Method for predicting melting point of nitrate-based fused cast explosive

Abstract

The invention discloses a melting point prediction method for a nitrate-based fused cast explosive. The method comprises the following steps: S1, constructing a data set matched with a nitrate-based energetic material; s2, constructing a user-defined molecular descriptor set of the melting points of the nitrate-based energetic materials; s3, based on the data set, optimizing the LightGBM, XGBoost and BPNN machine learning models by adopting an ablation experiment method and a training experiment, and obtaining an optimal model for predicting the melting point of the nitrate-based energetic material by comparing model evaluation indexes and errors; and S4, converting the newly designed nitrate-based energetic material I into a corresponding user-defined molecular descriptor set I, and taking the user-defined molecular descriptor set I as the input of the prediction machine learning model to obtain the output value of the melting point Tm. The method for predicting the melting point of the nitrate-based fused cast explosive, provided by the invention, has good prediction accuracy and interpretation capability, and can be used for predicting the performance of nitrate-based energetic materials.

Description

Technical Field

[0001] The present invention relates to the field of prediction of melting points of energetic materials, and more particularly to a method for predicting the melting point of nitrate-based fused-cast explosives. Background Art

[0002] Cast explosives are widely used in various military applications, such as mortars, grenades, armor-piercing ammunition, mines, and missile warheads. They offer significant advantages, including a simple charging process, high loading density, and sufficient lethality. The charging process of cast explosives is primarily dependent on the phase transformation of the carrier. Therefore, the physicochemical properties of the carrier play a crucial role in determining the overall performance of cast explosives.

[0003] An ideal cast explosive should have the following properties: 1. The melting point should be between 70 and 120°C; 2. It has high density and excellent explosive performance.

[0004] Nitrate-based energetic materials are among the most advanced types of melt-cast explosives. The introduction of nitrate groups increases molecular density, improves the molecular oxygen balance, and thus enhances explosive energy. The presence of -O- bonds in nitrate groups reduces the tensile rigidity of the nitro group, weakens the bond order, and results in lower thermal stability and increased molecular plasticity. Consequently, nitrate-based energetic materials are widely used in military applications as melt-cast explosives. However, PETN, one of the most advanced nitrate-based energetic materials, has a melting point that does not meet the requirements for an ideal melt-cast explosive. With the increasing demand for explosive power in modern weapons, the need to develop new nitrate-based high-energy melt-cast explosives with low melting points is becoming increasingly urgent. Traditional trial-and-error methods and chemical intuition are inefficient in developing promising high-performance energetic materials and are therefore unable to meet practical application requirements. Therefore, a key technological breakthrough lies in establishing a highly accurate melting point prediction method for nitrate-based melt-cast explosives to guide the design and development of high-performance energetic materials.

[0005] The prediction models trained by existing research work are often limited by the size of the training data set and the diversity of the structures of energetic compounds, resulting in insufficient versatility of the models. It is difficult to achieve ideal accuracy in predicting the properties of nitrate compounds. Furthermore, although the prior art involves the use of descriptors in the field of melting point prediction, such as a method for quickly predicting the melting point of low-melting-point alloys using ridge regression with patent application number: 202010848989.7, this patent is mainly aimed at low-melting-point alloys. Alloys are essentially mixtures of different elements mixed in different proportions, which are a mixture of multiple substances, while energetic compounds containing nitrate groups are single substances, that is, the prediction objects of the two are different. Also, because their prediction objects are different, the descriptors used are the component ratios of different metal elements and the electronegativity of each element, and other property information, while energetic material compounds do not have such information as the ratios of different substances. Therefore, this method is actually completely unsuitable for predicting the melting point of energetic compounds containing nitrate groups. That is, although the prior art introduces the concept of descriptors in melting point prediction, due to insufficient data and the lack of key descriptors (such as the average distance of substituents, the number of nitrate groups, etc.), the training accuracy of melting point prediction is not as good as other property prediction models. In the existing literature 1, “Predicting the performance and stability parameters of energetic materials (EMs) using a machine learning-based q-RASPR approach”, the melting point prediction model uses an optimized quantitative readout structure-property relationship (q-RASPR) method, and the prediction error index R 2 The R 2 The prediction accuracy is relatively improved, but it still cannot meet the requirements of prediction accuracy.

[0006] In the existing literature 2, “Application of Machine Learning to the Design of Energetic Materials Reliminary Experience and Comparison with Alternative Techniques”, the melting point prediction model adopts the information transfer neural network MPNN method, and its prediction error index R 2 The R 2 The prediction accuracy is 0.93, RMSE is 35.8, and MAE is 25.3. Compared with the existing literature 1, its prediction accuracy is also improved, but it still cannot meet the requirements of prediction accuracy.

[0007] In the existing literature 3 of “Machine learning transition temperatures from 2D structure”, the melting point prediction model adopts the ridge regression (UPPER-RR) method based on the unified physicochemical property estimation relationship (UPPER), and its prediction error index RMSE is 61.89 and MAE is 47.9. The RMSE of the gradient boosting (UPPER-GB) based on the unified physicochemical property estimation relationship (UPPER) is 56.32 and MAE is 43.76. The RMSE of all group composition and geometric descriptors using UPPER (ARL-UPPER) is 35.93 and MAE is 27.56. It can be seen that its measurement accuracy is also improved compared with the first two methods, but it still cannot meet the requirements of prediction accuracy.

[0008] In the existing document "Deciphering melting behaviors of energetic compounds using interpretable machine learning for melt-castable applications"4 and the patent document "A method for predicting the melting point of energetic materials based on an interpretable machine learning model", the melting point prediction in both documents is a classification problem, which means predicting a certain melting point range rather than a specific melting point value, and is not suitable for the accurate prediction of the melting point of nitrate-based energetic materials. Summary of the Invention

[0009] An object of the present invention is to solve at least the above problems and / or disadvantages and to provide at least the advantages which will be described hereinafter.

[0010] To achieve these objects and other advantages of the present invention, a method for predicting the melting point of a nitrate-based fused-cast explosive is provided, comprising: S1. Extract the melting points of nitrate-based energetic materials from existing literature by computer to construct a data set suitable for nitrate-based energetic materials; S2. Construct a custom molecular descriptor set for the melting point of nitrate-based energetic materials, and characterize and partition the dataset to obtain a training set and a test set. S3. Based on the training set and test set, the three machine learning models, LightGBM, XGBoost, and BPNN, were optimized using ablation experiments and training experiments. By comparing model evaluation indicators and errors, the optimal model for predicting the melting point of nitrate-based energetic materials was obtained. S4. converting the newly designed nitrate-based energetic material I into the corresponding custom molecular descriptor set I, and using the custom molecular descriptor set I as the input of the predictive machine learning model to obtain an output value of the melting point Tm; Wherein, in S2, the custom molecular descriptor set includes: RDKit molecular descriptors that can be directly converted from SMILES characters, and custom molecular descriptors obtained through molecular structure and performance analysis.

[0011] Preferably, in S1, the molecules in the data set contain multiple types of molecular skeletons and multiple types of substituents, and there are 48 melting point data in the data set sample distributed in the range of -40°C-154°C, and most of the melting point values ​​in the sample are distributed between 60°C-120°C.

[0012] Preferably, in S2, the RDKit molecular descriptor includes: calculating the similarity of properties maintained at a certain distance from each atom, the molar refractive index of the unified charge burden vector, the maximum portion of the charge on a single atom in the molecule, the minimum portion of the charge carried by a single atom in the molecule, the unified charge burden vector, the maximum absolute value of the partial charge of an atom in the molecule, the minimum absolute value of the partial charge of an atom in the molecule, the Wildman-Crippen logarithm, the lowest E-state index of all atoms in the molecule, the highest E-state index of all atoms in the molecule, calculating the weighted sum of ADS mapping properties, the topological polar surface area, the topological index for quantifying molecular complexity, the number of hydrogen bond acceptors, and the number of hydrogen bond donors; The custom molecular descriptors include: ring structure parameters, number of nitrate groups, average distance between nitrate groups in the molecular structure, short path distance between nitrate groups and other groups, molecular structure symmetry parameters, molecular mass, carbon mass fraction, hydrogen mass fraction, oxygen mass fraction, nitrogen mass fraction, and oxygen balance.

[0013] Preferably, the calculation rules for each descriptor in the custom molecular descriptor are as follows: The ring structure parameter is obtained by counting the non-conjugated rings in the molecular structure as 1 and the conjugated rings as 1.5, and then accumulating them; The number of nitrate groups was obtained by counting the number of nitrate groups in the molecular structure; The average distance between nitrate groups in the molecular structure is calculated by counting the total number of chemical bonds contained in the shortest connection path between each nitrate group and other nitrate groups along the molecular skeleton, summing up the total number of chemical bonds and taking the average value to obtain the average distance between a single nitrate group and other nitrate groups, and then taking the average value of the sum of the average distances; The distance of the short path between the nitrate group and other groups is obtained by counting the number of chemical bonds in the short path between the nitrate group and other groups; The molecular structure symmetry parameter is obtained by the following rule: if the molecular structure is centrosymmetric and axisymmetric, it is recorded as 2; if the molecular structure is centrosymmetric or axisymmetric, it is recorded as 1; if the molecular structure is neither centrosymmetric nor axisymmetric, it is recorded as 0; The oxygen balance OB is obtained by the following formula: In the above formula, C, H, O, and N are the number of carbon, hydrogen, oxygen, and nitrogen atoms, respectively.

[0014] Preferably, in S2, the training set and the test set are constructed as follows: S20. For each sample in the dataset, the corresponding chemical structure was drawn using a structural formula drawing software, and the SMILES characters corresponding to the chemical structure were exported. The SMILES characters were converted using the Python rdkit library to obtain 15 RDKit molecular descriptors. According to the calculation rules of each descriptor in the custom molecular descriptor, 11 custom molecular descriptors corresponding to the sample were obtained. S21. Divide the custom molecular descriptor set and its corresponding performance data into a training set and a test set in a ratio of 4:1 using a random partitioning code.

[0015] Preferably, in S3, the evaluation index and error include: The coefficient of determination was used to determine the degree of fit; The mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE) are used to quantify the gap between the experimental value and the predicted value.

[0016] Preferably, in S3, the method for optimizing the three machine learning models includes: S30. Use LightGBM, XGBoost, and BPNN machine learning algorithms to build prediction models, and conduct ablation experiments on the LightGBM model and BPNN model respectively; S31. Perform constrained optimization on the operating parameters of the three models: LightGBM, XGBoost, and BPNN.

[0017] The present invention has at least the following beneficial effects: the three machine learning models of LightGBM, XGBoost and BPNN are optimized by using ablation experiment method and training experiment, and the best model for predicting the melting point of nitrate-based energetic materials is obtained by comparing model evaluation indicators and errors: the best melting point prediction model is the LightGBM model, and the R 2 The average absolute error (MAE) is 0.9263, the RMSE is 12.9424, the MAE is 10.128, the average absolute error is 3.43 °C, and the minimum absolute error is 0.143 °C. These indicators show that the LightGBM model has a strong fitting ability for the nitrate-based energetic material data used in this study, has good prediction accuracy and explanatory power, and can be used to predict the properties of nitrate-based energetic materials. Furthermore, in the description of energetic substances, the present invention uses SMILES characters, which are unique to chemical compounds, to describe the elements, chemical bonds, and structural information within the molecules of the compound's single substance, and adopts the open source toolkit for chemical informatics - RDKit. At the same time, on the basis of basic information, some customized molecular structure information of chemical formulas is added, such as the average distance between nitrate groups and the closest distance between nitrate groups and other groups, taking into account the existence of internal rings in the compound and the conjugation situation, so that the performance of nitrate-based energetic materials can be effectively predicted.

[0018] Other advantages, objectives and features of the present invention will be reflected in part from the following description and will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a statistical distribution diagram of the melting points of the nitrate-based energetic materials in the present invention; Figure 2 This is a diagram of the LightGBM model structure established for the melting point of nitrate-based energetic materials in the present invention; Figure 3This is a structural diagram of the BPNN model established for the melting point of nitrate-based energetic materials in the present invention; Figure 4 is the error function R in the melting point prediction model of the present invention 2 Evaluation diagram; Figure 5 This is an evaluation graph of the error function RMSE in the melting point prediction model of the present invention; Figure 6 This is an evaluation diagram of the error function MAE in the melting point prediction model of the present invention; Figure 7 is the mean absolute error graph of the melting point prediction model test set in the present invention; Figure 8 A scatter plot comparing the melting point prediction value and the experimental value of the LightGBM model in the present invention; Figure 9 This is the residual plot of the melting point prediction value and the experimental value of the LightGBM model in the present invention; Figure 10 This is a diagram showing the application domain of the LightGBM model melting point prediction and experimental values ​​in the present invention; Figure 11 This is a scatter plot of the error data distribution between the melting point prediction value and the experimental value of the LightGBM model in the present invention; Figure 12 A comparison chart of the mean absolute error (MAE) when predicting melting points between the present invention and the prior art; Figure 13 A comparison chart of the root mean square error (RMSE) when predicting melting points between the present invention and the prior art; Figure 14 A comparison chart of the mean square error (MSE) when predicting melting points between the present invention and the prior art; Figure 15 is the chemical structural formula of the synthesized nitrate-based energetic material used as an example in the present invention; Figure 16 is the chemical structural formula of the nitrate-based energetic material not synthesized in the present invention. DETAILED DESCRIPTION

[0020] The present invention will be described in further detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0021] 1. Dataset Construction In order to accurately predict the melting point of nitrate-based high-energy cast explosives and improve the applicability of the model, we place special emphasis on the diversity of molecular properties when collecting data and strive to collect more experimental test data. By reviewing the literature on the synthesis and design of nitrate-based energetic materials, we collected the melting points of 81 nitrate-based energetic materials as a data set, and the 81 energetic molecular structures containing nitrate groups reported in the literature, including the melting point ( T m ) and density ( ρ ) and other attributes.

[0022] Furthermore, these samples contain a variety of typical nitrate energetic compounds, such as PETN, BIDN, BITN, BODN, etc. In addition, the molecules in the data set contain various types of molecular skeletons and various types of substituents, which basically cover the structural types of nitrate-based energetic materials that are currently being mainstreamed in the field of energetic materials. After subsequent cleaning and processing steps, there are 48 melting point-related data sets. In the melting point-related experiments, the melting point data are distributed between -40 ℃ and 154 ℃, and most of the melting point values ​​are distributed between 60 ℃ and 120 ℃, as shown below. Figure 1 The melting point distribution diagram of the nitrate-based dataset is shown. Compared with the existing dataset construction, this step collected the melting point data of 81 nitrate-based energetic materials, and after cleaning and processing (i.e., through manual sorting), constructed a more diverse dataset covering a variety of molecular skeletons and substituent types.

[0023] 2. Molecular description set construction (In addition to using RDKit molecular descriptors, the molecular description set also constructs additional custom descriptors, such as the average distance of substituents and the number of nitrate groups, to more comprehensively describe the relationship between molecular structure and performance) Melting point prediction performance primarily utilizes RDKit molecular descriptors and other custom molecular descriptors derived from molecular structure and property analysis. Using Python and the MoleculeDescriptors module from the chemical information package RDKit, SMILES strings of 81 energetic molecules containing nitrate esters were used as input to calculate the RDkit descriptors for all compound molecules. To better describe the various properties of the nitrate ester group, the relationship between the structural characteristics of each molecule and its own properties was analyzed in detail when selecting custom molecular descriptors. Custom molecular descriptors based on molecular structural characteristics were constructed, including oxygen balance value, carbon atomic mass ratio, hydrogen atomic mass ratio, oxygen atomic mass ratio, nitrogen atomic mass ratio, and the number of nitrate ester groups. The specific names and descriptions of the custom descriptor set for the melting point of nitrate ester-based energetic materials are shown in Table 1. This step primarily uses the custom descriptor set shown in Table 1 to characterize each substance under test. The custom molecular descriptor set and performance data are then randomly divided into training and test sets in a ratio of approximately 4:1 using code. The training set is used to build the prediction model, while the test set is used to evaluate the model's generalization ability and predictive performance. Table 1 In Table 1, 1-15 are RDKit molecular descriptors. 16-26 are custom molecular descriptors obtained by molecular structure and performance analysis. The calculation rules of the 11 custom descriptors are as follows: Presence of ring structure: used to calculate the number of rings in a molecular structure, where the non-conjugated ring count is 1 and the conjugated ring count is 1.5, and then the numbers are accumulated. For example, if there is no ring in the substance, it is recorded as 0, then the Presence of ring structure→0.

[0024] Number of nitrate groups. Used to calculate the number of nitrate groups in a molecule. For example, if a substance has 3 nitrate groups, then the number is 3, i.e., Number of nitrate groups → 3. Average distance between nitrate groups is calculated by first counting the total number of chemical bonds along the shortest path between each nitrate group and the other nitrate groups along the molecular backbone, then summing and averaging these bonds to obtain the average distance between each nitrate group. The sum of the average distances between each nitrate group is then calculated and divided by the number of nitrate groups.

[0025] For example: The average distance between nitrate group 1 and other nitrate groups is (5+3) / 2=4; The average distance between nitrate group 2 and other nitrate groups is (4+3) / 2=3.5; The average distance between nitrate group 3 and other nitrate groups is (5+4) / 2=4.5; Then the average distance between nitrate groups is (4+3.5+4.5) / 3=4, so Average distance between nitrate groups→4; Distance of nitrate group from other groups: The number of chemical bonds in the short path between the nitrate group and other groups. For example, if there are no other groups except the nitrate group, it is recorded as 0, that is, Distance of nitrate groupfrom other groups→0; Symmetry is measured as follows: if the molecular structure is centrosymmetric and axially symmetric, it is recorded as 2; if the molecular structure is centrosymmetric or axially symmetric, it is recorded as 1; if the molecular structure is neither centrosymmetric nor axially symmetric, it is recorded as 0. For example, if the substance has an asymmetric structure, it is recorded as 0, that is, Symmetry→0; ExactMolWt is the relative molecular mass. For example, if the relative molecular mass is 241, then ExactMolWt →241. Carbon_contents: mass fraction of carbon element. For example, (48.0000 / 241)×100=19.9, then Carbon_contents→19.9; 23. Hydrogen_contents: hydrogen mass fraction. For example, (7 / 241)×100=2.93, then Hydrogen_contents→2.93; Oxygen_contents Oxygen mass fraction, for example: (143 / 241)×100=59.7, then xygen_contents→59.7; Nitrogen_contents Nitrogen mass fraction, for example, (42 / 241)×100=17.4, then Nitrogen_contents→17.4: 26. Oxygen balance OB is obtained by the following formula: In the above formula, C, H, O, and N are the number of carbon, hydrogen, oxygen, and nitrogen atoms, respectively; example: Then Oxygen balance→-16.59.

[0026] Example 1: For any substance in the dataset, the custom descriptor set in Table 1 is used to characterize it. Figure 15 Taking the chemical structure of the substance in as an example, we can draw the relevant structure in the structural drawing software according to its structure, and export its SMILES character as: O=[N+](OCCC(O[N+]([O-])=O)CO[N+]([O-])=O)[O-] The SMILES was converted using the Python rdkit library to obtain the descriptors numbered 1-15 in Table 1.

[0027] The conversion code is: from rdkit import Chem from rdkit.Chem import Descriptors import pandas as pd # Read an existing Excel file input_file = 'C: / Users / 29351 / Desktop / SMILES.xlsx' data = pd.read_excel(input_file) # Extract the value of the SMILES column smiles_list = data.iloc[:, 0].tolist() # Define the molecule descriptor dictionary descriptors = { 'BCUT2D_MWHI': Descriptors.BCUT2D_MWHI, 'BCUT2D_MRLOW': Descriptors.BCUT2D_MRLOW, 'MaxPartialCharge': Descriptors.MaxPartialCharge, 'MinPartialCharge': Descriptors.MaxPartialCharge, 'BCUT2D_LOGPLOW': Descriptors.BCUT2D_LOGPLOW, 'MaxAbsPartialCharge': Descriptors.MaxAbsPartialCharge, 'MinAbsPartialCharge': Descriptors.MaxAbsPartialCharge, 'MolLogP': Descriptors.MolLogP, 'MinEStateIndex': Descriptors.MinEStateIndex, 'MaxEStateIndex': Descriptors.MaxEStateIndex, 'qed': Descriptors.qed, 'TPSA': Descriptors.TPSA, 'BertzCT':Descriptors.BertzCT, 'NumHAcceptors':Descriptors.NumHAcceptors, 'NumHDonors':Descriptors.NumHDonors, } # Create an empty DataFrame to store the results output_data = pd.DataFrame(columns=['SMILES'] + list(descriptors.keys())) # Calculate molecular descriptors and store the results for smiles in smiles_list: mol = Chem.MolFromSmiles(smiles) if mol: values = {'SMILES': smiles} for name, descriptor_func in descriptors.items(): value = descriptor_func(mol) values[name]= value # Use pd.concat instead of append output_data = pd.concat([output_data, pd.DataFrame([values])],ignore_index=True) # Write the results to a new Excel file output_file = 'Tm-des.xlsx' output_data.to_excel(output_file, index=False) print("The results have been saved to", output_file) Furthermore, the 11 custom descriptors 16-26 in Table 1 are obtained by calculation and organized in the standard format according to the provided data as follows: 1. BCUT2D_MWHI → 16.97705154 2. BCUT2D_MRLOW → -0.79175799 3. MaxPartialCharge → 0.294340936 4. MinPartialCharge → 0.294340936 5. BCUT2D_LOGPLOW → -2.260296498 6. MaxAbsPartialCharge → 0.313825413 7. MinAbsPartialCharge → 0.313825413 8. MolLogP → -0.63 9. MinEStateIndex → ​​-1.305231481 10. MaxEStateIndex → ​​9.934649943 11. QED → 0.377914863 12. TPSA → 157.11 13. BertzCT → 267.4797126 14. NumHAcceptors → 9 15. NumHDonors → 0 16. Presence of ring structure → 0 17. Number of nitrate groups → 3 18. Average distance between nitrate groups → 4 19. Distance of nitrate group from other groups → 0 20. Symmetry → 0 21. MolWt → 188 22. Carbon_contents → 19.9 23. Hydrogen_contents → 2.93 24. Oxygen_contents → 59.7 25. Nitrogen_contents → 17.4 26. Oxygen balance → -36.59 Third, the custom molecular descriptor set and its corresponding performance data are divided into a training set and a test set at a ratio of about 4:1 using a random partitioning code. The training set is used to build the prediction model, while the test set is used to evaluate the generalization ability and prediction performance of the model. It should be noted that the performance data for each parameter in Descriptor Table 1, such as the ring structure parameter, is the specific data corresponding to each parameter. For example, in NumHDonors → 0, NumHDonors is the descriptor, and 0 is the performance data corresponding to NumHDonors. S1. Prediction models were constructed using three machine learning algorithms: LightGBM, XGBoost, and BPNN. Ablation experiments were performed on both the LightGBM and BPNN models. In this step, the Lightweight Gradient Boosting Machine (LightGBM), the Extreme Gradient Boosting Algorithm (XGBoost), and the Back-Propagation Neural Network (BPNN) were trained and tested in conjunction with ablation experiments. The optimal machine learning model for predicting the melting point of nitrate-based energetic materials was determined. Mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) were used to comprehensively evaluate the model's fit. Relative or absolute error was used to evaluate the prediction accuracy of each model. The results showed that the optimal melting point prediction model was the LightGBM model using a leaf-wise tree growing strategy. The LightGBM model exhibited significant advantages in feature selection and key information extraction. This strategy enabled the model to focus on the most informative features, efficiently mining key features from limited training data, resulting in superior performance on both the training and test sets. The specific implementation process is as follows: Three machine learning algorithms, LightGBM, XGBoost, and BPNN, were used to build prediction models, and ablation experiments were conducted on the LightGBM model and the BPNN model respectively. Figure 2 and Figure 3 The LightGBM model and BPNN model structures of the optimal prediction of the melting point of nitrate-based energetic materials obtained after ablation experiments are shown in Figure 2. Figure 2 DT i It means the i A decision tree, f i ( x ) indicates the i The predicted value of a decision tree for a sample, i The values ​​are 1, 2, ... n , n represents the number of decision trees. n The value of is 1, 2…600, Figure 3 In, X m It represents the molecular descriptor, and the value of m is 1, 2...26. At the same time, since the ablation experiment is a routine operation, its process is not described here. The purpose of using the ablation experiment in this step is to screen out some descriptors that have negative effects through multiple runs.

[0028] S2. Perform constrained optimization on the operating parameters of the LightGBM, XGBoost, and BPNN models. The machine learning model construction in this step mainly includes fine-tuning the parameters of the three models, LightGBM, BPNN, and XGB, by running the code multiple times. The adjustment of the LightGBM parameters is as follows: 'learning_rate': 0.01, # learning rate 'n_estimators': 800, # Number of trees 'num_leaves': 10, # Number of leaf nodes 'max_depth': -1, # Do not limit the maximum depth of the tree, let LightGBM automatically adjust 'bagging_fraction': 0.8, # Increase the proportion of out-of-bag samples 'bagging_freq': 5, # Sampling frequency of out-of-bag samples 'feature_fraction': 0.85, # The ratio of feature selection 'min_data_in_leaf': 20, # Increase the minimum number of samples in the leaf node 'min_sum_hessian_in_leaf': 1e-3, # Increase the minimum Hessian sum in the leaf node The BPNN parameters are adjusted as follows: hidden_size = 50 # hidden layer size learning_rate = 0.001 num_epochs = 8000 # Number of training rounds batch_size = 25 # batch size dropout_prob = 0.5 # Dropout probability The adjustment of xgb parameters is as follows: 'max_depth': 8, # Maximum depth of the tree 'learning_rate': 0.02, # learning rate 'n_estimators': 100, # Number of trees 'gamma': 0.1, # Post-pruning parameter 'subsample': 0.9, # training data subsampling rate 'colsample_bytree': 0.8, # Feature subsampling rate 'reg_alpha': 0.2, # L1 regularization coefficient 'reg_lambda': 0.2, # L2 regularization coefficient Completed the training and testing of three models: LightGBM, XGBoost, and BPNN.

[0029] 5. Select the best hyperparameters from the preliminary results of the training set and test set. The reference indicators are: using the coefficient of determination (R 2 ) to determine the degree of fit; the mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE) are used to quantify the gap between the experimental value and the predicted value, and the optimal parameter is selected to obtain the final result. The main reference indicator is the test set R2, and a model of the test set R2 is selected as the final selected model. Finally, the true value and predicted value of the training set and test set are derived, and based on the derived data in actual application, the calculation formula, evaluation method and characteristics of each evaluation index in the training set and test set are shown in Table 2, where n is the number of samples, Y is the number of samples, and Y is the number of samples. i is the true value, Y i ' is the predicted value.

[0030] Table 2 Furthermore, the evaluation method of the melting point prediction model of nitrate ester energetic materials is as follows: like Figure 4 As shown in the figure, the dotted boxes represent the training set error function values ​​of the three machine learning models, and the solid boxes represent the test set error function values ​​of the three machine learning models. Figure 4 It can be found that the determination coefficient R² of the LightGBM model on the training set and test set reached 0.9988 and 0.9263 respectively. These two values ​​are closer to the perfect fitting threshold of 1 compared to the XGBoost model and BPNN model, indicating that the LightGBM model occupies a leading position in the fitting accuracy of melting point data. Secondly, the determination coefficient R² of the XGBoost model on the training set and test set are 0.9997 and 0.7753 respectively. Although the model shows excellent fitting ability on the training set, its performance on the test set drops significantly. Although the BPNN model can effectively learn the rules between melting point and molecular descriptors on the training set, its prediction of melting point in the test set is poor. Figure 5-Figure 6As shown in the figure, the root mean square error (RMSE) of the training set and test set of the LightGBM model are 1.7287 and 12.9424, respectively, and the mean absolute error (MAE) are 1.1908 and 10.1280, respectively. It can be seen that the RMSE and MAE of LightGBM are smaller than those of the XGBoost and BPNN prediction models, and the comprehensive training set and test set are the models with the best prediction effect.

[0031] like Figure 7 As shown in the figure, the solid line box represents the mean absolute error between the predicted value and the experimental value, and the dotted line box represents the minimum absolute error between the predicted value and the experimental value. Figure 7 It can be found that in the test sets of the three machine learning models, the average error of all models did not exceed 4.5 ℃, and the minimum relative error was less than 0.2 ℃. Among the machine learning models examined, the LightGBM model showed the best prediction performance, with an average absolute error of 3.43 ℃ and a minimum absolute error of 0.143 ℃, indicating that the model is closest to the true experimental value in terms of prediction accuracy. In addition, the LightGBM model predicted the melting point of PETN to be 142.0 ℃, which is 1 ℃ different from the experimental value, which indirectly shows that the LightGBM model can accurately predict the melting point of nitrate-based energetic materials. In summary, whether in terms of performance in the training set or the test set, the LightGBM model is significantly better than the other three machine learning models. In the task of predicting the melting point of nitrate-based energetic materials, the LightGBM model has significant advantages and wide applicability.

[0032] like Figure 8 The scatter plot of the melting point prediction value of the LightGBM model and the experimental value is shown. The square points represent the data points of the 38 training sets of the LightGBM model, and the circles represent the data points of the 6 test sets. Figure 8 It can be found that the data points of the training set and test set of the LightGBM model are basically distributed around y=x (where the solid line is located), with low deviation, indicating that the LightGBM model has high prediction accuracy.

[0033] like Figure 9 The residual plot of the LightGBM model's melting point predictions compared to the experimental values ​​is shown. The squares represent data points from the training set, and the circles represent data points from the test set. The residuals for most of the LightGBM model's data points are randomly and evenly distributed on both sides of the baseline, indicating that LightGBM does not produce significant systematic errors during modeling. The test set and the y=0 baseline are more densely distributed than the training set, consistent with the conclusions drawn from the scatter plot analysis.

[0034] like Figure 10Figure 2 shows the application domain of the LightGBM model's melting point predictions and experimental values. The dots represent the test set data points, and the three solid lines correspond to the standard residual bounds y = ±3 and the leverage effect warning threshold h* = 1.369. The rectangle enclosed by the three solid lines represents the application domain of the LightGBM model. As can be seen, all data points in the test set fall within the application domain, with no outliers.

[0035] like Figure 11 The following scatter plot shows the error distribution between the LightGBM model's predicted melting point values ​​and the experimental values. The solid dotted line and the dashed dotted line represent the curves of the experimental melting point values ​​and the LightGBM model's predicted values ​​in the test set, respectively. The gray dashed line encloses the ±10°C error band of the melting point experimental values. It can be seen that most of the predicted data points fall within the 10°C error band, close to the experimental values, with only two predicted data points exceeding the edge of the error band.

[0036] It can be seen from this step that the LightGBM model has a strong fitting ability for the melting point data of nitrate-based energetic materials used in this study, and has good prediction accuracy and explanatory ability. It can be used to predict the melting point properties of nitrate-based energetic materials. In this step, by comparing the three machine learning algorithms LightGBM, XGBoost and BPNN, and optimizing the model through ablation experiments, the LightGBM model was finally selected as the best prediction model. Its R² on the test set reached 0.9263, the average absolute error was 3.43℃, and the minimum absolute error was 0.143℃. The prediction accuracy is significantly better than the existing methods.

[0037] The test set verification shows that the prediction accuracy of the method of the present invention is significantly better than that of the existing method. In order to further prove that the error accuracy of the present invention is better than the existing level, the Figure 12-14 The comparison chart further illustrates this, where Figure 12-14In the paper, we compare LightGBM (lightweight gradient boosting machine), XGBoost (extreme gradient boosting algorithm), BPNN (back propagation neural network), 2006 Mohammad H (the method used by the author in the paper "Approximate prediction of melting point of nitramines, nitrate esters, nitrate salts and nitroaliphatics energetic compounds."), 2015 Mohammad H (the method used by the author in the paper "A New Computer Code for Prediction of Enthalpy of Fusion and Melting Point of Energetic Materials."), Jason A (the machine learning model used by the author in the paper "Development of quantitative structure property relationships for predicting the melting point of energetic materials."), Kong D (the author's optimal machine learning RF model in "Extended atom-based and bond-based group contribution descriptor and its application to melting point prediction of energetic compounds"), Kunal R (the author's optimal machine learning RF model in "Predicting the performance and stability parameters of energetic materials (EMs) using a machine learning-based q-RASPR approach".), Chen P (the optimal machine learning model used in the paper "Quantitatively determining melting properties forenergetic compounds via knowledge-infused molecular graphs and interpretable deep learning"), and Chen P (the optimal machine learning model used in the paper "Quantitatively determining melting properties forenergetic compounds via knowledge-infused molecular graphs and interpretable deep learning.") The error values ​​of the nine methods in terms of mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE) intuitively show that the error accuracy of the LightGBM (lightweight gradient boosting machine) trained by the present invention is much lower than that of other existing technologies, that is, from... Figure 12-14 It can be seen that the present invention has the advantage of using descriptors to achieve minimal prediction resource consumption, while its accuracy is comparable to the most accurate existing model.

[0038] Example: After the prediction model was built, a model was obtained that can accurately predict nitrate-based substances based on 26 descriptors. In actual application, a nitrate-based energetic material that has not been synthesized so far was designed based on the molecular design principle. Its chemical structure is as follows Figure 16 As shown, although its melting point is currently unknown, based on its structure, the relevant structure can be drawn in a structural drawing software (such as ChemDraw, KingDraw, InDraw, Alchemist), and then converted and exported into the following SMILES characters through the structural drawing software: [O-]N1C(C(O[N+]([O-])=O)N2C(C(O[N+]([O-])=O)O[N+]([O-])=O)=NC=N2)=NN=N1 The SMILES characters were converted using the Python rdkit library to obtain the following 15 RDKit molecular descriptors numbered 1-15 in Table 1: 1. BCUT2D_MWHI → 16.95262149 2. BCUT2D_MRLOW → -0.7669189 3. MaxPartialCharge → 0.389496805 4. MinPartialCharge → 0.389496805 5. BCUT2D_LOGPLOW → -2.074396925 6. MaxAbsPartialCharge → 0.389496805 7. MinAbsPartialCharge → 0.389496805 8. MolLogP → -0.0429 9. MinEStateIndex → ​​-1.006435185 10. MaxEStateIndex → ​​10.10742394 11. QED → 0.483195157 12. TPSA → 113.33 13. BertzCT → 333.0303063 14. NumHAcceptors → 7 15. NumHDonors → 0 The following 11 custom descriptors, numbered 16-26 in Table 1, are obtained by calculation: 16. Presence of ring structure → 3 17. Number of nitrate groups → 3 18. Average distance between nitrate groups → 4 19. Distance of nitrate group from other groups → 4 20. Symmetry → 0 21. MolWt → 363 22. Carbon_contents → 16.5 23. Hydrogen_contents → 0.8 24. Oxygen_contents → 44.1 25. Nitrogen_contents → 38.6 26. Oxygen balance → -6.61 The 15 RDKit molecular descriptors and 11 custom descriptors were imported as a test set into the trained prediction model, resulting in a predicted melting point of Tm = 136.6°C. This compares to existing techniques, which typically require density functional theory (DFT) calculations for descriptors such as dipole moment, electrostatic potential (ESP), and sublimation enthalpy, requiring significant time and computational resources. In contrast, the invented method uses all descriptors derived from the molecular structure diagram (either through RDKit conversion or manual calculation), saving significant time and cost. The above solution is only an illustration of a preferred embodiment, but is not limited thereto. When implementing the present invention, appropriate replacements and / or modifications can be made according to user needs.

[0039] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and exemplary embodiments. They can be applied to a variety of fields suitable for the present invention. Further modifications will be readily apparent to those skilled in the art. Therefore, the present invention is not limited to the specific details and illustrations shown and described herein without departing from the general concept defined by the claims and their equivalents.

Claims

1. A method for predicting the melting point of a nitrate-based melt-cast explosive, characterized in that: include: S1. Extract the melting points of nitrate-based energetic materials from existing literature by computer to construct a data set suitable for nitrate-based energetic materials; S2. Construct a custom molecular descriptor set for the melting point of nitrate-based energetic materials, and characterize and partition the dataset to obtain a training set and a test set. S3. Based on the training set and test set, the three machine learning models, LightGBM, XGBoost, and BPNN, were optimized using ablation experiments and training experiments. By comparing model evaluation indicators and errors, the optimal model for predicting the melting point of nitrate-based energetic materials was obtained. S4. converting the newly designed nitrate-based energetic material I into the corresponding custom molecular descriptor set I, and using the custom molecular descriptor set I as the input of the predictive machine learning model to obtain an output value of the melting point Tm; Wherein, in S2, the custom molecular descriptor set includes: RDKit molecular descriptors that can be directly converted from SMILES characters, and custom molecular descriptors obtained through molecular structure and performance analysis.

2. The method for predicting the melting point of a nitrate-based fused-cast explosive according to claim 1, wherein: In S1, the molecules in the dataset contain various types of molecular skeletons and various types of substituents, and there are 48 melting point data in the dataset samples distributed between -40°C and 154°C, and most of the melting point values ​​in the samples are distributed between 60°C and 120°C.

3. The method for predicting the melting point of a nitrate-based fused-cast explosive according to claim 1, wherein: In S2, the RDKit molecular descriptor includes: calculation of the similarity of properties at a certain distance from each atom, molar refractive index of the unified vector of burdened charge, the maximum part of the charge on a single atom in the molecule, the minimum part of the charge carried by a single atom in the molecule, the unified vector of burdened charge, the maximum absolute value of the partial charge of an atom in the molecule, the minimum absolute value of the partial charge of an atom in the molecule, the Wildman-Crippen logarithm, the lowest E-state index of all atoms in the molecule, the highest E-state index of all atoms in the molecule, calculation of the weighted sum of ADS mapping properties, topological polar surface area, topological index for quantifying molecular complexity, number of hydrogen bond acceptors, number of hydrogen bond donors; The custom molecular descriptors include: ring structure parameters, number of nitrate groups, average distance between nitrate groups in the molecular structure, short path distance between nitrate groups and other groups, molecular structure symmetry parameters, molecular mass, carbon mass fraction, hydrogen mass fraction, oxygen mass fraction, nitrogen mass fraction, and oxygen balance.

4. The method for predicting the melting point of a nitrate-based fused-cast explosive according to claim 3, wherein: The calculation rules for each descriptor in the custom molecular descriptor are as follows: The ring structure parameter is obtained by counting the non-conjugated rings in the molecular structure as 1 and the conjugated rings as 1.5, and then accumulating them; The number of nitrate groups was obtained by counting the number of nitrate groups in the molecular structure; The average distance between nitrate groups in the molecular structure is calculated by counting the total number of chemical bonds contained in the shortest connection path between each nitrate group and other nitrate groups along the molecular skeleton, summing up the total number of chemical bonds and taking the average value to obtain the average distance between a single nitrate group and other nitrate groups, and then taking the average value of the sum of the average distances; The distance of the short path between the nitrate group and other groups is obtained by counting the number of chemical bonds in the short path between the nitrate group and other groups; The molecular structure symmetry parameter is obtained by the following rule: if the molecular structure is centrosymmetric and axisymmetric, it is recorded as 2; if the molecular structure is centrosymmetric or axisymmetric, it is recorded as 1; if the molecular structure is neither centrosymmetric nor axisymmetric, it is recorded as 0; The oxygen balance OB is obtained by the following formula: In the above formula, C, H, O, and N are the number of carbon, hydrogen, oxygen, and nitrogen atoms, respectively.

5. The method for predicting the melting point of a nitrate-based fused-cast explosive according to claim 1, wherein: In S2, the training set and test set are constructed as follows: S20. For each sample in the dataset, the corresponding chemical structure was drawn using a structural formula drawing software, and the SMILES characters corresponding to the chemical structure were exported. The SMILES characters were converted using the Python rdkit library to obtain 15 RDKit molecular descriptors. According to the calculation rules of each descriptor in the custom molecular descriptor, 11 custom molecular descriptors corresponding to the sample were obtained. S21. Divide the custom molecular descriptor set and its corresponding performance data into a training set and a test set in a ratio of 4:1 using a random partitioning code.

6. The method for predicting the melting point of a nitrate-based fused-cast explosive according to claim 1, wherein: In S3, the evaluation indicators and errors include: The coefficient of determination was used to determine the degree of fit; The mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE) are used to quantify the gap between the experimental value and the predicted value.

7. The method for predicting the melting point of a nitrate-based fused-cast explosive according to claim 1, wherein: In S3, methods for optimizing three machine learning models include: S30. Use LightGBM, XGBoost, and BPNN machine learning algorithms to build prediction models, and conduct ablation experiments on the LightGBM model and BPNN model respectively; S31. Perform constrained optimization on the operating parameters of the three models: LightGBM, XGBoost, and BPNN.

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