Method for measuring key parameters based on simulated three-dimensional pet concentration field distribution

Abstract

The application belongs to the technical field of polyester fibers, and relates to a method for measuring and calculating key parameters based on simulation of a three-dimensional PET concentration field distribution. Firstly, the causal structure in a polyester fiber reactor is inferred according to information theory; secondly, the causal structure is classified and disassembled to obtain the disassembled causal structure and ; then each disassembled causal structure drives a stage in the training process to obtain output and ; then and are jointly input, weight initialization is performed by using a Causal-guided Init method, a deep neural network DNN is constructed, theoretical constraints are applied to the model, and a three-dimensional PET concentration field distribution is output; finally, the theoretical knowledge of polyester fibers is combined with the output three-dimensional PET concentration field distribution to measure and calculate key parameters. The method 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 accuracy.

Description

TECHNICAL FIELD

[0001] The application 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

[0002] Polyester fibers, commonly known as polyester fibers, are synthetic fibers obtained by spinning polyester obtained by polycondensation of organic diacid and diol. At present, polyester fibers are widely used in textile and industrial fields due to their high strength, good elastic recovery, good wrinkle resistance and good shape retention.

[0003] With the development of society, people have higher and higher requirements for polyester fibers. The core of the polyester fiber production process is the chemical reaction in the polymerization reactor, and the concentration distribution of the product polyethylene terephthalate (PET) in the reactor is directly related to multiple key parameters. However, there are no sensors in the factory to collect a large amount of data inside the reactor, resulting in a small amount of trainable data. In addition, due to the complexity of the mechanism inside the reactor, the reaction process involves turbulent flow and multiple physical field coupling, making it very difficult to accurately simulate the three-dimensional PET concentration field distribution.

[0004] So far, the research on polyester fibers mainly includes numerical simulation method and data-driven method. The core of the numerical simulation method is to convert the partial differential equation of polyester fibers into algebraic equation for easy solving. It mainly includes finite difference method, finite volume method, finite element method and spectral method. The finite difference method uses finite difference approximation to convert continuous mathematical equations into discrete equations for solving; the physical constraint of the finite volume method is completed by calculating the flux in the control volume; the finite element method is more flexible in handling complex boundary conditions through the variational principle; the spectral method reduces the computational cost through Fourier series. However, numerical simulation method usually requires a large amount of computing resources and time cost, and in order to speed up the calculation speed, the model of fluid motion is usually simplified and the turbulent effect is ignored, which makes it difficult for numerical simulation method to accurately simulate the three-dimensional PET concentration field in the polyester fiber polymerization reactor.

[0005] Data-driven method mainly uses training data to train the model, so that the model can better fit the nonlinear function. It roughly includes two aspects: discrete-dependent and discrete-independent. However, data-driven method highly depends on a large amount of training data. For the interior of polyester fiber polymerization reactor, it is difficult to arrange a large number of sensors, resulting in extremely limited amount of available data. Therefore, when simulating the three-dimensional PET concentration field distribution in the polymerization reactor, data-driven method faces great implementation challenges.

[0006] The emergence of physical information neural network (PINN) effectively makes up for the limitations of traditional data-driven methods. By integrating physical laws into the neural network architecture, the problem of data scarcity can be alleviated. Currently, PINN has been successfully applied in the field of computational fluid dynamics and other fields. However, these methods have a great limitation when applied to polyester fiber polymerization reactors. The reactor involves multi-physical field coupling, and the existing PINN model usually uses a single neural network to fit all physical field variables and equations. When facing multi-physical field coupling problems, it is difficult to accurately capture and express these complex coupling relationships, resulting in the failure of the existing PINN model when applied to simulate the three-dimensional PET concentration field distribution in the reactor.

[0007] For example, document 1 (Deeppipe: A two-stage physics-informed neural network for predicting mixed oil concentration distribution[J]. Energy. 2023, 276,127452) uses a physical information neural network to simulate the concentration distribution field, but this document does not consider the multi-physical field coupling problem, making the result 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

[0009] The purpose of the present application is to overcome the shortcomings of the prior art and provide a method for measuring key parameters based on simulation of three-dimensional PET concentration field distribution.

[0010] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

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

[0012] (1) According to the information theory knowledge, the causal structure in the polyester fiber polymerization reactor is inferred ;

[0013] (2) The obtained causal structure is classified and disassembled to obtain disassembled causal structures , and ;

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

[0015] (3.1) Let ; input spatial coordinate data ; build a deep neural network DNN 1, impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, output , let ;

[0016] (3.2) judge whether is established, if yes, input spatial coordinate data and , build a parallel deep neural network Parallel-DNN, use the Causal-guided Init method to initialize the weight of the output in step (3.1), impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, output , let ;

[0017] (3.3) judge whether is established, if yes, input spatial coordinate data and , build a deep neural network DNN 2, use the Causal-guided Init method to initialize the weight of the output in step (3.2), impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, output , let ;

[0018] (4) judge whether is established, if yes, input spatial coordinate data , and , and , use the Causal-guided Init method to initialize the weight, build a deep neural network DNN 3, impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, output three-dimensional PET concentration field distribution;

[0019] (5) utilize the theoretical knowledge of polyester fiber to measure key parameters combined with the output three-dimensional PET concentration field distribution.

[0020] The purpose of the application is to solve the problem that the prior art is difficult to accurately simulate the three-dimensional PET concentration field distribution in the polyester fiber polymerization reactor and then measure the key parameters when facing the problems of small amount of data in the polyester fiber polymerization reactor and multi-physical field coupling, and the specific principle is as follows:

[0021] This invention constructs theoretical constraints for 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; it decouples multiple physical fields through a causal-driven multi-stage training strategy; it accelerates the training process through a causal-guided neural network weight initialization method; and finally, it calculates key parameters based on the simulated three-dimensional PET concentration field distribution within the polyester fiber polymerization reactor.

[0022] As a preferred technical solution:

[0023] As described above, the method for calculating key parameters based on simulated three-dimensional PET concentration field distribution, in step (1), constructs the causal structure within the polymerization reactor, 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 through the eight variables in step (1.1) one by one as the target variables, and the covariate set is the eight variables;

[0026] (1.3) Let ;

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

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] In the formula Represents the digamma function. This indicates the number of nearest neighbors selected. Represents joint space Dimensions express Dimensions represents the dimension of , represents the Euclidean distance of the th nearest neighbor of the th sample in space, is the number of samples, represents the entropy function;

[0033] (1.5) judge whether the mutual information value is greater than the threshold value 0.15, let , if true, add to the parent node of the target variable , wherein is the causal strength of the variable and the variable ; (1.6) judge whether is true, if yes, go to step (1.7), otherwise, let

[0034] , return to step (1.4); (1.7) obtain the preliminary causal structure of the target variable ; for any

[0035] , S is any subset of (the meaning of removing x from the structure of , which is a general expression), calculate the conditional mutual information value and under the condition of S, and the formula used for calculation is as follows: ;

[0036] ;

[0037] (1.8) judge whether the conditional mutual information value is less than the threshold value 0.05, if true, remove from to obtain the verified causal undirected structure ;

[0038] (1.9) for any , infer the causal direction in , and the formula used for calculation is as follows:

[0039] ;

[0040] ;

[0041] ; ​​​

[0042] wherein is a causal pair, is a measure function of ANM algorithm, is a set threshold value 0.05;

[0043] (1.10) judging whether or not is established, if yes, entering step (1.11), otherwise, letting , returning to step (1.4);

[0044] (1.11) obtaining the causal structure in the polyester fiber polymerization reactor ; wherein represents a variable set in the reactor, represents a set of directed edges and causal strength between nodes in the DAG (Directed Acyclic Graph).

[0045] The method for measuring key parameters based on simulation of three-dimensional PET concentration field distribution as described above, the definition of hierarchical and disassembly rules in step (2) is as follows:

[0046] (2.1) hierarchical rule: the initial state node is located in the first level; if the node has only one parent node, the parent node of the first level node must be the second level node; if the node has multiple parent nodes, the lowest level parent node of the first level node should be the second level node, wherein ;

[0047] (2.2) disassembly rule: the causal network composed of the first level node and its parent nodes is recorded as .

[0048] The method for measuring key parameters based on simulation of three-dimensional PET concentration field distribution as described above, in step (4), the Causal-guided Init method is as follows: for the variable judged to have an existing causal relationship, the corresponding network weight matrix is decomposed into causal principal components, and the singular value (SVD) is used to constrain the weight direction; the calculation uses the following formula:

[0049] ;

[0050] ;

[0051] wherein is a principal component analysis process, the column vector of The principal component of the main component, ensure the weight direction and the parent variable characteristic space alignment; is an orthogonal matrix; meanwhile, the initial amplitude of the weight is adjusted according to the causal strength, and the calculation adopts the following formula:

[0052] ;

[0053] In the formula, is the causal strength; for variables without causal relationship, orthogonal initialization is adopted to avoid interference.

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

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

[0056] The method for measuring key parameters based on simulation of three-dimensional PET concentration field distribution as described above, in step (5), the key parameters are obtained from the PET concentration combined with the polyester fiber polymerization process theory measurement equation, and the specific measurement equation is as follows:

[0057] 1) Number average polymerization degree ;

[0058] ;

[0059] ;

[0060] ;

[0061] Wherein, is the reaction degree (i.e. the proportion of monomer converted into polymer), is the initial monomer concentration (bis-hydroxyethyl terephthalate, BHET), is the three-dimensional PET concentration field, is the unreacted monomer concentration;

[0062] 2) Number average molecular weight ;

[0063] The molecular weight of the PET repeat unit is 192 g / mol (molecular weight of ethylene terephthalate). Thus, the number average molecular weight is:

[0064] ;

[0065] 3) Weight average molecular weight ;

[0066] ;

[0067] wherein, is the weight average degree of polymerization; in the case of ideal polycondensation without side reactions, the molecular weight distribution follows the Flory distribution. In this case, the weight average degree of polymerization (Mw) is:

[0068] ;

[0069] 4) Intrinsic viscosity ;

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

[0071] ;

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

[0073] The method for calculating the key parameters based on the simulated three-dimensional PET concentration field distribution as described above has the following physical equations:

[0074] 1) Mass conservation equation and its physical equation, the calculation uses the following formula:

[0075] ;

[0076] ;

[0077] wherein is the velocity distribution, is the physical equation of mass conservation;

[0078] 2) Momentum conservation equation and its physical equation, the calculation uses the following form:

[0079] ;

[0080] ;

[0081] wherein is the fluid density,​​ P is the pressure in the reactor, μ is the molecular viscosity, μt is the turbulent viscosity, , , is the physical equation of momentum conservation;

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

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] where is the turbulent kinetic energy, is the turbulent dissipation rate, , , and are constants, , , , , the turbulent kinetic energy generation term , is the physical equation of the turbulent kinetic energy, is the physical equation of the dissipation rate;

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

[0089] ;

[0090] ;

[0091] where is the concentration profile of the component , is the diffusion coefficient of the component , is the reaction rate, is the physical equation of the kinetics;

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

[0093] ;

[0094] ;

[0095] wherein Cp is the constant pressure specific heat capacity, T is the temperature field, Keff is the effective thermal conductivity, the reaction exothermic , Q is the reaction heat; E is the physical equation of energy conservation.

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

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

[0098] ;

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] ;

[0104] wherein V0 is the initial value of the velocity distribution, 5 m / s, T0 is the initial value of the temperature distribution, 440 K, C0 is the initial value of the concentration distribution, 140 KJ / mol; V0 is the initial condition value of the velocity distribution; T0 is the initial condition value of the temperature distribution; C0 is the initial condition value of the concentration distribution; V is the boundary value of the velocity distribution; T is the boundary value of the temperature distribution; C is the boundary value of the concentration distribution; C is the concentration field distribution value.

[0105] 2) The boundary function uses the wall function to ensure that the model meets the flow profile near the wall, calculated as follows:

[0106] ;

[0107] ;

[0108] ;

[0109] ;

[0110] wherein is the friction velocity, is the turbulent kinetic energy distribution boundary value, is the turbulent dissipation rate distribution boundary value, the Karman constant , is the near-wall distance.

[0111] Advantages:

[0112] (1) The method for measuring key parameters according to a simulated three-dimensional PET concentration field distribution of the application constructs a related loss function by specific analysis of control equations and boundary conditions in a polyester fiber polymerization reactor, applies theoretical constraints to the model, reduces the dependence of the model on data, and makes the generated results conform to the mechanism in the reactor.

[0113] (2) The method for measuring key parameters according to a simulated three-dimensional PET concentration field distribution of the application decouples multiple physical fields by proposing a causal driving multi-stage training strategy.

[0114] (3) The method for measuring key parameters according to a simulated three-dimensional PET concentration field distribution of the application accelerates the training process by the proposed causal guidance weight initialization method; and through experimental verification, the method proposed in the application has a guiding role in simulating a three-dimensional PET concentration field distribution in a polyester fiber polymerization reactor.

[0115] (4) The method for measuring key parameters according to a simulated three-dimensional PET concentration field distribution of the application further measures key parameters by using theoretical knowledge of polyester fibers in combination with the output PET concentration distribution field. BRIEF DESCRIPTION OF DRAWINGS

[0116] Figure 1 is a flowchart of the method for measuring key parameters according to a simulated three-dimensional PET concentration field distribution of the application;

[0117] Figure 2 is a causal structure and a schematic diagram of the causal structure after grading and disassembly of the application; wherein I is an initial state, B is a velocity field , C is turbulent kinetic energy , D is turbulent dissipation rate , E is mass transfer efficiency , F is temperature field , G is reaction rate , H is three-dimensional PET concentration field , is a variable and the causal strength of the variable ;

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

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

[0120] Figure 5 a comparison result graph of real data, PINN and the present application (CD-MSPINN) at different positions under a data volume of 8000 in Example 1 of the present application;

[0121] Figure 6 a comparison result graph of real data, PINN and the present application (CD-MSPINN) at different positions under a data volume of 4800 in Example 2 of the present application.

[0122] wherein Figures 1-6 , backward() is a back propagation operation, and Causal-guided Init is a causal-guided initialization operation. DETAILED DESCRIPTION

[0123] The present application will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present application and not used to limit the scope of the present application. In addition, it should be understood that after reading the content taught by the present application, those skilled in the art can make various modifications or changes to the present application, and these equivalent forms also fall within the scope defined by the appended claims of the present application.

[0124] A method for measuring key parameters based on simulated three-dimensional PET concentration field distribution, as shown in Figure 1 , comprises the following steps:

[0125] (1) inferring the causal structure in the polyester fiber polymerization reactor according to information theory knowledge ;

[0126] (1.1) collect data of 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 ; define ; ;

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

[0128] (1.3) Let ;

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

[0130] ;

[0131] ;

[0132] ;

[0133] ;

[0134] In the formula Represents the digamma function. This indicates the number of nearest neighbors selected. Represents joint space Dimensions express Dimensions express Dimensions Indicates the first The nth sample in space The nearest neighbor European distance, It is the sample size. Represents the entropy function;

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

[0136] (1.6) Judgment Check if it is true. If yes, proceed to step (1.7); otherwise, let... Return to step (1.4);

[0137] (1.7) Obtain the target variable Preliminary causal structure For any S is For any subset of S, compute the following: compute S = S * ... and conditional mutual information value The formula used in the calculation is as follows:

[0138] ;

[0139] (1.8) Determine whether the conditional mutual information value is less than the threshold value 0.05, and if so, remove from to obtain the verified causal undirected structure ;

[0140] (1.9) For any , infer the causal direction in , and the formula used in the calculation is as follows:

[0141] ;

[0142] ;

[0143] ;

[0144] In the formula, is a causal pair, is a measurement function of the ANM algorithm, is a set threshold value 0.05;

[0145] (1.10) Determine whether is true, if so, proceed to step (1.11), otherwise, let , and return to step (1.4);

[0146] (1.11) Obtain the causal structure in the polyester fiber polymerization reactor ; wherein represents the variable set in the reactor, represents the set of directed edges and causal strengths between nodes in the DAG (Directed Acyclic Graph).

[0147] (2) As shown in Figure 2 , the obtained causal structure is classified and disassembled to obtain the disassembled causal structures , and ;

[0148] The definition of the classification and disassembly rules is as follows:

[0149] (2.1) Classification rule: the initial state node is at the first level; if a node has only one parent node, the parent node of the first level node must be the second First-level node; if a node has multiple parent nodes, then the first-level node... The lowest-level parent node of a level node should be the first level node. Level nodes, among which ;

[0150] (2.2) Disassembly rules: Disassemble the first... A causal network consisting of a first-level node and its parent node is denoted as .

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

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

[0153] (3.2) Judgment Is this condition met? If so, input spatial coordinate data. ,as well as Construct a parallel deep neural network (Parallel-DNN) and use the Causal-guided Init method to process the output of step (3.1). Perform weight initialization, apply theoretical constraints to the model based on relevant physical equations and boundary conditions, and output... ,make

[0154] (3.3) Judgment Is this condition met? If so, input spatial coordinate data. ,as well as Construct a deep neural network DNN 2, and use the Causal-guided Init method to process the output in step (3.2). Perform weight initialization, apply theoretical constraints to the model based on relevant physical equations and boundary conditions, and output... ,make ;

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

[0156] (a) Judgment Check if the condition is true or false. If not, proceed to step (b). If true, proceed to step (c). drive, The results show that the initial condition nodes mainly affect the velocity field and the turbulence model, so this stage (Stage One) mainly simulates the velocity distribution and the turbulence parameters. The training process is constrained by the physical and data errors related to the velocity distribution and the turbulence model. Considering that the velocity distribution and the turbulence model satisfy the mass conservation equation, the momentum conservation equation and the turbulence equation (Equations , ,

[0157]

[0158] wherein is the physical equation term weight, and N is the total number of sampling points in the domain. The residual loss of the PDE can be realized by automatic differentiation; is the physical information loss function of Stage One; is the mass conservation physical function; is the momentum conservation physical function; is the turbulent kinetic energy physical function; is the turbulent kinetic energy dissipation rate physical function.

[0159] The velocity distribution and the turbulence model also satisfy the initial condition and the boundary function, so the boundary constraint loss satisfied by Stage One is calculated using the following formula:

[0160]

[0161] wherein 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 boundary value.

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

[0163]

[0164]

[0165]

[0166] wherein X refers to the variable in the reactor, is the loss function term weight; is the data error loss function, is the data error loss function of Stage One, is the actual value, is the simulation value generated by the model;​​​​​

[0167] (b) determining whether it is true, if not, then go to step (c), if true, then it is driven, we find is a parallel causal structure, so the stage two driven by it is a parallel network structure, which is composed of two parallel DNN networks to simulate temperature distribution and mass transfer efficiency respectively. In the pre-regression network to simulate mass transfer efficiency, in addition to being constrained by stage one, it is also constrained by data. The calculation uses the following formula:

[0168] ;

[0169] ;

[0170] ;

[0171] where is the mass transfer efficiency; is the loss function of stage one; is the data error loss function; is the loss function of stage two; is the loss function of network 1 of stage two;

[0172] In the pre-regression network to simulate temperature distribution, in addition to the constraints of stage one module, it also needs to meet the constraints of heat transfer equation, boundary condition constraints and data constraints, and the total constraint calculation uses the following formula:

[0173] ;

[0174] ;

[0175] ;

[0176] ;

[0177] where is the temperature distribution; is the heat transfer physical function; is the temperature distribution boundary value; is the loss function of network 2 of stage two;

[0178] (c) stage three is driven, by 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 also needs to meet the constraints of kinetic equation, as well as data constraints, and the total constraint calculation uses the following formula:

[0179] ;

[0180] ;

[0181] ;

[0182] ;

[0183] wherein is the reaction rate; is the loss function of stage three; is the kinetic function.

[0184] (4) judge whether it is true, if yes, input the spatial coordinate data , and , and , the weight is initialized by the Causal-guided Init method, a deep neural network DNN 3 is constructed, the model is subjected to theoretical constraints according to the related physical equation and boundary condition, and the three-dimensional PET concentration field distribution is output;

[0185] The Causal-guided Init method is as follows: for the variables with causal relationship , the corresponding network weight matrix is decomposed into causal principal components, and the weight direction is constrained by singular value (SVD); the calculation is as follows:

[0186] ;

[0187] ;

[0188] wherein is the principal component analysis process, the column vector of is the principal component of , so as to ensure that the weight direction is aligned with the parent variable characteristic 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 as follows:

[0189] ;

[0190] wherein is the causal strength; for the variables without causal relationship, orthogonal initialization is adopted to avoid interference;

[0191] In steps (3) and (4), the physical equations satisfied in the polyester fiber polymerization reactor include mass conservation equation, momentum conservation equation, kinetic equation and energy equation, and the following equation is introduced Two equations of the model are further used to simulate 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] where is the velocity distribution, is the physical equation of mass conservation;

[0197] 2) The momentum conservation equation and its physical equation are calculated using the following formula:

[0198]

[0199]

[0200] where is the fluid density, is the pressure in the reactor, is the molecular viscosity, is the turbulent viscosity, is the physical equation of momentum conservation;

[0201] 3) The two equations of the model and its physical equation are calculated using the following formula:

[0202]

[0203]

[0204]

[0205]

[0206] where is the turbulent kinetic energy, is the turbulent dissipation rate, and are constants, , the turbulent kinetic energy generation term ​​​​​​​​​​​​​​​, Physical equation for turbulent kinetic energy, Physical equation for dissipation rate;

[0207] 4) Kinetic equation and its physical equation, the calculation is as follows:

[0208] ;

[0209] ;

[0210] where is the concentration distribution of component , is the diffusion coefficient of component , is the reaction rate, is the physical equation of kinetics;

[0211] 5) Energy conservation equation and its physical equation, the calculation is as follows:

[0212] ;

[0213] ;

[0214] where is the specific heat at constant pressure, is the temperature field, is the effective conduction coefficient, reaction exothermic , is the reaction heat; is the physical equation of energy conservation.

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

[0216] 1) Initial condition, the calculation is as follows:

[0217] ;

[0218] ;

[0219] ;

[0220] ;

[0221] ;

[0222] ;

[0223] where is 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; The initial condition value of the velocity distribution; The initial condition value of the temperature distribution; The initial condition value of the concentration distribution; The boundary value of the velocity distribution; The boundary value of the temperature distribution; The boundary value of the concentration distribution; The value of the concentration field distribution;

[0224] 2) The boundary function uses the wall function to ensure that the model meets the flow profile near the wall, and the calculation adopts the following form:

[0225] ;

[0226] ;

[0227] ;

[0228] ;

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

[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 is shown in Figure 3 .

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

[0237] 1) Number average polymerization degree ;

[0238] ;

[0239] ;

[0240] ;

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

[0242] 2) Number average molecular weight ;

[0243] ;

[0244] 3) Weight average molecular weight ;

[0245] ;

[0246] wherein, is the weight average polymerization degree;

[0247] ;

[0248] 4) Intrinsic viscosity ;

[0249] ;

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

[0251] The following two embodiments are used to illustrate the method for measuring and calculating the three-dimensional PET concentration field distribution in the polyester fiber polymerization reactor according to the present application based on simulation, and the details are as follows:

[0252] The simulation experiments are respectively carried out on the data amount of 8000 and the data amount of 4800, and the simulation process is simulated according to the above specific implementation steps to verify the data adaptability of the present application. The reactor structure in the two embodiments is shown in Figure 4 . The experimental related parameters are shown in Table 1.

[0253] Table 1. Experimental related parameters

[0254] Parameter Value Height of reactor (D) 20 m Diameter of reactor (L) 13 m Diffusivity 1 x 10 -8 ]] Density of catalyst solvent 2640 kg / m 3 ]] Heat capacity of catalyst solvent 2550 J / kg / K Inlet velocity 5 m / s Inlet temperature 440 K Heat of reaction 140 KJ / mol

[0255] Example 1

[0256] In this embodiment, the amount of data collected is 8000. In this embodiment, the model PINN 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 model CD-MSPINN of the present application are used to simulate the three-dimensional PET concentration field distribution, and the direct results of the two are compared. The comparison results of the two are shown in Figure 5 .

[0257] As can be seen from Figure 5 , the model CD-MSPINN of the present application has higher accuracy compared with the traditional PINN simulation method at different positions (0.1D, 0.2D, 0.5D, 0.8D), and can closely follow the effect of the real data; Specifically: by statistically analyzing the root mean square error of the data generated by the two models at different positions (0.1D, 0.2D, 0.5D, 0.8D), the root mean square error of the PINN model is 6.186, 4.158, 4.725, 2.631, and the root mean square error of the CD-MSPINN model is 3.672, 2.130, 2.257, 0.903.

[0258] Example 2

[0259] In this embodiment, the amount of data collected is 4800. In this embodiment, the traditional PINN is used to simulate the three-dimensional PET concentration field distribution, and the present application is simulated and the direct results of the two are compared. The comparison results of the two are shown in Figure 6 .

[0260] As can be seen from Figure 6It can be seen that the model CD-MSPINN of the application has higher accuracy compared with the traditional PINN simulation method at different positions (0.1D, 0.2D, 0.5D, 0.8D), and can closely follow the effect of the real data; specifically: by statistically analyzing the root mean square error of the data simulated by the two models at different positions (0.1D, 0.2D, 0.5D, 0.8D), the root mean square error of the PINN model is 13.109, 10.387, 10.388, 7.554 respectively, and the root mean square error of the CD-MSPINN model is 7.281, 5.393, 6.652, 2.665 respectively.

Claims

1. A method for calculating key parameters based on the distribution of the three-dimensional PET concentration field in a simulated polyester fiber polymerization reactor, characterized in that, The method comprises the following steps: (1) Inference of the causal structure in a polyester fiber polymerization reactor based on information theory knowledge ; (2) The obtained causal structure is graded and disassembled to obtain disassembled causal structures , , , and ; (3) one stage in each disassembled causal structure driving training process; (3.1) Let ; input spatial coordinate data ; construct a deep neural network DNN 1, impose theoretical constraints on the model according to relevant physical equations and boundary conditions, output , let ; (3.2) judge if yes, input spatial coordinate data and , construct a parallel deep neural network Parallel-DNN, use the Causal-guided Init method to initialize the weights of the output in step (3.1) , according to the related physical equation and boundary condition, impose theoretical constraints on the model, output , let ; (3.3) judge if yes, input spatial coordinate data and , construct a deep neural network DNN 2, use the Causal-guided Init method to initialize the weights of the output in step (3.2) , impose theoretical constraints on the model according to the relevant physical equations and boundary conditions, output , let ; (4) determine if yes, input spatial coordinate data and , and , weight initialization is performed by the Causal-guided Init method, a deep neural network DNN 3 is constructed, theoretical constraints are applied to the model according to related physical equations and boundary conditions, and a three-dimensional PET concentration field distribution is output. (5) using the theoretical knowledge of polyester fiber combined with the output three-dimensional PET concentration field distribution to measure the key parameters.

2. The method of determining the key parameters based on the three-dimensional PET concentration field distribution in the simulation-based polyester fiber polymerization reactor according to claim 1, characterized in that, In step (1), the causal structure in the polymerization reactor is constructed, specifically as follows: (1.1) Collect data on the following variables in the polyester fiber polymerization reactor: initial conditions , velocity field , turbulent kinetic energy , turbulent dissipation rate , mass transfer efficiency , temperature field , reaction rate , three-dimensional PET concentration field ; (1.2) the eight variables in step (1.1) are iterated in turn as target variables, and the covariate set is the eight variables; (1.3) Let ; (1.4) Computing the target variable Mutual information with covariates The formula used for the computation is as follows: ； ； ； ； wherein denotes the digamma function, z denotes the number of nearest neighbors selected, denotes the dimension of the joint space denotes the dimension of the joint space denotes the dimension of the joint space denotes the Euclidean distance of the th nearest neighbor of the th sample in the space, is the number of samples, denotes the entropy function;​​​ (1.5) judging the mutual information value whether it is greater than a threshold value 0.15, and if so, adding to the parent node of the target variable ​​ (1.6) judging if yes, then go to step (1.7), otherwise, let , return to step (1.4); (1.7) Obtain the target variable Preliminary causal structure For any S is For any subset of S, compute and Conditional mutual information value The formula used for the calculation is as follows: ； (1.8) judging conditional mutual information value whether less than threshold 0.05, if true then removing from , obtaining verified causal undirected structure ;​ (1.9) For any , infer the causal direction in , compute using the following formula: ； ； ； wherein is a causal pair, is a measure function for the ANM algorithm, is a set threshold value of 0.05; (1.10) judging if yes, then go to step (1.11), otherwise, let = 0, and return to step (1.4); (1.11) Obtaining a causal structure within a polyester fiber polymerization reactor ; wherein is represented as a set of variables within the reactor, is a set of directed edges between nodes in the DAG and causal strengths.

3. The method of determining the key parameters based on the three-dimensional PET concentration field distribution in the simulation-based polyester fiber polymerization reactor according to claim 1, characterized in that, In step (2), the definition of the hierarchical and disassembly rules is specifically as follows: (2.1) Hierarchy Rule: The initial state node is at the first level; if a node has only one parent, then the parent of the node must be at the second level; if a node has multiple parents, then the lowest level parent of the node should be at the second level. (2.2) Inheritance Rule: If a node has multiple parents, then the node inherits the properties of all its parents. (2.3) Inheritance Rule: If a node has multiple parents, then the node inherits the properties of all its parents. (2.4) Inheritance Rule: If a node has multiple parents, then the node inherits the properties of all its parents. (2.5) Inheritance Rule: If a node has multiple parents, then the node inherits the properties of all its parents. (2. (2.2) Disassembly rule: the causal network composed of the 2nd level node and its parent node is denoted as .

4. The method of determining the key parameters based on the three-dimensional PET concentration field distribution in the simulation-based polyester fiber polymerization reactor according to claim 1, characterized in that, In step (4), the Causal-guided Init method is as follows: for the variables with causal relationship , the corresponding network weight matrix is decomposed into causal principal components, and the singular value constraint weight direction is used; the calculation adopts the following formula: ； ； where is the principal component analysis process, the column vector of V is principal component of, ensures that the weight direction is aligned with the parent variable characteristic 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 uses the following formula: ； In the formula is the causal strength; for variables without a causal relationship, orthogonal initialization is used to avoid interference.

5. The method of determining the key parameters based on the three-dimensional PET concentration field distribution in the simulation-based polyester fiber polymerization reactor according to claim 1, characterized in that, In steps (3) and (4), the physical equations satisfied in the polyester fiber polymerization reactor include mass conservation equations, momentum conservation equations, kinetic equations, and energy equations, and the following are introduced Two equations of the model are further used to simulate turbulent flow in the reactor; the boundary conditions include initial conditions and boundary functions.

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

7. The method of determining the key parameters based on the three-dimensional PET concentration field distribution in the polymerization reactor of the simulated polyester fiber according to claim 6, characterized in that, In step (5), the key parameters are obtained from the PET concentration combined with the polyester fiber polymerization process theory measurement equation, and the specific measurement equation is as follows: 1) number average degree of polymerization ; ； ； ； wherein, is the extent of reaction, is the initial monomer concentration, is the three-dimensional PET concentration field, is the unreacted monomer concentration; 2) number average molecular weight ; ； 3) weight average molecular weight ; ； wherein, Mw is the weight average molecular weight; and Mn is the number average molecular weight; and ； 4) intrinsic viscosity ; ； wherein , .

8. The method of determining the key parameters based on the three-dimensional PET concentration field distribution in the simulation-based polyester fiber polymerization reactor according to claim 5, characterized in that, The physical equation is specifically as follows: 1) mass conservation equation and its physical equation, the calculation uses the following formula: ； ； wherein is the velocity distribution, is the mass-conservation physical equation; 2) momentum conservation equation and its physical equation, the calculation uses the following formula: ； ； wherein is the fluid density, pressure in the reactor, is the molecular viscosity, is the turbulent viscosity, , , is the physical equation of momentum conservation; 3) The two equations of the model and its physical equations are calculated in the following form: ； ； ； ； wherein is the turbulent kinetic energy, is the turbulent dissipation rate, , , and is a constant, , , , , the turbulent kinetic energy generation term , is the physical equation for the turbulent kinetic energy, is the physical equation for the dissipation rate; 4) kinetic equation and its physical equation, the calculation uses the following formula: ； ； wherein is the concentration of the component is the concentration profile of the component is the diffusion coefficient of the component is the reaction rate, is the reaction rate, is the physical equation of kinetics; 5) energy conservation equation and its physical equation, the calculation uses the following formula: ； ； wherein Cp is the constant pressure specific heat capacity, T is the temperature field, Keff is the effective thermal conductivity, the reaction exothermic , Q is the reaction heat; is the energy conservation physical equation.

9. The method of determining the key parameters based on the three-dimensional PET concentration field distribution in the polymerization reactor of the polyester fiber according to claim 5, wherein, The boundary condition is specifically as follows: 1) initial condition, the calculation is as follows: ； ； ； ； ； ； wherein is the initial value for the velocity distribution 5 m / s, is the initial value for the temperature distribution 440 K, is the initial value for the concentration distribution 140 KJ / mol; is the initial condition value for the velocity distribution; is the initial condition value for the temperature distribution; is the initial condition value for the concentration distribution; is the boundary value for the velocity distribution; is the boundary value for the temperature distribution; is the boundary value for the concentration distribution; is the concentration field distribution value; 2) the boundary function uses the wall function to ensure that the model meets the flow profile near the wall, and the calculation uses the following formula: ； ； ； ； wherein is the friction velocity, is the turbulent energy distribution boundary value, is the turbulent dissipation rate distribution boundary value, the Karman constant , is the near-wall distance.

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