A method for predicting dynamic performance of rock mass by decision tree guided deep neural network

Abstract

The present application belongs to the technical field of intelligent early warning of geotechnical engineering disasters, and specifically discloses a rock mass dynamic performance prediction method guided by a decision tree and a deep neural network. Dynamic impact experiment data under a small sample condition containing noise is acquired to construct a rock mass data set; the splitting of a decision tree regression model is completed by using the rock mass data set, and key structure parameters are extracted; the number of neurons in each hidden layer, the input layer feature neurons, the connection strategy, and the connection topological structure between the neurons in each hidden layer in the deep neural network prediction model are constructed; and the deep neural network prediction model can be used to realize accurate prediction of the dynamic performance of the rock mass. The present application can initialize the neural network structure and connection by using the information of the decision tree regression model under the condition of small samples and complex rock mass data, significantly improve the prediction accuracy, and provide a reliable basis for the safety warning of geotechnological engineering.

Description

Technical Field

[0001] This invention designs a method for predicting the dynamic performance of rock masses using a decision tree-guided deep neural network, belonging to the field of intelligent early warning technology for geotechnical engineering disasters. Background Technology

[0002] Existing prediction methods all rely on data obtained from rock mass experiments. However, these data contain noise, which is essentially a combination of factors such as instrument electronic interference, sensor coupling distortion, environmental background disturbance, spatial geometric deviation, and human operational errors. These factors cause systematic or random superposition and interference to the real measurement data. In addition, the limited number of experimental samples further reduces the accuracy of existing prediction methods. Developing a high-precision prediction method for the dynamic strength of rock mass that integrates multi-source features and adapts to complex environments has become a key technical bottleneck in improving the safety and control capabilities of geotechnical engineering.

[0003] Deep learning neural networks exhibit strong nonlinear mapping capabilities in predicting the dynamic strength of rock masses, capturing the complex relationship between multiple internal and external factors such as cracks and anchorage status and the bearing capacity of rock masses. However, their inherent black-box characteristics obscure key decision-making logic and make it difficult to trace the failure threshold. Furthermore, the high redundancy structure has limited generalization performance when faced with field errors and environmental disturbances. Although decision trees have good interpretability and can intuitively analyze the relationships between factors, their shallow structure makes it difficult to effectively fit the high-dimensional nonlinear process of dynamic coupling of multiple factors such as impact energy transfer, crack propagation and anchor interaction. Summary of the Invention

[0004] Technical Problem: To address the shortcomings of existing technologies, this paper proposes a method for predicting the dynamic performance of rock masses using a decision tree-guided deep neural network. By analyzing noisy dynamic impact test data of rock masses, this method can ensure prediction accuracy while being easy to implement and having good generalization ability, even for complex rock mass dynamic impact test data with a small number of samples.

[0005] Technical Solution: To achieve the above technical objectives, this invention provides a method for predicting the dynamic performance of rock masses using a decision tree-guided deep neural network, comprising the following steps:

[0006] S1. Obtain dynamic impact test data under noisy, small sample conditions and construct a rock mass dataset;

[0007] S2. Use the rock mass dataset to split the decision tree regression model, obtain the complete decision tree regression model, and extract the key structural parameters from it.

[0008] S3. Construct a deep neural network prediction model; determine the number of neurons in each hidden layer, and the connection strategy between the input layer feature neurons and the first hidden layer neurons; determine the connection topology between the neurons in each hidden layer.

[0009] S4. Once the deep neural network prediction model has been trained, it can accurately predict the dynamic performance of the rock mass.

[0010] Furthermore, in S1, dynamic impact experiments are conducted on rock masses with different fracture parameters and anchoring states as samples. Dynamic impact experiment data for multiple samples are collected. During this process, due to equipment factors and human factors, there is error noise in the dynamic impact experiment data. The following six feature types of data are obtained for each sample through dynamic impact experiments: fracture roughness coefficient JRC, fracture length, fracture angle, presence or absence of anchor bolts, impact velocity, and dynamic strength. Among them, fracture roughness coefficient JRC, fracture length, fracture angle, and impact velocity are continuous numerical features; presence or absence of anchor bolts is a Boolean feature.

[0011] Furthermore, the dynamic impact test data of all samples were preprocessed: all feature types were normalized to [0,1] to form a rock mass dataset, and 80% of the samples were randomly selected as the rock mass training set, with the remaining 20% ​​as the rock mass test set; among them, continuous numerical features and Boolean features were 5 input features, and dynamic intensity was 1 output feature; let the rock mass training set be... include There are 1 sample, denoted as _ . , No. Sample Given an input feature vector and corresponding output values Together they form a binary tuple. , where the input feature vector Feature Dimension , corresponding to 5 input features, specifically represented as Output value Output dimension This corresponds to one output feature.

[0012] Furthermore, the decision tree regression model is split using the rock mass dataset. The specific steps are as follows:

[0013] To build a decision tree regression model, key parameters for constructing the model are manually preset, including the maximum split parameter. Minimum number of samples for split nodes Minimum number of samples for leaf nodes Candidate node default tolerance ;

[0014] Rock Mass Training Set All samples are input into the initial state decision tree regression model, which contains only the unique root node of the decision tree. Rock mass training set All sample input root nodes Determine the root node Does it satisfy the following splitting condition:

[0015] (1),

[0016] In the formula, The minimum number of samples for a split node, if the root node Upper rock mass training set capacity Less than If the splitting condition is not met, the current root node is marked as the final leaf node, and the splitting ends; if the splitting condition is met, the current node is marked as the parent node region. Then the decision tree regression model will split;

[0017] For each input feature, including continuous numerical features and Boolean features: presence or absence of anchor bolts, crack roughness coefficient JRC, crack length, crack angle, and impact velocity, the parent node region is traversed. All inside For each sample, sort them according to the magnitude of the feature value, and calculate the adjacent samples where every two feature values ​​are different under that feature. and At the midpoint of the eigenvalues, select the region that makes the parent node's region... The midpoint of the eigenvalue with the largest reduction in mean squared error is used as the optimal splitting threshold. Samples with eigenvalues ​​less than or equal to the optimal splitting threshold are assigned to the left child node region, and samples with eigenvalues ​​greater than the optimal splitting threshold are assigned to the right child node region. The specific calculation process is as follows:

[0018] remember For the first Sample The 1 eigenvalue, For the first Sample The 1 eigenvalue, , For the first Sample and its neighboring samples In the If the midpoint of the eigenvalues ​​is:

[0019] (2),

[0020] Will As a candidate splitting threshold, the parent node region The divided left child node region and right child node region The eigenvalues ​​are represented as:

[0021] (3),

[0022] In the formula, Indicates the first The first sample One eigenvalue;

[0023] Record the parent node region Left child node region right child node region The number of samples within are respectively , , Parent node region Left child node region right child node region mean square error , , The calculation is performed using the following formula:

[0024] (4),

[0025] In the formula, Then they respectively represent The average value of the output dynamic intensity characteristic value of samples in each region;

[0026] The candidate split threshold is calculated using the following formula. The resulting reduction in mean square error :

[0027] (5),

[0028] The candidate splitting thresholds are obtained according to equation (5). The resulting reduction in mean square error And the optimal splitting scheme for this splitting is determined by equation (6). ):

[0029] (6),

[0030] In the formula, The index represents the best splitting feature, i.e., the best splitting feature selected from all features; This represents the sample index corresponding to the optimal splitting threshold, which is the optimal splitting position under the optimal splitting feature.

[0031] According to the optimal splitting scheme ( Split the node, and after the split, if the left child node region... right child node region The number of internal samples is less than the minimum number of samples in the leaf nodes. If the child node splits, the split ends; otherwise, the child node is treated as the parent node, and the split continues using equations (2) to (6) until any of the following conditions are met, at which point the split terminates: the number of splits. , Or the reduction in maximum mean square error < default tolerance .

[0032] Furthermore, after terminating the split, a complete decision tree regression model is obtained, and key structural parameters are extracted: maximum tree depth. That is, the total number of layers in the decision tree regression model; the first Number of branches in a layer That is, the first The number of split nodes in the layer, of which The layer index is used; and during multiple splits, the feature importance of each input feature is calculated synchronously. The specific steps are as follows:

[0033] Record No. The feature in the first The reduction in mean squared error of the decision tree regression model during each split is When the first The second split is based on the first The optimal splitting scheme for each feature ( When executed, ;otherwise, In the entire decision tree regression model During the second split, the first The cumulative sum of the reductions in the mean squared error of each feature in the decision tree regression model for:

[0034] (7),

[0035] In the formula, Indicates the first Number of samples in the parent node region of the second split; This indicates the total number of samples in the rock mass training set;

[0036] Using the following formula Normalization is performed to obtain the importance of each feature. :

[0037] (8).

[0038] Furthermore, by utilizing the key structural parameters of the complete decision tree regression model, the number of neurons in each hidden layer of the deep neural network prediction model and the connection strategy between the input layer feature neurons and the first hidden layer neurons are determined. The specific steps are as follows:

[0039] Mapping the decision tree regression model to a deep neural network: the root node of the decision tree regression model corresponds to the input layer of the network; the branching process of the decision tree regression model is implemented by the hidden layers; the maximum tree depth of the decision tree regression model is... Since the last layer of the decision tree regression model is a leaf node layer, the effective split depth is... , which corresponds to the total number of hidden layers in the network, and the output layer corresponds to the leaf node output of the final decision tree regression model;

[0040] The number of neurons in each layer of the deep neural network is calculated based on the number of input features in the rock mass training set. The number of input layer neurons in the network will be used to determine the number of output features within the rock mass training set. As the number of neurons in the output layer, the first... The number of neurons in the hidden layer is denoted as The number of neurons in the previous layer and the number of neurons in the decision tree regression model are determined by the number of neurons in the previous layer. Number of branches per layer Joint decision:

[0041] (9),

[0042] Utilizing feature importance The specific process for determining the neuron connection method between the input layer and the first hidden layer is as follows:

[0043] Calculate the first using formula (10) Input features Number of neurons in the first hidden layer :

[0044] (10)

[0045] In the formula, The function represents rounding the value within the parentheses; This represents the number of neurons in the first hidden layer of a deep neural network;

[0046] Formula (11) is used to constrain and optimize the neuron connections between the input features and the first hidden layer, ensuring that each input feature is connected to at least one neuron:

[0047] (11),

[0048] At the same time, ensure the number of neurons connected to all input features. Equal to the number of neurons in the first hidden layer ,when When, reduce the number of neuron connections for a feature of least importance; when At this point, increase the number of neuron connections for the feature with the highest importance; until the following equation is finally satisfied:

[0049] (12)

[0050] For each input feature of a deep neural network, the neurons are connected one by one. There are 1 first hidden layer neuron; add random connections to each input feature neuron, accounting for 5% of the total number of connections between the input feature and the first hidden layer neuron.

[0051] Furthermore, by utilizing the number of branches in each layer of the complete decision tree regression model, the connections between neurons in each hidden layer of the deep neural network are initialized, and the connection topology between neurons in each hidden layer of the deep neural network is constructed, thereby improving the prediction accuracy under noisy and small sample conditions.

[0052] The first in the deep neural network The first hidden layer and the previous hidden layer The neurons between them are connected in the following steps:

[0053] Determine the first Number of hidden layer neuron groups ; In the decision tree regression model, the first... Number of branches and the previous hidden layer of the corresponding deep neural network prediction model Number of neurons Minimum value in:

[0054] (13)

[0055] Define the neuron grouping mechanism between hidden layers; starting from the second hidden layer Start, hide the layer With neurons The neurons are synchronously divided into There are several groups; among them, the hidden layer Each group contains One neuron, hidden layer Each group contains The number of neurons is represented as follows:

[0056] , (14)

[0057] In the formula, , Hidden layers and The number of neurons; The parentheses for rounding down indicate that the value inside the parentheses is rounded down to the nearest integer.

[0058] Starting from the second hidden layer, according to For hidden layers The neurons in the sequence are grouped sequentially; the hidden layer is determined using the following formula. Index sequence of all neurons :

[0059] (15)

[0060] In the formula, Functions that generate sets of integers Random arrangement;

[0061] According to the hidden layer index sequence The hidden layer is determined using the following formula. The Middle Group number of each neuron :

[0062] (16)

[0063] In the formula, The parentheses for rounding up indicate that the value inside the parentheses is rounded up. Indicates in the hidden layer The Middle The index number of each neuron;

[0064] To be divided into Establish hidden layers for each group of neurons. and hidden layers Forward connections between layers; forward connections are in sparse connection mode: traversing hidden layers. and hidden layers Group number of all neurons and When neurons have the same group number, the hidden layer... and hidden layers Establish full connections between them;

[0065] Add a 30% probability random connection, meaning that each neuron in a hidden layer has a 30% probability of randomly connecting with any two neurons in the previous layer.

[0066] Furthermore, the root mean square error (RMSE) is used as a performance evaluation metric to train the deep neural network prediction model. The smaller the RMSE, the better the prediction performance of the deep neural network prediction model. The RMSE is calculated as follows:

[0067] (17)

[0068] In the formula, This represents the total number of samples used in training. These represent the sample values ​​that the deep neural network prediction model outputs during training. This represents the actual output value of the corresponding sample.

[0069] A computer device includes a processor and a memory, the processor being electrically connected to the memory, the memory being used to store instructions and data, and the processor being used to execute a rock mass dynamic performance prediction method guided by a decision tree deep neural network.

[0070] Beneficial Effects: This method constructs and initializes the neural network topology based on key structural information such as tree depth, number of branches per layer, and feature importance of the decision tree regression model. The prior knowledge of rules extracted from the decision tree reduces the network's dependence on the scale of training data, not only giving the network a precise initial direction to accelerate convergence and improve accuracy, but also integrating the powerful nonlinear modeling capabilities of neural networks with the interpretability of decision trees. The constructed prediction model exhibits significant advantages in the following aspects: 1) Higher prediction accuracy: The improved model has better prediction accuracy compared to a single model structure; 2) Stronger generalization and robustness: It shows better adaptability to noisy data, and the model stability is significantly improved; 3) Wider applicability: It can effectively handle multi-dimensional input features and small-sample dynamic rock impact experimental data, maintaining high accuracy even with high data complexity, while also possessing the advantages of ease of implementation and strong generalization ability. Attached Figure Description

[0071] Figure 1 This is a schematic diagram of the structure of a decision tree-guided deep neural network prediction model in an embodiment of the present invention.

[0072] Figure 2 The figure shows the experimental results of the prediction model based on the BP neural network in the comparative example of this invention on the rock mass test set: the horizontal axis represents the test set sample number, and the vertical axis represents the dynamic intensity; the blue broken line represents the true intensity value of the rock mass sample, and the red broken line represents the predicted intensity value of the BP neural network model; the image shows that the root mean square error (RMSE) of the experimental results of this model is 8.0149; the fitting degree between the predicted curve and the true value curve is poor, and there is a significant deviation in some sample points.

[0073] Figure 3The figure shows the experimental results of the prediction model based on decision tree regression in the comparative example of this invention on the rock mass test set: the horizontal axis represents the sample number of the test set, and the vertical axis represents the dynamic intensity; the blue broken line represents the true intensity value of the rock mass sample, and the red broken line represents the predicted intensity value of the decision tree regression model; the image shows that the root mean square error (RMSE) of the experimental results of this model is 5.5298; the fitting degree between the predicted curve and the true value curve is generally poor, and there is a large deviation in some sample points.

[0074] Figure 4 The figure shows the experimental results of the decision tree-guided deep neural network prediction model on the rock mass test set in this embodiment of the invention: the horizontal axis represents the test set sample number, and the vertical axis represents the dynamic intensity; the blue broken line represents the true intensity value of the rock mass sample, and the red broken line represents the predicted intensity value of this model; the image shows that the root mean square error (RMSE) of the experimental results of this model is 3.0911; the predicted curve fits the true value curve well, and there are slight deviations in some sample points. Detailed Implementation

[0075] The embodiments of the present invention will be further described below with reference to the accompanying drawings and tables:

[0076] like Figure 1 As shown, this invention discloses a method for predicting the dynamic performance of rock masses using a decision tree-guided deep neural network. The specific steps are as follows:

[0077] S1. Obtain dynamic impact test data under noisy, small sample conditions and construct a rock mass dataset;

[0078] S2. Use the rock mass dataset to split the decision tree regression model, obtain the complete decision tree regression model, and extract the key structural parameters from it.

[0079] S3. Construct a deep neural network prediction model; determine the number of neurons in each hidden layer, and the connection strategy between the input layer feature neurons and the first hidden layer neurons; determine the connection topology between the neurons in each hidden layer.

[0080] S4. Once the deep neural network prediction model has been trained, it can accurately predict the dynamic performance of the rock mass.

[0081] In this embodiment, dynamic impact test data under noisy, small-sample conditions is acquired to construct a rock mass dataset. Specific steps include: In S1, dynamic impact tests are conducted on rock masses with different fracture parameters and anchoring states as samples. Multiple samples of dynamic impact test data are collected. During this process, due to equipment and human factors, the dynamic impact test data contains error noise. Each sample obtains the following six feature types of data through dynamic impact tests: fracture roughness coefficient JRC, fracture length, fracture angle, presence or absence of anchor bolts, impact velocity, and dynamic intensity. Among these, the fracture roughness coefficient JRC, fracture length, fracture angle, and impact velocity are continuous numerical features; the presence or absence of anchor bolts is a Boolean feature. This simulation experiment was run in the MATLAB R2021b environment, using a PC with a 2.5GHz CPU and 32GB of RAM.

[0082] All dynamic impact test data of the samples were preprocessed: all feature types were normalized to [0,1] to form a rock mass dataset. The rock mass dataset consisted of 72 samples, and 80% of the samples were randomly selected as the rock mass training set, and the remaining 20% ​​were selected as the rock mass test set; that is, the rock mass training set had 58 samples and the test set had 14 samples; among them, continuous numerical features and Boolean features were 5 input features, and dynamic intensity was 1 output feature; let the rock mass training set... include There are 1 sample, denoted as _ . , No. Sample Given an input feature vector and corresponding output values Together they form a binary tuple. , where the input feature vector Feature Dimension , corresponding to 5 input features, specifically represented as Output value Output dimension This corresponds to one output feature.

[0083] In this embodiment, the decision tree regression model is split using a rock mass dataset. Specific steps include:

[0084] To build a decision tree regression model, key parameters for constructing the model are manually preset, including the maximum split parameter. Minimum number of samples for split nodes Minimum number of samples for leaf nodes Default tolerance for candidate nodes In the decision tree regression model, the parameters are set to... Set the default tolerance for candidate nodes. All ;

[0085] Rock Mass Training Set All samples are input into the initial state decision tree regression model, which contains only the unique root node of the decision tree. Rock mass training set All sample input root nodes Determine the root node Does it satisfy the following splitting condition:

[0086] (1),

[0087] The minimum number of samples for a split node, if the root node Upper rock mass training set capacity Less than If the splitting condition is not met, the current root node is marked as the final leaf node, and the splitting ends; if the splitting condition is met, the current node is marked as the parent node region. Then the decision tree regression model will split;

[0088] In the formula, The minimum number of samples for a split node, if the root node Upper rock mass training set capacity Less than If the splitting condition is not met, the current root node is marked as the final leaf node, and the splitting ends; if the splitting condition is met, the current node is marked as the parent node region. Then the decision tree regression model will split;

[0089] For each input feature, including continuous numerical features and Boolean features: presence or absence of anchor bolts, crack roughness coefficient JRC, crack length, crack angle, and impact velocity, the parent node region is traversed. All inside For each sample, sort them according to the magnitude of the feature value, and calculate the adjacent samples where every two feature values ​​are different under that feature. and At the midpoint of the eigenvalues, select the region that makes the parent node's region... The midpoint of the eigenvalue with the largest reduction in mean squared error is used as the optimal splitting threshold. Samples with eigenvalues ​​less than or equal to this threshold are assigned to the left child node region, and samples with eigenvalues ​​greater than this threshold are assigned to the right child node region. The specific calculation process is as follows:

[0090] remember For the first Sample The 1 eigenvalue, For the first Sample The 1 eigenvalue, , For the first Sample and its neighboring samples In the If the midpoint of each eigenvalue is a given eigenvalue, then:

[0091] (2),

[0092] Will As a candidate splitting threshold, the parent node region The divided left child node region and right child node region The eigenvalues ​​are represented as:

[0093] (3),

[0094] In the formula, Indicates the first The first sample One eigenvalue;

[0095] Record the parent node region Left child node region right child node region The number of samples within are respectively , , Parent node region Left child node region right child node region Mean square error , , The calculation is performed using the following formula:

[0096] (4),

[0097] In the formula, Then they respectively represent The average value of the output dynamic intensity characteristic value of samples in each region;

[0098] The candidate split threshold is calculated using the following formula. The resulting reduction in mean square error :

[0099] (5),

[0100] The candidate splitting thresholds are obtained according to equation (5). The resulting reduction in mean square error And the optimal splitting scheme for this splitting is determined by equation (6). ):

[0101] (6),

[0102] In the formula, The index represents the best splitting feature, i.e., the best splitting feature selected from all features; This represents the sample index corresponding to the optimal splitting threshold, which is the optimal splitting position under the optimal splitting feature.

[0103] According to the optimal splitting scheme ( Split the node, and after the split, if the left child node region... right child node region The number of internal samples is less than the minimum number of samples in the leaf nodes. If the child node splits, the split ends; otherwise, the child node is treated as the parent node, and the split continues using equations (2) to (6) until any of the following conditions are met, at which point the split terminates: the number of splits. , Or the maximum mean square error reduction < default tolerance .

[0104] In this embodiment, after terminating the split, a complete decision tree regression model is obtained, and the key structural parameter is extracted: maximum tree depth. That is, the total number of layers in the decision tree regression model; the first Number of branches in a layer That is, the first The number of split nodes in the layer, of which The layer index is used; and during multiple splits, the feature importance of each input feature is calculated synchronously. The specific steps include:

[0105] Record No. The feature in the first The reduction in mean squared error of the decision tree regression model during each split is When the first The second split is based on the first The optimal splitting scheme for each feature ( When executed, ;otherwise, In the entire decision tree regression model During the second split, the first The cumulative sum of the reductions in the mean squared error of each feature in the decision tree regression model for:

[0106] (7),

[0107] In the formula, Indicates the first Number of samples in the parent node region of the second split; Indicates the total number of samples in the rock mass training set;

[0108] right Normalization is performed to obtain the importance of each feature. :

[0109] (8),

[0110] In the decision tree regression model, the key structural parameters are: .

[0111] In this embodiment, the key structural parameters of the complete decision tree regression model are used to determine the number of neurons in each hidden layer of the deep neural network prediction model and the connection strategy between the input layer feature neurons and the first hidden layer neurons. Specific steps include:

[0112] Mapping the decision tree regression model to a deep neural network: In the decision tree model, the root node is defined as layer 0, and the depth of each layer increases progressively until the maximum tree depth is reached. Layer; due to the last layer (i.e., the first) The layer () only contains leaf nodes responsible for the final output, therefore the effective split depth for decision branches is Therefore, the root node of the decision tree regression model corresponds to the input layer of the network, the decision branching process is implemented by the hidden layers, and the effective split depth is limited. The corresponding number of hidden layers in the network corresponds to the output layer of the entire decision tree regression model, while the output layer corresponds to the leaf node output of the entire model.

[0113] The number of neurons in each layer of the deep neural network is calculated based on the number of input features in the rock mass training set. The number of input layer neurons in the network will be used to determine the number of output features within the rock mass training set. As the number of neurons in the output layer, the first... The number of neurons in the hidden layer is denoted as The number of neurons in the previous layer and the number of neurons in the decision tree regression model are determined by the number of neurons in the previous layer. Number of branches per layer Joint decision:

[0114] (9),

[0115] Utilizing feature importance The specific process for determining the neuron connection method between the input layer and the first hidden layer is as follows:

[0116] Calculate the first using formula (10) Input features Number of neurons in the first hidden layer :

[0117] (10)

[0118] In the formula, This represents the number of features of the input features. The function represents rounding the value within the parentheses; This represents the number of neurons in the first hidden layer of a deep neural network;

[0119] Formula (11) is used to constrain and optimize the neuron connections between the input features and the first hidden layer, ensuring that each input feature is connected to at least one neuron:

[0120] (11),

[0121] At the same time, ensure the number of neurons connected to all input features. Equal to the number of neurons in the first hidden layer ,when When, reduce the number of neuron connections for a feature of least importance; when At this point, increase the number of neuron connections for the feature with the highest importance; until the following equation is finally satisfied:

[0122] (12)

[0123] For each input feature of a deep neural network, the neurons are connected one by one. One first hidden layer neuron; add random connections to each input-connected feature neuron, accounting for 5% of the total number of connections between the input features and the first hidden layer neurons;

[0124] In the deep neural network prediction model, the input layer is 1 layer with 5 neurons, and the number of neurons distributed sequentially is... The hidden layers consist of 3 layers, with the following number of neurons in each layer: The output layer has one layer and one neuron.

[0125] In this embodiment, the number of branches in each layer of the complete decision tree regression model is used to initialize the connections between neurons in each hidden layer of the deep neural network, thereby constructing the connection topology between neurons in each hidden layer of the deep neural network and improving prediction accuracy under noisy small sample conditions.

[0126] The first in the deep neural network The first hidden layer and the previous hidden layer The neurons between them are connected, and the specific steps include:

[0127] Determine the first Number of hidden layer neuron groups ; In the decision tree regression model, the first... Number of branches per layer and the previous hidden layer of the corresponding deep neural network prediction model Number of neurons Minimum value in:

[0128] (13)

[0129] Define the neuron grouping mechanism between hidden layers; starting from the second hidden layer Start, hide the layer With neurons The neurons are synchronously divided into There are several groups; among them, the hidden layer... Each group contains One neuron, hidden layer Each group contains The number of neurons is represented as follows:

[0130] , (14)

[0131] In the formula, , Hidden layers and The number of neurons; The parentheses for rounding down indicate that the value inside the parentheses is rounded down to the nearest integer.

[0132] Starting from the second hidden layer, according to For hidden layers The neurons in the sequence are grouped sequentially; the hidden layer is determined using the following formula. Index sequence of all neurons :

[0133] (15)

[0134] In the formula, Functions that generate sets of integers Random arrangement;

[0135] According to the hidden layer index sequence The hidden layer is determined using the following formula. The Middle Group number of each neuron :

[0136] (16)

[0137] In the formula, The parentheses for rounding up indicate that the value inside the parentheses is rounded up. Indicates in the hidden layer The Middle The index number of each neuron;

[0138] To be divided into Establish hidden layers for each group of neurons. and hidden layers Forward connections between layers; forward connections are in sparse connection mode: traversing hidden layers. and hidden layers Group number of all neurons and When neurons have the same group number, the hidden layer... and hidden layers Establish full connections between them;

[0139] Add a 30% probability random connection, meaning that each neuron in a hidden layer has a 30% probability of randomly connecting with any two neurons in the previous layer.

[0140] In this embodiment, the constructed deep neural network prediction model is trained using a rock mass training set, which enables accurate prediction of the dynamic performance of the rock mass.

[0141] The following simulation experiment illustrates the effect. Specific details of the experiment are as follows:

[0142] 1) In the 72 sets of data in the rock mass dataset, the input features are fracture roughness JRC, fracture length, fracture angle, presence or absence of anchor bolts and impact velocity, and the output feature is dynamic strength. The rock mass dataset is divided into the same rock mass training set and test set, that is, the rock mass training set has 58 sets of samples and the test set has 14 sets of samples.

[0143] 2) In specific implementation, in order to objectively evaluate the performance superiority of the model proposed in this invention, this embodiment sets up two comparative examples, respectively using algorithms commonly used in the prior art, and conducting comparative experiments under the condition of completely identical training and test set partitioning:

[0144] Comparative Example 1: A prediction model based on a BP neural network. A traditional BP neural network was used to construct the prediction model, employing the same input and output features for training and prediction. 58 samples from the rock mass training set were substituted into the prediction model for training, and then 14 samples from the test set were used to test its prediction accuracy.

[0145] Comparative Example 2: A prediction model based on decision tree regression was constructed using the standard decision tree regression algorithm, with the same input and output features for training and prediction. Similarly, 58 samples from the rock mass training set were substituted into the prediction model for training, and then 14 samples from the test set were used to test its prediction accuracy.

[0146] 3) Obtain the prediction results of the prediction models in the two comparative examples and compare them with the experimental prediction results of the prediction model proposed in this invention.

[0147] Evaluation indicators:

[0148] The root mean square error (RMSE) is used as a performance evaluation metric for training deep neural network prediction models. The smaller the RMSE, the better the prediction performance of the model. The RMSE is calculated as follows:

[0149] (17)

[0150] In the formula, This represents the total number of samples used in training. The sample values ​​represent the output of the model training. This represents the actual output value of the corresponding sample.

[0151] Experimental results:

[0152] Different model algorithms were each run independently 30 times on the rock mass test set, and the mean and variance of the 30 experimental results were used as the final results and filled into Table 1. The corresponding fitting curves are shown in [reference]. Figures 2 to 4 :

[0153] Table 1: Results of the prediction models built using the three methods:

[0154] ,

[0155] From the comparison of the prediction results of each model in Table 1, it can be seen that the prediction model based on BP neural network has the largest error level and variance on the rock mass test set, far exceeding the other two prediction models. This indicates that the prediction model based on simple BP neural network has poor generalization ability, is prone to overfitting, and has weak robustness on datasets with multidimensional input, small sample size, and noise. The prediction model based on decision tree regression has better generalization ability, but its prediction accuracy is still lower than that of the prediction model constructed by the method provided in this invention. The prediction model constructed by the method provided in this invention not only has better prediction accuracy than other models, but also has lower variance in multiple runs, proving that the model has significant stability and reliability when processing such rock mass data.

[0156] from Figures 2 to 4 Comparing the fitted curves: the BP neural network, as a comparative example ( Figure 2 The RMSE was as high as 8.0149, indicating a poor fit between the predicted and actual curves, with significant deviations in some sample points; the decision tree regression model ( Figure 3 Although the RMSE of the proposed decision tree-guided deep neural network model was reduced to 5.5298, its fitting performance on some sample points was still relatively poor. In contrast, the proposed decision tree-guided deep neural network model... Figure 4 The RMSE was reduced to 3.0911, and the prediction curve closely matched the true value curve, which confirmed the prediction accuracy and generalization ability of the model under noisy small sample conditions.

[0157] To this end, this study innovatively proposes a decision tree-guided deep neural network method for predicting the dynamic performance of rock masses. The core of this method is to utilize key structural information such as the splitting path and feature importance of the decision tree to provide powerful guidance for the topological architecture and feature connection methods of the neural network. This not only gives the network a good initial search direction, enabling it to converge faster and achieve higher prediction accuracy, but also significantly improves the robustness and generalization performance of the model under complex interference environments by integrating the powerful nonlinear dynamic modeling capability of the neural network with the rule interpretability of the decision tree. Thus, this provides an innovative solution for real-time early warning of rock mass dynamic intensity that is efficient, accurate, noise-resistant, and potentially resolvable.

Claims

1. A method for predicting the dynamic performance of rock mass using a decision tree-guided deep neural network, characterized in that, The steps are as follows: S1. Obtain dynamic impact test data under noisy, small sample conditions and construct a rock mass dataset; S2. Use the rock mass dataset to split the decision tree regression model, obtain the complete decision tree regression model, and extract the key structural parameters from it. S3. Construct a deep neural network prediction model; determine the number of neurons in each hidden layer, and the connection strategy between the input layer feature neurons and the first hidden layer neurons; determine the connection topology between the neurons in each hidden layer. S4. Once the deep neural network prediction model has been trained, it can accurately predict the dynamic performance of the rock mass. The decision tree regression model is split using a rock mass dataset. The specific steps are as follows: To build a decision tree regression model, key parameters for constructing the decision tree regression model are preset manually: maximum split parameter, minimum number of samples in split nodes, minimum number of samples in leaf nodes, and default tolerance of candidate nodes. Rock Mass Training Set All samples are input into the initial state decision tree regression model, which contains only the unique root node of the decision tree. The rock mass training set... All samples are input into the root node, and it is determined whether the root node meets the splitting condition; if the splitting condition is met, the current node is marked as the parent node region and the decision tree regression model performs splitting. For each input feature, including continuous numerical and Boolean features: presence or absence of anchor bolts, crack roughness coefficient JRC, crack length, crack angle, and impact velocity, all samples within the parent node region are traversed. The samples are sorted according to their feature values. The midpoint between any two adjacent samples with different feature values ​​is calculated. The midpoint that maximizes the reduction in the mean square error of the parent node region is selected as the optimal splitting threshold. Samples with feature values ​​less than or equal to the optimal splitting threshold are assigned to the left child node region, and samples with feature values ​​greater than the optimal splitting threshold are assigned to the right child node region. The feature values ​​in the left and right child node regions divided from the parent node region are calculated. The values ​​in the parent node region and the left child node region are then calculated. The mean square error of the three components in the right child node region is calculated, and the reduction in mean square error is determined to identify the optimal splitting scheme. The splitting is then performed according to the optimal scheme. After splitting, if the left child node region... If the number of samples in the right child node region is less than the minimum number of samples in the leaf node, then the child node split is considered complete.

2. The rock mass dynamic performance prediction method using a decision tree-guided deep neural network according to claim 1, characterized in that: In S1, dynamic impact experiments were conducted on rock masses with different fracture parameters and anchoring states as samples. Dynamic impact experiment data for multiple samples were collected. During this process, due to equipment factors and human factors, there were errors and noise in the dynamic impact experiment data. The following six feature types of data were obtained for each sample through dynamic impact experiments: fracture roughness coefficient JRC, fracture length, fracture angle, presence or absence of anchor bolts, impact velocity, and dynamic strength. Among them, fracture roughness coefficient JRC, fracture length, fracture angle, and impact velocity are continuous numerical features; presence or absence of anchor bolts is a Boolean feature.

3. The rock mass dynamic performance prediction method using a decision tree-guided deep neural network according to claim 2, characterized in that: All dynamic impact test data were preprocessed: all feature types were normalized to [0,1] to form a rock mass dataset, and 80% of the samples were randomly selected as the rock mass training set, with the remaining 20% ​​as the rock mass test set; among them, continuous numerical features and Boolean features were 5 input features, and dynamic intensity was 1 output feature; let the rock mass training set be... include There are 1 sample, denoted as _ . , No. Sample Given an input feature vector and corresponding output values Together they form a binary tuple. , where the input feature vector Feature Dimension , corresponding to 5 input features, specifically represented as Output value Output dimension This corresponds to one output feature.

4. The rock mass dynamic performance prediction method using a decision tree-guided deep neural network according to claim 3, characterized in that, The decision tree regression model is split using a rock mass dataset. The specific steps are as follows: To build a decision tree regression model, key parameters for constructing the model are manually preset, including the maximum split parameter. Minimum number of samples for split nodes Minimum number of samples for leaf nodes Candidate node default tolerance ; Rock Mass Training Set All samples are input into the initial state decision tree regression model, which contains only the unique root node of the decision tree. Rock mass training set All sample input root nodes Determine the root node Does it satisfy the following splitting condition: （1）， In the formula, The minimum number of samples for a split node, if the root node Upper rock mass training set capacity Less than If the splitting condition is not met, the current root node is marked as the final leaf node, and the splitting ends; if the splitting condition is met, the current node is marked as the parent node region. Then the decision tree regression model will split; For each input feature, including continuous numerical and Boolean features: presence or absence of anchor bolts, crack roughness coefficient JRC, crack length, crack angle, and impact velocity, the parent node region is traversed. All inside For each sample, sort them according to the magnitude of the feature value, and calculate the adjacent samples where every two feature values ​​are different under that feature. and At the midpoint of the eigenvalues, select the region that makes the parent node's region... The midpoint of the eigenvalue with the largest reduction in mean squared error is taken as the optimal splitting threshold. Samples with eigenvalues ​​less than or equal to the optimal splitting threshold are assigned to the left child node region, and samples with eigenvalues ​​greater than the optimal splitting threshold are assigned to the right child node region. The specific calculation process is as follows: remember For the first Sample The 1 eigenvalue, For the first Sample The 1 eigenvalue, , For the first Sample and its neighboring samples In the If the midpoint of the eigenvalues ​​is: （2）， Will As a candidate splitting threshold, the parent node region The divided left child node region and right child node region The eigenvalues ​​are represented as: （3）， In the formula, Indicates the first The first sample One eigenvalue; Record the parent node region Left child node region right child node region The number of samples in each are respectively , , Parent node region Left child node region right child node region mean square error , , The calculation is performed using the following formula: （4）， In the formula, Then they respectively represent The average value of the output dynamic intensity characteristic value of samples in each region; The candidate split threshold is calculated using the following formula. The resulting reduction in mean square error : （5）， The candidate splitting thresholds are obtained according to equation (5). The resulting reduction in mean square error And the optimal splitting scheme for this splitting is determined by equation (6). ): （6）， In the formula, The index represents the best splitting feature, i.e., the best splitting feature selected from all features; This represents the sample index corresponding to the optimal splitting threshold, which is the optimal splitting position under the optimal splitting feature. According to the optimal splitting scheme ( Split the node, and after the split, if the left child node region... right child node region The number of internal samples is less than the minimum number of samples in the leaf nodes. If the child node splits, the split ends; otherwise, the child node is treated as the parent node, and the split continues using equations (2) to (6) until any of the following conditions are met, at which point the split terminates: the number of splits. , Or the reduction in maximum mean square error < default tolerance .

5. The rock mass dynamic performance prediction method using a decision tree-guided deep neural network according to claim 4, characterized in that, After terminating the split, a complete decision tree regression model is obtained, and the key structural parameters are extracted: maximum tree depth. That is, the total number of layers in the decision tree regression model; the first Number of branches in a layer That is, the first The number of split nodes in the layer, of which The layer index is used; and during multiple splits, the feature importance of each input feature is calculated synchronously. The specific steps are as follows: Record No. The feature in the first The reduction in mean squared error of the decision tree regression model during each split is When the first The second split is based on the first The optimal splitting scheme for each feature ( When executed, ; otherwise, ; In all decision tree regression models During the second split, the first The cumulative sum of the reductions in the mean squared error of each feature in the decision tree regression model for: （7）， In the formula, Indicates the first Number of samples in the parent node region of the second split; This indicates the total number of samples in the rock mass training set; Using the following formula Normalization is performed to obtain the importance of each feature. : （8）。 6. The rock mass dynamic performance prediction method using a decision tree-guided deep neural network according to claim 5, characterized in that: First, using the key structural parameters of the complete decision tree regression model, determine the number of neurons in each hidden layer of the deep neural network prediction model and the connection strategy between the input layer feature neurons and the first hidden layer neurons. The specific steps are as follows: Mapping the decision tree regression model to a deep neural network: the root node of the decision tree regression model corresponds to the input layer of the network; the branching process of the decision tree regression model is implemented by the hidden layers; the maximum tree depth of the decision tree regression model is... Since the last layer of the decision tree regression model is a leaf node layer, the effective split depth is... , which corresponds to the total number of hidden layers in the network, and the output layer corresponds to the leaf node output of the final decision tree regression model; The number of neurons in each layer of the deep neural network is calculated based on the number of input features in the rock mass training set. The number of input layer neurons in the network will be used to determine the number of output features within the rock mass training set. As the number of neurons in the output layer, the first... The number of neurons in the hidden layer is denoted as The number of neurons in the previous layer and the number of neurons in the decision tree regression model are determined by the number of neurons in the previous layer. Number of branches per layer Joint decision: （9）， Utilizing feature importance The specific process for determining the neuron connection method between the input layer and the first hidden layer is as follows: Calculate the first using formula (10) Input features Number of neurons in the first hidden layer : （10）， In the formula, The function represents rounding the value within the parentheses; This represents the number of neurons in the first hidden layer of a deep neural network; Formula (11) is used to constrain and optimize the neuron connections between the input features and the first hidden layer, ensuring that each input feature is connected to at least one neuron: （11）， At the same time, ensure the number of neurons connected to all input features. Equal to the number of neurons in the first hidden layer ,when When, reduce the number of neuron connections for a feature of least importance; when At this point, increase the number of neuron connections for the feature with the highest importance; until the following equation is finally satisfied: （12）， For each input feature of a deep neural network, the neurons are connected one by one. There are 1 first hidden layer neuron; add random connections to each input feature neuron, accounting for 5% of the total number of connections between the input feature and the first hidden layer neuron.

7. The rock mass dynamic performance prediction method using a decision tree-guided deep neural network according to claim 6, characterized in that, By utilizing the number of branches in each layer of the complete decision tree regression model, the connections between neurons in each hidden layer of the deep neural network are initialized, and the connection topology between neurons in each hidden layer of the deep neural network is constructed, thereby improving the prediction accuracy under noisy and small sample conditions. The first in the deep neural network The first hidden layer and the previous hidden layer The neurons between them are connected in the following steps: Determine the first Number of hidden layer neuron groups ; In the decision tree regression model, the first... Number of branches per layer and the previous hidden layer of the corresponding deep neural network prediction model Number of neurons Minimum value in: （13）， Define the neuron grouping mechanism between hidden layers; starting from the second hidden layer Start, hide the layer With neurons The neurons are synchronously divided into There are several groups; among them, the hidden layer... Each group contains One neuron, hidden layer Each group contains The number of neurons is represented as follows: , （14）， In the formula, , Hidden layers and The number of neurons; The parentheses for rounding down indicate that the value inside the parentheses is rounded down to the nearest integer. Starting from the second hidden layer, according to For hidden layers The neurons in the sequence are grouped sequentially; the hidden layer is determined using the following formula. Index sequence of all neurons : （15）， In the formula, Functions that generate sets of integers Random arrangement; According to the hidden layer index sequence The hidden layer is determined using the following formula. The Middle Group number of each neuron : （16）， In the formula, represents the upper rounding brackets, indicating that the value inside the brackets is rounded up; Indicates in the hidden layer The Middle The index number of each neuron; To be divided into Establish hidden layers for each group of neurons. and hidden layers Forward connections between layers; forward connections are in sparse connection mode: traversing hidden layers. and hidden layers Group number of all neurons and When neurons have the same group number, the hidden layer... and hidden layers Establish full connections between them; Add a 30% probability random connection, meaning that each neuron in a hidden layer has a 30% probability of randomly connecting with any two neurons in the previous layer.

8. The rock mass dynamic performance prediction method using a decision tree-guided deep neural network according to claim 7, characterized in that: The root mean square error (RMSE) is used as a performance evaluation metric to train the deep neural network prediction model. The smaller the RMSE, the better the prediction performance of the deep neural network prediction model. The RMSE is calculated as follows: （17）， In the formula, This represents the total number of samples used in training. These represent the sample values ​​that the deep neural network prediction model outputs during training. This represents the actual output value of the corresponding sample.

9. A computer device, characterized in that, It includes a processor and a memory, the processor being electrically connected to the memory, the memory being used to store instructions and data, and the processor being used to execute the rock mass dynamic performance prediction method of the decision tree-guided deep neural network as described in any one of claims 1-8.

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