A tungsten ball penetration steel target limit penetration speed prediction method based on physical information neural network

Abstract

This invention discloses a method for predicting the ultimate penetration velocity of a tungsten ball penetrating a steel target based on a physical information neural network, belonging to the field of fragment damage technology. This invention constructs a highly robust dataset and generates high-quality training samples through weighted averaging and data centrality filtering. Simultaneously, it constructs a prediction network model architecture based on a physical information neural network, using automatic differentiation technology to introduce the physical monotonicity constraint of the penetration damage effect into the loss function. This invention can simultaneously predict the ultimate penetration velocity of a tungsten ball penetrating both high-strength and low-carbon steel targets. Compared with traditional model formulas, this method reduces the error by approximately 26% and 31% for low-carbon steel and high-strength steel, respectively, significantly improving the model's generalization ability and robustness. It has the advantages of wide applicability, strong interpretability, and ease of system integration.

Description

Technical Field

[0001] This invention relates to a method for predicting the ultimate penetration velocity of a tungsten ball against a steel target based on a physical information neural network, specifically a method for predicting the ultimate penetration velocity of a tungsten ball against a typical steel target, and relates to the field of ballistic terminal effect and damage assessment technology. Background Technology

[0002] Tungsten alloy spherical fragments are commonly used damage elements in fragmentation / explosive fragmentation warheads, and their ultimate penetration velocity is a key parameter for assessing the destructive power of the warhead. In constructing a precise damage assessment system, simply integrating multiple empirical models inevitably leads to data gaps and even logical conflicts in the prediction results. Given the complexity of target types and structural materials on the modern battlefield, constructing a damage effect prediction model with broader applicability, higher robustness, and ease of system integration is urgently needed. Long-term research in this field, both domestically and internationally, has formed a research system mainly based on empirical formulas, theoretical derivations, and numerical simulations, resulting in numerous prediction models. However, while theoretical / empirical models offer advantages such as second-level computation, they are mostly based on fitting specific operating conditions, limiting their applicability and causing large prediction deviations across materials. Numerical simulations, due to computational efficiency bottlenecks, cannot meet the timeliness requirements of real-time assessment in actual combat. Therefore, it is urgent to explore new methods and approaches for calculating damage effects that can balance computational efficiency, accuracy, and material applicability.

[0003] In recent years, machine learning methods, due to their inherent sensitivity to data patterns, have provided new approaches to solving the problem of predicting damage effects involving strong nonlinearity and multiple parameters. Related research is rapidly growing, such as using artificial neural networks (ANNs) and support vector machines (SVMs) to predict the residual velocity or penetration depth of fragments on a target plate, and using neural networks and hybrid deep learning methods to predict impact energy absorption. While these studies have yielded some results, models obtained through purely data-driven methods still face two major problems: first, the sample size of penetration tests is limited and unevenly distributed, making the model highly dependent on data and prone to overfitting during direct training; second, there is a lack of physical consistency, as purely data-driven methods are essentially black-box mappings based on statistical laws, and cannot guarantee that prediction results outside the training domain conform to physical laws.

[0004] Physical Information Neural Networks (PINNs) are an emerging interdisciplinary approach that introduces physical information constraints on top of data-driven methods. This avoids the high data dependence and physical consistency problems of purely data-driven methods. PINNs are suitable for data with characteristics such as small samples and high noise. The physical constraints introduced can improve the interpretability and generalization of the model. PINNs can be further studied in depth on the problem of tungsten ball penetration of typical steel targets to improve the accuracy and robustness of damage effect prediction models. Summary of the Invention

[0005] To address the problems of large systematic errors, limited experimental data, and difficulty in systematically integrating traditional formulas in traditional models, this invention proposes a method for predicting the ultimate penetration velocity of a tungsten ball against a steel target based on a physical information neural network. This method first constructs a highly robust dataset through a multi-model joint generation strategy to solve the problems of limited and uneven data; simultaneously, it constructs a model network framework embedded with physical monotonic gradient constraints to ensure that the prediction results satisfy physical laws. The advantages of this invention include: (1) the model can generate highly robust training data through multi-model joint generation and data filtering; (2) the introduction of physical constraints into the model framework ensures the physical consistency of the prediction results; and (3) the model can simultaneously predict the ultimate penetration velocity of a tungsten ball against both low-carbon steel and high-strength steel targets.

[0006] The technical problem solved by this invention is as follows: To address the issues of limited experimental data, large systemic biases in existing empirical formulas, and difficulty in integration, a method for predicting the ultimate penetration velocity of a tungsten ball against a steel target based on a physical information neural network is proposed. This method constructs a neural network training dataset by using a proposed multi-model joint generation method to address the problems of limited experimental data and large systemic biases in existing empirical formulas. Physical constraints are introduced during the training process to solve the problem of physical consistency of prediction results. A new model architecture based on a physical information neural network is constructed to obtain a prediction model that can simultaneously predict the ultimate penetration velocity of a tungsten ball against both low-carbon steel and high-strength steel targets, thus solving the material adaptability problem of traditional models.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for predicting the ultimate penetration velocity of a tungsten ball against a steel target based on a physical information neural network includes the following steps: S1, collect data on tungsten ball penetration into steel target, and form the collected data on tungsten ball penetration into steel target into the original sample dataset; S2, Based on the multi-model joint generation strategy, the training dataset is constructed using the original sample dataset from step S1; S3, constructing a physical information neural network model architecture; S4. Use the training dataset from step S2 to train the physical information neural network model constructed in step S3 in stages. S5: After standardizing the parameters of the projectile target under the predicted working condition, input them into the physical information neural network model trained in step S4, output the standardized value, and then perform destandardization on the standardized value to obtain the predicted value of the ultimate penetration velocity of the tungsten ball into the steel target.

[0009] In S1, the characteristics of the tungsten ball penetrating the steel target data include fragment material, fragment yield strength, fragment ultimate strength, fragment material elongation, projectile diameter, target plate material, target plate Young's modulus, target plate yield strength, target plate ultimate strength, target plate material elongation, target plate thickness, and target plate tilt angle. The data for tungsten ball penetration of a steel target is labeled as the ultimate penetration velocity.

[0010] In S2, the method for constructing the training dataset is as follows: Select M preset penetration empirical formulas, fit each empirical formula using the original sample dataset established in step S1, and calculate the fitting accuracy index. and the fitting accuracy index The square of the value is used as the weight; the baseline predicted value is obtained by weighted averaging, and the relative deviation of each empirical formula is calculated based on the baseline predicted value; the empirical formula predicted values ​​with relative deviations exceeding a preset threshold are removed using a data centrality screening strategy, and the effective predicted values ​​after screening are fused a second time to generate highly robust training sample data. The training sample data includes features and labels. The features include tungsten ball size, target plate thickness, penetration angle, target plate Young's modulus, target plate ultimate strength, and target plate material elongation. The label is the ultimate penetration velocity.

[0011] The specific method for constructing the training dataset is as follows: S21, the predicted values ​​of each empirical formula for the same working condition are denoted as... The weights corresponding to each empirical formula are denoted as follows: Calculate the weighted average benchmark value For i = 1, 2, 3, ..., M, the calculation method is as follows:

[0012] S22, Calculate the predicted values ​​of each empirical formula. Relative to the baseline value relative deviation The calculation method is as follows:

[0013] S23, the relative deviation The predicted value is compared with a preset relative deviation threshold. If it is greater than the threshold, the predicted value is marked as an outlier and removed. If it is not greater than the threshold, the predicted value is retained. S24. Determine whether the remaining valid predicted values ​​meet the verification conditions. If they do, recalculate the weighted average using the remaining valid predicted values ​​and their corresponding weights as the final generated data. If they do not meet the verification conditions, directly use the weighted average benchmark value calculated in step S21. As the final generated data; The verification condition is met when at least one of the M preset penetration empirical formulas is not marked as an outlier. The verification condition is not met when all M preset penetration empirical formulas are marked as outliers and removed.

[0014] In S3, the constructed physical information neural network model architecture includes a physical information sub-network and a prediction main network; The input features of the input layer of the physical information subnetwork include the size of the tungsten ball, the thickness of the target plate, and the penetration angle. The loss calculation module of the physical information subnetwork incorporates physical monotonicity constraints. The input features of the input layer of the prediction master network include tungsten ball size, target thickness, penetration angle, target Young's modulus, target ultimate strength, and target material elongation.

[0015] In step S4, the training dataset is preprocessed before training, specifically as follows: The Z-Score normalization method is used to preprocess the parameters of the training dataset to eliminate scale differences between features of different scales. The parameters of the training dataset include the training dataset features and labels, and the calculation method is as follows:

[0016] in, For any parameter of the training dataset, The average value of any parameter in the training dataset. Let be the standard deviation of any parameter in the training dataset. This is the data after normalization of this parameter.

[0017] The phased training of the physical information neural network model includes two phases: The first stage involves training a physical information sub-network using the training dataset from step S2, and calculating the physical constraint loss using automatic differentiation techniques during the training process to obtain a sub-model that conforms to physical laws. The second stage involves generating enhanced data using a trained sub-model that conforms to physical laws. After fusing the enhanced data from different materials, the main prediction network is trained to obtain the optimal physical information neural network model for predicting the ultimate penetration speed.

[0018] In the first stage, physical monotonicity constraints are introduced into the loss function when training each physical information sub-network. The calculation formula is:

[0019] in, The mean squared error loss between the predicted value and the normalized training data value; Loss due to physical constraints; The weighting coefficients for the mean squared error loss are: The physical constraint loss weighting coefficient; The physical constraint loss The construction is based on the monotonicity of the tungsten sphere penetration process, and the calculation method specifically includes: calculating the limiting penetration velocity using automatic differentiation techniques. Regarding target plate thickness partial derivatives Extreme Penetration Speed Regarding fragment diameter partial derivatives Extreme Penetration Speed Regarding the angle of penetration partial derivatives ,like , , If any of the conditions is met, it is determined to violate the law of physical monotonicity, and a penalty value is generated and included. This forces the model to meet physical constraints; otherwise, , , If none of the conditions are met, the penalty value is 0.

[0020] When training the physical information subnetwork and the prediction main network, the training dataset is divided into a training set and a validation set in a 7:3 ratio. The training set is used to iteratively update the model parameters, and the validation set is used to evaluate the current generalization performance of the model and adjust the hyperparameters. The training method is as follows: the training set is input into the constructed network model for training, the validation set is input into the network model for validation, the loss value is output, and training is stopped when the loss value tends to stabilize.

[0021] In step S5, the formula for standardizing the projectile-target parameters of the predicted working condition is as follows:

[0022] Where Z represents the standardized data, and z represents the projectile-target parameters for the predicted working condition. The standard deviation of the corresponding data in the training sample set. The mean of the corresponding data in the training sample set; The formula for destandardizing standardized values ​​is:

[0023] in, For standardized values, The standard deviation of the limiting penetration velocity in the training sample set. The mean of the limiting penetration velocities in the training sample set. This is the predicted value of the ultimate penetration velocity of a tungsten ball into a steel target.

[0024] Beneficial effects 1) This invention constructs a prediction model for the ultimate penetration velocity of a tungsten ball penetrating a steel target based on a Physical Information Neural Network (PINN). The monotonicity of the penetration process is embedded as a constraint term into the loss function of the training model, achieving an effective combination of physical mechanisms and data-driven approaches. Compared with purely data-driven models, this invention's model avoids the problem of prediction results not conforming to physical laws, exhibiting good physical consistency and interpretability.

[0025] 2) The prediction model proposed in this invention significantly outperforms traditional methods in terms of accuracy and generalization ability. Through testing and verification, and by comparing the performance of the proposed model with traditional empirical formulas and traditional fully connected neural networks (FCNN), the results show that the proposed model exhibits excellent prediction accuracy under different working conditions and target material. Compared with traditional empirical formulas, the prediction errors of the proposed model for low-carbon steel and high-strength steel are reduced by approximately 26% and 31%, respectively. Compared with the traditional FCNN model, the average prediction error is reduced by 22.05% (high-strength steel) and 11.10% (low-carbon steel), effectively improving accuracy and maximum error, and further enhancing the robustness of the model.

[0026] 3) This invention designs a dataset construction strategy based on multi-model joint generation, which can effectively alleviate the problems of limited, highly discrete, and unevenly distributed penetration test data. By integrating multiple empirical formulas and introducing a weighted average and data centrality screening mechanism, this invention can generate highly robust training sample data without relying on a large amount of experimental data, reducing the dependence of model training on the amount of original experimental data, and improving the model's learning efficiency and extrapolation ability under small sample conditions.

[0027] 4) The prediction model of this invention has high engineering application value and computational efficiency. This model avoids the tedious process of refitting coefficients for new materials using traditional empirical formulas, and replaces computationally time-consuming numerical simulation methods. It also avoids data breakpoints and logical conflicts in prediction results caused by integrating multiple empirical formulas into the system. The model has a simple structure, fast computation speed, low hardware computing power requirements, and can run on most terminals, making it widely implementable and applicable on personal computers.

[0028] This invention discloses a method for predicting the ultimate penetration velocity of a tungsten ball penetrating a steel target based on a physical information neural network, belonging to the field of fragment damage technology. Addressing key issues such as large system bias, limited experimental data, and difficulty in system integration of traditional empirical formulas, this invention first proposes a method for jointly generating a highly robust dataset using multiple models. Penetration test data is collected, fitted, and integrated with multiple formulas to obtain weights. Through weighted averaging and data center selection, a highly robust dataset is constructed, generating high-quality training samples. Simultaneously, a prediction network model architecture based on a physical information neural network is constructed, utilizing automatic differentiation technology to introduce the physical monotonicity constraint of the penetration damage effect into the loss function. This invention can simultaneously predict the ultimate penetration velocity of a tungsten ball penetrating both high-strength and low-carbon steel targets. Compared with traditional model formulas, this method reduces errors for low-carbon steel and high-strength steel by approximately 26% and 31%, respectively, significantly improving the model's generalization ability and robustness. It has the advantages of wide applicability, strong interpretability, and ease of system integration. Attached Figure Description

[0029] Figure 1 This is a general flowchart of an embodiment of the method of the present invention; Figure 2 This is a structural diagram of the physical information neural network in this invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0031] This embodiment addresses the limitations of traditional empirical formulas, such as their limited applicability, large prediction bias across materials, and difficulty in integration into damage assessment systems. It proposes a method for predicting the ultimate penetration velocity of a tungsten sphere against a steel target based on a physical information neural network. This method uses tungsten alloy spherical fragments to simultaneously predict the ultimate penetration velocity parameters of steel targets made of different materials. Figure 1 As shown, it includes the following steps: S1, collect data on the penetration of tungsten balls into the steel target, and form the original sample dataset from the collected data.

[0032] This embodiment collects data based on the tungsten ball penetration test of a homogeneous steel target plate in the literature, and obtains the ultimate penetration velocity data corresponding to the test conditions. Parameters such as material strength not mentioned in the literature are supplemented based on the typical reference values ​​of the materials used.

[0033] A total of 143 raw experimental data points were collected, forming the original sample dataset: Features include: fragment material, fragment yield strength, fragment ultimate strength, fragment material elongation, projectile diameter, target plate material, target plate Young's modulus, target plate yield strength, target plate ultimate strength, target plate material elongation, target plate thickness, and target plate tilt angle. The tag is: Extreme Penetration Speed.

[0034] S2, based on the multi-model joint generation strategy, constructs the training dataset using the original sample dataset from step S1.

[0035] This embodiment selects a total of The eight empirical formulas, their corresponding names, calculation methods, and parameter declarations are shown in Tables 1 and 2.

[0036] Table 1. Penetration Model of Ultimate Penetration Velocity for Homogeneous Steel Target Plate

[0037] Table 2 Declaration of Parameters for the Ultimate Penetration Velocity of Homogeneous Steel Target Plate

[0038] Using the original sample dataset established in S1, fit the eight empirical formulas selected in Tables 1 and 2, and calculate the fitting accuracy index of each empirical formula. The results are shown in Table 3.

[0039] Table 3 Fitting accuracy indices for each empirical formula

[0040] The fitting accuracy index The square of the value is used as the weight for subsequent weighted average calculation. The fitted empirical formula generates data for low-carbon steel and high-strength steel according to the applicable materials. To ensure the reliability of the data generation, the data generation range is defined as: fragment diameter 4mm~11mm, target plate thickness 4mm~12mm, and penetration angle 0°~50°.

[0041] Within this range, fragment diameter and target plate thickness are set at 1mm intervals, and penetration angles at 5° intervals, and then substituted into empirical formulas to generate prediction data for the corresponding working conditions. Subsequently, a data centrality filtering strategy is used to process the data for the same working condition (the process is as follows). Figure 2 (As shown): First, calculate the weighted average benchmark value. Then, the relative deviations of each formula are calculated. Abnormal predicted values ​​with relative deviations exceeding a preset threshold (0.15) are removed, and finally, the effective predicted values ​​after screening are fused again to obtain highly robust training sample data.

[0042] For both low-carbon steel and high-strength steel targets, this embodiment generates 792 uniformly distributed training data points using this method.

[0043] S3. Construct a physical information neural network model architecture.

[0044] This embodiment constructs a composite model architecture that includes a physical information sub-network for both high-strength steel and low-carbon steel targets and a subsequent prediction main network. The specific implementation is as follows: 1) Construct physical information subnetworks for different material types For the training dataset generated in step S2, two identical physical information sub-networks are constructed, corresponding to low-carbon steel and high-strength steel materials, respectively. The input layer of each sub-network has three neurons, each receiving the input feature: the diameter of the tungsten sphere (…). ), target plate thickness ( ), penetration angle ( The subnetwork consists of three fully connected hidden layers, each with 64, 128, and 64 neurons, respectively, and each hidden layer uses the ReLU activation function. The output layer has one node, which outputs a standardized predicted value of the ultimate penetration velocity.

[0045] 2) Constructing a master network for universal material prediction The main network input layer is configured with 6 nodes to receive input features: tungsten sphere diameter ( ), target plate thickness ( and penetration angle ( ), target plate Young's modulus ( ), target plate ultimate strength ( ), target material elongation ( The subnetwork has three fully connected hidden layers, with 64, 128, and 64 neurons in each layer, respectively, and uses the Tanh activation function. The output layer has one output node, which outputs a standardized predicted value of the ultimate penetration velocity.

[0046] 3) Constructing a physical constraint mechanism In the physical information subnetwork, a computational graph path for calculating physical gradients is constructed based on the automatic differentiation function of the deep learning framework. Specifically, a limiting penetration velocity is defined. Partial derivative operator with respect to input variables: Define the partial derivative operator with respect to the target plate thickness. Define the partial derivative operator with respect to the diameter of the tungsten sphere. Define the partial derivative operator with respect to the penetration angle. This mechanism allows the gradient of the network output with respect to the input to be obtained in real time during the backpropagation process in subsequent training steps, thereby transforming the physical monotonicity constraint into an optimizable loss function term.

[0047] S4. Phased training of the physical information neural network model: In the first phase, physical constraints are introduced through automatic differentiation to train a material-specific sub-network that conforms to physical laws; in the second phase, the data generated by the sub-network is used to train the universal prediction main network. The specific steps are as follows.

[0048] 1) Subnetwork training.

[0049] The low-carbon steel dataset and high-strength steel dataset generated in step S2 are used as training data, respectively. The input features ( , , ) and tags ( Z-score standardization was performed to eliminate dimensional differences. The data was randomly divided into training and validation sets in a 7:3 ratio. The data was then converted to a tensor format that supports automatic differentiation calculation.

[0050] When training each physical information subnetwork, a composite loss function is defined. as follows:

[0051] in: The mean squared error loss between the predicted value and the normalized training data value; The physical constraint loss is constructed based on the monotonicity law of tungsten ball penetration. , To ensure a fixed weighting coefficient, all values ​​in this embodiment are set to 1. For dynamic weighting functions, physical weights With training rounds The physical constraints are increased linearly to strengthen them later in the training process.

[0052] Physical constraint loss The calculation logic is as follows: The gradient of the network output with respect to the input is calculated using automatic differentiation techniques, with the physical constraint objective set as follows: the velocity increases with increasing thickness and angle (i.e., the desired value). , ), decreases as diameter increases ( ).

[0053] For gradients that violate the above rules, a penalty term (ReLU function) is calculated: like Then calculate ; like Then calculate ; like Then calculate .

[0054] The expression for the total physical loss function is:

[0055] The Adam optimizer is used for iterative parameter updates. An initial learning rate of 0.01 is set, and an exponential decay strategy is applied (decay rate of 0.95 every 50 epochs), with a maximum of 5000 iterations. During training, the validation set RMSE and physical loss are monitored in real time. When the error stabilizes, the model parameters are saved to obtain the optimal subnetwork.

[0056] 2) Main network training.

[0057] Two pre-trained physical information sub-networks are used as data generators to perform dense sampling within a preset working condition space (sampling range and step size are the same as those set in S2). The working condition sampling parameters are input into the corresponding low-carbon steel sub-network and high-strength steel sub-network, respectively, to obtain predicted values ​​of the implicit physical laws. These predicted data are then combined with the corresponding high-strength steel and low-carbon steel material parameters (Young's modulus of the target plate, ultimate strength of the target plate, and elongation of the target plate material) to generate enhanced data.

[0058] The ultimate penetration velocity in the enhanced dataset is used as the label, and the working condition parameters and material parameters are used as input features. The dataset is also divided into training and validation sets in a 7:3 ratio and then Z-score standardized.

[0059] The Adam optimizer is used to train the main prediction network, with the initial learning rate and decay strategy being the same as those used for the sub-networks. At this stage, the loss function... Includes only mean squared error (MSE) loss :

[0060] During training, the mean square error of the validation set is monitored in real time. When the error stabilizes, the model parameters are saved to obtain the optimal prediction main network, which is the optimal limit penetration speed prediction model.

[0061] S5. Prediction of the ultimate penetration velocity of a tungsten ball into a steel target: The target parameters for the predicted working condition (in this embodiment, the original experimental data collected in S1 is used as the test object) are standardized and then input into the universal prediction main network trained in S4. The standardized values ​​predicted by the model are output, and then de-standardized to obtain the predicted value of the tungsten ball's penetration velocity into the steel target. Finally, the predicted value is compared with the original experimental data (true value) collected in S1, and the mean relative error (MAPE) and maximum relative error (MaxRE) are used to characterize the model's prediction accuracy.

[0062] 1. Standardization and destandardization calculation process: First, the projectile-target parameters of the predicted working condition ( Mapped to standardized data ):

[0063] in, To input standardized data into the network, The original projectile-target parameters for the predicted working conditions (including tungsten ball diameter, target plate thickness, penetration angle, target plate Young's modulus, target plate ultimate strength, and target plate material elongation) are given. and These are the mean and standard deviation of the features corresponding to the training sample set in step S4, respectively.

[0064] Will Inputting the generalized prediction master network yields the standardized prediction values ​​output by the model (denoted as ). ).

[0065] Finally, for After inverse standardization, the final predicted value of the ultimate penetration velocity is obtained. ):

[0066] in, The standardized values ​​output by the model. The standard deviation of the limiting penetration velocity in the training sample set. The mean of the limiting penetration velocities in the training sample set. This is the predicted ultimate penetration velocity with physical dimensions.

[0067] 2. Calculation of accuracy evaluation indicators The model performance is evaluated using the mean relative error (MAPE) and maximum relative error (MaxRE). The model is calculated as follows:

[0068]

[0069] in: For the model to the first The predicted ultimate penetration velocity of a sample (i.e., the result after inverse standardization). This corresponds to the original experimental data (true values). This represents the total number of data samples used in the validation process.

[0070] The prediction results of the traditional model, the traditional FCNN neural network model, and the model in this embodiment for two homogeneous steel target plates, namely high-strength steel and low-carbon steel, are listed in Tables 2 and 3.

[0071] Table 4 Comparison of Predicted Ultimate Penetration Velocity of High-Strength Steel

[0072] Table 5 Comparison of Predicted Ultimate Penetration Velocity for Low Carbon Steel

[0073] As shown in Tables 4 and 5, the universal prediction master network model constructed in this embodiment demonstrates excellent comprehensive performance in predicting the ultimate penetration velocity of two typical steel targets.

[0074] Regarding average prediction accuracy, the model in this embodiment achieves a mean relative error (MAPE) as low as 3.50% for high-strength steel and as low as 8.81% for low-carbon steel. Compared to the traditional data-driven FCNN neural network, the model in this embodiment reduces the average error by 22.05% and 11.10% for high-strength steel and low-carbon steel conditions, respectively. Compared to traditional empirical formulas, the model in this embodiment demonstrates a significant advantage in average accuracy; for example, it improves accuracy by approximately 31% compared to Zhang Jian's formula for high-strength steel and by approximately 26% compared to Liu Tielei's formula for low-carbon steel.

[0075] Regarding the maximum error of the model, the maximum relative error (MaxRE) of the model in this embodiment under high-strength steel and low-carbon steel conditions is 14.67% and 19.18%, respectively. Compared with the traditional FCNN model (maximum errors of 16.98% and 21.67%, respectively), the maximum error of the model in this embodiment is significantly reduced.

[0076] The above results demonstrate that the tungsten ball penetration velocity prediction method for steel targets based on a physical information neural network, as proposed in this invention, can capture the complex characteristics of the projectile-target penetration process based on data-driven and physical constraint methods, overcoming the limitations of traditional empirical formulas. This embodiment can predict the ultimate penetration velocity of two types of steel targets, avoiding the cumbersome process of refitting traditional models for new materials, and has advantages in engineering applicability and system integration.

[0077] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the ultimate penetration velocity of a tungsten ball into a steel target based on a physical information neural network, characterized in that... Includes the following steps: S1, collect data on tungsten ball penetration into steel target, and form the collected data on tungsten ball penetration into steel target into a raw sample dataset; S2, Based on the multi-model joint generation strategy, the training dataset is constructed using the original sample dataset from step S1; S3, constructing a physical information neural network model architecture; S4. Use the training dataset from step S2 to train the physical information neural network model constructed in step S3 in stages. S5: After standardizing the parameters of the projectile target under the predicted working condition, input them into the physical information neural network model trained in step S4, output the standardized value, and then perform destandardization on the standardized value to obtain the predicted value of the ultimate penetration velocity of the tungsten ball into the steel target.

2. The method for predicting the ultimate penetration velocity of a tungsten ball into a steel target based on a physical information neural network according to claim 1, characterized in that: In S1, the characteristics of the tungsten ball penetrating the steel target data include fragment material, fragment yield strength, fragment ultimate strength, fragment material elongation, projectile diameter, target plate material, target plate Young's modulus, target plate yield strength, target plate ultimate strength, target plate material elongation, target plate thickness, and target plate tilt angle. The data for tungsten ball penetration of a steel target is labeled as the ultimate penetration velocity.

3. The method for predicting the ultimate penetration velocity of a tungsten ball into a steel target based on a physical information neural network according to claim 1, characterized in that: In S2, the method for constructing the training dataset is as follows: Select M preset penetration empirical formulas, fit each empirical formula using the original sample dataset established in step S1, and calculate the fitting accuracy index. and the fitting accuracy index The exponentiation operation is used as the weight; A baseline predicted value is obtained by weighted averaging, and the relative deviation of each empirical formula is calculated based on the baseline predicted value. The empirical formula predicted values ​​with relative deviations exceeding a preset threshold are removed using a data centrality screening strategy. The effective predicted values ​​after screening are then fused a second time to generate highly robust training sample data. The training sample data includes features and labels. The features include tungsten ball size, target plate thickness, penetration angle, target plate Young's modulus, target plate ultimate strength, and target plate material elongation. The label is the ultimate penetration velocity.

4. The method for predicting the ultimate penetration velocity of a tungsten ball into a steel target based on a physical information neural network according to claim 3, characterized in that: The specific method for constructing the training dataset is as follows: S21, the predicted values ​​of each empirical formula for the same working condition are denoted as... The weights corresponding to each empirical formula are denoted as follows: Calculate the weighted average benchmark value For i = 1, 2, 3, ..., M, the calculation method is as follows: S22, Calculate the predicted values ​​of each empirical formula. Relative to the baseline value relative deviation The calculation method is as follows: S23, the relative deviation The predicted value is compared with a preset relative deviation threshold. If it is greater than the threshold, the predicted value is marked as an outlier and removed. If it is not greater than the threshold, the predicted value is retained. S24. Determine whether the remaining valid predicted values ​​meet the verification conditions. If they do, recalculate the weighted average using the remaining valid predicted values ​​and their corresponding weights as the final generated data. If the verification conditions are not met, the weighted average benchmark value calculated in step S21 is used directly. As the final generated data; The verification condition is met when at least one of the M preset penetration empirical formulas is not marked as an outlier. The verification condition is not met when all M preset penetration empirical formulas are marked as outliers and removed.

5. The method for predicting the ultimate penetration velocity of a tungsten ball into a steel target based on a physical information neural network according to claim 1, characterized in that: In S3, the constructed physical information neural network model architecture includes a physical information sub-network and a prediction main network; The input features of the input layer of the physical information subnetwork include the size of the tungsten ball, the thickness of the target plate, and the penetration angle. The loss calculation module of the physical information subnetwork incorporates physical monotonicity constraints. The input features of the input layer of the prediction master network include tungsten ball size, target thickness, penetration angle, target Young's modulus, target ultimate strength, and target material elongation.

6. The method for predicting the ultimate penetration velocity of a tungsten ball into a steel target based on a physical information neural network according to claim 1, characterized in that: In step S4, the training dataset is preprocessed before training, specifically as follows: The Z-Score normalization method is used to preprocess the parameters of the training dataset to eliminate scale differences between features of different scales. The parameters of the training dataset include the training dataset features and labels, and the calculation method is as follows: in, For any parameter of the training dataset, The average value of any parameter in the training dataset. Let be the standard deviation of any parameter in the training dataset. This is the data after normalization of this parameter.

7. The method for predicting the ultimate penetration velocity of a tungsten ball into a steel target based on a physical information neural network according to claim 1, characterized in that: The phased training of the physical information neural network model includes two phases: The first stage involves training a physical information sub-network using the training dataset from step S2, and calculating the physical constraint loss using automatic differentiation techniques during the training process to obtain a sub-model that conforms to physical laws. The second stage involves generating enhanced data using a trained sub-model that conforms to physical laws. After fusing the enhanced data from different materials, the main prediction network is trained to obtain the optimal physical information neural network model for predicting the ultimate penetration speed.

8. The method for predicting the ultimate penetration velocity of a tungsten ball into a steel target based on a physical information neural network according to claim 7, characterized in that: In the first stage, physical monotonicity constraints are introduced into the loss function when training each physical information sub-network. The calculation formula is: in, The mean squared error loss between the predicted value and the normalized training data value; Loss due to physical constraints; The weighting coefficients for the mean squared error loss are: The physical constraint loss weighting coefficient; The physical constraint loss The construction is based on the monotonicity of the tungsten sphere penetration process, and the calculation method specifically includes: calculating the limiting penetration velocity using automatic differentiation techniques. Regarding target plate thickness partial derivatives Extreme Penetration Speed Regarding fragment diameter partial derivatives Extreme Penetration Speed Regarding the angle of penetration partial derivatives ,like , , If any of the conditions is met, it is determined to violate the law of physical monotonicity, and a penalty value is generated and included. This forces the model to meet physical constraints; otherwise, , , If none of the conditions are met, the penalty value is 0.

9. The method for predicting the ultimate penetration velocity of a tungsten ball into a steel target based on a physical information neural network according to claim 1, characterized in that: When training the physical information subnetwork and the prediction main network, the training dataset is divided into a training set and a validation set in a 7:3 ratio. The training set is used to iteratively update the model parameters, and the validation set is used to evaluate the current generalization performance of the model and adjust the hyperparameters. The training method is as follows: the training set is input into the constructed network model for training, the validation set is input into the network model for validation, the loss value is output, and training is stopped when the loss value tends to stabilize.

10. The method for predicting the ultimate penetration velocity of a tungsten ball into a steel target based on a physical information neural network according to claim 1, characterized in that: In step S5, the formula for standardizing the projectile-target parameters of the predicted working condition is as follows: Where Z represents the standardized data, and z represents the projectile-target parameters for the predicted working condition. The standard deviation of the corresponding data in the training sample set. The mean of the corresponding data in the training sample set; The formula for destandardizing standardized values ​​is: in, For standardized values, The standard deviation of the limiting penetration velocity in the training sample set. The mean of the limiting penetration velocities in the training sample set. This is the predicted value of the ultimate penetration velocity of a tungsten ball into a steel target.

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