Decision-making method and system for shotcrete material construction parameters for underground mine support

Abstract

This invention provides a method and system for decision-making on construction parameters of shotcrete materials for underground mine support. The method includes collecting sample data containing historical construction parameters and effect indicators, constructing a gradient boosting decision tree model for indicator prediction, and determining whether positive and negative first-order gradients of samples within a node coexist when splitting nodes. If they coexist, a non-uniform split point search is performed; otherwise, all candidate points are traversed. The non-uniform search divides the samples into positive and negative gradient groups, calculates the Hessian weighted potential center of the two groups, uses a small index step size between potential centers and a large step size outside the potential centers, skips continuous segments with consistent gradient signs and gentle Hessian changes, calculates the information gain of each split point, selects the optimal value to complete the split, iterates until the termination condition is met to obtain the model, and then combines an optimization algorithm to search the parameter space to output a shotcrete construction parameter combination that matches the target construction effect.

Description

Technical Field

[0001] This application belongs to the field of decision-making, and in particular relates to a method and system for making decisions on construction parameters of shotcrete materials for underground mine support. Background Technology

[0002] The support effect of shotcrete or mortar, such as key performance indicators like early strength, later strength, bond strength, and rebound rate, depends not only on the material mix design but also on a series of parameters during construction, such as water-cement ratio, accelerator dosage, air pressure, and spraying distance and angle. Traditionally, setting shotcrete construction parameters relies on the experience of on-site construction personnel and repeated trial and error. This method is highly subjective and cannot guarantee the stability and optimization of construction quality, often leading to serious material waste, high rebound rates, excessive dust concentration, and substandard support performance. This not only increases project costs but also introduces potential safety hazards. Therefore, how to establish a scientific and accurate method for deciding shotcrete construction parameters based on historical data to achieve prediction and optimized control of support effects has become an urgent technical challenge in the intelligent construction of mines.

[0003] Gradient Boosting Decision Tree (GBDT) models are widely used due to their powerful nonlinear fitting capabilities, high prediction accuracy, and excellent detection of feature interactions. However, existing standard GBDT algorithms typically employ a strategy of sorting continuous feature values ​​and then iterating through them one by one, or using an approximate search strategy based on histograms, to find the optimal split point during the node splitting process. This search method is computationally intensive, resulting in excessively long model training times. Furthermore, this search process fails to fully utilize the gradient information of samples within nodes to intelligently guide the split point search, leading to a large amount of redundant gain calculations in informationless subintervals with uniform gradient signs and flat changes in second-order Hessian values. This not only reduces training efficiency but may also affect the model's ability to find the globally optimal split point if the search step size is set improperly, thus limiting the model's prediction accuracy and decision reliability. Summary of the Invention

[0004] To address the problems in existing gradient boosting decision trees, such as low search efficiency during node splitting, insufficient utilization of gradient information leading to long training times, and potential omission of optimal splitting points.

[0005] In the first aspect, this disclosure provides a method for determining the construction parameters of shotcrete materials for underground mine support, including: Obtain a sample dataset containing historical shotcrete construction parameters and corresponding construction effect indicators, and establish a gradient boosting decision tree model; When splitting at each node of the decision tree, a split point search process is performed for any continuous construction parameter feature to be split; the process performs a prerequisite judgment. If the prerequisite judgment is passed, the subsequent non-uniform search steps are performed; otherwise, a strategy of traversing all candidate split points is adopted for splitting. Based on the first-order gradient value and second-order Hessian value of each sample within a node, all samples with positive gradients are assigned to the positive gradient sample group, and samples with negative gradients are assigned to the negative gradient sample group. The Hessian weighted average of the two sample groups on the feature dimension of the construction parameters is calculated respectively, and the two average points are used as the potential center guided by the split; a non-uniform scanning strategy is constructed. During the scanning process, the information gain is calculated for each candidate split point determined by the sample index. At the same time, the continuous sample sequence sorted by the characteristic values ​​of construction parameters is checked. If all samples in a continuous sub-segment have the same first-order gradient sign and the second-order Hessian value changes smoothly, the evaluation of all candidate split points within the sub-segment is skipped. Among all evaluated candidate split points, the split point with the largest information gain is selected to complete the optimal split of the current node. The node splitting is repeated until the preset termination condition is met, a decision model is generated, and the model is used in combination with the optimization algorithm to obtain the combination of construction parameters for shotcrete material.

[0006] Optionally, the execution prerequisite judgment, if passed, proceeds to the subsequent non-uniform search steps, including: Calculate the first-order gradient value for each sample instance within the current node; Count the number of samples with positive first-order gradient values ​​and the number of samples with negative first-order gradient values ​​within a node. The prerequisite judgment is considered successful and the subsequent non-uniform search steps are executed if and only if both the number of samples with positive gradients and the number of samples with negative gradients are greater than zero.

[0007] Optionally, the step of calculating the Hessian weighted mean of the two sample groups on the feature dimension of the construction parameters, and using the two mean points as the potential centers guided by the split, includes: The samples within a node are divided into a positive gradient sample subset and a negative gradient sample subset based on the sign of the first-order gradient. The potential center guided by the split includes a positive gradient potential center and a negative gradient potential center. The positive gradient potential center is the value of all samples in the positive gradient sample subset on the construction parameter feature to be split, and the weighted average of the corresponding sample's second-order Hessian value. The negative gradient potential center is the value of all samples in the negative gradient sample subset on the current construction parameter feature to be split, and the weighted average of the corresponding samples' second-order Hessian values.

[0008] Optionally, the construction of the non-uniform scanning strategy includes: The sample index step size is related to the distance from the candidate split point to the central region formed by the two potential centers. A small step size is used inside the central region, and a large step size is used outside the region.

[0009] Optionally, the sample index step size is calculated by setting the starting position of the scan to the first sample index after the construction parameter features are sorted in ascending order in the current node samples; The scanning position is updated iteratively. The next scanning position is obtained by adding the sample index step size to the current sample index. The sample index step size consists of a minimum basic step size and an adjustment term. The minimum basic step size is equal to a preset percentage of the total number of node samples rounded up, and the adjustment term is proportional to the distance from the sample index of the current candidate split point to the sample indices corresponding to the two potential center points. Iterative scanning continues until the scanned position exceeds the maximum sample index of the feature.

[0010] Optionally, skipping the evaluation of all candidate split points within a sub-segment includes: Sort the samples within the node according to the current construction parameter feature values ​​from smallest to largest; During the scanning process, a continuous sample sequence is identified. If the signs of the first-order gradients of all samples in the sequence are the same, and the ratio of the standard deviation to the mean of the second-order Hessian values ​​of the sequence samples is less than a preset threshold, then the sample index of the scanning process is directly updated to the index corresponding to the last sample in the sequence, so that the next candidate split point to be evaluated is the midpoint between the feature values ​​of the last sample and the next sample, and all other candidate points within the sequence are skipped.

[0011] Optionally, the preset termination condition includes: The current tree depth has reached the preset maximum depth, or the number of samples contained in the current node is lower than the preset minimum number of samples, or the maximum information gain calculated after searching for split points of all features of the node is less than the preset minimum gain threshold.

[0012] Optionally, obtaining the combination of shotcrete material construction parameters using the model combined with the optimization algorithm includes: The particle swarm optimization algorithm is used for optimization. A population of 50 particles is initialized, with each particle representing a combination of shotcrete material construction parameters. The number of iterations is set to 100. In each iteration, the parameter combination of each particle is input into the generated gradient boosting decision tree model to obtain the predicted construction effect index as the fitness value of the particle. The velocity and position of each particle are updated based on its current fitness value, its historical best position, and the global best position of the population, until 100 iterations are completed, and the combination of construction parameters corresponding to the global best position is output.

[0013] In a second aspect, this disclosure also provides a decision-making system for shotcrete material construction parameters for underground mine support, including the following modules: A module is established to obtain a sample dataset containing historical shotcrete construction parameters and corresponding construction effect indicators, and to build a gradient boosting decision tree model. The execution module is used to perform a split point search process for any continuous construction parameter feature to be split when splitting at each node of the decision tree; the process performs a prerequisite judgment. If the prerequisite judgment is passed, the subsequent non-uniform search steps are executed; otherwise, a strategy of traversing all candidate split points is adopted for splitting. The module is used to classify all samples with positive gradients into a positive gradient sample group and samples with negative gradients into a negative gradient sample group based on the first-order gradient value and second-order Hessian value of each sample in the node. It also calculates the Hessian weighted average of the two sample groups on the feature dimension of the construction parameters and uses the two average points as the potential center for splitting; and constructs a non-uniform scanning strategy. The generation module is used to calculate the information gain for each candidate split point determined by the sample index during the scanning process. At the same time, it checks the continuous sample sequence after sorting by the feature values ​​of construction parameters. If it finds that all samples in a continuous sub-segment have the same first-order gradient sign and the second-order Hessian value changes smoothly, it skips the evaluation of all candidate split points within the sub-segment. Among all evaluated candidate split points, the split point with the largest information gain is selected to complete the optimal split of the current node. The node splitting is repeated until the preset termination condition is met, generating a decision model. The model is then used in conjunction with the optimization algorithm to obtain the combination of construction parameters for shotcrete materials.

[0014] Preferably, the execution prerequisite judgment, if passed, proceeds to the subsequent non-uniform search steps, including: Calculate the first-order gradient value for each sample instance within the current node; Count the number of samples with positive first-order gradient values ​​and the number of samples with negative first-order gradient values ​​within a node. The prerequisite judgment is considered successful and the subsequent non-uniform search steps are executed if and only if both the number of samples with positive gradients and the number of samples with negative gradients are greater than zero.

[0015] Preferably, the step of calculating the Hessian weighted mean of the two sample groups on the feature dimension of the construction parameters, and using the two mean points as the potential centers guided by the split, includes: The samples within a node are divided into a positive gradient sample subset and a negative gradient sample subset based on the sign of the first-order gradient. The potential center guided by the split includes a positive gradient potential center and a negative gradient potential center. The positive gradient potential center is the value of all samples in the positive gradient sample subset on the construction parameter feature to be split, and the weighted average of the corresponding sample's second-order Hessian value. The negative gradient potential center is the value of all samples in the negative gradient sample subset on the current construction parameter feature to be split, and the weighted average of the corresponding samples' second-order Hessian values.

[0016] Preferably, the construction of the non-uniform scanning strategy includes: The sample index step size is related to the distance from the candidate split point to the central region formed by the two potential centers. A small step size is used inside the central region, and a large step size is used outside the region.

[0017] Preferably, the sample index step size is calculated as follows: the starting position of the scan is set to the first sample index after the construction parameter features are sorted in ascending order in the current node samples; The scanning position is updated iteratively. The next scanning position is obtained by adding the sample index step size to the current sample index. The sample index step size consists of a minimum basic step size and an adjustment term. The minimum basic step size is equal to a preset percentage of the total number of node samples rounded up, and the adjustment term is proportional to the distance from the sample index of the current candidate split point to the sample indices corresponding to the two potential center points. Iterative scanning continues until the scanned position exceeds the maximum sample index of the feature.

[0018] Preferably, skipping the evaluation of all candidate split points within a sub-segment includes: Sort the samples within the node according to the current construction parameter feature values ​​from smallest to largest; During the scanning process, a continuous sample sequence is identified. If the signs of the first-order gradients of all samples in the sequence are the same, and the ratio of the standard deviation to the mean of the second-order Hessian values ​​of the sequence samples is less than a preset threshold, then the sample index of the scanning process is directly updated to the index corresponding to the last sample in the sequence, so that the next candidate split point to be evaluated is the midpoint between the feature values ​​of the last sample and the next sample, and all other candidate points within the sequence are skipped.

[0019] Preferably, the preset termination condition includes: The current tree depth has reached the preset maximum depth, or the number of samples contained in the current node is lower than the preset minimum number of samples, or the maximum information gain calculated after searching for split points of all features of the node is less than the preset minimum gain threshold.

[0020] Preferably, the step of using the model combined with the optimization algorithm to obtain the combination of construction parameters for the shotcrete material includes: The particle swarm optimization algorithm is used for optimization. A population of 50 particles is initialized, with each particle representing a combination of shotcrete material construction parameters. The number of iterations is set to 100. In each iteration, the parameter combination of each particle is input into the generated gradient boosting decision tree model to obtain the predicted construction effect index as the fitness value of the particle. The velocity and position of each particle are updated based on its current fitness value, its historical best position, and the global best position of the population, until 100 iterations are completed, and the combination of construction parameters corresponding to the global best position is output.

[0021] This invention utilizes a split point search mechanism during node splitting in a gradient boosting decision tree model. This mechanism prioritizes computational resources for complex splitting scenarios where positive and negative gradient samples coexist, avoiding unnecessary computational overhead, by pre-judging the gradient sign of samples within a node. It reduces the computational complexity of split point search by constructing a Hessian weighted mean as the potential center and performing a refined, non-uniform search around this region, focusing the search on key areas with the highest information gain. Furthermore, by skipping consecutive sample sub-segments with consistent gradient signs and gently changing Hessian values, redundant evaluation is further reduced. This improves the model's training speed and computational efficiency, enabling the faster construction of the mapping relationship between construction parameters and performance indicators while maintaining prediction accuracy. Attached Figure Description

[0022] Figure 1 A flowchart of the first embodiment; Figure 2 This is a schematic diagram illustrating the relationship between non-uniform scanning step size adjustment; Figure 3 A schematic diagram illustrating the principle of the same gradient sub-segment skipping mechanism; Figure 4 A schematic diagram of the convergence curve for particle swarm optimization. Detailed Implementation

[0023] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this specification as detailed in the appended claims.

[0024] It should be understood that the terms “comprising” and “having”, and any variations thereof, in the embodiments of this specification are intended to cover but not exclude inclusion. For example, a product or device that includes a series of components is not necessarily limited to those components that are explicitly listed, but may include other components that are not explicitly listed or that are inherent to such product or device.

[0025] In the first embodiment, the present invention proposes a method for determining the construction parameters of shotcrete materials for underground mine support, such as... Figure 1 As shown, it includes the following steps: S1. Obtain a sample dataset containing historical shotcrete construction parameters and corresponding construction effect indicators, and establish a gradient boosting decision tree model.

[0026] The `read_csv` or `read_excel` function is used to load historical data from a file, resulting in a DataFrame dataset. The dataset is divided into a feature matrix X, containing all construction parameters such as water-cement ratio, accelerator dosage, and wind pressure, and a target vector y, containing construction performance indicators such as early strength and rebound rate. Based on this dataset, a gradient boosting decision tree model is built from scratch. Instead of directly calling the `fit` method of existing libraries like XGBoost or LightGBM, the core iterative tree-building logic is implemented custom-. During model initialization, an initial prediction value is given, typically the mean of all target values. In each iteration, based on a predefined loss function, such as the L2 loss function (mean squared error), the negative gradient (pseudo-residual) and the second-order Hessian value for each sample are calculated. For L2 loss, the negative gradient is the true value minus the predicted value, and the second-order Hessian value is a constant 1. Using the model generated in the previous iteration as a foundation, a new decision tree is trained with the pseudo-residual as the target, and this tree is added to the model ensemble.

[0027] In an optional embodiment, the gradient boosting decision tree model is an additive model composed of multiple regression decision trees, used to receive construction parameters and predict construction effect indicators.

[0028] The gradient boosting decision tree model is an ensemble model consisting of K regression decision trees, with an additive structure.

[0029] The model is generated iteratively. The prediction function is obtained by weighted summation of the predicted values ​​from an initial constant and the prediction results from K trees. For an input sample of construction parameters x, the predicted value is... The calculation formula is: .in, It is the initial model, usually the mean of the target values ​​of the training samples. It is the k-th regression decision tree. It's the learning rate. Each tree They are all trained to fit the negative gradient predicted by the previous model.

[0030] The model's input is a feature vector x, representing a set of construction parameters for shotcrete materials. Each dimension of this vector corresponds to a specific construction parameter, such as water-cement ratio and accelerator dosage; the output is a scalar value. ,Right now The calculation results represent the predicted construction effect indicators under the input construction parameter combination, such as the predicted 28-day compressive strength.

[0031] S2, when splitting at each node of the decision tree, for any continuous construction parameter feature to be split, a split point search process is performed; the process performs a prerequisite judgment. If the prerequisite judgment is passed, the subsequent non-uniform search steps are performed; otherwise, a strategy of traversing all candidate split points is adopted for splitting.

[0032] When implementing the node splitting function `find_best_split` in the decision tree, the input parameters are the sample index set contained in the current node, the first-order gradient vector G of all samples, and the second-order Hessian vector H. For a given continuous feature, the first-order gradient values ​​of all samples within the node are extracted to form a gradient subset. Using the `any` function from the NumPy library, two parallel logical checks are performed: `numpy.any subset greater than zero` and `numpy.any subset less than zero`, to check if the gradient subset contains both positive and negative numbers. If this combined condition is true, the subsequent non-uniform search function is called. If it is false, the alternative standard split point search strategy is initiated. The samples within the current node are sorted in ascending order according to the feature value. All adjacent sample pairs with unequal feature values ​​are traversed, and the midpoint of their feature values ​​is used as a candidate split point. The information gain is calculated for each pair, and the split point with the largest gain is selected.

[0033] In an optional embodiment, the execution prerequisite judgment, if passed, proceeds to the subsequent non-uniform search steps, including: Calculate the first-order gradient value for each sample instance within the current node; Count the number of samples with positive first-order gradient values ​​and the number of samples with negative first-order gradient values ​​within a node. The prerequisite judgment is considered successful and the subsequent non-uniform search steps are executed if and only if both the number of samples with positive gradients and the number of samples with negative gradients are greater than zero.

[0034] Before splitting at any node of the gradient boosting decision tree, a premise judgment is performed on all N sample instances within the node. The first-order gradient with respect to the current model's predicted value is calculated for each sample i based on the loss function. For example, when using the squared loss function At that time, the first gradient The calculation formula is: Initialize two counters: count_pos = 0 for positive gradient samples and count_neg = 0 for negative gradient samples. Iterate through all samples within a node; if sample i... If > 0, then count_pos increments by 1; if If the count is less than 0, then count_neg increments by 1. A conditional check is performed: if and only if both count_pos > 0 and count_neg > 0, the condition is passed, indicating that the current node contains both over- and under-predicted samples, suggesting room for optimization. In this case, the subsequent non-uniform search split point strategy is initiated. If either counter is 0, it indicates that the prediction error direction of all samples is consistent, weakening the significance of the non-uniform search. In this case, the conventional search strategy of traversing all candidate split points is adopted.

[0035] S3. Based on the first-order gradient value and second-order Hessian value of each sample within the node, all samples with positive gradients are assigned to the positive gradient sample group, and samples with negative gradients are assigned to the negative gradient sample group. The Hessian weighted average of the two sample groups on the feature dimension of the construction parameters is calculated respectively, and the two average points are used as the potential center guided by the split; a non-uniform scanning strategy is constructed.

[0036] Using Boolean indexing or NumPy's `where` function, the sample index, feature value, gradient value, and Hessian value within the current node are filtered into two sets based on the sign of the first-order gradient: a positive gradient set and a negative gradient set. For the positive gradient set, the dot product of the feature value vector and the Hessian value vector is calculated using NumPy's `dot` function, and then divided by the sum of the Hessian value vectors, i.e., the formula is executed. in For eigenvalues, The Hessian value is used to obtain the positive gradient potential center. The same calculation is performed on the negative gradient set to obtain the negative gradient potential center. After determining the two potential centers, two integer step sizes are set, for example, a small step size of 1 and a large step size of 10. The samples within a node are sorted in ascending order according to their current feature values. A while loop is started, scanning from the first sorted sample index. Within the loop, it is determined whether the feature value of the current sample lies within the closed interval formed by the two potential centers. If yes, the sample index in the next iteration is increased by the small step size; otherwise, the large step size is increased. In each iteration, the midpoint of the feature values ​​between the sample pointed to by the current index and the sample pointed to by the next index is used as a candidate split point.

[0037] In an optional embodiment, calculating the Hessian weighted mean of the two sample groups on the construction parameter feature dimension, and using the two mean points as the potential center guided by the split, includes: The samples within a node are divided into a positive gradient sample subset and a negative gradient sample subset based on the sign of the first-order gradient. The potential center guided by the split includes a positive gradient potential center and a negative gradient potential center. The positive gradient potential center is the value of all samples in the positive gradient sample subset on the construction parameter feature to be split, and the weighted average of the corresponding sample's second-order Hessian value. The negative gradient potential center is the value of all samples in the negative gradient sample subset on the current construction parameter feature to be split, and the weighted average of the corresponding samples' second-order Hessian values.

[0038] After the prerequisite judgment is passed, the second-order Hessian value of each sample i within a node is calculated for a continuous construction parameter feature to be split. For the squared loss function, all All values ​​are 1. Create a subset of positive gradients. and negative gradient subset Traverse all samples within a node; if the gradient of sample i... If the value is greater than 0, then it is classified as... ;like If <0, then it belongs to Positive gradient potential center The calculation formula is: ,in This represents the value of sample i on feature f. Similarly, the negative gradient potential center is calculated. For example, regarding the water-cement ratio characteristic, if If the samples include {water-cement ratio: 0.45, H: 1.0} and {water-cement ratio: 0.48, H: 1.2}, then... ≈0.466. If If the samples include {water-cement ratio: 0.55, H: 1.1} and {water-cement ratio: 0.58, H: 0.9}, then... ≈0.564. The two potential center values ​​above, 0.466 and 0.564, indicate the core region where the split point with the greatest possible information gain is located.

[0039] In an optional embodiment, the construction of the non-uniform scanning strategy includes: The sample index step size is related to the distance from the candidate split point to the central region formed by the two potential centers. A small step size is used inside the central region, and a large step size is used outside the region.

[0040] After calculating the positive and negative gradient potential centers and Then, all samples within a node are sorted in ascending order based on the current construction parameter feature values. The approximate index position of the potential center in the sorted sample sequence is then determined. and Define the central region as the index[ , The scanning strategy starts with the first sample index and iteratively evaluates candidate split points. In each iteration, the next index step size is determined based on the relative position of the currently scanned sample index to the central region. If the current index is inside the central region, a smaller fixed step size, such as 1 or 2, is used for fine-grained searching. If the current index is outside the central region, a larger fixed step size, such as 5% of the total number of node samples rounded up, is used for fast jumping. In this way, computational resources are concentrated on the region most likely to produce high information gain, thereby improving search efficiency while ensuring split quality.

[0041] In an optional embodiment, the sample index step size is calculated by setting the starting position of the scan to the first sample index after the construction parameter features are sorted in ascending order in the current node samples; The scanning position is updated iteratively. The next scanning position is obtained by adding the sample index step size to the current sample index. The sample index step size consists of a minimum basic step size and an adjustment term. The minimum basic step size is equal to a preset percentage of the total number of node samples rounded up, and the adjustment term is proportional to the distance from the sample index of the current candidate split point to the sample indices corresponding to the two potential center points. Iterative scanning continues until the scanned position exceeds the maximum sample index of the feature.

[0042] Let the total number of samples within a node be N, and the indices of the samples sorted by feature values ​​be j = 0, 1, ..., N-1. The calculated potential center... and The feature values ​​are compared with the sorted sample sequence. Using binary search or nearest neighbor search strategies, the sample with the smallest absolute difference between the feature value and the center of gravity value is found. The indices of these samples are denoted as follows: and and determine the center point index. The scan begins at the current index current_idx = 0. In each iteration, the step size... The calculation is as follows: Calculate the minimum basic step size. , This indicates rounding up, ensuring a minimum forward increment even in the central region, for example, when N=2000. =2. Calculate the adjustment item. This value increases as the distance between the current position and the center point increases. Total step size. Update scan location: For example, N=2000, =1000. When current_idx=100, the distance is 900. =45, total step size is 47. When current_idx=990, the distance is 10. =0, total step size is 2. This process is repeated until the scan position exceeds N-1. The adjustment rule for non-uniform scan step size is as follows: Figure 2 As shown, the V-shaped curve intuitively reflects the step size design logic of this invention.

[0043] S4. During the scanning process, the information gain is calculated for each candidate split point determined by the sample index. At the same time, the continuous sample sequence sorted by the characteristic values ​​of the construction parameters is checked. If all samples in a continuous sub-segment have the same first-order gradient sign and the second-order Hessian value changes smoothly, the evaluation of all candidate split points within the sub-segment is skipped. Among all evaluated candidate split points, the split point with the largest information gain is selected to complete the optimal split of the current node.

[0044] For each candidate split point, the sample is divided into left and right child nodes. NumPy's `sum` function is used to calculate the sum of the first-order gradients (GL) and second-order Hessian gradients (HL) of the left child node, and the sum of the gradients (GR) and HR of the right child node. Then, the sum of the gradients of the entire node before the split is calculated. The sum of Hessian According to the gain calculation formula of gradient boosting decision trees. Perform calculations, where The L2 regularization coefficient is... This addresses the complexity cost of adding new leaf nodes. During the scan, a window size is set, for example, k=20. The k consecutive samples starting from the current index are examined, and NumPy's `sign` and `all` functions are used to determine if their first-order gradient signs are identical. Simultaneously, the second-order Hessian values ​​of these k samples are extracted, and the standard deviation is calculated using NumPy's `std` function. If the standard deviation is less than a preset minimum threshold `epsilon`, for example, 0.001, the Hessian value is considered to be changing smoothly. When both conditions are met, the sample scan index is advanced k positions forward, thus skipping the gain calculation for all potential split points within the stable sub-segments. After the entire scan is complete, from all evaluated candidate split points, the split point that maximizes the information gain (Gain) and its corresponding features are selected as the split decision for the current node.

[0045] In an optional embodiment, skipping the evaluation of all candidate split points within a sub-segment includes: Sort the samples within the node according to the current construction parameter feature values ​​from smallest to largest; During the scanning process, a continuous sample sequence is identified. If the signs of the first-order gradients of all samples in the sequence are the same, and the ratio of the standard deviation to the mean of the second-order Hessian values ​​of the sequence samples is less than a preset threshold, then the sample index of the scanning process is directly updated to the index corresponding to the last sample in the sequence, so that the next candidate split point to be evaluated is the midpoint between the feature values ​​of the last sample and the next sample, and all other candidate points within the sequence are skipped.

[0046] After sorting the samples by feature values, the scanning process pre-examines a continuous sequence of samples starting from the current index when moving to the current index. For example, it examines the sample sequence from index i to j. If the first-order gradient g of all samples in this sequence has the same sign, the second-order Hessian value H is further analyzed. The mean of the H values ​​of the samples in this sequence is calculated. and standard deviation Calculate the coefficient of variation. If the CV is less than the preset threshold of 0.01, it indicates that the error trends of the samples in this region are consistent and the curvature of the loss function is stable, making it unlikely that an optimal split point exists within this region. In this case, after evaluating the split point between index i-1 and i, the scanning process directly updates the current scanning index to the index j of the last sample in the stable sequence. This ensures that the next candidate split point to be extracted and calculated is the midpoint between the feature values ​​of sample j and sample j+1, thus skipping all candidate split points between i and j-1 and further accelerating the search process. Figure 3As shown in the figure, the gray area represents a stable sub-segment that meets the skipping condition: the samples in this area have consistent first-order gradient signs, their second-order Hessian values ​​change smoothly, and there are no high-gain split points. Therefore, by using the index to skip all candidate split points within the sub-segment, the search efficiency can be improved.

[0047] S5, repeat the node splitting until the preset termination condition is met, generate a decision model, and use the model in combination with the optimization algorithm to obtain the combination of sprayed grout material construction parameters.

[0048] The recursive process of node splitting is terminated under certain conditions, including the tree reaching a preset maximum depth, the number of samples within a node being lower than a preset minimum number of samples, or the information gain from splitting being less than a preset minimum gain threshold. When any of these conditions are met, the node stops splitting and becomes a leaf node. After all trees are built, a gradient boosting decision tree ensemble model is formed. An optimization algorithm library is used, selecting either Particle Swarm Optimization (PSO) or Bayesian optimization. An objective function is defined, whose input is a set of shotcrete material construction parameters, and whose output is the negative value of the construction effect index predicted by the trained decision model for these parameters, since optimization algorithms typically seek the minimum value. The range of values ​​for each construction parameter is set as the boundary constraint of the search space. The optimization algorithm is run, and after iterative search, a set of construction parameters that minimizes the objective function value is output. This parameter combination represents the optimal decision that achieves the target construction effect index.

[0049] In an optional embodiment, the preset termination condition includes: The current tree depth has reached the preset maximum depth, or the number of samples contained in the current node is lower than the preset minimum number of samples, or the maximum information gain calculated after searching for split points of all features of the node is less than the preset minimum gain threshold.

[0050] During the tree's growth, before attempting to split a node, the following three pre-pruning conditions are checked sequentially: The depth of the current node is checked (root node depth is 0, child nodes are 1, and so on). If the current node's depth has reached or exceeded the preset maximum depth of 6, the split stops, and the node becomes a leaf node. The number of samples contained in the current node is counted. If this number is less than the preset minimum number of samples of 10, the data volume is considered insufficient to support a reliable split, and the split stops. After performing an optimized split point search on all features of the current node, the maximum information gain value among all features and all candidate split points is obtained. If the maximum information gain value is less than the preset minimum gain threshold of 0.001, even the best split is considered to yield negligible benefits and is not worthwhile. The node splitting process terminates as long as any of the above conditions are met.

[0051] In an optional embodiment, obtaining the combination of shotcrete material construction parameters using the model combined with the optimization algorithm includes: The particle swarm optimization algorithm is used for optimization. A population of 50 particles is initialized, with each particle representing a combination of shotcrete material construction parameters. The number of iterations is set to 100. In each iteration, the parameter combination of each particle is input into the generated gradient boosting decision tree model to obtain the predicted construction effect index as the fitness value of the particle. The velocity and position of each particle are updated based on its current fitness value, its historical best position, and the global best position of the population, until 100 iterations are completed, and the combination of construction parameters corresponding to the global best position is output.

[0052] The particle swarm size is set to 50, and the maximum number of iterations is set to 100. A search space for construction parameters is defined, such as a water-cement ratio range of [0.40, 0.55] and a quick-setting agent dosage of [4.0%, 6.0%]. Fifty particles are randomly generated, each particle's position vector corresponding to a set of construction parameters within the specified range. In each iteration, for each particle, the position vector is used as input to call a pre-trained decision tree model for prediction, resulting in a construction performance index. This predicted value is the particle's fitness value. Based on the standard update formula of the particle swarm optimization algorithm, combined with the inertia weight w and the individual learning factor... and group learning factors The velocity and position of each particle are updated. A particle's new position is influenced by both its own historical best position and the global best position of the entire population. This process is repeated for 100 iterations. After the iterations, the combination of construction parameters represented by the global best position is the decision result, for example, {water-cement ratio: 0.42, accelerator dosage: 5.1%,...}. The convergence process of the particle swarm optimization algorithm is as follows: Figure 4 As shown.

[0053] In the specific implementation of the gradient boosting decision tree model, the optimization splitting process of each node begins with a prerequisite judgment. This judgment ensures that the non-uniform splitting point search algorithm is only initiated when there are samples with both over- and under-predicted values ​​within the node, by calculating and statistically analyzing the number of positive and negative first-order gradients of the samples within the node; otherwise, it degenerates into a regular global scan. Once the non-uniform search is initiated, the samples are divided into positive and negative subsets based on the sign of their first-order gradients. For the construction parameter feature to be split, the Hessian weighted mean of the two subsets on that feature dimension is calculated, and the two mean points are defined as potential centers, which identify the regions where the splitting point with the greatest information gain is most likely to occur. The subsequent splitting point scanning strategy revolves around these two potential centers, employing a step-size adjustment method. The step size consists of a very small base step size and a variable term proportional to the distance from the current scan position to the potential center. This allows for a larger step size in regions far from the potential center, enabling rapid exploration, while the step size automatically decreases in the core region near the potential center for a finer search. To further improve efficiency, the scanning process also identifies and skips continuous sample sub-segments with consistent internal gradient signs and gradual changes in Hessian values ​​in real time, as splitting within these regions yields extremely low returns. Tree growth follows strict pre-pruning rules: any node that meets any of the following conditions is stopped from splitting and becomes a leaf node, ensuring the model's simplicity and generalization ability. After model construction, the overall model is an additive model composed of multiple decision trees, receiving a set of construction parameters as input and outputting corresponding predicted construction effects. Particle swarm optimization (PSO) is used for global optimization in the multi-dimensional construction parameter space. A population of 50 particles undergoes 100 iterations, using the prediction results of the decision tree model as the fitness function, continuously adjusting the parameter combination until it converges to the optimal parameter configuration that achieves the target construction effect.

[0054] The experiment used the SP-CCS-2023 dataset, containing 5147 shotcrete construction records. This dataset includes 8 continuous construction parameter features and 2 categorical features, with the target being the 28-day compressive strength. The experimental software environment was Python 3.9. The control group used a gradient boosting decision tree model with a conventional split point search strategy based on histograms. The experimental group used an optimized model integrating premise judgment, center-of-potential guided non-uniform search, and a sub-segment skipping mechanism. Both models were configured with the same hyperparameters, including 100 trees, a learning rate of 0.1, a maximum depth of 6, and a minimum number of samples per node of 10. The evaluation metrics were the total training time and the root mean square error (RMSE) on the test set.

[0055] With the same training and test set partitioning, the two models underwent five repeated experiments, and the average value was taken. The control group model had an average training time of 15.23 seconds and a root mean square error (RMSE) of 2.45 MPa on the test set. The experimental group model, which adopted the optimized scheme, had an average training time of 9.87 seconds and a RMSE of 2.41 MPa on the test set. The data shows that the experimental group reduced the training time while maintaining or even slightly improving prediction accuracy.

[0056] Compared to the control group using a conventional split-point search strategy, the optimized model proposed in this invention demonstrates advantages in both efficiency and performance. The training speed of the experimental group model improved by 35.2 percentage points, with training time decreasing from 15.23s to 9.87s. In terms of prediction accuracy, the root mean square error of the experimental group model decreased by 1.6 percentage points, from 2.45MPa to 2.41MPa, showing stronger generalization ability. Premise judgments avoid complex searches at nodes with a single gradient direction, while the center of gravity calculation locks in potential regions for high-gain split points. The adjusted scan step size and the skipping strategy for consecutive sub-segments with the same gradient together constitute the pruning process, reducing the total number of candidate split points evaluated. The slight improvement in prediction accuracy stems from the reallocation of computational resources; the optimized algorithm allocates more computation to a refined search of the core region near the center of gravity, enabling the model to more accurately detect nonlinear relationships in the data, find higher-quality split points, and thus improve the performance of the base learner and the prediction accuracy of the entire additive model.

[0057] In a second embodiment, the present invention also provides a decision system for construction parameters of shotcrete materials for underground mine support, comprising the following modules: A module is established to obtain a sample dataset containing historical shotcrete construction parameters and corresponding construction effect indicators, and to build a gradient boosting decision tree model. The execution module is used to perform a split point search process for any continuous construction parameter feature to be split when splitting at each node of the decision tree; the process performs a prerequisite judgment. If the prerequisite judgment is passed, the subsequent non-uniform search steps are executed; otherwise, a strategy of traversing all candidate split points is adopted for splitting. The module is used to classify all samples with positive gradients into a positive gradient sample group and samples with negative gradients into a negative gradient sample group based on the first-order gradient value and second-order Hessian value of each sample in the node. It also calculates the Hessian weighted average of the two sample groups on the feature dimension of the construction parameters and uses the two average points as the potential center for splitting; and constructs a non-uniform scanning strategy. The generation module is used to calculate the information gain for each candidate split point determined by the sample index during the scanning process. At the same time, it checks the continuous sample sequence after sorting by the feature values ​​of construction parameters. If it finds that all samples in a continuous sub-segment have the same first-order gradient sign and the second-order Hessian value changes smoothly, it skips the evaluation of all candidate split points within the sub-segment. Among all evaluated candidate split points, the split point with the largest information gain is selected to complete the optimal split of the current node. The node splitting is repeated until the preset termination condition is met, generating a decision model. The model is then used in conjunction with the optimization algorithm to obtain the combination of construction parameters for shotcrete materials.

[0058] It should be understood that in the foregoing description of the embodiments in this specification, various features are combined in a single embodiment, drawing, or description for the purpose of simplifying the description and to aid in understanding a feature. However, this does not mean that the combination of these features is necessary, and those skilled in the art, upon reading this specification, may readily identify some of the devices as separate embodiments. That is, the embodiments in this specification can also be understood as an integration of multiple secondary embodiments. And the content of each secondary embodiment is valid even if it contains fewer than all the features of a single foregoing disclosed embodiment.

Claims

1. A method for determining construction parameters of shotcrete materials for underground mine support, characterized in that, Includes the following steps: Obtain a sample dataset containing historical shotcrete construction parameters and corresponding construction effect indicators, and establish a gradient boosting decision tree model; When splitting at each node of the decision tree, a split point search process is performed for any continuous construction parameter feature to be split; the process performs a prerequisite judgment. If the prerequisite judgment is passed, the subsequent non-uniform search steps are performed; otherwise, a strategy of traversing all candidate split points is adopted for splitting. Based on the first-order gradient value and second-order Hessian value of each sample within a node, all samples with positive gradients are assigned to the positive gradient sample group, and samples with negative gradients are assigned to the negative gradient sample group. The Hessian weighted average of the two sample groups on the feature dimension of the construction parameters is calculated respectively, and the two average points are used as the potential center guided by the split; a non-uniform scanning strategy is constructed. During the scanning process, the information gain is calculated for each candidate split point determined by the sample index. At the same time, the continuous sample sequence sorted by the characteristic values ​​of construction parameters is checked. If all samples in a continuous sub-segment have the same first-order gradient sign and the second-order Hessian value changes smoothly, the evaluation of all candidate split points within the sub-segment is skipped. Among all evaluated candidate split points, the split point with the largest information gain is selected to complete the optimal split of the current node. The node splitting is repeated until the preset termination condition is met, a decision model is generated, and the model is used in combination with the optimization algorithm to obtain the combination of construction parameters for shotcrete material.

2. The method according to claim 1, characterized in that, The execution prerequisite judgment, if passed, proceeds to the subsequent non-uniform search steps, including: Calculate the first-order gradient value for each sample instance within the current node; Count the number of samples with positive first-order gradient values ​​and the number of samples with negative first-order gradient values ​​within a node. The prerequisite judgment is considered successful and the subsequent non-uniform search steps are executed if and only if both the number of samples with positive gradients and the number of samples with negative gradients are greater than zero.

3. The method according to claim 1, characterized in that, The calculation of the Hessian weighted mean of the two sample groups on the feature dimension of the construction parameters, using the two mean points as the potential centers guided by the split, includes: The samples within a node are divided into a positive gradient sample subset and a negative gradient sample subset based on the sign of the first-order gradient. The potential center guided by the split includes a positive gradient potential center and a negative gradient potential center. The positive gradient potential center is the value of all samples in the positive gradient sample subset on the construction parameter feature to be split, and the weighted average of the corresponding sample's second-order Hessian value. The negative gradient potential center is the value of all samples in the negative gradient sample subset on the current construction parameter feature to be split, and the weighted average of the corresponding samples' second-order Hessian values.

4. The method according to claim 1, characterized in that, The non-uniform scanning strategy includes: The sample index step size is related to the distance from the candidate split point to the central region formed by the two potential centers. A small step size is used inside the central region, and a large step size is used outside the region.

5. The method according to claim 4, characterized in that, The sample index step size is calculated as follows: the starting position of the scan is set to the first sample index after the construction parameter features are sorted in ascending order in the current node samples; The scanning position is updated iteratively. The next scanning position is obtained by adding the sample index step size to the current sample index. The sample index step size consists of a minimum basic step size and an adjustment term. The minimum basic step size is equal to a preset percentage of the total number of node samples rounded up, and the adjustment term is proportional to the distance from the sample index of the current candidate split point to the sample indices corresponding to the two potential center points. Iterative scanning continues until the scanned position exceeds the maximum sample index of the feature.

6. The method according to claim 1, characterized in that, Skipping the evaluation of all candidate split points within a sub-segment includes: Sort the samples within the node according to the current construction parameter feature values ​​from smallest to largest; During the scanning process, a continuous sample sequence is identified. If the signs of the first-order gradients of all samples in the sequence are the same, and the ratio of the standard deviation to the mean of the second-order Hessian values ​​of the sequence samples is less than a preset threshold, then the sample index of the scanning process is directly updated to the index corresponding to the last sample in the sequence, so that the next candidate split point to be evaluated is the midpoint between the feature values ​​of the last sample and the next sample, and all other candidate points within the sequence are skipped.

7. The method according to claim 1, characterized in that, The preset termination conditions include: The current tree depth has reached the preset maximum depth, or the number of samples contained in the current node is lower than the preset minimum number of samples, or the maximum information gain calculated after searching for split points of all features of the node is less than the preset minimum gain threshold.

8. The method according to claim 1, characterized in that, The process of using the model combined with the optimization algorithm to obtain the combination of construction parameters for shotcrete materials includes: The particle swarm optimization algorithm is used for optimization. A population of 50 particles is initialized, with each particle representing a combination of shotcrete material construction parameters. The number of iterations is set to 100. In each iteration, the parameter combination of each particle is input into the generated gradient boosting decision tree model to obtain the predicted construction effect index as the fitness value of the particle. The velocity and position of each particle are updated based on its current fitness value, its historical best position, and the global best position of the population, until 100 iterations are completed, and the combination of construction parameters corresponding to the global best position is output.

9. A decision-making system for shotcrete material construction parameters for underground mine support, characterized in that, Includes the following modules: A module is established to obtain a sample dataset containing historical shotcrete construction parameters and corresponding construction effect indicators, and to build a gradient boosting decision tree model. The execution module is used to perform a split point search process for any continuous construction parameter feature to be split when splitting at each node of the decision tree; the process performs a prerequisite judgment. If the prerequisite judgment is passed, the subsequent non-uniform search steps are executed; otherwise, a strategy of traversing all candidate split points is adopted for splitting. The module is used to classify all samples with positive gradients into a positive gradient sample group and samples with negative gradients into a negative gradient sample group based on the first-order gradient value and second-order Hessian value of each sample in the node. It also calculates the Hessian weighted average of the two sample groups on the feature dimension of the construction parameters and uses the two average points as the potential center for splitting; and constructs a non-uniform scanning strategy. The generation module is used to calculate the information gain for each candidate split point determined by the sample index during the scanning process. At the same time, it checks the continuous sample sequence after sorting by the feature values ​​of construction parameters. If it finds that all samples in a continuous sub-segment have the same first-order gradient sign and the second-order Hessian value changes smoothly, it skips the evaluation of all candidate split points within the sub-segment. Among all evaluated candidate split points, the split point with the largest information gain is selected to complete the optimal split of the current node. The node splitting is repeated until the preset termination condition is met, generating a decision model. The model is then used in conjunction with the optimization algorithm to obtain the combination of construction parameters for shotcrete materials.

10. The system according to claim 9, characterized in that, The execution prerequisite judgment, if passed, proceeds to the subsequent non-uniform search steps, including: Calculate the first-order gradient value for each sample instance within the current node; Count the number of samples with positive first-order gradient values ​​and the number of samples with negative first-order gradient values ​​within a node. The prerequisite judgment is considered successful and the subsequent non-uniform search steps are executed if and only if both the number of samples with positive gradients and the number of samples with negative gradients are greater than zero.

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