A Carbon Nanotube Growth Prediction and Evaluation Model Based on Digital Twin and AI and Its Establishment Method

Abstract

The present invention discloses a carbon nanotube growth prediction and evaluation model based on digital twin and AI and a method for establishing the same, which relates to the field of materials science and engineering technology. It includes: obtaining the growth environment data of carbon nanotubes and establishing a digital twin model; setting at least one AI algorithm to simulate the digital twin model to obtain the predicted data of the growth characteristics of the carbon nanotubes; comparing the deviation rate with a preset deviation rate threshold according to the predicted data of the growth characteristics and the experimental measurement data to determine the existence state of the influencing factors; adjusting the simulation model to obtain the growth characteristic data of the carbon nanotubes. By combining a virtual simulation system driven by real-time data with machine learning algorithms, the present invention realizes the accurate modeling of complex non-linear dynamics in the carbon nanotube growth process, thereby improving the prediction accuracy, reducing the number of physical experiments, reducing costs, and accelerating the R & D cycle.

Description

Technical Field

[0001] The present invention relates to the technical field of materials science and engineering, and specifically to a carbon nanotube growth prediction and evaluation model based on digital twin and AI and a method for establishing the same. Background Technique

[0002] Due to their unique electrical, thermal, and mechanical properties, carbon nanotubes exhibit great application potential in many high-tech fields such as electronic devices, composite materials, and energy storage. However, the synthesis process of carbon nanotubes is complex and affected by multiple factors such as temperature, pressure, catalyst type, and concentration, which makes it extremely challenging to precisely control their structure and properties. Although traditional experimental methods can be used to study the influence of these factors on the growth of carbon nanotubes, they are not only time-consuming and costly but also difficult to comprehensively capture the complex dynamic change process.

[0003] The Chinese invention patent with publication number CN118898206A discloses a data acquisition and processing method and system based on a digital twin platform, including the following steps: S1: The digital twin platform determines the location of the sensor based on the coordinate system and creates a specific model for marking; S2: Real-time collect multi-source data in the actual environment; S3: Preliminarily process the collected data through an edge computing device; S4: Use a preset multi-modal data fusion algorithm for data fusion and enhancement; S5: Dynamically simulate and predict the actual environment; S6: Generate an optimized control instruction; S7: Regularly calibrate the model and adjust the parameters to continuously optimize the accuracy of the digital twin model. By integrating edge computing and multi-modal data fusion technologies, the efficiency and accuracy of data processing are achieved, and at the same time, physical simulation and machine learning are combined to improve the prediction accuracy, significantly enhancing the response speed and decision-making quality of the system.

[0004] In the process of predicting the growth of carbon nanotubes using the above-mentioned and similar processing methods, due to the difficulty of effectively comparing and integrating data between different laboratories, there will be significant quality differences even in the same type of data. And existing prediction and evaluation models often rely on specific experimental conditions and data characteristics, so when facing a new environment or a larger range of data, overfitting is likely to occur, which will further reduce the accuracy of the evaluation and prediction results of the carbon nanotube growth mechanism. Summary of the Invention

[0005] The purpose of the present invention is to provide a carbon nanotube growth prediction and evaluation model based on digital twin and AI and a method for establishing the same to solve the problems raised in the above background technique.

[0006] To achieve the above purpose, the present invention provides the following technical solution: A carbon nanotube growth prediction and evaluation model based on digital twin and AI, including:

[0007] Digital Twin Module: Set up a sensor network to obtain the growth environment data of carbon nanotubes, and establish a multi-scale mathematical model based on the growth environment data. At the same time, establish a digital twin model according to the multi-scale mathematical model;

[0008] Data Acquisition Module: Set at least one AI algorithm to simulate the digital twin model and obtain the predicted data of the growth characteristics of carbon nanotubes;

[0009] Data Comparison Module: Obtain the deviation rate based on the predicted data of the growth characteristics and the experimental measurement data, compare the deviation rate with the preset deviation rate threshold, and determine the existence status of the influencing factors according to the comparison result;

[0010] Prediction and Evaluation Module: Adjust the simulation model according to the existence status of the influencing factors, and obtain the growth characteristic data of the carbon nanotubes based on the adjusted simulation model, including:

[0011] SF1: Determine the influencing factors: Determine whether to adjust the simulation model according to the existence status of the influencing factors. Specifically:

[0012] When the influencing factors exist, adjust the temperature, catalyst type, and gas composition one by one to determine the influencing factors. At the same time, adjust the simulation model according to the influencing factors. The adjusted simulation model is the final simulation model. Otherwise, the simulation model is not adjusted and is the final simulation model;

[0013] SF2: Obtain the prediction result: Predict the growth state of the carbon nanotubes based on the final simulation model.

[0014] Furthermore, establish a multi-scale mathematical model, including:

[0015] SA1: Establish an atomic-level model: Obtain key parameters through molecular dynamics and transmit the key parameters to the mesoscopic scale model. The acquisition formula of the key parameters is specifically:

[0016] , where: is the diffusion coefficient, is the reaction rate constant, is the pre-exponential factor, is the diffusion activation energy, is the ideal gas constant, is the absolute temperature, is the frequency factor, is the activation energy;

[0017] SA2: Establish a mesoscopic scale model: According to the key parameters and the phase field equation, obtain the spatial distribution of the reaction products, specifically:

[0018] , where: is the substance concentration, is the mobility, is the chemical potential, is the source term, is the divergence operator, is the time;

[0019] SA3: Establish a macroscopic scale model: According to the spatial distribution of the reaction products, construct the continuity equation and the energy balance equation, specifically:

[0020] , where: is the divergence operator, is the density, is the velocity vector, is the time, is the source term, is the specific heat capacity, is the absolute temperature, is the thermal conductivity, is the internal heat source term.

[0021] Furthermore, simulate the growth environment of the carbon nanotubes, including:

[0022] SB1: Construct a digital twin architecture: Define the digital twin components and establish two-way communication between the defined digital twin components;

[0023] SB2: Integrate the multi-scale mathematical models: Integrate the atomic scale model, the mesoscopic scale model and the macroscopic scale model to obtain the integrated multi-scale mathematical model, and at the same time combine the integrated multi-scale mathematical model with the defined digital twin components;

[0024] SB3: Implement the simulation: According to the digital twin architecture and the multi-scale mathematical model, conduct the simulation of the carbon nanotube growth environment.

[0025] Furthermore, obtain the prediction data of the growth characteristics of the carbon nanotubes, including:

[0026] SC1: Conduct simulation through machine learning: Establish the mapping relationship between the input parameters and the output characteristics through machine learning algorithms to obtain the first growth characteristic prediction data of the carbon nanotubes;

[0027] SC2: Simulation via deep learning: Process spatio-temporal data through a neural network, and based on the processed data, obtain the predicted data of the second growth characteristics of the carbon nanotubes;

[0028] SC3: Simulation via support vector machine: Model classification problems through a support vector machine, and based on the modeled support vector machine model, obtain the predicted data of the third growth characteristics of the carbon nanotubes;

[0029] SC4: Obtain predicted data: Based on the predicted data of the first growth characteristics, the predicted data of the second growth characteristics, and the predicted data of the third growth characteristics, determine the final predicted data of the growth characteristics of the carbon nanotubes, specifically:

[0030] , where: is the final predicted data of the growth characteristics, is the predicted data of the first growth characteristics, is the predicted data of the second growth characteristics, is the predicted data of the third growth characteristics, , , are weight coefficients.

[0031] Furthermore, the formula for obtaining the weight coefficients is specifically:

[0032] , where: is the i-th weight coefficient, is the cross-validation score of the i-th model, is the cross-validation score of the j-th model, is an index variable.

[0033] Furthermore, determining the existence status of influencing factors includes:

[0034] SD1: Determine the preset deviation rate threshold: Based on the predicted data of the growth characteristics and the experimental measurement data, obtain statistical indicators, and based on the statistical indicators, determine the preset deviation rate threshold;

[0035] SD2: Determine influencing factors: Compare the preset deviation rate threshold with the deviation rate, and based on the comparison result, determine the existence status of the influencing factors, specifically:

[0036] When the deviation rate is not less than the prediction threshold, then the influencing factor does not exist, otherwise the influencing factor exists.

[0037] Furthermore, determining the preset deviation rate threshold includes:

[0038] SE1: Obtain the data distribution: Based on the predicted data of the growth characteristics and the experimentally measured data, obtain statistical indicators, draw a histogram, and based on the statistical indicators and the histogram, obtain the prediction deviation range.

[0039] SE2: Set the prediction threshold: Based on the prediction deviation range, set a preset deviation rate threshold.

[0040] A method for establishing a carbon nanotube growth prediction and evaluation model based on digital twin and AI, which uses the above-mentioned carbon nanotube growth prediction and evaluation model based on digital twin and AI.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] First: By combining a real-time data-driven virtual simulation system with a machine learning algorithm, the present invention realizes the accurate modeling of complex non-linear dynamics in the carbon nanotube growth process, thereby improving the prediction accuracy, reducing the number of physical experiments, lowering the cost, and accelerating the R & D cycle.

[0043] Second: Through the digital twin technology, the present invention enables users to intuitively observe every detail change in the carbon nanotube growth process, thereby facilitating the timely adjustment of process parameters to ensure the consistency of product quality. Brief Description of the Drawings

[0044] Figure 1 It is a schematic flow chart of the carbon nanotube growth prediction and evaluation model of the present invention;

[0045] Figure 2 It is a schematic flow chart of obtaining the growth characteristic prediction data in the present invention;

[0046] Figure 3 It is a schematic flow chart of obtaining the existence state of influencing factors in the present invention;

[0047] Figure 4 It is a histogram between the diameter and the absolute percentage error in the present invention. Detailed Embodiments

[0048] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0049] In the process of predicting the growth of carbon nanotubes by existing processing methods, due to the difficulty of effectively comparing and integrating data between different laboratories, there will be significant quality differences even in the same type of data. Existing prediction evaluation models often rely on specific experimental conditions and data characteristics, so when facing new environments or larger-scale data, overfitting is likely to occur, which will reduce the accuracy of the evaluation and prediction results of the carbon nanotube growth mechanism. The technical solution of this application improves product quality and reduces production costs by constructing a virtual simulation system tightly coupled with the actual production environment and analyzing operation data through machine learning algorithms to identify key parameters affecting the growth of carbon nanotubes and establishing a corresponding simulation model to predict the growth behavior of carbon nanotubes.

[0050] Reference Figures 1 - 4 , this embodiment provides a carbon nanotube growth prediction and evaluation model based on digital twin and AI. The prediction and evaluation model includes a digital twin module, a data acquisition module, a data comparison module, and a prediction and evaluation module. Specifically, the digital twin module obtains the growth environment data of carbon nanotubes by setting up a sensor network, establishes a multi-scale mathematical model based on the growth environment data, and at the same time, based on the multi-scale mathematical model, establishes a digital twin model. The data acquisition module simulates the digital twin model by setting at least one AI algorithm to obtain the predicted data of the growth characteristics of carbon nanotubes. The data comparison module obtains the deviation rate according to the predicted growth characteristic data and the experimental measurement data, compares the deviation rate with a preset deviation rate threshold, and determines the existence state of the influencing factors according to the comparison result. The prediction and evaluation module adjusts the simulation model according to the existence state of the influencing factors, and obtains the growth characteristic data of carbon nanotubes according to the adjusted simulation model.

[0051] In this embodiment, the digital twin module obtains the growth environment data of carbon nanotubes by setting up a sensor network, including but not limited to temperature, pressure, gas component concentration (such as hydrogen, methane, etc.) and other factors (such as catalyst active site density). At the same time, based on the obtained growth environment data of carbon nanotubes, a multi-scale mathematical model is established, and the multi-scale mathematical model is integrated with the digital twin module to simulate the growth environment of physical carbon nanotubes.

[0052] Specifically, by setting up a sensor network, the changes in the growth environment parameters of carbon nanotubes are obtained. Specifically, temperature data is obtained through a thermocouple or resistance thermometer with an accuracy of the mK level, pressure data is obtained through a pressure sensor with a resolution of the μPa level, and gas components are obtained through a gas analyzer based on spectroscopic technology. At the same time, the obtained growth environment parameters (i.e., sensor data) are preprocessed to maintain the consistency of their data quality. The preprocessing in this embodiment includes but is not limited to real-time data cleaning, anomaly detection, and filtering through a Kalman filter.

[0053] Furthermore, according to the uncertainties existing at each scale, namely the uncertainties in atomic-scale simulations, mesoscopic-scale simulations, and macroscopic-scale modeling, a multi-scale mathematical model is established. Specifically as follows:

[0054] Step SA1: Establish an atomic-scale model. Specifically, in chemical vapor deposition, carbon source gases (such as hydrogen, methane) will decompose into active carbon species at high temperatures and adsorb on the catalyst surface. However, in this process, it is affected by temperature and gas partial pressure. Temperature not only affects the decomposition rate of carbon source gases but also determines the diffusion behavior of carbon atoms on the catalyst surface. Higher temperatures usually increase the reaction rate but also lead to the formation of more by-products. Similarly, the ratio of different gases (such as the ratio of hydrogen, the ratio of methane) affects the generation rate and adsorption efficiency of carbon atoms. By adjusting the gas partial pressure, the quality and yield of carbon nanotubes can be controlled. Therefore, in this embodiment, the key parameters obtained through molecular dynamics simulation, such as the diffusion activation energy and reaction rate constant, are used as inputs and transmitted to the mesoscopic-scale model. The acquisition formulas for the diffusion activation energy and reaction rate constant are specifically:

[0055] , where: is the diffusion coefficient, is the reaction rate constant, is the pre-exponential factor, is the diffusion activation energy, is the ideal gas constant, is the absolute temperature, is the frequency factor, is the activation energy.

[0056] During the specific implementation process, in the CVD reactor, the temperature is set to 800K, the total pressure is set to 1 atm, and the ratio of methane to hydrogen is 1:5. That is to say, based on this data and actual experiments, the diffusion activation energy is determined to be 0.5 eV, that is, 8.01×10 -20 J. At the same time, the activation energy is 1.5 eV, that is, 2.403×10 -19J. It should be noted that the magnitude of the frequency factor here can be specifically determined according to the actual reaction mechanism. Therefore, in this embodiment, the description of specific numerical determination will not be carried out.

[0057] Step SA2: Establish a mesoscopic scale model. That is, obtain the bridging based on the gap between the atomic scale and the macroscopic scale. Specifically, the size of the catalyst particles directly affects the morphology and properties of the carbon nanotubes. That is, smaller particles are beneficial to the formation of carbon nanotubes with smaller diameters, while larger particles will form multi-walled carbon nanotubes. The temperature difference at different positions in the reaction chamber affects the decomposition rate of the carbon source gas and the diffusion behavior of carbon atoms. For example, when close to the heat source, a higher temperature will accelerate the reaction, while when far from the heat source, a lower temperature will slow down the reaction process. The gas flow rate not only affects the transport efficiency of the reactants but also determines the way of heat transfer. An appropriate flow rate can ensure a uniform temperature distribution and effective mass exchange, thereby improving the consistency and purity of CNT growth.

[0058] In this embodiment, based on the diffusion activation energy and reaction rate constant obtained in step SA1, and through the phase field equation, the distribution of carbon atoms or other reaction products in space is obtained, specifically as follows:

[0059] , where: is the substance concentration, is the mobility, is the chemical potential, is the source term, is the divergence operator, is the time.

[0060] That is to say, according to the obtained distribution of carbon atoms or other reaction products in space, the temperature gradient and gas flow rate changes under actual operating conditions can be determined, and then the corresponding probability distributions of the mobility and chemical potential can be clarified.

[0061] In the process of specific implementation, when growing single-walled carbon nanotubes in a CVD reactor, the temperature is set at 800K, the total pressure is set at 1 atm, the ratio of methane to hydrogen is 1:5, and the mobility of carbon atoms on the surface of the iron-based catalyst at a given temperature of 800K is 1×10 -9 m 2 / s. At the same time, the frequency factor is set at 1×10 13 s -1 , the activation energy is set at 2.403×10 - 19 J. Therefore, according to this data, it can be known that: the reaction rate constant is 1.7×10 10 s -1 , and the source term is 1.7×10 10 mol / (m3 · s). That is, according to the obtained data and the phase field equation, the variation law of the spatial distribution of carbon atoms in the reactor with time can be predicted.

[0062] Step SA3: Establish a macroscopic scale model. Specifically, during the growth process of carbon nanotubes, factors such as temperature, pressure, gas composition, and flow rate in the reaction chamber will all affect their growth. Specifically, a higher temperature can accelerate the decomposition of the carbon source gas, but too high a temperature will also lead to the formation of by-products or catalyst deactivation. The ratio of methane to hydrogen will affect the generation rate and adsorption effect of carbon atoms. At the same time, in addition to the main carbon source gas, other auxiliary gases (such as argon and nitrogen) will also participate in the reaction, changing the local chemical environment, and the presence of impurity gases will inhibit the growth of carbon nanotubes or cause structural defects. The gas flow rate not only affects the transport efficiency of reactants but also determines the way of heat transfer.

[0063] In this embodiment, according to the concentration distribution and other structural parameters obtained in step SA2, a continuity equation and an energy balance equation are constructed to predict the growth rate, length, and purity of carbon nanotubes, specifically:

[0064] , where: is the divergence operator, is the density, is the velocity vector, is the time, is the source term, is the specific heat capacity, is the absolute temperature, is the thermal conductivity, is the internal heat source term.

[0065] During the specific implementation process, single-walled carbon nanotubes are grown in a chemical vapor deposition reactor, with its temperature set at 800K, the total pressure set at 1 atm, the ratio of methane to hydrogen at 1:5, and at the same time the methane density is set at 0.49 kg / m 3 , the hydrogen density is set at 0.089 kg / m 3 , the gas flow rate is set at 0.5 m / s, the reaction rate constant is set at 1.7×10 10 s -1 , the methane concentration is set at 1 mol / m 3 , so the source term is 1.7×10 10 mol / (m 3 · s), that is, 2.04×10 8 kg / (m 3 · s).

[0066] Furthermore, the specific heat capacity of methane is set to 2.25 kJ / (kg·K), the thermal conductivity of methane is set to 0.035 W / (m·K), and the heat released per unit volume during the reaction is set to 10 6 W / m 3 . Therefore, the following energy balance equation can be obtained:

[0067] , that is to say, according to the above energy balance equation, the variation law of the temperature distribution in the reactor with time can be predicted, and thus the growth rate, length and purity indexes of carbon nanotubes can be obtained.

[0068] In this embodiment, by integrating the above-established multi-scale mathematical model with the digital twin module, the growth environment of physical carbon nanotubes is simulated. Specifically as follows:

[0069] Step SB1: Construct a digital twin architecture. That is, define digital twin components and establish two-way communication between the defined digital twin components. Specifically speaking, defining digital twin components means defining a physical system (i.e., the actual chemical vapor deposition reactor and its internal environment), a virtual system (i.e., a computer simulation environment established based on the multi-scale mathematical model), and a data connection (real-time sensor data acquisition and feedback mechanism). That is to say, establish two-way communication between the physical system and the virtual system to achieve data transmission from the physical system to the virtual system (such as temperature, pressure, gas composition, etc.) to facilitate timely updating of the state of the virtual model. At the same time, realize the transmission of control instructions from the virtual system to the physical system (such as adjusting the temperature set point, changing the gas flow rate, etc.) to optimize the growth conditions of carbon nanotubes.

[0070] Step SB2: Integrate the multi-scale mathematical model. That is, integrate the atomic-level model established in the above step SA1, the mesoscopic-scale model established in step SB2, and the macroscopic-scale model established in step SB3, and apply it to the virtual system defined in step SB1, so that the virtual system can operate according to the established multi-scale mathematical model, and thus can more comprehensively describe various phenomena during the growth process of carbon nanotubes.

[0071] Step SB3: Implement the simulation. That is, according to the digital twin architecture constructed in step SB1 and the multi-scale mathematical model integrated in step SB2, simulate the growth environment of carbon nanotubes. That is to say, set the initial state of the virtual system according to the operating conditions of the actual chemical vapor deposition reactor, start the simulation of the virtual system at the same time, and dynamically adjust the model parameters according to the real-time incoming sensor data to ensure the synchronization of the virtual system and the physical system. At the same time, predict the growth rate, length, diameter, purity and other indexes of carbon nanotubes through the multi-scale model, and monitor the change trend of the index parameters in real time.

[0072] In this embodiment, the data acquisition module sets at least one AI algorithm to simulate the digital twin model established in the digital twin module, so as to obtain prediction data on the growth characteristics of carbon nanotubes. Specifically, based on the created digital twin model, it is simulated by at least one AI algorithm (such as machine learning, deep learning, and support vector machine) to obtain prediction data on the growth characteristics of carbon nanotubes.

[0073] In this embodiment, three different AI algorithms, namely machine learning, deep learning, and support vector machine, are used to simulate the created digital twin model to obtain prediction data on the growth characteristics of carbon nanotubes, which specifically includes the following steps:

[0074] Step SC1: Simulate through machine learning. That is, through the obtained experimental data (operating conditions and index parameters), actual simulation is carried out to obtain the first predicted growth rate and other characteristics of carbon nanotubes. Specifically, the operating conditions include but are not limited to temperature, pressure, and gas composition ratio. The index parameters include but are not limited to the growth rate, length, diameter, and purity of carbon nanotubes.

[0075] Furthermore, according to the obtained experimental data, a mapping relationship between the input parameters (temperature, pressure, and gas composition ratio) and the output characteristics (length, diameter, and purity) is established through machine learning algorithms (such as regression analysis, random forest, and gradient boosting tree) for model training, so that the first growth characteristic prediction data of carbon nanotubes can be obtained according to the given operating conditions.

[0076] In the process of specific implementation, the obtained experimental data includes: temperature range: 700K - 1000K, pressure range: 0.5atm - 2atm, gas composition ratio (methane and hydrogen): 1:1 - 1:10, other conditions: different types of catalysts (iron, cobalt, nickel), different reaction times. And corresponding model training is carried out according to this experimental data.

[0077] Furthermore, according to the trained model, the corresponding growth rate of carbon nanotubes is obtained under the corresponding operating conditions. That is, the temperature is set to 820K, the total pressure is set to 1atm, and the ratio of methane to hydrogen is 1:5. Therefore, the corresponding operating condition data is [820, 1, 1 / 5], and the obtained prediction results are: growth rate is 0.35, length is 12μm, diameter is 10nm, and purity is 96%.

[0078] Step SC2: Simulation through deep learning. That is, process complex spatio-temporal data through convolutional neural networks or recurrent neural networks. For example, obtain the formation and development of the carbon nanotube wall layer through a convolutional neural network, and capture the effects of local chemical environment and temperature changes. Further, train the neural network based on the obtained experimental data (operating conditions and index parameters) to determine its corresponding weights and biases, thereby improving the accuracy of the neural network model. That is to say, according to the improved neural network model, conduct model training, so that the predicted data of the second growth characteristics of carbon nanotubes can be obtained based on the given operating conditions.

[0079] In this embodiment, a spatio-temporal data set is constructed, which includes temperature and pressure changes in the time series and the position and size of catalyst particles in the spatial distribution. For example, in a chemical vapor deposition reactor, record the temperature and pressure changes at different positions over time. And process the time series data in the spatio-temporal data set through a long short-term memory network to adjust the model weights to minimize the prediction error.

[0080] Step SC3: Simulation through support vector machines. That is, select the key parameters affecting the growth of carbon nanotubes (such as temperature, pressure, and gas flow rate), and model the classification problem through support vector machines, so that the quality of carbon nanotubes under different growth conditions can be distinguished. That is to say, according to the support vector machine model after modeling, obtain the predicted data of the third growth characteristics of carbon nanotubes.

[0081] Further, transform the prediction of the growth characteristics of carbon nanotubes into a classification problem. For example, classify carbon nanotubes into three categories of "short", "medium", and "long" according to their final length, and into three categories of "low", "medium", and "high" according to the purity level.

[0082] Step SC4: Obtain prediction data. That is, based on the predicted data of the first growth characteristics obtained through machine learning in Step SC1, the predicted data of the second growth characteristics obtained through deep learning in Step SC2, and the predicted data of the third growth characteristics obtained through support vector machines in Step SC3, determine the predicted data of the final growth characteristics of carbon nanotubes, specifically:

[0083] , where: is the predicted data of the final growth characteristics, is the predicted data of the first growth characteristics, is the predicted data of the second growth characteristics, is the predicted data of the third growth characteristics, , , are weight coefficients.

[0084] During the specific implementation process, the first growth characteristic prediction data is: length 5μm, diameter 1.2nm, the second growth characteristic prediction data is: length 6μm, diameter 1.3nm, and the third growth characteristic prediction data is: length 5.5μm, diameter 1.1nm. At the same time, the weight coefficients are set to 0.4, 0.3 and 0.3 respectively, so the final growth characteristic prediction data is: length 5.45μm, diameter 1.2nm.

[0085] In this embodiment, the weight coefficient is determined based on the average cross-validation score of the machine learning model, the average cross-validation score of the deep learning model, and the average cross-validation score of the support vector machine model. , and The size is:

[0086] ,in: is the i-th weight coefficient, is the cross-validation score of the ith model, is the cross-validation score of the j-th model, is the index variable.

[0087] It is worth noting that all weight coefficients , and The sum is 1. In the specific implementation process, the average cross-validation score of the machine learning model is set to 0.95, the average cross-validation score of the deep learning model is set to 0.92, and the average cross-validation score of the support vector machine model is set to 0.88, so the sum of the cross-validation scores of all models is 2.75. , and The sum is 1, so according to the above acquisition formula, the weight coefficient The size is 0.345, the weight coefficient The size is 0.334, and the weight coefficient The size of is 0.321.

[0088] In this embodiment, the data comparison module compares the predicted data obtained in the data acquisition module with the experimental measurement data, and obtains the deviation rate therefrom. At the same time, the obtained deviation rate is compared with the preset deviation rate, and according to the comparison result, the process of simulating the digital twin model by the AI ​​algorithm in the above data acquisition module is optimized and improved to obtain the final predicted data.

[0089] Furthermore, according to the comparison result of the obtained deviation rate and the preset deviation rate, the simulation model in the data acquisition module is optimized and improved. That is, according to the comparison result, the corresponding influencing factors are determined, and through the influencing factors, the model structure is adjusted, the hyperparameter settings are changed, or new feature variables are introduced to improve the accuracy of the simulation model. Specifically as follows:

[0090] Step SD1: Determine the preset deviation rate threshold. That is, according to the application requirements and objectives in the actual use process, statistical indicators (such as mean absolute percentage error and root mean square error) are obtained, and based on the obtained statistical indicators, the specific preset deviation rate threshold is obtained. Specifically as follows:

[0091] Step SE1: Obtain the data distribution. That is, according to the obtained statistical indicators, it is displayed by drawing the corresponding histogram or box plot, etc., and based on the drawn graph, the prediction deviation range is obtained.

[0092] In the process of specific implementation, the data in Table 1 below is obtained, specifically:

[0093] Table 1: Diameter data table

[0094] Serial number 1 2 3 4 5 6 7 8 9 10 Actual diameter / nm 1.2 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 Predicted diameter / nm 1.3 1.4 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 Absolute percentage error / % 8.33 6.67 5.88 5.26 4.76 4.35 4.00 3.70 3.45 3.23

[0095] According to the above data and Figure 4 It can be known that the mean absolute percentage error is 5.4%. Combining with the actual statistical data, it can be known that the mean absolute percentage error is between 3.23% - 8.33%, which is a reasonable range. Since 5.4% is within the range of 3.23% - 8.33%, in this predicted data, its absolute percentage error is within the reasonable range.

[0096] Step SE2: Set the prediction threshold. That is, according to the data distribution obtained in Step SE1, the prediction deviation is set. Specifically speaking, according to the obtained absolute percentage error above, the corresponding prediction threshold is set.

[0097] In the process of specific implementation, the absolute percentage error of the current model is 5.4%. Therefore, combining with the data requirements and objectives in the actual operation, in order to ensure long-term stability and adapt to possible future changes, the prediction threshold is set to 7%, that is to say, the deviation between the predicted value and the actual value does not exceed 7%.

[0098] Step SD2: Determine the influencing factors. That is, according to the prediction threshold set in Step SE2, it is compared with the obtained deviation rate, and according to the comparison result, it is determined whether the influencing factors exist.

[0099] Furthermore, by obtaining the predicted data on the growth characteristics of carbon nanotubes and the experimental data, the deviation rate corresponding to each data can be obtained, and the obtained deviation rate is compared with the prediction threshold. Specifically:

[0100] When the deviation rate is not less than the prediction threshold, it indicates that there are influencing factors in the simulation model in the data acquisition module, which causes the error of the predicted data on the growth characteristics of carbon nanotubes to be too large. On the contrary, it indicates that there are no influencing factors in the simulation model in the data acquisition module, and it can be directly used.

[0101] It should be noted that when it is determined that there are influencing factors in the simulation model, the model structure can be adjusted, the hyperparameter settings can be changed, or new feature variables can be introduced to improve the accuracy of the simulation model, and steps SC1 - step SD2 are repeated until it is determined that there are no influencing factors in the simulation model.

[0102] Specifically, adjusting the model structure means checking whether the existing model architecture is suitable for processing specific types of data or tasks. Changing the hyperparameter settings means adjusting hyperparameters such as the learning rate and batch size to improve the model's convergence and generalization ability. Introducing new feature variables means introducing more highly relevant feature variables, which helps to enhance the model's interpretability. For example, when predicting the growth of carbon nanotubes, the influence of environmental conditions such as temperature and pressure is considered.

[0103] In this embodiment, the prediction and evaluation module adjusts the simulation model in the data acquisition module according to the presence state of the influencing factors in the data comparison module, and predicts the growth state of the carbon nanotubes based on the adjusted simulation model to obtain the predicted data on the growth characteristics of the carbon nanotubes. Specifically, it includes the following steps:

[0104] Step SF1: Determine the influencing factors. When it is determined in step SD2 that there are influencing factors, adjust the temperature, catalyst type, and gas composition one by one to obtain the specific influencing factors. And according to the determined influencing factors, make corresponding adjustments to the simulation model. On the contrary, when it is determined in step SD2 that there are no influencing factors, the already obtained simulation model can be directly run.

[0105] That is to say, when the influencing factor is temperature, according to the identified key temperature range, modify the physical and chemical reaction equations related to temperature in the simulation model to ensure that corresponding prediction results can be obtained in all temperature ranges.

[0106] When the influencing factor is the catalyst type, through first-principles calculation, obtain the interaction strength between different catalysts and carbon atoms, and thus select appropriate parameter values.

[0107] When the influencing factor is the gas composition, all the gas flow rate and mixing ratio parameters involved in the simulation model are adjusted to ensure that the synergistic effect among the components can be correctly expressed.

[0108] Step SF2: Obtain the prediction result. That is, according to the influencing factor determined in step SF1, after adjusting the simulation model, the growth state of carbon nanotubes is predicted through the adjusted simulation model.

[0109] This embodiment also provides a method for establishing a carbon nanotube growth prediction and evaluation model based on digital twin and AI. This establishment method uses a carbon nanotube growth prediction and evaluation model based on digital twin and AI provided above.

[0110] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended embodiments and their equivalents.

Claims

1. A carbon nanotube growth prediction and evaluation model based on digital twins and AI, characterized in that: Included are: Digital twin module: obtain the growth environment data of carbon nanotubes and establish multi-scale mathematical models and digital twin models; Data acquisition module: simulating the digital twin model through an AI algorithm to obtain growth characteristic prediction data of the carbon nanotubes; Data comparison module: obtains the deviation rate between the growth characteristic prediction data and the experimental measurement data, and compares the deviation rate with a preset deviation rate threshold to determine the existence status of the influencing factors, including: SD1: Obtain statistical indicators based on the growth characteristic prediction data and experimental measurement data to determine a preset deviation rate threshold, including: SE1: Draw a histogram based on the statistical indicators to obtain the prediction deviation range; SE2: Setting a preset deviation rate threshold according to the predicted deviation range; SD2: Compare the preset deviation rate threshold with the deviation rate to determine the existence state of the influencing factor, specifically: When the deviation rate is not less than the prediction threshold, the influencing factor does not exist, otherwise the influencing factor exists; Prediction and evaluation module: According to the existence state of the influencing factors, the simulation model is adjusted to obtain the growth characteristic data of the carbon nanotubes, including: SF1: According to the existence status of the influencing factors, the simulation model is adjusted, specifically: When the influencing factors exist, the temperature, catalyst type and gas composition are adjusted one by one to determine the influencing factors, and the simulation model is adjusted according to the influencing factors, otherwise the simulation model is not adjusted; SF2: Based on the final simulation model, the growth state of the carbon nanotubes is predicted.

2. According to claim 1, a carbon nanotube growth prediction and evaluation model based on digital twin and AI is characterized in that: Establish a multi-scale mathematical model, including: SA1: Establishing an atomic-level model: Obtain key parameters through molecular dynamics, and transfer the key parameters to the mesoscopic scale model. The formula for obtaining the key parameters is as follows: ,in: is the diffusion coefficient, is the reaction rate constant, is the pre-exponential factor, is the diffusion activation energy, is the ideal gas constant, is the absolute temperature, is the frequency factor, is the activation energy; SA2: Establish a mesoscopic scale model: According to the key parameters and phase field equations, obtain the distribution of the reaction products in space, specifically: ,in: is the substance concentration, is the mobility, is the chemical potential, is the source term, is the divergence operator, For time; SA3: Establish a macro-scale model: According to the distribution of the reaction products in space, construct the continuity equation and energy balance equation, specifically: ,in: is the divergence operator, is the density, is the velocity vector, For time, is the source term, is the specific heat capacity, is the absolute temperature, is the thermal conductivity, is the internal heat source term.

3. The carbon nanotube growth prediction and evaluation model based on digital twin and AI according to claim 1, characterized in that: The growth environment of the carbon nanotubes is simulated, including: SB1: Build digital twin architecture: define digital twin components and establish two-way communication between the defined digital twin components; SB2: Integrate multi-scale mathematical models: Integrate the atomic-scale model, the mesoscale model, and the macroscale model to obtain an integrated multi-scale mathematical model, and combine the integrated multi-scale mathematical model with the defined digital twin components; SB3: Implement simulation: Based on the digital twin architecture and multi-scale mathematical model, simulate the carbon nanotube growth environment.

4. The carbon nanotube growth prediction and evaluation model based on digital twin and AI according to claim 1, characterized in that: Acquiring the growth characteristic prediction data of the carbon nanotubes, including: SC1: Simulating by machine learning: Establishing a mapping relationship between input parameters and output characteristics by a machine learning algorithm to obtain first growth characteristic prediction data of the carbon nanotube; SC2: Simulation by deep learning: Processing the spatiotemporal data by a neural network, and obtaining the second growth characteristic prediction data of the carbon nanotube according to the processed data; SC3: Simulating by support vector machine: Modeling the classification problem by support vector machine, and obtaining the third growth characteristic prediction data of the carbon nanotube according to the modeled support vector machine model; SC4: Obtaining prediction data: Determining final growth characteristic prediction data of the carbon nanotube according to the first growth characteristic prediction data, the second growth characteristic prediction data and the third growth characteristic prediction data, specifically: ,in: For the prediction of final growth characteristics, is the first growth characteristic prediction data, Predict data for the second growth characteristic, Prediction data for the third growth characteristic, , , is the weight coefficient.

5. The carbon nanotube growth prediction and evaluation model based on digital twin and AI according to claim 4, characterized in that: The formula for obtaining the weight coefficient is as follows: ,in: is the i-th weight coefficient, is the cross-validation score of the ith model, is the cross-validation score of the j-th model, is the index variable.

6. A method for establishing a carbon nanotube growth prediction and evaluation model based on digital twins and AI, characterized in that: The establishment method uses a carbon nanotube growth prediction and evaluation model based on digital twins and AI as described in any one of claims 1-5.

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