A method for predicting the size distribution of rock broken by open deep-hole blasting

Abstract

This invention discloses a method for predicting the rock fragmentation distribution in open-pit deep-hole blasting, comprising the following steps: acquiring historical blasting data; constructing a radial basis function neural network; inputting blasting design parameters and rock coefficients from the historical blasting data into a nonlinear feature cross layer to generate an enhanced feature vector; inputting the enhanced feature vector into a prior knowledge-guided hidden layer center selection layer to determine multiple center points of the radial basis functions, and assigning a corresponding radial basis function to each center point according to a preset rule; inputting the output result into a nonlinear output mapping layer to perform a nonlinear transformation on the output of the radial basis functions; inputting the nonlinearly transformed features into a multi-task output layer to simultaneously predict and output multiple different fragmentation feature values; and constructing a rock fragmentation distribution curve based on the multiple different fragmentation feature values ​​to complete the prediction of the blasting fragmentation distribution.

Description

Technical Field

[0001] This invention relates to the field of rock blasting technology, and in particular to a method for predicting the distribution of rock fragment size in open-pit deep-hole blasting. Background Technology

[0002] A method for predicting the rock fragment size distribution in open-pit deep-hole blasting is developed. This method establishes a scientifically sound model for predicting rock fragment size distribution, combining multiple factors such as rock physical and mechanical properties, explosive performance parameters, blasting hole network parameters, and geological structural characteristics. This comprehensive analysis enables accurate prediction and visualization of the rock fragment size distribution after blasting, providing a reliable basis for blasting design optimization, charge structure adjustment, detonation network layout, and blasting effect evaluation. Its significance lies not only in improving the accuracy and controllability of blasting operations, reducing the rate of large fragments and fine ore, decreasing secondary crushing costs and equipment wear, and improving the overall economic benefits of mining and engineering construction, but also in promoting efficient resource utilization and energy conservation and emission reduction through optimized fragment size distribution. It reduces environmental impacts such as blasting vibration, flyrock, and dust, ensuring the safety of personnel and stable equipment operation. Simultaneously, it promotes in-depth research in blasting theory, providing key technical support for the intelligent and green transformation of open-pit deep-hole blasting technology, ultimately achieving a synergistic improvement in economic, environmental, and social benefits.

[0003] Traditional methods use linear superposition formulas to calculate rock coefficients, treating rock mass description, density influence, and hardness coefficient as independent variables. However, in actual blasting engineering, these parameters have complex coupling relationships, and linear models cannot describe this nonlinear interaction effect where 1+1>2, leading to prediction results that deviate significantly from reality. Therefore, a method for predicting the rock fragmentation distribution in open-pit deep-hole blasting is proposed. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for predicting the distribution of rock fragments in open-pit deep-hole blasting.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting the rock fragment size distribution in open-pit deep-hole blasting includes the following steps: Historical blasting data is obtained, which includes blasting design parameters, rock coefficients, and actual block size distribution parameters after rock fragmentation. The rock coefficients are calculated based on rock mass description values, density influence values, and hardness coefficients that reflect rock properties. Specifically: The specific blasting design parameters include row spacing, hole spacing, step height, hole diameter, plugging length, single hole charge, and explosive coefficient. These parameters reflect the specific process design of the blasting operation. The rock coefficient is not a directly measured value, but a comprehensive index obtained through a specific calculation method based on rock mass description values, density influence values, and hardness coefficients that reflect the properties of the rock. The rock mass description values ​​are used to quantify the integrity and joint development of the rock, the density influence values ​​are used to reflect the influence of rock density on blasting effect, and the hardness coefficients are used to characterize the hardness of the rock. The actual block size distribution parameters after rock fragmentation are used as target values ​​for model training. Specifically, these parameters include the particle size when the cumulative distribution of rock fragments reaches 10%, 50%, and 90%, as well as one or more combinations of large block ratio, reasonable block ratio, and fine particle ratio. A radial basis function neural network is constructed, comprising a nonlinear feature cross layer, a hidden center selection layer guided by prior knowledge, a variable-width radial basis function layer, a nonlinear output mapping layer, and a multi-task output layer connected in sequence. The blasting design parameters and rock coefficients from the historical blasting data are input into the nonlinear feature cross layer. Nonlinear cross-coupling processing is performed on the rock mass description values, density influence values, and hardness coefficient to generate an enhanced feature vector. The enhanced feature vector is input into the hidden center selection layer guided by the prior knowledge. Combined with the pre-set prior knowledge of extreme working conditions, multiple center points of the radial basis function are determined in the feature space of the enhanced feature vector. Each center point is assigned a corresponding radial basis function in the variable width radial basis function layer according to a preset rule. The output result processed by the variable-width radial basis function layer is input to the nonlinear output mapping layer, and the output of the radial basis function is nonlinearly transformed by the nonlinear mapping function. The features after nonlinear transformation are input into the multi-task output layer, which simultaneously predicts and outputs multiple different block-level feature values. Based on the multiple different block size characteristic values, a complete rock fragmentation block size distribution curve is constructed to complete the prediction of the blasting block size distribution; When the current radial basis function neural network is used to predict a new blasting condition and the prediction deviation exceeds a preset threshold, the new blasting condition data is dynamically added to the variable width radial basis function layer as a new radial basis function neuron center, and only the weight parameters of the nonlinear output mapping layer and the multi-task output layer are finely adjusted and updated.

[0006] The above further includes: Furthermore, the nonlinear feature cross-layer is constructed, which employs a factorization machine mechanism for higher-order feature interactions, specifically as follows: The rock coefficient is composed of rock mass description values, density influence values, and hardness coefficients. The rock mass description values, density influence values, and hardness coefficients are extracted and combined into an original rock feature vector. A corresponding embedding vector is set for each component (i.e., rock mass description value, density influence value, and hardness coefficient) in the original rock feature vector. The embedding vector is used to map the original scalar values ​​to a high-dimensional distributed representation space in order to better capture the potential correlation between components. The system is configured with a first-order feature interaction part and a second-order feature interaction part. The first-order feature interaction part is used to retain the original linear contribution of each component, that is, to calculate the linear weighted sum of the rock mass description value, the density influence value, and the hardness coefficient respectively. The second-order feature interaction part is used to calculate the pairwise interaction between any two components. Specifically, it is used to characterize the nonlinear influence of the component combination on the final rock properties by calculating the inner product of the embedding vectors of the two components. A high-order feature interaction component is set up to capture the joint interaction effect when three components (i.e., rock mass description value, density influence value, and hardness coefficient) exist simultaneously. By introducing a third-order interaction term, the nonlinear coupling relationship under complex working conditions such as hard rock with dense joints and special density can be accurately characterized.

[0007] Furthermore, when performing center point selection, the hidden layer center selection layer guided by prior knowledge adopts a constraint clustering-based algorithm. Based on the orthogonal least squares method, it sets the extreme working condition data points containing ultra-deep boreholes and ultra-large hole spacing as forced cluster centers, ensuring that the hidden layer of the radial basis function neural network can cover these extreme working conditions with few samples.

[0008] Furthermore, the nonlinear output mapping layer is specifically a shallow neural network containing one or two layers of hidden neurons, used to learn and fit the nonlinear mapping relationship between the radial basis function output value and the final prediction target.

[0009] Furthermore, the nonlinear output mapping layer adopts a residual modeling structure, specifically including a linear output subnetwork for fitting the main trend of block size prediction, and one or more auxiliary nonlinear subnetworks for fitting the nonlinear effect of energy dissipation caused by rock joint conditions. The prediction result is the sum of the output of the linear output subnetwork and the output of the auxiliary nonlinear subnetwork.

[0010] Furthermore, the multi-task output layer includes multiple parallel output nodes, each of which corresponds to a different block size feature value. The block size feature value includes the particle size when the cumulative distribution reaches 10%, the particle size when the cumulative distribution reaches 50%, the particle size when the cumulative distribution reaches 90%, and one or more combinations of large block rate, reasonable block rate, and fine particle rate.

[0011] Furthermore, the multi-task output layer adopts a hybrid density network structure, and the output is a parameter set of a Gaussian mixture model. The parameter set includes the mean, variance and corresponding weight coefficients of multiple Gaussian components, which are used to describe the probability density distribution function of rock fragmentation size.

[0012] The present invention has the following beneficial effects: In this invention, the rock mass description values, density influence values, and hardness coefficient are coupled through a nonlinear feature cross layer, breaking the limitations of linear combination in traditional methods. This allows for accurate characterization of the nonlinear effects of explosion energy dissipation under complex geological conditions. At the same time, the variable-width radial basis function layer provides a wider radial basis function for extreme working conditions with sparse data, effectively expanding the influence range of the model. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating the steps of a method for predicting the distribution of rock fragments in open-pit deep-hole blasting proposed in this invention. Detailed Implementation

[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] Please see Figure 1 As shown, this invention is a method for predicting the distribution of rock fragment size in open-pit deep-hole blasting, comprising the following steps: Historical blasting data is obtained, which includes blasting design parameters, rock coefficients, and actual block size distribution parameters after rock fragmentation. The rock coefficients are calculated based on rock mass description values, density influence values, and hardness coefficients that reflect rock properties. Specifically: The specific blasting design parameters include row spacing, hole spacing, step height, hole diameter, plugging length, single hole charge, and explosive coefficient. These parameters reflect the specific process design of the blasting operation. The rock coefficient is not a directly measured value, but a comprehensive index obtained through a specific calculation method based on rock mass description values, density influence values, and hardness coefficients that reflect the properties of the rock. The rock mass description values ​​are used to quantify the integrity and joint development of the rock, the density influence values ​​are used to reflect the influence of rock density on blasting effect, and the hardness coefficients are used to characterize the hardness of the rock. The actual block size distribution parameters after rock fragmentation are used as target values ​​for model training. Specifically, these parameters include the particle size when the cumulative distribution of rock fragments reaches 10%, 50%, and 90%, as well as one or more combinations of large block ratio, reasonable block ratio, and fine particle ratio. A radial basis function neural network is constructed, comprising a nonlinear feature cross layer, a hidden center selection layer guided by prior knowledge, a variable-width radial basis function layer, a nonlinear output mapping layer, and a multi-task output layer connected in sequence. The blasting design parameters and rock coefficients from the historical blasting data are input into the nonlinear feature cross layer. Nonlinear cross-coupling processing is performed on the rock mass description values, density influence values, and hardness coefficient to generate an enhanced feature vector. The enhanced feature vector is input into the hidden center selection layer guided by the prior knowledge. Combined with the pre-set prior knowledge of extreme working conditions, multiple center points of the radial basis function are determined in the feature space of the enhanced feature vector. Each center point is assigned a corresponding radial basis function in the variable width radial basis function layer according to a preset rule. The output result processed by the variable-width radial basis function layer is input to the nonlinear output mapping layer, and the output of the radial basis function is nonlinearly transformed by the nonlinear mapping function. The features after nonlinear transformation are input into the multi-task output layer, which simultaneously predicts and outputs multiple different block-level feature values. Based on the multiple different block size characteristic values, a complete rock fragmentation block size distribution curve is constructed to complete the prediction of the blasting block size distribution; When the current radial basis function neural network is used to predict a new blasting condition and the prediction deviation exceeds a preset threshold, the new blasting condition data is dynamically added to the variable width radial basis function layer as a new radial basis function neuron center, and only the weight parameters of the nonlinear output mapping layer and the multi-task output layer are finely adjusted and updated.

[0016] In one embodiment, the nonlinear feature cross-layer is constructed, wherein the nonlinear feature cross-layer employs a factorization machine mechanism for high-order feature interactions, specifically as follows: The rock coefficient is composed of rock mass description values, density influence values, and hardness coefficients. The rock mass description values, density influence values, and hardness coefficients are extracted and combined into an original rock feature vector. A corresponding embedding vector is set for each component (i.e., rock mass description value, density influence value, and hardness coefficient) in the original rock feature vector. The embedding vector is used to map the original scalar values ​​to a high-dimensional distributed representation space in order to better capture the potential correlation between components. The system is configured with a first-order feature interaction part and a second-order feature interaction part. The first-order feature interaction part is used to retain the original linear contribution of each component, that is, to calculate the linear weighted sum of the rock mass description value, the density influence value, and the hardness coefficient respectively. The second-order feature interaction part is used to calculate the pairwise interaction between any two components. Specifically, it is used to characterize the nonlinear influence of the component combination on the final rock properties by calculating the inner product of the embedding vectors of the two components. A high-order feature interaction component is set up to capture the joint interaction effect when three components (i.e., rock mass description value, density influence value, and hardness coefficient) exist simultaneously. By introducing a third-order interaction term, the nonlinear coupling relationship under complex working conditions such as hard rock with dense joints and special density can be accurately characterized.

[0017] It should be noted that the specific analysis process for the nonlinear feature cross layer is as follows: Construction and input of the original feature vector: The preprocessed single historical blasting sample data is used to construct an original input vector, denoted as X. This vector is composed of two concatenated parts: The first part is the blasting design parameter vector, denoted as... ,in to Specifically, parameters include row spacing, hole spacing, step height, hole diameter, plugging length, single hole charge, and explosive coefficient; The second part is the rock coefficient, which is decomposed into basic constituent elements, namely the rock mass description value, the density effect value, and the hardness coefficient, denoted as . ; The original input vector received by the nonlinear feature cross layer is: ; Nonlinear coupling processing for rock coefficient components: Within the nonlinear characteristic cross layer, the core task is to... Deep cross-coupling is performed to generate enhanced features that reflect their complex interaction relationships; Specifically: The second-order feature interaction part: A latent vector is learned for each feature, and the inner product between latent vectors is used to represent the interaction between features. For the input vector... : ,in, represent , For corresponding features k-dimensional latent vectors, This represents the dot product of two latent vectors, used to measure the interaction weights between feature i and feature j. This represents the global bias term, used to fit the overall offset in the data, equivalent to the intercept in a regression model. This represents the first-order weight coefficients, which allows the factorization machine to capture all interaction information. The enhancement feature vector generation and fusion process involves fusing the original features with the newly generated features after the aforementioned nonlinear processing to form the final enhanced feature vector. : .

[0018] In one embodiment, the prior knowledge-guided hidden layer center selection layer employs a constraint clustering-based algorithm when performing center point selection. Based on the orthogonal least squares method, it sets data points from extreme working conditions, including ultra-deep boreholes and ultra-large hole spacing, as forced cluster centers to ensure that the hidden layer of the radial basis function neural network can cover these extreme working conditions with few samples.

[0019] It should be noted that the specific analysis process of the hidden center selection layer guided by prior knowledge is as follows: Enhanced candidate center initialization in feature space: Enhanced feature vectors constitute the dataset ,in Let X be the d-dimensional enhanced feature vector of the i-th sample, and N be the total number of historical blasting data samples. All samples X are used as candidate sets for radial basis function centers. At the same time, a subset of samples containing extreme operating conditions is identified and extracted from historical data. Where M≪N, the extreme working conditions include, but are not limited to, special cases such as ultra-deep drilling (hole depth greater than a preset threshold, such as 20 meters) and ultra-large hole spacing (hole spacing greater than a preset threshold, such as 6 meters), which have a low probability of occurring in actual blasting operations but have a significant impact on prediction accuracy. Constrained cluster center selection incorporating prior knowledge: An algorithm based on constrained clustering, using orthogonal least squares, ensures that the extreme case samples can be forcibly selected as hidden layer centers. The specific algorithm flow is as follows: Initialize the central set and orthogonal projection space: Let the initial central set be... Initial orthogonal projection space Set the expected number of hidden layer neurons to K, which can be determined based on experience or cross-validation, such as K=50; Forced selection of extreme operating condition center: This subset of extreme operating conditions... All samples The samples are added sequentially to the central set C, and for the first extreme case sample added... Take it as the first center And calculate its effect on the output vector. The projection of (i.e., the matrix formed by the actual block size distribution parameters): ,in For The radial basis function response vectors of all samples centered at the center. Let be Gaussian radial basis functions. Update the orthogonal projection space. and from the candidate set Remove from The remaining extreme condition samples are processed sequentially. to For the j-th extreme working condition sample Let it be the j-th center. Calculate its response vector and orthogonalize it to the space formed by the selected centers: Calculate the projection contribution after orthogonalization: ,Will Add to the orthogonal projection space S and remove from the candidate set ; Remaining center selection based on error reduction ratio: Having selected M extreme condition centers, the remaining KM centers to be selected are chosen using the error reduction ratio criterion of orthogonal least squares. For the candidate set... Each remaining sample Calculate its response vector and orthogonalize it into the orthogonal space formed by the currently selected centers: ,in, The orthogonalized vector corresponding to the selected extreme condition center, For the orthogonalized vectors of subsequently selected conventional centers (selected before the current round), calculate the error reduction rate that can be explained by the introduction of this candidate sample: , choose to The largest candidate sample is taken as the (M+1)th center. Its projection is calculated and the orthogonal space S is updated. This process is repeated until all K centers are selected. Adaptive Radial Basis Function Width Configuration Based on Data Distribution Density: For each determined center point, a corresponding radial basis function in a variable-width radial basis function layer is assigned to it. This invention uses a Gaussian function as the radial basis function, with the following form: ,in, Center point The corresponding width parameter (also known as the expansion constant), the width parameter The value is determined by the center point. The sample distribution density of the feature space region is adaptively determined, specifically following preset rules: The radial basis function is assigned a smaller width value in regions with dense data distribution, and a larger width value in regions with sparse data distribution and extreme operating conditions.

[0020] Calculate using the method based on average nearest neighbor distance : Determine the local sample set for each center: for each center point Find the P nearest sample points (including) in the enhanced feature space. The local sample set is defined as follows: P is a preset parameter, usually a small value (e.g., P=5 or P=10) to ensure accurate local density representation. ,in = The corresponding original sample; Calculate the local average distance: Calculate the center point To its local sample set The average Euclidean distance of the other P−1 samples: The average distance Reflects the center point Sample distribution density in the region The smaller the value, the denser the sample distribution in that area; The larger the value, the sparser the sample distribution in that area; Adaptive width calculation: based on the local average distance Calculate the center point Width parameter : ,in This is the width adjustment factor, an adjustable hyperparameter; Center point and width output: Determine the set of center points output by the hidden layer center selection layer guided by the prior knowledge, and the corresponding set of width parameters for each radial basis function in the variable-width radial basis function layer. This configuration result is used for subsequent network computation; that is, for any input sample x, its output of the k-th hidden layer neuron is: .

[0021] In one embodiment, the nonlinear output mapping layer is specifically a shallow neural network containing one or two layers of hidden neurons, used to learn and fit the nonlinear mapping relationship between the radial basis function output value and the final prediction target.

[0022] In one embodiment, the nonlinear output mapping layer adopts a residual modeling structure, specifically including a linear output subnetwork for fitting the main trend of block size prediction, and one or more auxiliary nonlinear subnetworks for fitting the nonlinear effect of energy dissipation caused by rock joint conditions. The prediction result is the sum of the output of the linear output subnetwork and the output of the auxiliary nonlinear subnetwork.

[0023] It should be noted that the specific analysis process of the nonlinear output mapping layer is as follows: Receive the output of the radial basis function layer; A nonlinear output mapping layer with a residual modeling structure is constructed. This layer specifically includes a linear output subnetwork and one or more auxiliary nonlinear subnetworks. The linear output subnetwork is used to fit the main trend of the blasting block size prediction, that is, to calculate the main part of the block size feature value based on the output of the radial basis function through a linear weighted sum. The structure of this subnetwork is relatively simple, consisting of a linear summation layer, whose weight coefficients are determined through model training. It represents the basic mapping relationship between the radial basis function output and the final block size under conventional geological conditions and blasting techniques. The auxiliary nonlinear subnetwork is used to fit the residual part caused by the nonlinear effect of energy dissipation due to rock joint conditions. Specifically, this sub-network is a shallow neural network containing one or two layers of hidden neurons. Its input is also the output of the variable-width radial basis function layer. However, through the nonlinear activation function of the hidden neurons, this sub-network can learn and capture the influence of complex nonlinear physical phenomena such as abnormal energy dissipation and crack propagation obstruction caused by special geological conditions (such as mud joints and loose joint surfaces) on the final block size distribution during the blasting process. The output of this sub-network is a residual value, which is used to correct the prediction results of the linear output sub-network. The received output from the variable-width radial basis function layer is simultaneously input into the linear output sub-network and the auxiliary nonlinear sub-network, allowing the two sub-networks to run in parallel. In the linear output sub-network, the input vector is linearly multiplied by the network weights and summed to obtain a preliminary block size feature prediction value. This value represents the mainstream prediction trend when complex nonlinear factors are ignored. In the auxiliary nonlinear sub-network, the input vector first undergoes a nonlinear transformation through one or more hidden layer neurons (e.g., using a hyperbolic tangent function or a linear rectified function as the activation function), and then is mapped to a scalar value through the output layer. This scalar value is the residual value used to correct the main trend. This residual value reflects the block size prediction deviation caused by nonlinear factors such as rock joint conditions under the blasting conditions corresponding to the current input sample. The block size prediction main trend value output by the linear output sub-network is algebraically summed with the residual value output by the auxiliary nonlinear sub-network to obtain the final prediction result. This final prediction result is passed to the next layer, the multi-task output layer, as the output of the nonlinear output mapping layer. Through the residual modeling structure, the linear output sub-network is responsible for capturing the linear principal components in the data, ensuring the stability and generalization ability of the model under normal working conditions, while the auxiliary nonlinear sub-network focuses on learning complex nonlinear details that are difficult to describe with linear relationships. The two complement each other and jointly improve the overall fitting accuracy of the model to the strongly nonlinear physical process of blasting block size. The final prediction result, which integrates the main trend and nonlinear residual correction, is input into the multi-task output layer. The nonlinear output mapping layer contains multiple parallel residual modeling structures, each corresponding to a different task in the multi-task output layer. For example, for the three prediction tasks of particle size when the cumulative distribution reaches 10%, 50%, and 90%, three independent residual modeling structures are constructed. Each structure contains its own linear output subnetwork and auxiliary nonlinear subnetwork, which simultaneously calculate three different block size feature values ​​in parallel. Finally, these values ​​are used to construct a complete rock fragmentation block size distribution curve.

[0024] In one embodiment, the multi-task output layer includes multiple parallel output nodes, each of which corresponds to a different block size feature value. The block size feature value includes the particle size when the cumulative distribution reaches 10%, the particle size when the cumulative distribution reaches 50%, the particle size when the cumulative distribution reaches 90%, and one or more combinations of large block rate, reasonable block rate, and fine particle rate.

[0025] In one embodiment, the multi-task output layer adopts a hybrid density network structure and outputs a parameter set of a Gaussian mixture model. The parameter set includes the mean, variance, and corresponding weight coefficients of multiple Gaussian components, which are used to describe the probability density distribution function of rock fragmentation size.

[0026] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the distribution of rock fragment size in open-pit deep-hole blasting, characterized in that, Includes the following steps: Acquire historical blasting data, which includes blasting design parameters, rock coefficient, and actual block size distribution parameters after rock fragmentation; A radial basis function neural network is constructed, comprising a nonlinear feature cross layer, a hidden center selection layer guided by prior knowledge, a variable-width radial basis function layer, a nonlinear output mapping layer, and a multi-task output layer connected in sequence. The blasting design parameters and rock coefficients from the historical blasting data are input into the nonlinear feature cross layer. Nonlinear cross-coupling processing is performed on the rock mass description values, density influence values, and hardness coefficient to generate an enhanced feature vector. The enhanced feature vector is input into the hidden center selection layer guided by the prior knowledge. Multiple center points of the radial basis function are determined in the feature space of the enhanced feature vector. Each center point is assigned a corresponding radial basis function in the variable width radial basis function layer according to a preset rule. The output result processed by the variable-width radial basis function layer is input to the nonlinear output mapping layer, and the output of the radial basis function is nonlinearly transformed by the nonlinear mapping function. The features after nonlinear transformation are input into the multi-task output layer, which simultaneously predicts and outputs multiple different block-level feature values. Based on the multiple different block size characteristic values, a rock fragmentation block size distribution curve is constructed to complete the prediction of the blasting block size distribution.

2. The method for predicting the rock fragment size distribution in open-pit deep-hole blasting according to claim 1, characterized in that, The nonlinear feature cross-layer is constructed, and the nonlinear feature cross-layer uses a factorization machine mechanism to perform high-order interactions of features, specifically as follows: The rock coefficient is composed of rock mass description value, density influence value and hardness coefficient. The rock mass description value, density influence value and hardness coefficient are extracted and combined into an original rock feature vector. A corresponding embedding vector is set for each component in the original rock feature vector. The system is configured with a first-order feature interaction part and a second-order feature interaction part. The first-order feature interaction part is used to retain the original linear contribution of each component, and the second-order feature interaction part is used to calculate the pairwise interaction between any two components. Specifically, it is used to characterize the nonlinear effect of the component combination on the final rock properties by calculating the inner product of the embedding vectors of the two components. A higher-order feature interaction component is set up to capture the joint interaction effect when the three components exist simultaneously.

3. The method for predicting the distribution of rock fragment size in open-pit deep-hole blasting according to claim 1, characterized in that, When performing center point selection, the hidden center selection layer guided by prior knowledge adopts a constraint clustering-based algorithm. Based on the orthogonal least squares method, it sets data points of extreme working conditions, including ultra-deep boreholes and ultra-large hole spacing, as forced cluster centers.

4. The method for predicting the distribution of rock fragment size in open-pit deep-hole blasting according to claim 1, characterized in that, The nonlinear output mapping layer is specifically a shallow neural network containing one or two layers of hidden neurons, used to learn and fit the nonlinear mapping relationship between the radial basis function output value and the final prediction target.

5. The method for predicting the distribution of rock fragment size in open-pit deep-hole blasting according to claim 1, characterized in that, The nonlinear output mapping layer adopts a residual modeling structure, specifically including a linear output subnetwork for fitting the main trend of block size prediction, and one or more auxiliary nonlinear subnetworks for fitting the nonlinear effect of energy dissipation caused by rock joint conditions. The prediction result is the sum of the output of the linear output subnetwork and the output of the auxiliary nonlinear subnetwork.

6. The method for predicting the distribution of rock fragment size in open-pit deep-hole blasting according to claim 1, characterized in that, The multi-task output layer contains multiple parallel output nodes, each of which corresponds to a different block size feature value. The block size feature value includes the particle size when the cumulative distribution reaches 10%, the particle size when the cumulative distribution reaches 50%, the particle size when the cumulative distribution reaches 90%, and one or more combinations of large block rate, reasonable block rate, and fine particle rate.

7. The method for predicting the distribution of rock fragment size in open-pit deep-hole blasting according to claim 1, characterized in that, The multi-task output layer adopts a hybrid density network structure and outputs a parameter set of a Gaussian mixture model. The parameter set includes the mean, variance, and corresponding weight coefficients of multiple Gaussian components, which are used to describe the probability density distribution function of rock fragmentation size.

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