Performance prediction method, system, and storage medium for yarn formulation optimization

Abstract

The application relates to the technical field of textile production, and discloses a performance prediction method and system for yarn formula optimization and a storage medium. The method comprises the following steps: collecting historical data, constructing a Gaussian process regression model, and obtaining a prediction uncertainty distribution; positioning a high-uncertainty area, calculating a prediction improvement value, and obtaining an exploration sequence; screening a to-be-verified scheme, performing simulation verification, and updating data; extracting a deviation feature, adjusting model parameters, generating an optimized exploration strategy, screening formulas according to the strategy, and selecting iterative input according to cost ranking; fusing simulation results and production efficiency indexes to determine performance ranking; screening qualified schemes and forming a complete formula optimization path. Through Gaussian process regression, uncertainty analysis, Bayesian optimization and low-cost iterative simulation, the application solves the problems of difficult prediction of yarn formula multivariable coupling, high test cost and low optimization efficiency, and improves formula accuracy, production adaptability and market competitiveness.

Description

Technical Field

[0001] This application relates to the field of textile production technology, and in particular to a performance prediction method, system and storage medium for yarn formulation optimization. Background Technology

[0002] Yarn performance is determined by multiple variables, including fiber ratio, twist, and spinning speed, and is a core aspect of textile production. Traditional formulation design relies on engineers' experience and repeated trial spinning, making it difficult to quantify the coupling relationships between parameters. Under the market demands for high performance, low cost, and fast delivery, there is an urgent need for intelligent and data-driven methods for performance prediction and formulation optimization.

[0003] Existing yarn formulation optimization methods generally suffer from four core defects: insufficient modeling capabilities, high experimental costs, blind optimization, and inability to be implemented in mass production. At the modeling level, most methods rely on empirical formulas, single-factor comparisons, or simple linear fitting, which can only handle a small number of independent parameters and cannot capture the nonlinear interactions between multiple variables such as fiber ratio, twist, humidity, and speed, resulting in large deviations between predicted and actual results. Some methods employ basic machine learning models, but these can only output single-point predictions, lacking uncertainty assessment capabilities and the ability to identify high-potential exploration areas, easily getting trapped in local optima. At the experimental level, most methods employ full-factor experiments, orthogonal experiments, or manual trial-and-error, resulting in numerous experiments, high raw material consumption, and long cycles, leading to high trial-and-error costs for enterprises. At the optimization strategy level, existing methods lack an "exploration-utilization" balance mechanism, either repeatedly verifying known stable areas or randomly exploring high-uncertainty areas, lacking specificity, priority, and closed-loop correction. At the indicator fusion level, only physical properties such as strength, elongation, and abrasion resistance are considered, ignoring production efficiency indicators such as yield, energy consumption, and loss rate, resulting in excellent laboratory formulation performance but inability to be mass-produced. Meanwhile, the deviation between the simulation verification results and the predicted values ​​cannot be extracted and fed back, the model cannot be continuously iterated and updated, and the prediction accuracy drops rapidly with changes in the production environment. Ultimately, this results in poor formula stability, unclear optimization path, and insufficient market competitiveness, making it difficult to meet the production needs of modern textiles for intelligence, efficiency, and low cost.

[0004] To address the above shortcomings, this application combines Gaussian process regression modeling, prediction uncertainty distribution analysis, Bayesian optimization, and low-cost iterative simulation to solve the problems of difficult prediction of multivariate coupling in yarn formulation, high experimental costs, and low optimization efficiency, thereby improving formulation accuracy, production adaptability, and market competitiveness. Summary of the Invention

[0005] This application provides a performance prediction method, system, and storage medium for yarn formulation optimization, which solves the problems of difficult prediction of multivariate coupling in yarn formulation, high experimental costs, and low optimization efficiency, and improves formulation accuracy, production adaptability, and market competitiveness.

[0006] In a first aspect, this application provides a performance prediction method for yarn formulation optimization, including: S1. Collect historical yarn formula data and corresponding performance indicators, establish the mapping relationship between yarn formula data and corresponding performance indicators using a Gaussian process regression model, and obtain the predicted uncertainty distribution based on the mapping relationship; S2. Based on the predicted uncertainty distribution, the region where the formula data combination with uncertainty index higher than the preset uncertainty threshold is located is identified as a high uncertainty region. The predicted improvement value of the potential formula scheme in the high uncertainty region is calculated to obtain the exploration sequence of the high uncertainty region. S3. The formulation schemes in the exploration sequence whose predicted improvement value exceeds the preset improvement threshold are identified as schemes to be verified. The performance of the schemes to be verified is simulated and verified, and the performance data is updated according to the simulation and verification results. S4. Extract the deviation features between the actual simulated performance and the predicted performance from the updated performance data, and dynamically adjust the parameters of the Gaussian process regression model based on the deviation features to generate an optimized exploration strategy. S5. Based on the optimized exploration strategy, extract matching formulation schemes from the formulation database to form an initial candidate set, calculate the experimental cost of each scheme in the initial candidate set and sort them according to the numerical value from smallest to largest, and select the formulation scheme with the cost ranking in the first preset position as the iterative input. S6. Simulate the formula schemes in the iterative input, integrate the simulation results with the production efficiency index, and determine the performance ranking of the yarn formula schemes. S7. Based on the performance ranking, combined with preset performance thresholds, cost thresholds, and mass production feasibility conditions, select yarn formulation schemes that meet the conditions, determine the parameter adjustment path based on the selected yarn formulation schemes, and form a complete path for yarn formulation optimization.

[0007] Secondly, this application provides a performance prediction system for yarn formulation optimization, used to implement the aforementioned performance prediction method for yarn formulation optimization, comprising: The data modeling module is used to collect historical yarn formula data and corresponding performance indicators, establish a mapping relationship between yarn formula data and corresponding performance indicators using a Gaussian process regression model, and obtain the prediction uncertainty distribution based on the mapping relationship. The region exploration module is used to identify regions where the uncertainty index of the formula data combination is higher than the preset uncertainty threshold as high uncertainty regions based on the predicted uncertainty distribution, calculate the predicted improvement value of potential formula schemes in the high uncertainty regions, and obtain the exploration sequence of the high uncertainty regions. The simulation verification module is used to identify the formulation schemes in the exploration sequence whose predicted improvement value exceeds a preset improvement threshold as the schemes to be verified, perform performance simulation verification on the schemes to be verified, and update the performance data based on the simulation verification results. The strategy optimization module is used to extract the deviation features between the actual simulated performance and the predicted performance from the updated performance data, dynamically adjust the parameters of the Gaussian process regression model based on the deviation features, and generate an optimized exploration strategy. The candidate generation module is used to extract matching formulation schemes from the formulation database according to the optimized exploration strategy to form an initial candidate set, calculate the experimental cost of each scheme in the initial candidate set and sort them according to the numerical value from smallest to largest, and select the formulation scheme with the cost ranking in the first preset position as the iterative input. The performance ranking module is used to simulate the formulation schemes in the iterative input, integrate the simulation results with the production efficiency index, and determine the performance ranking of the yarn formulation schemes. The path determination module is used to screen yarn formulation schemes that meet the conditions based on the performance ranking, combined with preset performance thresholds, cost thresholds and mass production feasibility conditions, and determine the parameter adjustment path based on the screened yarn formulation schemes to form a complete path for yarn formulation optimization.

[0008] Thirdly, this application provides a computer-readable storage medium storing instructions, characterized in that the instructions, when executed by a processor, implement the performance prediction method for yarn formulation optimization.

[0009] This application proposes a performance prediction method, system, and storage medium for yarn formulation optimization, solving the problems of difficult prediction due to multivariate coupling in yarn formulation, high experimental costs, and low optimization efficiency, thereby improving formulation accuracy, production adaptability, and market competitiveness. Compared with existing technologies, the beneficial effects of this application's technical solution are at least as follows: First, by collecting historical formula data, a Gaussian process regression model is constructed to accurately fit the nonlinear mapping relationship between formula parameters and performance indicators, outputting a predicted uncertain distribution, thereby achieving a quantitative description of complex relationships among multiple variables and improving the accuracy and reliability of performance prediction. Second, based on the predicted uncertainty distribution, high uncertainty areas are located, and the expected improvement values ​​are calculated to form an exploration sequence. High-potential solutions are verified first, avoiding the redundant consumption of random trial and error and full factorial and orthogonal experiments, which significantly reduces experimental costs and optimization cycle. Third, extract deviation features from the simulation verification results, and use Bayesian optimization to dynamically adjust model parameters and exploration strategies to form a closed-loop iterative mechanism of modeling-verification-correction, continuously improve prediction and exploration accuracy, and avoid optimization failure caused by model solidification. Fourth, when generating candidate formulation sets, prioritize combinations with low experimental costs, while taking into account performance indicators as well as mass production indicators such as production efficiency, energy consumption, and loss rate, to ensure that the optimized formulation meets actual production constraints and improves the feasibility of the solution and its market competitiveness. Fifth, by using performance ranking and market competitiveness screening, the parameter adjustment path is automatically derived to form a complete and executable formula optimization process, realizing the transformation of yarn formula from experience-driven to data-driven and intelligent optimization, and improving the level of intelligent textile production. Attached Figure Description

[0010] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a flowchart illustrating the performance prediction method for yarn formulation optimization in this application. Figure 2 This is a graph showing the convergence speed comparison results in this application; Figure 3 This is a comparison chart of prediction accuracy results in this application; Figure 4 This is a schematic diagram of the performance prediction system for yarn formulation optimization in this application. Detailed Implementation

[0012] This application provides a performance prediction method, system, and storage medium for yarn formulation optimization. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0013] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the performance prediction method for yarn formulation optimization in this application includes: S1. Collect historical yarn formulation data and corresponding performance indicators, and use a Gaussian process regression model to establish a mapping relationship between yarn formulation data and corresponding performance indicators. Based on the mapping relationship, obtain the predicted uncertainty distribution.

[0014] In one specific embodiment, performing step S1 includes the following steps: Historical yarn formulation data and corresponding performance index data were collected, and the formulation data and performance index data were cleaned, deduplicated, and standardized to form a standardized training dataset. The standardized training dataset is input into the Gaussian process regression model for training. The formula data is used as input and the performance index is used as output to establish a nonlinear mapping relationship between the formula data and the performance index. Based on nonlinear mapping relationships, predictions are made for combinations of unexperimented formulations, and the predicted mean and variance are obtained. Then, a predicted uncertainty distribution is generated based on the predicted mean and variance.

[0015] Specifically, historical yarn formulation data includes fiber ratio, twist, twist coefficient, spinning speed, raw material moisture content, and raw material fineness. Performance index data includes breaking strength, breaking elongation, yarn evenness, hairiness index, and abrasion resistance. This data is extracted from production and experimental testing databases using automated scripts. The extracted data retains the original data collection dimensions and correspondences, with each set of formulation data bound to a unique set of performance index data. Data cleaning removes missing parameters, abnormal test values, and data with inconsistent recording formats. Deduplication removes duplicate records of the same formulation and performance index, ensuring the uniqueness and validity of each record in the training dataset. Standardization uses Z-score transformation to convert formulation data such as fiber ratio and twist, as well as performance index data such as breaking strength and hairiness index, into a unified dimensional format. The transformation is based on the dataset mean and standard deviation, ensuring consistent data distribution after transformation. The standardized formulation data and performance index data maintain a one-to-one mapping, forming a standardized training dataset. This dataset serves as the input basis for the Gaussian process regression model, and the correspondence between input and output data remains unchanged.

[0016] The Gaussian process regression model is built on a Bayesian nonparametric framework, consisting of four parts: prior distribution, kernel function calculation, likelihood function optimization, and posterior inference output. These parts form a complete computational chain through matrix operations and probability distribution propagation, without a hierarchical network structure. All calculations revolve around the correlation between yarn formulation parameters and performance indicators. The model input is a yarn formulation data vector that has been Z-score standardized, containing values ​​for fiber ratio, twist, twist coefficient, spinning speed, raw material moisture content, and raw material fineness. The model output is the Gaussian distribution parameters for the corresponding performance indicators, including breaking strength, breaking elongation, yarn evenness, hairiness index, and abrasion resistance. The input and output vectors maintain a fixed correspondence between a single formulation and a single performance indicator, and this correspondence remains unchanged throughout the model computation. The model's prior distribution is set as a zero-mean Gaussian process, independent of the training data. It defines the covariance structure between data points solely through a kernel function, describing the probability distribution of performance indicators before any samples are added. The kernel function chosen is a radial basis function (RBF) adapted for continuous parameter fitting in the textile industry. The RDF calculates the similarity between any two sets of formulation parameter vectors, with the similarity decreasing monotonically as the distance between the vectors increases. The kernel function includes two types of optimizable hyperparameters: a length scale parameter and a noise parameter. The initial value of the length scale parameter is set to 1.0 to control the impact of formulation parameter variations on the covariance value. The initial value of the noise parameter is set to 0.1 to simulate random measurement errors in production and testing. Both hyperparameters are initialized before training begins and remain unchanged regardless of input data dimensions. During model training, a standardized training dataset is loaded. The dataset is stored in matrix form, with each row of the input matrix corresponding to a set of standardized formulation parameters, and each element of the output vector corresponding to a set of standardized performance indicators. The input matrix and output vector are bound one-to-one according to row and position order, with no misalignments, missing, or duplicate records. The model initiates the covariance matrix construction process based on the input matrix. The covariance matrix is ​​a square matrix with dimensions consistent with the number of training samples. Each element in the matrix is ​​obtained by operating the radial basis functions on two sets of corresponding formulation parameter vectors. The operation results characterize the similarity between the two sets of formulation parameters. The covariance matrix completely stores the nonlinear correlation features between all training samples and can automatically capture the coupling effects of multiple parameters such as fiber ratio, twist, and spinning speed without the need for manual setting of fitting formulas. After the covariance matrix is ​​constructed, the model enters the likelihood function optimization stage. Maximum likelihood estimation is used as the hyperparameter optimization criterion, and the log-likelihood function is used as the optimization objective. The length scale parameter and noise parameter are iteratively adjusted using the gradient descent algorithm. During each parameter adjustment in the iteration process, the covariance matrix and log-likelihood function values ​​are recalculated. The learning rate of the gradient descent algorithm is fixed at 0.01, and the iteration termination condition is set to the absolute value of the difference between the log-likelihood function values ​​of two adjacent iterations being less than 10. -6When the conditions are met, the hyperparameters are determined to be in an optimal state, the covariance matrix structure is stable, and the model training process terminates. The model after training termination retains the optimal hyperparameters and the stable covariance matrix, forming a nonlinear mapping relationship that can be used for prediction. This mapping relationship is probabilistic and can simultaneously output the central tendency and dispersion of the prediction results. For example, the coupled effect of the coordinated changes in cotton fiber ratio and twist on yarn breaking strength can be fully captured by the model without needing to be approximated by human experience or linear formulas.

[0017] Based on a trained Gaussian process regression model, standardized parameters of unexperimented formulation combinations are input. The model calculates the predicted mean and predicted variance of the corresponding performance indicators through posterior distribution. The predicted mean represents the expected value of the performance indicator, and the predicted variance represents the dispersion of the prediction results. The predicted mean and predicted variance are calculated independently, without shared variables or cross-interference. Batch prediction is performed for all unexperimented formulation combinations. A set of predicted means and predicted variances is generated for each combination. The predicted means and predicted variances of all combinations constitute the prediction uncertainty distribution. The prediction uncertainty distribution uses the formulation combination as the index and the predicted mean and predicted variance as distribution features, which can intuitively distinguish between regions with high prediction variance and regions with low prediction variance. The performance prediction results of formulation combinations in regions with high prediction variance show large fluctuations, while the performance prediction results of formulation combinations in regions with low prediction variance show stability.

[0018] The above steps quantify the multivariate coupling relationship of yarn formulation through data standardization and Gaussian process regression modeling, output the predicted uncertainty distribution, solve the problem that traditional methods cannot capture nonlinear interactions and have large prediction biases, reduce experimental costs, and improve formulation optimization efficiency.

[0019] S2. Based on the predicted uncertainty distribution, the region where the formula data combination with uncertainty index is higher than the preset uncertainty threshold is located is identified as the high uncertainty region. The predicted improvement value of potential formula schemes in the high uncertainty region is calculated to obtain the exploration sequence of the high uncertainty region.

[0020] In one specific embodiment, performing step S2 includes the following steps: The prediction variance in the uncertain distribution is extracted as an uncertainty index, and the region where the uncertainty index is higher than the preset uncertainty threshold is identified as a high uncertainty region. Based on the best performance value in the currently verified formulation, calculate the probability and improvement range of each potential formulation scheme exceeding the best performance value in the high uncertainty region, and determine the predicted improvement value by multiplying the probability and the improvement range. Potential formulations are sorted from highest to lowest based on predicted improvement values ​​to form a high-uncertainty region exploration sequence for priority exploration.

[0021] Specifically, the prediction uncertainty distribution includes the predicted mean and predicted variance for each unexperimented formulation combination. The predicted variance quantifies the dispersion of the performance prediction results, and its magnitude is positively correlated with the prediction uncertainty. The predicted variance is extracted from the prediction uncertainty distribution as an uncertainty index. This index uses the unexperimented formulation combinations as the basic index unit, establishing a unique mapping relationship with each formulation combination. The preset uncertainty threshold is determined using the statistical quantile method: performance data from historical stable production batches are collected, and the standard deviation and mean are calculated for each performance index. The coefficient of variation is calculated as (standard deviation / mean × 100%). The coefficient of variation corresponding to the 95th quantile of all historical data is taken as the preset uncertainty threshold, used to divide the prediction results into stable and unstable regions. The extracted predicted variance of each formulation combination is compared with the preset uncertainty threshold to determine the region to which the formulation combination belongs. The parameter region where the predicted variance of the unexperimented formulation combinations is higher than the preset uncertainty threshold is identified as a high uncertainty region. The boundary of the high uncertainty region is defined by the parameter range of all formulation combinations that satisfy the condition that the predicted variance is greater than a threshold. This region contains multiple potential yarn formulation schemes to be explored, each corresponding to a unique combination of parameters such as fiber ratio and twist, and all possessing a high risk of predictive fluctuation. For example, when a formulation combination containing a specific ratio of cotton and polyester fibers has a predicted hairiness index variance exceeding a preset uncertainty threshold, this formulation combination is classified into the high uncertainty region, and the parameter range it falls within constitutes part of this region.

[0022] The optimal performance value among all experimentally validated yarn formulations is used as a benchmark. This benchmark corresponds to the best measured results in key performance dimensions such as breaking strength and yarn evenness, serving as a reference standard for evaluating the performance improvement potential of potential formulation schemes within the high uncertainty region. The probability of each potential formulation scheme exceeding this benchmark performance value is calculated. This probability is based on the predicted mean and predicted variance output by the Gaussian process regression model, achieved through probability density integration. Specifically, the benchmark performance value is used as the upper limit of integration, and the probability of exceeding the benchmark value is obtained by subtracting the area under the Gaussian probability distribution curve centered at the predicted mean and with the predicted variance as the dispersion from 1. The integration process constructs a continuous Gaussian probability density function using the predicted mean as the mathematical expectation and the square root of the predicted variance as the standard deviation. ,in, Represents yarn performance indicators. This represents the predicted mean output by the Gaussian process regression model. This is the square root of the prediction variance output by the Gaussian process regression model. Pi is a constant. This represents the natural index operation. Integrating this function from negative infinity to the baseline performance value yields the cumulative probability that the performance is not higher than the baseline value. Subtracting this integral from 1 gives the probability that the potential formulation's performance is better than the current best measured value. This probability value ranges from 0 to 1; a higher value indicates a greater likelihood that the potential formulation will outperform the baseline. Furthermore, this probability value is directly related to the parameter combinations of the potential formulation; different parameter combinations correspond to different probability calculation results, maintaining an index correspondence with the predicted uncertain distribution.

[0023] The improvement margin of each potential formulation within the high uncertainty region is calculated. The improvement margin is the difference between the predicted mean of the potential formulation and the currently validated optimal performance value; this difference directly reflects the theoretical potential for performance improvement. The probability of exceeding the baseline performance value is multiplied by the improvement margin, and the resulting product is determined as the predicted improvement value. This indicator considers both the possibility and magnitude of performance improvement, comprehensively characterizing the exploratory value of potential formulations. A one-to-one correspondence is established between the predicted improvement value and each potential formulation; formulations with different parameter combinations correspond to different predicted improvement values ​​due to differences in probability and improvement margin. All potential formulations within the high uncertainty region are sorted in descending order of predicted improvement value, with the predicted improvement value as the core sorting criterion, ensuring that formulations with higher values ​​appear earlier in the sequence. After sorting, an exploration sequence for the high uncertainty region is formed for priority exploration. This sequence uses the parameter combinations of potential formulations as basic elements, arranged in descending order of predicted improvement value. Each item in the sequence contains complete formulation parameter information, the corresponding predicted improvement value, and relevant probability and improvement margin data. For example, if the average predicted fracture strength of a potential formulation is higher than the baseline value of 0.5 cN / dtex, the probability of it exceeding the baseline value is 0.7. The predicted improvement value obtained by multiplying the two is 0.35. When this value is higher than other formulations in the region, the formulation ranks higher in the exploration sequence and is given priority to be included in the experimental verification process.

[0024] The above steps extract the predicted variance as an uncertainty index to divide high uncertainty areas, combine probability and improvement magnitude to calculate predicted improvement values ​​and generate exploration sequences, accurately locate high-risk and high-potential areas, prioritize experimental verification, effectively improve the efficiency of formula optimization, reduce the number of invalid experiments, and quickly screen out high-performance yarn formulas.

[0025] S3. Identify the formulation schemes in the exploration sequence whose predicted improvement value exceeds the preset improvement threshold as the schemes to be verified, perform performance simulation verification on the schemes to be verified, and update the performance data based on the simulation verification results.

[0026] In one specific embodiment, performing step S3 includes the following steps: Traverse the high uncertainty region exploration sequence and screen the formulation schemes with predicted improvement values ​​greater than the preset improvement threshold as schemes to be verified; The yarn performance simulation tool was used to simulate and calculate the scheme to be verified, and the actual simulated performance results were obtained. The actual simulated performance results are associated with and stored with the corresponding formulation and predicted performance data to update the performance data.

[0027] Specifically, the high uncertainty region exploration sequence is sorted by predicted improvement value, and all potential formulation schemes are arranged in descending order. Each item in the sequence contains four types of data: formulation parameter combination, predicted improvement value, predicted mean, and predicted variance. The four types of data maintain a one-to-one binding relationship. The formulation parameter combination includes fiber ratio, twist, twist coefficient, spinning speed, raw material moisture, and raw material fineness. The predicted improvement value is obtained by multiplying the probability of exceeding the optimal performance value by the improvement range. The traversal operation reads the relevant data of each formulation scheme in the sorting order of the sequence. The traversal process does not change the internal sorting structure of the sequence, but only completes the data reading and comparison operations. The preset improvement threshold is set based on the performance improvement requirements of yarn production and the experimental cost control requirements. It is used to distinguish between formula schemes with verification value and conventional formula schemes. During the traversal, the predicted improvement value read is compared with the preset improvement threshold in real time. Formula schemes with predicted improvement values ​​greater than the preset improvement threshold are marked as schemes to be verified. The schemes to be verified retain the complete combination of formula parameters and the corresponding predicted performance data. The predicted performance data includes the predicted mean and the predicted variance. The schemes to be verified maintain a direct correspondence with the data items in the original sequence, without adding or deleting parameter dimensions. For example, a formula scheme containing a mixture of cotton fiber and regenerated cellulose fiber is ranked high in the sequence and has a predicted improvement value higher than the preset improvement threshold. This scheme is included in the set of schemes to be verified. All schemes in the set retain the original parameter and predicted data relationship.

[0028] The yarn performance simulation tool is built upon textile physics mechanisms and numerical calculation methods. It performs full-process simulation calculations on the formulation parameter combinations of the scheme to be validated. The calculation process covers the entire physical transformation of yarn from fiber aggregate to finished yarn, outputting performance indicators consistent with actual production testing. The formulation parameter combinations of the scheme to be validated are input into the simulation tool in a standardized vector form. The parameter vector includes fiber ratio, twist, twist coefficient, spinning speed, raw material moisture, and raw material fineness. The parameter input order is completely consistent with the input order of the Gaussian process regression model, ensuring that the parameter dimensions and physical meanings do not deviate. Internally, the simulation tool is divided into a fiber arrangement module, a twisting and forming module, a mechanical property calculation module, a yarn evenness and hairiness calculation module, and an abrasion resistance calculation module. Each module executes calculations in the order of the production process, with the output data of the previous module directly serving as the input data for the next module, forming a continuous simulation calculation chain. The fiber arrangement module receives fiber ratio and raw material fineness parameters, generates the spatial distribution of fibers based on random medium theory, calculates the number of contact points and overlapping areas between fibers, and uses the Monte Carlo method for the calculation process. The random sampling step size is set to 0.001 mm, and the number of samplings is positively correlated with the number of fibers to ensure that the fiber distribution closely matches the actual production state. After completing the calculation, the fiber arrangement module outputs a fiber spatial distribution matrix, which serves as input data for the twisting and forming module. The twisting and forming module receives twist, twist coefficient, and spinning speed parameters, and simulates the helical structure formation process of the fiber bundle during twisting based on the principles of torsional mechanics. The calculation process uses the Euler integral method with a fixed integration step size of 0.1 rpm. Through iterative calculation, the helix angle, fiber tension distribution, and structural density data of the yarn are obtained. These data together constitute the geometric structure and internal stress state of the yarn. The twisting and forming module outputs a yarn structure matrix, which is simultaneously transmitted to the mechanical property calculation module, the evenness and hairiness calculation module, and the abrasion resistance calculation module. The mechanical property calculation module, based on linear elasticity theory, receives the yarn structure matrix and raw material moisture parameters to calculate the stress-strain relationship of the yarn under axial tension. The calculation process constructs a tensile constitutive equation, incorporating fiber modulus, inter-fiber friction coefficient, and structural density variables. The equation is solved using the finite element method (FEM), with a difference mesh size set to 0.5 mm and the mesh number matched to the simulated yarn length. After solving, it outputs two indicators: breaking strength and breaking elongation. The calculation results for these two indicators maintain the same accuracy rules as actual testing equipment. The evenness and hairiness calculation module, based on yarn inhomogeneity theory, receives the fiber spatial distribution matrix and twisting parameters to calculate the diameter fluctuation and fiber protrusion along the yarn length. The calculation process uses power spectral density analysis, with an analysis window length set to 1 m and a window sliding step size of 0.1 m. Evenness is obtained by statistically analyzing the diameter variation coefficient, and hairiness is obtained by statistically analyzing the number and length of protruding fibers per unit length.The wear resistance calculation module is based on the friction and wear mechanism. It receives the yarn structure matrix and fiber ratio parameters, simulates the reciprocating contact process between the yarn and the friction medium, and adopts the Hertz contact model in the calculation process. The normal pressure is set to the industry standard test pressure, and the number of frictions is consistent with the actual wear resistance test process. The wear resistance index is obtained by calculating the wear amount on the yarn surface and the performance retention rate. After all modules complete their calculations, the simulation tool integrates the data from the five indicators to form the actual simulated performance results. These results include breaking strength, breaking elongation, yarn evenness, hairiness index, and abrasion resistance. The five indicators maintain a strict one-to-one correspondence with the input formula parameters. There is no data loss or dimension conversion deviation during the calculation process. All intermediate calculation results are stored in the tool's internal cache for subsequent data comparison and deviation calculation. For example, after inputting a fixed ratio of cotton and polyester fibers, a specific twist, and spinning speed parameters, the simulation tool sequentially completes the entire process of fiber arrangement, twisting, mechanical solution, yarn evenness analysis, and abrasion resistance simulation, outputting five performance values ​​that are consistent with the trends of actual trial spinning test results, providing an objective and complete basis for updating performance data.

[0029] After the actual simulation performance results are generated, a correlation storage operation is performed. This operation binds three types of data: the formulation parameter combination, predicted performance data, and actual simulation performance results of the scheme to be verified. The formulation parameter combination serves as a unique index, the predicted performance data includes the predicted mean and predicted variance, and the actual simulation performance results include five physical performance indicators. The three types of data are mapped one-to-one through the index. A relational database is used as the storage medium. The data table includes columns for formulation parameters, predicted mean, predicted variance, and actual simulation performance. The data types of each column are consistent with the previously generated data type of the predicted uncertain distribution to avoid format conflicts. The update operation overwrites the corresponding records in the original performance data, writes the newly added actual simulation performance results into the database, and retains the predicted performance data and formulation parameter combination. The updated performance data contains all the information from both the prediction and simulation verification stages, with complete data dimensions and clear correspondences. The update operation does not change the overall structure of the database or other unrelated records; it only modifies the records corresponding to the scheme to be verified, ensuring the consistency and stability of the data within the database. The updated performance data can be directly used for subsequent deviation feature extraction and exploration strategy optimization, achieving seamless data flow.

[0030] The above steps involve traversing and screening the solutions to be verified and conducting simulations. The simulation results are then linked and stored with the formula and prediction data. This reduces the raw material consumption and time costs of traditional trial-and-error experiments, solves the problems of high cost and blind optimization in formula optimization experiments, and improves the completeness and accuracy of performance data.

[0031] S4. Extract the deviation features between the actual simulated performance and the predicted performance from the updated performance data, dynamically adjust the parameters of the Gaussian process regression model based on the deviation features, and generate an optimized exploration strategy.

[0032] In one specific embodiment, performing step S4 includes the following steps: Extract the actual simulated performance and the corresponding predicted performance from the updated performance data; Calculate the absolute deviation, relative deviation, mean square deviation, and deviation trend between the actual simulation performance and the predicted performance, and integrate the above calculation results into deviation characteristics; Based on the bias characteristics, the Bayesian optimization algorithm is used to correct the kernel function parameters and noise parameters of the Gaussian process regression model, and the exploration weight parameters are adjusted at the same time. The exploration weight parameters are used to allocate the exploration intensity of high uncertainty areas and the mining intensity of high performance areas. The corrected model parameters are combined with the adjusted exploration weight parameters to generate an optimized exploration strategy that is adapted to the bias characteristics.

[0033] Specifically, the updated performance data uses the formula parameter combination as a unique index to store the predicted performance data and actual simulated performance results of the corresponding scheme to be verified. The predicted performance data includes the predicted mean and predicted variance output by the Gaussian process regression model, while the actual simulated performance results include yarn breaking strength, breaking elongation, yarn evenness, hairiness index, and abrasion resistance. These two types of performance data maintain a one-to-one mapping relationship with the formula parameter combination. The data extraction operation uses the formula parameter combination as the search condition to synchronously retrieve the predicted performance data and actual simulated performance results corresponding to the same formula from the storage structure. The extraction process maintains consistency in data dimensions and indicator types. The predicted performance data and actual simulated performance results are arranged in the same performance indicator order to ensure that the corresponding relationship of indicators does not become misaligned during subsequent deviation calculations. For example, for a formula scheme with a blend ratio of cotton fiber and polyester fiber, the extraction operation synchronously retrieves the predicted mean and actual simulated value of breaking strength corresponding to the scheme, maintaining the uniformity of indicator types and parameter objects, and providing a compliant data foundation for deviation calculations. The deviation characteristic calculation and integration process involves the following steps: Absolute deviation is the difference between the actual simulated performance value and the predicted performance value, directly reflecting the degree of deviation between the two types of data. The calculation process maintains the correspondence between indicator types and does not perform calculations across indicators. Relative deviation is the ratio of absolute deviation to the predicted performance value, used to characterize the relative magnitude of the deviation and eliminate the calculation influence caused by the difference in dimensions of different performance indicators. Mean square deviation is the square of the absolute deviation, used to amplify the impact of large deviations and highlight formulation schemes with significant prediction errors. The deviation change trend is calculated based on the deviation value sequence of multiple sets of schemes to be verified. By comparing the direction and magnitude of deviation value changes between adjacent formulation schemes, the deviation is characterized by its variation with formulation parameter adjustments. The overall variation pattern is analyzed, and the four types of deviation calculation results correspond to the same performance index. Different performance indices under the same combination of formulation parameters independently complete the four types of deviation calculations. All deviation calculation results are classified and integrated according to the combination of formulation parameters and the type of performance index to form deviation features that include numerical deviation, relative deviation, deviation amplification characteristics, and deviation variation patterns. The deviation features maintain a two-level correspondence with the combination of formulation parameters and the type of performance index, which can fully reflect the distribution of prediction errors of the Gaussian process regression model in different formulation regions and different performance index dimensions. The numerical form and distribution pattern of the deviation features are directly used as input for subsequent Bayesian optimization algorithms without additional data transformation processing.

[0034] The Bayesian optimization algorithm uses the kernel function parameters and noise parameters of the Gaussian process regression model as optimization variables, and constructs an optimization process with minimizing the model prediction bias as the objective function. In the initialization phase, the kernel function is set to a radial basis function, the length scale parameter is initialized to 1.0, and the noise parameter is initialized to 0.1. An expected improvement function is used as the acquisition function, which calculates the probability and magnitude of improvement of the candidate hyperparameter exceeding the current optimal bias, outputting the expected improvement score to guide the search for the optimal hyperparameter. The exploration weight is initially set to 0.5. During the iterative optimization process, the gradient descent algorithm is used to search for the optimal hyperparameter, with a fixed learning rate of 0.01. The iteration termination condition is set to the expected improvement value changing by less than 10 over five consecutive iterations. -6 During the iteration process, each set of hyperparameters is directly substituted into the original Gaussian process regression model for calculation. Based on the deviation characteristics, the corresponding prediction error is obtained, which drives the direction and magnitude of hyperparameter correction, completing the optimization of kernel function parameters and noise parameters. The corrected parameters can reduce model prediction bias and improve the fit between prediction results and actual simulation performance. Simultaneously, the exploration weight parameters are adjusted based on the deviation characteristics. The exploration weight parameters are used to allocate the exploration intensity of high uncertainty regions and the mining intensity of high performance regions. When the deviation characteristic value is large, the exploration weight is increased to increase the exploration proportion of high uncertainty regions; when the deviation characteristic value is small, the utilization weight is increased to enhance the mining intensity of high performance regions. The adjustment magnitude of the exploration weight parameters is positively correlated with the magnitude of the deviation characteristic value, and the parameter adjustment process conforms to the parameter distribution law of yarn formulation optimization. For example, when the deviation characteristic value related to fiber ratio is large, the Bayesian optimization algorithm simultaneously corrects the kernel function parameters and increases the exploration weight, so that the subsequent exploration process focuses on the high uncertainty region related to fiber ratio, improving the adaptability of parameter correction and exploration direction.

[0035] The revised Gaussian process regression model parameters and the adjusted exploration weight parameters enter the fusion operation. The fusion operation uses bias characteristics as global constraints to uniformly map the parameters characterizing the model's prediction logic with the parameters characterizing the regional exploration intensity. The revised Gaussian process regression model parameters include kernel function length scaling parameters and noise parameters. These parameters are used to determine the prediction calculation rules, which define the nonlinear mapping relationship between formulation parameters and performance indicators, determining how to calculate the predicted mean and variance of unexperimented formulation combinations. The adjusted exploration weight parameters are used to determine the exploration region allocation rules, which define high uncertainty regions and high performance regions. The sampling ratio, exploration priority, and traversal order of the regions are considered during the fusion operation. Two types of parameters are input into a preset mapping relationship, and deviation features serve as constraints to limit the mapping range. This ensures that the generated rules align with the model's error distribution and performance variation patterns. After fusion, the output is a set of rules containing four components: parameter selection range, exploration priority, iteration direction, and region proportion. The parameter selection range is determined based on the corrected kernel function parameters, eliminating recipe parameter ranges with low correlation to performance indicators and retaining sensitive parameter ranges pointed to by deviation features. Exploration priority is sorted according to the numerical value of the exploration weight parameters, with high-uncertainty regions having higher exploration weight values ​​listed first. High-performance stable regions with low weight values ​​are arranged last. The iteration direction is determined based on the trend of deviation changes, and the parameter adjustment path is set along the direction of decreasing deviation value. The region proportion is set according to the distribution density of deviation characteristics, with regions with concentrated deviation characteristics allocated a higher exploration proportion. Each item in the rule set corresponds to the combination of formulation parameters and performance indicators. The parameter selection range corresponds to specific parameter ranges such as fiber ratio, twist, and spinning speed. The exploration priority corresponds to the order of high uncertainty regions and high-performance regions. The iteration direction corresponds to the increasing or decreasing trend of parameter adjustment. The region proportion corresponds to the resource allocation ratio of different formulation spaces. The rule set as a whole constitutes an optimized exploration strategy. The optimized exploration strategy can be directly applied to the subsequent candidate formulation set generation process, guiding candidate solutions to prioritize formulation combinations with large model prediction bias and potential for performance improvement. At the same time, it follows iterative constraints to control the magnitude of parameter adjustments and experimental costs. The optimized exploration strategy retains the correlation with the original performance data and the data with uncertain prediction distribution throughout the process, without changing the historical data structure and index relationships. It only optimizes the exploration logic through parameter correction and weight adjustment, ensuring the continuity and stability of the overall formulation optimization process. This allows subsequent iterations to be executed based on more accurate prediction models and more reasonable exploration directions, continuously improving the screening efficiency and optimization effect of yarn formulation solutions.

[0036] The above steps correct model parameters and adjust exploration weights based on deviation characteristics to form an optimized exploration strategy that fits actual performance, solves the problem of model prediction bias, balances the relationship between exploration and utilization, reduces invalid experiments, lowers experimental costs, and improves the efficiency and accuracy of yarn formulation optimization.

[0037] S5. Based on the optimized exploration strategy, extract matching formulation schemes from the formulation database to form an initial candidate set. Calculate the experimental cost of each scheme in the initial candidate set and sort them in ascending order of value. Select the formulation scheme with the highest cost ranking as the iterative input.

[0038] In one specific embodiment, performing step S5 includes the following steps: The parameter selection range, exploration direction, and constraints are determined based on the optimized exploration strategy. According to the parameter screening range, exploration direction and constraints, the matching formula schemes are extracted from the formula database to form an initial candidate set; The raw material cost, experimental time cost, and simulation calculation cost of each formulation scheme in the initial candidate set are calculated using a cost evaluation model, and the experimental cost is obtained by summing them up. The formulation schemes in the initial candidate set are sorted according to the experimental cost from smallest to largest, and the formulation scheme ranked at the top of the preset position is selected as the iterative input.

[0039] Specifically, the optimized exploration strategy includes three core limiting information categories: parameter screening range, exploration direction, and constraints. All three categories are generated based on deviation characteristics, corrected Gaussian process regression model parameters, and adjusted exploration weight parameters. The parameter screening range defines the value range of the formulation parameters, covering the numerical ranges of fiber ratio, twist, twist coefficient, spinning speed, raw material moisture, and raw material fineness. This range corresponds to areas where model prediction deviations are concentrated and performance improvement potential is high, excluding parameter ranges with low performance correlation or sufficient prediction stability. The exploration direction defines the adjustment trend of the formulation parameters, determining the path of parameter increase or decrease based on the deviation change trend, ensuring that candidate scheme generation proceeds along the direction of deviation reduction and performance improvement. Constraints limit the generation boundary of the formulation scheme, including three types of limiting rules: performance index lower limit, parameter combination rationality, and production process adaptability. The values ​​of the constraints are determined based on yarn production process standards and historical qualified scheme statistical results. The parameter screening range, exploration direction, and constraints maintain a logical connection, jointly constituting the extraction rules for candidate formulation schemes. The rule content corresponds to the deviation characteristic distribution and model correction results, remaining consistent with the data foundation formed by previous calculations.

[0040] The formula database stores all formula scheme data generated from historical production, experiments, and simulations. Each formula scheme record contains complete parameter combinations and associated performance and cost information. Data records are indexed by parameter combinations to maintain consistency with the parameter dimensions in the optimization exploration strategy. The extraction operation uses parameter screening range, exploration direction, and constraints as search conditions. A full traversal matching is performed on the formula database. During the traversal, each record's parameter combination is checked sequentially to see if it is within the parameter screening range, if it conforms to the adjustment trend defined by the exploration direction, and if it meets the boundary requirements set by the constraints. Formula schemes that meet all search conditions are filtered and output. The filtering process does not change the original data record content; it only completes the aggregation operation of records that meet the conditions. All successfully matched formula schemes together constitute the initial candidate set. Each scheme in the initial candidate set retains complete parameter combination information and maintains a strict fit with the optimization exploration strategy. The number of schemes in the candidate set is consistent with the number of successfully matched records. The schemes are temporarily arranged according to the original storage order in the database without performing additional sorting processing.

[0041] The cost assessment model is constructed based on the entire process of yarn formulation experiments, using independent cost quantification calculations for each formulation scheme in the initial candidate set. The calculation process covers all consumption types related to formulation verification. The experimental cost is the sum of three types of costs: raw material cost, experimental time cost, and simulation calculation cost. All three types of costs are calculated using a unified unit of measurement to ensure the legality and consistency of the numerical summation. The raw material cost is calculated based on the fiber type, fiber ratio, and raw material consumption per unit length in the formulation scheme. The calculation process retrieves real-time raw material unit price data from the textile industry, multiplies the proportion of each type of fiber by the corresponding raw material unit price and raw material consumption per unit length, and then sums the results to obtain the raw material cost of the corresponding formulation scheme. The raw material cost is positively correlated with the fiber ratio and raw material unit price, and is related to the production loss coefficient. The calculation logic closely matches the raw material consumption rules in actual production. The experimental time cost is calculated by summing the parameter configuration time, simulation preparation time, and data recording time. The parameter configuration time increases with the increase in the dimension of the formula parameters. The simulation preparation time is consistent with the model loading time of the yarn performance simulation tool. The data recording time is related to the number of performance indicators. The experimental time cost is obtained by multiplying the unit time cost coefficient by the total time. The unit time cost coefficient is set according to the experimental resource usage standard. The time value is positively correlated with parameter complexity and simulation computation load, and can objectively reflect the consumption value of time. The simulation computation cost is determined according to the operation flow of the yarn performance simulation tool. The calculation basis includes the number of simulation steps, the number of iterations, the number of mesh divisions, and the hardware computing power utilization rate. The number of simulation steps is positively correlated with the simulated yarn length, the number of iterations is related to the simulation convergence condition, the number of mesh divisions is positively correlated with the simulation accuracy, and the hardware computing power utilization rate reflects the consumption of CPU and memory resources. The simulation computation cost is obtained by multiplying the unit cost of computing power by the amount of computing resources consumed. The more operation steps and iterations, the higher the corresponding simulation computation cost. The summation formula for the three types of costs is as follows: ,in Represents the cost of the experiment. Represents raw material costs, Represents the time cost of the experiment. This represents the cost of simulation calculations. The cost assessment model performs independent calculations for each formulation scheme in the initial candidate set. The calculation process does not interfere with the data correspondence between different schemes. Each combination of formulation parameters generates a unique experimental cost value. The experimental cost and the combination of formulation parameters maintain a one-to-one binding relationship. The calculation process incorporates all influencing factors related to experimental verification, fully covering the three types of consumption: materials, time, and computing power. It can objectively reflect the verification input of each formulation scheme.

[0042] All formulation schemes in the initial candidate set are sorted in ascending order according to their corresponding experimental cost values. The sorting process uses experimental cost as the sole criterion, with formulation schemes having lower experimental costs ranking higher. The sorting process does not change the parameter combinations or cost values ​​of the formulation schemes, only adjusting their order in the candidate set. After sorting, an ordered candidate list is formed, arranged from low to high experimental cost. The preset ranking is determined by quantifying the resource constraints, computational efficiency, and batch processing capacity of the iterative calculation. Specifically, the number of available CPU cores in the simulation equipment and the number of CPU cores used for a single formulation simulation are obtained. The former is divided by the latter and rounded down to obtain the maximum number of parallel simulations. The average time of a single simulation is calculated, and the maximum allowed duration of a single iteration is set. The latter is divided by the former and rounded down to obtain the simulation capability per unit time. The upper limit of the number of formulations that can be actually verified in a single iteration of the production line is taken as the upper limit of batch verification processing. The minimum value among the maximum number of parallel simulations, the simulation capability per unit time, and the upper limit of batch verification processing is taken as the preset ranking. For example: if the simulation equipment has 16 available CPU cores and a single formula simulation occupies 2 CPU cores, then the maximum number of parallel simulations is 8; if the average time for a single simulation is 5 minutes and the maximum allowed duration for a single iteration is 30 minutes, then the simulation capability per unit time is 6; if the production line can actually verify up to 10 formulas per iteration, then the maximum batch verification processing limit is 10; take the minimum value of 6 among the maximum number of parallel simulations, the simulation capability per unit time, and the maximum batch verification processing limit as the preset rank, and the preset rank is the first 6. The selection operation reads the formulation schemes ranked before a preset position in the ordered candidate list. The selected schemes have the dual characteristics of low experimental cost and high exploration priority. The selection process does not change the original data content of the schemes, but only completes the scheme aggregation operation. All selected formulation schemes together constitute the iterative input. The schemes in the iterative input maintain the cost sorting order and maintain a continuous data correspondence with the optimization exploration strategy and the initial candidate set. The iterative input is directly used for subsequent simulation calculations and performance ranking, ensuring efficient iterative optimization under the premise of controlling experimental costs. The selection rules are in line with the cost control requirements of yarn formulation optimization, avoiding high-cost ineffective schemes from entering the iterative process, and improving the economy and efficiency of the overall optimization process.

[0043] The above steps are based on an optimization exploration strategy to select low-cost formulation solutions as iterative inputs, taking into account both the rationality of the exploration direction and the control of experimental costs, reducing high-cost ineffective experiments, reducing resource consumption, solving the problems of high cost and strong blindness in traditional formulation optimization experiments, and improving iteration efficiency and optimization feasibility.

[0044] S6. Simulate the formula schemes in the iterative input, integrate the simulation results with the production efficiency index, and determine the performance ranking of the yarn formula schemes.

[0045] In one specific embodiment, performing step S6 includes the following steps: The yarn performance simulation tool was used to perform a full-process simulation of each formula scheme in the iterative input, and the simulated performance results including strength, elongation, yarn evenness, hairiness index and abrasion resistance were obtained. Obtain the production efficiency indicators of the corresponding formula scheme. The production efficiency indicators include output per unit hour, production energy consumption, and raw material loss rate. The simulation performance results and production efficiency indicators are weighted and integrated according to preset weights to obtain the comprehensive performance score of each formulation scheme. The yarn formulation solutions are ranked from highest to lowest based on their overall performance scores, and those with scores below a preset threshold are removed to form a performance ranking.

[0046] Specifically, each formula scheme in the iterative input is passed to the yarn performance simulation tool in the form of a standardized parameter combination. The parameter combination includes fiber ratio, twist, twist coefficient, spinning speed, raw material moisture, and raw material fineness. The parameter dimensions and input order are consistent with the previous model training. The yarn performance simulation tool performs a full-process simulation calculation according to the process of fiber arrangement, twisting and forming, mechanical response, evenness and hair generation, and friction loss. The calculation process adopts a fixed step size and number of iterations. The Monte Carlo sampling step size is set to 0.001 mm, and the Euler integration step size is set to 0.1 rpm. The finite difference grid size is set to 0.5 mm, the power spectral density analysis window length is set to 1 m, and the sliding step size is set to 0.1 m. The Hertz contact model uses standard test pressure and friction stroke. After the calculation is completed, the simulation performance results are output in a unified format. The simulation performance results include five indicators: strength, elongation, yarn uniformity, hairiness index, and abrasion resistance. Each indicator is uniquely bound to the corresponding formulation scheme, and there are no indicator misalignments or missing data. The simulation performance results directly reflect the performance status of the formulation scheme at the physical performance level, and the numerical caliber is consistent with the actual production testing standards.

[0047] Production efficiency indicators are used to characterize the operational efficiency of the formulation scheme in actual mass production. The indicators are sourced from the production process database and historical mass production records. Each set of iterative input formulation schemes corresponds to an independent set of production efficiency indicators. The production efficiency indicators include hourly output, production energy consumption, and raw material loss rate. Hourly output is determined by spinning speed, twist coefficient, and forming stability. The higher the value, the higher the production efficiency. Production energy consumption is calculated based on fiber type, raw material moisture, and equipment operating load. The lower the value, the higher the energy consumption control level. Raw material loss rate is related to fiber length, ratio uniformity, and spinning process stability. The lower the value, the higher the raw material utilization rate. The acquisition process uses the combination of formulation parameters as the index key value and retrieves the efficiency data that perfectly matches the formulation or has the closest process conditions from the production database. This ensures that the production efficiency indicators and simulation performance results belong to the same formulation object. The two types of data maintain a one-to-one correspondence and do not mix cross-formulation data. The data format is unified as standardized numerical values ​​to eliminate dimensional differences.

[0048] The simulated performance results and production efficiency indicators are weighted and fused together. The weighted fusion calculation adopts a linear weighted summation method. The preset weights are set according to the yarn product positioning, production demand, and market indicator priority. Strength, elongation, evenness, hairiness index, and abrasion resistance are assigned corresponding weights. Hourly output, production energy consumption, and raw material loss rate are also assigned corresponding weights. The sum of all weights is a fixed value and the weight allocation is not adjusted with changes in the formula. The calculation process first standardizes the simulated performance results and production efficiency indicators to ensure that data of different dimensions and units are in the same numerical range. Then, each indicator value is multiplied by its corresponding preset weight, and all products are summed to obtain the comprehensive performance score. The comprehensive performance score can simultaneously reflect the quality of physical properties and the level of mass production efficiency. Each formula corresponds to a unique comprehensive performance score, and the score value is positively correlated with the overall application value of the formula. The weighted calculation process maintains the stability of the data correspondence and does not change the original simulated performance results and production efficiency indicator values. It only achieves a unified quantitative evaluation of multi-dimensional indicators through weight allocation.

[0049] After the comprehensive performance score is generated, all iterative input formulation schemes are sorted in descending order. The sorting is based solely on the comprehensive performance score, with higher-scoring formulation schemes appearing earlier. After sorting, a preset threshold screening operation is performed. The preset threshold is set based on product qualification standards, production process baselines, and market access conditions to eliminate low-scoring schemes that lack practical application value. The screening process retains formulation schemes with scores higher than the preset threshold and eliminates those with scores lower than the preset threshold. The retained schemes maintain their original sorting order to form the final yarn formulation scheme performance ranking. The performance ranking is based on the comprehensive performance score as the core criterion, while also considering physical properties and mass production efficiency. The ranking results maintain a complete correspondence with the formulation parameter combinations, simulation performance results, and production efficiency indicators. Each scheme in the ranking is labeled with corresponding parameters, scores, and key indicator values. The ranking structure is clear and can be directly used for subsequent market competitiveness screening and optimization path generation. The ranking generation process does not introduce additional data interference and completes objective sorting based solely on simulation results and efficiency indicators.

[0050] The above steps combine and rank simulated performance and production efficiency indicators to achieve simultaneous evaluation of performance and mass production feasibility. This solves the problem of excellent laboratory formulations that cannot be mass-produced, improves the practicality of formulations, reduces ineffective solutions, and enhances optimization efficiency and implementation capabilities.

[0051] S7. Based on the performance ranking, combined with preset performance thresholds, cost thresholds, and mass production feasibility conditions, select yarn formulation schemes that meet the conditions, determine the parameter adjustment path based on the selected yarn formulation schemes, and form a complete path for yarn formulation optimization.

[0052] In one specific embodiment, performing step S7 includes the following steps: Based on the performance ranking, qualified formulation solutions that simultaneously meet the preset performance threshold, cost threshold, production process constraints, and mass production feasibility conditions are selected in turn. Extract the key formulation and process parameters of a qualified formulation scheme, including fiber ratio, twist coefficient, and spinning speed; Based on key formulation and process parameters, determine the step-by-step adjustment path from the initial formulation to the target optimal formulation, and clarify the direction and magnitude of parameter adjustment at each step; We will gradually adjust the path and integrate it with the exploration, verification, iteration, and screening processes to form a complete path for yarn formulation optimization that can be directly applied to actual production.

[0053] Specifically, performance rankings are arranged from highest to lowest based on overall performance scores. Each item within the ranking corresponds to a unique yarn formulation and is linked to simulated performance results, production efficiency indicators, experimental cost values, and complete formulation parameter information. The screening process is performed sequentially according to the ranking order without altering the original order. The screening process simultaneously verifies four limiting conditions: preset performance thresholds include minimum values ​​for strength, elongation, evenness, hairiness index, and abrasion resistance, set based on yarn product execution standards and market quality requirements; cost thresholds are the upper limits of experimental and mass production costs, determined based on production budgets and market pricing ranges; production process constraints include fiber ratio ranges, twist coefficient matching relationships, and spinning speed adaptation ranges, set based on existing spinning equipment operating parameters and process stability requirements; and mass production feasibility conditions include raw material supply stability, equipment compatibility, batch production consistency, and compatibility with downstream processes, requiring verification of stable supply channels for the fiber raw materials used in the corresponding formulation. The selection process requires four conditions to be met simultaneously: whether the formula parameters match the existing spinning equipment models and process parameters, whether the performance fluctuations during continuous batch production are within the allowable range, and whether the formulated yarn meets the processing requirements of subsequent processes such as weaving and dyeing. If any condition is not met, the corresponding formula scheme is eliminated. Only formula schemes that fully meet the preset performance threshold, cost threshold, production process constraints, and mass production feasibility conditions are marked as qualified formula schemes. Qualified formula schemes retain complete parameter information, performance information, cost information, and efficiency information, and maintain a corresponding relationship with the performance ranking. For example, a formula scheme with a high ranking has an intensity value higher than the preset performance threshold, an experimental cost lower than the cost threshold, parameters that meet the production process constraints, and stable mass production conditions. This scheme is included in the set of qualified formula schemes. The screening process achieves simultaneous constraints on the three goals of high performance, low cost, and mass production feasibility, avoiding the emergence of schemes with excellent performance but unable to be mass-produced or with excessively high costs.

[0054] Each scheme within the qualified formulation scheme set undergoes key parameter extraction. The extraction targets are divided into two categories: formulation parameters and process parameters. Both types of parameters have a significant impact on yarn performance and production efficiency. Key formulation parameters are centered on fiber ratios, including the proportions of various fibers, which directly determine the basic physical properties of the yarn. Key process parameters include twist coefficient and spinning speed. Twist coefficient affects yarn density, strength, and hairiness, while spinning speed affects production efficiency and yarn evenness. The extraction operation is based on the Pearson correlation coefficient between parameters and performance indicators. A correlation coefficient exceeding a set threshold is considered valid. The parameters are retained as key parameters to ensure that the extracted parameters have a clear performance impact correlation. The extraction process does not change the original values ​​and combination relationships of the parameters. Each qualified formulation scheme corresponds to a unique set of key formulation parameters and key process parameters. The parameter combination and the qualified formulation scheme maintain a one-to-one correspondence. The extraction results do not contain redundant parameters. All key parameters are directly used for subsequent adjustment path generation. For example, in a certain qualified formulation scheme, the ratio of cotton fiber to regenerated fiber, the set twist coefficient, and the running spinning speed have a significant impact on performance. The above parameters are completely extracted and used as the core basis for path derivation.

[0055] The step-by-step adjustment path starts with the initial formula used in production and ends with the target optimal formula, which exhibits the best overall performance among qualified formula schemes. It constructs a continuous adjustment logic based on key formula parameters and key process parameters. The adjustment direction is determined according to deviation characteristics and performance change trends, following the direction of reduced model prediction deviation and improved overall performance score. The adjustment magnitude is determined based on parameter sensitivity; parameters with high sensitivity are adjusted with small magnitudes to avoid drastic performance fluctuations, while parameters with low sensitivity are adjusted with conventional magnitudes to improve adjustment efficiency. The adjustment process follows parameter coordination constraint rules, maintaining process matching relationships between fiber ratio, twist coefficient, and spinning speed, and avoiding parameter combination conflicts. Each adjustment step corresponds to a unique parameter combination and expected performance change. The step-by-step adjustment path contains continuous parameter adjustment nodes with clear numerical progression relationships between nodes. All adjustment steps meet production process constraints and mass production feasibility conditions. The entire path does not contain parameter combinations that exceed equipment operating range or disrupt production stability. The step-by-step adjustment path clearly presents the entire process of transitioning from the initial formula to the target optimal formula, clearly defining the adjustment object, direction, and magnitude of each step, ensuring that the production process can directly execute parameter adjustments according to the path.

[0056] The process involves gradually adjusting the path and integrating it with the previous exploration, verification, iteration, and screening processes. The integration process retains all process nodes, including exploration of high-uncertainty regions based on predicted uncertain distributions, simulation verification of the proposed solutions, model parameter correction based on deviation characteristics, iteration of low-cost candidate sets, multi-dimensional performance ranking, and screening of qualified solutions under multiple conditions. Each process node is connected in sequence, and the gradually adjusted path serves as the final execution stage, connecting the initial data processing with actual production debugging. The integrated complete path encompasses all stages: data input, model building, region exploration, simulation verification, strategy optimization, iterative screening, parameter adjustment, and mass production implementation. All data within the path maintains a corresponding relationship, and parameter, performance, cost, and efficiency information are fully traceable. The complete path removes redundant operations and invalid steps, retaining only steps with practical guiding significance. It can be directly applied to formula debugging and optimization in actual production without requiring additional experience-based judgment or random trial-and-error. The path content aligns with actual yarn production scenarios, balancing prediction accuracy, experimental economy, mass production feasibility, and performance stability, achieving a closed-loop process from data input to production implementation.

[0057] The above steps screen qualified formulas through multiple conditions and derive executable parameter adjustment paths, transforming intelligent optimization results into mass production executable solutions. This solves the problems of traditional formulas being unable to be implemented and optimization paths being unclear, reducing trial and error costs and improving production stability and market adaptability.

[0058] Please see Figure 2 , Figure 2 The graph showing the convergence speed comparison results illustrates the performance convergence trends of our proposed method, the empirical formula method, and the response surface methodology as the number of experiments / iterations increases. Our proposed method achieves higher performance levels and tends to stabilize with fewer iterations. The empirical formula method and the response surface methodology exhibit low iteration efficiency, slow convergence, and ultimately lower performance. This demonstrates that our proposed method improves the iteration efficiency and convergence speed of yarn formulation optimization through Gaussian process regression, uncertainty exploration, and low-cost iterative simulation, thus solving the problems of redundancy and low efficiency in traditional yarn formulation optimization experiments.

[0059] Please see Figure 3 , Figure 3 The comparison chart of prediction accuracy shows a numerical comparison of the yarn performance prediction accuracy of this method, the empirical formula method, and the response surface method. The prediction accuracy of this method is higher than that of the empirical formula method and the response surface method, while the latter two have lower accuracy and larger errors. This indicates that this method relies on the Gaussian process regression model to accurately capture the nonlinear coupling relationship of multiple variables in the formula, thereby improving the accuracy and reliability of yarn performance prediction and solving the problems of insufficient modeling ability and large prediction deviation of traditional methods.

[0060] Please see Figure 4The performance prediction system for yarn formulation optimization in this application embodiment is described below. The performance prediction system for yarn formulation optimization includes: The data modeling module is used to collect historical yarn formula data and corresponding performance indicators, and to establish a mapping relationship between yarn formula data and corresponding performance indicators using a Gaussian process regression model. Based on the mapping relationship, the prediction uncertainty distribution is obtained. The region exploration module is used to identify regions where the uncertainty index of the formula data combination is higher than the preset uncertainty threshold as high uncertainty regions based on the predicted uncertainty distribution, calculate the predicted improvement value of potential formula schemes in high uncertainty regions, and obtain the exploration sequence of high uncertainty regions. The simulation verification module is used to identify formulations in the exploration sequence whose predicted improvement values ​​exceed a preset improvement threshold as the verification schemes, perform performance simulation verification on the verification schemes, and update the performance data based on the simulation verification results. The strategy optimization module is used to extract the deviation features between the actual simulated performance and the predicted performance from the updated performance data, dynamically adjust the parameters of the Gaussian process regression model based on the deviation features, and generate an optimized exploration strategy. The candidate generation module is used to extract matching formulation schemes from the formulation database according to the optimized exploration strategy to form an initial candidate set, calculate the experimental cost of each scheme in the initial candidate set and sort them in ascending order of value, and select the formulation scheme with the highest cost ranking as the iterative input. The performance ranking module is used to simulate the formula schemes in the iterative input, integrate the simulation results with the production efficiency index, and determine the performance ranking of the yarn formula schemes. The path determination module is used to select yarn formulation schemes that meet the conditions based on performance ranking, combined with preset performance thresholds, cost thresholds and mass production feasibility conditions, and determine the parameter adjustment path based on the selected yarn formulation schemes to form a complete path for yarn formulation optimization.

[0061] Through the collaborative efforts of the aforementioned components, this system constructs a data-driven, model-driven, and closed-loop iterative intelligent optimization system for yarn formulations. It achieves full-process automation and intelligence, from historical data modeling, exploration of uncertain regions, simulation verification and correction, low-cost iterative screening to outputting optimized production paths. Specifically: the data modeling module cleans, standardizes, and trains Gaussian process regression models for historical data, outputting predicted uncertain distributions to provide a foundation for global optimization; the region exploration module locates high-potential regions based on uncertainty indicators, generating efficient exploration sequences to address the blindness of traditional optimization; the simulation verification module replaces physical spinning trials with physical simulation, reducing experimental costs and updating performance datasets, forming a closed-loop feedback; the strategy optimization module corrects model parameters and exploration weights based on deviation characteristics, balancing exploration and utilization to continuously improve prediction accuracy; the candidate generation module selects iterative inputs based on a low-cost priority principle, controlling optimization costs and improving efficiency; the performance ranking module integrates physical performance and production efficiency indicators to achieve quantitative ranking of the comprehensive value of the formulation; and the path determination module completes the screening of qualified solutions under multiple conditions and generates parameter adjustment paths, transforming intelligent optimization results into a complete optimization process that can be directly implemented in production.

[0062] This application also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when executed on a computer, cause the computer to perform the steps of the performance prediction method for yarn formulation optimization.

[0063] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the methods and systems described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0064] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A performance prediction method for yarn formulation optimization, characterized in that, Includes the following steps: S1. Collect historical yarn formula data and corresponding performance indicators, establish the mapping relationship between yarn formula data and corresponding performance indicators using a Gaussian process regression model, and obtain the predicted uncertainty distribution based on the mapping relationship; S2. Based on the predicted uncertainty distribution, the region where the formula data combination with uncertainty index higher than the preset uncertainty threshold is located is identified as a high uncertainty region. The predicted improvement value of the potential formula scheme in the high uncertainty region is calculated to obtain the exploration sequence of the high uncertainty region. S3. The formulation schemes in the exploration sequence whose predicted improvement value exceeds the preset improvement threshold are identified as schemes to be verified. The performance of the schemes to be verified is simulated and verified, and the performance data is updated according to the simulation and verification results. S4. Extract the deviation features between the actual simulated performance and the predicted performance from the updated performance data, and dynamically adjust the parameters of the Gaussian process regression model based on the deviation features to generate an optimized exploration strategy. S5. Based on the optimized exploration strategy, extract matching formulation schemes from the formulation database to form an initial candidate set, calculate the experimental cost of each scheme in the initial candidate set and sort them according to the numerical value from smallest to largest, and select the formulation scheme with the cost ranking in the first preset position as the iterative input. S6. Simulate the formula schemes in the iterative input, integrate the simulation results with the production efficiency index, and determine the performance ranking of the yarn formula schemes. S7. Based on the performance ranking, combined with preset performance thresholds, cost thresholds, and mass production feasibility conditions, select yarn formulation schemes that meet the conditions, determine the parameter adjustment path based on the selected yarn formulation schemes, and form a complete path for yarn formulation optimization.

2. The method according to claim 1, characterized in that, Step S1 includes: Historical yarn formulation data and corresponding performance index data are collected, and the formulation data and performance index data are cleaned, deduplicated, and standardized to form a standardized training dataset. The standardized training dataset is input into the Gaussian process regression model for training. The formula data is used as input and the performance index is used as output to establish a nonlinear mapping relationship between the formula data and the performance index. Based on the nonlinear mapping relationship, predictions are made for combinations of unexperimented formulations to obtain the predicted mean and predicted variance, and a predicted uncertainty distribution is generated based on the predicted mean and predicted variance.

3. The method according to claim 1, characterized in that, Step S2 includes: The prediction variance in the predicted uncertainty distribution is extracted as an uncertainty index, and the region where the uncertainty index is higher than a preset uncertainty threshold is identified as a high uncertainty region. Based on the optimal performance value of the currently verified formulation, calculate the probability and improvement range of each potential formulation scheme exceeding the optimal performance value in the high uncertainty region, and determine the predicted improvement value by multiplying the probability and the improvement range. The potential formulations are sorted from highest to lowest according to the predicted improvement values ​​to form a high uncertainty region exploration sequence for priority exploration.

4. The method according to claim 1, characterized in that, Step S3 includes: Traverse the exploration sequence of the high uncertainty region and select the formulation schemes with predicted improvement values ​​greater than the preset improvement threshold as the schemes to be verified; The proposed scheme was simulated and calculated using a yarn performance simulation tool to obtain the actual simulated performance results. The actual simulated performance results are associated with and stored with the corresponding formulation and predicted performance data to update the performance data.

5. The method according to claim 1, characterized in that, Step S4 includes: Extract the actual simulated performance and the corresponding predicted performance from the updated performance data; Calculate the absolute deviation, relative deviation, mean square deviation, and deviation trend between the actual simulation performance and the predicted performance, and integrate the above calculation results into deviation characteristics; Based on the aforementioned deviation characteristics, a Bayesian optimization algorithm is used to correct the kernel function parameters and noise parameters of the Gaussian process regression model, while adjusting the exploration weight parameters. The exploration weight parameters are used to allocate the exploration intensity for high uncertainty regions and the mining intensity for high performance regions. The corrected model parameters are combined with the adjusted exploration weight parameters to generate an optimized exploration strategy that is adapted to the bias characteristics.

6. The method according to claim 1, characterized in that, Step S5 includes: The parameter selection range, exploration direction, and constraints are determined based on the optimized exploration strategy. According to the parameter filtering range, exploration direction and constraints, matching formula schemes are extracted from the formula database to form an initial candidate set; The raw material cost, experimental time cost, and simulation calculation cost of each formulation scheme in the initial candidate set are calculated using a cost evaluation model, and the experimental cost is obtained by summing them up. The formulation schemes in the initial candidate set are sorted from smallest to largest according to the experimental cost, and the formulation scheme ranked in the top preset position is selected as the iterative input.

7. The method according to claim 1, characterized in that, Step S6 includes: The yarn performance simulation tool is used to perform a full-process simulation of each formula scheme in the iterative input, and the simulated performance results including strength, elongation, yarn evenness, hairiness index and abrasion resistance are obtained. Obtain the production efficiency indicators of the corresponding formula scheme, including hourly output, production energy consumption, and raw material loss rate. The simulated performance results and production efficiency indicators are weighted and fused according to preset weights to obtain the comprehensive performance score of each formula scheme. The yarn formulation schemes are ranked from highest to lowest based on their comprehensive performance scores, and those with scores below a preset threshold are removed to form a performance ranking.

8. The method according to claim 1, characterized in that, Step S7 includes: Based on the performance ranking, qualified formulation solutions that simultaneously meet preset performance thresholds, cost thresholds, production process constraints, and mass production feasibility conditions are selected in sequence. Extract the key formulation parameters and process parameters of the qualified formulation scheme, including fiber ratio, twist coefficient, and spinning speed; Based on the key formulation parameters and process parameters, determine the step-by-step adjustment path from the initial formulation to the target optimal formulation, and clarify the direction and magnitude of parameter adjustment at each step; By integrating the aforementioned step-by-step adjustment path with the exploration, verification, iteration, and screening processes, a complete path for yarn formulation optimization that can be directly applied to actual production is formed.

9. A performance prediction system for yarn formulation optimization, used to implement the performance prediction method for yarn formulation optimization as described in any one of claims 1 to 8, characterized in that, include: The data modeling module is used to collect historical yarn formula data and corresponding performance indicators, establish a mapping relationship between yarn formula data and corresponding performance indicators using a Gaussian process regression model, and obtain the prediction uncertainty distribution based on the mapping relationship. The region exploration module is used to identify regions where the uncertainty index of the formula data combination is higher than the preset uncertainty threshold as high uncertainty regions based on the predicted uncertainty distribution, calculate the predicted improvement value of potential formula schemes in the high uncertainty regions, and obtain the exploration sequence of the high uncertainty regions. The simulation verification module is used to identify the formulation schemes in the exploration sequence whose predicted improvement value exceeds a preset improvement threshold as the schemes to be verified, perform performance simulation verification on the schemes to be verified, and update the performance data based on the simulation verification results. The strategy optimization module is used to extract the deviation features between the actual simulated performance and the predicted performance from the updated performance data, dynamically adjust the parameters of the Gaussian process regression model based on the deviation features, and generate an optimized exploration strategy. The candidate generation module is used to extract matching formulation schemes from the formulation database according to the optimized exploration strategy to form an initial candidate set, calculate the experimental cost of each scheme in the initial candidate set and sort them according to the numerical value from smallest to largest, and select the formulation scheme with the cost ranking in the first preset position as the iterative input. The performance ranking module is used to simulate the formulation schemes in the iterative input, integrate the simulation results with the production efficiency index, and determine the performance ranking of the yarn formulation schemes. The path determination module is used to screen yarn formulation schemes that meet the conditions based on the performance ranking, combined with preset performance thresholds, cost thresholds and mass production feasibility conditions, and determine the parameter adjustment path based on the screened yarn formulation schemes to form a complete path for yarn formulation optimization.

10. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is executed by a processor, it implements the performance prediction method for yarn formulation optimization as described in any one of claims 1-8.

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