An experimental optimization method, system, apparatus, and medium based on a melt spinning forming process
By using sensitivity analysis, experimental design, and actual identifiability analysis, the experimental design of the melt spinning process was optimized, solving the problems of complexity and high cost in determining model parameters, and achieving accuracy and cost-effectiveness in parameter estimation.
Patent Information
- Application Number
- CN202411468827.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-21
- Publication Date
- 2025-11-28
- Estimated Expiration
- 2044-10-21
AI Technical Summary
Determining the model parameters for the melt spinning process is complex, costly, and uncertain, making it difficult to accurately estimate the parameters from limited available measurement data.
Using sensitivity analysis, experimental design, and actual identifiability analysis, the optimal experimental design was determined through global sensitivity analysis and information matrix optimization. The mean and confidence interval of the parameters were evaluated by combining maximum likelihood estimation and profile likelihood estimation methods, thereby optimizing the experimental design.
Estimate parameters from limited available measurement data, reduce experimental costs and uncertainties, improve model accuracy and generalization ability, reduce sensor usage, and save energy.
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Figure CN119442620B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of melt spinning processing, in particular to an experimental optimization method, system, device and medium based on a melt spinning forming process. BACKGROUND
[0002] In the fiber production industry, modeling of the melt spinning process is critical to predict product quality. The model describes the relationship between cross-sectional area, velocity, temperature, and rheological force by four basic equations—continuity equation, momentum balance equation, energy equation, and constitutive equation—subsequent studies extend the model by incorporating additional factors such as orientation equation, crystallization equation, etc. Due to the high specificity of the melt spinning model, a set of specific parameters is generally applicable to a certain model, and different varieties or different processes require adjustment of parameters or consideration of other factors. Therefore, the modeling process inevitably uses experimental data to calibrate and fit the melt model. Stress-optical coefficient and stress-crystallization coefficient are important structural parameters of fibers, which are crucial to understanding how elongational flow affects molecular orientation and how crystallization occurs. However, the determination requires a highly sensitive optical system, usually involving complex laser equipment and polarimeters; the determination requires real-time monitoring of crystallization under different stress conditions, usually using advanced techniques such as in-situ x-ray scattering, differential scanning calorimetry, or other forms of crystallography. Therefore, the current melt spinning measurement is relatively complex, and there is a large uncertainty between experimental cost and parameter estimation. SUMMARY
[0003] The purpose of the present application is to provide an experimental optimization method, system, device and medium based on a melt spinning forming process, which can estimate parameters from limited available measurement data, balance experimental cost and uncertainty of parameter estimation.
[0004] To achieve the above-mentioned purpose, the present application provides the following scheme:
[0005] As a first aspect, the present application provides an experimental optimization method based on a melt spinning forming process, comprising:
[0006] Sensitivity analysis, experimental design, and actual identifiability analysis are sequentially performed based on the melt spinning forming process, the observation state of the melt spinning forming process is determined by the sensitivity analysis, the optimal experimental scheme is determined according to the observation state by the experimental design, and the effectiveness of the optimal experimental scheme is evaluated by the actual identifiability analysis;
[0007] The process of the sensitivity analysis is: selecting parameters of a forming process model in melt spinning as inputs, setting ranges of the corresponding parameters, using a global sensitivity analysis technique, quantifying contributions of each parameter acting alone and interacting with other parameters to total variance of each output, setting a threshold of a sensitivity matrix, and thus determining an observation state; the observation state is a most sensitive state in the forming process of the melt spinning model.
[0008] The process of the experimental design is: based on the observation state, selecting decision variables that need to be optimized, using an information matrix to construct an objective function of the experiment, using an E-optimal criterion to convert the information matrix into a scalar function for quantifying information acquisition in parameter identification, and determining an optimal experiment scheme by maximizing a minimum eigenvalue of the information matrix.
[0009] The process of the actual identifiability analysis is: assuming that measurement data are subject to Gaussian independent and identically distributed noise, inputting a number of runs, using maximum likelihood estimation and profile likelihood estimation methods to estimate unknown parameters, using a box plot to present mean values and average confidence intervals of the parameters to be estimated of the melt spinning forming process mathematical model, and evaluating effectiveness of the optimal experiment scheme compared with a standard experiment configuration.
[0010] Optionally, the mathematical model construction method of the forming process model in melt spinning is:
[0011] Material property viscosity, material mass flow, material temperature, cooling device air temperature, cooling device air speed, and spinneret hole diameter are taken as input parameters, and fiber cross-sectional area, fiber speed, fiber temperature, fiber stress, fiber orientation, and fiber crystallization are taken as operation variables to establish relevant control equations of the spinning forming process in melt spinning; the relevant control equations include mass conservation equation, momentum conservation equation, energy conservation equation, constitutive equation, crystallization equation, and orientation equation.
[0012] The relevant control equations are solved to obtain mathematical models with output process index functions; the process indexes include fiber cross-sectional area, fiber speed, fiber temperature, fiber stress, fiber orientation, and fiber crystallization.
[0013] Optionally, each of the mathematical models with output process index functions includes:
[0014] W = ρAu
[0015]
[0016] wherein z is a spatial distribution variable of the spinning duct, A, u, T, F, Θ, Δn are six state variables along the space, which correspond to the cross-sectional area of the fiber, the velocity, the temperature, the stress, the crystallization, the orientation in the forming process, respectively, W is the mass flow of the polymer, p is the density of the material, g is the acceleration of gravity, k n d are the resistance coefficient and the airflow coefficient, respectively, p a is the air density, μ a is the air kinematic viscosity, C p is the specific heat capacity of the material, h is the heat transfer coefficient, T a is the temperature of the cooling device, μ is the viscosity of the material, τ m is the relaxation time of the material, K(T) is the crystallization coefficient, Θ max is the maximum crystallization ratio, A op is the stress-orientation coefficient.
[0017] Optionally, the mathematical model of the crystallization coefficient is represented as:
[0018]
[0019] wherein K max is the maximum crystallization rate of the material, T max is the crystallization temperature corresponding to the maximum crystallization rate of the material, D is the half-width, A c is the stress-crystallization coefficient, and f is the stress crystallization factor.
[0020] Optionally, the mathematical model of the objective function is represented as:
[0021] max V f = λ min (F(p, V))
[0022] wherein p is a parameter vector to be estimated, V is a decision variable to be optimized, and λ min (·) represents the minimum eigenvalue of the objective function.
[0023] Optionally, the mathematical model of the information matrix is represented as:
[0024] F = {F ij}
[0025]
[0026] wherein p i represents the i-th estimated parameter, p j represents the j-th estimated parameter, σ k represents the standard deviation of the observed state y k , which depends on each observed state yk a maximum value of the function.
[0027] As a second aspect, the present application also provides an experimental optimization system based on a melt spinning forming process, comprising:
[0028] a system optimization unit for sequentially performing sensitivity analysis, experimental design and practical identifiability analysis based on the melt spinning forming process, determining an observation state of the melt spinning forming process from the sensitivity analysis, determining an optimal experimental scheme from the observation state according to the experimental design, and performing effectiveness evaluation on the optimal experimental scheme from the practical identifiability analysis;
[0029] a sensitivity analysis unit for selecting parameters of a model of the melt spinning forming process as inputs, setting ranges of the corresponding parameters, quantifying contributions of each parameter alone and interactions with other parameters to total variances of each output by using a global sensitivity analysis technique, setting a threshold of a sensitivity matrix, and thus determining the observation state; the observation state is a most sensitive state in the model of the melt spinning forming process;
[0030] an experimental design unit for selecting decision variables to be optimized based on the observation state, constructing an objective function of the experiment by using an information matrix, converting the information matrix into a scalar function by using an E-optimal criterion, quantifying information acquisition in parameter identification, and determining the optimal experimental scheme by maximizing a minimum eigenvalue of the information matrix;
[0031] a practical identifiability analysis unit for assuming that measurement data are subject to Gaussian independent and identically distributed noise, inputting a number of runs, estimating unknown parameters by using maximum likelihood estimation and profile likelihood estimation methods, presenting mean values and average confidence intervals of the parameters to be estimated of the mathematical model of the melt spinning forming process by using a box plot, and evaluating effectiveness of the optimal experimental scheme compared with a standard experimental configuration.
[0032] As a third aspect, the present application also provides an electronic device comprising a memory and a processor, the memory being used for storing a computer program, and the processor being used for running the computer program to make the electronic device execute the experimental optimization method based on the melt spinning forming process according to the above.
[0033] As a fourth aspect, the present application also provides a computer readable storage medium, characterized by storing a computer program, the computer program being executed by a processor to implement the experimental optimization method based on the melt spinning forming process according to the above.
[0034] According to the embodiments of the present application, the following technical effects are achieved:
[0035] This invention discloses an experimental optimization method based on the melt spinning process. The method includes sequentially performing sensitivity analysis, experimental design, and practical identifiability analysis based on the melt spinning process. The sensitivity analysis determines the observation state of the melt spinning process; the experimental design determines the optimal experimental scheme based on the observation state; and the practical identifiability analysis evaluates the effectiveness of the optimal experimental scheme. This invention can estimate parameters from limited available measurement data, balancing experimental cost and the uncertainty of parameter estimation. Attached Figure Description
[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0037] Figure 1 This is a flowchart illustrating the experimental optimization method of the present invention based on the melt spinning forming process;
[0038] Figure 2 This is a schematic diagram of the structure of an electronic device shown in this embodiment. Detailed Implementation
[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0040] The purpose of this invention is to provide an experimental optimization method, system, equipment, and medium based on the melt spinning process, which can estimate parameters from limited available measurement data and balance experimental costs and the uncertainty of parameter estimation.
[0041] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0042] like Figure 1 As shown, the present invention provides an experimental optimization method based on the melt spinning forming process, including: sensitivity analysis, experimental design, and actual identifiability analysis.
[0043] The sensitivity analysis: select the parameters of the forming process model in melt spinning as input, set the range of the corresponding parameters, use global sensitivity analysis technology, quantify the contribution of each parameter alone and interaction with other parameters to the total variance of each output, set the threshold of the sensitivity matrix, and select the most sensitive state in the forming process of the melt spinning model as the observation state.
[0044] The experimental design: by using the observation state selected in the foregoing, select the decision variables that need to be optimized, use the information matrix to construct the objective function of the experiment, use the E-optimal criterion to convert the information matrix into a scalar function, which is used to quantify the information acquisition in parameter identification, and obtain the optimal experimental design scheme by maximizing the minimum eigenvalue of the information matrix.
[0045] The mathematical model of the information matrix F = {F ij} is:
[0046]
[0047] Where, σ k is the maximum value of each observation state y k of the spinning forming process in melt spinning, p i represents the i-th estimated parameter, and p j represents the j-th estimated parameter.
[0048] The actual identifiability analysis: assuming that the measurement data obeys Gaussian independent and identically distributed noise, input the number of runs, estimate the unknown parameters using maximum likelihood estimation and profile likelihood estimation method, use box plot to present the mean and average confidence interval of the estimated parameters of the melt spinning forming process mathematical model, and evaluate the effectiveness of the optimal experimental design scheme compared with the standard experimental configuration.
[0049] In some embodiments, the establishing the static mathematical model of the melt spinning forming process comprises:
[0050] Step 11: Take the material properties viscosity, material mass flow, material temperature, cooling device air temperature, cooling device air speed, spinneret diameter as input parameters, and fiber cross-sectional area, fiber velocity, fiber temperature, fiber stress, fiber orientation, fiber crystallization as operation variables to establish the mass conservation equation, momentum conservation equation, energy conservation equation, constitutive equation, crystallization equation, orientation equation of the spinning forming process in melt spinning.
[0051] Step 12: obtaining a mathematical model capable of outputting process indicators by solving the mass conservation equation, momentum conservation equation, energy conservation equation, constitutive equation, crystallization equation, and orientation equation of the spinning forming process in the melt spinning, the process indicators including fiber cross-sectional area, fiber velocity, fiber temperature, fiber stress, fiber orientation, and fiber crystallization.
[0052] W = pAu
[0053]
[0054] wherein z is a spatial distribution variable of the spinning duct, A, u, T, F, Θ, and Δn correspond to the six state variables of the forming process, i.e., fiber cross-sectional area, velocity, temperature, stress, crystallization, and orientation, which vary along the space. W is the polymer mass flow, p is the material density, g is the gravitational acceleration, k n ,k d are the resistance coefficient and airflow coefficient, respectively, p a is the air density, μ a is the air kinematic viscosity, C p is the specific heat capacity of the material, h is the heat transfer coefficient, T a is the temperature of the cooling device, μ is the material viscosity, τ m is the material relaxation time, K(T) is the crystallization coefficient, Θ max is the maximum crystallization ratio, A op is the stress-orientation coefficient.
[0055] In some embodiments, the mathematical model of the established crystallization coefficient is:
[0056]
[0057] wherein K max is the maximum crystallization rate of the material, T max is the crystallization temperature corresponding to the maximum crystallization rate of the material, D is the half-width, h is the heat transfer coefficient, A c is the stress-crystallization coefficient, and f is the stress crystallization factor.
[0058] In some embodiments, the sensitivity analysis adopts a global sensitivity analysis method, selects the parameters of the forming process in the melt spinning as inputs, sets the ranges of the corresponding parameters, performs sensitivity analysis of each state of the mathematical model with respect to the parameters, quantifies the contributions of individual effects of each parameter and interactions with other parameters to each state. According to the sensitivity matrix of each state of the forming process in the melt spinning with respect to each parameter, a data table and its image are used to display the process indicators of the sensitivity matrix, a threshold value of the sensitivity analysis is set, and the most sensitive state in the forming process of the melt spinning model is selected as the observation state according to the threshold value.
[0059] In some embodiments, the experimental design employs an optimal experimental design method to design melt spinning experiments by using the selected observation states, to quantify the information acquisition of parameter estimation, the steps of the experimental design include:
[0060] Step 21: According to the selected observation states, an information matrix is used to construct an objective function of the optimal experimental design.
[0061] Step 22: The information matrix is converted into a scalar function using the E-optimal criterion, which is used to measure the amount of information contained in the experimental scheme, and the mathematical model of the objective function is:
[0062] max V f = λ min (F(p, V))
[0063] Where p is the parameter vector to be estimated, V is the decision variable to be optimized, and λ min (·) represents the minimum eigenvalue of the objective function.
[0064] Step 23: A program script of the experimental design is written, with mass flow rate, intrinsic viscosity, material temperature, cooling device air temperature, cooling device air speed, and spinneret aperture as inputs, and the decision variable to be optimized is set to obtain the optimal experimental scheme.
[0065] In some embodiments, the actual identifiability analysis assumes that the measurement data is subject to Gaussian independent and identically distributed noise, sets the number of runs, estimates the unknown parameters using maximum likelihood estimation and profile likelihood estimation methods, and presents the mean and average confidence interval of the parameters to be estimated in the forming process of the melt spinning using a box plot, to evaluate the effectiveness of the optimal experimental scheme compared with the standard experimental configuration.
[0066] Embodiment 1:
[0067] An optimal experimental design method for parameter identification of melt spinning forming process, as shown in Figure 1 , the method includes sensitivity analysis, experimental design, and actual identifiability analysis.
[0068] The sensitivity analysis: the parameters of the forming process model in melt spinning are selected as inputs, the ranges of the corresponding parameters are set, the global sensitivity analysis technique is used to quantify the contribution of each parameter acting alone and interacting with other parameters to the total variance of each output, the threshold of the sensitivity matrix is set, and the most sensitive state in the forming process of the melt spinning model is selected as the observation state.
[0069] The experimental design: by using the foregoing selected observation state, selecting the decision variable to be optimized, using the information matrix to construct the objective function of the experiment, using the E-optimal criterion to convert the information matrix into a scalar function, for quantifying information acquisition in parameter identification, and obtaining the optimal experimental design scheme by maximizing the minimum eigenvalue of the information matrix.
[0070] The actual identifiability analysis: assuming that the measurement data are subject to Gaussian independent and identically distributed noise, inputting the number of runs, estimating the unknown parameters using the maximum likelihood estimation and profile likelihood estimation methods, presenting the mean and average confidence interval of the parameters to be estimated of the melt spinning forming process mathematical model using the box plot, and evaluating the effectiveness of the optimal experimental design scheme compared with the standard experimental configuration.
[0071] The establishment of the static mathematical model of the melt spinning forming process includes:
[0072] Step 101: setting the material characteristic viscosity IV to 0.67, the material mass flow W to 0.009 g / s, the material temperature T0 to 298℃, the cooling device air temperature T a to 15℃, the cooling device air speed u a to 30 cm / s, the spinneret diameter D to 0.022 cm, and the fiber cross-sectional area A, fiber velocity u, fiber temperature T, fiber stress F, fiber orientation Θ, and fiber crystallization Δn as the operating variables to establish the mass conservation equation, momentum conservation equation, energy conservation equation, constitutive equation, crystallization equation, and orientation equation of the spinning forming process in melt spinning.
[0073] Step 102: by solving the mass conservation equation, momentum conservation equation, energy conservation equation, constitutive equation, crystallization equation, and orientation equation of the spinning forming process in melt spinning, a mathematical model capable of outputting process indicators is obtained, and the process indicators include the fiber cross-sectional area, fiber velocity, fiber temperature, fiber stress, fiber orientation, and fiber crystallization.
[0074] W = ρAu
[0075]
[0076] wherein z is the spatial distribution variable of the spinning duct, A, u, T, F, Θ, and Δn correspond to the fiber cross-sectional area, velocity, temperature, stress, crystallization, and orientation in the forming process, respectively, which are six state variables varying along the space. ρ is the material density, set to 1.356-5×10 4 Tg / cm 3 g is the acceleration of gravity, set to 980 cm / s 2 k n kd respectively, are set to 0.61, 0.37, p a -3 3 a -4 p -4 m max
[0077] The mathematical equation of the established crystallization coefficient is:
[0078]
[0079] max -1 max
[0080] The mathematical model of the melt spinning forming process, stress-crystallization coefficient A c op c op
[0081] Sensitivity analysis considers the interaction of multi-dimensional parameters, as well as the nonlinear and non-additive effects, and uses global sensitivity analysis technology to quantify the contribution of each parameter acting alone and interacting with other parameters to the total variance of each output, so as to select the most sensitive state in the melt spinning model forming process as the observation state. The sensitivity analysis method for establishing the melt spinning forming process includes:
[0082] Step 201: using the selected parameters of the melt spinning forming process as input, setting the upper and lower limits of the parameters, executing the program script of Sobol sensitivity analysis, and performing sensitivity analysis of each state of the mathematical model on each parameter.
[0083] The Sobol sensitivity analysis depends on the variance V(y j ) of each model state y j on a single parameter p i or the interaction between different parameters.
[0084] V(y j ) = V i [E -i [y j | p i ]] + E i [V -i [y j | p i ]]
[0085] where E(·) is the expectation, and the subscript -i indicates that the variance or expectation is calculated for all parameters except p i . The first-order sensitivity index quantifies the contribution of each parameter p i to the total variance of the state y j , and the total index evaluates the total contribution of the individual effect of the parameter p i and its interaction with other parameters to the state y j .
[0086]
[0087] Step 202: Use data tables and images to display the individual effect of each parameter and the contribution of interaction with other parameters to each state, with green and yellow as the main colors, and the color gradient from light green (lower value) to light yellow (higher value).
[0088] Step 203: The threshold of the sensitivity analysis is set to 0.8, and the most sensitive state in the melt spinning model forming process is selected as the observation state h(x, p) = [A, u, Θ, Δn] according to the threshold.
[0089] The experimental design uses the optimal experimental design method to design the melt spinning experiment by optimizing the information matrix using the observation state selected in the foregoing, to quantify the information acquisition of parameter estimation, and the steps of the experimental design include:
[0090] Step 301: According to the selected observation state, the speed u L of the winding shaft end and the spatial measurement sequence z are selected as the decision variables to be optimized, and an information matrix is used to construct an objective function for optimizing the experimental design, and the mathematical model of the information matrix F = {F ij} is:
[0091]
[0092] where σ k each observed state y of the shaping of the melt spinning k .
[0093] Step 302: use the E-optimal criterion to find the minimum eigenvalue of the objective function, which is used to measure the amount of information contained in the observed sequence.
[0094] f = λ min (F(p,z,u L ))
[0095] Step 303: write a program script for the experimental design, set the mass flow rate W = 0.009 g / s, the intrinsic viscosity IV = 0.67, the material temperature T0 = 298℃, the cooling device air temperature T a = 15℃, the cooling device air speed u a = 30 cm / s, the spinneret diameter d = 0.022 cm as input, set the point set of the expected sequence {4, 5, 6, 7, 8, 9, 10}, and get the spatial measurement sequence z and the winding shaft end spinning speed u L corresponding to each point number.
[0096] Step 304: use the image to show the spatial position of each measurement point when the measurement point number is specified, and observe its distribution, and summarize the law.
[0097] The actual identifiability analysis assumes that the measurement data is subject to Gaussian independent and identically distributed noise, sets the number of runs, estimates the unknown parameters using maximum likelihood estimation and profile likelihood estimation methods, presents the mean and average confidence interval of the parameters to be estimated in the forming process of the melt spinning using a box plot, and evaluates the effectiveness of the optimal experimental scheme compared with the standard experimental configuration.
[0098] Figure 2 A structural diagram of an electronic device according to an embodiment of the present application, which includes a processor, a memory, a display screen and an input device connected through a system bus. The processor of the electronic device is used to provide computing and control capabilities. The memory of the electronic device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The display screen of the electronic device can be a liquid crystal display screen or an electronic ink display screen. The input device of the electronic device can be a touch layer overlaid on the display screen, or a key, trackball or touchpad provided on the housing of the electronic device, or an external keyboard, touchpad or mouse, etc.
[0099] Those skilled in the art can understand, Figure 2The structure shown in the figure is only a structure diagram of part of the technical solution of the present disclosure, and does not constitute a limitation on the electronic device to which the scheme of the present application is applied.
[0100] The third aspect of the present application discloses a storage medium, specifically a computer readable storage medium, and the computer readable storage medium stores a computer program.
[0101] As can be seen from the above technical solution, the scheme proposed by the present application can optimize the experimental design of the spinning forming process in the melt spinning process, so that the operator can obtain information from the experiment to the maximum extent in advance through the program, obtain an experimental scheme with the maximum amount of information, estimate parameters from limited available measurement data, reduce experimental cost and parameter estimation uncertainty, and make the model have higher accuracy and generalization ability. Application of digital technology and computer technology improves the operator's cognition of the actual melt spinning production process and environment, and the experimental design method can be used for different industrial models, which helps to reduce measurement cost and improve model accuracy. Therefore, the advantages of the present application are: 1. Energy saving. 2. No need for a large number of sensors, reducing the impact of sensor density and reducing measurement cost. 3. Maximum effective information from limited available data, more accurate estimation effect. 4. Systematic study of parameter estimation uncertainty in melt spinning process, which can guide the experimental design of melt spinning process.
[0102] Each embodiment in the specification is described in a progressive manner, and each embodiment focuses on the difference from other embodiments, and the same or similar parts between each embodiment can be referred to each other.
[0103] The principles and implementation modes of the present application are described by applying specific examples in this paper, and the above description of the embodiments is only used to help understand the core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed. In view of the above, the content of the specification should not be understood as a limitation of the present application.
Claims
1. A method for experimental optimization of a melt spinning process, characterized in that The method comprises the following steps: The sensitivity analysis process is as follows: the parameters of the melt spinning forming process model are selected as inputs, the ranges of the corresponding parameters are set, the global sensitivity analysis technique is adopted, the contribution of each parameter alone and the interaction with other parameters to the total variance of each output is quantified, the threshold of the sensitivity matrix is set, and thus the observation state is determined; The observation state is the most sensitive state in the melt spinning model forming process; The experimental design process is as follows: based on the observation state, the decision variables that need to be optimized are selected, the information matrix is used to construct the objective function of the experiment, the E-optimal criterion is used to convert the information matrix into a scalar function, which is used to quantify the information acquisition in parameter identification, and the optimal experimental scheme is determined by maximizing the minimum eigenvalue of the information matrix; The process of the actual identifiability analysis is as follows: it is assumed that the measurement data are subject to Gaussian independent and identically distributed noise, the number of runs is input, the maximum likelihood estimation and the profile likelihood estimation method are used to estimate the unknown parameters, the box plot is used to present the mean and the average confidence interval of the parameters to be estimated of the melt spinning forming process mathematical model, and the effectiveness of the optimal experimental scheme compared with the standard experimental configuration is evaluated; The mathematical model construction method of the melt spinning forming process model is as follows: The material properties, the material mass flow, the material temperature, the cooling device air temperature, the cooling device air speed, and the spinneret hole diameter are used as input parameters, and the fiber cross-sectional area, the fiber velocity, the fiber temperature, the fiber stress, the fiber orientation, and the fiber crystallization are used as operation variables to establish the related control equations of the melt spinning forming process; The related control equations include the mass conservation equation, the momentum conservation equation, the energy conservation equation, the constitutive equation, the crystallization equation, and the orientation equation; By solving the related control equations, the mathematical models with output process index functions are obtained; the process indexes include the fiber cross-sectional area, the fiber velocity, the fiber temperature, the fiber stress, the fiber orientation, and the fiber crystallization; Each mathematical model with the output process index function includes: The mathematical model of the crystallization coefficient is represented as: where z is the spatial variable of the spinning duct, A, u, T, F, Θ, Δn are the six state variables of the fiber cross-sectional area, velocity, temperature, stress, crystallinity, orientation, respectively, W is the polymer mass flow rate, p is the material density, g is the gravitational acceleration, k n , d are the drag coefficient and the air flow coefficient, respectively, p a is the air density, μ a is the air kinematic viscosity, C p is the material specific heat, h is the heat transfer coefficient, T a is the temperature of the cooling device, μ is the material viscosity, τ m is the material relaxation time, K(T) is the crystallization coefficient, Θ max is the maximum crystallization ratio, A op is the stress-orientation coefficient; The mathematical model of the objective function is represented as: wherein K max is the maximum crystallization rate of the material, T max is the crystallization temperature corresponding to the maximum crystallization rate of the material, D is the half-height width, A c is the stress-crystallization coefficient, and f is the stress crystallization factor.
2. The experimental optimization method based on melt spinning forming process according to claim 1, characterized in that, The mathematical model of the information matrix is represented as: max V f = λ min (F(p, V)) where p is the parameter vector to be estimated, V is the decision variable to be optimized, λ min (·) denotes the minimum eigenvalue of the objective function.
3. The experimental optimization method based on melt spinning forming process according to claim 1, characterized in that, The system optimization unit is configured to sequentially perform the sensitivity analysis, the experimental design, and the actual identifiability analysis based on the melt spinning forming process, determine the observation state of the melt spinning forming process by the sensitivity analysis, determine the optimal experimental scheme according to the observation state by the experimental design, and evaluate the effectiveness of the optimal experimental scheme by the actual identifiability analysis. F = {F ij} where p i represents the i-th parameter to be estimated, p j represents the j-th parameter to be estimated, σ k represents the observation state y k corresponding standard deviation, which depends on the maximum value of the observation state y k in the spinning formation process in melt spinning.
4. A system for experimental optimization of a melt spinning forming process, applying the method according to any one of claims 1 to 3, characterized in that, The sensitivity analysis unit is configured to select parameters of a forming process model in melt spinning as inputs, set ranges of the corresponding parameters, quantize contributions of each parameter alone and interactions with other parameters to total variances of each output by using a global sensitivity analysis technique, set a threshold of a sensitivity matrix, and determine an observation state; The observation state is a most sensitive state in the forming process of the melt spinning model; The experimental design unit is configured to select decision variables to be optimized based on the observation state, construct an objective function of an experiment by using an information matrix, convert the information matrix into a scalar function by using an E-optimal criterion, quantize information acquisition in parameter identification, and determine an optimal experiment scheme by maximizing a minimum eigenvalue of the information matrix; The actual identifiability analysis unit is configured to assume that measurement data are subject to Gaussian independent and identically distributed noise, input a number of runs, estimate unknown parameters by using maximum likelihood estimation and profile likelihood estimation, present mean values and average confidence intervals of the parameters to be estimated of the melt spinning forming process mathematical model by using a box plot, and evaluate effectiveness of the optimal experiment scheme compared with a standard experiment configuration.
5. An electronic device, comprising: The electronic device comprises a memory and a processor, the memory is configured to store a computer program, and the processor is configured to execute the computer program to enable the electronic device to perform the experiment optimization method based on a melt spinning forming process according to any one of claims 1-3.
6. A computer readable storage medium characterized by The computer program is stored in the memory and is executed by the processor to implement the experiment optimization method based on a melt spinning forming process according to any one of claims 1-3.
Citation Information
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