Physical information neural network-based granular mixture forming density prediction method and system

Abstract

The invention provides a granular mixture molding density prediction method and system based on a physical information neural network, and relates to the technical field of intelligent manufacturing and granular mixture compression molding process optimization. The method comprises the following steps: constructing a physical feature adaptive lightweight physical information neural network; based on a physical densification theory, defining a composite physical loss function; based on the key process variable and the target variable, constructing an initial training set through initial sparse sampling, and performing iterative sample expansion based on residual feedback to obtain a dynamic training data set based on active learning; and based on the composite physical loss function, training the lightweight physical information neural network on the dynamic training data set based on active learning to obtain the lightweight physical information neural network based on the optimal strategy so as to predict the granular mixture forming density. According to the method, the prediction precision of the forming density can be ensured under the complex working conditions of small samples and unstable loading, so that the intelligent management and control level of a granular mixture forming process in precision manufacturing is improved.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and granular material compression molding process optimization technology, and in particular to a method and system for predicting granular material molding density based on physical information neural networks. Background Technology

[0002] Propellant charges are products of granular material compression molding, and their molding density directly determines the product's mechanical properties, combustion performance, stability, and safety, making it a core quality indicator for achieving precise process control. Currently, there are many limitations in the industry's methods for predicting the molding density of granular materials.

[0003] First, while traditional modeling methods based on empirical formulas and physical mechanisms can ensure that the prediction results conform to physical laws, they are difficult to accurately describe the complex nonlinear relationships in the powder pressing process, resulting in generally low prediction accuracy. Second, although pure data-driven machine learning prediction methods have strong nonlinear fitting capabilities, their application effectiveness is severely limited by the quantity and quality of training data. On the one hand, they are highly dependent on data, requiring a large amount of high-quality data covering the entire parameter space for effective training. However, in actual production, obtaining a large amount of effective data is costly, and existing historical data is often concentrated around a few fixed process parameters, making model training difficult and prone to overfitting under small sample conditions, with prediction accuracy even far lower than that of simple linear models. On the other hand, and more seriously, because they rely entirely on statistical laws in the data and lack physical guidance, such models often produce prediction results that violate basic physical common sense, such as predicting the absurd conclusion that "increasing the pressing pressure will actually decrease the molding density," making their prediction results unreliable. They also have the defect of poor extrapolation and generalization ability. The model performs well within the parameter range covered by the training data, but its performance drops sharply once it is used to predict new, unexplored process conditions. Given the fundamental shortcomings of existing prediction methods, current production practices still rely on cumbersome trial-and-error experiments to determine process parameters, resulting in low efficiency and high costs. Therefore, developing a new method that integrates the advantages of both physical mechanisms and data-driven approaches, achieving high accuracy and strict physical consistency in quality prediction even under small sample conditions, has become a key technical challenge that urgently needs to be addressed in this field. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention directly embeds physical laws into the loss function of a neural network, constructs a high-quality dataset through an active learning strategy, and utilizes a neural network with embedded physical constraints to achieve high-precision prediction under small sample conditions. It proposes a method and system for predicting granular forming density based on a Physics-Informed Neural Network (PINN), aiming to achieve high-precision prediction even with limited data and ensure the physical reasonableness of the results.

[0005] On the one hand, this invention proposes a method for predicting the forming density of granules based on a physical information neural network, which includes the following process:

[0006] Determine the key process variables and target variables for granular material compression molding;

[0007] We construct a lightweight physical information neural network that adapts to physical features, and define a composite physical loss function based on the theory of physical densification.

[0008] Based on the key process variables and target variables, an initial training set is constructed through initial sparse sampling.

[0009] By iteratively expanding the initial training set based on residual feedback, a dynamic training dataset based on active learning is obtained.

[0010] Based on the composite physical loss function, the lightweight physical information neural network is trained on a dynamic training dataset based on active learning to obtain a lightweight physical information neural network based on the optimal strategy.

[0011] The key process variables of the working condition to be predicted are obtained and input into a lightweight physical information neural network based on the optimal strategy to obtain the predicted molding density.

[0012] Furthermore, the specific details of determining the key process variables and target variables for granular material compression molding are as follows:

[0013] The key process variables for the granular material compression molding process are defined, including: compression pressure. Holding time Pressurization speed and molding quality ;

[0014] Set the value range for each key process variable separately;

[0015] The target variable for granular material compression molding is set as molding density. .

[0016] Furthermore, the method for constructing a lightweight physical information neural network that adapts to physical features is as follows:

[0017] A lightweight fully connected neural network MLP is constructed based on the key process variables and target variables of granular material compression molding.

[0018] The lightweight fully connected neural network MLP includes: an input layer, a hidden layer, and an output layer;

[0019] The number of neurons in the input layer is the same as the number of key process variables; there are two hidden layers, and each hidden layer has 8 neurons; the number of neurons in the output layer is the same as the number of target variables.

[0020] The hidden layer uses the Tanh hyperbolic tangent activation function as the activation function and adopts an adaptive weight initialization strategy for weight initialization, setting the initial bias to 0; wherein the adaptive weight initialization strategy includes, but is not limited to: Xavier uniform distribution and orthogonal initialization.

[0021] Furthermore, the method for defining the composite physical loss function based on the physical densification theory is as follows:

[0022] Based on the configurable composite physical loss function framework, a composite physical loss function is constructed, consisting of a data fitting term and optional physical constraint terms; wherein the optional physical constraint terms are: a weighted sum of monotonicity constraint terms, concave constraint terms, and upper bound constraint terms;

[0023] The composite physical loss function is used to train the lightweight physical information neural network; during the training process, for any batch of training samples input into the lightweight physical information neural network, the predicted forming density of all training samples in the current batch is obtained.

[0024] Each training sample contains a set of key process variables and target variables;

[0025] For the training samples in the current batch, the Huber Loss loss function is used to calculate the data fitting loss value of the training samples in the current batch based on the predicted and measured forming densities of all training samples.

[0026] Based on the predicted forming density and pressing pressure of all training samples, the constraint violation amounts of the monotonicity constraint term, concave constraint term, and upper bound constraint term are calculated respectively.

[0027] The constraint violation of the monotonicity constraint term is the negative value of the partial derivative of the predicted molding density with respect to the pressing pressure.

[0028] The constraint violation of the concave constraint term is: the second derivative of the predicted molding density with respect to the pressing pressure.

[0029] The constraint violation amount of the upper bound constraint term is: the difference between the predicted molding density and the preset maximum compaction density;

[0030] For any constraint violation among the monotonicity constraint, concave constraint, and upper bound constraint, the constraint violation is input into a linear rectifier function. The output value of the linear rectifier function is squared to obtain the penalty value for each training sample. The arithmetic mean operator is used to calculate the average of all penalty values, which is used as the loss value for that constraint.

[0031] Furthermore, the specific content of constructing the initial training set through initial sparse sampling based on the key process variables and target variables is as follows:

[0032] Based on the value range of all key process variables, sparse sampling is used to obtain... The key process variable samples for each group; each group of key process variable samples includes: pressing pressure. Holding time Pressurization speed and molding quality ;

[0033] use Preliminary granulation experiments were conducted on samples of key process variables, and the measured molding density corresponding to each set of key process variable samples was recorded. Each set of key process variable samples and its corresponding measured molding density were then used as a training set to construct an initial training set. .

[0034] Furthermore, the specific content of the dynamic training dataset based on active learning obtained by iteratively expanding the initial training set based on residual feedback is as follows:

[0035] The initial training set is processed according to a pre-defined sample size sequence. Expand the system in batches, and perform the following operations during each expansion process:

[0036] A preliminary model is constructed by initializing the model parameters of the lightweight physical information neural network;

[0037] Based on the composite physical loss function, a preliminary model is trained using the current training set, and the model parameters of the preliminary model are optimized until the preset training termination condition is met, thus obtaining a trained preliminary model.

[0038] On the trained preliminary model, the range of values ​​for all key process variables is used as the parameter space, and the distribution of predicted residuals within the parameter space is calculated.

[0039] Based on the calculated predicted residual distribution, regions exceeding the preset residual threshold are identified;

[0040] In the identified region, the local Latin hypercube sampling method is used to generate several sets of key process variable samples to be supplemented;

[0041] Data standardization preprocessing is performed on all samples of key process variables to be supplemented to obtain standardized samples of key process variables to be supplemented.

[0042] Based on all standardized samples of key process variables to be supplemented, compression molding experiments were carried out in sequence to obtain the mass and final height of the molded propellant for each group of key process variable samples to be supplemented, and then the measured molding density of each group of key process variable samples to be supplemented was calculated.

[0043] A set of key process variables to be supplemented and the measured molding density corresponding to the set of key process variables to be supplemented are used as a set of training samples to be supplemented.

[0044] Add all the training samples to be supplemented to the current training set to obtain the complete training set for the current expansion process;

[0045] The complete training set obtained from the final augmentation process is used as the dynamic training dataset based on active learning.

[0046] Furthermore, the preset residual threshold is set to be more than twice the standard deviation of process repeatability.

[0047] Furthermore, the specific content of training the lightweight physical information neural network on the dynamic training dataset based on active learning based on the composite physical loss function to obtain the lightweight physical information neural network based on the optimal policy is as follows:

[0048] Based on the lightweight physical information neural network and the composite physical loss function, a physical ablation variant space containing several model variants is constructed;

[0049] On the dynamic training dataset based on active learning, according to the preset training configuration, leave-one-out cross-validation is used to train each model variant in the physical ablation variant space and obtain the cross-validation index of each model variant.

[0050] The Bootstrap resampling generalization error estimation method is adopted to resample each model variant in the physical ablation variant space and calculate the generalization performance index of each model variant.

[0051] The dynamic training dataset based on active learning is input into each model variant to predict the forming density, and the original predicted value output by each model variant is obtained. The original predicted value is then post-processed and calibrated using the ordinal-preserving regression method to obtain the calibrated predicted value.

[0052] Based on the cross-validation metrics, generalization performance metrics, and calibrated predictions of all model variants, the optimal model variant is selected from the physical ablation variant space as a lightweight physical information neural network based on the optimal strategy.

[0053] Further, the model variant is defined as follows: a weight combination is set for the optional physical constraint terms in the composite physical loss function to obtain a composite physical loss function configuration scheme and it is assigned to a lightweight physical information neural network, and the lightweight physical information neural network configured with the composite physical loss function configuration scheme is used as a model variant.

[0054] The configuration scheme of the composite physical loss function is different for each model variant.

[0055] On the other hand, this invention proposes a granular mass forming density prediction system based on a physical information neural network, the system comprising:

[0056] The network building module is used to construct a lightweight physical information neural network that adapts to physical features, and defines a composite physical loss function based on the theory of physical densification.

[0057] The initial sampling module is used to construct an initial training set based on key process variables and target variables through initial sparse sampling.

[0058] The dynamic expansion module is used to obtain a dynamic training dataset based on active learning by iteratively expanding the initial training set based on residual feedback.

[0059] The training optimization module is used to train the lightweight physical information neural network on a dynamic training dataset based on active learning based on a composite physical loss function, so as to obtain a lightweight physical information neural network based on the optimal strategy.

[0060] The density prediction module is used to obtain the key process variables of the working condition to be predicted and input them into a lightweight physical information neural network based on the optimal strategy to obtain the predicted molding density.

[0061] The beneficial effects of adopting the above technical solution are as follows:

[0062] This invention's method can automatically construct high-quality dynamic training datasets under complex operating conditions with small samples and unstable loading through an active learning strategy. It automatically identifies high-uncertainty regions based on model residual feedback and supplements experimental samples accordingly, avoiding the high cost and blind trial-and-error of traditional full-factor experiments. This ensures effective coverage of the process parameter space with minimal experimental cost. Furthermore, during model construction and training, this method utilizes a lightweight neural network with embedded monotonic physical constraints to force the model to follow the physical law of a positive correlation between pressure and density. This effectively solves the problem of overfitting and physical paradoxes in purely data-driven models under small sample conditions, significantly improving the model's generalization ability and physical consistency. The prediction accuracy approaches the physical limit of the system's inherent noise, saving significant manpower and material costs and enhancing the intelligent control level of granular material forming processes in precision manufacturing, demonstrating significant engineering application prospects. Attached Figure Description

[0063] Figure 1 This is a flowchart of the particle forming density prediction method based on physical information neural network in an embodiment of the present invention;

[0064] Figure 2 This is a schematic diagram of the overall process and physical information neural network architecture of the method provided in the embodiments of the present invention;

[0065] Figure 3 This is a scatter plot comparing the predicted and actual values ​​of the physical ablation experiment optimization strategy (M1 model) in an embodiment of the present invention under internal cross-validation.

[0066] Figure 4 This is a comparison chart of the comprehensive performance of each model variant (M0-M3) in the physical ablation experiment in the embodiments of the present invention with the traditional baseline model (A1, B1); where (a) is a comparison chart of root mean square error; and (b) is a comparison chart of coefficient of determination.

[0067] Figure 5 This is a scatter plot of the prediction results of the M1 model on the external blind test set in an embodiment of the present invention;

[0068] Figure 6 This is a Bland-Altman consistency analysis diagram of the M1 model on an external blind test set in an embodiment of the present invention;

[0069] Figure 7 The figures show a performance comparison between the PINN-M1 model of this invention and the traditional baseline models (A1, B1) under leave-one-out cross-validation; where (a) is a comparison of root mean square error; (b) is a comparison of mean absolute error; and (c) is a comparison of coefficient of determination.

[0070] Figure 8This is a comparison chart of the generalization error between the model of this invention embodiment and the traditional baseline model under the .632+Bootstrap evaluation;

[0071] Figure 9 This is a structural diagram of the granular mass forming density prediction system based on a physical information neural network in an embodiment of the present invention. Detailed Implementation

[0072] To facilitate understanding of this application, specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. The following embodiments are illustrative of the invention but are not intended to limit its scope. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of this application.

[0073] Example 1:

[0074] This embodiment presents a method for predicting the forming density of granules based on a physical information neural network, such as... Figure 1 As shown, the method includes the following steps:

[0075] Determine the key process variables and target variables for granular material compression molding.

[0076] The specific details of determining the key process variables and target variables for granular material compression molding are as follows:

[0077] The key process variables for the granular material compression molding process are defined, including: compression pressure. Holding time Pressurization speed and molding quality .

[0078] Set the value range for each key process variable separately.

[0079] The target variable for granular material compression molding is set as molding density. .

[0080] In this embodiment, four key physical quantities, i.e. key process variables, that affect the density of granular material during compression molding are identified: compression pressure. Holding time Pressurization speed and molding quality The molding quality is introduced as an input feature to eliminate the impact of density fluctuations caused by loading errors or powder shedding in actual production. The target variable to be predicted is the molding density. And the physical value range of each parameter is set as follows:

[0081] (1) Suppressive pressure 150MPa to 450MPa, i.e. The unit is MPa;

[0082] (2) Holding time 10s to 300s, that is The unit is seconds (s).

[0083] (3) Pressurization rate 0.05 mm / s to 0.3 mm / s, i.e. The unit is mm / s;

[0084] (4) Molding quality : Based on the actual weighing records within the mold volume range of 0.1g to 1g, i.e. The unit is g.

[0085] We construct a lightweight physical information neural network that adapts to physical features and define a composite physical loss function based on the theory of physical densification.

[0086] The method for constructing a lightweight physical information neural network that adapts to physical features is as follows:

[0087] A lightweight fully connected neural network MLP is constructed based on the key process variables and target variables of granular material compression molding.

[0088] The lightweight fully connected neural network MLP includes an input layer, a hidden layer, and an output layer.

[0089] The number of neurons in the input layer is the same as the number of key process variables; there are two hidden layers, and each hidden layer has 8 neurons; the number of neurons in the output layer is the same as the number of target variables.

[0090] In this embodiment, as Figure 2 As shown, a lightweight, fully connected neural network (Multilayer Perceptron, MLP) designed to resist overfitting is proposed to address the small sample size characteristics of granulation compression data. The input layer contains four neurons, each corresponding to a compression pressure. Holding time Pressurization speed and molding quality The hidden layer is designed with a narrow depth structure, containing two hidden layers, each with only 8 neurons (Hidden Dim=8); the output layer has one neuron and is used to output the predicted shaping density. .

[0091] The hidden layer uses the Tanh hyperbolic tangent activation function as the activation function and adopts an adaptive weight initialization strategy for weight initialization, setting the initial bias to 0; wherein the adaptive weight initialization strategy includes, but is not limited to: Xavier uniform distribution and orthogonal initialization.

[0092] In this embodiment, the hidden layer uses the Tanh hyperbolic tangent activation function, which utilizes its zero-centered and smooth properties to accelerate the convergence of small-scale networks. Since the hidden layer uses the hyperbolic tangent Tanh function as the activation function, the weights are initialized using Xavier Uniform or Orthogonal Initialization, and the biases are initialized to 0.

[0093] The method for defining the composite physical loss function based on physical densification theory is as follows:

[0094] Based on a configurable composite physical loss function framework, a composite physical loss function is constructed, consisting of a data fitting term and optional physical constraint terms. The optional physical constraint terms are a weighted sum of monotonicity constraints, concave constraints, and upper bound constraints, expressed as:

[0095] (1)

[0096] in To ensure that the prediction results conform to physical laws, a general physical constraint loss function is constructed as follows: , to represent the weighted sum of the data fitting term and three optional physical constraint terms; For data fitting terms; This is a monotonicity constraint term; For concave constraint terms; This is an upper bound constraint term; , and These are the weight coefficients for the monotonicity constraint, the concave constraint, and the upper bound constraint, respectively.

[0097] The composite physical loss function is used to train the lightweight physical information neural network; during the training process, for any batch of training samples input into the lightweight physical information neural network, the predicted forming density of all training samples in the current batch is obtained.

[0098] Each training sample contains a set of key process variables and target variables.

[0099] For the training samples in the current batch, the Huber Loss loss function is used to calculate the data fitting loss value of the training samples in the current batch, based on the predicted and measured forming densities of all training samples.

[0100] In this embodiment, the data fitting term The Huber Loss function is used (the threshold parameter is set to...). It replaces the traditional mean squared error (MSE) to reduce the interference of potential outliers in the experimental data on the model gradient.

[0101] Based on the predicted molding density and pressing pressure of all training samples, the constraint violation amounts of the monotonicity constraint term, the concave constraint term, and the upper bound constraint term are calculated respectively; wherein the constraint violation amount of the monotonicity constraint term is: the negative value of the partial derivative of the predicted molding density with respect to the pressing pressure; the constraint violation amount of the concave constraint term is: the second derivative of the predicted molding density with respect to the pressing pressure; and the constraint violation amount of the upper bound constraint term is: the difference between the predicted molding density and the preset maximum compaction density.

[0102] For any constraint violation among the monotonicity constraint, concave constraint, and upper bound constraint, the constraint violation is input into a linear rectifier function. The output value of the linear rectifier function is squared to obtain the penalty value for each training sample. The arithmetic mean operator is used to calculate the average of all penalty values, which is used as the loss value for that constraint.

[0103] In this embodiment, taking the monotonicity constraint term as an example, the monotonicity constraint term... This is used to penalize non-physical inverse fluctuations in the pressure-density relationship, constraining the predicted molding density to increase monotonically with increasing pressure. The calculation formula is:

[0104] (2)

[0105] in To predict the partial derivative of molding density with respect to pressing pressure, it is obtained through automatic differential calculation; This represents a linear rectified function used to apply ReLU penalties only to negative gradients that violate physical laws. This represents the arithmetic mean operator. Specifically, for any input vector or tensor containing n elements... The sum of all elements in the vector divided by the total number of elements is defined by the following formula:

[0106] (3)

[0107] In the loss function calculation of this embodiment, the operator is used to calculate the average of the error or penalty term generated by all sample points in the current training batch (Batch) to ensure that the gradient direction of model optimization is not affected by the sample size.

[0108] The concave constraint term Used to penalize anomalous accelerations in the density growth rate, i.e., the second derivative. The situation.

[0109] The upper bound constraint term This is used to penalize prediction densities that exceed the theoretical maximum approximate density. The situation.

[0110] Based on the key process variables and target variables, an initial training set is constructed through initial sparse sampling.

[0111] The specific content of constructing the initial training set based on the key process variables and target variables through initial sparse sampling is as follows:

[0112] Based on the value range of all key process variables, sparse sampling is used to obtain... The key process variable samples for each group; each group of key process variable samples includes: pressing pressure. Holding time Pressurization speed and molding quality .

[0113] use Preliminary granulation experiments were conducted on samples of key process variables, and the measured molding density corresponding to each set of key process variable samples was recorded. Each set of key process variable samples and its corresponding measured molding density were then used as a training set to construct an initial training set. .

[0114] In this embodiment, as Figure 2 As shown, within the set process parameter space, initial sparse sampling is performed using Latin Hypercube Sampling (LHS) or orthogonal design methods to select a small number of representative sample points. In this embodiment, [the following is a sample number]. Conduct preliminary compression experiments. Record the actual input parameters for each experimental group. , , , and measured molding density Construct the initial training set .

[0115] By iteratively expanding the initial training set based on residual feedback, a dynamic training dataset based on active learning is obtained.

[0116] In this embodiment, in order to capture complex nonlinear laws with the fewest number of experiments, this embodiment abandons the traditional fixed full factorial experiment and adopts an iterative strategy of "training-evaluation-expansion" to carry out iterative expansion based on model residual feedback.

[0117] The specific content of the dynamic training dataset based on active learning obtained by iteratively expanding the initial training set based on residual feedback is as follows:

[0118] The initial training set is processed according to a pre-defined sample size sequence. The model is expanded in batches, and the following operations are performed during each expansion: a preliminary model is constructed by initializing the model parameters of the lightweight physical information neural network.

[0119] Based on the composite physical loss function, a preliminary model is trained using the current training set, and the model parameters of the preliminary model are optimized until the preset training termination condition is met, thus obtaining a trained preliminary model.

[0120] On the trained preliminary model, the range of values ​​for all key process variables is used as the parameter space, and the distribution of predicted residuals within the parameter space is calculated.

[0121] Based on the calculated predicted residual distribution, regions exceeding a preset residual threshold are identified; wherein the preset residual threshold is set to be more than twice the standard deviation of process repeatability.

[0122] In the identified regions, a local Latin hypercube sampling method is used to generate several sets of samples of key process variables to be supplemented.

[0123] Data standardization preprocessing is performed on all samples of key process variables to be supplemented to obtain standardized samples of key process variables to be supplemented.

[0124] In this embodiment, the samples of key process variables to be supplemented undergo data standardization preprocessing, including: standardization (Z-score Normalization) or normalization (Min-Max Scaling), so that they fall within the sensitive region of the neural network. Specifically, the suppression pressure... According to the pressure of suppression Scaling is performed, where For standardized suppression pressure, This is the scaling factor, which is set to 0.002 in this embodiment. Scaling factor This ensures that the input values ​​are distributed within the sensitive region of the neural network, which is beneficial for the accurate calculation of the physical constraint gradient, matching the initial distribution of the network weights and promoting optimization convergence; for other features... , , Standardization or normalization adaptation is performed separately.

[0125] Based on all standardized samples of key process variables to be supplemented, compression molding experiments were carried out sequentially to obtain the mass and final height of the molded propellant for each group of key process variable samples to be supplemented, and then the measured molding density of each group of key process variable samples to be supplemented was calculated.

[0126] In this embodiment, the key process variable parameters after data standardization and preprocessing are used to conduct compression molding experiments sequentially: for each experimental sample, the mass of the molded propellant column is measured using a high-precision electronic balance with an accuracy of 0.001g, and the final height of the compressed propellant column is measured using a vernier caliper with an accuracy of 0.02mm; according to the law of conservation of mass, the measured molding density of each group of samples to be supplemented with key process variables is calculated. for:

[0127] (4)

[0128] in This indicates the initial charge mass, also known as the forming mass. The bottom area of ​​the mold; This represents the final height of the propellant column.

[0129] A set of key process variable samples to be supplemented and the measured molding density corresponding to the set of key process variable samples to be supplemented are used as a set of training samples to be supplemented.

[0130] Add all the training samples to be supplemented to the current training set to obtain the complete training set for the current expansion process.

[0131] The complete training set obtained from the final augmentation process is used as the dynamic training dataset based on active learning.

[0132] In this embodiment, based on a preset residual threshold (set to 0.015 g / cm³ in this embodiment), regions with high prediction uncertainty or large residuals (such as high-pressure short-term pressure holding conditions) are identified, and supplementary experimental points are designed accordingly. Experimental data are supplemented in batches according to the sequence n=12-24-36-45-55, ultimately forming a complete training set containing 55 high-quality samples. .

[0133] Based on the composite physical loss function, the lightweight physical information neural network is trained on a dynamic training dataset based on active learning to obtain a lightweight physical information neural network based on the optimal strategy.

[0134] In this embodiment, a multi-level physical ablation experiment and optimal strategy selection were conducted. In order to prove the effectiveness of the physical constraints and determine the optimal combination of constraints, this embodiment did not directly specify the parameters, but instead designed and executed a rigorous multi-level physical ablation study to achieve the selection of the optimal strategy.

[0135] The specific content of training the lightweight physical information neural network on the dynamic training dataset based on active learning based on the composite physical loss function to obtain the lightweight physical information neural network based on the optimal policy is as follows:

[0136] Based on the lightweight physical information neural network and the composite physical loss function, a physical ablation variant space containing several model variants is constructed.

[0137] The model variant is defined as follows: a weight combination is set for the optional physical constraint terms in the composite physical loss function, the weight combination is substituted into the composite physical loss function to generate a composite physical loss function configuration scheme and assigned to a lightweight physical information neural network, and the lightweight physical information neural network configured with the composite physical loss function configuration scheme is used as a model variant.

[0138] The configuration scheme of the composite physical loss function is different for each model variant.

[0139] In this embodiment, four model variants are defined in the physical ablation variant space for comparative experiments. Each model variant is a lightweight physical information neural network configured with different composite physical loss functions. The four model variants are: unconstrained model M0, monotonicity-only constraint model M1, monotonicity-constrained and concave constraint model M2, and fully constrained model M3. Specifically, the unconstrained model M0 (Baseline) is a purely data-driven model, i.e., it sets... , and No physical priors are introduced; only monotonic constraints are introduced in the model M1 (Monotonic), that is, only monotonic constraints are set. , and In this embodiment, we take The monotonicity and concavity constraint model M2 (Mono + Concavity) introduces monotonicity and concavity constraints, i.e., sets... , and The fully constrained model M3 (Full Physics) introduces monotonicity, concavity, and upper bound constraints, i.e., sets... , and .

[0140] In this embodiment, in order to obtain the most unbiased model performance estimate with limited samples, a composite evaluation system including LOOCV, .632+Bootstrap, and confidence interval evaluation is constructed.

[0141] On a dynamic training dataset based on active learning, leave-one-out cross-validation is used according to a preset training configuration to train each model variant in the physical ablation variant space and obtain the cross-validation metric for each model variant.

[0142] In this embodiment, leave-one-out cross-validation is performed on 55 sets of samples for each of the four variants M0-M3. For each set of samples, the Adam optimizer is used, and the model is trained independently for 1500 epochs at a preset learning rate of 1e-3. Figure 3 As shown.

[0143] The Bootstrap resampling generalization error estimation method is adopted to resample each model variant in the physical ablation variant space and calculate the generalization performance index of each model variant.

[0144] In this embodiment, to more accurately estimate the model's performance on unknown data, the .632+ Bootstrap method is employed. A training set and an out-of-bag (OOB) test set are constructed through 2000 resampling cycles with replacement. The training error and OOB error are weighted and combined to calculate the final generalization performance index. Experimental results show that the .632+ RMSE of the PINN-M1 model is significantly lower than other comparative models, demonstrating its excellent generalization ability.

[0145] The dynamic training dataset based on active learning is input into each model variant to predict the forming density, and the original predicted value output by each model variant is obtained. The original predicted value is then post-processed and calibrated using the ordinal-preserving regression method to obtain the calibrated predicted value.

[0146] In this embodiment, isotonic regression is applied to the raw predictions output by each model variant for post-processing calibration. This is used to verify the model performance without physical constraints, eliminate systematic biases, and obtain calibrated predictions. It should be noted that, in addition to isotonic regression, those skilled in the art can use other conventional mathematical regression methods capable of fitting the relationship between density and pressure for comparison, such as monotonic splines, polynomial regression, or support vector regression (SVR). However, while these methods can mathematically approximate data trends, due to the lack of physical constraints on material forming mechanisms (such as specific monotonicity and concavity penalties), their prediction stability under sparse data is generally better or worse than the solution in this embodiment, thus serving as a valid reference for verifying the technical effectiveness of this application. By comparing with these unstable results, the technical effectiveness of the technical solution in this embodiment (introducing physical constraints) in improving the robustness and accuracy of predictions under sparse data can be clearly verified and highlighted.

[0147] Based on the cross-validation metrics, generalization performance metrics, and calibrated predictions of all model variants, the optimal model variant is selected from the physical ablation variant space as a lightweight physical information neural network based on the optimal strategy.

[0148] Through the above evaluation process, the three physical constraints—monotonality constraint, concave constraint, and upper bound constraint—are separated and added to the model separately. By observing the changes in model performance caused by each physical constraint, the M1 model is determined to be the optimal model.

[0149] Building upon this, to verify that the performance improvement brought about by physical constraints is not due to random error, nonparametric statistical tests are used to quantify the confidence intervals of performance differences between model variants, thereby verifying whether the performance improvement of the optimal physical prior combination relative to the baseline scheme is statistically significant. Therefore, this embodiment employs the paired bootstrap method to statistically test each model variant in the physical ablation variant space, eliminating random errors introduced by the randomness of small sample data partitioning, and establishing the true effectiveness and robustness of the selected physical constraint strategy (such as monotonicity constraints) in improving the model's generalization ability. The specific process is as follows:

[0150] Set the Bootstrap resampling count B=2000, and calculate the prediction error difference between M1, M2, and M3 and M0 respectively.

[0151] (5)

[0152] in This represents the difference in prediction error; Represents the root mean square error of any model variant among M1, M2, or M3; This represents the root mean square error of M0.

[0153] Statistical analysis between different model variants The distribution of the difference and the 95% confidence interval. Experimental results show that the mean difference (Mean Delta RMSE) between the M1 model and the baseline model is negative (approximately -0.0014), and the confidence interval is mainly distributed in the negative region, proving that introducing physical constraints can effectively reduce prediction errors in most cases.

[0154] In this embodiment, the Physical Shape Metrics, in addition to accuracy metrics, further trains an ensemble model on the full dataset (i.e., the training dataset obtained by expanding the dataset in the current iteration) to quantitatively diagnose the conformity to physical laws, including: calculating the monotonicity violation rate (Mono%); and checking the prediction curve for... The interval proportion; calculate the concavity / convexity anomaly rate (Convex%): check the proportion of second-order derivative anomalies in the prediction curve. The ensemble model mentioned here specifically refers to a homogeneous deep ensemble. That is, using the exact same neural network architecture and hyperparameter configuration, only changing the random initialization seed, N independent sub-models (e.g., N=20) are trained in parallel, and the arithmetic mean of their outputs is taken as the prediction result. The prediction variance between the sub-models is used to quantify the epistemic uncertainty.

[0155] In this embodiment, experimental data shows that model M0 exhibits significant physical violations; while models M2 and M3 demonstrate strong physical compliance, their overly stringent constraints lead to underfitting; model M1 achieves the lowest generalization error of .632+ while maintaining 0% monotonicity violation. Paired bootstrapping analysis reveals that the mean DeltaRMSE of the error difference between M1 and the pure data model M0 is negative (approximately -0.0014), demonstrating the statistical significance of this strategy. Therefore, this embodiment selects strategy M1 as the optimal implementation.

[0156] To further evaluate the model's generalization performance and engineering practical value on non-homogeneous data, this embodiment constructs an independent external blind test dataset. This dataset was obtained by the inventors through physical experiments conducted on the same material system, but under conditions completely independent of the training set collection time and experimental batches (containing a total of 39 samples).

[0157] It is important to note that this external blind test dataset is strictly isolated (held out) during the model construction, parameter training, and hyperparameter optimization stages (such as the LOOCV process described above). It is only used as a final third-party benchmark to verify the model's prediction accuracy and robustness after the optimal model architecture (i.e., the M1 model with monotonicity constraints) is determined. This setup aims to simulate the real-world scenario of training and predicting future batches of experiments using historical data in industrial applications, thereby objectively reflecting the practical application effect of the technical solution of this invention.

[0158] The trained model is evaluated using a test set, and its coefficient of determination R² and root mean square error RMSE are recorded to quantify the model's prediction accuracy. Based on the above evaluation metrics, the model performance of different combinations of physical priors (such as monotonicity constraints only vs. monotonicity + concave constraints) is compared to select the optimal objective function configuration (i.e., the M1 model in the example) that can balance data fitting accuracy and consistency with physical laws.

[0159] In the internal comparison of PINN variants, the M1 model (which only introduces monotonicity constraints) exhibits the best overall performance. While its RMSE (0.0134) is on par with the unconstrained model M0 (0.0133), M1 has the lowest mean absolute error (MAE) of all models (0.0102) and completely eliminates physical violations present in the M0 model (such as anomalous predictions of density decrease due to increased pressure). In contrast, the M2 and M3 models, which introduce more constraints, experience a slight decrease in accuracy due to overly strong constraints. Therefore, as... Figure 4 As shown, this embodiment selects M1 as the final optimal implementation configuration, which is scientifically sound and reasonable.

[0160] In this embodiment, the model final training and external blind test validation based on the optimal strategy include the following process: Based on the obtained ablation experiment conclusions, the M1 strategy is locked, that is, only the monotonicity constraint is enabled. , and As the final implementation, the model was fully trained using the acquired complete training dataset n=55. The training parameters remained consistent: Adam optimizer, learning rate 0.001, maximum training epochs 1500, and an early stopping mechanism with Patience=80 to ensure sufficient model convergence and prevent overfitting.

[0161] To objectively evaluate the model's generalization ability, an external test set (BlindTest Set) was constructed, completely isolated from the training set. This test set contains 39 independent experimental datasets, covering process conditions not present in the training set. These datasets remain invisible throughout the model development and parameter tuning phases and are used solely for final performance verification.

[0162] The trained PINN-M1 model was applied to an external blind test set, and the prediction results were compared with the actual measurement density. The statistical evaluation results are as follows:

[0163] In this embodiment, the model is applied to an external test set, such as Figure 5 As shown, at the key evaluation points, the coefficient of determination between the model predictions and the actual values... The RMS value reached 0.86, indicating that the model explained 86% of the density variation. The root mean square error (RMSE) was as low as 0.0087 g / cm³, and the mean absolute error (MAE) was 0.0072 g / cm³.

[0164] like Figure 6 As shown, the Bland-Altman analysis revealed that the vast majority of predicted residuals fell within the 95% consensus limit (LoA) and did not exhibit significant systematic bias. This demonstrates that the model exhibits excellent robustness over a wide parameter range.

[0165] System noise ceiling and model performance limit analysis;

[0166] Under fixed process parameters (pressure, time, speed, and charge quantity are all consistent), multiple repeated pressing experiments were conducted (in this embodiment). The standard deviation of the measured molding density under the same operating conditions was calculated and used as the inherent random noise basis of the production system. The calculation results show that the inherent noise standard deviation of this compression molding system is... Approximately 0.0071 g / cm³. This represents the lower limit of the unavoidable physical error introduced by uneven powder filling, equipment hydraulic fluctuations, and measurement errors;

[0167] The obtained model external prediction error RMSE = 0.0087 g / cm³ was compared with the system's inherent noise. The comparison shows that the external prediction error of this model, 0.0087 g / cm³, is extremely close to the system noise floor of 0.0071 g / cm³, and the model's prediction error is only slightly higher than the system noise (the difference is <0.002 g / cm³). This indicates that the PINN model constructed in this embodiment has almost completely captured all predictable physical laws, and the remaining small residuals mainly come from the randomness of the system itself.

[0168] like Figure 7 and Figure 8 As shown, to further verify the superiority of the PINN-M1 model over existing technologies, the PINN-M1 model was compared with two typical benchmark models on the same external blind test set: the A1 model based on ordinal-preserving regression and the B1 model based on Heckel's formula. The comparison results show that the PINN-M1 model's root mean square error (RMSE) and mean absolute error (MAE) are significantly lower than those of the A1 and B1 models, demonstrating its higher prediction accuracy and stronger generalization ability on real unknown data.

[0169] The key process variables of the working condition to be predicted are obtained and input into a lightweight physical information neural network based on the optimal strategy to obtain the predicted molding density.

[0170] Example 2:

[0171] This embodiment presents a granular mass forming density prediction system based on a physical information neural network, such as... Figure 9 As shown, the system includes:

[0172] The network building module is used to construct a lightweight physical information neural network that adapts to physical features, and defines a composite physical loss function based on the theory of physical densification.

[0173] The initial sampling module is used to construct an initial training set based on key process variables and target variables through initial sparse sampling.

[0174] The dynamic expansion module is used to obtain a dynamic training dataset based on active learning by iteratively expanding the initial training set based on residual feedback.

[0175] The training optimization module is used to train the lightweight physical information neural network on a dynamic training dataset based on active learning, based on a composite physical loss function, to obtain a lightweight physical information neural network based on the optimal strategy.

[0176] The density prediction module is used to obtain the key process variables of the working condition to be predicted and input them into a lightweight physical information neural network based on the optimal strategy to obtain the predicted molding density.

[0177] Example 3:

[0178] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the granular mass compression molding density prediction method based on physical information neural network.

[0179] The electronic device may be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements the granular mass compression molding density prediction method based on a physical information neural network as described in the embodiments. It is understood that the electronic device may also include an input / output (I / O) interface and communication components.

[0180] The processor is used to execute all or part of the steps in the granular mass compression molding density prediction method based on a physical information neural network as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in the electronic device, as well as application-related data.

[0181] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the granular mass compression molding density prediction method based on physical information neural network described in the above embodiments.

[0182] Example 4:

[0183] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0184] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the granular mass compression molding density prediction method based on physical information neural networks described in the various embodiments of this application.

[0185] The aforementioned storage media include: flash memory, hard disks, multimedia cards, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disks, optical discs, servers, APP (Application) application stores, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the aforementioned method for predicting the density of pellet compression molding based on a physical information neural network.

[0186] Example 5:

[0187] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned method for predicting the density of granular material compression molding based on a physical information neural network.

[0188] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0189] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0190] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of this disclosure and its equivalents, then the intent of this disclosure also includes these modifications and variations.

Claims

1. A method for predicting the forming density of granules based on a physical information neural network, characterized in that, This method includes the following steps: Determine the key process variables and target variables for granular material compression molding; We construct a lightweight physical information neural network that adapts to physical features, and define a composite physical loss function based on the theory of physical densification. Based on the key process variables and target variables, an initial training set is constructed through initial sparse sampling. By iteratively expanding the initial training set based on residual feedback, a dynamic training dataset based on active learning is obtained. Based on the composite physical loss function, the lightweight physical information neural network is trained on a dynamic training dataset based on active learning to obtain a lightweight physical information neural network based on the optimal strategy. The key process variables of the working condition to be predicted are obtained and input into a lightweight physical information neural network based on the optimal strategy to obtain the predicted molding density.

2. The method for predicting the formation density of granules based on a physical information neural network according to claim 1, characterized in that, The specific details of determining the key process variables and target variables for granular material compression molding are as follows: The key process variables for the granular material compression molding process are defined, including: compression pressure. Holding time Pressurization speed and molding quality ; Set the value range for each key process variable separately; The target variable for granular material compression molding is set as molding density. .

3. The method for predicting the formation density of granules based on a physical information neural network according to claim 2, characterized in that, The method for constructing a lightweight physical information neural network that adapts to physical features is as follows: A lightweight fully connected neural network MLP is constructed based on the key process variables and target variables of granular material compression molding. The lightweight fully connected neural network MLP includes: an input layer, a hidden layer, and an output layer; The number of neurons in the input layer is the same as the number of key process variables; there are two hidden layers, and each hidden layer has 8 neurons; the number of neurons in the output layer is the same as the number of target variables. The hidden layer uses the Tanh hyperbolic tangent activation function as the activation function and adopts an adaptive weight initialization strategy for weight initialization, setting the initial bias to 0; wherein the adaptive weight initialization strategy includes, but is not limited to: Xavier uniform distribution and orthogonal initialization.

4. The method for predicting the formation density of granules based on a physical information neural network according to claim 3, characterized in that, The method for defining the composite physical loss function based on physical densification theory is as follows: Based on the configurable composite physical loss function framework, a composite physical loss function is constructed, consisting of a data fitting term and optional physical constraint terms; wherein the optional physical constraint terms are: a weighted sum of monotonicity constraint terms, concave constraint terms, and upper bound constraint terms; The composite physical loss function is used to train the lightweight physical information neural network; during the training process, for any batch of training samples input into the lightweight physical information neural network, the predicted forming density of all training samples in the current batch is obtained. Each training sample contains a set of key process variables and target variables; For the training samples in the current batch, the Huber Loss loss function is used to calculate the data fitting loss value of the training samples in the current batch based on the predicted and measured forming densities of all training samples. Based on the predicted forming density and pressing pressure of all training samples, the constraint violation amounts of the monotonicity constraint term, concave constraint term, and upper bound constraint term are calculated respectively. The constraint violation of the monotonicity constraint term is the negative value of the partial derivative of the predicted molding density with respect to the pressing pressure. The constraint violation of the concave constraint term is: the second derivative of the predicted molding density with respect to the pressing pressure. The constraint violation amount of the upper bound constraint term is: the difference between the predicted molding density and the preset maximum compaction density; For any constraint violation among the monotonicity constraint, concave constraint, and upper bound constraint, the constraint violation is input into a linear rectifier function. The output value of the linear rectifier function is squared to obtain the penalty value for each training sample. The arithmetic mean operator is used to calculate the average of all penalty values, which is used as the loss value for that constraint.

5. The method for predicting the forming density of granules based on a physical information neural network according to claim 2, characterized in that, The specific content of constructing the initial training set based on the key process variables and target variables through initial sparse sampling is as follows: Based on the value range of all key process variables, sparse sampling is used to obtain... Key process variables sample for the group; Each set of key process variable samples includes: pressing pressure. Holding time Pressurization speed and molding quality ; use Preliminary granulation experiments were conducted on samples of key process variables, and the measured molding density corresponding to each set of key process variable samples was recorded. Each set of key process variable samples and its corresponding measured molding density were then used as a training set to construct an initial training set. .

6. The method for predicting the forming density of granules based on a physical information neural network according to claim 5, characterized in that, The specific content of the dynamic training dataset based on active learning obtained by iteratively expanding the initial training set based on residual feedback is as follows: The initial training set is processed according to a pre-defined sample size sequence. Expand the system in batches, and perform the following operations during each expansion process: A preliminary model is constructed by initializing the model parameters of the lightweight physical information neural network; Based on the composite physical loss function, a preliminary model is trained using the current training set, and the model parameters of the preliminary model are optimized until the preset training termination condition is met, thus obtaining a trained preliminary model. On the trained preliminary model, the range of values ​​for all key process variables is used as the parameter space, and the distribution of predicted residuals within the parameter space is calculated. Based on the calculated predicted residual distribution, regions exceeding the preset residual threshold are identified; In the identified region, the local Latin hypercube sampling method is used to generate several sets of key process variable samples to be supplemented; Data standardization preprocessing is performed on all samples of key process variables to be supplemented to obtain standardized samples of key process variables to be supplemented. Based on all standardized samples of key process variables to be supplemented, compression molding experiments were carried out in sequence to obtain the mass and final height of the molded propellant for each group of key process variable samples to be supplemented, and then the measured molding density of each group of key process variable samples to be supplemented was calculated. A set of key process variables to be supplemented and the measured molding density corresponding to the set of key process variables to be supplemented are used as a set of training samples to be supplemented. Add all the training samples to be supplemented to the current training set to obtain the complete training set for the current expansion process; The complete training set obtained from the final augmentation process is used as the dynamic training dataset based on active learning.

7. The method for predicting the forming density of granules based on a physical information neural network according to claim 6, characterized in that, The preset residual threshold is set to be more than twice the standard deviation of process repeatability.

8. The method for predicting the forming density of granules based on a physical information neural network according to claim 7, characterized in that, The specific content of training the lightweight physical information neural network on the dynamic training dataset based on active learning based on the composite physical loss function to obtain the lightweight physical information neural network based on the optimal policy is as follows: Based on the lightweight physical information neural network and the composite physical loss function, a physical ablation variant space containing several model variants is constructed; On the dynamic training dataset based on active learning, according to the preset training configuration, leave-one-out cross-validation is used to train each model variant in the physical ablation variant space and obtain the cross-validation index of each model variant. The Bootstrap resampling generalization error estimation method is adopted to resample each model variant in the physical ablation variant space and calculate the generalization performance index of each model variant. The dynamic training dataset based on active learning is input into each model variant to predict the forming density, and the original predicted value output by each model variant is obtained. The original predicted value is then post-processed and calibrated using the ordinal-preserving regression method to obtain the calibrated predicted value. Based on the cross-validation metrics, generalization performance metrics, and calibrated predictions of all model variants, the optimal model variant is selected from the physical ablation variant space as a lightweight physical information neural network based on the optimal strategy.

9. The method for predicting the forming density of granules based on a physical information neural network according to claim 8, characterized in that, The model variant is defined as follows: a weight combination is set for the optional physical constraint terms in the composite physical loss function to obtain a composite physical loss function configuration scheme and it is assigned to a lightweight physical information neural network. The lightweight physical information neural network configured with the composite physical loss function configuration scheme is used as a model variant. The configuration scheme of the composite physical loss function is different for each model variant.

10. A granular mass forming density prediction system based on a physical information neural network, used to implement the granular mass forming density prediction method based on a physical information neural network as described in any one of claims 1-9, characterized in that, The system includes: The network building module is used to construct a lightweight physical information neural network that adapts to physical features, and defines a composite physical loss function based on the theory of physical densification. The initial sampling module is used to construct an initial training set based on key process variables and target variables through initial sparse sampling. The dynamic expansion module is used to obtain a dynamic training dataset based on active learning by iteratively expanding the initial training set based on residual feedback. The training optimization module is used to train the lightweight physical information neural network on a dynamic training dataset based on active learning based on a composite physical loss function, so as to obtain a lightweight physical information neural network based on the optimal strategy. The density prediction module is used to obtain the key process variables of the working condition to be predicted and input them into a lightweight physical information neural network based on the optimal strategy to obtain the predicted molding density.

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