Carbon nanotube growth prediction and evaluation model based on digital twinning and AI and establishment method thereof

Abstract

The invention discloses a carbon nanotube growth prediction and evaluation model based on digital twinning and AI and an establishment method thereof, and relates to the technical field of material science and engineering. Comprising the following steps: acquiring growth environment data of a carbon nanotube, and establishing a digital twinborn model; setting at least one AI algorithm to simulate the digital twinborn model, and obtaining growth characteristic prediction data of the carbon nanotube; according to the growth characteristic prediction data and the experimental measurement data, comparing the deviation ratio with a preset deviation ratio threshold value, and determining the existence state of the influence factors; and adjusting the simulation model to obtain growth characteristic data of the carbon nanotube. According to the method, a real-time data-driven virtual simulation system is combined with a machine learning algorithm, so that complex nonlinear dynamic accurate modeling in the growth process of the carbon nanotubes is realized, the prediction precision is improved, the number of physical experiments is reduced, the cost is reduced, and the research and development period is shortened.

Description

Technical Field

[0001] The present invention relates to the field of materials science and engineering technology, and specifically to a carbon nanotube growth prediction and evaluation model based on digital twins and AI and an establishment method thereof. Background Art

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

[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 acquisition of multi-source data in the actual environment; S3: Preliminary processing of the collected data through edge computing devices; S4: Data fusion and enhancement using a preset multimodal data fusion algorithm; S5: Dynamic simulation and prediction of the actual environment; S6: Generate optimization control instructions; S7: Regularly perform model calibration and parameter adjustment to continuously optimize the accuracy of the digital twin model. By integrating edge computing and multimodal data fusion technology, the efficiency and accuracy of data processing are achieved, while physical simulation and machine learning are combined to improve prediction accuracy, significantly improving the system's response speed and decision-making quality.

[0004] In the process of carbon nanotube growth prediction, the above and similar processing methods are difficult to effectively compare and integrate data between different laboratories, which will lead to significant quality differences even in the same type of data. Existing prediction and evaluation models often rely on specific experimental conditions and data characteristics, which are prone to overfitting when facing new environments or larger ranges of data, which will reduce the accuracy of carbon nanotube growth mechanism evaluation prediction results. 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 twins and AI and a method for establishing the same, so as to solve the problems raised in the above-mentioned background technology.

[0006] To achieve the above objectives, the present invention provides the following technical solutions: a carbon nanotube growth prediction and evaluation model based on digital twins and AI, comprising: Digital twin module: setting up a sensor network to obtain the growth environment data of carbon nanotubes, and establishing a multi-scale mathematical model based on the growth environment data, and at the same time establishing a digital twin model based on the multi-scale mathematical model; Data acquisition module: setting at least one AI algorithm to simulate the digital twin model to obtain the growth characteristic prediction data of the carbon nanotubes; Data comparison module: obtaining a deviation rate according to the growth characteristic prediction data and the experimental measurement data, and comparing the deviation rate with a preset deviation rate threshold, and determining the existence state of the influencing factor according to the comparison result; Prediction and evaluation module: adjusts the simulation model according to the existence state of the influencing factors, and obtains the growth characteristic data of the carbon nanotubes according to the adjusted simulation model, including: SF1: Determine the influencing factors: Determine whether to adjust the simulation model according to the existence status of the influencing factors, specifically: When the influencing factors exist, the temperature, the catalyst type and the gas composition are adjusted one by one to determine the influencing factors, and the simulation model is adjusted 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; SF2: Obtain prediction results: predict the growth state of the carbon nanotubes according to the final simulation model.

[0007] Furthermore, a multi-scale mathematical model is established, 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.

[0008] Furthermore, 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.

[0009] Furthermore, obtaining the growth characteristic prediction data of the carbon nanotubes includes: 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.

[0010] Furthermore, 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.

[0011] Furthermore, the existence of influencing factors is determined, including: SD1: Determine a preset deviation rate threshold: Obtain statistical indicators based on the growth characteristic prediction data and experimental measurement data, and determine a preset deviation rate threshold based on the statistical indicators; SD2: Determine the influencing factors: compare the preset deviation rate threshold with the deviation rate, and determine the existence state of the influencing factors according to the comparison result, specifically: When the deviation rate is not less than the prediction threshold, the influencing factor does not exist, otherwise the influencing factor exists.

[0012] Furthermore, the preset deviation rate threshold is determined, including: SE1: Obtain data distribution: Obtain statistical indicators based on the growth characteristic prediction data and experimental measurement data, draw a histogram, and obtain the prediction deviation range based on the statistical indicators and the histogram; SE2: Set prediction threshold: Set a preset deviation rate threshold according to the prediction deviation range.

[0013] A method for establishing a carbon nanotube growth prediction and evaluation model based on digital twins and AI, wherein the establishment method uses the above-mentioned carbon nanotube growth prediction and evaluation model based on digital twins and AI.

[0014] Compared with the prior art, the present invention has the following beneficial effects: First, the present invention combines a real-time data-driven virtual simulation system with a machine learning algorithm to achieve accurate modeling of the complex nonlinear dynamics of carbon nanotube growth, thereby improving prediction accuracy, reducing the number of physical experiments, and reducing costs, thereby accelerating the R&D cycle; Second: Through the digital twin technology, the present invention allows users to intuitively observe every detail change in the growth process of carbon nanotubes, thereby facilitating timely adjustment of process parameters to ensure consistency of product quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A schematic diagram of the process of the carbon nanotube growth prediction and evaluation model of the present invention; Figure 2 A schematic diagram of the process of obtaining growth characteristic prediction data in the present invention; Figure 3 A schematic diagram of a process for obtaining the existence status of influencing factors in the present invention; Figure 4 It is a histogram between diameter and absolute percentage error in the present invention. DETAILED DESCRIPTION

[0016] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0017] In the process of predicting carbon nanotube growth, the existing processing methods are difficult to effectively compare and integrate data between different laboratories, which will lead to significant quality differences even in the same type of data. Existing prediction and evaluation models often rely on specific experimental conditions and data characteristics, which are prone to overfitting when facing new environments or larger ranges of data, which will reduce the accuracy of the prediction results of carbon nanotube growth mechanism evaluation. The technical solution of the present application constructs a virtual simulation system that is closely coupled with the actual production environment, and analyzes the operating data through a machine learning algorithm to identify the key parameters that affect the growth of carbon nanotubes, and establish a corresponding simulation model to predict the growth behavior of carbon nanotubes, thereby improving product quality and reducing production costs.

[0018] refer to Figure 1-Figure 4, this embodiment provides a carbon nanotube growth prediction and evaluation model based on digital twins and AI, and 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 the carbon nanotubes by setting up a sensor network, and establishes a multi-scale mathematical model based on the growth environment data, and at the same time establishes a digital twin model based on the multi-scale mathematical model. The data acquisition module simulates the digital twin model by setting at least one AI algorithm to obtain the growth characteristic prediction data of the carbon nanotubes. The data comparison module obtains the deviation rate based on the growth characteristic prediction data and the experimental measurement data, and compares the deviation rate with the preset deviation rate threshold, and determines the existence state of the influencing factor based on the comparison result. The prediction and evaluation module adjusts the simulation model according to the existence state of the influencing factor, and obtains the growth characteristic data of the carbon nanotube according to the adjusted simulation model.

[0019] In this embodiment, the digital twin module acquires 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, a multi-scale mathematical model is established based on the acquired carbon nanotube growth environment data, and the multi-scale mathematical model is integrated with the digital twin module to simulate the growth environment of physical carbon nanotubes.

[0020] Specifically, by setting up a sensor network, changes in the growth environment parameters of carbon nanotubes are obtained. Specifically, temperature data is obtained through a thermocouple or resistance thermometer with mK level accuracy, pressure data is obtained through a pressure sensor with μPa level resolution, and gas composition is obtained through a gas analyzer based on spectral technology. At the same time, the acquired 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.

[0021] Furthermore, a multi-scale mathematical model is established based on the uncertainties existing at each scale, namely the uncertainty in atomic-scale simulation, the uncertainty in mesoscopic-scale simulation, and the uncertainty in macroscopic-scale modeling. The details are as follows: Step SA1: Establish an atomic-level model. Specifically, in the chemical vapor deposition method, the carbon source gas (such as hydrogen, methane) will decompose into active carbon species at high temperature and adsorb on the catalyst surface. However, in this process, it will be affected by temperature and gas partial pressure. The temperature not only affects the decomposition rate of the carbon source gas, 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) will affect 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, the key parameters obtained by molecular dynamics simulation in this embodiment, such as diffusion activation energy and reaction rate constant, and the obtained diffusion activation energy and reaction rate constant are used as input and transmitted to the mesoscale model. The formula for obtaining the diffusion activation energy and reaction rate constant is specifically: ,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.

[0022] In the specific implementation process, in the CVD reactor, the temperature is set to 800K, the total pressure is set to 1atm, and the ratio of methane to hydrogen is 1:5. That is, according to the data and actual experiments, the diffusion activation energy is determined to be 0.5eV, that is, 8.01×10 -20 J. At the same time, the activation energy is 1.5 eV, which is 2.403×10 -19 J. It is worth noting that the magnitude of the frequency factor here can be specifically determined according to the actual reaction mechanism, so in this embodiment, the determination and description of the specific numerical value will not be given.

[0023] Step SA2: Establish a mesoscale model. That is, bridge the gap between the atomic level and the macroscopic scale. Specifically, the size of the catalyst particles directly affects the morphology and properties of carbon nanotubes. That is, smaller particles are conducive to the generation 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 will affect the decomposition rate of the carbon source gas and the diffusion behavior of carbon atoms. For example, when close to the heat source, higher temperatures will accelerate the reaction, while when away from the heat source, lower temperatures will slow down the reaction process. The gas flow rate not only affects the transfer efficiency of the reactants, but also determines the way the heat is transferred. The appropriate flow rate can ensure uniform temperature distribution and effective material exchange, thereby improving the consistency and purity of CNT growth.

[0024] In this embodiment, according to the diffusion activation energy and reaction rate constant obtained in step SA1, the distribution of carbon atoms or other reaction products in space is obtained through the phase field equation, specifically: ,in: is the substance concentration, is the mobility, is the chemical potential, is the source term, is the divergence operator, For time.

[0025] In other words, based on 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 distribution of mobility and chemical potential can be clarified.

[0026] In the specific implementation process, single-walled carbon nanotubes were grown in a CVD reactor, the temperature was set to 800K, the total pressure was set to 1atm, the ratio of methane to hydrogen was 1:5, and the carbon atom mobility on the surface of the iron-based catalyst at a given temperature of 800K was 1×10 -9 m 2 / s. At the same time, the frequency factor is set to 1×10 13 s -1 , the activation energy is set to 2.403×10 - 19 J. Therefore, according to the data, the reaction rate constant is 1.7×10 10 s -1 , the source term is 1.7×10 10 mol / (m 3 ·s). In other words, based on the acquired data and the phase field equation, the temporal change pattern of the spatial distribution of carbon atoms in the reactor can be predicted.

[0027] Step SA3: Establish a macro-scale model. Specifically, during the growth of carbon nanotubes, factors such as temperature, pressure, gas composition and flow rate in the reaction chamber will affect their growth. Specifically, higher temperatures can accelerate the decomposition of carbon source gases, but too high temperatures can also lead to the formation of by-products or catalyst deactivation. The ratio of methane and hydrogen will affect the generation rate and adsorption effect of carbon atoms. 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 transfer efficiency of the reactants, but also determines the way heat is transferred.

[0028] 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 the carbon nanotubes, 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.

[0029] In the specific implementation process, single-walled carbon nanotubes are grown in a chemical vapor deposition reactor, the temperature is set to 800K, the total pressure is set to 1atm, the ratio of methane to hydrogen is 1:5, and the methane density is set to 0.49kg / m 3 , the hydrogen density is set to 0.089kg / m 3 , the gas flow rate was set to 0.5 m / s, and the reaction rate constant was set to 1.7 × 10 10 s -1 , the methane concentration is set to 1 mol / m 3 , so the source term is 1.7×10 10 mol / (m 3 ·s), which is 2.04×10 8 kg / (m 3 ·s).

[0030] 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: That is to say, according to the above energy balance equation, the change law of the temperature distribution in the reactor over time can be predicted, so that the growth rate, length and purity index of the carbon nanotubes can be obtained.

[0031] In this embodiment, the growth environment of physical carbon nanotubes is simulated by integrating the multi-scale mathematical model established above with the digital twin module. The details are as follows: Step SB1: Build a digital twin architecture. That is, define the digital twin components and establish two-way communication between the defined digital twin components. Specifically, define the digital twin components, that is, define the physical system (i.e., the actual chemical vapor deposition reactor and its internal environment), the virtual system (i.e., the computer simulation environment established based on the multi-scale mathematical model) and the data connection (real-time sensor data acquisition and feedback mechanism). In other words, establish two-way communication between the physical system and the virtual system to realize data transmission from the physical system to the virtual system (such as temperature, pressure, gas composition, etc.) so as to update the status of the virtual model in a timely manner. 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.

[0032] Step SB2: Integrate the multi-scale mathematical model. The atomic-scale model established in step SA1, the mesoscopic-scale model established in step SB2, and the macroscopic-scale model established in step SB3 are integrated and applied to the virtual system defined in step SB1, so that the virtual system can operate according to the established multi-scale mathematical model, thereby being able to more comprehensively describe various phenomena in the growth process of carbon nanotubes.

[0033] Step SB3: Implement simulation. That is, according to the digital twin architecture constructed in step SB1 and the multi-scale mathematical model integrated in step SB2, the carbon nanotube growth environment is simulated. In other words, the initial state of the virtual system is set according to the operating conditions of the actual chemical vapor deposition reactor, and the simulation of the virtual system is started at the same time, and the model parameters are dynamically adjusted according to the real-time incoming sensor data to ensure the synchronization of the virtual system and the physical system. At the same time, the growth rate, length, diameter, purity and other indicators of carbon nanotubes are predicted through the multi-scale model, and the changing trend of the indicator parameters is monitored in real time.

[0034] 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 to obtain the predicted data of the growth characteristics of carbon nanotubes. Specifically, based on the created digital twin model, at least one AI algorithm (such as machine learning, deep learning and support vector machine) is used to simulate it to obtain the predicted data on the growth characteristics of carbon nanotubes.

[0035] In this embodiment, the created digital twin model is simulated by three different AI algorithms, namely machine learning, deep learning and support vector machine, to obtain prediction data on the growth characteristics of carbon nanotubes, specifically including the following steps: Step SC1: Simulate by machine learning. That is, by acquiring the experimental data (operating conditions and index parameters), actual simulation is performed to obtain the first predicted growth rate and other characteristics of the 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 the carbon nanotubes.

[0036] Furthermore, based on the experimental data obtained, a mapping relationship between input parameters (temperature, pressure and gas composition ratio) and output characteristics (length, diameter and purity) is established through machine learning algorithms (such as regression analysis, random forest and gradient boosting tree) to perform model training, so that the first growth characteristic prediction data of carbon nanotubes can be obtained according to given operating conditions.

[0037] In the process of specific implementation, the experimental data obtained include: 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 according to the experimental data, the corresponding model training is carried out.

[0038] Furthermore, according to the trained model, the corresponding carbon nanotube growth rate 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, so the corresponding operating condition data is [820,1,1 / 5], so the obtained prediction results are: growth rate is 0.35, length is 12μm, diameter is 10nm, and purity is 96%.

[0039] Step SC2: Simulate through deep learning. That is, through convolutional neural networks or recurrent neural networks, complex spatiotemporal data are processed. For example, the formation and development of the carbon nanotube wall layer is obtained through convolutional neural networks, capturing the influence of local chemical environment and temperature changes. Furthermore, by obtaining the obtained experimental data (operating conditions and indicator parameters), the neural network is trained to determine its corresponding weights and biases, thereby improving the accuracy of the neural network model. In other words, according to the improved neural network model, model training is performed, so that the second growth characteristic prediction data of carbon nanotubes can be obtained according to the given operating conditions.

[0040] In this embodiment, a spatiotemporal data set is constructed, which includes the temperature and pressure changes in the time series and the catalyst particle position and size in the spatial distribution. For example, in a chemical vapor deposition reactor, the temperature and pressure changes at different positions are recorded over time. The time series data in the spatiotemporal data set is processed by a long short-term memory network, and the model weights are adjusted to minimize the prediction error.

[0041] Step SC3: Simulate by support vector machine. That is, by selecting key parameters that affect the growth of carbon nanotubes (such as temperature, pressure and gas flow rate), and modeling the classification problem by support vector machine, the quality of carbon nanotubes under different growth conditions can be distinguished. In other words, according to the modeled support vector machine model, the third growth characteristic prediction data of carbon nanotubes is obtained.

[0042] Furthermore, the prediction of the growth characteristics of carbon nanotubes is transformed into a classification problem. For example, carbon nanotubes are classified into three categories according to their final length: "short", "medium" and "long", and they are classified into "low", "medium" and "high" according to their purity level.

[0043] Step SC4: Obtain prediction data. That is, according to the first growth characteristic prediction data obtained by machine learning in step SC1, the second growth characteristic prediction data obtained by deep learning in step SC2, and the third growth characteristic prediction data obtained by support vector machine in step SC3, the final growth characteristic prediction data of carbon nanotubes is determined, 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.

[0044] 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.

[0045] 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: ,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.

[0046] 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.

[0047] 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.

[0048] Furthermore, according to the comparison result between 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 characteristic variables are introduced to improve the accuracy of the simulation model. The details are as follows: Step SD1: Determine the preset deviation rate threshold. That is, according to the application requirements and goals in the actual use process, obtain statistical indicators (such as mean absolute percentage error and root mean square error), and obtain the specific preset deviation rate threshold based on the obtained statistical indicators. The details are as follows: Step SE1: Obtain data distribution. That is, based on the obtained statistical indicators, display them by drawing corresponding histograms or box plots, and obtain the prediction deviation range from the drawn graphs.

[0049] In the process of specific implementation, the data in Table 1 below are obtained, specifically:

[0050] Table 1: Diameter data table 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 According to the above data and Figure 4 It can be seen that the average absolute percentage error is 5.4%. Combined with actual statistical data, it can be seen that the average absolute percentage error is between 3.23% and 8.33%, which is a reasonable range. Since 5.4% is within the range of 3.23%-8.33%, in this forecast data, its absolute percentage error is within a reasonable range.

[0051] Step SE2: Setting the prediction threshold. That is, setting the prediction deviation according to the data distribution obtained in step SE1. Specifically, setting the corresponding prediction threshold according to the absolute percentage error obtained above.

[0052] During the specific implementation process, the absolute percentage error of the current model is 5.4%. Therefore, combined with the data requirements and goals in actual operation, that is, in order to ensure long-term stability and adapt to possible changes in the future, the prediction threshold is set to 7%. In other words, the deviation between the predicted value and the actual value does not exceed 7%.

[0053] Step SD2: Determine the influencing factors. That is, compare the prediction threshold set in step SE2 with the obtained deviation rate, and determine whether the influencing factors exist based on the comparison result.

[0054] Furthermore, by acquiring the predicted data and experimental data of the growth characteristics of carbon nanotubes, the deviation rate corresponding to each data can be obtained, and the obtained deviation rate is compared with the prediction threshold, specifically: When the deviation rate is not less than the prediction threshold, it indicates that the simulation model in the data acquisition module has influencing factors, that is, the obtained carbon nanotube growth characteristic prediction data error is too large. Otherwise, it indicates that the simulation model in the data acquisition module has no influencing factors and can be used directly.

[0055] It is worth noting that when it is determined that there are influencing factors in the simulation model, the accuracy of the simulation model can be improved by adjusting the model structure, changing the hyperparameter settings, or introducing new feature variables, and repeating steps SC1-SD2 until it is determined that there are no influencing factors in the simulation model.

[0056] Specifically, adjusting the model structure means checking whether the existing model architecture is suitable for processing a specific type of data or task. Changing the hyperparameter settings means adjusting hyperparameters such as learning rate and batch size to improve model convergence and generalization. Introducing new feature variables means introducing more highly correlated feature variables to help improve the model's explanatory power. For example, when predicting the growth of carbon nanotubes, the influence of environmental conditions such as temperature and pressure is considered.

[0057] In this embodiment, the prediction and evaluation module adjusts the simulation model in the data acquisition module according to the existence of the influencing factors in the data comparison module, and predicts the growth state of the carbon nanotubes according to the adjusted simulation model to obtain the growth characteristic prediction data of the carbon nanotubes. Specifically, the steps include: Step SF1: Determine the influencing factors. When it is determined in step SD2 that there are influencing factors, the temperature, catalyst type and gas composition are adjusted one by one to obtain specific influencing factors. And according to the determined influencing factors, the simulation model is adjusted accordingly. On the contrary, when it is determined in step SD2 that there are no influencing factors, the simulation model that has been obtained can be directly run.

[0058] That is, when the influencing factor is temperature, the temperature-related physical and chemical reaction equations in the simulation model are modified according to the identified critical temperature range to ensure that the corresponding prediction results can be obtained in all temperature ranges.

[0059] When the influencing factor is the type of catalyst, the interaction strength between different catalysts and carbon atoms is obtained through first-principles calculations, so as to select the appropriate parameter value.

[0060] When the influencing factor is the gas composition, all gas flow rates and mixing ratio parameters involved in the simulation model are adjusted to ensure that the synergistic effect between the components can be correctly expressed.

[0061] Step SF2: Obtain prediction results, that is, after adjusting the simulation model according to the influencing factors determined in step SF1, the growth state of the carbon nanotubes is predicted through the adjusted simulation model.

[0062] This embodiment also provides a method for establishing a carbon nanotube growth prediction and evaluation model based on digital twins and AI. The establishment method uses the carbon nanotube growth prediction and evaluation model based on digital twins and AI provided above.

[0063] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is limited by the attached 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: setting up a sensor network to obtain the growth environment data of carbon nanotubes, and establishing a multi-scale mathematical model based on the growth environment data, and at the same time establishing a digital twin model based on the multi-scale mathematical model; Data acquisition module: setting at least one AI algorithm to simulate the digital twin model to obtain the growth characteristic prediction data of the carbon nanotubes; Data comparison module: obtaining a deviation rate according to the growth characteristic prediction data and the experimental measurement data, and comparing the deviation rate with a preset deviation rate threshold, and determining the existence state of the influencing factor according to the comparison result; Prediction and evaluation module: adjusts the simulation model according to the existence state of the influencing factors, and obtains the growth characteristic data of the carbon nanotubes according to the adjusted simulation model, including: SF1: Determine the influencing factors: Determine whether to adjust the simulation model according to the existence status of the influencing factors, specifically: When the influencing factors exist, the temperature, the catalyst type and the gas composition are adjusted one by one to determine the influencing factors, and the simulation model is adjusted 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; SF2: Obtain prediction results: predict the growth state of the carbon nanotubes according to the final simulation model.

2. According to claim 1, a carbon nanotube growth prediction and evaluation model based on digital twins 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. The carbon nanotube growth prediction and evaluation model based on digital twin and AI according to claim 1, characterized in that: Determine the presence of influencing factors, including: SD1: Determine a preset deviation rate threshold: Obtain statistical indicators based on the growth characteristic prediction data and the experimental measurement data, and determine a preset deviation rate threshold based on the statistical indicators; SD2: Determine the influencing factors: compare the preset deviation rate threshold with the deviation rate, and determine the existence state of the influencing factors according to the comparison result, specifically: When the deviation rate is not less than the prediction threshold, the influencing factor does not exist, otherwise the influencing factor exists.

7. The carbon nanotube growth prediction and evaluation model based on digital twin and AI according to claim 6, characterized in that: Determine the preset deviation rate threshold, including: SE1: Obtain data distribution: Obtain statistical indicators based on the growth characteristic prediction data and experimental measurement data, draw a histogram, and obtain the prediction deviation range based on the statistical indicators and the histogram; SE2: Set prediction threshold: Set a preset deviation rate threshold according to the prediction deviation range.

8. 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 1-7.

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