A rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition

Abstract

This invention belongs to the field of carbon nanotube preparation and reaction process optimization technology, specifically involving a rapid surrogate modeling and parameter optimization method for carbon nanotube preparation via fluidized bed chemical vapor deposition. This method utilizes a CFD-PBM model to generate high-fidelity multiphysics field data and transforms the simulation results on unstructured meshes into a graph data structure. A graph neural network surrogate model is then constructed to achieve rapid prediction of the temperature field and carbon nanotube generation concentration field within the fluidized bed reactor. Based on the graph neural network surrogate model, a deep reinforcement learning optimization framework is built to achieve rapid optimization of key processes. This invention can improve the prediction accuracy of the GNN surrogate model for high-gradient regions, boundary transition regions, and key reaction regions; it can reduce the computational cost in the multi-condition search process and improve the rapid prediction efficiency of the carbon nanotube generation process in the fluidized bed reactor.

Description

Technical Field

[0001] This invention belongs to the field of carbon nanotube preparation and reaction process optimization technology, specifically involving a rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition based on computational fluid dynamics, population equilibrium model, and graph neural network. Background Technology

[0002] Carbon nanotubes possess excellent mechanical, electrical, thermal, and energy storage properties, and have broad application prospects in composite materials, conductive films, catalyst supports, and energy storage devices. Fluidized bed reactors, due to their sufficient gas-solid contact, high heat and mass transfer efficiency, and suitability for continuous and large-scale production, have become one of the important reactor types for the continuous and large-scale preparation of carbon nanotubes.

[0003] The formation of carbon nanotubes in fluidized beds involves multiple physicochemical processes, including gas-solid two-phase flow, heat and mass transfer, hydrocarbon cracking reactions, and particle size evolution. These processes exhibit significant multi-scale and multi-parameter coupling characteristics, leading to significant challenges in process prediction and control. Among existing technologies, computational fluid dynamics (CFD) methods can accurately characterize the flow, concentration, and temperature fields within a reactor. However, the complex flow structure within fluidized bed reactors presents challenges due to the large computational load and long computation time required when dealing with multi-parameter coupling and complex reaction dynamics. In particular, when coupled with a population balance model (PBM) to describe particle size distribution changes, the scale and computational dimensions of the equations further increase, making numerical solutions even more time-consuming and limiting their practical application in large-scale parameter scanning and process optimization.

[0004] In recent years, data-driven methods have been increasingly used for rapid prediction of fluid physics fields. For example, Convolutional Neural Networks (CNNs) are better suited to structured Cartesian grids, while numerical simulations of fluidized bed reactors often use unstructured grids, leading to limitations in representing grid topology and modeling complex local interactions. Furthermore, while traditional alternatives such as Kriging, Support Vector Regression (SVR), and reduced-order models based on Proper Orthogonal Decomposition (POD) can improve prediction efficiency to some extent, they still suffer from insufficient adaptability, limited prediction accuracy, and weak generalization ability when dealing with unstructured grids, multi-physics coupling, and cross-condition prediction problems. Moreover, current process optimization typically relies on empirical trial and error or directly calling high-cost numerical models, lacking an intelligent optimization method for process parameters that can effectively couple with high-precision surrogate models and balance prediction efficiency with optimization performance. Therefore, there is an urgent need for a rapid prediction and optimization method that can adapt to unstructured meshes, multi-physics coupling characteristics, and can be combined with process parameter optimization. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention discloses a rapid surrogate modeling and parameter optimization method for the preparation of carbon nanotubes by fluidized bed chemical vapor deposition. This method utilizes a CFD-PBM model to generate high-fidelity multiphysics field data and transforms the simulation results on unstructured meshes into a graph data structure. A graph neural network surrogate model is then constructed to achieve rapid prediction of the temperature field and carbon nanotube concentration field within the fluidized bed reactor. Based on the graph neural network surrogate model, a deep reinforcement learning optimization framework is constructed to achieve rapid optimization of key processes.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition includes the following steps: S1 constructs a CFD-PBM numerical model of a fluidized bed reactor, calculates different operating conditions, and obtains high-fidelity sample data of temperature field and carbon nanotube mass concentration field. S2 constructs a graph data structure based on the CFD-PBM calculation results, extracts node features, edge features, and characterization information of the reaction active region where catalyst particles and carbon nanotubes are locally enriched in the fluidized bed reactor, and forms graph learning samples. S3 constructs a GNN proxy model and trains the graph learning samples based on a weighted training strategy driven by local gradient information and reaction activity information, which is based on the locally enriched reaction activity region of catalyst particles and carbon nanotubes in the fluidized bed reactor, to obtain a graph proxy model for fast prediction. S4 uses a graph surrogate model to quickly predict the temperature field and carbon nanotube mass concentration field in a fluidized bed reactor under given operating conditions. S5 constructs a deep reinforcement learning optimization framework based on the graph surrogate model, and uses temperature uniformity RSD as the optimization objective to search for the apparent gas velocity Ug, wall temperature Tw, and propylene mole fraction xC3H6 to obtain the optimal combination of process parameters.

[0007] Preferably, step S1 includes: establishing a three-dimensional reactor computational domain based on the geometry, boundary conditions, propylene molar fraction, and catalyst parameters of the fluidized bed reactor; constructing a coupled model of gas-solid two-phase flow, heat transfer, component transport, and reaction kinetics within the fluidized bed based on the computational domain, and combining it with a population equilibrium model to describe the particle size distribution evolution of catalyst particles during the reaction process; and performing multiple sets of calculations under different operating conditions by changing the apparent gas velocity, wall temperature, propylene molar fraction, and catalyst concentration to obtain high-fidelity sample data covering different operating states for subsequent training and validation of the graph surrogate model.

[0008] Preferably, step S2 includes: using the center of the unstructured grid unit of the discretized fluidized bed reactor as a graph node, and the topological connection relationship between adjacent units on the shared surface as a graph edge to construct a graph data structure; extracting the spatial coordinates, region identifiers and corresponding operating parameters of the nodes as input features, and using the reactor internal temperature and carbon nanotube mass concentration field as prediction targets to form graph learning samples.

[0009] Preferably, in step S3, the GNN proxy model includes an input layer, a graph feature extraction layer, a feature compression and reconstruction layer, and an output layer. The input layer is used to receive node features, graph topology, and operating parameters. The graph feature extraction layer is used to extract local neighborhood topological features and multi-physics coupling features on the unstructured grid. The feature compression and reconstruction layer is used to reduce high-dimensional feature redundancy and enhance the expressive power of key features. The output layer is used to output the prediction results of the temperature field and carbon nanotube mass concentration field. The key features refer to the feature information used to characterize the active reaction region of local enrichment of catalyst particles and carbon nanotubes in the fluidized bed reactor.

[0010] Preferably, in step S3, the graph feature extraction layer adopts a graph attention network (GAT), which uses the attention mechanism between nodes and neighboring nodes to perform information transmission and feature aggregation, thereby realizing graph feature updates and enhancing the model's ability to represent unstructured grid topological relationships and local physical field coupling features.

[0011] Preferably, in step S3, the feature compression and reconstruction layer adopts an autoencoder structure to compress, encode, and reconstruct the high-dimensional node features output by the graph feature extraction layer, thereby reducing redundant information in the high-dimensional physical field data and improving the prediction efficiency of the graph neural network surrogate model for complex physical quantities.

[0012] Preferably, in step S3, during the training of the GNN surrogate model, key regions are determined based on the local gradient information of the target physical field, and a weighted training strategy is constructed based on the key regions to improve the model's learning ability for high-gradient regions, boundary transition regions, and key regions. The weighted training strategy includes: constructing sample sampling weights based on local gradient information to increase the sampling probability of key region samples during training; and constructing loss weights based on local gradient information to increase the contribution of the key region error term in the loss function, thereby improving the prediction accuracy and generalization performance of the graph surrogate model under complex non-uniform physical field conditions. The key regions include high-gradient regions of temperature field, high-gradient regions of carbon nanotube mass concentration field, and boundary transition regions.

[0013] Preferably, in step S4, the graph surrogate model is used to quickly output the predicted results of the internal temperature field and carbon nanotube mass concentration field of the fluidized bed reactor under a given operating condition, in order to replace the repeated solution in the multi-condition search process of traditional CFD-PBM numerical simulation, thereby reducing the computational cost of multi-condition evaluation and improving the efficiency of rapid prediction.

[0014] Preferably, in step S5, the current combination of process parameters is used as the reinforcement learning state, the adjustment amounts of apparent gas velocity, wall temperature and propylene mole fraction are used as variables to be optimized, and one or more of temperature field uniformity (Relative Standard Deviation, RSD) and constraint penalty are used to construct the reward function. The optimal combination of process parameters is obtained by iteratively updating the strategy through the Soft Actor-Critic (SAC) algorithm.

[0015] The beneficial effects of the rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition of the present invention are as follows: This invention constructs an unstructured mesh of a fluidized bed reactor into a GNN data structure and extracts node and edge features, which can directly characterize complex mesh topological relationships and local geometric connections, reducing information loss caused by regularization. By constructing sample sampling weights and loss weights based on local gradient information, the prediction accuracy of the GNN surrogate model for high gradient regions, boundary transition regions, and key reaction regions can be improved. By using the trained GNN surrogate model to replace the repeated calls of traditional CFD-PBM numerical simulations, the computational cost in the multi-condition search process can be reduced, and the rapid prediction efficiency of carbon nanotube generation in fluidized bed reactors can be improved. Based on the rapid prediction, this invention is further used for process parameter optimization, improving process optimization efficiency and result reliability. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition, as an embodiment of the present invention. Detailed Implementation

[0017] The following description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0018] This invention provides a rapid surrogate modeling and parameter optimization method for carbon nanotube preparation via fluidized bed chemical vapor deposition, based on Computational Fluid Dynamics (CFD), Population Balance Model (PBM), Graph Neural Network (GNN), and Deep Reinforcement Learning (DRL). The method generally comprises three stages: high-fidelity dataset construction, GNN surrogate modeling, and deep reinforcement learning parameter optimization. The high-fidelity dataset construction stage obtains temperature and carbon nanotube mass concentration field data within the fluidized bed reactor under different operating conditions. The GNN surrogate modeling stage establishes a rapid prediction model under unstructured grid conditions. A weighted training strategy is used to train the graph surrogate model, enabling it to rapidly predict the temperature and carbon nanotube mass concentration fields. The deep reinforcement learning parameter optimization stage searches for the optimal combination of process parameters based on the trained surrogate model.

[0019] refer to Figure 1 As shown, the embodiments of the present invention will be described in detail below.

[0020] In the initial implementation, a three-dimensional geometric model of the fluidized bed reactor is first established. The fluidized bed reactor preferably includes a main body, a gas inlet, a gas outlet, and a catalyst bed region. Based on the actual reactor structure, its geometric dimensions, inlet location, outlet location, bed height, and catalyst loading parameters are obtained to establish the three-dimensional reactor computational domain.

[0021] The computational domain of the three-dimensional reactor was meshed using ANSYS ICEM software. Preferably, a three-dimensional unstructured mesh was used to discretize the fluidized bed reactor to accommodate the complex geometry and local flow variations of the fluidized bed reactor. Local mesh refinement was applied to the inlet region, bed region, and main reaction zone.

[0022] In a further embodiment, the total number of grid cells in the reactor computational domain is 590,000. After verification of grid independence and comparison with experimental pressure drop results, the relative error between the numerical simulation results and experimental results is less than 7%. Therefore, 590,000 grid cells were selected as the final computational grid.

[0023] After completing the mesh generation, set the reactor boundary conditions, including setting the velocity inlet, inlet temperature, inlet propylene mole fraction, and protective gas concentration; the preferred carbon source gas is propylene (C3H6), and the preferred protective gas is nitrogen (N2). The apparent gas velocity can be expressed as: U g =Q g / A; Among them U g Q represents the apparent gas velocity. g The inlet gas volumetric flow rate is represented by A, and the reactor inlet cross-sectional area is represented by A. The outlet boundary condition is preferably set as a pressure outlet boundary. The wall boundary condition is set as an isothermal wall. Preferably, the inlet temperature can be set to 300 K, the wall temperature to 923.15 K, the catalyst loading to 2 g, and the initial catalyst distribution is set through a local initialization region, with an initial particle volume fraction of 0.6. The initial particle size distribution of the PBM model can be set based on an initial average catalyst particle size of 298 μm, and the particle density is preferably 1923 kg / m³.

[0024] To construct multiple sets of operating condition datasets for numerical simulation, the inlet apparent gas velocity, inlet temperature, carbon source concentration, and catalyst loading conditions can be further varied. The catalyst loading conditions preferably include one or more of the following: catalyst loading amount, initial distribution area, and initial particle volume fraction. By varying these parameters, high-fidelity simulation results of the fluidized bed reactor under different operating conditions can be obtained.

[0025] In a further embodiment, a CFD model is established based on the fluidized bed reactor. The CFD model is used to describe the gas-solid two-phase flow, heat and mass transfer, and component transport processes within the fluidized bed reactor, and to solve for the flow field, temperature field, and carbon source component distribution inside the reactor. Specifically, the CFD model preferably adopts an Euler-Euler Two-Fluid Model (TFM), including the continuity equations, momentum conservation equations, energy conservation equations, and component transport equations for both the gas and solid phases. Preferably, the gas-solid interphase drag force adopts the Symlal-O'Brien model, and the turbulence model adopts the RNG k-ε turbulence model.

[0026] In a further embodiment, the energy equation is activated and a multi-component transport process is considered. The reaction kinetics model of propylene decomposition to carbon nanotubes is introduced as a source term into the component transport equation and the energy conservation equation. This source term is preferably loaded into the numerical solver via a user-defined function (UDF) to characterize carbon source consumption, product formation, and heat changes during the reaction. During the numerical solution process, the pressure-velocity coupling preferably employs the Phase-Coupled SIMPLE algorithm, with a time step preferably set to 1×10⁻⁶. -3 The total simulation time for each set of working conditions is preferably set to 30 seconds. It is preferable to perform time-averaging on the simulation results within the last 20 seconds to obtain statistically stable, high-fidelity data. The convergence criterion is preferably set to 1×10⁻⁶. -5 The above method enables the coupled solution of flow, heat transfer, mass transfer, chemical reaction, and particle evolution processes, providing a high-fidelity data foundation for subsequent GNN surrogate model training.

[0027] In a further embodiment, the PBM model uses particle size distribution as the descriptive object to characterize the dynamic evolution behavior of catalyst particles during the reaction process. The PBM model can be expressed as: ; Wherein, n(L;x,t), v, and G L These represent the particle number density function based on diameter, the particle size spatial migration velocity, and the growth rate, respectively. In this embodiment, the migration velocity v in the particle size space can be represented by the particle size growth rate G. L Sure.

[0028] As a preferred embodiment, the PBM model employs a discretized particle size grouping method, dividing the particles into multiple particle size intervals and solving the evolution process of the particle population within each interval. In this embodiment, after a discretization independence test, it is preferable to divide the particles into 30 particle size intervals to balance the accuracy of particle size distribution calculation and computational efficiency. The PBM model preferably only considers the particle growth process, ignoring particle nucleation, aggregation, and fragmentation processes.

[0029] In a further embodiment, the PBM model and CFD model are coupled and calculated using a combination of Fluent and PBM / UDF. The CFD model provides information on the local flow field, temperature field, and component concentration field, while the PBM model updates the particle size distribution and related statistics based on local reaction conditions. Through this coupled calculation, high-fidelity results of the carbon nanotube mass concentration field within the fluidized bed reactor can be output, characterizing the spatial distribution features and overall evolution of the carbon nanotube generation process, and further serving as training samples for the GNN surrogate model.

[0030] In a further implementation, based on the Box-Behnken Design (BBD), and supplemented and expanded with additional operating conditions, CFD-PBM numerical simulations are conducted under multiple operating conditions to obtain high-fidelity data for each condition. During the numerical simulations under each operating condition, it is preferable to perform time-averaging on the temperature field and carbon nanotube mass concentration field data after the system reaches statistical stability. In a preferred embodiment, time-averaging is performed on the simulation results within the last 20 seconds to reduce the impact of transient fluctuations on the sample data.

[0031] In a further embodiment, cell-level distribution data is exported from the CFD-PBM numerical simulation results and saved as a structured data file, preferably in CSV format. The CSV file includes information such as grid cell number, cell center spatial coordinates, region identifier, local temperature, and carbon nanotube mass concentration. To reduce the dimensional differences between different input features, the exported data is preferably standardized to meet the input requirements of the GNN model.

[0032] After obtaining high-fidelity CFD-PBM data for multiple operating conditions of the fluidized bed reactor, the CFD-PBM simulation results are processed into a graph structure. Specifically, based on the cell-level distribution data of the unstructured mesh, the center of the grid cell in the discretized unstructured mesh of the fluidized bed reactor is defined as a graph node. Each node corresponds to one grid cell. The adjacency relationship between adjacent cells sharing a face is defined as a graph edge. In this embodiment, grid cell i and grid cell j share an edge, and an edge e is added to the graph.ij The constructed graph data structure is represented as follows: ; Where V represents the set of graph nodes. E represents the graph edge set, and each graph node corresponds one-to-one with a grid cell.

[0033] For each graph node, its spatial location features and physical field characteristic parameters are extracted as node input features. The spatial location features include the node's three-dimensional coordinate information, i.e., CoordX. i CoordY i CoordZ i This is used to characterize the spatial location within a fluidized bed reactor. The regional attribute features include the region type to which the node belongs, boundary type identifier, and bed region identifier; the operating condition parameter feature θ is preferably determined by the apparent gas velocity U. g Wall temperature T w propylene mole fraction x C3H6 The feature vector of the i-th graph node is constructed and copied and concatenated to the input feature vector of each graph node. The feature vector of the i-th graph node can be represented as: ; Where, x i CoordX represents the input feature vector of the i-th node. i CoordY i CoordZ i Represent the three-dimensional coordinates of the i-th graph node, R. i The feature vector representing the node region, θ represents the working condition parameter vector, and the symbol "||" represents feature connection.

[0034] In this way, the local spatial information, regional attribute information, and global working condition information of nodes are uniformly represented as graph node input features, and paired with the high-fidelity target physical field values ​​at the corresponding nodes, thereby constructing supervised learning samples for GNN training. After constructing the supervised learning samples, in a preferred embodiment, the ratio of the training set, validation set, and test set is 8:1:1.

[0035] After obtaining the supervised sample dataset, a GNN surrogate model is constructed based on the graph-structured temperature field and carbon nanotube mass concentration field data to rapidly predict the target physical field during the carbon nanotube generation process in the fluidized bed reactor. The GNN surrogate model is preferably implemented using the PyTorch deep learning framework and adopts an encoder-decoder overall architecture, including a graph feature extraction module, an encoding module, a feature reconstruction module, and an output module. The graph feature extraction module preferably employs a Graph Attention Network (GAT).

[0036] As a preferred embodiment, the GNN surrogate model outputs the internal temperature field and carbon nanotube mass concentration field of the reactor. The graph feature propagation process in the graph neural network surrogate model can be represented as: ; in, Let N(i) represent the feature representation of the i-th graph node in the l-th layer, and let N(i) represent the set of neighboring nodes of the i-th graph node. ij Let W represent the attention weight of node j to node i, and let W represent the trainable weight matrix. This represents a non-linear activation function.

[0037] As a preferred embodiment, the attention weights This can be further expressed as: ; Where α represents the trainable parameter vector of the attention mechanism, LeakyReLU represents the vector concatenation operation, and it represents the linear unit activation function with leakage correction.

[0038] The high-dimensional features of the nodes updated by the GAT network are further input into the encoding module, and the encoding module and the feature reconstruction module together constitute an autoencoder structure.

[0039] The encoding process can be represented as follows: ; The decoding process is as follows: ; Among them, h i z represents the high-dimensional features of the nodes in the input encoding module. i This represents the compressed potential representation. W represents the reconstructed node features. e and W d These represent the weight matrices of the encoder and decoder, respectively. and These represent the bias terms of the encoder and decoder, respectively. and These represent the activation functions of the encoder and decoder, respectively.

[0040] To improve the stability of GNN surrogate model training, normalization processing is preferably performed on the input features and supervision targets. The input features preferably include the three-dimensional coordinates of the grid nodes and operating parameters, and the supervision targets include the temperature field and the carbon nanotube mass concentration field. The min-max normalization method is preferably used, and its expression is: ; in, Represents the original feature values. and These represent the minimum and maximum values ​​of the corresponding features in the sample data, respectively. This represents the normalized eigenvalues.

[0041] Because the spatial gradient of carbon nanotube mass concentration varies significantly, the local carbon nanotube mass concentration gradient at each node in the graph is further calculated. Its expression is: ; Among them, g i Let N(i) represent the carbon nanotube mass concentration at the i-th graph node, and let N(i) represent the set of neighboring nodes of node i. ij This represents the Euclidean distance between node i and node j. To prevent the denominator from being too small, a regularization factor of 1×10 is preferred. -7 .

[0042] In a further implementation, to improve the learning ability of the graph neural network model for high-gradient regions and critical response regions, a gradient-weighted sampling strategy is preferably adopted. Specifically, sampling weights are assigned to different nodes based on the local gradient information of each node, so that nodes in high-gradient regions have a higher sampling probability during training. This can be expressed as: ; in, Indicates the first The sampling probability of each node. This represents the sampling weight coefficient. When β is 2, it can accurately improve the prediction accuracy of the model in the high gradient region.

[0043] In a further embodiment, the GNN surrogate model is trained using a weighted loss function to improve the model's ability to fit key regions. The weighted loss function preferably includes a mean squared error (MSE), a mean absolute error (MAE), and a regularization term. The following example uses a weighted mean squared error term combined with a regularization term; its expression can be given as: ; Where L represents the total loss function, and N represents the total number of nodes participating in the loss calculation. Indicates the first The gradient weights corresponding to each node This represents the model's predicted value. This indicates a high-fidelity simulation of the true value. Represents the regularization term, This represents the regularization weight coefficient.

[0044] As a preferred embodiment, the gradient weight w i It can be obtained from the local gradient information g of the nodes i It is certain that its expression can be represented as: Where γ represents the gradient weight coefficient, used to adjust the contribution of high gradient regions to the loss function. Preferably, the value of γ is 2.

[0045] As a preferred option, the regularization term L2 regularization can be used, and its expression can be represented as: ; in, This represents the set of all trainable parameters in the GNN surrogate model. Preferably, the regularization weight coefficients... The preferred value is 1×10. -4 .

[0046] In a further implementation, to improve the training efficiency of the GNN surrogate model while preserving local topological information, a micro-batch graph sampling strategy based on NeighborLoader is preferably adopted during training to load and train graph data in batches. The batch size can be set according to the graph size and the GPU memory capacity. Preferably, to suppress model overfitting and improve training stability, a dropout strategy and an early stopping strategy are introduced during training. The hyperparameters are preferably automatically searched using a Bayesian optimization method. Preferably, the Tree-structured Parzen Estimator (TPE) algorithm in the Optuna framework is used for hyperparameter optimization to search for at least one of the following parameters: number of hidden layer neurons, number of graph attention network layers, number of hidden layer neurons in the autoencoder, learning rate, weight decay coefficient, random dropout ratio, and gradient weight-related parameters.

[0047] In this embodiment, after hyperparameter optimization, the hidden layer dimension is set to 1024, the number of neurons in the autoencoder hidden layer is set to 1024, the number of layers in the 1st, 2nd, and 3rd graph attention layers are set to 1, 2, and 1 respectively, the learning rate can be set to 0.00043, and the weight decay coefficient can be set to 8.33 × 10⁻⁶. -5 The random inactivation ratio is set to 0.236, and the gradient weight coefficient can be set to 0.998.

[0048] In a further embodiment, after training the GNN surrogate model, a deep reinforcement learning optimization framework is further constructed based on the surrogate model to achieve intelligent optimization of key process parameters of the fluidized bed reactor. Preferably, the deep reinforcement learning algorithm employs the SAC algorithm to adapt to the wall temperature T. w propylene mole fraction x C3H6 and apparent air velocity U g The joint optimization problem of continuous process variables.

[0049] In a further embodiment, the SAC optimization framework is preferably implemented in a Python environment, and preferably uses the PyTorch deep learning framework to construct the policy network (Actor) and value network (Critic). The trained GNN agent model is used to replace the traditional CFD-PBM numerical simulation to quickly predict new working conditions generated during reinforcement learning, serving as a fast evaluation model in the reinforcement learning environment to reduce the computational overhead in the parameter search process.

[0050] In a further embodiment, the reinforcement learning state is used to characterize the current operating parameters and their corresponding temperature field characteristics. Preferably, the state variable s t It can be represented as: ; Among them, T w Indicates wall temperature, x C3H6 U represents the mole fraction of propylene. g Represents apparent gas velocity, RSD T This represents the relative standard deviation of the internal temperature field of the reactor predicted by the GNN surrogate model. The state vector has a dimension of 4.

[0051] In a further embodiment, the reinforcement learning action is used to characterize the adjustment amount of the current process parameter. Preferably, the action variable a... t It can be represented as: ; in, , and These represent the adjustments made to the wall temperature, carbon source mole fraction, and apparent gas velocity, respectively. In a preferred embodiment, the wall temperature is 723.1 K-973.15 K, the carbon source mole fraction can be 0.1-0.6, and the apparent gas velocity is 0.1 m / s-0.2 m / s.

[0052] In a further embodiment, the optimization objective is preferably temperature uniformity. Preferably, the temperature uniformity is characterized by the relative standard deviation (RSD) of the temperature field inside the reactor; the smaller the RSD, the more uniform the temperature field. Preferably, the relative standard deviation of the temperature field can be expressed as: ; in, Indicates the first Temperature value at each grid cell This represents the total number of temperature samples. This represents the average temperature field. To enable the reinforcement learning process to iterate policies based on temperature uniformity, the reward function is constructed as follows: ; in, Indicates time The reward value, This represents the relative standard deviation of the temperature field inside the reactor under the current operating conditions. This represents a constraint penalty term used to limit the range of wall temperature, propylene mole fraction, and apparent gas velocity. This represents the penalty coefficient, with a preferred value of 1.

[0053] As a preferred embodiment, the constraint penalty term It can be represented as: ; in, This indicates the penalty for exceeding the wall temperature limit. This indicates a penalty for exceeding the limit on the carbon source mole fraction. This indicates a penalty for exceeding the apparent air velocity limit.

[0054] In a further embodiment, the SAC algorithm preferably includes a policy network, a dual-commentator network, and a target commentator network. Preferably, a replay buffer is used to store state transition samples during training. The network parameters are updated using a small-batch random sampling method.

[0055] In this embodiment, the target value of the critic network can be expressed as: ; in, This represents the discount factor, with a preferred value of 0.99. Indicates the first A network of target commentators; Represents a policy network; This represents the entropy temperature coefficient.

[0056] As a preferred approach, the commentator network loss function can be expressed as: .

[0057] The objective function of the policy network can be expressed as: ; in, Indicates the number of samples in the batch.

[0058] As a preferred approach, the target network parameters are iterated using a soft update method, which can be expressed as: ; in, This represents the soft update coefficient, with a preferred value of 0.005.

[0059] In a further embodiment, the SAC algorithm iteratively learns the process parameter adjustment strategy in the continuous action space through alternating training of the Actor-Critic network. After each strategy update, the updated wall temperature, carbon source mole fraction, and apparent gas velocity are input into the trained GNN surrogate model to quickly obtain the temperature field prediction result under the corresponding operating condition, and further calculate the relative standard deviation of the temperature field. The algorithm assigns a reward value to guide subsequent strategy updates. After multiple rounds of training iterations, the SAC algorithm outputs a combination of process parameters that satisfies preset process constraints and optimizes temperature uniformity. Preferably, the optimal combination of process parameters includes the optimal wall temperature, the optimal carbon source mole fraction, and the optimal apparent gas velocity.

[0060] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A rapid proxy modeling and parameter optimization method for the preparation of carbon nanotubes by fluidized bed chemical vapor deposition, characterized in that, Includes the following steps: S1 constructs a CFD-PBM numerical model of a fluidized bed reactor, calculates different operating conditions, and obtains high-fidelity sample data of temperature field and carbon nanotube mass concentration field. S2 constructs a graph data structure based on the CFD-PBM calculation results, extracts node features, edge features, and characterization information of the reaction active regions where catalyst particles and carbon nanotubes are locally enriched in the fluidized bed reactor, and forms graph learning samples. S3 constructs a GNN proxy model and trains the graph learning samples based on a weighted training strategy driven by local gradient information and reaction activity information, which is based on the locally enriched reaction activity region of catalyst particles and carbon nanotubes in the fluidized bed reactor, to obtain a graph proxy model for fast prediction. S4 uses a graph surrogate model to quickly predict the temperature field and carbon nanotube mass concentration field in a fluidized bed reactor under given operating conditions. S5 constructs a deep reinforcement learning optimization framework based on the graph surrogate model, and uses temperature uniformity RSD as the optimization objective to search for the apparent gas velocity Ug, wall temperature Tw, and propylene mole fraction xC3H6 to obtain the optimal combination of process parameters.

2. The rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition as described in claim 1, characterized in that, Step S1 includes: establishing a three-dimensional reactor computational domain based on the geometry, boundary conditions, propylene molar fraction, and catalyst parameters of the fluidized bed reactor; constructing a coupled model of gas-solid two-phase flow, heat transfer, component transport, and reaction kinetics within the fluidized bed based on the computational domain, and combining it with a population equilibrium model to describe the particle size distribution evolution of catalyst particles during the reaction process; and performing calculations under multiple operating conditions by changing the apparent gas velocity, wall temperature, propylene molar fraction, and catalyst concentration to obtain high-fidelity sample data covering different operating states for subsequent training and validation of the graph surrogate model.

3. The rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition as described in claim 2, characterized in that, Step S2 includes: using the center of the unstructured grid unit of the discretized fluidized bed reactor as a graph node, and the topological connection relationship between adjacent units on the shared surface as a graph edge to construct a graph data structure; extracting the spatial coordinates, region identifiers and corresponding operating parameters of the nodes as input features, and using the reactor internal temperature and carbon nanotube mass concentration field as prediction targets to form graph learning samples.

4. The rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition as described in claim 3, characterized in that, In step S3, the GNN surrogate model includes an input layer, a graph feature extraction layer, a feature compression and reconstruction layer, and an output layer. The input layer is used to receive node features, graph topology, and operating parameters. The graph feature extraction layer is used to extract local neighborhood topological features and multi-physics coupling features on the unstructured grid. The feature compression and reconstruction layer is used to reduce high-dimensional feature redundancy and enhance the expressive power of key features. The output layer is used to output the prediction results of the temperature field and carbon nanotube mass concentration field. The key features refer to the feature information used to characterize the active reaction regions of catalyst particles and carbon nanotubes in the fluidized bed reactor.

5. The rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition as described in claim 4, characterized in that, In step S3, the graph feature extraction layer uses a graph attention network, which uses the attention mechanism between nodes and neighboring nodes to transmit information and aggregate features, thereby updating graph features and enhancing the model's ability to represent unstructured grid topological relationships and local physical field coupling features.

6. The rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition as described in claim 5, characterized in that, In step S3, the feature compression and reconstruction layer adopts an autoencoder structure to compress, encode, and reconstruct the high-dimensional node features output by the graph feature extraction layer, thereby reducing redundant information in the high-dimensional physical field data and improving the prediction efficiency of the graph neural network surrogate model for complex physical quantities.

7. The rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition as described in claim 6, characterized in that, In step S3, during the training of the GNN proxy model, key regions are determined based on the local gradient information of the target physical field, and a weighted training strategy is constructed based on the key regions to improve the model's learning ability for high gradient regions, boundary transition regions and key regions. The weighted training strategy includes: constructing sample sampling weights based on local gradient information to increase the sampling probability of samples in key regions during the training process; Loss weights are constructed based on local gradient information to increase the contribution of error terms in key regions to the loss function, thereby improving the prediction accuracy and generalization performance of the graph surrogate model under complex non-uniform physical field conditions; the key regions include high gradient regions of temperature field, high gradient regions of carbon nanotube mass concentration field, and boundary transition regions.

8. The rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition as described in claim 7, characterized in that, In step S4, the graph surrogate model is used to quickly output the predicted results of the internal temperature field and carbon nanotube mass concentration field of the fluidized bed reactor under given operating conditions.

9. The rapid proxy modeling and parameter optimization method for preparing carbon nanotubes by fluidized bed chemical vapor deposition as described in claim 8, characterized in that, In step S5, the current combination of process parameters is used as the reinforcement learning state, the adjustment amounts of apparent gas velocity, wall temperature and propylene mole fraction are used as variables to be optimized, and one or more of temperature field uniformity and constraint penalty are used as the reward function. The optimal combination of process parameters is obtained by iteratively updating the strategy through the soft actor-commentator algorithm.

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