Method for predicting the properties of a graft polypropylene for high voltage power cables

Abstract

The application belongs to the field of organic polymers, and particularly discloses a method for predicting the performance of grafted polypropylene for high-voltage power cables. In the method, a performance prediction model of the grafted polypropylene is constructed based on a multilayer perception model and a random forest model, which solves the problem that traditional machine learning models mainly rely on a large amount of data and are not suitable for small data sets. The relationship between the graft structure and the mechanical performance is quantitatively established from experimental data, the required data amount is small, the data is easy to obtain, and the prediction accuracy is high, thereby providing a reliable graft group for the grafted polypropylene material for high-voltage power cables.

Description

Technical Field

[0001] This invention belongs to the field of organic polymers, and specifically relates to a method for predicting the performance of grafted polypropylene for high-voltage power cables. Background Technology

[0002] Cross-linked polyethylene (XLPE) is commonly used as insulation material in high-voltage power cables (cables with rated voltages greater than or equal to 6kV and less than 500kV in power systems). However, the numerous byproducts generated during XLPE production degrade its electrical performance. Compared to XLPE, polypropylene (PP) possesses high-temperature resistance and excellent electrical properties, and is gradually replacing XLPE. Its recyclability and environmental friendliness have led to its application in high-voltage power cables. However, in terms of mechanical properties, the introduction of methyl side groups in PP makes it less flexible than polyethylene. In applications requiring bending, such as passing through grounding interfaces, PP cables are more difficult to bend. Traditionally, doping the PP matrix with elastomers softens the composite material, but the introduction of elastomers increases the risk of interfacial separation and leads to a decrease in electrical performance. Chemical grafting can improve the mechanical properties of PP by introducing polar side groups onto the side chains, altering the molecular structure and free volume. Simultaneously, the polar side chain groups can adsorb charge carriers, forming deep traps at the interface between the PP and the grafted groups, thereby improving the electrical properties of the PP material.

[0003] Chemically grafted polypropylene (CPPP) modification is still in its early stages. Limited by practical costs, experimental conditions, and the complexity of chemical grafting groups, it is difficult to obtain large-scale mechanical property data for grafted polypropylene materials in the short term. Research indicates that machine learning models can provide relatively quick and low-cost predictions with a degree of reliability to guide practical research and applications. The constructed machine model is crucial for predictive calculations; however, currently, traditionally constructed machine models suffer from drawbacks such as large data requirements and low reliability of prediction results, making them unsuitable for direct application in the study of the mechanical properties of chemically grafted polypropylene. Summary of the Invention

[0004] To address the shortcomings of the aforementioned machine learning models, such as large data requirements and low reliability of prediction results, this invention provides a method for predicting the performance of grafted polypropylene for high-voltage power cables.

[0005] To achieve the above objectives, the following technical solutions are specifically included:

[0006] A method for predicting the performance of grafted polypropylene for high-voltage power cables includes the following steps:

[0007] (1) Obtain the dataset, which includes multiple sample data, each of which includes at least one of the following: molecular property information, atomic property information, and performance parameters of grafted polypropylene;

[0008] (2) Based on the dataset, the glass transition temperature is first used as sample data to input the multilayer perceptron model for pre-training. After the pre-training is completed, the parameters of all hidden layers in the multilayer perceptron model are frozen, and the last layer of the multilayer perceptron model is replaced by a random forest model to construct a prediction model for the mechanical properties of grafted polypropylene. Then, based on the dataset, the prediction model for the mechanical properties of grafted polypropylene is used for transfer training to obtain the predicted mechanical property values ​​of grafted polypropylene.

[0009] In the multilayer perceptron model, ReLU activation function and squared loss function are used for optimization, and Dropout function is used to avoid overfitting.

[0010] In one embodiment, the grafted polypropylene is prepared by initiating a grafting reaction between monomers and polypropylene under heating conditions using an initiator. The monomers include at least one of styrene, vinyltriethoxysilane, glycidyl methacrylate, vinylpyridine, vinylcarbazole, styrene-maleic anhydride, methyl methacrylate, N-vinylpyrrolidone, methyl acrylate-acrylic acid, vinyl acetate, vinyltriethoxysilane, maleic anhydride, and vinylimidazole.

[0011] In one embodiment, the chemical structural fragments of the monomer splitting include at least one of the following chemical structural formulas:

[0012]

[0013] In one embodiment, the multilayer perceptron model includes a neural network input layer, an output layer, a hidden layer, and a number of neurons in the hidden layer. The number of hidden layers is 4, and the dimensions are 300, 50, 20, and 4, respectively.

[0014] In one embodiment, the properties of the grafted polypropylene include at least one of heat distortion temperature, flexural modulus, room temperature impact strength, and flexural strength.

[0015] In one embodiment, during the pre-training and transfer training, 80% of the dataset is used as the training set and 20% is used as the test set.

[0016] In one embodiment, the transfer training employs a k-fold method to increase the number of training sets, wherein k = 5 in the k-fold method.

[0017] In one embodiment, the sample data includes dielectric constant, band gap, CBM level, VBM level, mass density, glass transition temperature, melting temperature, and molecular or atomic descriptors; the molecular or atomic descriptors are written in Python.

[0018] In one embodiment, the molecular or atomic descriptor includes the average atomic mass, heavy atom density, density of NH functional groups, density of OH functional groups, hydrogen bond acceptor density, hydrogen bond donor density, heteroatom density, valence electron density, amine bond density, ring density, ring structure density, rotatable bond density, density of sp3 hybridized carbon atoms, density of sp2 hybridized carbon atoms, density of sp hybridized carbon atoms, bridgehead atom density, spiro atom density, and Labut of the polymer monomer. ASA descriptor, MOE-like descriptor described using partial charge and surface area, MOE-like descriptor described using MR and surface area, MOE-like descriptor described using LogP and surface area, hybrid EState-VSA descriptor, molecular weight of polymer monomers, Chi index of polymer monomers, HallKierAlpha descriptor describing molecular topology, topological polar surface area of ​​molecules, MolLogP descriptor of polymer monomer molecules, Kappa shape index of polymer monomer molecules, BalabanJ descriptor of polymer monomer molecules, a topological index quantifying the "complexity" of monomer molecules, Ipc descriptor describing the topological information of monomer molecules, descriptor describing the flexibility of monomer molecules, proportion of main chain atoms to total atoms in a polymer, ratio of shortest distance between polymer branches to main chain length, density of structural fragments in polymers and main chains from the MACC library, density of structural fragments in polymers and main chains from the Morgan library, density of structural fragments in polymers and main chains, density of different atoms in polymer main chains, branches, and monomers, at least one of the following:

[0019] In one embodiment, the Shapley coefficient is used to evaluate the contribution of functional groups in grafted polypropylene to the flexural modulus, with the density of functional groups in grafted polypropylene as the input to the prediction model of the mechanical properties of grafted polypropylene and the flexural modulus of grafted polypropylene as the output of the prediction model of the mechanical properties of grafted polypropylene.

[0020] In one embodiment, sample data of CBM, VBM energy levels, and charge traps of grafted polypropylene and pure polypropylene are used as a dataset. The data is input into the prediction model of the mechanical properties of the grafted polypropylene, the flexural modulus is output, and the correlation between charge trap depth and flexural modulus and chemical structural fragments of grafted polypropylene is determined.

[0021] In one embodiment, the chemical structural fragments of the grafted polypropylene include at least one of the following chemical structural formulas:

[0022]

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] (1) It solves the problem that traditional machine learning models mainly rely on a large amount of data and are not suitable for small datasets;

[0025] (2) The relationship between grafting structure and mechanical properties was quantitatively established from experimental data. The mechanical properties of grafted polypropylene insulation material system were analyzed by applying transfer learning model. The required amount of data is small, the data is easy to obtain, and the prediction accuracy is high. This provides a reliable grafting group for polypropylene materials in high voltage cables.

[0026] (3) Establish the correlation between glass transition temperature and mechanical properties of polypropylene, and consider the existence of traps separately. Combine the influence of trap depth and use the prediction model of this invention to screen graft structures that are soft and have a deep trap level in a confined chemical space; divide the grafted side chain structure into segments. Attached Figure Description

[0027] Figure 1 A flowchart illustrating the method for predicting the properties of grafted polypropylene.

[0028] Figure 2 This is a schematic diagram illustrating the grafting reaction principle of grafted polypropylene.

[0029] Figure 3 The flexural modulus distributions of five types of grafted polypropylene are shown.

[0030] Figure 4 This is a schematic diagram of an MLP model.

[0031] Figure 5 This is a schematic diagram of MLP model pre-training.

[0032] Figure 6 This is a schematic diagram showing the relationship between the predicted glass transition temperature and the measured flexural modulus.

[0033] Figure 7 This is a schematic diagram of the transfer learning prediction model of the present invention.

[0034] Figure 8 The correlation coefficient R for the test set is 0.834, which is the predicted result for the glass transition temperature Tg.

[0035] Figure 9 The predicted results are for (a) heat distortion temperature, (b) flexural modulus, (c) room temperature impact strength, and (d) flexural strength.

[0036] Figure 10 It consists of nine structural fragments separated from a single entity.

[0037] Figure 11 The selected structural fragments are characterized by low bending modules and high charge trap depth values. Detailed Implementation

[0038] To better illustrate the purpose, technical solution, and advantages of this invention, specific embodiments will be used to further explain the invention below. Unless otherwise specified, the test methods used in the embodiments and / or comparative examples are conventional methods; the materials and reagents used, unless otherwise specified, are commercially available.

[0039] Example 1

[0040] A method for predicting the performance of grafted polypropylene for high-voltage power cables, the flowchart of which is shown below. Figure 1 As shown, it includes the following steps:

[0041] (1) The experimental test dataset was obtained as follows:

[0042] Grafted polypropylene was prepared by a grafting reaction between a certain monomer and polypropylene, initiated by benzoyl peroxide at a temperature of 100°C.

[0043] The monomers include styrene, vinyltriethoxysilane, glycidyl methacrylate, vinylpyridine, vinylcarbazole, styrene-maleic anhydride, methyl methacrylate, N-vinylpyrrolidone, methyl acrylate-acrylic acid, vinyl acetate, vinyltriethoxysilane, maleic anhydride, and vinylimidazole, totaling 11 types. Different monomers contain different functional groups and functional group densities, molecular structures, and the main chain atomic arrangement and branch chain atomic arrangement of the molecular chain. The chemical structure of each monomer is shown in Table 1.

[0044] Table 1

[0045]

[0046]

[0047] Each monomer was reacted with polypropylene and an initiator, and each monomer was used to prepare grafted polypropylene with a monomer volume fraction of 2% and 5%, respectively, resulting in a total of 22 kinds of grafted polypropylene.

[0048] The principle of polypropylene grafting reaction: In the grafting reaction, the initiator benzoyl peroxide (BPO) first decomposes upon heating to form primary free radicals. These primary free radicals have strong chemical reactivity and can capture tertiary hydrogen atoms on the polypropylene (PP) molecular chain. The BPO initiator forms active sites on the PP backbone, generating PP macromolecular free radicals. The carbon-carbon double bonds in the grafting monomer undergo an additional reaction with the PP macromolecular free radicals, grafting them onto the PP molecular chain, such as... Figure 2 As shown in the figure, R represents a monomeric group.

[0049] The heat distortion temperature, flexural modulus, room temperature impact strength, and flexural strength of the 22 grafted polypropylene and pure polypropylene materials prepared above were tested, and a total of 23 sets of test data were collected as the experimental test dataset of this embodiment. The test conditions were the same for different materials. Among them, the mechanical properties were tested using an MTS CMT4304 microcomputer-controlled electronic universal testing machine. Dumbbell-shaped tensile test samples were obtained using a punching machine. Tensile tests were conducted at room temperature at a tensile rate of 20 mm / min until the sample broke, and the flexural strength and elongation at break of the sample were obtained. Due to the dispersion of tensile test results, each sample was tested five times, and the average value was calculated based on these tests.

[0050] Appendix Figure 3 The flexural modulus of five different polypropylene grafted structures is shown. It can be seen that the flexural modulus of the system changes significantly with the introduction of graft groups. Among them, the polypropylene material grafted with vinyltriethoxysilane exhibits the best flexibility, while the flexibility of other structures with polar graft groups shows a decreasing trend.

[0051] Because the silicon-oxygen bond (-Si-O-) is relatively long and rotatable, grafting vinyltriethoxysilane reduces the flexural modulus of the structure compared to pure polypropylene. Simultaneously, the polar groups in the side chains, such as styrene, glycidyl methacrylate, vinylpyridine, and vinyl acetate, increase the internal rotation activation energy and intermolecular forces. This increased resistance to internal rotation leads to increased stiffness in the grafted polypropylene structure, making it more difficult to bend.

[0052] However, it should be noted that since grafted polypropylene polymers are essentially mixtures and not perfectly structured grafted monomers, the grafted segments may copolymerize. Therefore, compared to pure polymers, the grafted groups have a smaller impact on the mechanical properties of the grafted polypropylene system. Nevertheless, since all samples are within grafted polypropylene systems, the data can be compared.

[0053] Meanwhile, since the grafted polypropylene side-group structures used for model training in this embodiment (i.e., obtained by monomer grafting) contain only a small number of structural fragments, representing only a tiny fraction of the common functional groups in the entire chemical space, the limited number of structural fragment types makes it difficult to directly apply the established fast prediction model to a larger chemical space. To avoid blindly generalizing the results / experiences trained on a small dataset to a larger chemical space and to avoid potential prediction pitfalls, the grafted structures in the test dataset were broken down into nine common structural fragments (see attached diagram). Figure 10 ), attached Figure 10The image shows nine structural fragments that have been broken down. Since these chemical structural fragments all come from a small dataset used to gain experience, these fragments are spliced ​​together to form the final chemical spatial structure of the grafted polypropylene used for prediction.

[0054] (2) Construct a prediction model for the mechanical properties of grafted polypropylene. The prediction model for the mechanical properties of grafted polypropylene includes a multilayer perceptron (MLP) model and a random forest model. Based on the experimental test dataset in step (1) and the dataset collected in step (2-1), the dataset is used as the dataset for the prediction model. The dataset is converted into a language that can be computed and input into the prediction model for pre-training and transfer training. The mechanical property value of grafted polypropylene with a specific chemical structure is output.

[0055] Specifically, the steps include the following:

[0056] (2-1) Collect the dataset:

[0057] The collected dataset is shown in Table 2. The four parameters related to grafted polypropylene—dielectric constant, band gap, CBM level, and VBM level—were calculated, and the data were sourced from the Khazana database and high-throughput computing. The laboratory-characterized mass density, glass transition temperature, and melting temperature data were primarily obtained from the PolyInfo database. In selecting experimental performance data from the database, for performance data of different polypropylene material configurations (e.g., isotactic, syndiotactic, and atactic configurations), the selection criterion was to choose the most common and widely used structural performance parameters. Furthermore, since various measurement methods can be used to obtain the glass transition temperature and melting temperature performance data of polypropylene materials, data obtained using conventional measurement methods were selected from the dataset. Additionally, some obviously unconventional parameter performance values ​​were manually removed from the dataset.

[0058] Table 2. Types and Number of Datasets

[0059] Parameter performance Data volume Data source Dielectric constant (calculation) 385 Khazana+ High Flow Band gap (calculation) 1209 Khazana+ High Flow CBM level (calculated) 373 Khazana+ High Flow VBM level (calculated) 373 Khazana+ High Flow Mass density (experimental) 174 PolyInfo Glass transition temperature (experimental) 2988 PolyInfo Melting temperature (experimental) 529 PolyInfo

[0060] Obtaining descriptors for grafted polypropylene: The fingerprint database for grafted polypropylene contains two parts of descriptors. One part consists of polypropylene descriptors evolved from traditional organic small molecule fingerprint descriptors, containing the density of different structural unit fragments within polypropylene. These structural unit fragments are mainly collected from publicly available MACCS public keys and Morgan; this part also includes some traditional molecular fingerprint feature descriptors, such as BalabanJ and TPSA. The other part consists of descriptors representing fingerprint features specifically targeting the unique characteristics of polypropylene, such as main chain length, longest branch length, maximum distance between branches, and density of structural unit fragments within the main chain. These two parts of descriptors together construct a fingerprint feature library for polypropylene structures, totaling 812 sets of descriptors. Some fingerprint feature descriptors are shown in Table 3. Based on the characteristics of grafted polypropylene, it is "encoded," and various chemical structures related to grafted polypropylene are compiled into symbols capable of computation, forming a fingerprint spectrum dataset for grafted polypropylene. In this embodiment, the fingerprint feature descriptor extraction program uses Python, and most fingerprint feature descriptors are extracted using the Python extension package RDkit.

[0061] Based on the collected grafted polypropylene fingerprint database (chemical structure information) and parameter properties, the chemical structure of grafted polypropylene can be constructed, and the correlation between the four parameter properties related to grafted polypropylene—dielectric constant, band gap, CBM level, and VBM level—can be established. Once a grafted polypropylene or its structural fragments with a specific chemical structure are determined, its specific parameter properties can be identified.

[0062] Chemical structure, related dielectric constant, band gap, CBM level, and VBM level are all characteristic parameters of the macroscopic mechanical properties of materials. Based on these characteristic parameters, the mechanical properties of a substance with a certain chemical structure can be predicted.

[0063] Table 3

[0064]

[0065]

[0066] (2-2) Pre-training before transfer learning:

[0067] In machine learning models, transfer learning improves learning in new tasks by transferring knowledge from related tasks that have already been completed. It can be trained on the basis of an already completed training model to achieve rapid convergence. Therefore, in order to construct the transfer learning method of this invention, it is necessary to select performance parameters related to the mechanical properties of grafted polypropylene as pre-training performance parameters.

[0068] The glass transition refers to the transition between the glassy and elastic states of amorphous polymers. Glass transition can also occur in the amorphous regions of crystalline or semi-crystalline polymers, significantly impacting polymer properties, especially mechanical properties. The temperature at which the glass transition occurs is called the glass transition temperature, a characteristic temperature of the polymer. The glass transition temperature is closely related to the flexibility of the polymer chain segments. Generally, the more flexible the polymer, the lower the glass transition temperature; conversely, the greater the rigidity of the chain segments, the higher the glass transition temperature. Therefore, based on the relationship between glass transition temperature and mechanical properties, this embodiment selects glass transition temperature performance (with abundant data) as a performance parameter related to the mechanical properties of grafted polypropylene. Pre-training is performed using transfer learning, and then transfer training is conducted on mechanical properties (with less data) based on the trained glass transition temperature prediction model. This reflects the reliability of the selected trained glass transition temperature model.

[0069] Construct a pre-trained model of glass transition temperature performance:

[0070] An MLP neural network model was used as the pre-trained model for glass transition temperature performance. This MLP includes an input layer, an output layer, hidden layers, and the number of neurons in the hidden layers. The hidden layers consist of four layers with dimensions of 300, 50, 20, and 4, respectively. The model employs the ReLU activation function and the squared loss function (Loss). i Optimize by using the Dropout function to avoid overfitting:

[0071] (a) MLP model

[0072] The MLP model can be considered a generalized linear model, as illustrated in the attached diagram. Figure 4 As shown, for the linear model,

[0073] y=w[1]*x[1]+w[2]*x[2]+w[3]*x[3]+b (Formula 1);

[0074] For MLP, x and y represent the input layer and output layer, respectively, w is the weight, b is the bias, and an additional h module is added between x and y, called the hidden layer.

[0075] The relationship between y, h, and x is:

[0076] h[1]=f(w[1,1]x[1]+w[2,1]x[2]+w[3,1]x[3]+b[0]) (Formula 2);

[0077] h[2]=f(w[1,2]x[1]+w[2,2]x[2]+w[3,2]x[3]+b[1]) (Formula 3);

[0078] y=v[1]h[1]+v[2]h[2]+s (Formula 4);

[0079] Where f(·) is a nonlinear function called the activation function;

[0080] This model uses the ReLU activation function: Where f(x) is the ReLU function and x is the input value of the hidden layer neuron;

[0081] In this embodiment, the input layer, output layer, hidden layer, and number of neurons in the hidden layer of the MLP neural network are determined. There are 4 hidden layers, and the number of neurons in each hidden layer is 300, 50, 20, and 4, respectively.

[0082] (2) Construct the squared loss function:

[0083] To minimize the prediction error of the MLP for a given sample, the error can be defined as follows: The above equation becomes

[0084] Loss = [y - (v1f(w)] 11 x1+w 21 x2+w 31 x3+b0)+v2f(w 12 x1+w 22 x2+w 32 x3+b1)+s)] 2 (Equation 7);

[0085] If there are N samples in the training set, then the error of each sample needs to be summed and minimized: In the above equation, the variables to be optimized are v, w, b, and s, and since it is an unconstrained problem, it can be solved using gradient-based algorithms. Classic gradient-based algorithms include: steepest descent, Newton's method, and quasi-Newton methods. Driven by the need to improve training efficiency, algorithms like steepest descent, which only require a first-order gradient, are generally chosen as the basic algorithm.

[0086] Before calculating, we need to clarify that the gradient here refers to the gradient of the loss function Loss with respect to the optimization variables v, w, b, and s. Let's take the gradient of Loss with respect to w as an example to illustrate the solution process. Using the same MLP example, and writing the expression in matrix form:

[0087]

[0088] According to the chain rule for differentiation:

[0089]

[0090] This is what we often call: error backpropagation. Here, it can be understood as the gradient calculation process being derived step by step from back to front.

[0091] The above describes the gradient calculation process for a single sample. To obtain accurate gradient values, this process needs to be repeated for every single sample. If our training sample size is large, the gradient calculation process will be very slow. If we approach it differently, calculating the gradient value for only one sample at a time and using that value as the final gradient value, the result is that the gradient calculation process is fast, but the value is not very accurate. Therefore, we should select a subset of samples each time, calculate their gradient values, and use this as the overall gradient value. By adjusting the number of samples, we can balance computational efficiency and accuracy.

[0092] Having established the gradient, let's review the basic iterative formulas for gradient-based algorithms:

[0093] θ k+1 =θ k -η k ·d k (Equation 13);

[0094] Where θ represents the optimization variable, η k and d k These are the iteration step size (more commonly referred to as the "learning rate" in MLP) and the iteration direction, respectively.

[0095] The basic formula for the steepest descent method is:

[0096]

[0097] (3) Dropout function formula:

[0098]

[0099] Where z represents the input vector; l represents the layer number; y represents the output vector; W represents the weights; b represents the bias; f represents the activation function; and r represents the value after Bernoulli distribution.

[0100] (b) Pre-training:

[0101] Based on the glass transition temperature sample data from the dataset obtained in step (2-1) above and the grafted polypropylene fingerprint database (chemical structure fragments) that can determine chemical structure information, the dataset fingerprint recognition is converted into a computational language input for pre-training of a pre-built MLP model. The output value is the glass transition temperature of a grafted polypropylene with a certain chemical structure. 80% of the dataset is used as the training set and 20% is used as the test set. Based on the pre-training results, the predicted glass transition temperature of a grafted polypropylene composed of chemical structure fragments can be determined. Therefore, based on the pre-training results, the predicted glass transition temperature corresponding to pure PP and the grafted polypropylene structure formed after monomer grafting can be obtained. This predicted glass transition temperature is used as the x-axis data, and the flexural modulus of the grafted polypropylene measured in step (1) above is used as the y-axis data. The results are shown in the appendix. Figure 6 As shown.

[0102] For linear polar graft groups (such as VP, VAC, GMA, etc.), the flexural modulus of the grafted polypropylene structure increases with the predicted glass transition temperature, meaning the grafted system becomes more rigid. Meanwhile, cyclic structures in the grafted structure (such as VK, NVP, etc.) lead to an increase in glass transition temperature but a decrease in flexural modulus, making the system more flexible. This may be related to the increased free volume of the cyclic structure. Therefore, it can be concluded that the mechanical properties, glass transition temperature, and chemical structure of grafted polypropylene are correlated.

[0103] (c) Training with a small amount of mechanical performance data:

[0104] After the pre-training is completed, the parameters in the hidden layer are frozen (all are frozen), and the last layer of the model is replaced with a random forest layer. The MLP consists of an input layer, hidden layers, and an output layer, with the last layer being the output layer. Therefore, the output layer is replaced with a random forest layer, and the final output layer is the output of the random forest model, which is then used as the model for transfer learning training.

[0105] Based on the experimental test dataset (mechanical properties) and the dataset (chemical structure information) collected in step (2-1) as the overall transfer learning dataset, the dataset fingerprints are converted into a computational language and input into the transfer learning training model. The output value is the mechanical properties of grafted polypropylene with a specific chemical structure. 80% of the dataset is used as the training set, and 20% is used as the test set. During training, the k-fold method (k=5) is used to increase the number of training parameters. In addition, a 10% random parameter removal process is used during training to avoid overfitting.

[0106] The process model of pre-training and transfer learning training is as follows: Figure 5 and 7 As shown.

[0107] Based on the results of transfer training, the predicted mechanical properties of a grafted polypropylene composed of chemical structure fragments can be determined.

[0108] Regarding the relationship between the k-fold method and random forest models: Machine learning methods often cannot directly model data because they learn specific features from the training set that are not present in the test set. Since a model's fair performance is correlated with its training and test sets, simply splitting the data into training and test sets does not truly reveal the model's performance. Therefore, a common approach is to divide the dataset into k parts: k-1 parts for training and one for validation / testing. This would allow us to divide the dataset into 5 folds, with 4 folds used for training the model and the remaining folds used for evaluating its performance. However, this partitioning requires changing the fold position used for evaluation each time, repeating this process 5 times.

[0109] The final output of the Random Forest (RF) prediction model: f(x) is the predicted output value, M is the number of trees in the Random Forest (RF) prediction model, and fm(x) is the prediction result of the m-th decision tree. In the prediction model of this invention, different input quantities correspond to different output quantities. f(x) can be one of the following: heat distortion temperature, flexural modulus, room temperature impact strength, and flexural strength.

[0110] (d) Predicted mechanical properties of the grafted polypropylene system:

[0111] After training, the data points for glass transition temperature are as follows: Figure 8 As shown in the figure. The correlation coefficient of the test set is 0.834, indicating that the training results have good consistency. The mechanical property parameters involved in the prediction include heat distortion temperature, flexural modulus, impact strength at room temperature, and flexural strength, and the results are shown in the attached figure. Figure 9 The correlation coefficients of the four performance data test sets in the prediction results were 0.78, 0.89, 0.57 and 0.87, respectively. Except for the poor prediction result of the impact strength at room temperature, the prediction accuracy of the other three mechanical performance parameters was relatively high.

[0112] To quantitatively study the impact of different structural fragments on flexural modulus performance, based on the trained transfer learning model, the Shapley coefficients of different chemical structural components were calculated using the density of each functional group as input. This allowed for the analysis of the contribution of different functional group structures as side groups to the flexural modulus. The test results showed that the siloxane and pyrrolidone functional groups had the lowest Shapley coefficients (-0.28 and -0.11 respectively) among the selected structural fragments, indicating that these functional groups contribute to overall flexibility. The highest coefficients were found in pyridine and ester groups, with Shapley coefficients of 0.17 and 0.09 respectively. This is consistent with the experimental results and indirectly confirms the accuracy of the predictive model.

[0113] The Shapley coefficient is calculated using the Shapley value method, including:

[0114] When data i participates in set S, there are (|S|-1)! sorting possibilities, where |S| represents the number of data points in set S. The remaining (n-|S|) data points have (n-|S|)! sorting possibilities. The weight of the benefit that data i should receive from the set as a whole is the sum of all the different sorting combinations that data i participates in, divided by the random sorting combinations of the n data points. This weight is denoted as [(|S|-1)! (n-|S|)! ] / (n!).

[0115] If data i participates in different sets S as a form of data optimization, denoted as [v(S)-v(S\{i})], then the benefit that data i receives from optimizing the overall v(N) is:

[0116]

[0117] In the formula, S{i} represents the set after deleting element i from set S. Shapley coefficient;

[0118] When functional group density is used as input and flexural modulus as output, the Shapley coefficients for siloxane bonds and pyrrolidone functional groups are -0.28 and -0.11, respectively, and the Shapley coefficients for pyridine functional groups and ester bonds are 0.17 and 0.09, respectively. This indicates that siloxane bonds and pyrrolidone functional groups can improve the flexibility of grafted polypropylene, while pyridine functional groups and ester bonds can reduce its flexibility.

[0119] The predicted chemical spatial structure of the grafted polypropylene, as described above, is shown in the appendix. Figure 10In this study, CBM (conduction band minimum) / VBM level (electron / hole carrier trap) datasets of grafted polypropylene and pure polypropylene materials were selected, combined with the charge trap dataset, and input into the above prediction model for prediction. This yielded three sets of structural fragments that are softer than polypropylene structures (low flexural modulus) and have high charge trap depth. Figure 11 As can be seen, the structure of the silicon-oxygen bond provides a flexible foundation, while the pyrrolidone structure also provides a large trap density, which can effectively capture electrons. Therefore, the predictive model of this invention can also accurately predict the ideal chemical spatial structure of grafted polypropylene, which can be used to guide the subsequent synthesis of grafted polypropylene.

[0120] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A method for predicting the performance of grafted polypropylene for high-voltage power cables, characterized in that, Includes the following steps: (1) Obtain the dataset, which includes multiple sample data, each of which includes at least one of the following: molecular property information, atomic property information, and performance parameters of grafted polypropylene; (2) Based on the dataset, the glass transition temperature is first used as sample data to input the multilayer perceptron model for pre-training. After the pre-training is completed, the parameters of all hidden layers in the multilayer perceptron model are frozen, and the last layer of the multilayer perceptron model is replaced by a random forest model to construct a prediction model for the mechanical properties of grafted polypropylene. Then, based on the dataset, the prediction model for the mechanical properties of grafted polypropylene is used for transfer training to obtain the predicted mechanical property values ​​of grafted polypropylene. In the multilayer perceptron model, ReLU activation function and squared loss function are used for optimization, and Dropout function is used to avoid overfitting.

2. The method for predicting the performance of grafted polypropylene for high-voltage power cables as described in claim 1, characterized in that, The grafted polypropylene is prepared by a grafting reaction between monomers and polypropylene under heating conditions using an initiator. The monomers include at least one of styrene, vinyltriethoxysilane, glycidyl methacrylate, vinylpyridine, vinylcarbazole, styrene-maleic anhydride, methyl methacrylate, N-vinylpyrrolidone, methyl acrylate-acrylic acid, vinyl acetate, vinyltriethoxysilane, maleic anhydride, and vinylimidazole.

3. The method for predicting the performance of grafted polypropylene for high-voltage power cables as described in claim 2, characterized in that, The chemical structural fragments of the monomer splitting include at least one of the following chemical structural formulas:

4. The method for predicting the performance of grafted polypropylene for high-voltage power cables as described in claim 1, characterized in that, The multilayer perceptron model includes a neural network input layer, output layer, hidden layer, and the number of neurons in the hidden layer. The number of hidden layers is 4, and the dimensions are 300, 50, 20, and 4, respectively.

5. The method for predicting the performance of grafted polypropylene for high-voltage power cables as described in claim 1, characterized in that, The properties of the grafted polypropylene include at least one of heat distortion temperature, flexural modulus, room temperature impact strength, and flexural strength.

6. The method for predicting the performance of grafted polypropylene for high-voltage power cables as described in claim 1, characterized in that, In the pre-training and transfer training, 80% of the dataset is used as the training set and 20% is used as the test set.

7. The method for predicting the performance of grafted polypropylene for high-voltage power cables as described in claim 1, characterized in that, In the transfer training, the k-fold method is used to increase the number of training sets, where k = 5 in the k-fold method.

8. The method for predicting the performance of grafted polypropylene for high-voltage power cables as described in claim 1, characterized in that, The sample data includes dielectric constant, band gap, CBM level, VBM level, mass density, glass transition temperature, melting temperature, and molecular or atomic descriptors; the molecular or atomic descriptors are written in Python.

9. The method for predicting the performance of grafted polypropylene for high-voltage power cables as described in claim 7, characterized in that, The molecular or atomic descriptors include average atomic mass, heavy atom density, NH functional group density, OH functional group density, hydrogen bond acceptor density, hydrogen bond donor density, heteroatom density, valence electron density, amino bond density, ring density, ring structure density, rotatable bond density, sp3 hybridized carbon atom density, sp2 hybridized carbon atom density, sp hybridized carbon atom density, bridgehead atom density, spiro atom density, and the Labut density of the polymer monomer. ASA descriptor, MOE-like descriptor described using partial charge and surface area, MOE-like descriptor described using MR and surface area, MOE-like descriptor described using LogP and surface area, hybrid EState-VSA descriptor, molecular weight of polymer monomers, Chi index of polymer monomers, HallKierAlpha descriptor describing molecular topology, topological polar surface area of ​​molecules, MolLogP descriptor of polymer monomer molecules, Kappa shape index of polymer monomer molecules, BalabanJ descriptor of polymer monomer molecules, a topological index quantifying the "complexity" of monomer molecules, Ipc descriptor describing the topological information of monomer molecules, descriptor describing the flexibility of monomer molecules, proportion of main chain atoms to total atoms in a polymer, ratio of shortest distance between polymer branches to main chain length, density of structural fragments in polymers and main chains from the MACC library, density of structural fragments in polymers and main chains from the Morgan library, density of structural fragments in polymers and main chains, density of different atoms in polymer main chains, branches, and monomers, at least one of the following:

10. The method for predicting the performance of grafted polypropylene for high-voltage power cables as described in claim 1, characterized in that, Includes at least one of the following A and B: A. Using the density of functional groups in grafted polypropylene as the input to the prediction model of the mechanical properties of grafted polypropylene, and the flexural modulus of grafted polypropylene as the output of the prediction model of the mechanical properties of grafted polypropylene, the Shapley coefficient is then used to evaluate the contribution of functional groups in grafted polypropylene to the flexural modulus. B. Using sample data of CBM, VBM energy levels, and charge traps of grafted polypropylene and pure polypropylene as a dataset, input the data into the prediction model of the mechanical properties of the grafted polypropylene, output the flexural modulus, and determine the correlation between charge trap depth and flexural modulus and chemical structure fragments of grafted polypropylene.

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