Method for measuring and calculating key parameters based on simulated three-dimensional PET concentration field distribution

Abstract

The invention belongs to the technical field of polyester fibers, and relates to a method for measuring and calculating key parameters based on simulated three-dimensional PET concentration field distribution, which comprises the following steps: firstly, deducing a causal structure in a polyester fiber reactor according to an information theory, secondly, grading and disassembling the causal structure to obtain a disassembled causal structure, and finally, calculating the key parameters of the polyester fiber reactor according to the disassembled causal structure. Driving one stage in the training process through each disassembled causal structure to obtain an output and a sum; the method comprises the following steps of: firstly, carrying out common input, and carrying out weight initialization by using a Caul-guide Init method, constructing a deep neural network (DNN), applying theoretical constraint to a model, and outputting three-dimensional PET concentration field distribution; and finally, measuring and calculating key parameters by utilizing theoretical knowledge of the polyester fibers and combining the output three-dimensional PET concentration field distribution. The method provided by the invention can accurately simulate the three-dimensional PET concentration field in the polyester fiber polymerization reactor, is used for measuring and calculating key parameters, and improves the measurement and calculation precision.

Description

Technical Field

[0001] The invention belongs to the technical field of polyester fibers and relates to a method for measuring key parameters based on simulated three-dimensional PET concentration field distribution. Background Art

[0002] Polyester fiber, commonly known as polyester, is a synthetic fiber made by spinning polyester, a product of the polycondensation of organic dibasic acids and diols. Due to its high strength, excellent elastic recovery, wrinkle resistance, and shape retention, polyester fiber is widely used in textile and industrial applications.

[0003] With the development of society, people's requirements for polyester fibers are becoming increasingly demanding. The core of the polyester fiber production process lies in the chemical reactions within the polymerization reactor. The concentration distribution of the product, polyethylene terephthalate (PET), is directly related to multiple key parameters. However, factories currently lack sensors that can collect large amounts of data from within the reactor, resulting in a limited amount of training data. Furthermore, the complex mechanisms within the reactor, the turbulent flow involved in the reaction process, and the coupling of multiple physical fields make accurate simulation of the three-dimensional PET concentration field distribution significantly more difficult.

[0004] To date, research on polyester fibers has primarily focused on numerical simulation and data-driven approaches. The core of numerical simulation is to convert the partial differential equations for polyester fibers into algebraic equations for easier solution. These methods primarily include the finite difference method, the finite volume method, the finite element method, and the spectral method. The finite difference method utilizes the inverse of finite differences to convert continuous mathematical equations into discrete equations for solution; the finite volume method implements physical constraints by calculating fluxes within a control volume; the finite element method utilizes the variational principle to provide greater flexibility in handling complex boundary conditions; and the spectral method utilizes Fourier series to reduce computational costs. However, numerical simulation methods typically require significant computational resources and time. To speed up the calculation, the fluid motion in the model is often simplified, and turbulence effects are often ignored. This makes it difficult for numerical simulation methods to accurately simulate the three-dimensional PET concentration field within a polyester fiber polymerization reactor.

[0005] Data-driven approaches primarily utilize training data to train models, enabling them to better fit nonlinear functions. These approaches broadly encompass both discretization-dependent and discretization-independent approaches. However, data-driven approaches rely heavily on large amounts of training data. For the interior of a polyester fiber polymerization reactor, the difficulty of deploying a large number of sensors results in an extremely limited amount of available data. Therefore, data-driven approaches face significant implementation challenges when simulating the three-dimensional PET concentration distribution within the reactor.

[0006] The emergence of physical information neural networks (PINNs) effectively overcomes the limitations of traditional data-driven methods. By incorporating physical laws into the neural network architecture, the data scarcity problem can be alleviated. Currently, PINNs have been successfully applied in fields such as computational fluid dynamics. However, these methods face a significant limitation when applied to polyester fiber polymerization reactors. The reactor involves multi-physics coupling, and existing PINN models typically use a single neural network to fit all physical field variables and equations. When faced with multi-physics coupling problems, it is difficult to accurately capture and express these complex coupling relationships, resulting in the failure of existing PINN models when applied to simulate the three-dimensional PET concentration field distribution within the reactor.

[0007] For example, reference 1 (Deeppipe: A two-stage physics-informed neural network forpredicting mixed oil concentration distribution[J]. Energy. 2023, 276,127452) used a physical information neural network to simulate the concentration distribution field, but the reference did not consider the multi-physics field coupling problem, making the results inaccurate.

[0008] Therefore, it is of great significance to study a method for measuring key parameters based on simulation of three-dimensional PET concentration field distribution. Summary of the Invention

[0009] The purpose of the present invention is to address the deficiencies of the prior art and provide a method for calculating key parameters based on simulated three-dimensional PET concentration field distribution.

[0010] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0011] The method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor comprises the following steps:

[0012] (1) Inferring the causal structure in the polyester fiber polymerization reactor based on information theory knowledge ;

[0013] (2) The causal structure obtained , perform grading and decomposition to obtain the decomposed causal structure 、 and ;

[0014] (3) Each disassembled causal structure drives a stage in the training process;

[0015] (3.1) Order ; Input is spatial coordinate data ; Build a deep neural network DNN 1, impose theoretical constraints on the model according to relevant physical equations and boundary conditions, and output ,make ;

[0016] (3.2) Judgment Is it true? If so, input is spatial coordinate data ,as well as , build a parallel deep neural network Parallel-DNN, use the Causal-guided Init method to the output of step (3.1) Initialize the weights, impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, and output ,make ;

[0017] (3.3) Judgment Is it true? If so, input is spatial coordinate data ,as well as , build a deep neural network DNN 2, and use the Causal-guided Init method to the output of step (3.2) Initialize the weights, impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, and output ,make ;

[0018] (4) Judgment Is it true? If so, input is spatial coordinate data ,as well as 、 and , using the Causal-guided Init method to initialize weights, construct a deep neural network DNN 3, impose theoretical constraints on the model according to relevant physical equations and boundary conditions, and output the three-dimensional PET concentration field distribution;

[0019] (5) Calculate key parameters using theoretical knowledge of polyester fibers combined with the output of three-dimensional PET concentration field distribution.

[0020] The present invention aims to solve the problem in the prior art that it is difficult to accurately simulate the three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor and thus measure key parameters when faced with a small amount of data and multi-physics field coupling. The specific principles are as follows:

[0021] The present invention constructs the theoretical constraints of the model by analyzing the physical equations and boundary conditions of the polyester fiber polymerization reactor, which can effectively alleviate the problem of insufficient data volume; decouples multiple physical fields through a causal-driven multi-stage training strategy; accelerates the training process through a causal-guided neural network weight initialization method; and finally calculates key parameters based on the three-dimensional PET concentration field distribution in the simulated polyester fiber polymerization reactor.

[0022] As the preferred technical solution:

[0023] In the method for calculating key parameters based on the simulated three-dimensional PET concentration field distribution, in step (1), a causal structure in the polymerization reactor is constructed as follows:

[0024] (1.1) Collect data on the following variables in the polyester fiber polymerization reactor: initial state , velocity field , turbulent kinetic energy , turbulent dissipation rate , mass transfer efficiency , temperature field , reaction rate , three-dimensional PET concentration field ;definition ; ;

[0025] (1.2) Iterate the eight variables in step (1.1) as target variables in turn, and the covariate set is the eight variables;

[0026] (1.3) Order ;

[0027] (1.4) Calculate the target variable With covariates The mutual information of is calculated using the following formula:

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] In the formula represents the digamma function, Indicates the number of selected nearest neighbor points, Representing the joint space Dimensions, express Dimensions, express Dimensions, Indicates the The first sample in the space The Euclidean distance to the nearest neighbor, is the sample size, represents the entropy function;

[0033] (1.5) Determine the mutual information value Is it greater than the threshold 0.15? , if established, then Add to target variable The parent node Among them For variables With variables the causal strength of

[0034] (1.6) Judgment Is it true? If so, go to step (1.7). Otherwise, let , return to step (1.4);

[0035] (1.7) Get the target variable The preliminary causal structure ; For any , S is (referring to The meaning of removing x from the structure is a universal expression) is any subset of S, given S, calculate and The conditional mutual information value of , the calculation formula is as follows:

[0036] ;

[0037] (1.8) Determine the mutual information value of the condition Is it less than the threshold 0.05? If so, from Remove it and get the verified causal undirected structure ;

[0038] (1.9) For any ,infer The causal direction in is calculated using the following formula:

[0039] ;

[0040] ;

[0041] ;

[0042] In the formula It is a cause-effect pair. is the measurement function of the ANM algorithm, The threshold value is set to 0.05;

[0043] (1.10) Judgment Is it true? If so, go to step (1.11). Otherwise, let , return to step (1.4);

[0044] (1.11) Obtain the causal structure in the polyester fiber polymerization reactor ;in Represented as a set of variables within the reactor, Represents a set of directed edges and causal strengths between nodes in a DAG (directed acyclic graph).

[0045] In the above-mentioned method for calculating key parameters based on the simulated three-dimensional PET concentration field distribution, the classification and decomposition rules in step (2) are defined as follows:

[0046] (2.1) Hierarchical rules: The initial state node is at the first level; if the node has only one parent node, then the The parent node of the level node must be the Level node; if the node has multiple parent nodes, the The lowest level parent node of a level node should be Level nodes, where ;

[0047] (2.2) Disassembly rules: The causal network composed of the level node and its parent node is recorded as .

[0048] In the method for calculating key parameters based on the simulated three-dimensional PET concentration field distribution, in step (4), the Causal-guided Init method is as follows: for the variables that have been determined to have a causal relationship , the corresponding network weight matrix Decompose into causal principal components and use singular value deviation (SVD) to constrain the weight direction; the calculation uses the following formula:

[0049] ;

[0050] ;

[0051] In the formula The principal component analysis process is The column vector of The principal components of ,ensure that the weight direction is aligned with the parent variable feature space; is an orthogonal matrix; at the same time, the initial amplitude of the weight is adjusted according to the causal strength, and the calculation is based on the following formula:

[0052] ;

[0053] In the formula is the causal strength; for variables that do not have a causal relationship, orthogonal initialization is used to avoid interference.

[0054] In the method for calculating key parameters based on the simulated three-dimensional PET concentration field distribution, in steps (3) and (4), the physical equations satisfied in the polyester fiber polymerization reactor include the mass conservation equation, momentum conservation equation, kinetic equation and energy equation, and the introduction of The two equations of the model are used to further simulate the turbulent flow in the reactor; the boundary conditions include initial conditions and boundary functions.

[0055] In the method for calculating key parameters based on the simulated three-dimensional PET concentration field distribution as described above, the key parameters in step (5) include the number average degree of polymerization , number average molecular weight , weight average molecular weight and intrinsic viscosity .

[0056] In the method for calculating key parameters based on the simulated three-dimensional PET concentration field distribution described above, in step (5), the key parameters are obtained by combining the PET concentration with the theoretical calculation equation of the polyester fiber polymerization process. The specific calculation equation is as follows:

[0057] 1) Number average degree of polymerization ;

[0058] ;

[0059] ;

[0060] ;

[0061] in, is the degree of reaction (i.e. the ratio of monomers converted to polymers), is the initial monomer concentration (bis(hydroxyethyl)terephthalate, BHET), is the three-dimensional PET concentration field, is the concentration of unreacted monomer;

[0062] 2) Number average molecular weight ;

[0063] The molecular weight of the PET repeating unit is 192 g / mol (the molecular weight of ethylene terephthalate). The amount is:

[0064] ;

[0065] 3) Weight average molecular weight ;

[0066] ;

[0067] in, is the weight-average degree of polymerization; in the case of ideal polycondensation and no side reactions, the molecular weight distribution satisfies the Flory distribution. )for:

[0068] ;

[0069] 4) Intrinsic viscosity ;

[0070] The relationship between intrinsic viscosity and molecular weight is given by the Mark-Houwink equation:

[0071] ;

[0072] Among them, for PET in a specific solvent, the commonly used parameters are: , .

[0073] The physical equations for calculating key parameters based on the simulated three-dimensional PET concentration field distribution are as follows:

[0074] 1) The mass conservation equation and its physical equation are calculated using the following formula:

[0075] ;

[0076] ;

[0077] In the formula is the velocity distribution, The physical equation for conservation of mass;

[0078] 2) The momentum conservation equation and its physical equations are calculated in the following form:

[0079] ;

[0080] ;

[0081] In the formula is the fluid density, is the pressure inside the reactor, is the molecular viscosity, is the turbulent viscosity, , , The physical equation for conservation of momentum;

[0082] 3) The two equations of the model and its physical equations are calculated in the following form:

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] In the formula is the turbulent kinetic energy, is the turbulent dissipation rate, 、 、 and is a constant, , , , , turbulent kinetic energy generation term , is the physical equation for turbulent kinetic energy, is the physical equation for the dissipation rate;

[0088] 4) The dynamic equation and its physical equation are calculated in the following form:

[0089] ;

[0090] ;

[0091] In the formula For components The concentration distribution of For components The diffusion coefficient, is the reaction rate, is the physical equation of dynamics;

[0092] 5) The energy conservation equation and its physical equations are calculated in the following form:

[0093] ;

[0094] ;

[0095] In the formula is the specific heat capacity at constant pressure, is the temperature field, is the effective conductivity coefficient, the reaction is exothermic , is the heat of reaction; This is the physical equation for conservation of energy.

[0096] The boundary conditions of the method for calculating key parameters based on the simulated three-dimensional PET concentration field distribution described above include initial conditions and boundary functions, which are as follows:

[0097] 1) Initial conditions, calculated as follows:

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] ;

[0104] In the formula The initial value of the velocity distribution is 5 m / s, The initial value of the temperature distribution is 440 K, The initial value of the concentration distribution is 140 KJ / mol; is the initial condition value of velocity distribution; is the initial condition value of temperature distribution; is the initial condition value of concentration distribution; is the velocity distribution boundary value; is the boundary value of temperature distribution; is the boundary value of concentration distribution; is the concentration field distribution value.

[0105] 2) The boundary function uses the wall function to ensure that the model satisfies the flow profile near the wall. The calculation is as follows:

[0106] ;

[0107] ;

[0108] ;

[0109] ;

[0110] In the formula is the friction speed, is the boundary value of turbulent kinetic energy distribution, is the boundary value of turbulent dissipation rate distribution, Karman constant , is the near-wall distance.

[0111] Beneficial effects:

[0112] (1) The present invention provides a method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution. By specifically analyzing the control equations and boundary conditions within a polyester fiber polymerization reactor, a related loss function is constructed, theoretical constraints are imposed on the model, the model's dependence on data is reduced, and the generated results are consistent with the mechanism within the reactor.

[0113] (2) The present invention provides a method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution, which decouples multiple physical fields by proposing a causal-driven multi-stage training strategy.

[0114] (3) The present invention provides a method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution, which accelerates the training process by proposing a causal-guided weight initialization method. Experimental verification shows that the method proposed in the present invention plays a guiding role in simulating the three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor.

[0115] (4) The present invention provides a method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution, which utilizes theoretical knowledge of polyester fibers combined with the output PET concentration distribution field to further calculate key parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] Figure 1 Flowchart of a method for calculating key parameters based on simulated three-dimensional PET concentration field distribution according to the present invention;

[0117] Figure 2 The schematic diagram of the causal structure of the present invention and its classification and disassembly is shown in FIG. 1 , wherein I is the initial state and B is the velocity field. , C is the turbulent kinetic energy , D is the turbulent dissipation rate , E is the mass transfer efficiency , F is the temperature field , G is the reaction rate , H is the three-dimensional PET concentration field , For variables With variables the causal strength of

[0118] Figure 3 A schematic diagram of the causal-driven multi-stage training strategy of the present invention;

[0119] Figure 4 is a schematic diagram of a polyester fiber polymerization reactor of the present invention;

[0120] Figure 5 1 is a comparison chart of real data at different locations under 8000 data volumes in Example 1 of the present invention, PINN, and the present invention (CD-MSPINN);

[0121] Figure 6 This figure shows the comparison results of real data at different locations under the data volume of 4800 in Example 2 of the present invention, PINN, and the present invention (CD-MSPINN).

[0122] in Figures 1 to 6 In the example, backward() is the backpropagation operation, and Causal-guided Init is the causal-guided initialization operation. DETAILED DESCRIPTION

[0123] Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiments are only used to illustrate the present invention and are not used in limiting the scope of the present invention.In addition, should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall equally within the scope limited by the appended claims of the application.

[0124] Methods for calculating key parameters based on simulated three-dimensional PET concentration field distribution, such as Figure 1 As shown, the following steps are included:

[0125] (1) Inferring the causal structure in the polyester fiber polymerization reactor based on information theory knowledge ;

[0126] (1.1) Collect data on the following variables in the polyester fiber polymerization reactor: initial state , velocity field , turbulent kinetic energy , turbulent dissipation rate , mass transfer efficiency , temperature field , reaction rate , three-dimensional PET concentration field ;definition ; ;

[0127] (1.2) Iterate the eight variables in step (1.1) as target variables in turn, and the covariate set is the eight variables;

[0128] (1.3) Order ;

[0129] (1.4) Calculate the target variable With covariates The mutual information of is calculated using the following formula:

[0130] ;

[0131] ;

[0132] ;

[0133] ;

[0134] In the formula represents the digamma function, Indicates the number of selected nearest neighbor points, Representing the joint space Dimensions, express Dimensions, express Dimensions, Indicates the The first sample in the space The Euclidean distance to the nearest neighbor, is the sample size, represents the entropy function;

[0135] (1.5) Determine the mutual information value Is it greater than the threshold 0.15? , if established, then Add to target variable Parent and child nodes Among them For variables With variables the causal strength of

[0136] (1.6) Judgment Is it true? If so, go to step (1.7). Otherwise, let , return to step (1.4);

[0137] (1.7) Get the target variable The preliminary causal structure ; For any , S is For any subset of S, calculate and The conditional mutual information value of , the calculation formula is as follows:

[0138] ;

[0139] (1.8) Determine the mutual information value of the condition Is it less than the threshold 0.05? If so, from Remove it and get the verified causal undirected structure ;

[0140] (1.9) For any ,infer The causal direction in is calculated using the following formula:

[0141] ;

[0142] ;

[0143] ;

[0144] In the formula It is a cause-effect pair. is the measurement function of the ANM algorithm, The threshold value is set to 0.05;

[0145] (1.10) Judgment Is it true? If so, go to step (1.11). Otherwise, let , return to step (1.4);

[0146] (1.11) Obtain the causal structure in the polyester fiber polymerization reactor ;in Represented as a set of variables within the reactor, Represents a set of directed edges and causal strengths between nodes in a DAG (directed acyclic graph).

[0147] (2) If Figure 2 As shown, the causal structure obtained , perform grading and decomposition to obtain the decomposed causal structure 、 and ;

[0148] The definitions of classification and disassembly rules are as follows:

[0149] (2.1) Hierarchical rules: The initial state node is at the first level; if the node has only one parent node, then the The parent node of the level node must be the Level node; if the node has multiple parent nodes, the The lowest level parent node of a level node should be Level nodes, where ;

[0150] (2.2) Disassembly rules: The causal network composed of the level node and its parent node is recorded as .

[0151] (3) Each disassembled causal structure drives a stage in the training process;

[0152] (3.1) Order ; Input is spatial coordinate data ; Build a deep neural network DNN 1, impose theoretical constraints on the model according to relevant physical equations and boundary conditions, and output ,make ;

[0153] (3.2) Judgment Is it true? If so, input is spatial coordinate data ,as well as , build a parallel deep neural network Parallel-DNN, use the Causal-guided Init method to the output of step (3.1) Initialize the weights, impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, and output ,make

[0154] (3.3) Judgment Is it true? If so, input is spatial coordinate data ,as well as , build a deep neural network DNN 2, and use the Causal-guided Init method to the output of step (3.2) Initialize the weights, impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, and output ,make ;

[0155] Theoretical constraints are imposed on the model based on relevant physical equations and boundary conditions, including:

[0156] (a) Judgment Is it true? If not, go to step (b). If it is true, then drive, The results show that the initial state node mainly affects the velocity field and turbulence model. Therefore, this stage (stage 1) mainly simulates the velocity distribution and turbulence parameters. The physical and data errors related to the velocity distribution and turbulence model are used to constrain the training process. Considering that the velocity distribution and turbulence model satisfy the mass conservation equation, momentum conservation equation and turbulence equation ( equation, Equation), so the physical constraint loss function satisfied in stage 1 is calculated using the following formula:

[0157] ;

[0158] In the formula is the weight of the physical equation, Refers to the total number of sampling points in the domain. The residual loss of PDE can be achieved through automatic differentiation; is the physical information loss function of stage 1; is the mass conservation physical function; is the momentum conservation physical function; is the turbulent kinetic energy physical function; is the physical function of turbulent kinetic energy dissipation rate.

[0159] The velocity distribution and turbulence model also satisfy the initial conditions and boundary functions, so the boundary constraint loss satisfied in stage 1 is calculated using the following formula:

[0160] ;

[0161] in is the total number of boundary sampling points; is the boundary loss function of stage one, is the velocity distribution boundary value; is the turbulent kinetic energy k and the turbulent kinetic energy dissipation rate The boundary value of .

[0162] The total loss function is calculated using the following formula:

[0163] ;

[0164] ;

[0165] ;

[0166] Where X refers to the variable in the reactor, is the weight of the loss function; is the data error loss function, is the data error loss function of stage one, is the actual value, Simulated values ​​generated for the model;

[0167] (b) Judgment Is it true? If not, go to step (c). If it is true, then Drive, we found Because it is a parallel causal structure, the second stage driven by it is a parallel network structure consisting of two parallel DNN networks to simulate temperature distribution and mass transfer efficiency respectively. In the pre-regression network simulating mass transfer efficiency, in addition to the constraints of the first stage, it is also subject to data constraints. The calculation uses the following formula:

[0168] ;

[0169] ;

[0170] ;

[0171] In the formula is the mass transfer efficiency; is the loss function of stage 1; is the data error loss function; is the loss function of stage 2; is the loss function of network 1 in stage 2;

[0172] In the pre-regression network simulating temperature distribution, in addition to the constraints of the stage 1 module, the constraints of the heat transfer equation, boundary condition constraints, and data constraints must also be met. The overall constraint calculation uses the following formula:

[0173] ;

[0174] ;

[0175] ;

[0176] ;

[0177] In the formula is the temperature distribution; is the heat transfer physical function; is the boundary value of temperature distribution; is the loss function of network 2 in stage 2;

[0178] (c) Phase 3 is Driven by It can be found that temperature distribution and mass transfer efficiency affect the reaction rate at the same time, so stage three is used to simulate the reaction rate. In addition to meeting the constraints of stage two, it is also necessary to meet the constraints of the kinetic equation and data constraints. The overall constraint calculation uses the following formula:

[0179] ;

[0180] ;

[0181] ;

[0182] ;

[0183] In the formula is the reaction rate; is the loss function of stage three; is the dynamic function.

[0184] (4) Judgment Is it true? If so, input is spatial coordinate data ,as well as 、 and , using the Causal-guided Init method to initialize weights, construct a deep neural network DNN 3, impose theoretical constraints on the model according to relevant physical equations and boundary conditions, and output the three-dimensional PET concentration field distribution;

[0185] The Causal-guided Init method is as follows: For variables with causal relationships , the corresponding network weight matrix Decompose into causal principal components and use singular value deviation (SVD) to constrain the weight direction; the calculation uses the following formula:

[0186] ;

[0187] ;

[0188] In the formula The principal component analysis process is The column vector of The principal components of ,ensure that the weight direction is aligned with the parent variable feature space; is an orthogonal matrix; at the same time, the initial amplitude of the weight is adjusted according to the causal strength, and the calculation is based on the following formula:

[0189] ;

[0190] In the formula is the causal strength; for variables that do not have a causal relationship, orthogonal initialization is used to avoid interference;

[0191] In step (3) and step (4), the physical equations satisfied in the polyester fiber polymerization reactor include the mass conservation equation, momentum conservation equation, kinetic equation and energy equation, and the introduction of The two equations of the model are used to further simulate the turbulent flow in the reactor; the boundary conditions include initial conditions and boundary functions;

[0192] The physical equations are as follows:

[0193] 1) The mass conservation equation and its physical equation are calculated using the following formula:

[0194] ;

[0195] ;

[0196] In the formula is the velocity distribution, The physical equation for conservation of mass;

[0197] 2) The momentum conservation equation and its physical equations are calculated in the following form:

[0198] ;

[0199] ;

[0200] In the formula is the fluid density, is the pressure inside the reactor, is the molecular viscosity, is the turbulent viscosity, , , The physical equation for conservation of momentum;

[0201] 3) The two equations of the model and its physical equations are calculated in the following form:

[0202] ;

[0203] ;

[0204] ;

[0205] ;

[0206] In the formula is the turbulent kinetic energy, is the turbulent dissipation rate, 、 、 and is a constant, , , , , turbulent kinetic energy generation term , is the physical equation for turbulent kinetic energy, is the physical equation for the dissipation rate;

[0207] 4) The dynamic equation and its physical equation are calculated in the following form:

[0208] ;

[0209] ;

[0210] In the formula For components The concentration distribution of For components The diffusion coefficient, is the reaction rate, is the physical equation of dynamics;

[0211] 5) The energy conservation equation and its physical equations are calculated in the following form:

[0212] ;

[0213] ;

[0214] In the formula is the specific heat capacity at constant pressure, is the temperature field, is the effective conductivity coefficient, the reaction is exothermic , is the heat of reaction; This is the physical equation for conservation of energy.

[0215] Boundary conditions include initial conditions and boundary functions, as follows:

[0216] 1) Initial conditions, calculated as follows:

[0217] ;

[0218] ;

[0219] ;

[0220] ;

[0221] ;

[0222] ;

[0223] In the formula The initial value of the velocity distribution is 5 m / s, The initial value of the temperature distribution is 440 K, The initial value of the concentration distribution is 140 KJ / mol; is the initial condition value of velocity distribution; is the initial condition value of temperature distribution; is the initial condition value of concentration distribution; is the velocity distribution boundary value; is the boundary value of temperature distribution; is the boundary value of concentration distribution; is the concentration field distribution value;

[0224] 2) The boundary function uses the wall function to ensure that the model satisfies the flow profile near the wall. The calculation is as follows:

[0225] ;

[0226] ;

[0227] ;

[0228] ;

[0229] In the formula is the friction speed, is the boundary value of turbulent kinetic energy distribution, is the boundary value of turbulent dissipation rate distribution, Karman constant , Karman constant , is the distance near the wall;

[0230] The theoretical constraint calculation adopts the following formula:

[0231] ;

[0232] ;

[0233] ;

[0234] ;

[0235] In the formula is the boundary value of the concentration field; is the physical information loss function; the entire training process diagram is as follows Figure 3 shown.

[0236] (5) Calculate key parameters using theoretical knowledge of polyester fiber combined with the output of three-dimensional PET concentration field distribution; key parameters include number average degree of polymerization , number average molecular weight , weight average molecular weight and intrinsic viscosity ; The specific calculation equation is as follows:

[0237] 1) Number average degree of polymerization ;

[0238] ;

[0239] ;

[0240] ;

[0241] in, is the degree of reaction, is the initial monomer concentration, is the three-dimensional PET concentration field, is the concentration of unreacted monomer;

[0242] 2) Number average molecular weight ;

[0243] ;

[0244] 3) Weight average molecular weight ;

[0245] ;

[0246] in, is the weight average degree of polymerization;

[0247] ;

[0248] 4) Intrinsic viscosity ;

[0249] ;

[0250] in, , , The initial value of the concentration distribution is 140 KJ / mol.

[0251] The following two specific examples illustrate the method of calculating key parameters based on the simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor of the present invention, as follows:

[0252] The simulation experiments were conducted on data volumes of 8000 and 4800, respectively. The simulation process was simulated according to the above specific implementation steps to verify the data adaptability of the present invention. The reactor structures in the two embodiments are as follows: Figure 4 The experimental parameters are shown in Table 1.

[0253] Table 1. Experimental parameters parameter Numerical Reactor height (D) 20 m Reactor diameter (L) 13 m Diffusion rate <![CDATA[1×10 -8 ]]> Density of catalyst solvent <![CDATA[2640 kg / m 3 ]]> Heat capacity of catalyst solvent 2550 J / kg / K Inlet velocity 5 m / s Inlet temperature 440 K Reaction heat 140 kJ / mol

[0254] Example 1

[0255] In this embodiment, the amount of data collected is 8000. In this embodiment, the PINN model of literature 2 (A physics-informed neural network for turbulent wake simulations behind wind turbines. Physics of Fluids 1 January 2025; 37 (1): 015110.) and the CD-MSPINN model of the present invention are simulated and compared with each other. The comparison results are shown in Figure 2. Figure 5 shown.

[0256] from Figure 5 It can be seen that at different positions (0.1D, 0.2D, 0.5D, 0.8D), the model CD-MSPINN of the present invention has higher accuracy than the traditional PINN simulation method, and can closely follow the effect of real data; specifically: by statistically analyzing the root mean square errors of the data simulated by the two models at different positions (0.1D, 0.2D, 0.5D, 0.8D), the root mean square errors of the PINN model are 6.186, 4.158, 4.725, and 2.631, respectively, and the root mean square errors of the CD-MSPINN model are 3.672, 2.130, 2.257, and 0.903, respectively.

[0257] Example 2

[0258] In this embodiment, the amount of data collected is 4800. In this embodiment, the traditional PINN simulation of three-dimensional PET concentration field distribution and the present invention are simulated and the direct results of the two are compared. Figure 6 shown.

[0259] from Figure 6It can be seen that at different positions (0.1D, 0.2D, 0.5D, 0.8D), the model CD-MSPINN of the present invention has higher accuracy than the traditional PINN simulation method, and can closely follow the effect of real data; specifically: by statistically analyzing the root mean square errors of the data simulated by the two models at different positions (0.1D, 0.2D, 0.5D, 0.8D), the root mean square errors of the PINN model are 13.109, 10.387, 10.388, and 7.554, respectively, and the root mean square errors of the CD-MSPINN model are 7.281, 5.393, 6.652, and 2.665, respectively.

Claims

1. A method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor, characterized in that: The following steps are involved: (1) Inferring the causal structure in the polyester fiber polymerization reactor based on information theory knowledge ; (2) The causal structure obtained , perform grading and decomposition to obtain the decomposed causal structure 、 and ; (3) Each disassembled causal structure drives a stage in the training process; (3.1) Order ; Input is spatial coordinate data ; Build a deep neural network DNN 1, impose theoretical constraints on the model according to relevant physical equations and boundary conditions, and output ,make ; (3.2) Judgment Is it true? If so, input is spatial coordinate data ,as well as , build a parallel deep neural network Parallel-DNN, use the Causal-guided Init method to the output of step (3.1) Initialize the weights, impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, and output ,make ; (3.3) Judgment Is it true? If so, input is spatial coordinate data ,as well as , build a deep neural network DNN 2, and use the Causal-guided Init method to the output of step (3.2) Initialize the weights, impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, and output ,make ; (4) Judgment Is it true? If so, input is spatial coordinate data ,as well as 、 and , using the Causal-guided Init method to initialize weights, construct a deep neural network DNN 3, impose theoretical constraints on the model according to relevant physical equations and boundary conditions, and output the three-dimensional PET concentration field distribution; (5) Calculate key parameters using theoretical knowledge of polyester fibers combined with the output of three-dimensional PET concentration field distribution.

2. The method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor according to claim 1, characterized in that: In step (1), the causal structure in the polymerization reactor is constructed as follows: (1.1) Collect data on the following variables in the polyester fiber polymerization reactor: initial state , velocity field , turbulent kinetic energy , turbulent dissipation rate , mass transfer efficiency , temperature field , reaction rate , three-dimensional PET concentration field ; (1.2) Iterate the eight variables in step (1.1) as target variables in turn, and the covariate set is the eight variables; (1.3) Order ; (1.4) Calculate the target variable With covariates The mutual information of is calculated using the following formula: ； ； ； ； In the formula represents the digamma function, z represents the number of selected nearest neighbor points, Representing the joint space Dimensions, express Dimensions, express Dimensions, Indicates the The first sample in the space The Euclidean distance to the nearest neighbor, is the sample size, represents the entropy function; (1.5) Determine the mutual information value Is it greater than the threshold 0.15? If so, Add to target variable The parent node of middle; (1.6) Judgment Is it true? If so, go to step (1.7). Otherwise, let , return to step (1.4); (1.7) Get the target variable The preliminary causal structure of ; For any , S is For any subset of and The conditional mutual information value of , the calculation formula is as follows: ； (1.8) Determine the mutual information value of the condition Is it less than the threshold value 0.05? If so, from Remove it and get the verified causal undirected structure ; (1.9) For any ,infer The causal direction in is calculated using the following formula: ； ； ； In the formula It is a cause-effect pair. is the measurement function of the ANM algorithm, The threshold value is set to 0.05; (1.10) Judgment Is it true? If so, go to step (1.11). Otherwise, let , return to step (1.4); (1.11) Obtain the causal structure in the polyester fiber polymerization reactor ;in Represented as a set of variables within the reactor, Represents the set of directed edges and causal strengths between nodes in a DAG.

3. The method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor according to claim 1, characterized in that: The definitions of the classification and disassembly rules in step (2) are as follows: (2.1) Hierarchical rules: The initial state node is at the first level; if the node has only one parent node, then The parent node of the level node must be the Level node; if the node has multiple parent nodes, the The lowest level parent node of a level node should be Level nodes, where ; (2.2) Disassembly rules: The causal network composed of the level node and its parent node is recorded as .

4. The method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor according to claim 1, characterized in that: In step (4), the Causal-guided Init method is as follows: For variables with causal relationships , the corresponding network weight matrix Decompose into causal principal components and use singular values ​​to constrain the weight direction; the calculation uses the following formula: ； ； In the formula For the principal component analysis process, the column vector of V is The principal components of ,ensure that the weight direction is aligned with the parent variable feature space; is an orthogonal matrix; at the same time, the initial amplitude of the weight is adjusted according to the causal strength, and the calculation is based on the following formula: ； In the formula is the causal strength; for variables that do not have a causal relationship, orthogonal initialization is used to avoid interference.

5. The method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor according to claim 1, characterized in that: In step (3) and step (4), the physical equations satisfied in the polyester fiber polymerization reactor include the mass conservation equation, momentum conservation equation, kinetic equation and energy equation, and the introduction of The two equations of the model are used to further simulate the turbulent flow in the reactor; the boundary conditions include initial conditions and boundary functions.

6. The method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor according to claim 1, characterized in that: The key parameters in step (5) include the number average degree of polymerization , number average molecular weight , weight average molecular weight and intrinsic viscosity .

7. The method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor according to claim 6, characterized in that: In step (5), the key parameters are obtained by combining the PET concentration with the theoretical calculation equation of the polyester fiber polymerization process. The specific calculation equation is as follows: 1) Number average degree of polymerization ; ； ； ； in, is the degree of reaction, is the initial monomer concentration, is the three-dimensional PET concentration field, is the concentration of unreacted monomer; 2) Number average molecular weight ; ； 3) Weight average molecular weight ; ； in, is the weight average degree of polymerization; ； 4) Intrinsic viscosity ; ； in, , .

8. The method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor according to claim 5, characterized in that: The physical equations are as follows: 1) The mass conservation equation and its physical equation are calculated using the following formula: ； ； In the formula is the velocity distribution, The physical equation for conservation of mass; 2) The momentum conservation equation and its physical equations are calculated in the following form: ； ； In the formula is the fluid density, The pressure inside the reactor, is the molecular viscosity, is the turbulent viscosity, , , The physical equation for conservation of momentum; 3) The two equations of the model and its physical equations are calculated in the following form: ； ； ； ； In the formula is the turbulent kinetic energy, is the turbulent dissipation rate, 、 、 and is a constant, , , , , turbulent kinetic energy generation term , is the physical equation for turbulent kinetic energy, is the physical equation for the dissipation rate; 4) The dynamic equation and its physical equation are calculated in the following form: ； ； In the formula For components The concentration distribution of For components The diffusion coefficient, is the reaction rate, is the physical equation of dynamics; 5) The energy conservation equation and its physical equations are calculated in the following form: ； ； In the formula is the specific heat capacity at constant pressure, is the temperature field, is the effective conductivity coefficient, the reaction is exothermic , is the heat of reaction; This is the physical equation for conservation of energy.

9. The method for calculating key parameters based on a simulated three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor according to claim 5, characterized in that: The boundary conditions are as follows: 1) Initial conditions, calculated as follows: ； ； ； ； ； ； In the formula The initial value of the velocity distribution is 5 m / s, The initial value of the temperature distribution is 440 K, The initial value of the concentration distribution is 140 KJ / mol; is the initial condition value of velocity distribution; is the initial condition value of temperature distribution; is the initial condition value of concentration distribution; is the velocity distribution boundary value; is the boundary value of temperature distribution; is the boundary value of concentration distribution; is the concentration field distribution value; 2) The boundary function uses the wall function to ensure that the model satisfies the flow profile near the wall. The calculation is as follows: ； ； ； ； In the formula is the friction speed, is the boundary value of turbulent kinetic energy distribution, is the boundary value of turbulent dissipation rate distribution, Karman constant , is the near-wall distance.

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