Rock penetration depth prediction integrated learning method based on residual supervision enhancement

Abstract

The application is a kind of rock penetration depth prediction integrated learning method based on residual supervision enhancement. It includes collecting projectile physical parameters and rock mechanical parameters, forming the penetration characteristic parameter input set, calculating the residual of penetration depth prediction value and actual value, and constructing the penetration depth output set; the physical information neural network (PINN) is introduced, the joint loss function of data fitting term and physical constraint term is constructed, the fusion of data driving and physical priori knowledge is realized; the grey wolf optimization algorithm (GWO) is introduced to globally optimize the core hyperparameters and weight distribution mechanism of the Adaboost integrated learning model. The application breaks through the working condition application range limitation of the traditional method, has the physical interpretability and the generalization of data driving, and can be widely applied to the projectile penetration rock depth prediction in the fields of national defense engineering, geotechnical engineering, armor piercing bullet design and the like, and provides high-precision prediction basis for the scheme design and safety evaluation of penetration engineering.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of projectile penetration engineering technology and machine learning, specifically involving an ensemble learning method for predicting rock penetration depth based on residual supervision enhancement. Background Technology

[0002] Projectile penetration into rock is a typical mechanical problem in engineering projects such as national defense strikes and soil and rock excavation. As a core evaluation indicator, the accurate prediction of penetration depth is of crucial significance for engineering scheme design and equipment performance optimization. Currently, methods for predicting projectile penetration depth into rock are mainly divided into three categories: theoretical analytical methods, experimental measurement methods, and numerical simulation methods.

[0003] Theoretical analytical methods derive penetration depth calculation formulas by establishing mechanical models, such as the cavity expansion theory and the drag function method. Among them, the rigid projectile penetration analytical model for brittle rock proposed by Forrestal et al. (Forrestal MJ, Tzou D Y. Penetration of rigid projectiles into geologic media[J]. International Journal of Impact Engineering, 1997, 19(1-2): 135-156.) is widely used. However, this model assumes that the rock is an ideal brittle material and ignores factors such as material nonlinearity and projectile deformation, resulting in large prediction errors under complex working conditions. Domestic scholars Wang Mingyang et al. improved the penetration model based on the cavity expansion theory (Wang Mingyang, Deng Guoqiang, Qian Qihu. Theoretical and experimental research progress on projectile penetration of rock[J]. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(11): 2201-2212.), which improved the accuracy to a certain extent, but it is still difficult to adapt to complex scenarios with multiple parameter coupling.

[0004] Experimental measurement methods obtain depth data through real penetration tests, which has the advantage of high reliability, but also have problems such as high test costs, long cycles, and poor controllability of working conditions. For example, the projectile penetration test of granite conducted by Zhang Lei et al. (Zhang Lei, Huang Fenglei, Weng Chunsheng. Experimental study on projectile penetration of granite [J]. Explosion and Shock, 2015, 35(3):321-326.) has a single test cost of over 100,000 yuan and is difficult to cover all working conditions with different projectile parameters and rock properties.

[0005] Numerical simulation methods, using software such as finite element method and discrete element method to simulate the penetration process, such as LS-DYNA and PFC3D, can compensate for the shortcomings of experimental methods. Li Shucai et al. used LS-DYNA to conduct numerical simulation of projectile penetration into jointed rocks (Li Shucai, Li Liping, Zhang Qingsong. Research progress on disaster mechanism and key prevention and control technologies of deep rock engineering [J]. Science in China: Technological Science, 2020, 50(1): 1-28.), but this method has extremely high requirements for mesh generation and constitutive model parameter settings, and the calculation time is long, making it difficult to meet the real-time prediction needs of engineering.

[0006] In recent years, machine learning methods have begun to be applied to the field of penetration depth prediction due to their strong nonlinear fitting capabilities. Liu Jun et al. used BP neural networks to predict projectile penetration depth (Liu Jun, Wang Shushan, Zhao Handong. Application of BP neural network in projectile penetration depth prediction [J]. Firepower and Command Control, 2018, 43(8): 162-165.), but traditional BP neural networks have defects such as random initial weights and biases, easy to get trapped in local optima, and poor generalization ability. To solve this problem, scholars have tried to improve neural networks by using optimization algorithms. For example, Zhao Yun et al. used particle swarm optimization (PSO) to improve BP neural networks (Zhao Yun, Li Ming, Zhang Xiaodong. Research on the application of PSO-BP neural network in penetration depth prediction [J]. Computer Simulation, 2022, 39(5): 18-22.), but the optimization effect is still limited by the algorithm's optimization ability. Meanwhile, the predictive stability of a single machine learning model is insufficient and it is difficult to adapt to complex and ever-changing penetration conditions. Therefore, building a high-precision, highly generalizable ensemble learning prediction model has become a research hotspot and urgent need in the field of penetration depth prediction. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing methods for predicting the depth of projectile penetration in rock, such as insufficient accuracy of theoretical analytical methods, high cost of experimental measurement methods, long time consumption of numerical simulation methods, and the tendency of single machine learning models to get trapped in local optima and have poor generalization ability. This invention proposes an ensemble learning method for predicting rock penetration depth based on residual supervision, incorporating physical information and an uncertainty-driven mechanism. The ensemble learning framework introduces prior physical information about the penetration mechanism. First, it calculates the physical baseline penetration depth based on a penetration theory model. Then, the learning model performs residual correction on the systematic deviations of the physical baseline. Physical consistency constraints are applied during training, thereby improving the generalization ability and stability under complex conditions such as cross-rock types and cross-velocity ranges. Furthermore, a prediction uncertainty modeling mechanism is introduced, simultaneously providing an uncertainty metric for the model output, and... Uncertainty is addressed by introducing a Boosting sample weight update and weak predictor weight allocation strategy, which prioritizes high-error and high-uncertainty sample regions during model training, thereby improving prediction stability and outputting usable confidence interval information. The initial weights and biases of the Physical Information Neural Network (PINN) are optimized using the Gray Wolf Optimizer (GWO) to solve the local optima problem and improve single-model prediction accuracy. Furthermore, multiple GWO-PINN weak predictors are integrated based on the AdaBoost strategy to enhance the model's generalization ability and prediction stability. Finally, a complete process from data preprocessing and model training to depth prediction is constructed to achieve accurate and efficient prediction of projectile penetration depth in rock, providing reliable data support for the optimization of penetration engineering schemes and filling the gap in real-time prediction under complex working conditions using existing methods.

[0008] The technical solution to achieve the purpose of this invention is: an ensemble learning method for predicting rock penetration depth based on residual supervision enhancement, comprising the following steps:

[0009] Step (1): Penetration feature data preprocessing and dataset partitioning: Collect projectile physical parameters and rock mechanical parameters to form penetration feature parameters. Perform normalization on the data, and divide the processed dataset into training set, validation set and test set according to a preset ratio;

[0010] Step (2): Physical baseline calculation and residual sample construction: based on penetration feature parameters The penetration depth of the physical baseline is calculated using a pre-defined penetration theory model. Constructing physical derived features The residual labels are constructed using the difference between the actual penetration depth and the physical baseline penetration depth, and the residuals are used as the target output of supervised learning.

[0011] Step (3): Construct a GWO-PINN weak predictor with physical consistency constraints: Construct a GWO-PINN weak predictor with physical consistency constraints. As input, with residual The output is PINN; the initial weights and biases of PINN are optimized by GWO to train a GWO-PINN weak predictor.

[0012] Step (4): Uncertainty modeling and estimation of weak predictors: introduce random deactivation or equivalent random perturbation structure into the weak predictor so that the model can output the uncertainty measure of the residual prediction when making predictions; use the validation set to determine parameters such as the number of forward propagations and random deactivation rate so that the uncertainty measure meets the preset coverage requirements.

[0013] Step (5): Uncertainty-driven AdaBoost ensemble strong predictor: Repeat steps (3) and (4) to train multiple GWO-PINN weak predictors; during the AdaBoost iteration, update the sample weights and introduce an uncertainty adjustment mechanism into the fusion weights of the weak predictors to obtain the ensemble strong predictor;

[0014] Step (6): Penetration depth prediction and confidence interval output: Output the penetration feature parameters to be predicted. Normalize according to step (1) and calculate the physical baseline penetration depth. Physically derived features The input is integrated into a strong predictor to obtain residual predictions and uncertainty measures. The residual predictions are then combined with the physical baseline to obtain the penetration depth prediction results, and the corresponding prediction confidence intervals are output.

[0015] Compared with the prior art, the significant advantages of this invention are:

[0016] (1) Effectively solves the technical pain points of poor generalization ability and limited adaptability of existing penetration depth prediction models, and further enhances cross-condition stability. In existing technologies related to projectile penetration depth prediction, traditional theoretical models rely on simplified assumptions of specific penetration stages, and can usually only adapt to a narrow velocity range and limited lithological conditions; when the corresponding velocity range is exceeded or the rock mechanical parameters change, the prediction accuracy is prone to significant decrease. Although some machine learning models introduce data-driven methods, they have not fully solved the problem that a single model is prone to getting trapped in local optima, and their suitability for complex and variable projectile-target parameter sets is insufficient. This invention avoids the defect of PINN being prone to getting trapped in local optima by optimizing the initial weights and biases of PINN through GWO; at the same time, it uses the AdaBoost ensemble strategy to fuse multiple weak predictors, so that the model can adapt to different projectile physical parameters, rock mechanical parameters and different penetration velocity conditions, significantly improving the model's generalization ability and environmental adaptability. Furthermore, this invention introduces a physical baseline and residual correction mechanism, so that the model can still maintain more stable prediction performance when crossing velocity ranges, crossing lithology or data distribution changes.

[0017] (2) The "baseline-residual" model incorporating physical information enhances physical rationality, interpretability, and robustness under small sample conditions. Existing pure data-driven prediction models are prone to result distortion under small sample, strong nonlinear, and extrapolation scenarios, and the prediction results lack physical constraints and engineering credibility. This invention calculates the physical baseline penetration depth based on a pre-defined penetration theory model. ,by Residual labels are constructed and used as supervised learning outputs, enabling the learning model to focus on learning systematic biases not covered by the physical model; simultaneously, physical derived features are constructed. And introduce a physical consistency constraint term into the training objective. It effectively suppresses abnormal predictions that violate engineering principles (such as trend deviations and out-of-bounds errors), thereby improving the physical consistency, cross-condition transferability, and engineering interpretability of prediction results.

[0018] (3) Uncertainty modeling and the "uncertainty-driven" Boosting mechanism significantly improve prediction stability and provide reliable quantitative output: Most existing penetration depth prediction methods only output a single prediction value, which is difficult to quantify prediction risk; when there is a lot of noise, the sample is scarce, or the new working condition deviates from the training distribution, the model may exhibit "high confidence error" and cannot be identified. This invention introduces Dropout into the weak predictor to achieve sample-level uncertainty estimation; and in the AdaBoost iteration process, "error and uncertainty" are used together for sample weight update, while uncertainty adjustment is introduced into the fusion weight of the weak predictor, so that the training process is more focused on the difficult sample region with high error and high uncertainty, thereby enhancing the robustness and prediction stability of the model; the confidence interval of penetration depth can be output in the prediction stage, providing a dual output basis of "predicted value + credibility" for engineering decision-making.

[0019] (4) By relying on the unbiased feature screening mechanism, the model's ability to capture key influencing factors is enhanced, and the prediction accuracy is improved: In the existing penetration depth prediction technology, some models do not systematically screen the input features, which is easily affected by redundant information, making it difficult for the model to focus on the core influencing factors of the penetration process; even if feature selection methods are introduced, there may be problems of strong subjectivity and lack of quantitative basis. In the feature processing stage, this invention integrates the projectile physical parameters and rock mechanical parameters to construct a comprehensive feature space, and realizes unbiased key feature identification and redundant information suppression through the natural quantitative feedback of feature contribution during model training, so that the model can more accurately capture the intrinsic relationship between core factors such as projectile diameter, projectile velocity, and rock compressive strength and penetration depth; combined with the fitting ability of GWO-PINN for nonlinear relationships and the error correction ability of AdaBoost, the prediction accuracy and result reliability under complex working conditions are further improved.

[0020] (5) The model has stronger interpretability and engineering applicability, and is easier to deploy and iteratively optimize: Although some existing ensemble learning models can improve prediction accuracy, the fusion logic and parameter optimization mechanism of weak predictors are not clear, and the interpretability is insufficient, which is not conducive to engineers' understanding and debugging. This invention clearly defines the optimization logic of GWO, the topology of PINN and the integration rules of AdaBoost, and outputs the predicted value and confidence interval through the standardized process of "physical baseline - residual correction - uncertainty assessment", making the model operation logic clear and highly debuggable; engineers can adjust the constraint weights according to the actual working conditions. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the prediction process of the method of the present invention.

[0022] Figure 2 This is a flowchart of the machine learning model training process of the present invention.

[0023] Figure 3 This describes the iterative process of the method of the present invention.

[0024] Figure 4 This is a comparison chart of the predicted and actual values ​​of this invention.

[0025] Figure 5 The radar chart shows the performance of the four evaluation indicators of this invention. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings.

[0027] An ensemble learning method for predicting rock penetration depth based on residual supervision enhancement includes the following steps:

[0028] Step (1): Penetration feature data preprocessing and dataset partitioning: Collect projectile physical parameters and rock mechanical parameters to form penetration feature parameters. The data is normalized and divided into training, validation and test sets according to a preset ratio.

[0029] Step (2): Physical baseline calculation and residual sample construction: based on penetration feature parameters The physical baseline penetration depth is calculated using a pre-defined penetration theory model. And construct physical derived features With true penetration depth and construct residual labels from the differences The residual is used as the target output of supervised learning.

[0030] Step (3): Construct a GWO-PINN weak predictor with physical consistency constraints: Construct a GWO-PINN weak predictor with physical consistency constraints. As input, with residual The output is PINN; the initial weights and biases of PINN are optimized by GWO to train the GWO-PINN weak predictor.

[0031] Step (4): Uncertainty modeling and estimation of weak predictors: introduce random deactivation or equivalent random perturbation structure into the weak predictor so that the model can output the uncertainty measure of the residual prediction when making predictions; use the validation set to determine parameters such as the number of forward propagation and random deactivation rate so that the uncertainty measure meets the preset coverage requirements.

[0032] Step (5): Uncertainty-driven AdaBoost ensemble strong predictor: Repeat steps (3) and (4) to train multiple GWO-PINN weak predictors; during the AdaBoost iteration, update the sample weights and introduce an uncertainty adjustment mechanism into the fusion weights of the weak predictors to obtain the ensemble strong predictor.

[0033] Step (6): Penetration depth prediction and confidence interval output: Output the penetration feature parameters to be predicted. Normalize according to step (1) and calculate and The input is integrated into a strong predictor to obtain residual predictions and their uncertainty measures. The residual predictions are then combined with the physical baseline to obtain the penetration depth prediction results, and the corresponding prediction confidence intervals are output.

[0034] The specific method for data preprocessing in step (1) is as follows:

[0035] The projectile penetration-related characteristic parameters include projectile physical parameters (projectile diameter, projectile length, nose shape coefficient, projectile mass, projectile velocity, projectile material hardness, and projectile material tensile strength) and rock mechanics parameters (compressive strength, tensile strength, and density). Based on these penetration characteristic parameters, the physical baseline penetration depth is calculated using a preset penetration theory model. And construct physical derived features The physical derived features use momentum-related terms. The dataset is represented as follows: ,in Let i be the penetration feature parameters of the i-th group. To correspond to the depth of the projectile penetrating the rock, the residual dataset is further defined as follows: The residual is used as the target output for supervised learning; the normalization formula is: ; ,in , Let the maximum and minimum values ​​of the j-th feature dimension parameter be denoted as . , The maximum and minimum values ​​of the training set residuals are used. The normalized dataset is randomly divided into training, validation, and test sets in a 7:2:1 ratio based on the total number of samples. When calculating prediction uncertainty requires multiple forward propagations, the validation set is retained to determine the number of forward propagations. And random inactivation rate parameters, so that the uncertainty measure meets the preset coverage requirements on the validation set.

[0036] Step (3) Constructing the GWO-PINN weak predictor specifically includes the following steps:

[0037] Step (31): GWO population initialization: Map the individual gray wolf positions to the initial weights of the BP neural network. With bias Initialize parameters such as population size and maximum number of iterations;

[0038] Step (32): GWO position update: Using the mean square error of PINN prediction as the fitness function, the GWO position update formula is iteratively optimized. The update formula is:

[0039] ; ; ;

[0040] in , , The positions of the individuals with the best, second best, and third best fitness in the current population; , , The convergence factor vector in the Grey Wolf optimization algorithm is used to control the step size and search range; , , For the current individual gray wolf and , , Distance vector between wolves; For the first The new position vector of the individual gray wolf in the next iteration; The current iteration number of the GWO algorithm; with residuals With residual prediction The mean squared error is used as the fitness, and a physical consistency penalty term can be introduced into the fitness function to form the joint fitness F:

[0041]

[0042] The mean square error The mean square error of the residual prediction error; ; This includes: output upper and lower bound constraint penalties, and engineering rule consistency penalties;

[0043] Step (33): PINN training: Select the parameters corresponding to the optimal position obtained by GWO optimization as the initial weights and biases of the BP neural network. PINN includes an input layer, a hidden layer, and an output layer. The number of neurons in the input layer is consistent with the dimension of the penetration feature parameters, and the number of neurons in the output layer is 1 (corresponding to the residual prediction value). The hidden layer introduces a random dropout structure, allowing the same sample to generate multiple random forward propagation outputs during the prediction phase; using joint loss... The loss function is used to update the parameters and train the GWO-PINN weak predictor.

[0044] Step (4): Uncertainty estimation: Performed on the same input sample The random forward propagation yields Calculate the mean of the residual prediction With variance ,Will As a measure of uncertainty for this sample.

[0045] Step (5) AdaBoost integrates strong predictors, specifically including the following steps:

[0046] Step (51): Initialize the training sample weight distribution: , where N is the total number of training samples;

[0047] Step (52): Resample the training subset: with the current sample weights Based on this, a training subset Tr is drawn from the training set with replacement;

[0048] Step (53): Based on step (3), obtain multiple GWO-PINN weak predictors, and obtain the weak predictors. Its output is the predicted residual value. After training is complete, an uncertainty metric is calculated for the training samples. The uncertainty measure is obtained by multiple random forward propagation variances or by the divergence of multiple weak predictor outputs;

[0049] Step (54): Calculate the sample weight error: For each training sample, calculate the weight error (the original error calculation can be retained as the basic error term), and introduce uncertainty into the original error to construct a joint difficulty index.

[0050] Normalization error:

[0051] Normalized uncertainty:

[0052] Combined difficulty:

[0053] in These are the predicted residual values; ε is a measure of uncertainty; ε is a preset positive stability factor used to avoid division by zero during normalization and to improve computational stability. This represents the participation coefficient for uncertainty.

[0054] Step (55): Sample weight update: based on joint difficulty Update sample weights : ,in To update the step size coefficient.

[0055] Step (56): Calculate the weights of the weak predictor: First, calculate the weight factors of the weak predictor. Then calculate the weights of the weak predictor. The overall uncertainty level of the weak predictor is introduced into the weighting factor of the weak predictor. The penalty or adjustment item is specifically implemented as follows:

[0056]

[0057] in Let be the average uncertainty of the t-th weak predictor. The preset uncertainty penalty coefficient allows weaker predictors with lower uncertainty to receive higher weights under the same error conditions.

[0058] Step (57): Sample weight normalization: , ;

[0059] Step (58): Repeat steps (52)-(57) until K weak GWO-PINN predictors are obtained, and then strong predictors are obtained by weighted summation and fusion: The output is the fused residual prediction value. .

[0060] The method for predicting the penetration depth of the projectile in step (6) is as follows:

[0061] Step (61): The projectile penetration characteristic parameters to be predicted Perform normalization processing according to step (1) to obtain normalized parameters. Based on the penetration feature parameters to be predicted... Calculate the penetration depth of the physical baseline Simultaneously construct physical derived features ;

[0062] Step (62): Input the trained strong predictor to obtain normalized residual predictions. Simultaneously, a measure of the uncertainty in residual prediction is obtained. And calculate the mean of the residual predictions. ;

[0063] Step (63): For Performing inverse normalization yields the predicted residual values. , and according to Output the actual penetration depth; output the confidence interval based on the uncertainty measure: ,in To provide a dimension of residual uncertainty consistent with inverse normalization, is the confidence coefficient.

[0064] Physical baseline penetration depth Based on penetration characteristic parameters The penetration depth is calculated using a pre-defined penetration theory model; the penetration theory model includes a penetration model based on a drag function and an empirical penetration model based on energy conservation; and the physical baseline penetration depth is... It is used as one of the input features of the model in the training of the weak predictor.

[0065] Weak predictors with residuals As the learning objective, among which For true penetration depth, The physical baseline penetration depth; the output of the weak predictor is the residual prediction value. In the prediction phase, the residual prediction value is combined with the physical baseline penetration depth to form the final penetration depth prediction value: Then, a physical consistency constraint term is introduced during the training process. This forms a joint loss function:

[0066]

[0067] in To constrain the weighting coefficients, and Include at least one of the following:

[0068] (1) Monotonicity constraint penalty term: makes the predicted penetration depth Regarding the physical priors that key variables such as bullet velocity satisfy the overall monotonicity;

[0069] (2) Boundary constraint penalty term: makes Satisfy upper and lower bound constraints;

[0070] (3) Engineering rule consistency penalty item: makes It meets the empirical rule consistency requirements between the preset material strength ratio, density ratio, or geometric dimensionless combination and the penetration depth.

[0071] Uncertainty measurement The reliability of the penetration depth prediction results is characterized by the following method:

[0072] (1) Multiple forward propagation estimation based on random deactivation: a Dropout structure is introduced into the hidden layer of the weak predictor; during the prediction stage, the input of the same sample is [ Perform M random forward propagations to obtain the residual prediction sequence. And calculate the mean and variance of the residual predictions:

[0073]

[0074] in The uncertainty measure of the sample is M, which is a preset positive integer, preferably 10 to 100.

[0075] (2) Committee estimation based on weak predictor divergence: using multiple weak predictors obtained through AdaBoost iteration Output residual prediction values ​​for the same sample And calculate the uncertainty measure based on the output divergence:

[0076]

[0077] in For the first The weights of each weak predictor This serves as a measure of uncertainty for the sample. Further, the confidence interval for the penetration depth prediction is calculated based on the uncertainty measure and satisfies: .in and The corresponding dimensions are consistent (obtained through inverse normalization transformation if necessary). For pre-set confidence coefficients.

[0078] During AdaBoost training, sample weight updates are performed based on the joint difficulty of error and uncertainty. For the ... In the first round of training Given training samples, the true residual value is defined as... The output of the weak predictor is The uncertainty measure is And construct the normalized error term and the normalized uncertainty term:

[0079] Normalization error:

[0080] Normalized uncertainty:

[0081] Combined difficulty:

[0082] Where ε is a preset positive stability factor, used to avoid division by zero during normalization and improve computational stability; This represents the participation coefficient for uncertainty. The sample weights are then updated based on the joint difficulty.

[0083]

[0084] in For the first Round sample weights, The total number of training samples, Update the step size coefficients for the weights. Further, the weak predictor weights... An uncertainty penalty or adjustment term is introduced on top of the error-based weighting factor to give a higher fusion weight to the weaker predictor with lower uncertainty. The adjustment term includes at least one of the following:

[0085] (1) Overall uncertainty of weak predictors Applying exponential decay, i.e.:

[0086]

[0087] in For the first The average uncertainty of a weak predictor on the training samples The penalty coefficient is... No. Weighted error rate of weak predictors;

[0088] (2) The denominator of the weighting factor is introduced as a penalty term, that is:

[0089]

[0090] The above method enables weaker predictors with lower uncertainty to obtain higher fusion weights.

[0091] Example 1

[0092] This implementation demonstrates the complete operational logic from data input to result output for the specific engineering scenario of "rock penetration depth" using a pre-trained GWO-PINN-AdaBoost prediction model. Based on the completed model training, this method utilizes a strong predictor composed of 10 PINNs optimized using the Grey Wolf Algorithm (GWO) to predict the depth of the target working condition.

[0093] 1. Model component preparation before execution

[0094] Before executing the prediction process, the system needs to call the following core components from computer-readable storage media:

[0095] Component 1 (Weak Predictor Array): Contains A trained GWO-PINN weak predictor Each predictor has established a 4-6-1 network topology and stored the initial weights determined by the GWO algorithm. and bias .

[0096] Component 2 (Integrated Weights): The set of weights for the weak predictor The weights are calculated by the AdaBoost strategy based on the training error and are used for subsequent weighted ensembles.

[0097] Component 3 (Feature Parameters): Records the extreme values ​​of features in each dimension of the training set and the penetration depth. , , , ), used to normalize and denormalize the data to be predicted.

[0098] 2. Acquisition and Feature Preprocessing of Data to be Predicted

[0099] The system first extracts the samples to be predicted from the prediction dataset:

[0100] Feature Acquisition: Obtain the input feature vector for the current working condition, including projectile physical parameters (projectile diameter, projectile length, nose shape coefficient, projectile mass, initial velocity, etc.) and rock mechanical parameters (compressive strength, tensile strength, and density). For example: projectile velocity. Bullet length ,quality Rock strength .

[0101] Normalization: By calling the extreme value parameters in component 3, the feature is mapped to the $[0, 1]$ interval using the range transformation method.

[0102]

[0103] 3. Penetration depth prediction calculation based on ensemble learning

[0104] The system will normalize the feature vectors The input is fed into the integrated strong predictor for computation:

[0105] Weak predictor parallel computation: Ten GWO-PINN weak predictors are input sequentially. Each predictor computes and outputs a normalized weak prediction value through its hidden layer (Sigmoid activation function) and output layer (linear activation function). .

[0106] Strong predictor integration and fusion: based on the set of weak predictor weights Perform weighted summation (corresponding to the flowchart) (Module), calculate the integrated output of the strong predictor:

[0107]

[0108] 4. Result Post-processing and Iterative Looping

[0109] Inverse normalization restoration: Integrating predicted values Restored to the true physical depth value :

[0110]

[0111] Example: If the calculation yields After substituting the extreme values ​​from the training set and restoring them, the final predicted penetration depth is: .

[0112] Output and Decision: The system outputs the final prediction results and stores them in the database for optimizing rock penetration strategies. The system then determines if there is still data to be processed: if yes, it returns to the "Get Next Sample" step; otherwise, it terminates the process.

Claims

1. An ensemble learning method for predicting rock penetration depth based on residual supervision enhancement, characterized in that, Includes the following steps: Step (1): Penetration feature data preprocessing and dataset partitioning: Collect projectile physical parameters and rock mechanical parameters to form penetration feature parameters. Perform normalization on the data, and divide the processed dataset into training set, validation set and test set according to a preset ratio; Step (2): Physical baseline calculation and residual sample construction: based on penetration feature parameters The penetration depth of the physical baseline is calculated using a pre-defined penetration theory model. Constructing physical derived features The residual labels are constructed using the difference between the actual penetration depth and the physical baseline penetration depth, and the residuals are used as the target output of supervised learning. Step (3): Construct a GWO-PINN weak predictor with physical consistency constraints: Construct a GWO-PINN weak predictor with physical consistency constraints. As input, with residual The output is PINN; the initial weights and biases of PINN are optimized by GWO to train a GWO-PINN weak predictor. Step (4): Uncertainty modeling and estimation of weak predictors: introduce random deactivation or equivalent random perturbation structure into the weak predictor so that the model can output the uncertainty measure of the residual prediction when making predictions; The number of forward propagations and the random inactivation rate are determined using the validation set, so that the uncertainty measure meets the preset coverage requirements; Step (5): Uncertainty-driven AdaBoost ensemble strong predictor: Repeat steps (3) and (4) to train multiple GWO-PINN weak predictors; during the AdaBoost iteration, update the sample weights and introduce an uncertainty adjustment mechanism into the fusion weights of the weak predictors to obtain the ensemble strong predictor; Step (6): Penetration depth prediction and confidence interval output: Output the penetration feature parameters to be predicted. Normalize according to step (1) and calculate the physical baseline penetration depth. Physically derived features The input is integrated into a strong predictor to obtain residual predictions and uncertainty measures. The residual predictions are then combined with the physical baseline to obtain the penetration depth prediction results, and the corresponding prediction confidence intervals are output.

2. The method according to claim 1, characterized in that, The physical parameters of the projectile in step (1) are projectile diameter, projectile length, nose shape coefficient, projectile mass, projectile velocity, projectile material hardness, and projectile material tensile strength; the rock mechanics parameters are compressive strength, tensile strength, and density. The formula for data normalization is: ,in , These are the maximum and minimum values ​​of the j-th feature dimension parameter.

3. The method according to claim 2, characterized in that, The step (2) of "constructing residual labels based on the difference between the actual penetration depth and the physical baseline penetration depth" specifically means: Define residual: , in Let be the depth to which the i-th projectile penetrates the rock. Let be the physical baseline penetration depth of the i-th projectile; The formula for normalizing the residuals is: ,in , These are the maximum and minimum values ​​of the residuals in the training set.

4. The method according to claim 3, characterized in that, Step (3) is as follows: Step (31): GWO population initialization: Map the individual gray wolf positions to the initial weights of the BP neural network. With bias Initialize the population size and maximum number of iterations; Step (32): GWO position update: Using the mean square error of PINN prediction as the fitness function, the GWO position update formula is iteratively optimized. The update formula is: ； ； ； ， in , , The positions of the individuals with the best, second best, and third best fitness in the current population; , , The convergence factor vector in the Grey Wolf optimization algorithm is used to control the step size and search range; , , For the current individual gray wolf and , , Distance vector between wolves; For the first The new position vector of the individual gray wolf in the next iteration; This represents the current iteration number of the GWO algorithm; With residuals With residual prediction The mean squared error is used as the fitness, and a physical consistency penalty term is introduced into the fitness function to form the joint fitness F: ， Mean square error The mean square error of the residual prediction error; These are the constraint weighting coefficients; This includes: monotonicity constraint penalty, output upper and lower bound constraint penalty, and engineering rule consistency penalty; Step (33): PINN training: Select the parameters corresponding to the optimal position obtained by GWO optimization as the initial weights and biases of the BP neural network. The hidden layer of PINN introduces a random deactivation Dropout structure, so that the same sample generates multiple random forward propagation outputs during the prediction stage; using joint loss The loss function is used to update the parameters and train the GWO-PINN weak predictor.

5. The method according to claim 4, characterized in that, Step (4) specifically involves: performing the following on the same input sample. The random forward propagation yields Calculate the mean of the residual prediction With variance ,Will As a measure of uncertainty for this sample.

6. The method according to claim 5, characterized in that, Uncertainty measurement The reliability of the penetration depth prediction results is characterized by multiple forward propagation estimations based on random inactivation: A Dropout structure is introduced in the hidden layer of the weak predictor; during the prediction phase, the input of the same sample is […]. Perform M random forward propagations to obtain the residual prediction sequence. And calculate the mean and variance of the residual predictions: ， in As a measure of the uncertainty of the sample, M is a preset positive integer, preferably 10 to 100.

7. The method according to claim 5, characterized in that, Uncertainty measurement The committee estimate, based on weak predictor divergence, is used to characterize the reliability of the penetration depth prediction results. Multiple weak predictors obtained through AdaBoost iteration Output residual prediction values ​​for the same sample And calculate the uncertainty measure based on the output divergence: ， in For the first The weights of each weak predictor As a measure of uncertainty for the sample, the confidence interval for penetration depth prediction is calculated based on the uncertainty measure and satisfies: ,in and The corresponding dimensions are consistent. For pre-set confidence coefficients.

8. The method according to claim 6 or 7, characterized in that, Step (5) AdaBoost integrates strong predictors, specifically including the following steps: Step (51): Initialize the training sample weight distribution: , where N is the total number of training samples; Step (52): Resample the training subset: with the current sample weights Based on this, a training subset Tr is extracted from the training set with replacement; Step (53): Based on step (3), obtain multiple GWO-PINN weak predictors, and obtain the weak predictors. Its output is the predicted residual value. After training is complete, an uncertainty metric is calculated for the training samples. ; Step (54): Calculate the sample weight error: For each training sample, calculate the weight error, and introduce uncertainty into the original error to construct a joint difficulty index: Normalization error: , Normalized uncertainty: , Combined difficulty: , in These are the predicted residual values; ε is a measure of uncertainty; ε is a pre-defined positive stability factor. The participation coefficient for uncertainty; Step (55): Sample weight update: based on joint difficulty Update sample weights; Step (56): Calculate the weights of the weak predictor: First, calculate the weight factors of the weak predictor. Then calculate the weights of the weak predictor. The overall uncertainty level of the weak predictor is introduced into the weighting factors of the weak predictor. Punishment or adjustment items; Step (57): Sample weight normalization: , ; Step (58): Repeat steps (52)-(57) until K weak GWO-PINN predictors are obtained, and then strong predictors are obtained by weighted summation and fusion: The output is the fused residual prediction value. .

9. The method according to claim 8, characterized in that, Step (55) specifically involves updating the sample weights based on the joint difficulty: ， in For the first Round sample weights, The total number of training samples, Update the step size coefficient for the weights; In step (56), the overall uncertainty level of the weak predictor is introduced into the weighting factor of the weak predictor. The "adjustment or penalty items" are specifically: Overall uncertainty of weak predictors Applying exponential decay, i.e.: ， in For the first The average uncertainty of a weak predictor on the training samples The penalty coefficient is... No. Weighted error rate of weak predictors; Or The denominator of the weighting factor is introduced as a penalty term, that is: 。 10. The method according to claim 9, characterized in that, Step (6) specifically involves: Step (61): The projectile penetration characteristic parameters to be predicted Perform normalization processing according to step (1) to obtain normalized parameters. Based on the penetration feature parameters to be predicted Calculate the penetration depth of the physical baseline Simultaneously construct physical derived features ; Step (62): Input the trained strong predictor to obtain normalized residual predictions. Simultaneously, a measure of the uncertainty in residual prediction is obtained. And calculate the mean of the residual predictions. ; Step (63): For Performing inverse normalization yields the predicted residual values. , and according to Output the actual penetration depth result; Output confidence intervals based on uncertainty metrics: .

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