Epoxy hardener compatibility test and formula system optimization method and system

Abstract

The invention provides an epoxy curing agent compatibility test and formula system optimization method and system, and relates to the technical field of material testing, and the method comprises the following steps: collecting curing performance data and standardizing; adopting a collaborative entropy weight method to construct a coupling strength matrix to obtain comprehensive evaluation; constructing a performance feature directed acyclic graph, and obtaining a curing agent compatibility index by using a performance association tracking algorithm; taking a compatibility index as an optimization target, and screening a formula through adaptive variation and similarity cross; an optimal formula is obtained through experimental verification. According to the method, the compatibility evaluation accuracy of the epoxy curing agent is improved, and accurate optimization of a formula system is realized.

Description

Technical Field

[0001] This invention relates to the field of materials testing technology, and in particular to a method and system for testing the compatibility of epoxy curing agents and optimizing their formulation systems. Background Technology

[0002] Epoxy resin curing agents are key components in epoxy resin curing systems, and their performance directly determines the overall performance of the cured resin material. With the widespread application of high-performance composite materials in aerospace, electronics, new energy, and other fields, the performance requirements for epoxy curing systems are constantly increasing. Single curing agents often cannot meet diverse performance demands, making curing agent compounding technology a hot research topic in the industry. Currently, epoxy curing agent compounding mainly relies on experience and extensive trial-and-error experiments, lacking scientific compatibility evaluation and formulation optimization methods.

[0003] Compatibility issues between curing agents are a major challenge in compound systems. Different types of curing agents differ in chemical structure, reaction mechanism, and curing kinetics; simple mixing can lead to uneven curing, interfacial defects, and performance degradation. Traditional compatibility evaluations mainly rely on comparisons of isolated curing parameters and simple experimental observations, failing to systematically reveal the synergistic or antagonistic mechanisms between curing agents.

[0004] Existing technologies still have shortcomings, including: traditional curing agent compatibility evaluation lacks a comprehensive analysis method for multi-dimensional performance parameters, making it difficult to objectively reflect the actual synergistic effect of different curing agent combinations; existing research lacks in-depth exploration of the intrinsic correlation between curing performance parameters, making it impossible to establish an accurate mapping relationship between curing agent performance and formulation composition; curing agent formulation optimization generally adopts single parameter optimization or simple orthogonal experimental methods, which are computationally inefficient and prone to getting trapped in local optima, making it difficult to find the globally optimal formulation in a multi-dimensional performance space. Summary of the Invention

[0005] This invention provides a method and system for testing the compatibility of epoxy curing agents and optimizing their formulation systems, which can solve the problems in the prior art.

[0006] A first aspect of this invention provides a method for testing the compatibility of epoxy curing agents and optimizing formulation systems, comprising:

[0007] Multiple sets of curing performance data of the curing agent were collected, including curing exothermic enthalpy, curing peak temperature and glass transition temperature, and standardized to obtain an initial evaluation matrix;

[0008] The interaction strength between curing performance data is calculated using the collaborative entropy weight method, a coupling strength matrix is ​​constructed, and the initial evaluation matrix is ​​corrected based on the coupling strength matrix to obtain the comprehensive evaluation result.

[0009] Based on the comprehensive evaluation results, curing performance characteristics are extracted, a directed acyclic graph of curing performance characteristics is constructed, a performance association tracking algorithm is used to explore the curing agent performance combination path, and the curing agent compatibility index is obtained by calculating connectivity and performance gradient.

[0010] The compatibility index of the curing agent was set as the optimization target. An orthogonally distributed initial population was constructed in a uniformly divided formulation space. Offspring individuals were generated through adaptive mutation and similarity crossover, and the optimized curing agent formulation set was obtained by screening.

[0011] The optimized curing agent formulation set was experimentally verified, and the formulation that met the preset performance requirements was selected as the optimal curing agent formulation.

[0012] In one optional embodiment, the interaction strength between curing performance data is calculated using the collaborative entropy weighting method, a coupling strength matrix is ​​constructed, and the initial evaluation matrix is ​​corrected based on the coupling strength matrix to obtain a comprehensive evaluation result, including:

[0013] Calculate the information entropy of the solidification performance data, and obtain the entropy weight of each performance data based on the information entropy;

[0014] A synergy matrix of solidification performance data is constructed, wherein the elements of the synergy matrix are obtained by calculating the nonlinear correlation coefficients between pairs of performance data.

[0015] The interaction strength is obtained by coupling the entropy weight with the synergy matrix.

[0016] Construct a coupling strength matrix based on the interaction strength;

[0017] The eigenvalues ​​of the coupling strength matrix are normalized to obtain an initial correction factor; the trend coefficient of the curing performance data is calculated; the initial correction factor and the trend coefficient are multiplied to obtain a dynamic correction factor.

[0018] The dynamic correction factor is coupled with the initial evaluation matrix to obtain the corrected evaluation matrix; the corrected evaluation matrix is ​​then subjected to data fusion processing to obtain the comprehensive evaluation result.

[0019] In one optional embodiment, the data fusion process includes:

[0020] The modified evaluation matrix is ​​clustered using the K-means clustering algorithm. The Euclidean distance between data points in the modified evaluation matrix is ​​calculated. The data points are initially classified based on the minimum distance principle. The cluster center positions are iteratively updated until convergence, and the performance characteristic clusters are determined.

[0021] Calculate the mean of the data points in each dimension of each performance feature cluster to obtain the cluster centroid coordinates, and combine the cluster centroid coordinates to form a centroid vector;

[0022] Select any two centroid vectors to determine a centroid vector pair, calculate the Mahalanobis distance between the centroid vector pairs, and construct a distance matrix.

[0023] The distance matrix is ​​normalized, and the normalized distance values ​​are converted into similarity values ​​using a Gaussian kernel function to obtain the inter-class coupling coefficient.

[0024] The relative importance of each performance feature cluster is determined by the sum of the coupling coefficients of each cluster with all other performance feature clusters, and the adaptive weights are obtained by normalization.

[0025] The adaptive weights are linearly weighted and summed with the corresponding performance feature clusters to obtain the comprehensive evaluation result.

[0026] In one optional embodiment, extracting curing performance characteristics based on the comprehensive evaluation results and constructing a directed acyclic graph of the curing performance characteristics includes:

[0027] The comprehensive evaluation results are used to establish a correspondence table based on the relationship between curing performance indicators and evaluation values, and the correspondence table is then transformed into a curing performance indicator matrix.

[0028] The relationships between the curing performance indicators in the curing performance index matrix are analyzed to obtain the interaction relationship matrix between different curing performance indicators. The importance of each curing performance indicator is determined according to the interaction relationship matrix. The curing performance indicator with the highest importance is selected as the curing performance feature according to the preset screening percentage.

[0029] The curing performance characteristics are set as performance characteristic nodes. The degree of mutual influence between the performance characteristic nodes is calculated. When the influence of the first performance characteristic node on the second performance characteristic node is greater than the influence of the second performance characteristic node on the first performance characteristic node, the direction of action is determined to be from the first performance characteristic node to the second performance characteristic node.

[0030] A directed graph is constructed by connecting performance characteristic nodes according to the described direction of action. Cyclic action structures in the directed graph are detected, and the connection with the least impact in the cyclic action structure is disconnected to obtain a directed acyclic graph of the curing performance characteristics.

[0031] In one optional embodiment, the performance correlation tracing algorithm includes:

[0032] The performance feature node with zero in-degree in the directed acyclic graph is selected as the search starting node, the corresponding influence factor is calculated, and the importance of the search starting node is sorted according to the influence factor to obtain the node importance sequence.

[0033] The performance feature nodes in the directed acyclic graph are constructed into a node hierarchy structure according to their connection relationships. Based on the node importance sequence, the jump constraints between adjacent level nodes in the node hierarchy structure are determined to obtain the hierarchy transfer matrix.

[0034] Calculate the performance change response value between adjacent performance characteristic nodes in the node hierarchy, analyze the transmission attenuation coefficient between performance characteristic nodes based on the hierarchy transmission matrix, and combine the performance change response value with the transmission attenuation coefficient to calculate the cumulative transmission impact value.

[0035] Based on the cumulative propagation impact value, the path influence intensity between performance feature nodes is calculated, the performance parameter deviation value of the performance feature node is determined, and the path dynamic adjustment is triggered based on the performance parameter deviation value to obtain an optimized path set.

[0036] The performance conflict resolution priority between the performance feature nodes is set according to the cumulative transmission impact value, the path combination score is calculated based on the optimized path set, and the path with the highest path combination score is selected as the curing agent performance combination path.

[0037] In an optional embodiment, the curing agent compatibility index is obtained by calculating connectivity and performance gradient, including:

[0038] Extract the node connection relationships in the optimal performance combination path, construct the direct connectivity matrix corresponding to the node connection relationships, and count the number of path connections in the direct connectivity matrix to obtain the direct connectivity degree.

[0039] The second-order connection relationship between nodes is identified based on the direct connectivity matrix and converted into indirect connectivity strength. The direct connectivity and indirect connectivity strength are combined to obtain the comprehensive connectivity.

[0040] Calculate the rate of performance change between adjacent nodes in the optimal performance combination path to obtain the local performance gradient. Determine the performance transition critical value based on the local performance gradient and construct the local gradient matrix corresponding to the local performance gradient and the performance transition critical value.

[0041] Based on the local gradient matrix, the cumulative change trend on the performance transfer chain is analyzed, the cumulative change trend is transformed into a performance decay coefficient, and a global gradient distribution is constructed based on the performance decay coefficient.

[0042] The contribution ratio of the comprehensive connectivity to the compatibility of the curing agent is analyzed to obtain the connectivity weight coefficient. The influence of the global gradient distribution on the compatibility of the curing agent is calculated to obtain the gradient influence coefficient. A dynamic weight matrix is ​​established based on the connectivity weight coefficient and the gradient influence coefficient.

[0043] The curing agent compatibility index is obtained by combining the comprehensive connectivity and global gradient distribution according to the dynamic weight matrix and then normalizing them.

[0044] In one optional embodiment, the curing agent compatibility index is set as the optimization objective. An orthogonally distributed initial population is constructed within a uniformly divided formulation space. Offspring individuals are generated through adaptive mutation and similarity crossover, and an optimized set of curing agent formulations is obtained by screening, including:

[0045] The formulation space is divided into multiple uniform subspaces. Sampling points that satisfy orthogonal distribution are randomly selected in the subspaces to construct an initial solution space. The initial solution space is then corrected by combining it with a preset curing agent formulation knowledge base to determine the initial population.

[0046] Calculate the Euclidean distance between individuals in the initial population, adaptively adjust the scaling factor of the mutation operation based on the Euclidean distance, and perform the mutation operation on the initial population to obtain mutated individuals;

[0047] Calculate the similarity between the mutant individuals and the initial population, determine the optimal crossover region based on the similarity, select a crossover position within the optimal crossover region, and perform a crossover operation on the mutant individuals to obtain offspring individuals;

[0048] Calculate the curing agent compatibility index corresponding to the offspring individuals, classify the offspring individuals into different superior and inferior grades based on the preset curing agent compatibility index classification, and calculate the distribution distance of individuals within each superior and inferior grade.

[0049] Based on the quality level and distribution distance, the dominant individuals are selected, and the composition ratio of the dominant individuals is compared with the historical data in the curing agent formulation knowledge base. Based on the comparison results, the composition ratio of the dominant individuals is adjusted to obtain an adjusted formulation set.

[0050] The formulations in the adjusted formulation set are sorted in descending order according to the curing agent compatibility index, and the formulations ranked first are selected to form the optimized curing agent formulation set according to a preset ratio.

[0051] A second aspect of this invention provides a system for testing the compatibility of epoxy curing agents and optimizing formulation systems, comprising:

[0052] The first unit is used to collect multiple sets of curing performance data of the curing agent, including curing exothermic enthalpy, curing peak temperature and glass transition temperature, and to perform standardization processing to obtain an initial evaluation matrix.

[0053] The second unit is used to calculate the interaction strength between curing performance data using the collaborative entropy weight method, construct a coupling strength matrix, and correct the initial evaluation matrix based on the coupling strength matrix to obtain the comprehensive evaluation result.

[0054] The third unit is used to extract curing performance characteristics based on the comprehensive evaluation results, construct a directed acyclic graph of curing performance characteristics, explore the performance combination path of curing agent using the performance association tracking algorithm, and obtain the curing agent compatibility index by calculating connectivity and performance gradient.

[0055] The fourth unit is used to set the compatibility index of the curing agent as the optimization target, construct an orthogonally distributed initial population in a uniformly divided formulation space, generate offspring individuals through adaptive mutation and similarity crossover, and screen to obtain an optimized set of curing agent formulations.

[0056] The fifth unit is used to conduct experimental verification of the optimized curing agent formulation set and select the formulation that meets the preset performance requirements as the optimal curing agent formulation.

[0057] A third aspect of the present invention provides an electronic device, comprising:

[0058] processor;

[0059] Memory used to store processor-executable instructions;

[0060] The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0061] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0062] In this embodiment of the invention, the collaborative entropy weight method is used to comprehensively evaluate curing performance data, taking into account the interaction between different curing properties. This overcomes the limitations of traditional single-index evaluation and achieves a comprehensive and objective evaluation of curing agent performance, providing a reliable basis for formulation optimization. By constructing a directed acyclic graph of curing performance characteristics and a performance correlation tracking algorithm, the compatibility mechanism between different curing agents is revealed, and the synergistic effect of formulation combinations is quantitatively characterized. This solves the problem of multi-component formulation optimization in traditional empirical formulation design and significantly reduces experimental costs. This invention adopts an adaptive optimization strategy based on compatibility index to quickly locate the optimal formulation region in a broad formulation space, avoiding the risk of getting trapped in local optima and improving the efficiency of formulation optimization. The resulting optimized formulation has been experimentally verified to have good curing performance and application stability. Attached Figure Description

[0063] Figure 1 This is a schematic flowchart of the epoxy curing agent compatibility testing and formulation system optimization method according to an embodiment of the present invention;

[0064] Figure 2 Flowchart for optimizing the performance combination path of curing agents. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0067] Figure 1 This is a schematic flowchart of the epoxy curing agent compatibility testing and formulation system optimization method according to an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes:

[0068] Multiple sets of curing performance data of the curing agent were collected, including curing exothermic enthalpy, curing peak temperature and glass transition temperature, and standardized to obtain an initial evaluation matrix;

[0069] The interaction strength between curing performance data is calculated using the collaborative entropy weight method, a coupling strength matrix is ​​constructed, and the initial evaluation matrix is ​​corrected based on the coupling strength matrix to obtain the comprehensive evaluation result.

[0070] Based on the comprehensive evaluation results, curing performance characteristics are extracted, a directed acyclic graph of curing performance characteristics is constructed, a performance association tracking algorithm is used to explore the curing agent performance combination path, and the curing agent compatibility index is obtained by calculating connectivity and performance gradient.

[0071] The compatibility index of the curing agent was set as the optimization target. An orthogonally distributed initial population was constructed in a uniformly divided formulation space. Offspring individuals were generated through adaptive mutation and similarity crossover, and the optimized curing agent formulation set was obtained by screening.

[0072] The optimized curing agent formulation set was experimentally verified, and the formulation that met the preset performance requirements was selected as the optimal curing agent formulation.

[0073] In one specific implementation, multiple sets of curing performance data for the curing agent are collected, including the curing exothermic enthalpy, curing peak temperature, and glass transition temperature. These data are standardized to eliminate dimensional differences, forming an initial evaluation matrix that allows for comprehensive comparison of different performance indicators.

[0074] After obtaining the initial evaluation matrix, the interaction strength between various curing performance data is calculated using the collaborative entropy weighting method. This step analyzes the correlation between performance indicators and constructs a coupling strength matrix, reflecting the mutual influence between performance indicators. Based on the established coupling strength matrix, the initial evaluation matrix is ​​revised to obtain a more comprehensive and objective integrated evaluation result, which fully considers the interaction between various performance indicators.

[0075] Based on the comprehensive evaluation results, curing performance characteristics are extracted, and a directed acyclic graph (DAG) of these characteristics is constructed. This graphical representation clearly shows the influence paths and dependencies between various performance indicators. Then, a performance association tracing algorithm is used to explore the performance combination paths of the curing agent, and the curing agent compatibility index is obtained by calculating connectivity and performance gradients. Connectivity reflects the complexity of the performance network, while the performance gradient represents the trend and magnitude of performance changes. Together, they constitute the compatibility index, used to evaluate the synergistic effects between curing agent components.

[0076] The compatibility index of the curing agent is set as the optimization objective, and an orthogonally distributed initial population is constructed within a uniformly partitioned formulation space. Adaptive mutation and similarity crossover operations are used to generate offspring individuals; these operations effectively avoid local optima and improve the algorithm's global search capability. During the iteration process, individuals are evaluated and selected based on the compatibility index and performance requirements to obtain an optimized set of curing agent formulations.

[0077] The optimized set of curing agent formulations was experimentally validated. Through actual preparation and testing, the formulation that met the preset performance requirements was selected as the optimal curing agent formulation. The experimental validation process included sample preparation, performance testing, and data analysis to ensure the reliability and effectiveness of the optimization results in practical applications. This systematic evaluation and optimization method allows for the efficient development of high-performance curing agent formulations to meet specific application needs.

[0078] In one optional implementation, the interaction strength between curing performance data is calculated using the collaborative entropy weighting method, a coupling strength matrix is ​​constructed, and the initial evaluation matrix is ​​corrected based on the coupling strength matrix to obtain a comprehensive evaluation result, including:

[0079] Calculate the information entropy of the solidification performance data, and obtain the entropy weight of each performance data based on the information entropy;

[0080] A synergy matrix of solidification performance data is constructed, wherein the elements of the synergy matrix are obtained by calculating the nonlinear correlation coefficients between pairs of performance data.

[0081] The interaction strength is obtained by coupling the entropy weight with the synergy matrix.

[0082] Construct a coupling strength matrix based on the interaction strength;

[0083] The eigenvalues ​​of the coupling strength matrix are normalized to obtain an initial correction factor; the trend coefficient of the curing performance data is calculated; the initial correction factor and the trend coefficient are multiplied to obtain a dynamic correction factor.

[0084] The dynamic correction factor is coupled with the initial evaluation matrix to obtain the corrected evaluation matrix; the corrected evaluation matrix is ​​then subjected to data fusion processing to obtain the comprehensive evaluation result.

[0085] In one specific implementation, information entropy is calculated for the collected epoxy curing agent compatibility performance data. The original performance data is standardized, converting data of different dimensions into dimensionless comparison values. For positive performance indicators, such as curing speed and crosslinking density, standardization is performed by dividing the value by the maximum value of the indicator; for negative indicators, such as curing shrinkage rate and moisture absorption rate, standardization is performed by dividing the minimum value by the value. After standardization, the information entropy of each performance indicator is calculated. Taking a certain formulation system as an example, five performance indicators—curing speed, heat resistance, moisture resistance, mechanical strength, and chemical resistance—are selected. The standardized data are 0.85, 0.92, 0.78, 0.88, and 0.82, respectively. The calculated information entropies for these five indicators are 0.43, 0.25, 0.52, 0.38, and 0.47, respectively.

[0086] Based on the calculated information entropy, the entropy weights of each performance data point are calculated. The entropy weight calculation uses the entropy value method, normalizing the information entropy values ​​after differential processing. For the five performance indicators in the above case, the calculated entropy weights are 0.22, 0.29, 0.18, 0.24, and 0.07, respectively, with a sum of 1. The entropy weights reflect the objective importance of each performance indicator in the overall evaluation; the smaller the information entropy, the more effective information the indicator provides, and thus the greater its weight.

[0087] A synergy matrix of curing performance data was constructed. This matrix reflects the degree of mutual influence between performance data points and is obtained by calculating the nonlinear correlation coefficients between each pair of performance data. For the characteristics of epoxy curing agents, grey relational analysis was used to calculate the nonlinear correlation coefficients. The calculation first calculates the difference sequences between each pair of standardized performance data, and then calculates the correlation coefficients based on these difference sequences. Taking the above case as an example, in the constructed 5×5 synergy matrix, the correlation coefficient between curing speed and heat resistance is 0.78, indicating a strong synergistic relationship; while the correlation coefficient between curing speed and chemical resistance is only 0.45, indicating a weaker synergy.

[0088] The interaction strength is obtained by coupling the entropy weights with the synergy matrix. The coupling calculation uses the product of the weight vector and the synergy matrix to reflect the comprehensive effect strength of each performance index after considering their mutual influence. For the data in the case study, in the calculated interaction strength matrix, the effect strength of curing speed on heat resistance is 0.17, and the effect strength of heat resistance on curing speed is 0.23.

[0089] A coupling strength matrix is ​​constructed based on the interaction strength. This matrix reflects the overall influence between various performance indicators and is obtained by symmetrizing the interaction strengths. Specifically, the geometric mean of the corresponding elements in the interaction strength matrix is ​​taken as the element of the coupling strength matrix. In the case study, the coupling strength between curing speed and heat resistance is 0.20, indicating a strong mutual influence between the two.

[0090] The eigenvalues ​​of the coupling strength matrix are normalized to obtain the initial correction factors. By solving for the eigenvalues ​​and eigenvectors of the coupling strength matrix, the eigenvector corresponding to the largest eigenvalue is normalized to obtain the initial correction factors. For the data in the case study, the calculated initial correction factors are 0.26, 0.32, 0.15, 0.19, and 0.08. These initial correction factors reflect the fundamental importance of each performance index in the solidified system.

[0091] The trend coefficients of the curing performance data were calculated. These coefficients reflect the sensitivity of each performance indicator to changes in environmental conditions and are calculated by testing the fluctuations in performance data under different temperature and humidity conditions. Specifically, samples were tested under standard conditions, high-temperature conditions, high-humidity conditions, and cyclic aging conditions. The coefficients of variation of the performance data were calculated and normalized. In this case, the trend coefficients of variation for the five performance indicators were 1.05, 0.92, 1.15, 0.98, and 1.10, respectively.

[0092] The initial correction factor is multiplied by the trend coefficient to obtain the dynamic correction factor. The dynamic correction factor comprehensively considers both the fundamental importance and environmental adaptability of performance indicators, thus reflecting the importance of each performance indicator in practical applications more fully. In the case study, the calculated dynamic correction factors were 0.27, 0.29, 0.17, 0.19, and 0.09, and were then normalized.

[0093] The modified evaluation matrix is ​​obtained by coupling the dynamic correction factor with the initial evaluation matrix. The initial evaluation matrix is ​​composed of standardized performance data, and the coupling operation is performed using a weighted average method. In the example, if the initial evaluation value of a certain formula is [0.85, 0.92, 0.78, 0.88, 0.82], after coupling with the dynamic correction factor, the evaluation value of the formula in the modified evaluation matrix becomes [0.87, 0.93, 0.76, 0.89, 0.80].

[0094] The modified evaluation matrix was subjected to data fusion processing to obtain a comprehensive evaluation result. The data fusion employed a weighted comprehensive scoring method, summing the performance indicators in the modified evaluation matrix according to their entropy weights. For the formulation in the case study, the final comprehensive evaluation score was 0.89, which can be used as a basis for judging the quality of the epoxy curing agent formulation.

[0095] To verify the effectiveness of this method, ten different epoxy curing agent formulations were selected for testing. These formulations included curing agents containing different types and proportions of amines, anhydrides, and imidazoles. The comprehensive evaluation results calculated by this method showed good consistency with the actual application results, with a correlation coefficient of 0.92. The formulation with the highest comprehensive score exhibited excellent performance in curing speed, heat resistance, and mechanical strength, with good balance among various performance indicators. It also demonstrated the most ideal curing effect in practical applications, proving the effective guiding role of this method in epoxy curing agent compatibility testing and formulation optimization.

[0096] In one optional implementation, the data fusion process includes:

[0097] The modified evaluation matrix is ​​clustered using the K-means clustering algorithm. The Euclidean distance between data points in the modified evaluation matrix is ​​calculated. The data points are initially classified based on the minimum distance principle. The cluster center positions are iteratively updated until convergence, and the performance characteristic clusters are determined.

[0098] Calculate the mean of the data points in each dimension of each performance feature cluster to obtain the cluster centroid coordinates, and combine the cluster centroid coordinates to form a centroid vector;

[0099] Select any two centroid vectors to determine a centroid vector pair, calculate the Mahalanobis distance between the centroid vector pairs, and construct a distance matrix.

[0100] The distance matrix is ​​normalized, and the normalized distance values ​​are converted into similarity values ​​using a Gaussian kernel function to obtain the inter-class coupling coefficient.

[0101] The relative importance of each performance feature cluster is determined by the sum of the coupling coefficients of each cluster with all other performance feature clusters, and the adaptive weights are obtained by normalization.

[0102] The adaptive weights are linearly weighted and summed with the corresponding performance feature clusters to obtain the comprehensive evaluation result.

[0103] In one specific implementation, after obtaining the modified evaluation matrix, the K-means clustering algorithm is used to perform cluster analysis on the modified evaluation matrix, and the Euclidean distance between every two data points in the modified evaluation matrix is ​​calculated as a similarity metric. Taking a certain epoxy curing agent formulation system as an example, the modified evaluation matrix contains 15 formulation samples, each sample having 5 performance indicators (curing speed, heat resistance, moisture resistance, mechanical strength, and chemical resistance). The calculated Euclidean distance between sample 1 and sample 2 in the five-dimensional feature space is 0.153, indicating that the two formulations are relatively similar in performance characteristics. After determining the distance metric, the data points are initially classified based on the minimum distance principle. Three initial cluster centers are randomly selected, namely sample 3, sample 8, and sample 12, and the remaining sample points are assigned to the nearest cluster. Subsequently, iterative optimization is performed, calculating the average position of all data points in each cluster as the new cluster center, and redistributing data points until the cluster center positions no longer change or change very little. In this case, the algorithm converged after 7 iterations, and finally divided the 15 samples into 3 performance feature clusters: cluster A contains samples 1, 3, 5, 9, and 14, cluster B contains samples 2, 6, 8, 10, and 13, and cluster C contains samples 4, 7, 11, 12, and 15.

[0104] The centroid coordinates of each cluster are obtained by calculating the mean of the data points in each dimension within each performance characteristic cluster. For the three clusters in the above example, the centroid coordinates of cluster A are [0.87, 0.76, 0.92, 0.81, 0.68], indicating that this cluster performs excellently in terms of curing speed and moisture resistance; the centroid coordinates of cluster B are [0.75, 0.89, 0.72, 0.84, 0.91], indicating that this cluster has advantages in terms of heat resistance and chemical resistance; and the centroid coordinates of cluster C are [0.82, 0.85, 0.79, 0.93, 0.77], indicating that this cluster performs best in terms of mechanical strength. Combining the centroid coordinates of each cluster forms a centroid vector, constituting the performance characteristic cluster space of the epoxy curing agent formulation.

[0105] By selecting any two centroid vectors to determine a centroid vector pair, the Mahalanobis distance between the centroid vector pairs is calculated, and a distance matrix is ​​constructed. Mahalanobis distance considers the covariance structure of the data and can more accurately reflect the actual differences between different clusters in the performance feature space. For the above case, the calculated Mahalanobis distance matrix is ​​as follows: the distance between clusters A and B is 2.87, the distance between A and C is 1.92, and the distance between B and C is 2.14. This indicates that the performance characteristics of clusters A and C are relatively similar, while the difference between clusters A and B is the greatest.

[0106] The distance matrix was normalized, and the normalized distance values ​​were converted into similarity values ​​using a Gaussian kernel function to obtain the inter-class coupling coefficients. The normalization process employed a minimax method, mapping the distance values ​​to the interval [0, 1]. The normalized distance matrix was then converted into similarity values ​​using a Gaussian kernel function. The kernel width parameter of the Gaussian kernel function was determined to be 0.5 using cross-validation. After the conversion, the coupling coefficient between clusters A and B was 0.29, between A and C was 0.56, and between B and C was 0.43. A larger coupling coefficient indicates more similar performance characteristics between the two clusters and a higher degree of mutual influence.

[0107] The relative importance of each performance characteristic cluster is determined by summing the coupling coefficients of each cluster with all other performance characteristic clusters, and then normalized to obtain adaptive weights. In the above case, the total coupling coefficient of cluster A is 0.85, that of cluster B is 0.72, and that of cluster C is 0.99. After normalization, the adaptive weights for clusters A, B, and C are 0.33, 0.28, and 0.39, respectively. These adaptive weights reflect the importance of each performance characteristic cluster in the overall epoxy curing agent formulation system; a higher weight indicates a higher degree of coupling between that cluster and other clusters, and a greater impact on the overall evaluation.

[0108] The adaptive weights are linearly weighted and summed with the corresponding performance feature clusters to obtain the comprehensive evaluation result. The linear weighted summation method involves multiplying the centroid coordinates of each cluster by its corresponding adaptive weight and then summing the results to obtain the weighted centroid coordinates. For the above case, the weighted centroid coordinates are [0.82, 0.83, 0.82, 0.86, 0.78]. Furthermore, the components of the weighted centroid coordinates are weighted according to the importance of the performance indicators to obtain the final comprehensive evaluation score. Assuming the importance weights of the five performance indicators are 0.25, 0.20, 0.15, 0.25, and 0.15 respectively, the final comprehensive evaluation score is 0.83. This evaluation score allows for an objective assessment of the comprehensive performance of the epoxy curing agent formulation, providing a basis for formulation optimization.

[0109] This embodiment addresses the limitations of traditional epoxy curing agent formulation evaluation methods. Traditional methods typically employ simple linear weighting or analytic hierarchy process (AHP) for comprehensive evaluation, failing to fully consider the coupling relationships and nonlinear interactions between different performance indicators. In existing technologies, the weights of evaluation indicators are usually determined based on expert experience or simple data statistics, making it difficult to adapt to the dynamic changes in different application scenarios. This embodiment introduces K-means clustering and Mahalanobis distance analysis to establish an adaptive evaluation method that considers the coupling relationships between performance indicators. This method fully explores the intrinsic connections between various performance indicators in epoxy curing agent formulations, dynamically adjusting evaluation weights through cluster analysis of performance characteristic clusters and calculation of coupling coefficients, resulting in more objective and comprehensive evaluation results.

[0110] In one optional implementation, extracting curing performance characteristics based on the comprehensive evaluation results and constructing a directed acyclic graph of the curing performance characteristics includes:

[0111] The comprehensive evaluation results are used to establish a correspondence table based on the relationship between curing performance indicators and evaluation values, and the correspondence table is then transformed into a curing performance indicator matrix.

[0112] The relationships between the curing performance indicators in the curing performance index matrix are analyzed to obtain the interaction relationship matrix between different curing performance indicators. The importance of each curing performance indicator is determined according to the interaction relationship matrix. The curing performance indicator with the highest importance is selected as the curing performance feature according to the preset screening percentage.

[0113] The curing performance characteristics are set as performance characteristic nodes. The degree of mutual influence between the performance characteristic nodes is calculated. When the influence of the first performance characteristic node on the second performance characteristic node is greater than the influence of the second performance characteristic node on the first performance characteristic node, the direction of action is determined to be from the first performance characteristic node to the second performance characteristic node.

[0114] A directed graph is constructed by connecting performance characteristic nodes according to the described direction of action. Cyclic action structures in the directed graph are detected, and the connection with the least impact in the cyclic action structure is disconnected to obtain a directed acyclic graph of the curing performance characteristics.

[0115] In one specific implementation, a correspondence table is established based on the relationship between the comprehensive evaluation results and the evaluation values ​​of the curing performance indicators. For example, for an epoxy resin curing system, selectable curing performance indicators include: glass transition temperature, fracture toughness, flexural strength, tensile strength, elastic modulus, and elongation at break. For a certain batch of epoxy resin cured samples, specific values ​​of each indicator are obtained through testing, such as a glass transition temperature of 135℃ and a fracture toughness of 1.2 MPa·m. 1 / 2The flexural strength is 110 MPa, the tensile strength is 85 MPa, the elastic modulus is 2.8 GPa, and the elongation at break is 3.5%. These indicators and their corresponding evaluation values ​​are organized in a row-column manner to form a curing performance index matrix. The rows of this matrix represent different curing performance indicators, the columns represent different samples or test conditions, and the matrix element values ​​are the corresponding test data.

[0116] The relationships between the indicators in the curing performance index matrix are analyzed, and the correlations between the indicators are calculated using data analysis techniques to obtain the interaction matrix. For example, when analyzing the index relationships of the epoxy resin curing system, the correlation coefficient between glass transition temperature and elastic modulus is found to be 0.85, indicating a strong positive correlation; while the correlation coefficient between glass transition temperature and elongation at break is -0.72, indicating a negative correlation. Based on the interaction matrix, the importance of each indicator can be calculated. The importance calculation can use network analysis methods to consider the direct and indirect effects between indicators. Assume the importance analysis results for the six curing performance indicators are: glass transition temperature 0.25, elastic modulus 0.22, tensile strength 0.18, flexural strength 0.15, fracture toughness 0.12, and elongation at break 0.08. If the preset screening percentage is 80%, then the indicators with a cumulative importance of 0.8 are selected as curing performance characteristics, namely, glass transition temperature, elastic modulus, tensile strength, and flexural strength.

[0117] The selected curing performance characteristics are set as performance characteristic nodes, and the degree of mutual influence between nodes is calculated. The degree of influence is calculated based on the strength of the relationship between corresponding indicators in the interaction matrix. For example, the influence degree of glass transition temperature on elastic modulus is 0.85, while the influence degree of elastic modulus on glass transition temperature is 0.62. Since the former is greater than the latter, the direction of influence is determined to be from glass transition temperature to elastic modulus. Similarly, other node pairs are analyzed to obtain the complete direction of interaction between nodes. For glass transition temperature and tensile strength, their mutual influence degrees are 0.70 and 0.65, respectively, and the direction of influence is determined to be from glass transition temperature to tensile strength. For elastic modulus and flexural strength, their mutual influence degrees are 0.75 and 0.58, respectively, and the direction of influence is determined to be from elastic modulus to flexural strength. For tensile strength and flexural strength, their mutual influence degrees are 0.80 and 0.78, respectively, and the direction of influence is determined to be from tensile strength to flexural strength.

[0118] Connect the performance feature nodes according to the determined direction of influence to construct a preliminary directed graph. In this step, the performance feature nodes are connected by directed edges, where the direction of the edge represents the direction of influence, from the source of influence to the affected object. During the construction process, cyclic action structures may appear, forming closed loops. For example, in this instance, a cyclic structure of glass transition temperature → elastic modulus → flexural strength → tensile strength → glass transition temperature may occur. After detecting such a cyclic structure, the connection with the least influence in the cycle needs to be broken to ensure the acyclicity of the graph. In the above cycle, if the influence of tensile strength on glass transition temperature is 0.45, which is the smallest in the cycle, then the connection from tensile strength to glass transition temperature is broken, while other connections are retained.

[0119] By disconnecting the least influential connections in the cyclic structure, a directed acyclic graph (DAG) of the curing performance characteristics is obtained, reflecting the causal network between these characteristics. Each node represents a curing performance characteristic, and the directed edges between nodes represent the influence relationships between features, with the direction of the edges indicating the direction of the influence. In this example, the final DAG is as follows: the glass transition temperature serves as the source node, pointing to the elastic modulus and tensile strength, respectively; the elastic modulus points to the flexural strength; and the tensile strength also points to the flexural strength. This DAG structure clearly demonstrates the hierarchical relationships and influence paths between curing performance characteristics, providing an effective tool for further analysis of curing performance.

[0120] This directed acyclic graph (DAG) can be used to guide the optimization of curing processes. By adjusting the glass transition temperature, a source node parameter, it can effectively influence downstream performance indicators such as elastic modulus, tensile strength, and flexural strength, thereby achieving a comprehensive improvement in curing performance. Furthermore, the graph can also be used for performance prediction and anomaly diagnosis. When a performance indicator becomes abnormal, the possible causal indicators can be traced along the path in the graph.

[0121] In one optional implementation, the performance correlation tracing algorithm includes:

[0122] The performance feature node with zero in-degree in the directed acyclic graph is selected as the search starting node, the corresponding influence factor is calculated, and the importance of the search starting node is sorted according to the influence factor to obtain the node importance sequence.

[0123] The performance feature nodes in the directed acyclic graph are constructed into a node hierarchy structure according to their connection relationships. Based on the node importance sequence, the jump constraints between adjacent level nodes in the node hierarchy structure are determined to obtain the hierarchy transfer matrix.

[0124] Calculate the performance change response value between adjacent performance characteristic nodes in the node hierarchy, analyze the transmission attenuation coefficient between performance characteristic nodes based on the hierarchy transmission matrix, and combine the performance change response value with the transmission attenuation coefficient to calculate the cumulative transmission impact value.

[0125] Based on the cumulative propagation impact value, the path influence intensity between performance feature nodes is calculated, the performance parameter deviation value of the performance feature node is determined, and the path dynamic adjustment is triggered based on the performance parameter deviation value to obtain an optimized path set.

[0126] The performance conflict resolution priority between the performance feature nodes is set according to the cumulative transmission impact value, the path combination score is calculated based on the optimized path set, and the path with the highest path combination score is selected as the curing agent performance combination path.

[0127] In one specific implementation, the method for testing the compatibility of epoxy curing agents and optimizing the formulation system involves constructing a directed acyclic graph (DAG) model for performance characteristic node analysis and optimization path selection. This method selects performance characteristic nodes with zero in-degree in the DAG as the starting point nodes for the search and calculates the influence factor for each starting point node. The influence factor calculation is based on the node's connectivity in the network, the range of its transmitted influence, and its performance contribution weight. For example, for the amine value node in the curing agent, its influence factor is obtained by statistically analyzing the number of downstream nodes directly connected to it (such as gel time, glass transition temperature, etc.), multiplying it by the respective connection weights (such as 0.65, 0.78, etc.), and then combining this with the node's own performance contribution coefficient (such as 0.82). By calculating and ranking the influence factors of all nodes with zero in-degree, a node importance sequence such as "amine value-viscosity-pH value-active hydrogen content" can be obtained.

[0128] The performance characteristic nodes in the directed acyclic graph are used to construct a hierarchical structure based on their connectivity relationships. For example, the first layer might contain amine value and pH value, the second layer might contain curing rate and viscosity, and the third layer might contain glass transition temperature and mechanical strength. Jump constraints between adjacent level nodes are determined based on the node importance sequence, and a hierarchical transfer matrix is ​​constructed. For instance, the jump weight from the amine value node to the curing rate node is 0.75, and the jump weight to the viscosity node is 0.45; the jump weight from the pH value node to the curing rate node is 0.65, and the jump weight to the viscosity node is 0.35. These weights constitute the elements of the hierarchical transfer matrix and are used for subsequent path influence calculations.

[0129] The performance change response values ​​between adjacent performance characteristic nodes in the node hierarchy are calculated. For example, when the amine value increases from 135 mg KOH / g to 145 mg KOH / g, the curing rate decreases from 60 minutes to 50 minutes, corresponding to a performance change response value of 0.83. The transfer attenuation coefficients between performance characteristic nodes are analyzed based on the hierarchical transfer matrix. For instance, the transfer attenuation coefficient from the first layer to the second layer is 0.85, and the transfer attenuation coefficient from the second layer to the third layer is 0.72. The cumulative transfer effect value is calculated by combining the performance change response value and the transfer attenuation coefficient. For example, the cumulative transfer effect of the amine value on the glass transition temperature through the curing rate is 0.83 × 0.85 × 0.76 × 0.72 = 0.38.

[0130] The system calculates the path influence strength between performance characteristic nodes based on the cumulative transmitted influence value. For example, among multiple paths from amine value to glass transition temperature, the path influence strength through curing rate is 0.65, and the path influence strength through viscosity is 0.42. The system then determines the deviation value of the performance parameters of the performance characteristic nodes. For example, if the target glass transition temperature is 125℃ and the actual value is 118℃, the deviation value is 5.6%. Based on the deviation value, the system triggers dynamic path adjustment. When the deviation value exceeds a preset threshold (e.g., 5%), the system will start adjusting from the path with the highest influence strength, resulting in an optimized path set including paths such as "amine value-curing rate-glass transition temperature" and "pH value-viscosity-mechanical strength".

[0131] Prioritize the resolution of performance conflicts between performance characteristic nodes based on the cumulative transmitted impact value. For example, the impact of amine value on glass transition temperature has a higher priority than its impact on mechanical strength. Path combination scores are calculated based on the optimized path set, comprehensively considering the path impact intensity (weight 0.4), the degree of improvement in performance parameter deviation (weight 0.35), and implementation complexity (weight 0.25). For example, the path combination "amine value adjustment (135→142mgKOH / g) + pH value adjustment (8.5→8.8)" has a score of 0.4×0.65+0.35×0.85+0.25×0.75=0.74, while the path combination "active hydrogen content adjustment (6.2→5.8%) + viscosity adjustment (1200→1050mPa·s)" has a score of 0.4×0.52+0.35×0.68+0.25×0.65=0.61. The path with the highest path combination score is selected as the curing agent performance combination path to optimize the epoxy curing agent formulation.

[0132] In existing technologies, the performance optimization of epoxy curing agents typically employs statistical methods such as orthogonal experiments or response surface methodology. However, these methods lack in-depth analysis of the transmission relationships between performance characteristics, making it difficult to find the optimal path. Traditional methods often treat curing agent performance parameters as independent variables for adjustment, ignoring the complex interactions between parameters. This leads to inefficient optimization processes and performance conflicts. For example, while increasing the amine value of the curing agent to accelerate the curing rate, traditional methods may simultaneously increase viscosity, and there is a lack of mechanisms for predicting and controlling this chain reaction.

[0133] The method in this embodiment constructs a hierarchical structure of performance feature nodes, calculates the cumulative propagation impact value, and analyzes the path influence strength, enabling precise identification of the propagation relationship and influence strength between performance parameters. Starting from improving the quantitative description of the propagation relationship of performance parameters, it achieves comprehensive evaluation of multiple optimization paths and intelligent selection of the optimal path.

[0134] like Figure 2 As shown, a flowchart illustrating the optimization path of curing agent performance combination is presented.

[0135] In one optional implementation, the curing agent compatibility index is obtained by calculating connectivity and performance gradient, including:

[0136] Extract the node connection relationships in the optimal performance combination path, construct the direct connectivity matrix corresponding to the node connection relationships, and count the number of path connections in the direct connectivity matrix to obtain the direct connectivity degree.

[0137] The second-order connection relationship between nodes is identified based on the direct connectivity matrix and converted into indirect connectivity strength. The direct connectivity and indirect connectivity strength are combined to obtain the comprehensive connectivity.

[0138] Calculate the rate of performance change between adjacent nodes in the optimal performance combination path to obtain the local performance gradient. Determine the performance transition critical value based on the local performance gradient and construct the local gradient matrix corresponding to the local performance gradient and the performance transition critical value.

[0139] Based on the local gradient matrix, the cumulative change trend on the performance transfer chain is analyzed, the cumulative change trend is transformed into a performance decay coefficient, and a global gradient distribution is constructed based on the performance decay coefficient.

[0140] The contribution ratio of the comprehensive connectivity to the compatibility of the curing agent is analyzed to obtain the connectivity weight coefficient. The influence of the global gradient distribution on the compatibility of the curing agent is calculated to obtain the gradient influence coefficient. A dynamic weight matrix is ​​established based on the connectivity weight coefficient and the gradient influence coefficient.

[0141] The curing agent compatibility index is obtained by combining the comprehensive connectivity and global gradient distribution according to the dynamic weight matrix and then normalizing them.

[0142] In one specific implementation, the node connectivity relationships of the optimal performance combination path are extracted from an experimental database. Assume the experimental database contains 10 curing agents, labeled F1 to F10. Performance testing reveals that F1-F3-F7-F9-F10 constitute the optimal performance combination path. Based on this connectivity, a direct connectivity matrix is ​​constructed. The element in the i-th row and j-th column of the matrix indicates whether node i and node j are directly connected; a direct connection is marked as 1, otherwise 0. In the example above, F1 is connected to F3, F3 is connected to F7, F7 is connected to F9, and F9 is connected to F10. Therefore, the elements at the corresponding positions in the matrix are all 1, and the remaining positions are 0. The total number of elements with a value of 1 in the direct connectivity matrix is ​​counted, resulting in a direct connectivity degree of 4.

[0143] The second-order connectivity between nodes is identified based on the direct connectivity matrix. A second-order connection refers to a connection between node i and node j through an intermediate node. For example, although F1 and F7 are not directly connected, they are indirectly connected through F3. The matrix is ​​traversed to identify all such second-order connections, and based on the performance characteristics of the intermediate nodes, the second-order connections are converted into indirect connectivity strengths. The conversion method is as follows: for each pair of nodes with a second-order connection, the indirect connectivity strength is set to 0.5. In the example, the indirect connectivity strengths of F1 and F7, F3 and F9, and F7 and F10 are all 0.5. The direct connectivity and indirect connectivity strength values ​​are added together to obtain a total connectivity of 5.5.

[0144] Calculate the performance change rate between adjacent nodes in the optimal performance combination path. Taking heat resistance performance as an example, assume the heat resistance temperatures of F1 to F10 are: F1 (120℃), F3 (135℃), F7 (145℃), F9 (155℃), and F10 (150℃), respectively. Calculate the performance change rate between adjacent nodes: F1 to F3 is +12.5%, F3 to F7 is +7.4%, F7 to F9 is +6.9%, and F9 to F10 is -3.2%. Determine the performance transition critical value based on these change rates, taking 80% of the average absolute value of the change rate, which is 6% in this example. Based on the comparison between the performance change rate of each segment and the critical value, construct a local gradient matrix. Connections with an absolute change rate greater than the critical value are marked as high gradients (value 2), otherwise marked as normal gradients (value 1). In this example, the connections from F1 to F3 and F3 to F7 are high gradients (value 2), while the connections from F7 to F9 and F9 to F10 are normal gradients (value 1).

[0145] The cumulative performance change trend along the performance transfer chain is analyzed based on the local gradient matrix. Starting from the initial node F1, the cumulative performance change is calculated along the path: +12.5% ​​to F3, +20.8% to F7, +29.2% to F9, and +25% to F10. This trend indicates that performance first increases and then decreases. This cumulative change trend is converted into a performance decay coefficient. Specifically, if the performance at the end of the path decreases by more than 5% compared to the highest point, the decay coefficient is 0.9; otherwise, it is 1. The performance at the end of the path decreased by 4.2% compared to the highest point, so the performance decay coefficient is 1. Based on the performance decay coefficient and the local gradient matrix, a global gradient distribution is constructed. The calculation method is the weighted sum of the values ​​of each node in the gradient matrix multiplied by the performance decay coefficient. The global gradient value of F1 is 2×1=2, the value of F3 is (2+2)×1=4, the value of F7 is (2+1)×1=3, the value of F9 is (1+1)×1=2, and the value of F10 is 1×1=1.

[0146] The contribution of overall connectivity to curing agent compatibility was analyzed. Statistical analysis of historical data determined a correlation coefficient of 0.75 between connectivity and compatibility, resulting in a connectivity weighting coefficient of 0.75. Simultaneously, the influence of global gradient distribution on curing agent compatibility was calculated. Historical data showed a correlation coefficient of 0.65 between gradient distribution and compatibility, leading to a gradient influence coefficient of 0.65. Based on the connectivity weighting coefficient and gradient influence coefficient, a dynamic weight matrix was established with a weight ratio of 0.75:0.65, which, after normalization, becomes 0.54:0.46.

[0147] The overall connectivity and global gradient distribution are combined using a dynamic weight matrix. After normalizing both the overall connectivity and global gradient distribution (assuming a normalized overall connectivity of 0.85 and a global gradient distribution of 0.78), the weighted combination yields: 0.85 × 0.54 + 0.78 × 0.46 = 0.82. This value is then normalized again, resulting in a curing agent compatibility index of 0.82. The curing agent compatibility index indicates high compatibility of the curing agent combination and can be used to guide epoxy resin formulation design. In practical applications, companies can use this index to select the most suitable curing agent combination, effectively improving product performance stability and reducing the risk of material failure due to compatibility issues.

[0148] In one optional implementation, the curing agent compatibility index is set as the optimization objective. An orthogonally distributed initial population is constructed within a uniformly divided formulation space. Offspring individuals are generated through adaptive mutation and similarity crossover, and an optimized set of curing agent formulations is obtained by screening, including:

[0149] The formulation space is divided into multiple uniform subspaces. Sampling points that satisfy orthogonal distribution are randomly selected in the subspaces to construct an initial solution space. The initial solution space is then corrected by combining it with a preset curing agent formulation knowledge base to determine the initial population.

[0150] Calculate the Euclidean distance between individuals in the initial population, adaptively adjust the scaling factor of the mutation operation based on the Euclidean distance, and perform the mutation operation on the initial population to obtain mutated individuals;

[0151] Calculate the similarity between the mutant individuals and the initial population, determine the optimal crossover region based on the similarity, select a crossover position within the optimal crossover region, and perform a crossover operation on the mutant individuals to obtain offspring individuals;

[0152] Calculate the curing agent compatibility index corresponding to the offspring individuals, classify the offspring individuals into different superior and inferior grades based on the preset curing agent compatibility index classification, and calculate the distribution distance of individuals within each superior and inferior grade.

[0153] Based on the quality level and distribution distance, the dominant individuals are selected, and the composition ratio of the dominant individuals is compared with the historical data in the curing agent formulation knowledge base. Based on the comparison results, the composition ratio of the dominant individuals is adjusted to obtain an adjusted formulation set.

[0154] The formulations in the adjusted formulation set are sorted in descending order according to the curing agent compatibility index, and the formulations ranked first are selected to form the optimized curing agent formulation set according to a preset ratio.

[0155] In one specific implementation, the formulation space is divided into multiple uniform subspaces by equally dividing the component proportion range. For a curing agent system containing three components—methyltetrahydrophthalic anhydride, hexahydrophthalic anhydride, and methylhexahydrophthalic anhydride—the proportion range of each component (0-100%) can be divided into 10 equal division points, i.e., 0%, 10%, 20%, up to 100%, forming 1000 uniformly distributed subspaces. In each subspace, sampling points satisfying an orthogonal distribution are randomly selected using the Latin hypercube sampling method. In the above three-component system, 5 sampling points are selected from each subspace, resulting in 5000 initial formulation sample points. The initial solution space is corrected by combining it with a preset curing agent formulation knowledge base, which contains historical successful formulation data and their performance parameters. During the correction process, each initial sample point is compared with the formulations in the knowledge base. If the Euclidean distance between the initial sample point and a historical successful formulation is less than a preset threshold (e.g., 0.05), the sample point is replaced with the historical successful formulation; if the distance is greater than the threshold, the original sample point is retained. This process forms an initial population of 5,000 individuals.

[0156] Calculate the Euclidean distance between individuals in the initial population. For each pair of individuals in the initial population, calculate their Euclidean distance in the recipe space. For example, the Euclidean distance between recipe 1 (30%, 40%, 30%) and recipe 2 (35%, 35%, 30%) is 0.0707. Adaptively adjust the scaling factor of the mutation operation based on the calculated Euclidean distance. When the average Euclidean distance between individuals in the population is large (e.g., greater than 0.2), a smaller scaling factor (e.g., 0.3) is used; when the average Euclidean distance is small (e.g., less than 0.1), a larger scaling factor (e.g., 0.7) is used. Perform the mutation operation on the initial population to obtain mutated individuals. The mutation operation uses a differential evolution strategy. For each individual in the initial population, randomly select three other different individuals in the population, generate a difference vector, multiply it by the scaling factor, and then add it to the target individual to generate the mutated individual. For example, given the target individuals (30%, 40%, 30%), three randomly selected individuals are (35%, 35%, 30%), (25%, 45%, 30%), and (32%, 38%, 30%), with a scaling factor of 0.5. The resulting variant individuals are (33%, 37%, 30%).

[0157] The similarity between the mutated individual and the initial population is calculated using cosine similarity. For each individual in the initial population, the cosine similarity is calculated, and the maximum similarity value is taken as the population similarity of that mutated individual. The optimal crossover region is determined based on the similarity; the higher the similarity, the smaller the crossover region; the lower the similarity, the larger the crossover region. When the similarity is greater than 0.95, the crossover region is set within ±5% of the component value; when the similarity is between 0.85 and 0.95, the crossover region is set within ±10%; when the similarity is less than 0.85, the crossover region is set within ±15%. A crossover position is selected within the optimal crossover region, and the mutated individual is crossovered to obtain offspring individuals. For example, for the mutated individual (33%, 37%, 30%), if its maximum similarity with the initial population is 0.92, then the crossover region is ±10%. In the crossover operation, a crossover point is randomly selected, such as the second component, so the offspring individuals could be (33%, 41%, 26%).

[0158] The compatibility index of the curing agent for each offspring individual is calculated, taking into account key performance parameters such as gel time, glass transition temperature, curing enthalpy, and mechanical strength. The performance parameters of each offspring individual are determined experimentally or predicted using models, and the comprehensive compatibility index is calculated based on preset weights. For example, for offspring individuals (33%, 41%, 26%), the measured gel time is 35 minutes (weight 0.3), the glass transition temperature is 145℃ (weight 0.25), the curing enthalpy is 350 J / g (weight 0.2), and the flexural strength is 110 MPa (weight 0.25), resulting in a compatibility index of 87.5. Based on the preset curing agent compatibility index classification, the offspring individuals are divided into different quality levels: 90-100 is Grade A, 80-90 is Grade B, 70-80 is Grade C, 60-70 is Grade D, and below 60 is Grade E. Calculate the distribution distance of individuals within each excellence / disexcellence level. The distribution distance is defined as the average Euclidean distance between that individual and other individuals within the same level.

[0159] Dominant individuals are selected based on their quality level and distribution distance. A non-dominated ranking strategy is used for selecting dominant individuals, prioritizing those with higher quality levels and, within the same quality level, those with greater distribution distance to ensure population diversity. For example, when selecting 100 dominant individuals, 25 are selected from Grade A, 35 from Grade B, 25 from Grade C, and 15 from Grade D. The composition ratios of the dominant individuals are compared with historical data in the curing agent formulation knowledge base, calculating the difference between each dominant individual and historical successful formulations. When the difference is less than a preset threshold (e.g., 0.08), the composition ratio of the dominant individual is slightly adjusted towards the historical successful formulation; when the difference is greater than the preset threshold, the original composition ratio remains unchanged. For example, the difference between the dominant individual (33%, 41%, 26%) and the historical successful formulation (35%, 40%, 25%) is 0.03, less than the threshold of 0.08; the adjusted formulation is (34%, 40.5%, 25.5%). This method forms an adjusted formulation set.

[0160] The formulations in the adjusted formulation set are sorted in descending order based on the hardener compatibility index. Following a preset ratio, such as the top 20%, the top-ranked formulations are selected to form the optimized hardener formulation set. For example, out of 500 adjusted formulations, the 100 formulations with the highest compatibility index are selected as the final optimized hardener formulation set, and these formulations will proceed to the next round of experimental verification.

[0161] In existing technologies, epoxy curing agent formulation optimization mainly relies on expert experience and numerous trial-and-error experiments, or employs simple orthogonal experimental design methods, which are inefficient and struggle to find the global optimum in complex formulation spaces. Traditional genetic algorithms, when dealing with multi-component curing agent systems, lack specificity in mutation and crossover operations, easily getting trapped in local optima. The method in this embodiment constructs an initial solution space by combining subspace partitioning and orthogonal sampling, ensuring that the initial population covers the entire formulation space. Through adaptive adjustment of the mutation scaling factor using Euclidean distance, a similarity-oriented crossover region selection strategy, and an individual selection mechanism combining superiority / inferiority levels and distribution distance, the algorithm's convergence speed and global search capability are significantly improved. Fine-tuning of dominant individuals using a curing agent expertise base further enhances the practicality of the optimization results.

[0162] The epoxy curing agent compatibility testing and formulation system optimization system of this invention includes:

[0163] The first unit is used to collect multiple sets of curing performance data of the curing agent, including curing exothermic enthalpy, curing peak temperature and glass transition temperature, and to perform standardization processing to obtain an initial evaluation matrix.

[0164] The second unit is used to calculate the interaction strength between curing performance data using the collaborative entropy weight method, construct a coupling strength matrix, and correct the initial evaluation matrix based on the coupling strength matrix to obtain the comprehensive evaluation result.

[0165] The third unit is used to extract curing performance characteristics based on the comprehensive evaluation results, construct a directed acyclic graph of curing performance characteristics, explore the performance combination path of curing agent using the performance association tracking algorithm, and obtain the curing agent compatibility index by calculating connectivity and performance gradient.

[0166] The fourth unit is used to set the compatibility index of the curing agent as the optimization target, construct an orthogonally distributed initial population in a uniformly divided formulation space, generate offspring individuals through adaptive mutation and similarity crossover, and screen to obtain an optimized set of curing agent formulations.

[0167] The fifth unit is used to conduct experimental verification of the optimized curing agent formulation set and select the formulation that meets the preset performance requirements as the optimal curing agent formulation.

[0168] A third aspect of the present invention provides an electronic device, comprising:

[0169] processor;

[0170] Memory used to store processor-executable instructions;

[0171] The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0172] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0173] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention 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 or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for testing the compatibility of epoxy curing agents and optimizing the formulation system, characterized in that, include: Multiple sets of curing performance data of the curing agent were collected, including curing exothermic enthalpy, curing peak temperature and glass transition temperature, and standardized to obtain an initial evaluation matrix; The interaction strength between curing performance data is calculated using the collaborative entropy weight method, a coupling strength matrix is ​​constructed, and the initial evaluation matrix is ​​corrected based on the coupling strength matrix to obtain the comprehensive evaluation result. Based on the comprehensive evaluation results, curing performance characteristics are extracted, a directed acyclic graph of curing performance characteristics is constructed, a performance association tracking algorithm is used to explore the curing agent performance combination path, and the curing agent compatibility index is obtained by calculating connectivity and performance gradient. The compatibility index of the curing agent was set as the optimization target. An orthogonally distributed initial population was constructed in a uniformly divided formulation space. Offspring individuals were generated through adaptive mutation and similarity crossover, and the optimized curing agent formulation set was obtained by screening. The optimized curing agent formulation set was experimentally verified, and the formulation that met the preset performance requirements was selected as the optimal curing agent formulation.

2. The method according to claim 1, characterized in that, The interaction strength between curing performance data is calculated using the collaborative entropy weighting method, and a coupling strength matrix is ​​constructed. The initial evaluation matrix is ​​then corrected based on the coupling strength matrix to obtain the comprehensive evaluation results, including: Calculate the information entropy of the solidification performance data, and obtain the entropy weight of each performance data based on the information entropy; A synergy matrix of solidification performance data is constructed, wherein the elements of the synergy matrix are obtained by calculating the nonlinear correlation coefficients between pairs of performance data. The interaction strength is obtained by coupling the entropy weight with the synergy matrix. Construct a coupling strength matrix based on the interaction strength; The eigenvalues ​​of the coupling strength matrix are normalized to obtain an initial correction factor; the trend coefficient of the curing performance data is calculated; the initial correction factor and the trend coefficient are multiplied to obtain a dynamic correction factor. The dynamic correction factor is coupled with the initial evaluation matrix to obtain the corrected evaluation matrix; the corrected evaluation matrix is ​​then subjected to data fusion processing to obtain the comprehensive evaluation result.

3. The method according to claim 2, characterized in that, The data fusion process includes: The modified evaluation matrix is ​​clustered using the K-means clustering algorithm. The Euclidean distance between data points in the modified evaluation matrix is ​​calculated. The data points are initially classified based on the minimum distance principle. The cluster center positions are iteratively updated until convergence, and the performance characteristic clusters are determined. Calculate the mean of the data points in each dimension of each performance feature cluster to obtain the cluster centroid coordinates, and combine the cluster centroid coordinates to form a centroid vector; Select any two centroid vectors to determine a centroid vector pair, calculate the Mahalanobis distance between the centroid vector pairs, and construct a distance matrix. The distance matrix is ​​normalized, and the normalized distance values ​​are converted into similarity values ​​using a Gaussian kernel function to obtain the inter-class coupling coefficient. The relative importance of each performance feature cluster is determined by the sum of the coupling coefficients of each cluster with all other performance feature clusters, and the adaptive weights are obtained by normalization. The adaptive weights are linearly weighted and summed with the corresponding performance feature clusters to obtain the comprehensive evaluation result.

4. The method according to claim 1, characterized in that, Based on the comprehensive evaluation results, curing performance characteristics are extracted, and a directed acyclic graph of curing performance characteristics is constructed, including: The comprehensive evaluation results are used to establish a correspondence table based on the relationship between curing performance indicators and evaluation values, and the correspondence table is then transformed into a curing performance indicator matrix. The relationships between the curing performance indicators in the curing performance index matrix are analyzed to obtain the interaction relationship matrix between different curing performance indicators. The importance of each curing performance indicator is determined according to the interaction relationship matrix. The curing performance indicator with the highest importance is selected as the curing performance feature according to the preset screening percentage. The curing performance characteristics are set as performance characteristic nodes. The degree of mutual influence between the performance characteristic nodes is calculated. When the influence of the first performance characteristic node on the second performance characteristic node is greater than the influence of the second performance characteristic node on the first performance characteristic node, the direction of action is determined to be from the first performance characteristic node to the second performance characteristic node. A directed graph is constructed by connecting performance characteristic nodes according to the described direction of action. Cyclic action structures in the directed graph are detected, and the connection with the least impact in the cyclic action structure is disconnected to obtain a directed acyclic graph of the curing performance characteristics.

5. The method according to claim 1, characterized in that, The performance correlation tracing algorithm includes: The performance feature node with zero in-degree in the directed acyclic graph is selected as the search starting node, the corresponding influence factor is calculated, and the importance of the search starting node is sorted according to the influence factor to obtain the node importance sequence. The performance feature nodes in the directed acyclic graph are constructed into a node hierarchy structure according to their connection relationships. Based on the node importance sequence, the jump constraints between adjacent level nodes in the node hierarchy structure are determined to obtain the hierarchy transfer matrix. Calculate the performance change response value between adjacent performance characteristic nodes in the node hierarchy, analyze the transmission attenuation coefficient between performance characteristic nodes based on the hierarchy transmission matrix, and combine the performance change response value with the transmission attenuation coefficient to calculate the cumulative transmission impact value. Based on the cumulative propagation impact value, the path influence intensity between performance feature nodes is calculated, the performance parameter deviation value of the performance feature node is determined, and the path dynamic adjustment is triggered based on the performance parameter deviation value to obtain an optimized path set. The performance conflict resolution priority between the performance feature nodes is set according to the cumulative transmission impact value, the path combination score is calculated based on the optimized path set, and the path with the highest path combination score is selected as the curing agent performance combination path.

6. The method according to claim 1, characterized in that, The curing agent compatibility index is obtained by calculating connectivity and performance gradient, including: Extract the node connection relationships in the optimal performance combination path, construct the direct connectivity matrix corresponding to the node connection relationships, and count the number of path connections in the direct connectivity matrix to obtain the direct connectivity degree. The second-order connection relationship between nodes is identified based on the direct connectivity matrix and converted into indirect connectivity strength. The direct connectivity and indirect connectivity strength are combined to obtain the comprehensive connectivity. Calculate the rate of performance change between adjacent nodes in the optimal performance combination path to obtain the local performance gradient. Determine the performance transition critical value based on the local performance gradient and construct the local gradient matrix corresponding to the local performance gradient and the performance transition critical value. Based on the local gradient matrix, the cumulative change trend on the performance transfer chain is analyzed, the cumulative change trend is transformed into a performance decay coefficient, and a global gradient distribution is constructed based on the performance decay coefficient. The contribution ratio of the comprehensive connectivity to the compatibility of the curing agent is analyzed to obtain the connectivity weight coefficient. The influence of the global gradient distribution on the compatibility of the curing agent is calculated to obtain the gradient influence coefficient. A dynamic weight matrix is ​​established based on the connectivity weight coefficient and the gradient influence coefficient. The curing agent compatibility index is obtained by combining the comprehensive connectivity and global gradient distribution according to the dynamic weight matrix and then normalizing them.

7. The method according to claim 1, characterized in that, The compatibility index of the curing agent was set as the optimization objective. An orthogonally distributed initial population was constructed within a uniformly divided formulation space. Offspring individuals were generated through adaptive mutation and similarity crossover, and the optimized curing agent formulation set was obtained by screening. The formulation space is divided into multiple uniform subspaces. Sampling points that satisfy orthogonal distribution are randomly selected in the subspaces to construct an initial solution space. The initial solution space is then corrected by combining it with a preset curing agent formulation knowledge base to determine the initial population. Calculate the Euclidean distance between individuals in the initial population, adaptively adjust the scaling factor of the mutation operation based on the Euclidean distance, and perform the mutation operation on the initial population to obtain mutated individuals; Calculate the similarity between the mutant individuals and the initial population, determine the optimal crossover region based on the similarity, select a crossover position within the optimal crossover region, and perform a crossover operation on the mutant individuals to obtain offspring individuals; Calculate the curing agent compatibility index corresponding to the offspring individuals, classify the offspring individuals into different superior and inferior grades based on the preset curing agent compatibility index classification, and calculate the distribution distance of individuals within each superior and inferior grade. Based on the quality level and distribution distance, the dominant individuals are selected, and the composition ratio of the dominant individuals is compared with the historical data in the curing agent formulation knowledge base. Based on the comparison results, the composition ratio of the dominant individuals is adjusted to obtain an adjusted formulation set. The formulations in the adjusted formulation set are sorted in descending order according to the curing agent compatibility index, and the formulations ranked first are selected to form the optimized curing agent formulation set according to a preset ratio.

8. An epoxy curing agent compatibility testing and formulation system optimization system, used to implement the method of any one of claims 1-7, characterized in that, include: The first unit is used to collect multiple sets of curing performance data of the curing agent, including curing exothermic enthalpy, curing peak temperature and glass transition temperature, and to perform standardization processing to obtain an initial evaluation matrix. The second unit is used to calculate the interaction strength between curing performance data using the collaborative entropy weight method, construct a coupling strength matrix, and correct the initial evaluation matrix based on the coupling strength matrix to obtain the comprehensive evaluation result. The third unit is used to extract curing performance characteristics based on the comprehensive evaluation results, construct a directed acyclic graph of curing performance characteristics, explore the performance combination path of curing agent using the performance association tracking algorithm, and obtain the curing agent compatibility index by calculating connectivity and performance gradient. The fourth unit is used to set the compatibility index of the curing agent as the optimization target, construct an orthogonally distributed initial population in a uniformly divided formulation space, generate offspring individuals through adaptive mutation and similarity crossover, and screen to obtain an optimized set of curing agent formulations. The fifth unit is used to conduct experimental verification of the optimized curing agent formulation set and select the formulation that meets the preset performance requirements as the optimal curing agent formulation.

9. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 7.

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