A spinning bath multi-parameter coupling optimization system and method
By employing a multi-parameter coupled optimization method involving data analysis, numerical solution, and iterative computation modules during the preparation of polyacrylonitrile fibers, the process window boundaries and robustness indices were precisely delineated. This solved the problems of nonlinear relationships and parameter contribution differences in multi-parameter coupled optimization, achieving efficient parameter optimization and stability control.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHANGSHU XIANGYING SPECIAL FIBER
- Filing Date
- 2025-06-23
- Publication Date
- 2026-07-14
AI Technical Summary
In the preparation of polyacrylonitrile fibers, the high-dimensional nonlinear relationship between multiple parameters is difficult to express accurately. The contribution of parameters to the calculation results varies significantly. Existing algorithms cannot adaptively adjust and lack effective mathematical tools to evaluate potential data outliers and deviation trends, resulting in low optimization effect and computational efficiency.
The data analysis module obtains multi-parameter combinations to define the process window boundary, calculates the robustness index, establishes a set of mathematical equations for the process, uses the numerical solution module to obtain microstructural characteristic parameters and defect precursor information, and combines the iterative calculation module to generate a set of multi-parameter combinations to be evaluated using a differentiation mechanism, and iteratively optimizes to obtain the optimal combination.
It achieves precise partitioning and dynamic identification of the parameter space, improves the efficiency and stability of parameter optimization, significantly enhances the accuracy and stability of multi-parameter coupling optimization of spinning bath, and solves the problem of precise control of microstructure and stabilization characteristics.
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Figure CN120781606B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of data processing technology, specifically to a multi-parameter coupling optimization system and method for a spinning bath. Background Technology
[0002] In modern manufacturing, industrial information and data processing technologies have become crucial for improving production efficiency and product quality. With the enrichment of data acquisition methods and the enhancement of computing power, digital computing methods have demonstrated enormous potential in the field of multi-parameter optimization. These methods process high-dimensional data by establishing complex mathematical models, solve partial differential equations using numerical analysis techniques, simplify complex calculations using matrix operations, and quantify parameter impacts using function evaluation tools. Currently, statistical analysis uncovers patterns in industrial data, multi-objective optimization techniques seek optimal balance points, and data preprocessing methods ensure the reliability of the computational foundation. This mathematics-based computational approach has been widely applied to parameter optimization problems in fields such as chemical engineering, materials science, and energy, exhibiting significant advantages, particularly in handling nonlinear relationships and multi-parameter coupling. Industrial information and data processing systems combine these mathematical tools with practical process knowledge, using logical operations and structured analysis to improve production flexibility while ensuring process quality.
[0003] However, existing numerical computation methods face unique challenges in the preparation of polyacrylonitrile fibers. The high-dimensional nonlinear relationships between multiple parameters are difficult to accurately express using conventional mathematical functions; the contribution of parameters to the calculation results varies significantly, but effective mathematical tools are lacking for evaluation; different regions within the parameter space exhibit different mathematical characteristics, and existing algorithms, employing a uniform computational strategy, cannot adaptively adjust; and the analysis methods lack effective prediction mechanisms for potential data outliers and deviation trends. These problems restrict the application effectiveness and computational efficiency of related numerical optimization methods.
[0004] To address this, a multi-parameter coupled optimization system and method for spinning baths is proposed. Summary of the Invention
[0005] The purpose of this invention is to provide a multi-parameter coupled optimization system and method for spinning baths. This system comprises a data analysis module, a numerical solution module, a parameter evaluation module, and an iterative calculation module. The method includes the following steps: acquiring multi-parameter combinations from historical data, defining process window boundaries, and calculating robustness indices; dividing the parameter space into sub-regions based on the process window boundaries and robustness indices; calculating the influence sensitivity of the stabilization index to obtain parameter importance metrics; establishing a set of mathematical equations for the process; solving the equations based on the multi-parameter combinations to obtain microstructural characteristic parameters and defect precursor information; calculating the stabilization index and defect probability; generating a set of multi-parameter combinations to be evaluated using a differentiation mechanism based on the parameter space sub-regions and parameter importance metrics; establishing a function set based on the stabilization index and defect probability; evaluating the set of multi-parameter combinations using the function set; and iteratively calculating the optimal multi-parameter combination.
[0006] To achieve the above objectives, the present invention provides the following technical solution:
[0007] A multi-parameter coupled optimization system for a spinning bath includes:
[0008] The data analysis module obtains multi-parameter combinations from historical data to delineate process window boundaries, calculates robustness indices based on process window boundaries, divides parameter space sub-regions based on process window boundaries and robustness indices, calculates the sensitivity of each spinning bath parameter to the stabilization index, and obtains parameter importance metrics.
[0009] The numerical solution module establishes a set of mathematical equations for the process and obtains microstructural characteristic parameters and defect precursor information by solving the set of equations based on a combination of multiple parameters.
[0010] The parameter evaluation module calculates the stabilization index based on the microstructure characteristic parameters and converts the defect precursor information into defect probability.
[0011] The iterative calculation module generates a set of multi-parameter combinations to be evaluated using a differentiation mechanism based on the parameter space sub-region and the parameter importance metric. It establishes a function group based on the stabilization index and the defect probability, uses the function group to evaluate the set of multi-parameter combinations to be evaluated, and iteratively calculates the optimal multi-parameter combination.
[0012] Preferably, the process window boundaries include feasible domain process window boundaries, transition domain process window boundaries, and failure domain process window boundaries. The steps for defining the process window boundaries are as follows: obtaining multi-parameter combinations and the corresponding spinning result validity from historical data; constructing a discriminant function using a support vector classification method; determining the boundary between the feasible domain and the failure domain in the overall parameter space based on the discriminant function; setting the boundary range of the transition domain between the feasible domain and the failure domain; calculating the gradient distribution of the discriminant function in the overall parameter space; correcting the boundary shape according to the gradient magnitude and direction; and outputting the determined feasible domain process window boundaries, transition domain process window boundaries, and failure domain process window boundaries.
[0013] Preferably, a robustness index is calculated based on the parameter space distance between each multi-parameter combination and the boundary of the feasible region process window, as well as the stability score of the multi-parameter combination. Based on the process window boundary and the robustness index, the overall parameter space is divided into multiple sub-regions by combining density clustering and Markov random fields. The geometric characteristics and robustness index distribution characteristics of each sub-region are analyzed to obtain parameter space sub-regions. The overall parameter space is the value range of each spinning bath parameter.
[0014] Preferably, the numerical solution module specifically includes: establishing a set of mathematical equations for the process, including flow field equations, temperature field equations, concentration field equations, and phase separation equations; determining the computational grid and boundary conditions; using the finite element method to discretize and solve the set of mathematical equations along the time axis to obtain the distribution data of the flow field, temperature field, concentration field, and phase separation field at each time point; and extracting microstructural feature parameters and defect precursor information based on the distribution data. The microstructural feature parameters include average pore size, pore size distribution standard deviation, skin density, skin thickness, core homogeneity parameters, and molecular chain orientation. The defect precursor information includes defect precursor density and defect precursor average size.
[0015] Preferably, the parameter evaluation module specifically includes: a nonlinear mapping model based on a deep neural network, used to establish the mapping relationship between microstructure feature parameters and stabilization index; and a statistical regression model, used to convert defect precursor density and defect precursor average size into defect probability values.
[0016] Preferably, the parameter space sub-region includes a first space sub-region, a second space sub-region, and a third space sub-region; the differentiation mechanism is as follows: a first optimization algorithm is applied to the first space sub-region, a second optimization algorithm is applied to the second space sub-region, and a third optimization algorithm is applied to the third space sub-region; the search rules for the spinning bath parameters are adjusted according to the parameter importance metric value to generate the set of multi-parameter combinations to be evaluated.
[0017] Preferably, evaluating the set of multi-parameter combinations to be evaluated using a function set and iteratively calculating the optimal multi-parameter combination specifically includes: constructing a multi-objective function set containing maximization of the stabilization index and minimization of the defect probability; sorting the multi-parameter combinations to be evaluated using the Pareto ranking method to form different Pareto levels; selecting multi-parameter combinations at the Pareto first level and other levels of multi-parameter combinations with comprehensive scores higher than a preset threshold to retain for the next iteration; updating the process window boundary and robustness index, re-dividing the parameter space sub-regions based on the updated process window boundary and robustness index, and recalculating the parameter importance metric; generating new multi-parameter combinations to be evaluated based on the updated parameter space sub-regions and parameter importance metric; determining whether the iteration termination condition is met; if the termination condition is met, outputting the optimal multi-parameter combination; otherwise, continuing the iterative calculation.
[0018] This invention also provides a multi-parameter coupling optimization method for a spinning bath, used to execute a multi-parameter coupling optimization system for a spinning bath, comprising:
[0019] The process window boundary is defined by obtaining multiple parameter combinations from historical data. The robustness index is calculated based on the process window boundary. The parameter space sub-region is defined based on the process window boundary and the robustness index. The sensitivity of each spinning bath parameter to the stabilization index is calculated to obtain the parameter importance metric.
[0020] Establish a set of mathematical equations for the process, and obtain microstructural characteristic parameters and defect precursor information by solving the set of equations based on multi-parameter combinations;
[0021] The stabilization index is calculated based on the microstructure characteristic parameters, and the defect precursor information is converted into defect probability.
[0022] Based on the parameter space sub-region and the parameter importance metric, a set of multi-parameter combinations to be evaluated is generated using a differentiation mechanism. A function set is established based on the stabilization index and the defect probability. The function set is used to evaluate the set of multi-parameter combinations to be evaluated, and the optimal multi-parameter combination is obtained through iterative calculation.
[0023] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0024] 1. This invention precisely divides the overall parameter space into three regions: feasible region, transition region, and failure region. It introduces the concept of a robustness index and quantitatively evaluates the process stability of parameter combinations by calculating the parameter space distance between each parameter combination and the feasible region boundary, along with its stability score. This quantitative method can intuitively determine the stability and disturbance resistance of multi-parameter combinations in actual production. Furthermore, based on the process window boundary and the robustness index distribution, this invention divides the overall parameter space into sub-regions with different characteristics, laying the foundation for subsequent differentiated optimization strategies. This invention can dynamically identify changes in the process window, accurately describe the complex characteristics of the parameter space, effectively avoid the risk of the optimization process falling into unstable regions, provide reliable parameter space cognition capabilities, and significantly improve the accuracy and stability of multi-parameter coupled optimization of spinning baths, thereby effectively solving the problem of precise control of microstructure and stabilization characteristics.
[0025] 2. This invention calculates the sensitivity of each spinning bath parameter to the stabilization index, accurately quantifies the importance of each parameter, and forms a parameter importance metric. This enables intelligent adjustment of parameter search rules, improving the efficiency of parameter optimization. Combined with the parameter space sub-region partitioning results, this invention proposes a differentiated optimization mechanism, selecting the most suitable optimization algorithm for parameter space sub-regions with different characteristics, significantly improving the algorithm's search efficiency in various regions. During iterative optimization, the process window boundary and robustness index are continuously updated, and the parameter importance metric and sub-region partitioning are dynamically adjusted, enabling the optimization process to adaptively track the changing characteristics of the parameter space. The parameter importance metric and differentiated optimization strategy provide efficient and intelligent search capabilities for the multi-parameter coupled optimization system of the spinning bath, accelerating the discovery of the optimal parameter combination.
[0026] 3. This invention establishes a coupled set of mathematical equations—flow field equation, temperature field equation, concentration field equation, and phase separation equation—and uses the finite element method for precise solution to obtain microstructural characteristic parameters and defect precursor information during fiber structure evolution. Based on this, a mapping relationship between stabilization indices is introduced to quantitatively evaluate the intrinsic potential of the precursor fiber to form a uniform and complete trapezoidal structure during pre-oxidation. Simultaneously, defect precursor information is converted into defect probability values to provide early warning of potential quality problems. Based on these two key indicators, a multi-objective function set is constructed, and the Pareto ranking method is used to evaluate the parameter combinations. The stabilization index evaluation and multi-objective optimization iterative framework establishes a precise mathematical correlation between spinning process parameters and precursor fiber quality characteristics, achieving comprehensive prediction and optimization from microstructure to carbonization potential. Attached Figure Description
[0027] Figure 1 This is a schematic diagram of a multi-parameter coupling optimization system for a spinning bath according to an embodiment of the present invention;
[0028] Figure 2 This is a schematic diagram of the iterative calculation module according to an embodiment of the present invention;
[0029] Figure 3 This is a schematic diagram of a multi-parameter coupling optimization method for a spinning bath according to an embodiment of the present invention. Detailed Implementation
[0030] 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.
[0031] Please see Figures 1 to 3 This invention provides a multi-parameter coupling optimization system and method for spinning baths, the technical solution of which is as follows:
[0032] Example 1:
[0033] This embodiment is used for the production of T800 grade carbon fiber precursor in a PAN-based carbon fiber production line, employing a wet spinning process using DMSO as the solvent. To address the challenges faced by this production line, such as unstable microstructure of PAN precursor, difficulty in controlling the core-sheath structure gradient, and easy fiber breakage during pre-oxidation, a multi-parameter coupled optimization system for the spinning bath is applied to intelligently optimize and control the quality of the spinning process. Specifically, this includes:
[0034] The data analysis module obtains multi-parameter combinations from historical data to delineate process window boundaries, calculates robustness indices based on process window boundaries, divides parameter space sub-regions based on process window boundaries and robustness indices, calculates the sensitivity of each spinning bath parameter to the stabilization index, and obtains parameter importance metrics.
[0035] The numerical solution module establishes a set of mathematical equations for the process and obtains microstructural characteristic parameters and defect precursor information by solving the set of equations based on a combination of multiple parameters.
[0036] The parameter evaluation module calculates the stabilization index based on the microstructure characteristic parameters and converts the defect precursor information into defect probability.
[0037] The iterative calculation module generates a set of multi-parameter combinations to be evaluated using a differentiation mechanism based on the parameter space sub-region and the parameter importance metric. It establishes a function group based on the stabilization index and the defect probability, uses the function group to evaluate the set of multi-parameter combinations to be evaluated, and iteratively calculates the optimal multi-parameter combination.
[0038] Furthermore, the process window boundaries include feasible domain process window boundaries, transition domain process window boundaries, and failure domain process window boundaries. The steps for defining the process window boundaries are as follows: obtaining multi-parameter combinations and the corresponding spinning result validity from historical data; constructing a discriminant function using a support vector classification method; determining the boundary between the feasible domain and the failure domain in the overall parameter space based on the discriminant function; setting the boundary range of the transition domain between the feasible domain and the failure domain; calculating the gradient distribution of the discriminant function in the overall parameter space; correcting the boundary shape according to the gradient magnitude and direction; and outputting the determined feasible domain process window boundaries, transition domain process window boundaries, and failure domain process window boundaries.
[0039] In this embodiment, a dataset containing spinning bath parameter combinations and their corresponding spinning result validity is first extracted from the production line historical database. The extracted parameters include: coagulation bath temperature, solvent removal bath temperature, coagulant concentration, second bath concentration, main stream velocity, side stream velocity, immersion time, bath draw ratio, and hot draw ratio. The extracted spinning result validity labels are divided into "success" and "failure," indicating whether the parameter combination produced qualified precursor yarn. Data preprocessing includes: removing outliers (data points outside the reasonable range of parameters), handling missing values (filling with the average value of similar parameter combinations), and parameter normalization (normalizing each parameter to the 0-1 range). After preprocessing, 842 samples are obtained, including 625 successful samples and 217 failed samples.
[0040] During the training of the support vector classifier, samples near the boundary are given higher weights. Thresholds are set based on the discriminant function value to divide the system into three regions: feasible region (discriminant function value greater than 0.5), transition region (discriminant function value between -0.5 and 0.5), and failure region (discriminant function value less than -0.5). Threshold selection is based on ROC curve analysis, aiming to minimize misclassification while ensuring that over 90% of successful samples are correctly classified. The gradient distribution of the discriminant function in the overall parameter space is calculated, and regions with drastic gradient changes are identified as high-sensitivity areas. Sampling points are increased in these areas, and the classifier is retrained. After three iterations, a stable process window boundary is obtained.
[0041] The division of the process window boundary takes into account the correspondence between multi-parameter combinations in historical data and spinning results. Through gradient distribution analysis and boundary correction, the accuracy of the process window boundary is ensured, providing a reliable basis for subsequent robustness assessment and optimization algorithm selection. This effectively improves the system's ability to understand the complexity of the parameter space and reduces the risk of getting stuck in an unstable region during the optimization process.
[0042] Table 1 shows the results of the process window boundary division test for five typical combinations of spinning bath parameters, which are highly consistent with the actual experimental verification results.
[0043] Table 1 Results of process window boundary division
[0044]
[0045] Furthermore, a robustness index is calculated based on the parameter space distance between each multi-parameter combination and the boundary of the feasible region process window, as well as the stability score of the multi-parameter combination. Based on the process window boundary and the robustness index, the overall parameter space is divided into multiple sub-regions by combining density clustering and Markov random fields. The geometric characteristics and robustness index distribution characteristics of each sub-region are analyzed to obtain parameter space sub-regions. The overall parameter space is the value range of each spinning bath parameter.
[0046] The specific steps for calculating the robustness index are as follows:
[0047] The minimum parameter space distance from a multi-parameter combination to the feasible region process window boundary is calculated. The calculation method includes: for a given multi-parameter combination point, determining the closest point on the feasible region process window boundary, and calculating the distance between the two points (using Euclidean or Mahalanobis distance). For parameter combination points located inside the feasible region, this distance is kept positive, representing the safety margin between the parameter point and the process failure boundary. For parameter combination points located outside the feasible region (i.e., in the transition or failure domain), this distance is assigned a negative value, still representing the actual distance, but the sign indicates that the point has exceeded the feasible region boundary. The partial derivatives of the stabilization index with respect to each parameter in historical data are calculated, representing the degree of influence of small changes in each parameter on the stabilization index. The sum of the squares of these partial derivatives is multiplied by a negative scaling factor, and the index is taken to obtain a stability score ranging from 0 to 1. The final robustness index is equal to the product of the minimum parameter space distance and the stability score.
[0048] A combination of density clustering and Markov random fields is used to partition the parameter space. Specifically, uniformly distributed grid points are first generated in the overall parameter space, and the discriminant function value of each point is calculated (based on the discriminant function value, the grid points are initially labeled as feasible, transitional, or failure regions, serving as prior information for density clustering) and robustness index. The DBSCAN density clustering algorithm is used for preliminary clustering to identify high-density regions, transitional regions, and noise points. Then, a Markov random field model is constructed based on the clustering results. An energy function containing data terms and a smoothing term is defined, where the data term reflects the relationship between the point and the process window boundary. A graph cutting algorithm is used to solve the energy minimization problem, resulting in preliminary sub-region partitioning. Geometric feature analysis (including volume, shape complexity, convexity, boundary curvature, etc.) and robustness index distribution feature analysis (including statistics, distribution pattern, spatial gradient, etc.) are performed on each sub-region. Based on these features, sub-region optimization is performed, including merging similar small regions and splitting heterogeneous large regions. Finally, the sub-regions are classified into three main types.
[0049] The robustness index combined with parameter space partitioning not only quantifies the process stability of parameter combinations but also considers the local characteristics of the parameter space, providing a scientific basis for differentiated optimization strategies. By analyzing the geometric features and robustness index distribution characteristics of each sub-region, the system can identify stable, sensitive, and transitional regions in the parameter space, improving the accuracy of parameter space cognition, enhancing the system's adaptability, and enabling the optimization algorithm to adaptively adjust according to the characteristics of different regions, thereby improving optimization efficiency and result reliability.
[0050] Furthermore, the numerical solution module specifically includes: establishing a set of mathematical equations for the process, including flow field equations, temperature field equations, concentration field equations, and phase separation equations; determining the computational grid and boundary conditions; using the finite element method to discretize and solve the set of mathematical equations along the time axis to obtain the distribution data of the flow field, temperature field, concentration field, and phase separation field at each time point; and extracting microstructural feature parameters and defect precursor information based on the distribution data. The microstructural feature parameters include average pore size, pore size distribution standard deviation, skin density, skin thickness, core uniformity parameters, and molecular chain orientation. The defect precursor information includes defect precursor density and defect precursor average size.
[0051] This embodiment uses the COMSOL Multiphysics software platform to achieve multiphysics coupling simulation. Specific steps include: establishing a three-dimensional geometric model containing a spinneret, coagulation bath, solvent extraction bath, and hot water bath; to improve computational efficiency, utilizing system symmetry, only one-quarter of the model is constructed and symmetrical boundary conditions are set; the flow field equation uses the k-epsilon turbulence model, setting the inlet velocity, wall no-slip condition, and outlet pressure condition; the temperature field equation uses the heat conduction equation, setting the inlet temperature, wall convective heat transfer condition, and ambient temperature; the concentration field equation uses the component diffusion equation, setting the initial concentration distribution and component diffusion coefficient; and the phase separation process... The Flory-Huggins thermodynamic model was adopted, and interaction parameters and mobility were set. The physical properties of materials such as PAN solution, coagulation bath liquid and fiber were defined, including density, viscosity, heat capacity, thermal conductivity, diffusion coefficient, etc. These parameters were obtained through experimental measurement or literature data. An unstructured mesh was used, and the mesh was refined in key areas (such as the fiber surface). A fully coupled solver was selected, the time step was set to 0.01s, and the total simulation time was the actual residence time of the fiber in the coagulation bath (usually 25 to 55s). The convergence criterion was set to a relative error of less than (1e-4) or a maximum number of iterations of 30.
[0052] The specific steps for extracting microstructural feature parameters include: exporting phase separation field data of fiber cross-sections and longitudinal sections in the COMSOL post-processing module, and using MATLAB to extract microstructural feature parameters.
[0053] Average pore size: Cross-sectional phase separation field data were binarized (threshold set to 0.5), and pores were identified using region connectivity analysis to calculate the average equivalent diameter;
[0054] Pore size distribution standard deviation: Calculate the standard deviation of the equivalent diameter of all pores;
[0055] Cortex compaction: Calculate the average PAN phase volume fraction within a 2 μm thickness range on the fiber surface;
[0056] Cord thickness: The distance from the fiber surface to the center in a radial section is defined as the distance when the volume fraction of the PAN phase drops to 85% of the surface value.
[0057] Core uniformity parameter: Calculate the coefficient of variation of PAN phase volume fraction in the fiber center region (radius < 50% of fiber radius);
[0058] Molecular chain orientation degree: The orientation tensor is calculated based on velocity gradient field data, and the largest eigenvalue is taken as the orientation degree.
[0059] The specific steps for extracting defect precursor information include: identifying various defect precursors: when the local solvent concentration exceeds 25%, it is marked as a solvent-rich region; when the local pore diameter exceeds 100 nm, it is marked as a large-size pore; when the local gradient of the phase separation field exceeds 0.2 / μm, it is marked as a phase separation inhomogeneous region; when the local stress exceeds 5 MPa, it is marked as a stress concentration region; calculating the number of various defect precursors per unit volume as the defect precursor density, and calculating the arithmetic mean of the sizes of all defect precursors as the average size of the defect precursors.
[0060] The multiphysics coupled simulation method of the mathematical equations of the spinning process reveals the intrinsic relationship between spinning bath parameters and fiber microstructure formation, significantly improving prediction accuracy. Considering the interaction and dynamic evolution of multiphysics fields, it can accurately capture key phenomena in the fiber formation process, providing reliable microstructure data for subsequent stabilization index assessment, thus achieving a precise mapping from process parameters to microstructure.
[0061] Furthermore, the parameter evaluation module specifically includes: a nonlinear mapping model based on a deep neural network, used to establish the mapping relationship between microstructure feature parameters and stabilization index; and a statistical regression model, used to convert defect precursor density and defect precursor average size into defect probability values.
[0062] In this embodiment, a nonlinear mapping model is constructed using a fully connected network and an activation function. A negative binomial regression model is selected to transform the defect probability value. The independent variables of the negative binomial regression model are the defect precursor density and the average size of the defect precursor, and the dependent variable is the number of defects actually observed. The nonlinear mapping model is trained using historical data, including microstructural characteristic parameters, pre-oxidation process parameters, and pre-oxidation results (cyclization index, DSC curve characteristics, etc.). Based on the pre-oxidation results in the historical data, the true value of the stabilization index for each group of historical samples is calculated. The stabilization index is defined as a comprehensive evaluation index reflecting the potential of the precursor fiber to form a uniform and complete trapezoidal structure under standard pre-oxidation conditions. The specific calculation method is as follows:
[0063] First, calculate the pre-oxidation efficiency coefficient = (actual cyclization index / theoretical maximum cyclization index) × (1 - cyclization degree variation coefficient);
[0064] Calculate the structural uniformity coefficient = (1 - radial circumduction gradient) × (1 - DSC exothermic peak width / standard width);
[0065] Calculate the defect sensitivity coefficient as follows: 1 - (actual number of defects / average number of defects in the standard sample);
[0066] The final stabilization index is the weighted average of the three coefficients above.
[0067] By employing a nonlinear mapping model based on deep neural networks and a statistical regression model, the conversion relationships between microstructural characteristic parameters and stabilization indices, and between defect precursor information and defect probability, were established. The deep neural network, trained on a large amount of historical data, can capture the complex nonlinear relationship between microstructure and pre-oxidation performance, while the statistical regression model provides a reliable assessment of potential defect risks. This assessment method establishes a quantitative correlation between fiber microstructure and subsequent processing performance, enabling the system to accurately predict the carbonization potential of the precursor fiber during the spinning stage, providing a scientific basis for multi-objective optimization.
[0068] Furthermore, the parameter space sub-region includes a first space sub-region, a second space sub-region, and a third space sub-region; the differentiation mechanism is as follows: a first optimization algorithm is applied to the first space sub-region, a second optimization algorithm is applied to the second space sub-region, and a third optimization algorithm is applied to the third space sub-region. The search rules for the spinning bath parameters are adjusted according to the parameter importance metric value to generate the set of multi-parameter combinations to be evaluated.
[0069] The characteristics of the first parameter space sub-region are: high shape complexity, large boundary curvature, local non-convexity, usually accounting for 20% to 30% of the overall parameter space; narrow robustness index range (usually between 0.5 and 2.5), moderate mean, large standard deviation, skewed distribution, and uneven spatial gradient; located within the feasible region but close to the boundary of the transition region, with high parameter sensitivity. This type of region is suitable for using a hybrid algorithm of simulated annealing and tabu search to fully utilize its global search capability to cope with complex parameter spaces.
[0070] The second parameter space sub-region is characterized by: a near-convex shape, small boundary curvature, smooth boundaries, and typically occupying 15%–25% of the overall parameter space; a wide robustness index range (usually between 2.5 and 5.5), high mean, small standard deviation, approximate normal distribution, and uniform and small spatial gradient; located in the core region of the feasible region, exhibiting high process stability and weak coupling effects between parameters. This type of region displays smooth response surface characteristics, making it suitable for efficient local optimization algorithms combining response surface methodology and gradient descent.
[0071] The third parameter space sub-region is characterized by: extremely irregular shape, a large proportion of high-curvature boundary points, numerous non-convex areas, complex boundaries, and typically accounting for 10%–15% of the overall parameter space; an extremely narrow robustness index range (usually between 0.0 and 0.8), low mean, exhibiting a bimodal distribution, and a steep spatial gradient; it crosses the boundaries between the feasible and transitional regions, resulting in high uncertainty in process outcomes and strong parameter coupling effects. This type of region represents the true boundary of the process window and is suitable for using adaptive mesh local refinement and boundary tracking algorithms, requiring precise characterization of the boundary shape.
[0072] The calculation process of the Parameter Importance Measure (PIM) includes: selecting 200 representative points in the parameter space, applying a small perturbation (±5%) to each parameter dimension, calculating the rate of change of the stabilization index as the local sensitivity, and for each parameter, calculating the square root of the sum of squares of the sensitivity of the 200 points to obtain the overall sensitivity of the parameter; multiplying the overall sensitivity of the parameter by its normalized range of change, and then dividing by the standard deviation of the stabilization index to obtain the parameter importance measure.
[0073] The search rules for spinning bath parameters are adjusted based on the parameter importance metric, specifically including:
[0074] Search step size adjustment: Important parameters (PIM>1.0): Search step size = baseline step size × 0.2; Medium-important parameters (0.5≤PIM≤1.0): Search step size = baseline step size × 0.5; Minor parameters (PIM<0.5): Search step size = baseline step size; where the baseline step size is set to 5% of the parameter range;
[0075] Exploration frequency adjustment: Important parameter: Exploration frequency = Base frequency × 2.5; Medium important parameter: Exploration frequency = Base frequency × 1.5; Minor parameter: Exploration frequency = Base frequency; Wherein, the base frequency is set to 10 times / round;
[0076] Convergence criterion adjustment: Important parameter: Convergence criterion = Baseline criterion × 0.25; Moderately important parameter: Convergence criterion = Baseline criterion × 0.5; Minor parameter: Convergence criterion = Baseline criterion; Wherein, the baseline criterion is set to 1% of the parameter range.
[0077] The differentiation mechanism employs different optimization algorithms for different sub-regions of the parameter space and adjusts the search rules based on the parameter importance metric. This overcomes the limitations of traditional single algorithms in complex parameter spaces, improves search efficiency, and achieves a reasonable allocation of computing resources. The intelligent differentiation mechanism significantly enhances the system's exploration capability in high-dimensional parameter spaces, accelerates the discovery of optimal parameter combinations, and provides an efficient solution for complex process optimization.
[0078] Further, the evaluation of the set of multi-parameter combinations to be evaluated using a function set, and the iterative calculation to obtain the optimal multi-parameter combination, specifically includes: constructing a multi-objective function set containing maximization of the stabilization index and minimization of the defect probability; sorting the multi-parameter combinations to be evaluated using the Pareto ranking method to form different Pareto levels; selecting multi-parameter combinations at the Pareto first level and other levels of multi-parameter combinations with comprehensive scores higher than a preset threshold and retaining them for the next iteration; updating the process window boundary and robustness index, re-dividing the parameter space sub-regions according to the updated process window boundary and robustness index, and recalculating the parameter importance metric; generating new multi-parameter combinations to be evaluated based on the updated parameter space sub-regions and parameter importance metric; determining whether the iteration termination condition is met; if the termination condition is met, outputting the optimal multi-parameter combination; if not, continuing the iterative calculation.
[0079] The flowchart of the iterative operation module is as follows: Figure 2 As shown. The Pareto sorting steps are: a) find all non-dominated solutions in the current set and mark them as first level; b) remove these solutions from the set, and repeat step a for the remaining solutions, marking them as second level; c) repeat the above process until all solutions are classified; the overall score is the weighted average of the stabilization index and the defect probability.
[0080] The specific settings for the iteration termination conditions include: a maximum of 30 iterations; in three consecutive iterations, the relative improvement of the optimal stabilization index is less than 0.1% and the relative improvement of the optimal defect probability is less than 0.5%; the total computation time exceeds 48 hours; in practical applications, the system will check these three conditions simultaneously, and the iteration will terminate if any one of the conditions is met.
[0081] By constructing a multi-objective function set that includes maximizing the stabilization index and minimizing the defect probability, comprehensive optimization of PAN precursor fiber quality was achieved. After each iteration, the process window boundary, robustness index, and parameter space partitioning are dynamically updated, enabling the optimization process to adaptively track changes in parameter space characteristics and achieve continuous evolution and self-improvement.
[0082] Table 2 Comparison of Production Indicators
[0083]
[0084] Table 2 shows a comparison of various production indicators before and after one month of system application. After application, the qualified rate of raw yarn increased by 6.7%, the qualified rate of pre-oxidized yarn increased by 8.5%, the qualified rate of carbon fiber increased by 8.7%, the high-strength and high-modulus rate increased by 51.7%, the average number of yarn breaks decreased by 64.3%, and energy consumption decreased by 7.7%.
[0085] The system first delineates the process window boundaries based on historical data, calculates the robustness index, divides the parameter space into sub-regions, and obtains parameter importance metrics, establishing a precise understanding of the parameter space. Then, through a numerical solution module, it establishes a set of mathematical equations for the process, accurately predicting the microstructural features and defect precursor information under different parameter combinations. Next, the parameter evaluation module transforms microstructural features into stabilization indices and defect precursor information into defect probabilities, achieving a quantitative correlation between process parameters and quality characteristics. Finally, through an iterative calculation module, it generates parameter combinations using a differentiated mechanism, and uses a multi-objective function set for evaluation and iterative optimization until the optimal multi-parameter combination is obtained. This systematic and intelligent parameter optimization method achieves precise control of multiple parameters in the spinning bath, significantly improving the structural uniformity, defect control capability, and stabilization characteristics of PAN precursor fibers.
[0086] Example 2:
[0087] This embodiment further illustrates a multi-parameter coupling optimization method for a spinning bath, such as... Figure 3 As shown, it includes:
[0088] The process window boundary is defined by obtaining multiple parameter combinations from historical data. The robustness index is calculated based on the process window boundary. The parameter space sub-region is defined based on the process window boundary and the robustness index. The sensitivity of each spinning bath parameter to the stabilization index is calculated to obtain the parameter importance metric.
[0089] Furthermore, the process window boundaries include feasible domain process window boundaries, transition domain process window boundaries, and failure domain process window boundaries. The steps for defining the process window boundaries are as follows: obtaining multi-parameter combinations and corresponding spinning result validity from historical data; constructing a discriminant function using a support vector classification method; determining the boundary between the feasible domain and the failure domain in the overall parameter space based on the discriminant function; setting the boundary range of the transition domain between the feasible domain and the failure domain; calculating the gradient distribution of the discriminant function in the overall parameter space; correcting the boundary shape according to the gradient magnitude and direction; and outputting the determined feasible domain process window boundaries, transition domain process window boundaries, and failure domain process window boundaries.
[0090] Furthermore, a robustness index is calculated based on the parameter space distance between each multi-parameter combination and the boundary of the feasible region process window, as well as the stability score of the multi-parameter combination. Based on the process window boundary and the robustness index, the overall parameter space is divided into multiple sub-regions using density clustering and Markov random fields. The geometric characteristics and robustness index distribution characteristics of each sub-region are analyzed to obtain parameter space sub-regions. The overall parameter space is the range of values for each spinning bath parameter.
[0091] Establish a set of mathematical equations for the process, and obtain microstructural characteristic parameters and defect precursor information by solving the set of equations based on multi-parameter combinations;
[0092] Furthermore, establishing the process mathematical equation set specifically includes: establishing a process mathematical equation set comprising flow field equations, temperature field equations, concentration field equations, and phase separation equations; determining the computational grid and boundary conditions; and using the finite element method to discretize and solve the process mathematical equation set along the time axis to obtain the distribution data of the flow field, temperature field, concentration field, and phase separation field at each time point; and extracting microstructural feature parameters and defect precursor information based on the distribution data; wherein, the microstructural feature parameters include average pore size, pore size distribution standard deviation, skin density, skin thickness, core uniformity parameters, and molecular chain orientation; and the defect precursor information includes defect precursor density and defect precursor average size.
[0093] The stabilization index is calculated based on the microstructure characteristic parameters, and the defect precursor information is converted into defect probability.
[0094] Furthermore, a nonlinear mapping model based on deep neural networks is used to establish the mapping relationship between microstructure feature parameters and stabilization index; a statistical regression model is used to convert defect precursor density and defect precursor average size into defect probability values.
[0095] Based on the parameter space sub-region and the parameter importance metric, a set of multi-parameter combinations to be evaluated is generated using a differentiation mechanism. A function group is established based on the stabilization index and the defect probability. The function group is used to evaluate the set of multi-parameter combinations to be evaluated, and the optimal multi-parameter combination is obtained through iterative calculation.
[0096] Furthermore, the parameter space sub-region includes a first space sub-region, a second space sub-region, and a third space sub-region; the differentiation mechanism is as follows: a first optimization algorithm is applied to the first space sub-region, a second optimization algorithm is applied to the second space sub-region, and a third optimization algorithm is applied to the third space sub-region. The search rules for the spinning bath parameters are adjusted according to the parameter importance metric value to generate the set of multi-parameter combinations to be evaluated.
[0097] Further, the evaluation of the set of multi-parameter combinations to be evaluated using a function set, and the iterative calculation to obtain the optimal multi-parameter combination, specifically includes: constructing a multi-objective function set containing maximization of the stabilization index and minimization of the defect probability; sorting the multi-parameter combinations to be evaluated using the Pareto ranking method to form different Pareto levels; selecting multi-parameter combinations at the Pareto first level and other levels of multi-parameter combinations with comprehensive scores higher than a preset threshold and retaining them for the next iteration; updating the process window boundary and robustness index, re-dividing the parameter space sub-regions according to the updated process window boundary and robustness index, and recalculating the parameter importance metric; generating new multi-parameter combinations to be evaluated based on the updated parameter space sub-regions and parameter importance metric; determining whether the iteration termination condition is met; if the termination condition is met, outputting the optimal multi-parameter combination; if not, continuing the iterative calculation.
[0098] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A multi-parameter coupling optimization system for a spinning bath, characterized in that, include: The data analysis module obtains multi-parameter combinations from historical data to delineate process window boundaries. The steps for delineating process window boundaries are as follows: using support vector classification to construct a discriminant function to determine the boundary between the feasible region and the failure region; setting the boundary range of the transition region between the feasible region and the failure region; calculating the gradient distribution of the discriminant function in the overall parameter space; and correcting the boundary shape according to the gradient magnitude and direction to determine the process window boundaries of the feasible region, the transition region, and the failure region. Based on the parameter space distance between each multi-parameter combination and the feasible region process window boundary, and the stability score of the multi-parameter combination, a robustness index is calculated. The stability score calculation process involves calculating the partial derivatives of the stabilization index with respect to each parameter in historical data, multiplying the sum of squares of the partial derivatives by a negative scaling factor, and then taking the index. The stabilization index is defined as a comprehensive evaluation index reflecting the potential of the precursor fiber to form a uniform and complete trapezoidal structure under standard pre-oxidation conditions, and its calculation method is as follows: Pre-oxidation efficiency coefficient = (actual cyclization index / theoretical maximum cyclization index) × (1 - coefficient of variation of cyclization degree); Structural uniformity coefficient = (1 - radial circumduction gradient) × (1 - DSC exothermic peak width / standard width); defect Sensitivity coefficient = 1 - (actual number of defects / average number of defects in standard samples); Stabilization index is the weighted average of pre-oxidation efficiency coefficient, structural uniformity coefficient and defect sensitivity coefficient; The parameter space is divided into sub-regions based on the process window boundary and the robustness index. The rate of change of the stabilization index is calculated as the local sensitivity. For each parameter, the square root of the sum of squares of sensitivity is calculated to obtain the overall sensitivity. The overall sensitivity of the parameter is multiplied by its normalized range of change and then divided by the standard deviation of the stabilization index to obtain the parameter importance measure. The numerical solution module establishes a set of mathematical equations for the process and obtains microstructural characteristic parameters and defect precursor information by solving the set of equations based on a combination of multiple parameters. The microstructural characteristic parameters include average pore size, pore size distribution standard deviation, skin density, skin thickness, core uniformity parameters, and molecular chain orientation. The defect precursor information includes defect precursor density and defect precursor average size. The parameter evaluation module calculates the stabilization index based on the microstructure characteristic parameters and converts the defect precursor information into defect probability. The iterative calculation module, based on the parameter space sub-regions and the parameter importance metric, defines the parameter space sub-regions as follows: a first sub-region with high shape complexity, large boundary curvature, and local non-convexity; a second sub-region with a near-convex shape, small boundary curvature, and smooth boundaries; and a third sub-region with extremely irregular shape. A differentiation mechanism is used to generate a set of multi-parameter combinations to be evaluated. This involves applying a first optimization algorithm to the first sub-region, a second optimization algorithm to the second sub-region, and a third optimization algorithm to the third sub-region. The search rules for the spinning bath parameters are adjusted according to the parameter importance metric to generate the set of multi-parameter combinations to be evaluated. A function set is established based on the stabilization index and defect probability. This function set is used to evaluate the set of multi-parameter combinations to be evaluated, and iterative calculations yield the optimal multi-parameter combination.
2. The multi-parameter coupling optimization system for a spinning bath according to claim 1, characterized in that: Based on the process window boundary and robustness index, the overall parameter space is divided into multiple sub-regions by combining density clustering and Markov random fields. The geometric characteristics and robustness index distribution characteristics of each sub-region are analyzed to obtain the parameter space sub-regions. The overall parameter space is the range of values for each spinning bath parameter.
3. The multi-parameter coupling optimization system for a spinning bath according to claim 1, characterized in that, The numerical solution module specifically includes: establishing a set of mathematical equations for the process, including flow field equation, temperature field equation, concentration field equation, and phase separation equation; determining the computational grid and boundary conditions; using the finite element method to discretize and solve the set of mathematical equations for the process along the time axis to obtain the distribution data of the flow field, temperature field, concentration field, and phase separation field at each time point; and extracting microstructural characteristic parameters and defect precursor information based on the distribution data.
4. The multi-parameter coupling optimization system for a spinning bath according to claim 1, characterized in that, The parameter evaluation module specifically includes: a nonlinear mapping model based on a deep neural network, used to establish the mapping relationship between microstructure feature parameters and stabilization index; and a statistical regression model, used to convert defect precursor density and defect precursor average size into defect probability values.
5. The multi-parameter coupling optimization system for a spinning bath according to claim 1, characterized in that, The parameter space sub-region includes a first space sub-region, a second space sub-region, and a third space sub-region; the differentiation mechanism is as follows: a first optimization algorithm is applied to the first space sub-region, a second optimization algorithm is applied to the second space sub-region, and a third optimization algorithm is applied to the third space sub-region. The search rules for the spinning bath parameters are adjusted according to the parameter importance metric to generate the set of multi-parameter combinations to be evaluated.
6. The multi-parameter coupling optimization system for a spinning bath according to claim 1, characterized in that, The evaluation of the set of multi-parameter combinations to be evaluated using a function set, and the iterative calculation to obtain the optimal multi-parameter combination, specifically includes: constructing a multi-objective function set containing the maximization of the stabilization index and the minimization of the defect probability; sorting the multi-parameter combinations to be evaluated using the Pareto ranking method to form different Pareto levels; selecting multi-parameter combinations at the Pareto first level and other levels of multi-parameter combinations with comprehensive scores higher than a preset threshold and retaining them for the next iteration; updating the process window boundary and robustness index, re-dividing the parameter space sub-regions based on the updated process window boundary and robustness index, and recalculating the parameter importance metric; generating new multi-parameter combinations to be evaluated based on the updated parameter space sub-regions and parameter importance metric; determining whether the iteration termination condition is met; if the termination condition is met, outputting the optimal multi-parameter combination; otherwise, continuing the iterative calculation.
7. A multi-parameter coupling optimization method for a spinning bath, comprising executing the multi-parameter coupling optimization system for a spinning bath as described in claim 1, characterized in that, include: The process window boundary is defined by obtaining multiple parameter combinations from historical data. The robustness index is calculated based on the process window boundary. The parameter space sub-region is defined based on the process window boundary and the robustness index. The sensitivity of each spinning bath parameter to the stabilization index is calculated to obtain the parameter importance metric. Establish a set of mathematical equations for the process, and obtain microstructural characteristic parameters and defect precursor information by solving the set of equations based on multi-parameter combinations; The stabilization index is calculated based on the microstructure characteristic parameters, and the defect precursor information is converted into defect probability. Based on the parameter space sub-region and the parameter importance metric, a set of multi-parameter combinations to be evaluated is generated using a differentiation mechanism. A function set is established based on the stabilization index and the defect probability. The function set is used to evaluate the set of multi-parameter combinations to be evaluated, and the optimal multi-parameter combination is obtained through iterative calculation.