 22.39 31.58 464.00 2.84 none … 87.29 32 semicircular arch Anchor spray 19.49 27.41 569.00 2.84 none … 87.63 33 semicircular arch Anchor spray 16.40 17.20 84.37 3.81 none … 84.52 34 semicircular arch Anchor spray 18.60 19.50 667.50 3.82 none … 74.94 2. Data augmentation experiments and ISMOTE algorithm performance testing To verify the influence of key factors such as structures on the frictional resistance coefficient and to clarify the targeted objectives of data augmentation, categorical variables such as cross-sectional shape, support type, and structures were first numerically coded. Then, Spearman rank correlation analysis was used to assess the monotonic relationships between the variables. The analysis results were visualized using a heatmap, where the color intensity represents the magnitude of the correlation coefficient (* represents p < 0.05, ** represents p < 0.01, and *** represents p < 0.001).

[0094] Figure 3The study revealed a statistically significant correlation between the roadway friction resistance coefficient and key indicators. Cross-sectional area and equivalent diameter showed a strong negative correlation with the friction resistance coefficient, with correlation coefficients reaching -0.82 and -0.79, respectively. Indicators representing facilities such as air doors and windows also showed a strong negative correlation, with a correlation coefficient of -0.76, directly confirming that these structural features play a crucial role in suppressing ventilation resistance. Roadway length showed a strong positive correlation with the friction resistance coefficient, with a correlation coefficient as high as 0.85, indicating that roadway extension and bends significantly enhance the cumulative effect of friction resistance. Regarding secondary correlations, structures showed a weak negative correlation with temperature, with a correlation coefficient of -0.31; perimeter showed a moderate positive correlation with roadway elevation difference, with a correlation coefficient of 0.62; and wind speed showed a weak positive correlation with temperature, with a correlation coefficient of 0.28. These complex multi-factor coupling relationships reveal the inherent complexity of mine ventilation systems, particularly highlighting the dominant role of core indicators such as structures and cross-sectional shapes in system resistance. Therefore, focusing on enhancing the sample coverage of such key factors through the ISMOTE algorithm becomes an inevitable choice to improve the robustness of the prediction model.

[0095] This experiment employs five-fold cross-validation to evaluate the effectiveness of data augmentation methods. This involves alternating between different data partitions for training and validation to ensure comprehensiveness and robustness of the evaluation. Each experiment uses a different combination of training subsets. During the training phase, only the training set is augmented, while the validation and test sets maintain their original distributions to avoid data leakage. Three training data configurations are set up: the original training set, the SMOTE augmentation set (augmentation factor of 4), and the ISMOTE augmentation set (augmentation factor of 4). Specifically, experiments A1, A4, etc., use the original data; experiments A2, A5, etc., use SMOTE; and experiments A3, A6, etc., use ISMOTE. All experiments use the same XGBoost default parameters and hardware environment, with RMSE and R² used as evaluation metrics.

[0096] The experimental results clearly reveal the performance differences between the different methods. For example... Figure 4As shown in Table 2, the model exhibits significant overfitting characteristics under training with the original data. For example, the R² of the training set in experiment A1 reaches 0.998, but the R² of the validation and test sets drops to -0.144 and -0.164, respectively, indicating a severe lack of generalization ability. While SMOTE enhancement provides some improvement, such as increasing the R² of the test set in experiment A2 to 0.367, some experiments, such as A8 and A11, still show negative R² values, reflecting fluctuations in the quality of the generated samples. In contrast, the ISMOTE method demonstrates stability: the R² of the test sets in experiments A3, A6, and A9 reach 0.815, 0.790, and 0.635, respectively, and experiments A12 and A15 also maintain reliable performance of 0.725 and 0.689. These results demonstrate that ISMOTE effectively enhances the robustness of the model in small-sample scenarios by improving the quality of the synthesized samples.

[0097] Table 2 Results of the data augmentation experiment Table 2 Results of Data augmentation experiments

[0098] 3. Performance Comparison of Optimized Algorithms To verify the global optimization capability and sophistication of AGDO, this study introduced algorithms such as PSO (Particle Swarm Optimization), WOA (Whale Optimization Algorithm), SSA (Sparrow Search Algorithm), DBO (Dung Beetle Optimizer), ESC (Escape Algorithm), and GWO (Grey Wolf Optimization), and tested them using the IEEE CEC 2022 standard test set. To ensure fairness in the simulation experiments, all algorithms were run on the same test platform with the same experimental parameters. The processor used was a 12th generation Intel(R) Core(TM) i5-12600KF (3.70 GHz), and all experiments were implemented using MATLAB 2024a. The population size for all four algorithms was set to 20, the number of iterations to 100, the test function dimension to 10, and the number of runs to 50. Finally, the average fitness function iteration curves, average optimal fitness values, box plots of the optimal solutions, and algorithm performance comparisons were obtained for each algorithm after running 50 times in functions F1 to F12 respectively.

[0099] like Figure 5As shown, the convergence characteristics of various optimization algorithms during the solution process are illustrated. Among them, the AGDO algorithm exhibits faster convergence speed and a more stable descent trend on all test functions, with its curve approaching the global optimum earlier. In contrast, algorithms such as PSO, WOA, and GWO show premature convergence on most functions and limited search capabilities in the later stages of iteration. The curve shape reflects the advantage of AGDO in balancing exploration and exploitation, effectively avoiding local optima traps.

[0100] Table 3 presents a quantitative comparison of the optimal solutions of each algorithm on the CEC2022 test set, clearly demonstrating the differences in algorithm performance. AGDO achieved the lowest average optimal solution in all 12 test functions, significantly outperforming the compared algorithms. Traditional algorithms such as WOA achieved an optimal solution of 10343.50 on the F1 function, while AGDO only achieved 311.60; GWO achieved an average optimal solution of 9933.31 on the F6 function, while AGDO only achieved 1883.26.

[0101] Table 3 shows the optimal solutions for each function on the CEC2022 test set using various algorithms. Table 3 Shows the optimal solutions of various algorithms for each function in the CEC2022 test set test function PSO WOA SSA DBO ESC GWO AGDO F1 332.46 10343.50 1924.29 4549.21 3525.26 1311.06 311.60 F2 400.06 429.11 400.46 483.96 401.04 401.92 400.04 F3 600.20 622.96 606.00 616.95 600.02 600.78 600.00 F4 805.97 829.12 811.02 831.57 821.44 806.20 804.01 F5 900.18 1096.43 949.67 1093.44 900.13 900.27 900.00 F6 1882.04 8072.98 1940.42 772335.46 1940.65 9933.31 1883.26 F7 2015.47 2053.92 2021.68 2060.38 2010.46 2025.22 2000.22 F8 2221.17 2226.95 2221.14 2229.77 2216.38 2211.53 2201.92 F9 2530.28 2579.69 2529.32 2574.81 2529.29 2529.75 2529.28 F10 2500.37 2501.16 2500.37 2503.12 2500.39 2500.45 2500.24 F11 2600.58 2810.02 2620.08 2828.88 2915.44 2749.65 2600.12 F12 2864.85 2866.78 2861.46 2870.52 2861.53 2862.96 2858.64 Figure 6 The study revealed the distribution characteristics of the algorithm's solution quality. AGDO had the narrowest solution distribution range and the lowest median, indicating that its results from multiple runs were concentrated close to the theoretical optimal solution, demonstrating significantly better stability than other algorithms. While ESC and GWO achieved good results on some functions, their long solution bins and numerous outliers indicated significant performance fluctuations. DBO and WOA algorithms had the widest solution distribution range, reflecting insufficient convergence consistency. In summary, AGDO demonstrated a clear advantage in both solution accuracy and stability.

[0102] 4. Comparison of Model Prediction Performance Using ISMOTE-enhanced experimental data (corresponding to groups A3, A6, A9, A12, and A15), the hyperparameters of the XGBoost model were optimized using the AGDO algorithm. Experiments were renumbered AX1 to AX5, and the hyperparameter search range covered the number of trees (50-200), maximum tree depth (1-20), minimum sum of sample weights (1-10), random sampling ratio (0.5-1), initial learning rate (0.00001-0.01), and leaf node splitting threshold (0.1-0.5). Based on the five-fold cross-validation results, the average values ​​of the optimized hyperparameters were: approximately 97 trees, maximum tree depth 9 layers, minimum sum of sample weights 1.8, random sampling ratio 0.53, initial learning rate 0.0019, and leaf node splitting threshold 0.29.

[0103] Figure 7 The dynamic changes of the validation set RMSE with the number of iterations in the five-fold experiment are depicted in detail. All five curves exhibit a consistent pattern: a rapid initial decrease followed by a smooth convergence to a low value. The RMSE of AX5 drops sharply from a high level to 6.2564, while AX1, AX2, AX3, and AX4 perform better, converging to 5.740, 5.659, 5.257, and 5.726, respectively. This trend not only verifies the efficiency of the AGDO algorithm but also highlights its stability on different data subsets. The curves all enter a flat phase in the middle of the iterations, indicating that the algorithm effectively avoids the risk of overfitting, providing a reliable guarantee for improving model performance.

[0104] Figure 8 and Figure 9 Together, they revealed the predictive performance of the AGDO-XGBoost model. Figure 9 The distribution of predicted friction coefficients on the five-fold cross-validation test set is shown. Overall, the trends of the actual and predicted values ​​are highly consistent, but the model performs exceptionally well at two extreme points. For the second sample in group AX1, the actual value is 987.866, the predicted value is 987.172, and the error is only 0.705. For the second sample in group AX4, the actual value is 1636.736, the predicted value is 1633.219, and the error is 3.517. Although these points are at the extremes of the numerical range, the predicted values ​​still closely match the actual values, strongly demonstrating the model's stable predictive ability across different numerical ranges. Figure 9 The distribution of error values ​​on the test set is presented visually. All error values ​​are concentrated in the range of [-10, 12], and the absolute values ​​of the errors are generally small, mostly falling within ±5, indicating that the model has high prediction accuracy. The error distribution is dense and uniform, with no outliers or shifts, indicating that the optimized model can effectively control the deviation range.

[0105] As can be seen from the two figures, the systematic hyperparameter optimization of AGDO significantly improves the generalization performance of XGBoost, enabling the prediction of friction resistance coefficient to exhibit high accuracy and strong consistency in different numerical ranges. This method provides reliable support for the prediction of mine ventilation parameters.

[0106] To evaluate the overall performance of the AGDO-XGBoost model, a systematic comparison was conducted with benchmark models such as Random Forest (RF), Extreme Learning Machine (ELM), and LightGBM. Table 4 shows that AGDO-XGBoost exhibits significant advantages across all evaluation metrics. Its MAE is as low as 4.703, far lower than the traditional XGBoost's 49.972; its RMSE is 5.728, better than the traditional XGBoost's 71.822; and its R² is 0.952, approaching a perfect fit. Compared to other optimized models, AGDO-RF and AGDO-LightGBM still have relatively high error metrics, with AGDO-RF's RMSE at 59.496. AGDO-ELM's MAE reaches 156.755, reflecting its shortcomings in capturing complex patterns. These differences highlight the unique advantage of AGDO-XGBoost in balancing accuracy and generalization ability.

[0107] Table 4 Comparison of Model Performance Indicators Table 4 Performance Comparison of Model Indicators Model and parameters MAE MAPE RMSE <![CDATA[R 2 ]]> XGBoost 49.972 25.152 71.822 0.731 AGDO-RF 59.376 23.252 59.496 0.855 AGDO-ELM 156.755 81.682 96.954 0.264 AGDO-LightGBM 64.022 19.054 62.104 0.840 AGDO-XGBoost 4.703 7.364 5.728 0.952 5. SHAP Analysis and Evaluation SHAP analysis clearly demonstrates the degree and mechanism of influence of each input feature on the friction drag coefficient prediction model. For example... Figure 10 As shown, structures dominate with a contribution of 32.9%, becoming the most influential feature. Their SHAP values ​​are concentrated in the range of 0.1 to 0.16, indicating that facilities such as ventilation doors and windows have a stable and significant positive impact on the model output. Following closely are cross-sectional area and support type, contributing 23.3% and 18.3% respectively, with their SHAP value distributions also showing a strong positive influence. In contrast, features such as tunnel length and perimeter contribute less than 6%, while the influence of temperature features is negligible.

[0108] The physical mechanisms by which each feature affects the frictional resistance coefficient are highly consistent with the SHAP analysis results. As the dominant feature, the physical essence of the structure lies in the fact that obstacles placed within the tunnel significantly increase local absolute roughness, leading to a marked increase in the frictional resistance coefficient. The effect of cross-sectional area is reflected in fluid dynamics principles; a larger cross-sectional area reduces the relative contact ratio between the fluid and the wall, thereby reducing relative roughness. The complex influence mechanism of support type is meticulously revealed through SHAP analysis; the differences in wall smoothness corresponding to different support methods directly determine the value of the frictional resistance coefficient.

[0109] 6. Comparison of Confidence Interval Prediction Performance like Figure 11 As shown in Table 5, the KDE method demonstrates superior overall performance compared to the Gaussian assumption method in confidence interval prediction. At a 90% confidence level, KDE achieves a prediction interval coverage of 73.5%, higher than the 70.5% of the Gaussian method. Simultaneously, its average interval width is 0.007, narrower than the 0.009 of the Gaussian method, indicating not only more comprehensive coverage but also more compact intervals, thus improving prediction accuracy while maintaining reliability. When the confidence level drops to 60%, KDE's advantages become even more apparent, with its coverage rising to 94.1%, significantly exceeding the nominal confidence level, demonstrating a good adaptability to data distribution characteristics. This performance stems from the fact that KDE does not presuppose that the residuals follow a normal distribution; instead, it directly captures the actual shape of the error through kernel density estimation, thereby avoiding the interval shift or distortion problems caused by the traditional Gaussian method in asymmetric or heavy-tailed cases due to the imposition of symmetry assumptions.

[0110] Furthermore, the prediction results for samples AX1 to AX5 show that the measured values ​​are basically completely contained within the prediction intervals generated by KDE, and the upper and lower boundaries closely match the actual trend of change, without significant divergence or gaps. As the confidence level decreases from 90% to 60%, the prediction interval gradually narrows, and the structure becomes more focused, while still effectively encompassing the true values, demonstrating good stability and sensitivity. In summary, KDE breaks free from the rigid constraints of parametric methods on the distribution form, and can flexibly construct probability intervals based on the characteristics of the data itself, balancing coverage quality and interval accuracy. It provides a more reliable and practical uncertainty quantification method for engineering parameters such as mine friction resistance coefficient, which are affected by multiple factors and have complex data distributions.

[0111] Table 5. Performance Comparison of KDE and Gaussian Probability Prediction Indices Table 5 Performance Comparison between KDE and Gaussian ProbabilityPrediction Index

[0112] 7. Simulation and solution of the overall scheme To verify the reliability and engineering applicability of the AGDO-XGBoost-KDE fusion model in the intelligent design of mine ventilation systems, this experiment selected the "North No. 2 Auxiliary Transport Main Roadway" connection project of Shaanxi Coal Huangling No. 2 Coal Mine as the verification object. Figure 12 As shown, the tunnel is designed to be 1120m long and is responsible for the key ventilation task of connecting the North 2 mining area and the North 2 conveyor belt main roadway No. 15 connecting roadway. The accurate prediction of its friction resistance coefficient directly determines the stability of the airflow distribution of the system after the tunnel is completed.

[0113] The input feature parameters of the model are set as follows: the tunnel adopts a semi-circular arch cross-section masonry support, with a cross-sectional area of ​​23.2m², a perimeter of 19.5m, an equivalent diameter of 4.8m, a tunnel elevation difference of 15m, an ambient temperature of 18.5℃, and no damping structures such as air doors or windows.

[0114] The model outputs a point prediction value of 70.56 × 10⁻⁶ for the frictional resistance coefficient of this roadway. 4 N·s² / m 4 Meanwhile, the prediction interval output by KDE at a 90% confidence level is [67.72, 74.99] × 10. 4 N·s² / m 4 Using the boundary and point prediction values ​​of this interval as key parameters, and keeping the operating conditions of the main mine fans constant, a steady-state simulation was performed on the ventilation network of the entire mine after it was connected, in order to evaluate the system response under uncertainty conditions.

[0115] The calculated parameters, including key branch airflow, air velocity, and total system resistance, were compared and analyzed with the field measured data after the tunnel was connected (see Table 6). The results show that the fused model has extremely high engineering fidelity. (1) The simulated air volume values ​​of each main air intake channel (such as No. 2 air shaft and No. 1 auxiliary inclined shaft) are highly consistent with the measured values, and the average relative error is strictly controlled within ±3%. The air volume of the working face fully meets the air demand requirements.

[0116] (2) The simulated wind speeds were all within the safe range of 0.25 to 4 m / s as specified in the Coal Mine Safety Regulations, and no wind speed exceeded the limit or there was a light wind.

[0117] (3) The simulated total resistance of the system is 2642 Pa. Compared with the measured value of 2685 Pa after the fan was connected, the relative deviation is only 1.6%, which verifies that the predicted parameters can accurately reflect the real physical wind resistance characteristics.

[0118] In the boundary test within the 90% confidence interval, the ventilation network solution results remained in a steady state, indicating that the North 2 No. 1 auxiliary haulage roadway excavation scheme has good robustness and anti-interference ability. This engineering practice confirms that the AGDO-XGBoost-KDE fusion model can not only provide high-precision point predictions, but also effectively quantify the uncertainty risks in actual working conditions through interval predictions. This study, through "data-driven model + on-site closed-loop verification," has achieved a leap from traditional "experience-based table lookup" to "intelligent quantitative prediction" in obtaining the friction resistance coefficient, providing a solid decision-making basis for the refined management and optimized design of complex ventilation systems.

[0119] Table 6 Simulated air volume after the completion of the North 2 No. 1 Auxiliary Transport Main Roadway Table 6 Simulation Calculation of air Volume after the connection of the No. 1 Auxiliary Transport Main roadway of North No. 2

[0120] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or apparatus comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes said element.

[0121] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for predicting the coefficient of frictional resistance, characterized in that, Includes the following steps: Data processing steps: Obtain a historical sample set and train the XGBoost model based on the historical sample set; each sample in the historical sample set includes input features and measured values ​​of friction drag coefficient; Hyperparameter optimization steps: The AGDO algorithm is used to optimize the hyperparameters of the XGBoost model to obtain the optimized XGBoost model; the AGDO algorithm realizes global optimization of hyperparameters through the asymptotic gradient momentum integral rule, dynamic gradient interaction rule and optimization operator rule; Model prediction steps: Use the XGBoost optimization model to predict the sample to be predicted, and obtain the point prediction results of the friction drag coefficient.

2. The method for predicting the friction resistance coefficient according to claim 1, characterized in that, The AGDO algorithm includes the following steps in the hyperparameter optimization process: Population initialization steps: In the hyperparameter search space of the XGBoost model, an initial population of N individuals is randomly generated, with each individual corresponding to a set of hyperparameter combinations to be optimized; Fitness evaluation steps: Substitute the hyperparameter combination corresponding to each individual into the XGBoost model, train on the training set and calculate the prediction error on the validation set, and use the prediction error as the fitness value of the current individual; Global exploration steps: Perturbation is generated through the asymptotic gradient momentum integral rule to update the individual's position and guide the individual to move in the direction that reduces the prediction error within the search space; Local development and optimization steps: Nearest neighbor sample interaction is performed through the dynamic gradient interaction rule, and Levy flight is introduced through the optimization operator rule to perform long and short step jumps, update the individual position, and avoid getting trapped in local optima; Optimal solution output steps: After the iteration is completed, select the hyperparameter combination corresponding to the individual with the smallest fitness value as the optimal hyperparameter output.

3. The method for predicting the friction resistance coefficient according to claim 1 or 2, characterized in that, In the hyperparameter optimization step In the asymptotic gradient momentum integral rule, the individual position update adopts the following piecewise function form: In the formula, For individuals In the The position at the next iteration; These are dynamic parameters; For individuals The random phase parameter; For segmented indexes; is the total number of iterations; D is the number of hyperparameters to be optimized; A random number uniformly distributed within the interval [0,1]. For individuals In the The position at the next iteration; In the dynamic gradient interaction rule, the individual position is updated through a pre-utilization phase and a post-utilization phase, as shown in the following formula: In the formula, This is the updated position after the pre-use phase; The location will be updated in the later utilization phase; For individuals In the The position at the next iteration; This is the system direction pointer; This is a dynamic scaling factor; Use as a reference point; and For random selection Nearest neighbor samples; In the optimization operator rule, the Levy flight strategy is introduced to update the individual position, as shown in the following formula: In the formula, For individuals Position after updating the optimized operator rules; This represents the current optimal individual position. For flight functions; For flight parameters; and It is the attenuation factor; For individuals In the The position at the next iteration; and for Random numbers within a certain range; These are random numbers distributed according to a standard normal distribution. These are the stable distribution parameters.

4. The method for predicting the friction resistance coefficient according to claim 1, characterized in that, In the data processing step, the ISMOTE algorithm is used to augment the historical sample set to generate an augmented training set, and the XGBoost model is trained based on the augmented training set. The ISMOTE algorithm augments the data by introducing Mahalanobis distance, diversity interpolation strategy and uniqueness verification mechanism.

5. The method for predicting the friction resistance coefficient according to claim 4, characterized in that, In the data processing steps, The formula for calculating the Mahalanobis distance is as follows: In the formula, Indicates sample With sample Mahalanobis distance between them The inverse matrix of the covariance matrix of the training set; In the aforementioned diversity interpolation strategy, the formula for generating new samples is as follows: In the formula, For new samples; For the selected minority class samples; To and The nearest neighbor sample in Mahalanobis distance; These are the interpolation coefficients. ,in, The random numbers are uniformly distributed in the range [0,1]. These are random numbers from a standard normal distribution. For diversity adjustment parameters; The uniqueness verification mechanism must meet the following conditions: In the formula, For any sample; X For historical sample sets; The preset threshold; This is a new sample.

6. The method for predicting the friction resistance coefficient according to claim 1, characterized in that, It also includes a confidence interval prediction step, which uses kernel density estimation to perform nonparametric fitting on the prediction residuals generated during the prediction process of the XGBoost optimization model to construct the prediction confidence interval of the point prediction result.

7. The method for predicting the friction resistance coefficient according to claim 6, characterized in that, In the interval prediction step, the kernel density estimation is calculated using the following formula: In the formula, For residuals in numerical The probability density estimate at point ; For kernel functions; For bandwidth parameters; This represents the number of residual samples; For the first One predicted residual.

8. The method for predicting the friction resistance coefficient according to claim 1, characterized in that, It also includes an interpretability analysis step, which uses the SHAP analysis method to analyze each input feature in the historical sample set to obtain the corresponding average marginal contribution, and measures the impact of each input feature on the point prediction result based on the average marginal contribution. The formula for calculating the average marginal contribution is as follows: In the formula, For the first The average marginal contribution of each input feature; The input is the complete set of features; This is a subset of input features that does not include input feature i. The point prediction results for the input feature subset S; - Features Marginal contribution under the current feature set S.

9. The method for predicting the friction resistance coefficient according to claim 1 or 8, characterized in that, In the data processing step, the input features include roadway attributes, geometric parameters, environmental conditions, and operating condition information.

10. A friction resistance coefficient prediction system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the friction resistance coefficient prediction method according to any one of claims 1-9.

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