A method for predicting the performance of a paint formulation

Abstract

The application discloses a coating formula performance prediction method, comprising: obtaining a to-be-tested coating formula and determining a target paint type; constructing a performance characteristic candidate pool for a to-be-predicted performance, the candidate pool comprising at least one of a formula composition characteristic, a theoretical parameter, a general mechanism characteristic, a performance-specific mechanism characteristic, a test condition, a key characteristic missing marker and a combined characteristic determined based on the to-be-tested formula; obtaining historical formula measured data corresponding to the target paint type and the to-be-tested performance, statistically screening the candidate characteristics, and then performing constraint verification on the candidate characteristics retained after the statistical screening to obtain an effective characteristic set; and calling a machine learning model corresponding to the to-be-tested performance based on the effective characteristic set to perform prediction. The application improves the pertinence of the characteristic expression to the target paint type and the to-be-tested performance, and the reliability of the prediction result.

Description

Technical Field

[0001] This invention relates to the field of intelligent design technology for coating formulations, and in particular to a method for predicting the performance of coating formulations. Background Technology

[0002] Predicting the performance of coating formulations is a crucial step in coating research and development. Preliminary evaluation of the performance of the formulation to be tested before laboratory paint production helps to eliminate unreasonable formulations and reduce experimental trial and error. Existing technologies mainly include three categories: purely data-driven models, mechanistic models, and comprehensive AI-based predictions. Purely data-driven models, based on technologies such as XGBoost, random forests, support vector regression, and neural networks, establish a direct mapping from formulation composition to performance indicators. However, their predictive ability is highly dependent on the formulation space covered by the training samples. Their extrapolation ability is weak when introducing new raw materials or pushing to extreme proportions. Furthermore, they typically use the raw material name and addition ratio directly as input, lacking utilization of the mechanism of coating performance formation. They are easily affected by data leakage, batch randomness, and spurious correlations, and struggle to correctly handle new raw materials not encountered during the training phase. The black-box nature of the model also limits interpretability. Mechanistic models, based on theoretical parameters such as pigment volume concentration, critical pigment volume concentration, equivalence ratio, and solids content, are calculated using deterministic formulas. While their physical meaning is clear, they only cover a limited number of quantifiable parameters and lack direct predictive ability for complex engineering properties such as adhesion, salt spray resistance, and hardness. Furthermore, they struggle to map high-dimensional raw material information to a unified feature space and adaptively adjust with new data. Although AI-based comprehensive prediction methods attempt to combine data-driven approaches with domain descriptors, their feature systems still primarily rely on manually fixed features or general descriptors. They fail to establish a candidate pool of performance features tailored to the target paint type and the predicted performance, making it difficult to form a differentiated and effective feature set. They also lack a screening mechanism that simultaneously considers statistical significance and consistency with knowledge in the coatings domain.

[0003] Further analysis reveals common shortcomings in the feature construction and selection aspects of existing technologies: They lack a unified candidate pool encompassing formulation composition features, theoretical parameters, general mechanistic features, and performance-specific mechanistic features for the target paint type and the performance to be predicted; they lack a mechanism for statistically screening and constraining candidate features based on historical measured data, easily retaining spurious correlation features or mistakenly deleting necessary mechanistic features; they lack systematic handling of new raw materials not present during the training phase, known raw materials not included, and data gaps when calculating key features, easily leading to feature mapping errors or unreliable extrapolation; they typically only output a single predicted value, without determining whether it exceeds the coverage of the training data or generating a prediction reliability level; and they lack a deterministic fusion mechanism between the original formulation composition, mechanistic features, machine learning prediction results, and historical measured data. Therefore, how to determine the target paint type and construct a performance feature candidate pool, statistically screen and constrain candidate features based on historical measured data to obtain an effective feature set, and then use this effective feature set to call a machine learning model for performance prediction has become a technical problem that needs to be solved in this field. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the performance of coating formulations. This method constructs a candidate pool of performance features for the coating formulation to be tested, including formulation composition characteristics, theoretical parameters, general mechanistic features, and performance-specific mechanistic features. Based on historical measured data corresponding to the target paint type and the performance to be predicted, the candidate features are first statistically screened, and then the retained candidate features are constrained and verified to obtain an effective feature set corresponding to the performance to be tested. This improves the relevance of feature expression to the target paint type and the performance to be predicted, and enhances the reliability of the prediction results. It also solves the problems in existing technologies where feature construction relies on manually fixed features or original formulation ratios, data-driven approaches are disconnected from coating domain knowledge, and extrapolation predictions are unreliable when training sample coverage is insufficient.

[0005] To address the aforementioned technical problems, a first aspect of this invention provides a method for predicting the performance of coating formulations, comprising the following steps: S1, obtain the coating formula to be tested, and determine the target paint type to which the coating formula to be tested belongs.

[0006] S2, for the predicted performance of the coating formulation to be tested, a performance feature candidate pool is constructed. The performance feature candidate pool is a set of candidate features, including at least the formulation composition features determined based on the coating formulation to be tested, theoretical parameters calculated from the coating formulation to be tested, general mechanism features applicable to multiple performance indicators, and performance-specific mechanism features corresponding to the performance to be tested, as well as at least one of test conditions, key feature missing markers, and combined features.

[0007] S3, acquire historical formula test data corresponding to the target paint type and the performance to be tested. Based on the historical formula test data, statistically filter the candidate features in the performance feature candidate pool, and then perform constraint verification on the candidate features retained after statistical filtering to obtain a subset of candidate features corresponding to the performance to be tested. This subset of candidate features is then used as the effective feature set corresponding to the performance to be tested. The statistical filtering involves calculating the statistical correlation index between the candidate features and the performance to be tested based on the historical formula test data and retaining or deleting candidate features accordingly. The constraint verification involves deleting candidate features that do not conform to the preset coating performance mechanism rules.

[0008] S4. Based on the effective feature set, call the machine learning model corresponding to the performance to be tested to predict the performance of the coating formulation to be tested, and obtain the performance prediction result of the coating formulation to be tested.

[0009] Further, in step S2, constructing a candidate pool of performance features for the predicted performance of the coating formulation to be tested includes: S21. Based on the coating formulation to be tested and the target paint type, determine the candidate feature sources corresponding to the performance to be tested. The candidate feature sources include formulation composition features, theoretical parameters, general mechanism features and performance-specific mechanism features, as well as test conditions, key feature missing markers and combination features. The formulation composition features are determined based on the unique raw material identifier and addition ratio of the raw materials in the coating formulation to be tested. The unique raw material identifier is the identification information used to uniquely identify a raw material in a pre-set raw material identifier system.

[0010] S22, Based on the candidate feature source and the unique raw material identifier, a fixed-dimensional candidate feature column is constructed, wherein the candidate features corresponding to the formulation composition features correspond one-to-one with the unique raw material identifier, and the theoretical parameters, the general mechanism features, and the performance-specific mechanism features correspond to preset feature identifiers respectively.

[0011] S23, exclude candidate features from the candidate feature column that are related to the measured value of the performance to be tested. The association includes direct association and indirect association. The direct association is that the candidate feature itself is the measured value of the performance to be tested or its derived statistics. The indirect association is that the candidate feature can uniquely determine the value of the measured value of the performance to be tested.

[0012] S24, the test conditions corresponding to the coating formulation to be tested, the key feature missing markers, and the combined features generated according to the preset feature construction rules are included in the candidate feature column and summarized into the performance feature candidate pool. The key feature missing marker is used to characterize the missing data required to calculate the formulation composition features, theoretical parameters, general mechanism features, or performance-specific mechanism features, or the state where all raw materials corresponding to a certain raw material functional category in the coating formulation to be tested are not included in the coating formulation to be tested.

[0013] Furthermore, the construction of the fixed-dimensional candidate feature column in step S22 further includes: S2211, Identify new raw materials in the coating formulation to be tested that have not appeared in the modeling sample corresponding to the historical formulation test data.

[0014] S2212, determine the functional category of the new raw material in the preset raw material functional category system, wherein the preset raw material functional category system is a pre-set system for classifying raw materials according to their functions.

[0015] S2213, determine whether the functional category belongs to the raw material functional category related to the performance to be tested.

[0016] S2214, if the functional category belongs to the raw material functional category related to the performance to be tested, then the mass percentage of the new raw material in the coating formulation to be tested is calculated as an out-of-distribution identification statistic. The mass percentage is the absolute mass fraction of the new raw material in the mixed coating. The out-of-distribution identification statistic is not used as an input feature of the machine learning model.

[0017] S2215, compare the out-of-distribution identification statistics with a preset trigger threshold. If the out-of-distribution identification statistics reach the preset trigger threshold, mark the performance to be tested as out-of-distribution, output out-of-distribution warning information, and terminate the performance prediction of the performance to be tested.

[0018] Furthermore, the construction of the fixed-dimensional candidate feature column in step S22 further includes: S2221, For known raw materials not included in the coating formulation to be tested, determine the functional category of the known raw material in the pre-set raw material functional category system.

[0019] S2222, determine whether the functional category is completely missing in the coating formulation to be tested, wherein the complete absence means that all raw materials corresponding to the functional category are not included in the coating formulation to be tested.

[0020] S2223, if the functional category is entirely missing in the coating formulation to be tested, a key feature missing marker is generated. This key feature missing marker is used in step S24 to be included as an independent candidate feature in the candidate feature list. The key feature missing marker is an identifier indicating that all raw materials corresponding to the functional category are not included in the coating formulation to be tested.

[0021] S2224, if the functional category is not entirely missing in the coating formulation to be tested, then the candidate feature corresponding to the known raw material is set as a null value marker, and the null value marker is a preset sentinel value that is different from the effective numerical range.

[0022] Further, the statistical screening of candidate features in the performance feature candidate pool based on the historical formula test data in step S3 includes: S311, the historical formulation test data are grouped according to the basic formulation series, raw material batch, and collection time, and training and validation datasets are divided while maintaining group isolation and time isolation. The basic formulation series is a set of formulations with the same film-forming resin system and curing agent system. The grouping is to group historical samples with the same basic formulation series identifier and the same raw material batch identifier into the same historical sample group. The group isolation is that historical samples within the same historical sample group do not cross between the training and validation datasets, and the time isolation is that historical samples collected later are not included in the training dataset.

[0023] S312, Calculate the statistical correlation index between the candidate feature and the performance to be tested based on the training dataset, and perform repeated cross-validation on the candidate feature based on the validation dataset, and statistically analyze the frequency of the candidate feature being selected and the degree to which the correlation direction remains consistent in the repeated cross-validation. The statistical correlation index is an indicator characterizing the degree of correlation or importance between the candidate feature and the performance to be tested, and the correlation direction is a positive or negative correlation between the candidate feature and the performance to be tested.

[0024] S313, determine the comprehensive screening score based on the statistical correlation index, the selected frequency, and the degree of consistency of the correlation direction, retain candidate features that reach the preset admission threshold and the preset stability threshold, and delete candidate features that do not reach the preset admission threshold or the preset stability threshold.

[0025] S314, if a candidate feature belongs to a preset knowledge-mandated retention feature set, then even if the preset admission threshold or the preset stability threshold is not reached, it is still retained in the candidate feature subset and marked as a knowledge-mandated retention feature, and the missing state and ablation evaluation result of the knowledge-mandated retention feature are recorded. The knowledge-mandated retention feature set is a set of candidate features predetermined according to the coating performance formation mechanism, which have the necessary influence on the performance to be tested and cannot be replaced by other candidate features.

[0026] Further, step S312, which involves calculating the statistical correlation index between the candidate features and the performance to be tested based on the training dataset, and performing repeated cross-validation on the candidate features based on the validation dataset, includes: S3121, Based on the training dataset, calculate the mutual information, permutation importance, or sample-level contribution between the candidate features and the performance to be tested, and use the calculation results as the statistical correlation index.

[0027] S3122, Based on the validation dataset, perform repeated cross-validation on the candidate features, record whether the candidate feature is selected in each cross-validation, and record the correlation direction between the candidate feature and the performance to be tested when the candidate feature is selected.

[0028] S3123, Based on the records of multiple cross-validations, calculate the frequency at which the candidate feature is selected and the degree to which the association direction remains consistent in the repeated cross-validations.

[0029] S3124, for the candidate features retained in step S313, ablation verification is performed on independent validation data. Candidate features that reduce the prediction error of the machine learning model or improve the grade evaluation index are retained, while candidate features that increase the prediction error or worsen the grade evaluation index are deleted. The grade evaluation index is an indicator used to evaluate the accuracy of the machine learning model in classifying the performance under test. The independent validation data is historical formula test data that has not participated in the corresponding screening and verification.

[0030] Further, step S313, which involves determining the comprehensive screening score based on the statistical correlation indicators, the frequency of selection, and the degree of consistency between the correlation direction, includes: S3131, the statistical correlation index is determined as the prediction contribution item, the selected frequency is determined as the selection stability item, the degree of consistency of the correlation direction is determined as the directional stability item, the consistency result of the coating performance mechanism obtained by performing a pre-set coating performance mechanism rule verification on the candidate features is determined as the coating performance mechanism consistency item, and the degree of redundancy between the candidate features and the selected candidate features is determined as the redundancy item. The coating performance mechanism consistency item is a scoring item used to calculate the comprehensive screening score, and the coating performance mechanism consistency result is the degree of consistency between the candidate features and the pre-set coating performance mechanism rules.

[0031] S3132, the prediction contribution term, the selection stability term, the directional stability term, the coating performance mechanism consistency term, and the redundancy term are weighted and summed according to preset weighting coefficients to obtain the comprehensive screening score of the candidate features.

[0032] S3133, compare the comprehensive screening score with a preset admission threshold, and compare the selected frequency with a preset stability threshold. Retain candidate features that simultaneously reach the preset admission threshold and the preset stability threshold, and delete candidate features that do not reach the preset admission threshold or the preset stability threshold.

[0033] Further, step S3 involves constraining and validating the candidate features in the performance feature candidate pool based on the historical formula test data, including: S321, for the candidate features retained after the statistical screening, a mechanism consistency check is performed based on the raw material functional category and reaction relationship, and candidate features that are inconsistent with the preset coating performance mechanism rules are deleted. The preset coating performance mechanism rules are the allowed correlations between candidate features and the performance to be tested, which are predetermined based on the coating performance formation mechanism.

[0034] S322, for the candidate features retained after the mechanism consistency verification, based on whether the dimension of the candidate feature belongs to the set of allowed dimensions corresponding to the performance to be tested, and whether the value range of the candidate feature is within the preset value range, delete the candidate features whose dimension does not belong to the set of allowed dimensions or whose value range exceeds the preset value range.

[0035] S323, for the candidate features retained after the dimensional consistency check, perform an influence direction check according to the preset monotonicity rule, and delete the candidate features whose influence direction is inconsistent with the preset monotonicity rule.

[0036] S324, For the candidate features retained after the influence direction verification, perform collinearity checks and ablation verification. The ablation verification is a final confirmatory ablation verification performed on the candidate features retained after the aforementioned steps in the constraint verification. Candidate features that reduce the prediction error of the machine learning model or improve the grade evaluation index on independent verification data are retained. The finally retained candidate features are used as a subset of candidate features after constraint verification. The collinearity check involves calculating the correlation coefficient between candidate features, and when the correlation coefficient is higher than a preset correlation coefficient threshold, deleting candidate features with high redundancy compared to the retained candidate features. The independent verification data are historical formula test data that did not participate in the corresponding screening and verification.

[0037] Furthermore, the mechanism consistency verification performed in step S321 based on the functional categories of raw materials and reaction relationships includes: S3211, Determine the functional category of the raw material corresponding to the candidate feature in the preset raw material functional category system.

[0038] S3212, determine the reaction relationship of the raw materials corresponding to the candidate features in the coating formulation to be tested.

[0039] S3213, Based on the preset coating performance mechanism rules, determine whether the functional category and the reaction relationship belong to an allowed combination related to the performance to be tested.

[0040] S3214, if the functional category and the response relationship do not belong to the allowed combination, then delete the candidate feature; if the functional category and the response relationship belong to the allowed combination, then retain the candidate feature.

[0041] S3215, based on the preset raw material compatibility rule library, determine whether there is a prohibited combination between the functional category and reaction relationship of the raw material corresponding to the candidate feature and the functional category and reaction relationship of other raw materials in the coating formulation to be tested; if there is a prohibited combination, delete all candidate features involved in the prohibited combination.

[0042] Furthermore, the step S323, which involves performing influence direction verification according to a preset monotonicity rule, includes: S3231, determine the correlation direction between the candidate feature and the performance to be tested.

[0043] S3232, Read the preset monotonicity rule corresponding to the performance to be tested.

[0044] S3233, determine whether the association direction is consistent with the preset monotonicity rule.

[0045] S3234, if the correlation direction is inconsistent with the preset monotonicity rule, then the candidate feature is deleted; if the correlation direction is consistent with the preset monotonicity rule, then the candidate feature is retained, and the correlation direction is recorded as the expected influence direction of the candidate feature. Simultaneously, the feature identifier of the candidate feature and its corresponding expected influence direction are recorded. The expected influence direction is the permissible positive or negative correlation between the candidate feature and the performance to be tested.

[0046] Accordingly, a second aspect of the present invention provides a coating formulation performance prediction system, which predicts the performance of coating formulations based on the above-described prediction method, including... The data acquisition module is used to acquire the coating formula to be tested and determine the target paint type to which the coating formula to be tested belongs; The candidate pool construction module is used to construct a performance feature candidate pool for the predicted performance of the coating formulation to be tested. The performance feature candidate pool is a set of candidate features, including at least the formulation composition features determined based on the coating formulation to be tested, theoretical parameters calculated from the coating formulation to be tested, general mechanism features applicable to multiple performance indicators, and performance-specific mechanism features corresponding to the performance to be tested, as well as at least one of the following: test conditions, key feature missing markers, and combined features. The screening and verification module is used to acquire historical formula test data corresponding to the target paint type and the performance to be tested. Based on the historical formula test data, the candidate features in the performance feature candidate pool are first statistically screened, and then the candidate features retained after the statistical screening are constrained and verified to obtain a subset of candidate features corresponding to the performance to be tested. The subset of candidate features is used as the effective feature set corresponding to the performance to be tested. The statistical screening is to calculate the statistical correlation index between the candidate features and the performance to be tested based on the historical formula test data and retain or delete the candidate features accordingly. The constraint verification is to delete candidate features that do not conform to the preset coating performance mechanism rules according to the preset coating performance mechanism rules. The performance prediction module is used to call the machine learning model corresponding to the performance to be tested based on the effective feature set, and to perform performance prediction on the coating formulation to be tested, so as to obtain the performance prediction result of the coating formulation to be tested.

[0047] Accordingly, a third aspect of the present invention provides an electronic device, comprising: at least one processor; and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described coating formulation performance prediction method.

[0048] Accordingly, a fourth aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described method for predicting the performance of coating formulations.

[0049] The above-described technical solutions of the embodiments of the present invention have the following beneficial technical effects: 1. This application constructs a candidate pool of performance features for the predicted performance of a coating formulation, including formulation composition characteristics, theoretical parameters, general mechanism characteristics, and performance-specific mechanism characteristics. Based on historical measured data corresponding to the target paint type and the predicted performance, the candidate features are first statistically screened, and then the retained candidate features are constrained and verified to obtain an effective feature set corresponding to the performance to be tested. This application organically integrates data-driven screening with knowledge verification in the coating field, so that the effective feature set simultaneously satisfies statistical significance and mechanism consistency. This improves the relevance of feature expression to the target paint type and the predicted performance in coating formulation performance prediction and the reliability of prediction results. It solves the problems in the prior art where feature construction relies on manually fixed features or original formulation ratios, data-driven approaches are disconnected from knowledge in the coating field, and extrapolation prediction is unreliable when training sample coverage is insufficient. 2. By identifying new raw materials in the coating formulation that do not appear in the modeling samples corresponding to the historical formulation test data, determining their functional categories, and calculating their mass proportion as an out-of-distribution identification statistic when they belong to the relevant raw material functional category, this statistic is not used as the input feature of the machine learning model. At the same time, when a preset trigger threshold is reached, the out-of-distribution state is marked and an out-of-distribution warning message is output and the performance prediction is terminated. This application effectively avoids the extrapolation distortion caused by new raw materials being incorrectly mapped to existing raw materials or their mass proportion being directly input into the model. Furthermore, by judging whether the functional category is missing as a whole for the absence of known raw materials, generating a key feature missing label, or setting a null value label, this application systematically handles the situation of missing raw materials and missing functional categories in the formulation, thereby improving the credibility and security of coating formulation performance prediction when training data coverage is insufficient, new raw materials are present, or raw materials are missing. 3. By performing repeated cross-validation on candidate features based on the validation dataset, the frequency of candidate feature selection and the degree of consistency of the correlation direction in repeated cross-validation are statistically analyzed. The direction stability term, prediction contribution term, selection stability term, coating performance mechanism consistency term, and redundancy term are jointly included in the comprehensive screening score. At the same time, candidate features belonging to the knowledge-mandated feature set are retained even if they do not reach the statistical threshold, and their missing state and ablation evaluation results are recorded. This application enables the screening process of the effective feature set to identify and eliminate statistically significant but unstable pseudo-correlation features, prevents the accidental deletion of necessary mechanism features with clear physicochemical significance, and improves the traceability, reproducibility, and interpretability of the feature selection process by recording the expected influence direction and feature identifier of candidate features. Attached Figure Description

[0050] Figure 1 This is a flowchart of the coating formulation performance prediction method provided in the embodiments of the present invention; Figure 2 This is a block diagram of the coating formulation performance prediction system provided in an embodiment of the present invention.

[0051] Figure label: 1. Data acquisition module; 2. Candidate pool construction module; 3. Filtering and verification module; 4. Performance prediction module. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0053] Please refer to Figure 1 The first aspect of this invention provides a method for predicting the performance of coating formulations, comprising the following steps: S1, obtain the coating formula to be tested, and determine the target paint type to which the coating formula to be tested belongs.

[0054] The coating formulation to be tested can be a two-component coating system consisting of a main agent formulation, a curing agent formulation, and the mixing ratio of the main agent and the curing agent, or a one-component coating system consisting of a single formulation. Each raw material must include at least the raw material name or unique raw material identifier and the addition ratio. The addition ratio is usually expressed as a percentage of the wet basis mass in the raw material supply state. The main-to-solid ratio refers to the ratio of the wet basis mass of the main agent and the curing agent in the supply state. When the main-to-solid ratio entered by the user is a volume ratio, the volume ratio is converted into a mass ratio based on the density of the main agent mixture and the density of the curing agent mixture. Let the volume ratio of the main agent to the curing agent be a to b, and the corresponding densities be the first density and the second density, respectively. Then the converted mass ratio is the ratio of the volume ratio to the product of the corresponding density. When the corresponding density cannot be obtained, the volume ratio is not directly used as the mass ratio, but a density supplementary prompt is output. For two-component coating systems, based on the mixing mass ratio of the main agent and the curing agent, the partial mass percentages in the main agent and curing agent formulations are converted into absolute mass fractions in the mixed coating. Let the mass ratio of the main agent to the curing agent be a:b, the partial mass fraction of the i-th raw material in the main agent be the first partial mass fraction, and the partial mass fraction of the j-th raw material in the curing agent be the second partial mass fraction. Then, the absolute mass fraction of the corresponding raw material in the mixed coating is equal to the ratio of the main agent mass ratio to the total mass ratio multiplied by the first partial mass fraction, and the ratio of the curing agent mass ratio to the total mass ratio multiplied by the second partial mass fraction, respectively. When the input ratio is expressed as a percentage, it is first divided by 100 to convert it into a partial mass fraction between 0 and 1, and then the absolute mass fraction is calculated. For single-component coating systems, the partial mass fractions of each raw material are directly used as absolute mass fractions. Subsequent theoretical parameter calculations, mechanism feature construction, historical similarity retrieval, and machine learning predictions all use absolute mass fractions. The ratio and error of the main agent or curing agent due to numerical rounding must not exceed ±0.01 percentage points. If the error exceeds the error range, an abnormal ratio prompt will be output and subsequent predictions will be stopped.

[0055] The system processes the input content through a structured parsing module, which includes format parsing rules and / or a large language model. This module identifies the main agent, curing agent, and other key components, extracts the raw material name, addition ratio, main-to-solid ratio, and user-specified paint type, and converts it into a preset JSON format. The system performs necessary field, numerical format, raw material identifier uniqueness, and ratio range checks on the parsing results. When the parsing result lacks necessary fields, the raw material ratio cannot be converted into a numerical value, or the raw material name cannot be mapped to a unique raw material identifier, the error message is fed back to the parsing module for reprocessing. When multiple entries in the same formulation are mapped to the same unique raw material identifier, the addition ratios of the entries are merged, and the original addition stage information of each entry is retained, without directly judging them as parsing errors. When entries with the same name are mapped to different raw material identifiers and cannot be automatically confirmed, a raw material identity confirmation prompt is output. If the parsing verification still fails after two preset retries, subsequent predictions are stopped and a format error prompt is output.

[0056] Test conditions are determined based on the performance to be predicted, including one or more of the following: test method, substrate type, substrate treatment, wet film thickness or dry film thickness, curing temperature, curing time, ambient temperature, and ambient humidity. The purpose of identifying the target paint type is that different paint types differ in theoretical parameter calculation methods, performance characteristics, machine learning model selection, and test condition matching rules. For example, the reaction equivalence ratio of epoxy primers is defined as the ratio of the total active hydrogen equivalents on the curing agent side to the total epoxy group equivalents on the resin side, while the reaction equivalence ratio of acrylic polyurethane topcoats is defined as the ratio of the isocyanate group equivalents to the hydroxyl group equivalents. If the paint type cannot be correctly identified, subsequent theoretical parameter calculations and model calls will use incorrect methods, leading to prediction results deviating from reality. Paint type identification can be performed based on explicit user specification, formulation number prefixes, or a combination of keywords from the film-forming resin and curing agent system. When different identification criteria conflict or the paint type to which the formulation belongs cannot be determined, the paint type identification status is set to "needs confirmation," and the use of paint type-specific theoretical parameter calculation methods and machine learning models is stopped to avoid misjudging an unknown paint type by default. Currently supported paint types include, but are not limited to, epoxy primers and acrylic polyurethane topcoats, and the framework remains open to adding new paint types in the future. Through this method, the coating formulation and its testing conditions are uniformly converted into standardized inputs usable in subsequent steps, providing a data foundation for constructing the performance characteristic candidate pool.

[0057] The rationality of the analyzed formulation is verified in advance, including formulation integrity verification, ratio verification, main solids ratio verification, raw material property integrity verification, raw material compatibility verification, and basic film-forming property verification. The formulation integrity check includes verifying whether it contains film-forming resin, necessary curing components, and corresponding additives; the proportion and verification check whether the proportions of each component of the main agent and curing agent are within 100% ± 0.01 percentage points; the main solids ratio check determines whether the main solids ratio is within the allowable range of the corresponding resin and curing agent system based on the target paint type configuration file; the raw material property integrity check checks whether the solid content, density, raw material category, and equivalent, oil absorption, NCO content, hydroxyl value, or empirical coefficient used for characteristic calculations exist; the raw material compatibility check determines whether there are any raw material combinations in the formulation that are prohibited from being used together in the raw material compatibility rule library; the basic film-forming property check determines whether the formulation has basic film-forming conditions based on the film-forming resin content, non-volatile matter, and curing component integrity. When CPVC data is available, it further determines whether the pigment and filler volume concentration may lead to insufficient film-forming continuity based on the relationship between PVC and CPVC. When CPVC data is missing, the PVC and CPVC film-forming judgment is not performed, and the CPVC missing mark is set to 1. When necessary raw material properties are missing, the corresponding mechanism features are set as missing and a missing value label is output. When missing properties cause the reaction equivalence ratio, PVC, PVC to CPVC ratio, or other key features to be uncalculated, and the corresponding machine learning model does not use a validated missing value handling mechanism, the numerical prediction of the corresponding performance indicators is stopped and supplementary data prompts are output. When the model has a validated missing value handling mechanism, prediction is allowed to continue, and the corresponding key feature missing value label is recorded.

[0058] S2. For the predicted performance of the coating formulation to be tested, a performance feature candidate pool is constructed. The performance feature candidate pool is a set of candidate features, including at least the formulation composition features determined based on the coating formulation to be tested, the theoretical parameters calculated from the coating formulation to be tested, the general mechanism features applicable to multiple performance indicators, and the performance-specific mechanism features corresponding to the performance to be tested, as well as at least one of the following: test conditions, key feature missing markers, and combined features.

[0059] The formulation composition characteristics are determined based on the unique raw material identifiers and addition ratios of the raw materials in the coating formulation to be tested. The unique raw material identifier is the identification information used to uniquely identify a single raw material in a pre-set raw material identifier system. A fixed-dimensional candidate feature column is established according to the unique raw material identifier, so that the candidate features corresponding to the formulation composition characteristics correspond one-to-one with the unique raw material identifier. Theoretical parameters are calculated from the coating formulation to be tested, including one or more of the following: mass solids content, volume solids content, pigment-to-binder ratio, pigment volume concentration, reaction equivalence ratio, volatile organic compound content, and critical pigment volume concentration. Mass solids content equals the sum of the products of the mass of each raw material in its supplied state and its corresponding solid mass fraction, divided by the sum of the masses of each raw material in its supplied state; volume solids content equals the sum of the quotients obtained by multiplying the mass of each raw material in its supplied state and its corresponding solid mass fraction by the corresponding non-volatile fraction density, divided by the sum of the quotients obtained by dividing the mass of each raw material in its supplied state by its corresponding wet density; pigment-to-binder ratio equals the sum of the products of the masses of each raw material in the pigment and filler set in its supplied state and their corresponding solid mass fractions, divided by the sum of the products of the masses of each raw material in the non-volatile binder set in its supplied state and their corresponding solid mass fractions; pigment volume concentration equals the sum of the quotients obtained by multiplying the mass of each raw material in the pigment and filler set in its supplied state and its corresponding solid mass fraction by the corresponding non-volatile fraction density, divided by the sum of the sum of these quotients and the sum of the quotients obtained by multiplying the mass of each raw material in the non-volatile binder set in its supplied state and its corresponding solid mass fraction by the corresponding non-volatile fraction density. For epoxy systems, the total epoxy equivalent number is equal to the sum of the quotients obtained by dividing the effective metered mass of each epoxy resin component by its corresponding epoxy equivalent number; the total active hydrogen equivalent number is equal to the sum of the quotients obtained by dividing the effective metered mass of each curing agent component by its corresponding active hydrogen equivalent number; and the reaction equivalent ratio is equal to the total active hydrogen equivalent number divided by the total epoxy equivalent number. For polyurethane systems, the NCO equivalent number is equal to the sum of the quotients obtained by multiplying the effective metered mass of each isocyanate curing agent by its corresponding NCO mass fraction by 42.02; the OH equivalent number is equal to the sum of the quotients obtained by multiplying the effective metered mass of each hydroxyl resin by its corresponding hydroxyl value by 56100; and the reaction equivalent ratio is equal to the NCO equivalent number divided by the OH equivalent number. The volatile organic compound (VOC) content is equal to the sum of the products of the mass of each raw material in its supplied state and the corresponding mass fraction of VOCs to be included, divided by the sum of the quotients obtained by dividing the mass of each raw material in its supplied state by its corresponding wet density, and then multiplied by 1000. The critical pigment volume concentration is preferably obtained from experimentally calibrated values ​​in the paint formulation file. The record should include at least the applicable paint type, resin system, pigment / filler system, testing or calibration method, calibration value, and version information. When a validated critical pigment volume concentration calculation model is available, it can be calculated based on the pigment / filler oil absorption, pigment / filler density, and binder properties, and the version of the calculation model used should be recorded. Unvalidated estimates should not be used as formal input for the ratio of pigment volume concentration to critical pigment volume concentration. These theoretical parameters map high-dimensional, raw material-dependent formulation information to a low-dimensional parameter space with physicochemical meaning.

[0060] The general mechanistic features are applicable to multiple performance indicators, including equivalence ratio offset, stoichiometric utilization index, and non-reactive solids dilution index. The equivalence ratio offset is the absolute value of the difference between the reaction equivalence ratio and the theoretical stoichiometric point 1, and its value is not less than 0. The smaller the value, the closer the theoretical stoichiometric relationship of the reactants is to the stoichiometric point. The stoichiometric utilization index is the ratio of the smaller to the larger of the total equivalent numbers of the two types of reactive groups participating in the curing reaction. For epoxy systems, this is the total epoxy equivalent number and the total active hydrogen equivalent number; for polyurethane systems, it is the NCO equivalent number and the OH equivalent number. When either of the two types of reactive groups is 0, the stoichiometric utilization index is not calculated, and a corresponding key feature missing marker is set. The non-reactive solids dilution index is equal to 1 minus the total mass of the non-volatile resin and curing agent participating in the curing reaction, divided by the total mass of all non-volatile components in the formulation.

[0061] The specific mechanism characteristics are those applicable only to the tested performance. For example, for adhesion performance, the absolute mass fraction of the interface-promoting component and the absolute mass fraction of the film-forming resin are used. The interface-promoting component includes silane coupling agents, adhesion promoters, and other raw materials marked in the feature library as having interface bonding promoting effects. For salt spray resistance performance, the film-forming density barrier index and the ion diffusion path enhancement factor are used. The film-forming density barrier index is equal to the larger value between 0 and 1 between the volume solids fraction multiplied by 1 and the ratio of pigment volume concentration to critical pigment volume concentration. Among them, pigment volume concentration, critical pigment volume concentration, and volume solids fraction are all uniformly converted to decimal representation between 0 and 1 before being substituted into the formula. The diffusion path enhancement factor is equal to the sum of the products of the absolute mass fraction of each pigment or filler and the corresponding empirical coefficient of the rust prevention or diffusion path; for hardness performance, the rigid component contribution and average rigidity coefficient are as follows: the rigid component contribution is equal to the sum of the products of the absolute mass fraction of each component in the set of non-volatile components with rigid contribution and the corresponding empirical rigidity coefficient, and the average rigidity coefficient is equal to the rigid component contribution divided by the sum of the absolute mass fractions of each component in the set; for gloss performance, the absolute mass fraction of the matting agent and the surface roughness proxy characteristics are as follows: the surface roughness proxy characteristics are equal to the sum of the products of the absolute mass fraction of each raw material in the set of matting agents and pigments and fillers that can affect surface roughness and the corresponding surface roughness contribution coefficient.

[0062] Test conditions include substrate type, substrate treatment method, test method, film thickness, curing temperature, curing time, ambient temperature, and ambient humidity, which are directly related to the performance test results and need to be included in the candidate pool for subsequent screening. Key feature missing markers are used to characterize the absence of data required for calculating formulation composition features, theoretical parameters, general mechanism features, or performance-specific mechanism features, or the absence of all raw materials corresponding to the functional category in the coating formulation under test. This ensures that the missing information itself is retained as an independent candidate feature, rather than being simply filled in or deleted. Combination features are proportional terms, interaction terms, or nonlinear transformation terms generated from formulation composition features, theoretical parameters, general mechanism features, or performance-specific mechanism features according to preset feature construction rules. By constructing a performance feature candidate pool, the original formulation composition, theoretical parameters, general mechanism features, performance-specific mechanism features, test conditions, missing markers, and combination features are uniformly included in the candidate feature set, providing a complete candidate space for subsequent statistical screening and constraint verification based on historical formulation test data.

[0063] Furthermore, in step S2, a candidate pool of performance features is constructed for the predicted performance of the coating formulation to be tested, including: S21. Based on the coating formulation and target paint type to be tested, determine the candidate feature sources corresponding to the performance to be tested. The candidate feature sources include formulation composition features, theoretical parameters, general mechanism features and performance-specific mechanism features, as well as test conditions, key feature missing markers and combination features. The formulation composition features are determined based on the unique raw material identifier and addition ratio of the raw materials in the coating formulation to be tested. The unique raw material identifier is the identification information used to uniquely identify a raw material in the pre-set raw material identifier system.

[0064] The purpose of identifying candidate feature sources is to clarify which dimensions should be used to construct candidate features for different target paint types and predicted performance. Formulation composition features directly reflect the types and amounts of raw materials in the formulation, serving as the original input information for performance prediction. Theoretical parameters are calculated from the coating formulation, mapping high-dimensional raw material names to a low-dimensional parameter space with physicochemical meaning. General mechanism features are applicable to multiple performance indicators, reflecting the stoichiometric matching degree between reactive components and the dilution effect of non-volatile solid components on the film-forming structure. Performance-specific mechanism features are only applicable to the tested performance, reflecting different physicochemical factors for different performances. For example, adhesion performance corresponds to the absolute mass fraction of interface-promoting components and the absolute mass fraction of film-forming resin; salt spray resistance performance corresponds to the film-forming density barrier index and ion diffusion path enhancement factor; hardness performance corresponds to the contribution of rigid components and the average rigidity coefficient; gloss performance corresponds to the absolute mass fraction of matting agents and surface roughness proxy features. Test conditions are directly related to performance test results, including substrate type, substrate treatment method, test method, film thickness, curing temperature, curing time, ambient temperature, and ambient humidity, and should be included in the candidate feature sources for subsequent screening. Key feature missing markers are used to characterize situations where the data required for calculating candidate feature sources is missing, or where all raw materials corresponding to a certain raw material functional category are not included in the coating formulation under test. Combined features are proportional terms, interactive terms, or nonlinear transformation terms generated from formulation composition features, theoretical parameters, general mechanism features, or performance-specific mechanism features according to preset feature construction rules. By determining the source of candidate features, formulation composition, theoretical parameters, general mechanism features, performance-specific mechanism features, test conditions, missing markers, and combined features are uniformly included in the construction scope of subsequent candidate feature columns, avoiding the omission of feature dimensions that affect predicted performance.

[0065] S22. Based on the source of candidate features and unique raw material identifier, construct a candidate feature column with fixed dimensions. The candidate features corresponding to the formulation composition features correspond one-to-one with the unique raw material identifier. The theoretical parameters, general mechanism features and performance-specific mechanism features correspond to the preset feature identifiers respectively.

[0066] The purpose of constructing fixed-dimensional candidate feature columns is to ensure that the candidate feature columns corresponding to different coating formulations under test have the same dimensional structure, facilitating processing by machine learning models. For formulation composition features, feature columns are established according to the unique raw material identifiers in the pre-set raw material identifier system. Each known raw material corresponds to a fixed feature position. Known raw materials not included in the coating formulation under test are filled with a preset value indicating non-inclusion or a null value in their corresponding feature positions. New raw materials not appearing during the training phase are not mapped to the unique raw material identifiers of existing raw materials, nor are their total mass scores used as input features for the machine learning model. For theoretical parameters, general mechanism features, and performance-specific mechanism features, feature columns are established according to pre-set feature identifiers, with each theoretical parameter, general mechanism feature, or performance-specific mechanism feature corresponding to a fixed feature position. For categorical test conditions such as substrate type, substrate treatment method, and test method, unique thermal coding or preset category coding is used. Numerical conditions such as film thickness, curing temperature, curing time, ambient temperature, and ambient humidity use raw values ​​and are uniformly converted according to the unit specifications established in the training data. Through the above method, the candidate feature columns of different coating formulations to be tested maintain a consistent dimensional structure. The differences between formulations are reflected in the different values ​​at each feature position, rather than differences in the feature column structure. The fixed-dimensional candidate feature columns also facilitate the subsequent alignment of historical formulation test data according to unique raw material identifiers and preset feature identifiers, thereby calculating the compositional similarity between the coating formulation to be tested and historical formulations, and performing statistical screening and constraint verification.

[0067] S23. Remove candidate features from the candidate feature column that are related to the measured value of the performance to be tested. The relationship includes direct relationship and indirect relationship. Direct relationship means that the candidate feature itself is the measured value of the performance to be tested or its derived statistics. Indirect relationship means that the candidate feature can uniquely determine the value of the measured value of the performance to be tested.

[0068] The purpose of excluding candidate features that are correlated with the measured values ​​of the target performance is to prevent the machine learning model from encountering information that can directly or indirectly derive the measured values ​​of the target performance during training, thus avoiding the model learning false mapping relationships. Directly correlated candidate features include the measured values ​​of the target performance themselves, the average of the measured values, the variance of the measured values, or other statistics directly calculated from the measured values ​​of the target performance. Indirectly correlated candidate features include information that uniquely identifies the measured values ​​of the target performance, such as recipe numbers, batch numbers, and collection time labels. When there is a one-to-one correspondence between the recipe number, batch number, or collection time label and the measured value of the target performance, the model may directly derive the measured value of the target performance from these labels, rather than learning the true mapping relationship from the recipe composition and theoretical parameters. By excluding these candidate features, the input of the machine learning model only includes features that have a reasonable correlation with the target performance, avoiding data leakage that could cause the model to perform well on the training set but fail in actual predictions.

[0069] S24. The test conditions corresponding to the coating formulation to be tested, the key feature missing markers, and the combined features generated according to the preset feature construction rules are included in the candidate feature column and summarized into the performance feature candidate pool. The key feature missing marker is used to characterize the missing data required for calculating the formulation composition features, theoretical parameters, general mechanism features, or performance-specific mechanism features, or the state where all raw materials corresponding to a certain raw material functional category in the coating formulation to be tested are not included in the coating formulation to be tested.

[0070] The purpose of including test conditions in the candidate feature list is that the same formulation may exhibit different performance results under different test conditions. For example, the adhesion, salt spray resistance, and drying time of the same formulation may differ under different film thicknesses, curing temperatures, or ambient humidity conditions. Including test conditions as candidate features allows the machine learning model to consider the impact of test conditions during prediction. The purpose of including key feature missing markers as independent candidate features in the candidate feature list is to retain the missing information itself as a feature, rather than simply filling or deleting it. When data required for calculating the reaction equivalence ratio, the ratio of pigment volume concentration to critical pigment volume concentration, or other key features is missing, the key feature missing marker can indicate to the machine learning model that the corresponding feature is unavailable, preventing the model from misclassifying missing values ​​as valid values. The purpose of including combined features in the candidate feature list is to ensure that the candidate feature list not only includes original formulation composition features, theoretical parameters, general mechanism features, and performance-specific mechanism features, but also includes proportional terms, interaction terms, or nonlinear transformation terms generated by the above features according to preset feature construction rules. This expands the expressive range of candidate features and provides a richer candidate space for subsequent statistical screening and constraint verification. Through the above methods, the performance feature candidate pool summarizes the formulation composition features, theoretical parameters, general mechanism features, performance-specific mechanism features, test conditions, key feature missing markers, and combination features, providing a complete set of candidate features for subsequent statistical screening and constraint verification based on historical formulation test data.

[0071] By determining the source of candidate features based on the coating formulation and target paint type, a fixed-dimensional candidate feature column is constructed according to the unique raw material identifier and pre-set feature identifier. Candidate features that are directly or indirectly related to the measured performance value are excluded from the candidate feature column. Test conditions, key feature missing markers, and combined features are included in the candidate feature column and summarized into a performance feature candidate pool. This improves the uniformity of the dimensional structure of the candidate feature column and the standardization of the input data of the machine learning model, avoids data leakage that leads to the model learning false mapping relationships, and solves the problems of inconsistent feature column dimensions, leakage of measured performance values ​​by labels such as formulation number and batch number, and simple filling or deletion of missing information in the existing technology.

[0072] Furthermore, the construction of the fixed-dimensional candidate feature column in step S22 also includes: S2211, Identify new raw materials in the coating formulation to be tested that have not appeared in the modeled samples corresponding to the historical formulation test data.

[0073] The modeling samples corresponding to the historical formula test data refer to the historical formula data set used to train and validate the machine learning model. Each raw material in this set has a unique raw material identifier and has been registered in a pre-set raw material identifier system. When a raw material appears in the coating formula to be tested, and its raw material name or unique raw material identifier is not within the range of raw materials included in the modeling samples, this raw material is identified as a new raw material. New raw materials may come from various situations, such as supplier changes leading to changes in raw material names, the addition of functional additives, replacement of film-forming resins or curing agents, etc. For new raw materials, directly mapping them to the unique raw material identifiers of existing raw materials will cause the model to confuse the feature values ​​of new raw materials with the feature values ​​of existing raw materials, causing the prediction results to deviate from reality. If the mass proportion of new raw materials is directly used as the input feature of the machine learning model, since the model has never seen this raw material during the training phase, the model cannot establish an effective mapping relationship for this feature, which may give unreliable extrapolation prediction results. Therefore, identifying new raw materials is a prerequisite for subsequent special processing.

[0074] S2212, Determine the functional category of the new raw material in the pre-set raw material functional category system. The pre-set raw material functional category system is a pre-defined system for classifying raw materials by function.

[0075] The pre-defined raw material functional category system classifies raw materials according to their function in the coating formulation, such as film-forming resins, curing agents, pigments, fillers, solvents, matting agents, dispersants, leveling agents, defoamers, thixotropic agents, adhesion promoters, and rust-inhibiting pigments. The purpose of determining the functional category of a new raw material is to determine whether it belongs to a category related to the test property, thereby determining whether the new raw material may affect the test property. For example, when the test property is adhesion, the functional categories related to adhesion include film-forming resins, curing agents, adhesion promoters, and substrate treatment-related raw materials; when the test property is gloss, the functional categories related to gloss include matting agents, film-forming resins, and pigments. If the functional category of a new raw material does not belong to a category related to the test property, then the new raw material has a small impact on the test property and does not need to be used as an out-of-distribution identification statistic. By determining the functional category, the treatment of new raw materials can be differentiated according to the test property, avoiding overly conservative approaches by uniformly labeling all new raw materials as out-of-distribution.

[0076] S2213, determine whether the function category belongs to the raw material function category related to the performance to be tested.

[0077] The functional categories of raw materials related to the test performance are predefined categories that influence the test performance. The purpose of this judgment is to screen out new raw materials that may significantly affect the test performance. New raw materials whose functional categories are unrelated to the test performance are not included in the out-of-distribution identification statistics, thus avoiding the termination of performance prediction due to irrelevant new raw materials triggering out-of-distribution marking. For example, when the test performance is gloss, if a new raw material belongs to the matting agent or film-forming resin functional category, it belongs to the raw material functional category related to gloss; if a new raw material belongs to the anti-settling agent functional category, it usually does not belong to the raw material functional category directly related to gloss. Through the above judgment, a correlation is established between the out-of-distribution identification treatment of new raw materials and the test performance, improving the targeting and accuracy of out-of-distribution identification.

[0078] S2214, if the functional category belongs to the raw material functional category related to the performance to be tested, then the mass percentage of the new raw material in the coating formulation to be tested is calculated as an out-of-distribution identification statistic. The mass percentage is the absolute mass fraction of the new raw material in the mixed coating. The out-of-distribution identification statistic is not used as an input feature of the machine learning model.

[0079] The core processing method in this step is to use the mass percentage of the new raw material as an out-of-distribution identification statistic rather than as an input feature of the machine learning model. Since the machine learning model has not encountered this new raw material during the training phase, if its mass percentage is input, the model cannot provide reliable predictions based on this feature. However, the mass percentage of the new raw material can reflect the degree to which the tested coating formulation deviates from the coverage of the training data. Therefore, it is used as an out-of-distribution identification statistic to subsequently determine whether the tested performance exceeds the coverage of the training data. The mass percentage is the absolute mass fraction of the new raw material in the mixed coating. For two-component coating systems, the local mass percentage of the new raw material in the main agent or hardener needs to be converted to an absolute mass fraction in the mixed coating based on the mixing mass ratio of the main agent and the hardener. Through this processing, the information of the new raw material is used for out-of-distribution identification instead of entering the input channel of the machine learning model, preventing the model from generating unreliable extrapolated predictions due to the new raw material.

[0080] S2215 compares the out-of-distribution identification statistic with the preset trigger threshold. If the out-of-distribution identification statistic reaches the preset trigger threshold, the performance to be tested is marked as out-of-distribution, and out-of-distribution warning information and performance prediction of the performance to be tested are terminated.

[0081] The preset trigger threshold is a pre-defined threshold used to determine whether the out-of-distribution identification statistic has reached the out-of-distribution state. When the out-of-distribution identification statistic reaches the preset trigger threshold, it indicates that the amount of the new raw material related to the performance being tested in the coating formulation has reached a level that may significantly affect the reliability of the prediction. At this time, the performance being tested is marked as out-of-distribution. The purpose of outputting out-of-distribution warning information is to inform R&D personnel that there is a new raw material in the coating formulation being tested that did not appear during the training phase, and that the amount of this new raw material has reached the preset trigger threshold, and the prediction result may be unreliable. The purpose of terminating the performance prediction of the performance being tested is to avoid outputting seemingly normal prediction values ​​when the model cannot reliably extrapolate, and to prevent R&D personnel from using unreliable prediction results as the basis for formula selection. Through the above processing, the out-of-distribution identification of new raw materials forms a complete processing chain from identification, classification, statistics, comparison to marking, warning and termination of prediction, improving the credibility and safety of coating formulation performance prediction when new raw materials are present.

[0082] By identifying new raw materials in the coating formulation that do not appear in the modeling samples corresponding to the historical formulation test data, the functional category of the raw material is determined. When the functional category belongs to the raw material functional category related to the performance to be tested, its mass proportion is counted as an out-of-distribution identification statistic. This statistic is not used as the input feature of the machine learning model. At the same time, when the out-of-distribution identification statistic reaches a preset trigger threshold, the out-of-distribution state is marked, an out-of-distribution warning message is output, and the performance prediction of the performance to be tested is terminated. This avoids the unreliable extrapolation prediction caused by the new raw material being incorrectly mapped to existing raw materials or its mass proportion being directly input into the machine learning model. It solves the problem in the prior art that new raw materials that do not appear in the training phase cannot be correctly processed and the model makes unreliable extrapolations of new raw materials.

[0083] Furthermore, the construction of the fixed-dimensional candidate feature column in step S22 also includes: S2221, For known raw materials not included in the coating formulation to be tested, determine the corresponding functional category of the known raw materials in the pre-set raw material functional category system.

[0084] Known raw materials refer to those that have appeared in the modeling samples corresponding to the historical formulation test data and have been registered with a unique raw material identifier in the pre-set raw material identification system. Known raw materials not included in the coating formulation to be tested refer to those that exist in the modeling samples but are not used in the current coating formulation to be tested. For each unincluded known raw material, its corresponding functional category in the pre-set raw material functional category system is determined, such as film-forming resin, curing agent, pigment, filler, solvent, matting agent, dispersant, leveling agent, defoamer, thixotropic agent, adhesion promoter, rust-inhibiting pigment, etc. The purpose of determining the functional category is to determine whether the functional category corresponding to the known raw material is entirely missing in the coating formulation to be tested. If only a certain known raw material is determined to be missing, it is impossible to distinguish whether the raw material is an isolated unused ingredient or whether all raw materials in its functional category are unused. By determining the functional category, the unincluded known raw materials are grouped according to their functional categories, providing a basis for subsequent determination of the overall absence of functional categories.

[0085] S2222, determine whether the functional category is completely missing in the coating formulation to be tested. Complete missing means that all raw materials corresponding to the functional category are not included in the coating formulation to be tested.

[0086] The determination of overall absence is based on functional categories, not individual raw materials. When all raw materials corresponding to a certain functional category are not included in the tested coating formulation, that functional category is considered to be entirely absent; when at least one raw material in a functional category is included in the tested coating formulation, that functional category is considered not entirely absent. For example, if the tested coating formulation does not contain matting agent A and matting agent B, but the matting agent functional category only contains matting agent A and matting agent B, then that functional category is entirely absent; if the tested coating formulation does not contain matting agent A but contains matting agent B, then that functional category is not entirely absent. The purpose of distinguishing between unused raw materials and overall absence of functional categories is that when a functional category is entirely absent, the performance impact mechanism corresponding to that functional category may fundamentally change, rather than simply being zero in the amount of a single raw material. For example, when the matting agent functional category is entirely absent, the gloss of the tested coating formulation may be significantly higher than that of a formulation containing matting agents. The model needs to know the information about the overall absence of the functional category, not just the zero amount of a single matting agent.

[0087] S2223, if the functional category is entirely missing in the coating formulation to be tested, a key feature missing marker is generated. This key feature missing marker is used in step S24 to be included as an independent candidate feature in the candidate feature list. The key feature missing marker is an identifier indicating that all raw materials corresponding to the functional category are not included in the coating formulation to be tested.

[0088] The purpose of including key feature missing markers as independent candidate features in the candidate feature list is to enable the machine learning model to distinguish between two scenarios: a raw material not being used and a functional category being entirely missing. If only candidate features corresponding to known raw materials that are not included are set to null values ​​or zero, the model cannot distinguish between two scenarios: a raw material not being used but similar functional materials being present, and a functional category being entirely missing. This could lead to misjudging the content of a functional category being entirely missing as zero. By generating key feature missing markers, the model can understand the information about the overall absence of a functional category, thus considering the impact of this absence on performance during prediction. Key feature missing markers, as independent candidate features, do not replace candidate features corresponding to known raw materials not included; rather, they are included together with these candidate features in the candidate feature list.

[0089] S2224 If the functional category is not completely missing in the coating formulation to be tested, the candidate features corresponding to the known raw materials are set as null values. The null values ​​are preset sentinel values ​​that are different from the valid numerical range.

[0090] When a functional category is not entirely missing, it indicates that at least one raw material in that category is included in the tested coating formulation. In this case, the missing known raw material represents an individual unused case, and its corresponding candidate feature can be marked as a null value. The null value marker is a preset sentinel value that distinguishes it from the valid numerical range, such as zero or other preset values ​​that do not affect the model calculation. It allows the model to distinguish that the known raw material corresponding to that feature position is not included in the tested coating formulation, rather than indicating that the amount of that raw material is zero. By setting the candidate features corresponding to the unincluded known raw materials as null values, the candidate feature column maintains a fixed-dimensional structure. The differences between different tested coating formulations are reflected in the different values ​​at each feature position, rather than differences in the feature column structure.

[0091] By determining the functional categories of known raw materials not included in the coating formulation to be tested, and judging whether the functional categories are completely missing, if they are completely missing, a key feature missing marker is generated and included as an independent candidate feature in the candidate feature column. If they are not completely missing, the candidate features corresponding to the known raw materials are set to null values. This enables the machine learning model to distinguish between the two situations: raw materials not used and functional categories completely missing. This improves the ability of the candidate feature column to express the formulation structure information and solves the problem in the existing technology that the model cannot distinguish between raw materials not used and functional categories completely missing when only the raw materials not included are set to zero.

[0092] S3: Obtain historical formula test data corresponding to the target paint type and the performance to be tested. Based on the historical formula test data, statistically filter the candidate features in the performance feature candidate pool, and then perform constraint verification on the candidate features retained after statistical filtering to obtain a subset of candidate features corresponding to the performance to be tested. This subset of candidate features is taken as the effective feature set corresponding to the performance to be tested. Statistical filtering involves calculating the statistical correlation index between candidate features and the performance to be tested based on historical formula test data and retaining or deleting candidate features accordingly. Constraint verification involves deleting candidate features that do not conform to the preset coating performance mechanism rules.

[0093] The purpose of statistical screening is to identify candidate features that are statistically correlated with the performance to be tested from the candidate pool, avoiding inputting features that are unrelated to performance or have a weak correlation into the machine learning model. The purpose of constraint verification is to further examine the candidate features retained after statistical screening at the domain knowledge level, deleting candidate features that conflict with the performance formation mechanism or do not conform to the basic laws of the coatings field, and avoiding retaining spurious features based solely on statistical correlation. The order of statistical screening followed by constraint verification ensures that the constraint verification targets only the candidate features retained after statistical screening, avoiding unnecessary computational overhead from performing constraint verification on all candidate features, while allowing statistical screening and constraint verification to play different screening roles. Through the combination of statistical screening and constraint verification, an effective feature set corresponding to the performance to be tested is obtained. This effective feature set simultaneously satisfies statistical correlation and consistency with the mechanisms of the coatings field, overcoming the shortcomings of single data-driven screening, which easily retains spurious features, and single manual rule screening, which cannot adaptively adjust to data.

[0094] Furthermore, in step S3, the candidate features in the performance feature candidate pool are statistically screened based on historical formula test data, including: S311. Historical formulation test data are grouped according to basic formulation series, raw material batch, and collection time. Training and validation datasets are then created while maintaining group and time isolation. The basic formulation series consists of formulations with the same film-forming resin system and curing agent system. Grouping involves grouping historical samples with the same basic formulation series identifier and the same raw material batch identifier into the same historical sample group. Group isolation ensures that historical samples within the same historical sample group do not cross between the training and validation datasets. Time isolation ensures that historical samples collected later are not included in the training dataset.

[0095] The purpose of grouping historical formulation test data is to address the potential for numerous nearly identical samples within this data set. Examples include multiple formulation variations within the same basic formulation series with only slight differences in the dosage of a single ingredient, or duplicate records obtained from multiple preparations and tests within the same ingredient batch. If the historical formulation test data is randomly partitioned directly, samples from the same basic formulation series or the same ingredient batch may appear simultaneously in both the training and validation datasets. This results in highly similar samples in the validation dataset to those in the training dataset, leading to an overestimation of the model's performance on the validation dataset and failing to accurately reflect the model's predictive ability for unseen formulations. Grouping by basic formulation series, ingredient batch, and collection time, and grouping historical samples with the same basic formulation series identifier and the same ingredient batch identifier into the same historical sample group, ensures that nearly identical samples and samples from the same batch are assigned to the same subset of data. Group segregation requires that historical samples within the same historical sample group do not cross between the training and validation datasets, preventing samples from the same historical sample group from being used for both training and validation simultaneously. Temporal isolation requires that historical samples collected later be excluded from the training dataset, ensuring that the samples in the training dataset are earlier than those in the validation dataset. This simulates real-world scenarios where historical data is used to train models and predict future recipes. Through this grouping and isolation, the division between the training and validation datasets more accurately reflects the model's predictive ability for unseen recipes, preventing inflated model evaluation results due to data leakage.

[0096] S312 calculates the statistical correlation index between candidate features and the performance to be tested based on the training dataset, and performs repeated cross-validation on the candidate features based on the validation dataset, statistically analyzing the frequency of candidate feature selection and the degree to which the correlation direction remains consistent in the repeated cross-validation. The statistical correlation index is an indicator that characterizes the degree of correlation or importance between candidate features and the performance to be tested, and the correlation direction is a positive or negative correlation between the candidate features and the performance to be tested.

[0097] The purpose of calculating statistical association metrics on the training dataset is to identify candidate features that are statistically correlated with the performance to be tested. A higher statistical association metric indicates a stronger correlation between the candidate feature and the performance, or a greater importance of the candidate feature in predicting the performance. The purpose of performing repeated cross-validation on candidate features on the validation dataset is to evaluate the stability of candidate feature selection under different data partitioning conditions. Repeated cross-validation involves partitioning the training and validation datasets multiple times, selecting candidate features in each partition, and recording the selected candidate features in each partition. The frequency of candidate feature selection—the percentage of times a candidate feature is selected into a subset of candidate features in multiple cross-validations—reflects the stability of candidate feature selection. A higher selection frequency indicates more stable selection of the candidate feature under different data partitioning conditions, and a more reliable correlation between the candidate feature and the performance to be tested. The degree to which the statistical correlation direction remains consistent across repeated cross-validation—that is, the proportion of times the positive or negative correlation between the candidate feature and the performance being tested remains the same across multiple cross-validations—reflects the stability of the candidate feature's correlation direction. A higher degree of consistency indicates a more stable correlation between the candidate feature and the performance being tested, and prevents the correlation direction from reversing under different data partitioning conditions. By analyzing the frequency of candidate feature selection and the consistency of the correlation direction, we can identify candidate features with high statistical correlation indicators but unstable selection or reversed correlation direction under different data partitioning conditions, thus avoiding retaining such spuriously correlated features in the effective feature set.

[0098] S313. Determine the comprehensive screening score based on the statistical correlation indicators, the frequency of selection, and the degree of consistency of the correlation direction. Retain candidate features that meet the preset admission threshold and preset stability threshold, and delete candidate features that do not meet the preset admission threshold or preset stability threshold.

[0099] The comprehensive screening score comprehensively characterizes the degree of correlation and stability between candidate features and the performance to be tested. It is determined by statistical correlation indicators, the frequency of selection, and the degree of consistency in the direction of correlation. Statistical correlation indicators reflect the degree of correlation or importance between candidate features and the performance to be tested; the frequency of selection reflects the stability of the candidate feature selection under different data partitioning conditions; and the degree of consistency in the direction of correlation reflects the stability of the candidate feature's correlation direction. Incorporating these three factors into the comprehensive screening score ensures that the selection of candidate features considers not only their statistical correlation with the performance to be tested but also their stability and the consistency of the correlation direction under different data partitioning conditions. Preset admission thresholds and preset stability thresholds are used to determine the comprehensive screening score and the frequency of candidate feature selection, respectively. Retaining candidate features that meet both the preset admission and stability thresholds indicates that the candidate feature simultaneously satisfies the requirements of statistical correlation and stability; deleting candidate features that do not meet the preset admission or stability thresholds indicates that the candidate feature is deficient in terms of statistical correlation or stability. By setting two judgment conditions, namely a preset admission threshold and a preset stability threshold, it is possible to avoid retaining pseudo-correlation features with high statistical correlation but unstable or reversed correlation direction under different data partitioning conditions when selecting features based solely on statistical correlation indicators.

[0100] S314, if a candidate feature belongs to a pre-defined set of mandatory knowledge retention features, it will still be retained in the subset of candidate features and marked as a mandatory knowledge retention feature, even if it does not reach the preset admission threshold or the preset stability threshold. The missing status and ablation evaluation result of the mandatory knowledge retention feature will be recorded. The set of mandatory knowledge retention features is a set of candidate features that are predetermined based on the coating performance formation mechanism, have a necessary influence on the performance to be tested, and cannot be replaced by other candidate features.

[0101] The purpose of setting a mandatory knowledge retention feature set is to avoid the accidental deletion of essential mechanistic features with clear physicochemical significance due to improperly set statistical screening thresholds or insufficient training data samples. In coating formulation performance prediction, certain mechanistic features have a necessary impact on the performance to be tested, such as reaction equivalence ratio, pigment volume concentration to critical pigment volume concentration ratio, and absolute mass fraction of film-forming resin. These features should not be deleted even if they do not reach the statistical screening threshold under certain training data partitioning conditions. The mandatory knowledge retention feature set is predetermined based on the coating performance formation mechanism, and the candidate features it includes have a necessary impact on the performance to be tested and cannot be replaced by other candidate features. For candidate features belonging to the mandatory knowledge retention feature set, even if they do not reach the preset admission threshold or preset stability threshold, they are still retained in the candidate feature subset and marked as mandatory knowledge retention features, so that subsequent machine learning models can use the above-mentioned essential mechanistic features for prediction. The purpose of recording the missing state and ablation evaluation results of mandatory knowledge retention features is to make the retention process of mandatory knowledge retention features traceable and evaluable. The missing state is used to record whether the data required for the computation of knowledge-forced retention features is missing. The ablation evaluation result is used to record the evaluation results of the change in the predictive performance of the machine learning model after removing the knowledge-forced retention features while keeping other candidate features unchanged. The above records provide a basis for subsequent evaluation of the necessity of knowledge-forced retention features.

[0102] By grouping historical formula test data according to basic formula series, raw material batches, and collection time, and dividing the training and validation datasets while maintaining group and time isolation, statistical correlation indices are calculated based on the training dataset, and repeated cross-validation is performed on the validation dataset. The frequency of candidate feature selection and the degree of consistency of correlation direction are statistically analyzed. Based on the statistical correlation indices, the frequency of selection, and the degree of consistency of correlation direction, a comprehensive screening score is determined, and candidate features that reach the threshold are retained. At the same time, candidate features belonging to the knowledge-mandated feature set are retained even if they do not reach the threshold, and their missing status and ablation evaluation results are recorded. This improves the ability to prevent data leakage during the effective feature set screening process, the ability to identify spurious correlation features with unstable selection and reversed correlation direction, and the ability to protect necessary mechanism features with clear physicochemical significance. It solves the problems in the existing technology where random division of training and validation datasets leads to inflated model evaluation results, the easy retention of spurious correlation features when selecting features based solely on statistical correlation indices, and the accidental deletion of necessary mechanism features due to insufficient samples.

[0103] Further, step S312 calculates the statistical correlation index between candidate features and the performance to be tested based on the training dataset, and performs repeated cross-validation on the candidate features based on the validation dataset, including: S3121, based on the training dataset, calculates the mutual information, permutation importance or sample-level contribution between candidate features and the performance to be tested, and uses the calculation results as statistical correlation indicators.

[0104] Mutual information measures the degree of interdependence between candidate features and the performance being tested. High mutual information indicates a strong statistical correlation, and the distribution of candidate feature values ​​correlates with the distribution of performance values. Permutation importance measures the importance of candidate features in predicting the performance. It is determined by observing the decline in machine learning model prediction performance after changing the order of candidate feature values ​​or shuffling their distribution. A significant decrease in model prediction performance after shuffling a candidate feature indicates its high importance to the prediction result. Sample-level contribution calculates the contribution of candidate features to the prediction result of a single historical sample, reflecting the distribution of the contribution across different samples. Using one or more of mutual information, permutation importance, or sample-level contribution as statistical correlation indicators allows for evaluation of the correlation between candidate features and the performance being tested from different perspectives, avoiding biases that may arise from a single evaluation method.

[0105] S3122, based on the validation dataset, performs repeated cross-validation on candidate features, records whether a candidate feature is selected in each cross-validation, and records the correlation direction between the candidate feature and the performance to be tested when the candidate feature is selected.

[0106] Repeated cross-validation involves splitting the training and validation datasets multiple times, selecting candidate features in each split, and recording the selected features in each split. The purpose of recording whether a candidate feature is selected is to statistically analyze the stability of its selection under different data splitting conditions. If a candidate feature is selected in multiple cross-validations, it indicates a relatively stable correlation between it and the performance being tested. If a candidate feature is selected only in some cross-validations, it suggests that the correlation between it and the performance being tested may be affected by the data splitting method. When a candidate feature is selected, the direction of the correlation between the candidate feature and the performance being tested is recorded. The correlation direction is either positive or negative. A positive correlation indicates that the predicted performance value increases as the candidate feature value increases, while a negative correlation indicates that the predicted performance value decreases as the candidate feature value increases. The purpose of recording the correlation direction is to evaluate the consistency of the correlation direction of candidate features under different data partitioning conditions. If the correlation direction of a candidate feature remains consistent in multiple cross-validations, it indicates that the correlation direction between it and the performance to be tested is relatively stable. If a candidate feature is positively correlated in some cross-validations but negatively correlated in others, it indicates that its correlation direction is unstable and there may be a risk of spurious correlation.

[0107] S3123, based on the records of multiple cross-validations, calculate the frequency of candidate features being selected and the degree to which the association direction remains consistent in repeated cross-validations.

[0108] The frequency of candidate feature selection is the percentage of times a candidate feature is selected into a subset of candidate features in multiple cross-validations, reflecting the stability of candidate feature selection under different data partitioning conditions. A higher selection frequency indicates more stable selection of the candidate feature under different data partitioning conditions, and a more reliable correlation between it and the performance being tested; a lower selection frequency indicates greater influence of the data partitioning method on the selection of the candidate feature, and a less stable correlation between it and the performance being tested. The degree to which the correlation direction remains consistent in repeated cross-validations is the percentage of times the correlation direction remains the same across multiple cross-validations, reflecting the stability of the candidate feature's correlation direction. A higher degree of consistency indicates a more consistent correlation direction between the candidate feature and the performance being tested under different data partitioning conditions; a lower degree of consistency indicates that the correlation direction may reverse under different data partitioning conditions. By statistically analyzing the frequency of candidate feature selection and the degree of consistency in correlation direction, candidate features can be evaluated from two dimensions: selection stability and directional stability. This avoids retaining spurious features with high statistical correlation but unstable selection or reversed correlation direction under different data partitioning conditions when selecting features solely based on statistical correlation indicators.

[0109] S3124. For the retained candidate features, perform ablation verification on independent validation data. Retain candidate features that reduce the prediction error of the machine learning model or improve the grading metric, and delete candidate features that increase the prediction error or worsen the grading metric. The grading metric is an indicator used to evaluate the accuracy of the machine learning model in classifying the performance of the test. Independent validation data refers to historical formula test data that did not participate in the corresponding screening and verification.

[0110] Ablation testing involves removing a candidate feature while keeping other candidate features unchanged and evaluating the change in the predictive performance of the machine learning model after removal. If removing a candidate feature reduces the prediction error or improves the ranking metric, it indicates that the candidate feature has a negative impact on the prediction results, and retaining it in the effective feature set may reduce the model's predictive performance; therefore, the candidate feature is deleted. Conversely, if removing a candidate feature increases the prediction error or worsens the ranking metric, it indicates that the candidate feature makes a positive contribution to the prediction results, and retaining it in the effective feature set helps improve the model's predictive performance; therefore, the candidate feature is retained. The purpose of performing ablation testing on independent validation data is that, since independent validation data has not participated in the screening and verification process, the evaluation results on it can more realistically reflect the predictive contribution of candidate features to unseen formulas, avoiding inflated evaluation results due to data leakage when performing ablation testing on training or validation datasets. Through ablation testing, all candidate features retained in the effective feature set are proven to have a positive contribution to predictive performance on independent validation data, further improving the reliability of the effective feature set.

[0111] By calculating the mutual information, permutation importance, or sample-level contribution between candidate features and the performance to be tested as statistical correlation indicators, repeated cross-validation is performed on the validation dataset, and the selection of candidate features and the correlation direction between candidate features and the performance to be tested are recorded. The frequency of candidate feature selection and the degree of consistency of correlation direction are statistically analyzed. Ablation validation is performed on independent validation data that did not participate in the corresponding screening and verification for the retained candidate features. Candidate features that reduce prediction error or improve the grade evaluation index are retained. This improves the ability to evaluate the stability of candidate feature selection and correlation direction stability and the ability to verify the prediction contribution of candidate features during the statistical screening process. It solves the problems in the prior art that it is easy to retain unstable or spurious correlation features with reversed correlation direction when selecting features based solely on statistical correlation indicators, and the problem that the evaluation results are inflated when evaluating feature contribution on the training or validation datasets.

[0112] Furthermore, in step S313, a comprehensive screening score is determined based on statistical correlation indicators, the frequency of selection, and the degree of consistency in the direction of correlation, including: S3131 defines the statistical correlation index as the predictive contribution item, the selected frequency as the selection stability item, the degree of consistency in the correlation direction as the directional stability item, the consistency result of the coating performance mechanism obtained by performing pre-set coating performance mechanism rule verification on the candidate features as the coating performance mechanism consistency item, and the degree of redundancy between the candidate features and the selected candidate features as the redundancy item. The coating performance mechanism consistency item is a scoring item used to calculate the comprehensive screening score, and the coating performance mechanism consistency result is the degree of consistency between the candidate features and the pre-set coating performance mechanism rules.

[0113] The purpose of defining statistical correlation indicators, selection frequency, consistency of correlation direction, consistency of coating performance mechanism, and redundancy as the predictive contribution, selection stability, directional stability, coating performance mechanism consistency, and redundancy items, respectively, is to ensure that the comprehensive screening score can simultaneously reflect the performance of candidate features across multiple dimensions. The predictive contribution reflects the degree of correlation or importance between the candidate feature and the performance to be tested; the selection stability reflects the selection stability of the candidate feature under different data partitioning conditions; the directional stability reflects the stability of the correlation direction of the candidate feature; the coating performance mechanism consistency reflects the degree of consistency between the candidate feature and the pre-defined coating performance mechanism rules; and the redundancy reflects the degree of redundancy between the candidate feature and the already selected candidate features. Including the coating performance mechanism consistency item in the comprehensive screening score aims to ensure that the comprehensive screening score considers not only the statistical correlation and stability of candidate features but also the consistency between candidate features and the mechanism rules in the coating field, avoiding the retention of candidate features inconsistent with the coating performance formation mechanism solely based on statistical correlation. The purpose of incorporating the redundancy item into the comprehensive screening score is to enable the comprehensive screening score to evaluate the degree of redundancy between candidate features and selected candidate features, avoiding the retention of candidate features that are highly redundant with the selected candidate features. By incorporating the above five scoring items into the comprehensive screening score, the comprehensive screening score can comprehensively evaluate candidate features from five dimensions: predictive contribution, selection stability, directional stability, consistency of coating performance mechanism, and redundancy.

[0114] S3132, the prediction contribution item, selection stability item, directional stability item, coating performance mechanism consistency item and redundancy item are weighted and summed according to the preset weighting coefficients to obtain the comprehensive screening score of the candidate features.

[0115] The preset weighting coefficients are pre-defined non-negative coefficients corresponding to the prediction contribution, selection stability, directional stability, coating performance mechanism consistency, and redundancy items, respectively. These preset weighting coefficients can be set based on factors such as the characteristics of the performance to be tested, the scale and quality of historical formulation test data, and the reliability of mechanistic rules in the coating field. The purpose of weighted summation of the prediction contribution, selection stability, directional stability, coating performance mechanism consistency, and redundancy items is to ensure that the comprehensive screening score is combined according to the importance of each scoring item, avoiding the dilution of the effect of important scoring items due to simple addition of scoring items. Through weighted summation, the comprehensive screening score comprehensively reflects the performance of candidate features in the five dimensions of prediction contribution, selection stability, directional stability, coating performance mechanism consistency, and redundancy, providing a quantitative basis for subsequent retention or deletion of candidate features.

[0116] S3133, compare the comprehensive screening score with the preset admission threshold, and compare the selected frequency with the preset stability threshold. Retain candidate features that simultaneously meet the preset admission threshold and the preset stability threshold, and delete candidate features that do not meet the preset admission threshold or the preset stability threshold.

[0117] A preset admission threshold is used to determine the overall screening score, and a preset stability threshold is used to determine the frequency of candidate feature selection. Candidate features that simultaneously meet both the preset admission and stability thresholds are retained, indicating that the candidate feature satisfies both the overall screening score and selection stability requirements. Candidate features that do not meet either the preset admission or stability thresholds are deleted, indicating that the candidate feature is deficient in either the overall screening score or selection stability. The purpose of setting these two judgment conditions is to avoid retaining candidate features with high overall screening scores but unstable selection under different data partitioning conditions when selecting features solely based on overall screening scores, and to avoid retaining candidate features with high selection stability but low overall screening scores when selecting features solely based on selection stability. Through this dual judgment, the candidate features retained in the candidate feature subset have both high overall screening scores and high selection stability, improving the reliability of the candidate feature subset.

[0118] By defining statistical correlation indicators, the frequency of selection, the degree of consistency of correlation direction, the consistency of coating performance mechanism, and redundancy as prediction contribution, selection stability, directional stability, coating performance mechanism consistency, and redundancy, respectively, and by weighting and summing the above five scoring items according to preset weighting coefficients, a comprehensive screening score is obtained. The comprehensive screening score and the frequency of selection are compared with preset admission threshold and preset stability threshold, respectively, and candidate features that meet both thresholds are retained. This improves the comprehensiveness of the comprehensive screening score in evaluating candidate features and the reliability of candidate feature subsets. It solves the problems in the prior art where the comprehensive screening score only considers statistical correlation and selection stability, does not consider the consistency between candidate features and coating performance formation mechanism, and the redundancy between candidate features, and easily retains candidate features that do not meet the multi-dimensional requirements when selecting candidate features based on a single threshold.

[0119] Furthermore, in step S3, the candidate features in the performance feature candidate pool are constrained and validated based on historical formula test data, including: S321. For the candidate features retained after statistical screening, a mechanism consistency check is performed based on the functional category of the raw materials and the reaction relationship. Candidate features that are inconsistent with the preset coating performance mechanism rules are deleted. The preset coating performance mechanism rules are the allowed correlations between candidate features and the performance to be tested, which are predetermined based on the coating performance formation mechanism.

[0120] Although the candidate features retained after statistical screening meet the requirements in terms of statistical correlation and selection stability, their correlation with the test performance may not conform to the coating performance formation mechanism. Therefore, further mechanism consistency verification is required. The basis for mechanism consistency verification includes the functional categories and reaction relationships of raw materials. The functional categories of raw materials reflect the functions they play in the coating formulation, such as film-forming resins, curing agents, pigments, fillers, solvents, matting agents, adhesion promoters, and rust-inhibiting pigments. The reaction relationships reflect the chemical or physical interactions between raw materials and other raw materials during coating curing or film formation. Pre-defined coating performance mechanism rules pre-determine the permissible correlations between candidate features and the test performance based on the coating performance formation mechanism. These rules specify which combinations of raw material functional categories and reaction relationships are reasonable for correlation with the test performance. When the correlation between the raw material functional category and reaction relationship corresponding to a candidate feature and the test performance does not conform to the pre-defined coating performance mechanism rules, the candidate feature is deemed inconsistent with the formation mechanism of the test performance and is deleted. For example, regarding gloss performance, if a candidate feature corresponds to a raw material belonging to the matting agent functional category and its correlation with gloss is positive, then it is inconsistent with the mechanism by which matting agents reduce gloss in coatings, and this candidate feature should be deleted. Mechanism consistency verification can remove candidate features that are inconsistent with the mechanism of coating performance formation after statistical screening, avoiding the retention of spurious correlation features based solely on statistical correlation.

[0121] S322, for the candidate features retained after the mechanism consistency verification, based on whether the dimension of the candidate feature belongs to the set of allowed dimensions corresponding to the performance to be tested, and whether the value range of the candidate feature is within the preset value range, delete the candidate features whose dimension does not belong to the set of allowed dimensions or whose value range exceeds the preset value range.

[0122] Although the candidate features retained after mechanism consistency verification conform to the formation mechanism of coating performance in relation to the test performance, their dimensions and value ranges may not conform to the physical meaning of the test performance. Therefore, further dimension consistency verification and value range verification are required. The permissible dimension set corresponding to the test performance is a pre-determined set of dimensions allowed for candidate features based on the physical meaning of the test performance. It specifies which dimensions of candidate features can be used to predict the test performance. For example, for test performances measured in time, such as activation period, surface drying time, complete drying time, and salt spray resistance time, the permissible dimension set includes the dimension of time; for test performances measured in mass, such as hiding power, the permissible dimension set includes the dimension of mass per unit area. If the dimension of a candidate feature does not belong to the permissible dimension set corresponding to the test performance, it indicates that the candidate feature is inconsistent with the test performance in a physical sense, and it is deleted. The preset value range is a pre-determined range of values ​​allowed for candidate features based on the physical meaning of the test performance and historical formula test data. It specifies the reasonable range of values ​​for candidate features. If the value range of a candidate feature exceeds the preset value range, it indicates that the candidate feature may have data anomalies or exceed the reasonable range of the coating formulation, and it should be deleted. By verifying dimensional consistency and value range, candidate features whose dimensions or value ranges are inconsistent with the physical meaning of the performance to be measured can be deleted, thus preventing candidate features with inconsistent dimensions or abnormal value ranges from entering the machine learning model.

[0123] S323, for the candidate features retained after dimensional consistency verification, perform influence direction verification according to the preset monotonicity rules, and delete candidate features whose influence direction is inconsistent with the preset monotonicity rules.

[0124] Although the candidate features retained after dimensional consistency verification meet the requirements in terms of dimensions and value range, the direction of their influence on the test performance may not conform to the coating performance formation mechanism. Therefore, further influence direction verification is required. The preset monotonicity rule is a pre-determined, permissible direction of influence between candidate features and the test performance based on the coating performance formation mechanism. It specifies whether the predicted value of the test performance should increase or decrease when the value of the candidate feature changes. For example, for gloss performance, the absolute mass fraction of matting agent should have a negative correlation with gloss, meaning that the predicted gloss value decreases when the absolute mass fraction of matting agent increases. For adhesion performance, the predicted adhesion value should increase when the reaction equivalence ratio is close to the theoretical stoichiometric point, and decrease when the reaction equivalence ratio deviates significantly from the theoretical stoichiometric point. The process of influence direction verification involves determining the correlation direction between candidate features and the performance to be measured. This correlation direction is then compared with a preset monotonicity rule. If the correlation direction is inconsistent with the preset monotonicity rule, it indicates that the influence direction between the candidate feature and the performance to be measured does not conform to the coating performance formation mechanism, and the feature is deleted. If the correlation direction is consistent with the preset monotonicity rule, the candidate feature is retained, and its correlation direction is recorded as the expected influence direction of the candidate feature. Through influence direction verification, candidate features whose statistical correlation direction is inconsistent with the coating performance formation mechanism can be deleted, avoiding the retention of spurious correlation features with reversed correlation directions based solely on statistical correlation.

[0125] S324. For the candidate features retained after influence direction verification, perform collinearity checks and ablation verification. Ablation verification is a final confirmatory ablation verification performed on the candidate features retained in the aforementioned steps of constraint verification. Candidate features that reduce the prediction error of the machine learning model or improve the grade evaluation index on independent validation data are retained. The finally retained candidate features are used as a subset of candidate features after constraint verification. Collinearity checks involve calculating the correlation coefficient between candidate features and deleting candidate features with high redundancy from the retained candidate features when the correlation coefficient exceeds a preset correlation coefficient threshold. Independent validation data refers to historical formula measured data that did not participate in the corresponding screening and verification.

[0126] The purpose of collinearity checking is to identify whether there is a high correlation between candidate features retained after influence direction verification. When the correlation coefficient between candidate features is higher than a preset correlation coefficient threshold, it indicates that there is high redundancy among the candidate features. Retaining all candidate features may lead to multicollinearity among the input features of the machine learning model, affecting the stability of model parameter estimation and the interpretability of prediction results. In this case, candidate features with high redundancy with the retained candidate features are deleted, while candidate features with low redundancy are retained, so that the candidate features in the effective feature set maintain low redundancy. Ablation verification is a final confirmatory ablation verification performed on the candidate features retained after the aforementioned steps in constraint verification. The difference between it and the ablation verification performed in the statistical screening stage is that the ablation verification in the statistical screening stage is used to select candidate features that have a positive contribution to prediction performance from the candidate features retained in the statistical screening, while the ablation verification in the constraint verification stage is used to finally confirm the candidate features retained after mechanism consistency verification, dimensional consistency verification, influence direction verification, and collinearity checking, and to confirm whether the above candidate features reduce the prediction error of the machine learning model or improve the rating index on independent validation data. Independent validation data consists of historical formulation test data that did not participate in the corresponding screening and validation. These data were not subjected to statistical screening, mechanism consistency verification, dimensional consistency verification, influence direction verification, or collinearity checks. Therefore, the evaluation results on these data more accurately reflect the predictive contribution of candidate features to unseen formulations. Through collinearity checks and final confirmatory ablation validation, the redundancy among the ultimately retained candidate features is low, and all features have been proven to contribute positively to predictive performance on independent validation data, further improving the reliability of the effective feature set.

[0127] By performing mechanism consistency verification based on the functional category of raw materials and reaction relationship, and performing dimensional consistency verification and value range verification based on whether the dimensions of candidate features belong to the allowable dimension set corresponding to the test performance and whether the value range of candidate features is within the preset value range, and performing influence direction verification based on preset monotonicity rules, and performing collinearity check and final confirmatory ablation verification on the candidate features retained after the above verification, the candidate features in the effective feature set simultaneously meet the requirements of statistical correlation, selection stability, directional stability, consistency of coating performance mechanism, dimensional consistency, reasonable value range and low redundancy. This solves the problems in the prior art where candidate features retained only by statistical screening are inconsistent with the coating performance formation mechanism, the dimensions or value range do not match the physical meaning of the test performance, the correlation direction contradicts the mechanism rules, and the high redundancy among candidate features affects the stability of model parameter estimation.

[0128] Furthermore, step S321 performs a mechanism consistency check based on the functional categories of the raw materials and the reaction relationship, including: S3211, Determine the functional category of the raw material corresponding to the candidate feature in the preset raw material functional category system.

[0129] Candidate features may originate directly from specific raw materials in the formulation, such as the proportion of a particular raw material in the formulation composition characteristics, or the absolute mass fraction of a particular raw material in the performance-specific mechanism characteristics. For such candidate features, it is necessary to determine the functional category of the corresponding raw material within a pre-defined raw material functional category system. This pre-defined system categorizes raw materials according to their functions within the coating formulation, classifying them into several categories such as film-forming resins, curing agents, pigments, fillers, solvents, matting agents, dispersants, leveling agents, defoamers, thixotropic agents, adhesion promoters, and rust-inhibiting pigments. The purpose of determining the functional category is to group specific raw material names down to the functional level, allowing subsequent mechanism consistency verification to be based on the functional category, rather than establishing rules for each specific raw material. For example, regardless of the specific brand of matting agent, its functional category is classified as matting agent, and its mechanistic relationship with gloss performance is common. By determining the functional category, the processing of candidate features is elevated from the specific raw material level to the functional category level, providing a basis for subsequent judgments on permissible combinations and compatibility.

[0130] S3212, determine the reaction relationship of the raw materials corresponding to the candidate features in the coating formulation to be tested.

[0131] Reaction relationships refer to the chemical or physical interactions between raw materials and other raw materials during the curing or film-forming process of coatings. For film-forming resins and curing agents, the reaction relationship is usually a chemical cross-linking reaction, such as the ring-opening reaction between epoxy groups in epoxy resins and active hydrogen in curing agents, or the addition reaction between isocyanate groups and hydroxyl groups in polyurethane systems. For pigments and fillers, the reaction relationship is usually a physical filling and stacking effect, affecting the density and barrier properties of the coating. For additives, the reaction relationship may be a physical effect such as interfacial adsorption, surface migration, or rheological regulation. The purpose of determining the reaction relationship is to clarify the mechanism by which the raw materials corresponding to the candidate characteristics function in the coating formulation under test, thereby determining whether the combination of the functional category of the raw material and the reaction relationship is consistent with the formation mechanism of the test performance. For example, for adhesion performance, the combination of the functional category of the film-forming resin and the chemical cross-linking reaction relationship may have a positive effect on adhesion; for gloss performance, the combination of the functional category of the matting agent and the physical roughening reaction relationship may have a negative effect on gloss. By determining the reaction relationship, the mechanism consistency verification can comprehensively judge whether the correlation between candidate features and the performance to be tested is reasonable from two dimensions: functional category and reaction relationship.

[0132] S3213, based on the pre-set coating performance mechanism rules, determine whether the functional category and reaction relationship belong to the permissible combination related to the performance to be tested.

[0133] The pre-defined rules for coating performance mechanisms are permissible correlations between candidate features and the properties to be tested, predetermined based on the coating performance formation mechanism. These rules specify which combinations of raw material functional categories and reaction relationships are reasonable in relation to the properties to be tested. Permissible combinations are those specified in the pre-defined rules for coating performance mechanisms that relate to the properties to be tested. For example, for gloss performance, the combination of matting agent functional categories and physical roughening reaction relationships is a permissible combination, and its correlation with gloss should be negative; similarly, the combination of film-forming resin functional categories and chemical crosslinking reaction relationships is a permissible combination, and its correlation with gloss should be positive or neutral. The purpose of determining whether functional categories and reaction relationships belong to permissible combinations is to examine the reasonableness of the correlation between candidate features and the properties to be tested from the perspective of the coating performance formation mechanism. If the functional category and reaction relationship of a candidate feature do not belong to a permissible combination, it indicates that the correlation between the candidate feature and the properties to be tested does not conform to the coating performance formation mechanism and may be a spurious correlation feature retained due to data randomness during the statistical screening process. Based on the above judgment, candidate features that are inconsistent with the formation mechanism of the performance to be tested can be identified.

[0134] S3214: If the functional category and response relationship do not belong to the allowed combinations, then delete the candidate feature. If the functional category and response relationship belong to the allowed combinations, then retain the candidate feature.

[0135] Based on the judgment result of S3213, a deletion or retention operation is performed. When the functional category and reaction relationship do not belong to the allowed combination, it indicates that the mechanism by which the raw material corresponding to the candidate feature functions in the coating formulation under test is inconsistent with the formation mechanism of the performance under test. Retaining it in the effective feature set may cause the machine learning model to learn an incorrect mapping relationship, so the candidate feature is deleted. When the functional category and reaction relationship belong to the allowed combination, it indicates that the mechanism by which the raw material corresponding to the candidate feature functions in the coating formulation under test is consistent with the formation mechanism of the performance under test. Retaining it in the effective feature set helps the machine learning model to make predictions based on reasonable mechanism relationships, so the candidate feature is retained. Through the above deletion or retention operations, the candidate features retained after mechanism consistency verification all meet the requirement that the functional category and reaction relationship are consistent with the formation mechanism of the performance under test, avoiding the retention of pseudo-correlation features that are inconsistent with the formation mechanism of coating performance based solely on statistical correlation.

[0136] S3215, based on a pre-set raw material compatibility rule base, determine whether there are any prohibited combinations between the functional categories and reaction relationships of the raw materials corresponding to the candidate features and the functional categories and reaction relationships of other raw materials in the coating formulation to be tested. If prohibited combinations exist, delete all candidate features involved in the prohibited combinations.

[0137] The raw material compatibility rule base is a pre-defined rule base that records prohibited combinations of raw materials. It is established based on well-known knowledge of raw material compatibility in the coatings industry. For example, some curing agents cannot be used with certain resins, some additives may react adversely with certain pigments, and some solvents have poor compatibility with certain film-forming resins. Unlike S3213, which only judges whether the candidate feature's own functional category and reaction relationship belong to an allowed combination, S3215 further judges whether there are prohibited combinations between the raw material corresponding to the candidate feature and other raw materials in the coating formulation to be tested. If prohibited combinations exist, it indicates that there may be compatibility issues between the raw material corresponding to the candidate feature and other raw materials in the coating formulation to be tested. Retaining this candidate feature may lead the machine learning model to learn unreliable mapping relationships; therefore, all candidate features involved in prohibited combinations are deleted. Through the above compatibility judgment, the candidate features retained after mechanism consistency verification not only meet the requirement that their own functional category and reaction relationship are consistent with the formation mechanism of the tested performance, but also meet the requirement of good compatibility with other raw materials in the coating formulation to be tested, further improving the reliability of the effective feature set.

[0138] By determining the functional category of the raw material corresponding to the candidate feature in the pre-set raw material functional category system, the reaction relationship it participates in is determined. Based on the pre-set coating performance mechanism rules, it is judged whether the functional category and reaction relationship belong to the permissible combination related to the performance to be tested. If it does not belong to the permissible combination, the candidate feature is deleted; if it belongs to the permissible combination, the candidate feature is retained. Based on the pre-set raw material compatibility rule library, it is judged whether there is a prohibited combination between the raw material corresponding to the candidate feature and other raw materials in the coating formulation to be tested. If there is, all candidate features involved in the prohibited combination are deleted. This allows the mechanism consistency verification to comprehensively judge whether the correlation between the candidate feature and the performance to be tested is reasonable from four levels: functional category, reaction relationship, permissible combination, and compatibility. This improves the conformity of the coating performance formation mechanism and the ability to prevent raw material compatibility problems during the effective feature set screening process. It solves the problem that the existing technology, which only retains candidate features based on statistical correlation, is prone to introducing pseudo-correlation features that are inconsistent with the coating performance formation mechanism or have raw material compatibility problems.

[0139] Further, step S323 involves performing an influence direction check based on preset monotonicity rules, including: S3231, determine the correlation direction between candidate features and the performance to be tested.

[0140] For candidate features retained after dimensional consistency verification, it is necessary to determine their correlation direction with the performance to be tested. The correlation direction is either a positive or negative correlation between the candidate feature and the performance to be tested. A positive correlation indicates that the predicted value of the performance to be tested increases as the value of the candidate feature increases, while a negative correlation indicates that the predicted value of the performance to be tested decreases as the value of the candidate feature increases. The correlation direction can be determined based on the statistical relationship between the candidate feature and the measured value of the performance to be tested in historical formulation test data. For example, the correlation direction can be determined by calculating the sign of the correlation coefficient between the candidate feature and the measured value of the performance to be tested, or it can be determined based on the contribution direction of the candidate feature by the machine learning model. Regardless of the method used, the correlation direction characterizes the trend of the predicted value of the performance to be tested when the value of the candidate feature changes. The purpose of determining the correlation direction is to provide a basis for subsequent comparison with preset monotonicity rules and to determine whether the correlation direction between the candidate feature and the performance to be tested conforms to the coating performance formation mechanism.

[0141] S3232, read the preset monotonicity rule corresponding to the performance under test.

[0142] Preset monotonicity rules are pre-determined, based on the coating performance formation mechanism, permissible influence directions between candidate features and the test performance. They specify whether the predicted value of the test performance should increase or decrease when the value of the candidate feature changes. Preset monotonicity rules are set separately for each test performance, with different rules corresponding to different test performances. For example, for gloss performance, the absolute mass fraction of matting agent should have a negative correlation with gloss, meaning that the predicted gloss value decreases when the absolute mass fraction of matting agent increases; for adhesion performance, the predicted adhesion value should increase when the reaction equivalence ratio is close to the theoretical stoichiometric point, and decrease when the reaction equivalence ratio deviates significantly from the theoretical stoichiometric point; for hardness performance, the predicted hardness value should increase when the contribution of rigid components increases. These preset monotonicity rules are established based on well-known performance formation mechanisms in the coating field. They do not rely on historical formulation test data but rather serve as prior knowledge to constrain the correlation direction between candidate features and the test performance. The purpose of reading the preset monotonicity rules corresponding to the test performance is to provide a comparison benchmark for subsequently judging whether the correlation direction of candidate features is consistent with the coating performance formation mechanism.

[0143] S3233, determine whether the association direction is consistent with the preset monotonicity rule.

[0144] The correlation direction between the candidate features determined in S3231 and the performance to be tested is compared with the preset monotonicity rule corresponding to the performance to be tested read in S3232. If the correlation direction of the candidate feature is the same as the influence direction specified by the preset monotonicity rule, it is determined that the correlation direction is consistent with the preset monotonicity rule; if the correlation direction of the candidate feature is opposite to the influence direction specified by the preset monotonicity rule, it is determined that the correlation direction is inconsistent with the preset monotonicity rule. For example, if the correlation direction between a candidate feature and gloss performance is negative, and the preset monotonicity rule corresponding to gloss performance stipulates that the candidate feature and gloss should be negatively correlated, then they are determined to be consistent; if the correlation direction between the candidate feature and gloss performance is positive, then they are determined to be inconsistent. The purpose of determining whether the correlation direction is consistent with the preset monotonicity rule is to identify candidate features whose statistical correlation direction contradicts the formation mechanism of coating performance. Such candidate features may be spurious correlation features retained due to data randomness during the statistical screening process.

[0145] S3234. If the correlation direction is inconsistent with the preset monotonicity rule, the candidate feature is deleted. If the correlation direction is consistent with the preset monotonicity rule, the candidate feature is retained, and the correlation direction is recorded as the expected influence direction of the candidate feature. The feature identifier of the candidate feature and its corresponding expected influence direction are also recorded. The expected influence direction is the allowed positive or negative correlation between the candidate feature and the performance to be tested.

[0146] When the correlation direction is inconsistent with the preset monotonicity rule, it indicates that the correlation direction between the candidate feature and the performance to be tested does not conform to the coating performance formation mechanism. Retaining it in the effective feature set may lead the machine learning model to learn an incorrect mapping relationship; therefore, the candidate feature is deleted. When the correlation direction is consistent with the preset monotonicity rule, it indicates that the correlation direction between the candidate feature and the performance to be tested conforms to the coating performance formation mechanism. Retaining it in the effective feature set helps the machine learning model make predictions based on reasonable mechanistic relationships; therefore, the candidate feature is retained, and the correlation direction is recorded as the expected influence direction of the candidate feature. The purpose of recording the feature identifier of the candidate feature and its corresponding expected influence direction is to make the influence direction of the candidate feature traceable and reproducible, providing a basis for the interpretation of subsequent machine learning model prediction results and the traceability of the feature selection process. Through the above deletion or retention operations, the candidate features retained after influence direction verification all meet the requirement that the correlation direction is consistent with the preset monotonicity rule, avoiding the retention of pseudo-correlation features that contradict the coating performance formation mechanism based solely on statistical correlation.

[0147] By determining the correlation direction between candidate features and the performance to be tested, reading the preset monotonicity rule corresponding to the performance to be tested, and judging whether the correlation direction is consistent with the preset monotonicity rule, the candidate feature is deleted when inconsistent and retained when consistent, and the correlation direction is recorded as the expected influence direction of the candidate feature. At the same time, the feature identifier of the candidate feature and its corresponding expected influence direction are recorded, so that the influence direction verification can identify and eliminate pseudo-correlation features that contradict the statistical correlation direction and the formation mechanism of coating performance. Candidate features whose correlation direction is consistent with the formation mechanism of coating performance are retained and their influence direction is traceable and reproducible, which improves the consistency and interpretability of the mechanism of the effective feature set. It solves the problem that the existing technology of retaining candidate features based solely on statistical correlation is prone to introducing pseudo-correlation features that contradict the formation mechanism of coating performance.

[0148] S4. Based on the effective feature set, the machine learning model corresponding to the performance to be tested is invoked to predict the performance of the coating formulation to be tested, and the performance prediction result of the coating formulation to be tested is obtained.

[0149] The effective feature set is determined after statistical screening and constraint verification. It contains fewer candidate features than the performance feature candidate pool, and each candidate feature passes statistical correlation tests and consistency tests with coating mechanisms. The machine learning model is invoked according to the target paint type and the performance index to be predicted. For continuous numerical performance indicators such as salt spray resistance time, activation period, surface drying time, hard drying time, thick coating properties, hiding power, gloss, and pull-out adhesion, a regression model is used. For ordered grade performance indicators such as cross-cut adhesion level, pencil hardness level, chalking level, and discoloration level, an ordinal regression model or ordered classification model that utilizes the grade order is used, and the output is limited or projected to a preset set of legal grades. In one implementation, the legal grades are mapped to increasing ordinal numbers before training the regression model, and then the predicted ordinal numbers are projected to the nearest legal grade. The input to the machine learning model includes the effective feature set and test conditions, and its output is the predicted value or predicted grade of the performance to be tested. In one implementation, historical samples are first grouped according to basic formula series, raw material batches, preparation or test batches, and collection time. Then, they are divided into training, validation, and test sets at approximately 70%, 15%, and 15% respectively. The same formula number, similar variants of the same basic formula, the same batch, or repeated test records must be assigned to the same data subset. When there is a clear time sequence, earlier samples are prioritized for training and validation, while later samples are tested independently to avoid leakage of near-duplicate sample and batch information. Example initial parameters for the regression model include 300 trees, a maximum tree depth of 4, a learning rate of 0.05, a sample sampling ratio of 80%, a feature sampling ratio of 80%, and a random seed of 42. For the regression model, the normalized mean absolute error (NAR) is obtained by dividing the mean absolute error of the test set by the difference between the 99th percentile and the 1st percentile of the corresponding performance index in the training samples. The regression model is considered to have passed the test set evaluation when the normalized mean absolute error is not higher than 15% and the coefficient of determination is not lower than 0.70. For ordered hierarchical models, the mean absolute ordinal error, accuracy within adjacent levels, and weighted Kappa coefficient are used for evaluation, with accuracy and macro-average F1 score serving as supplementary indicators. Each threshold is pre-calibrated during the validation phase based on the repeatability of the corresponding experiment and the enterprise's allowable level deviation, and is fixed before independent testing. Models that fail the test set evaluation are not used to output formal baseline predictions and require readjustment of training features, model parameters, or training samples.

[0150] Furthermore, after using a machine learning model to predict performance based on the effective feature set, the process also includes historical similarity formula retrieval. All raw materials in the current and historical formulas are aligned using a unified raw material identifier, with the proportion of missing raw materials set to 0. The compositional similarity between the current formula and the j-th historical formula is equal to 1 minus half the sum of the absolute differences in the absolute mass fractions of all raw materials. All absolute mass fractions in the current and historical formulas are normalized to a sum equal to 1. When rounding results in a similarity value less than 0, the similarity is truncated to 0; when it is greater than 1, the similarity is truncated to 1. Historical formulas and the formula to be tested should use the same performance testing methods. Categorical test conditions such as substrate type, substrate treatment method, and light source type should be consistent. Numerical test conditions such as film thickness, curing temperature, curing time, ambient temperature, and ambient humidity are judged for matching according to preset allowable deviations. In one implementation, the relative deviation of film thickness does not exceed 10%, the absolute deviation of curing temperature and ambient temperature does not exceed 2 degrees Celsius, the absolute deviation of relative humidity does not exceed 5 percentage points, and the relative deviation of curing time does not exceed 10%. Historical formulations exceeding the allowable deviation are not used for historical data estimation. The system selects only the top 5 historical formulations with the highest compositional similarity from historical samples with the same paint type and testing method, testing conditions that meet the allowable deviation requirements, and compositional similarity not lower than the preset lower limit. In one implementation, the similarity lower limit is 0.80 and can be calibrated separately according to performance indicators. When there are fewer than 5 historical formulations reaching the similarity lower limit, the actual number of historical formulations that can be obtained is used. When there are no historical formulations reaching the lower limit, historical data estimation is not calculated, the nearest neighbor similarity is recorded as missing, and a mark indicating insufficient historical reference data is output. For continuous numerical performance indicators, the estimated historical data value is equal to the sum of the products of the similarity of each historical formula composition and the corresponding measured value, divided by the sum of the similarity of each historical formula composition. For ordered hierarchical performance indicators, a weighted voting method based on the similarity of historical formulas is used to calculate the historical weighted probability of each legal level, without using the arithmetic mean of the level ordinal numbers as the historical data estimation result.

[0151] Furthermore, after obtaining the basic machine learning predictions and historical data estimates, the system also includes performance distribution out-of-specification identification and prediction reliability grading. For each performance indicator, the system determines whether the formula to be tested exceeds the training data coverage of the performance model, and the determination includes single feature coverage checking, joint feature distribution density estimation, and model prediction uncertainty assessment. The corresponding performance will be marked as out-of-distribution when at least one of the following conditions is met: The formula to be tested contains raw materials not present in the training samples of the corresponding performance model, and the functional category of the raw material belongs to the relevant raw material category of the performance model; the absolute mass fraction of the unseen raw material reaches a preset trigger threshold; the out-of-distribution condition is triggered when the absolute mass fraction of the unseen raw material is not less than 0.1%; if it is less than 0.1%, a trace unseen raw material marker is set, but the prediction reliability level is not set to low based solely on this; the absolute mass fraction of the known raw materials in the input feature set of the corresponding performance model exceeds the training coverage range corresponding to the raw material; any mechanistic feature in the corresponding performance feature vector exceeds the training coverage range corresponding to the feature, where the training coverage range is determined by the interval from the 1st percentile to the 99th percentile of the training samples or by effective upper and lower limits confirmed by engineers; the test method or test conditions are not covered by the training samples; and the nearest neighbor... The similarity of historical formulas is less than 0.80; the formula to be tested is located in a low-density region in the joint feature space of the corresponding performance. First, the continuous features are robustly standardized using the median and interquartile range of the training data. Then, at least one of the following is used to calculate the joint distribution anomaly: shrinking covariance Mahalanobis distance, k-nearest neighbor distance, local outlier factor, isolated forest, or autoencoder reconstruction error. The joint distribution anomaly is then converted into anomaly quantile values ​​of 0 to 1 according to the empirical distribution of the validation set. When the prediction uncertainty of the machine learning model for the formula to be tested reaches the trigger threshold, for continuous numerical performance, a model set is formed by different random seeds, training sample bootstrapping, or different model structures. The normalized uncertainty is calculated using the set prediction standard deviation, prediction interval width, or conformal prediction interval width. For ordered hierarchical performance, the normalized uncertainty is calculated using the prediction probability entropy, the complement of the highest level probability, or the hierarchical divergence between model sets. The system further calculates the comprehensive out-of-distribution score, which is equal to the sum of the products of each weight multiplied by the joint distribution anomaly, model uncertainty, normalized sum of single feature out-of-bounds magnitude, unseen related raw material indicators, and test condition-uncovered indicators. Each weight is non-negative and the sum is 1. The weights and grading thresholds are calibrated and recorded using samples within the known training range on the validation set and simulated extrapolated samples. Even if no single variable hard threshold is triggered, when the comprehensive out-of-distribution score reaches the out-of-distribution threshold, the performance is still marked as out-of-distribution.

[0152] Furthermore, the prediction reliability levels are categorized as high, medium, and low. A high prediction reliability level is achieved when no single feature is triggered, no out-of-distribution conditions for raw materials or testing conditions are observed, the joint distribution anomaly and model uncertainty are both below the corresponding attention threshold, the overall out-of-distribution score is below the medium reliability threshold, and the nearest neighbor historical formulation similarity is not less than 0.90. A medium prediction reliability level is achieved when no related raw materials or testing conditions are triggered, the nearest neighbor similarity is less than 0.90 but not less than 0.80, or only one of the raw material proportion exceeding the limit or the mechanism feature exceeding the limit is triggered and the relative exceedance does not exceed 10%, or the joint distribution anomaly, model uncertainty, or overall out-of-distribution score is between the corresponding attention threshold and the out-of-distribution threshold. If the tested formulation triggers conditions such as "no relevant raw materials," "test methods," or "test conditions not covered," and simultaneously triggers two or more out-of-distribution conditions for a single feature, or if the relative magnitude of any raw material proportion or mechanism feature exceeding the training range boundary exceeds 10%, the nearest neighbor similarity is below 0.80, and the joint distribution anomaly or model uncertainty reaches its respective out-of-distribution threshold, or the comprehensive out-of-distribution score reaches the comprehensive out-of-distribution threshold, the prediction reliability level is low. If there is a marker indicating insufficient historical reference data, it is not directly treated as having a nearest neighbor similarity below 0.80. If the tested formulation does not trigger other out-of-distribution conditions for single features or test conditions, and the joint distribution anomaly, model uncertainty, and comprehensive out-of-distribution score are all below the corresponding out-of-distribution threshold, the prediction reliability level is set to medium at its highest. If at least one of the following is triggered simultaneously: no raw materials, feature exceeding limits, test conditions not covered, joint distribution low density, or high model uncertainty, the prediction reliability level is set to low. After determining the initial prediction reliability level, the missing key feature markers are further checked. When at least one key feature is handled by a validated missing value handling mechanism, the initial prediction reliability level is downgraded by one level, i.e., high is adjusted to medium, medium is adjusted to low, and the initial level remains low.

[0153] Furthermore, for the test formulation with high or medium reliability, machine learning confidence and historical data confidence are calculated separately. In one implementation, the machine learning confidence equals the product of the normalized evaluation score of the corresponding model on the independent test set, 1 minus model uncertainty, 1 minus joint distribution anomaly, and single feature coverage; the historical data confidence equals the product of the independent validation score of the historical estimation method, the number of effective historical samples divided by the sum of the number of effective historical samples and the smoothing constant, the average similarity of nearest neighbors, 1 minus the normalized result of the dispersion of the nearest neighbor measured values, and the degree of matching of the test conditions; the number of effective historical samples equals the effective sample statistic calculated using the nearest neighbor similarity. All items are converted to the range of 0 to 1. The sample-level weight predicted by machine learning equals the machine learning confidence divided by the sum of the machine learning confidence and the historical data confidence, and the weight estimated by historical data equals 1 minus the sample-level weight predicted by machine learning. The system can set verified upper and lower limits for weights according to high and medium reliability to prevent a single information source from obtaining extreme weights when there are insufficient samples. The confidence score calculation formula, normalization parameters, smoothing constant, and upper and lower weight limits are all fixed during the validation phase and written into the performance configuration file. During inference, they are determined based on the actual density, uncertainty, and nearest neighbor statistics of each test formulation. When either the machine learning confidence score or the historical data confidence score cannot be calculated due to the lack of necessary statistics, it is not replaced by a fixed weight. Instead, the machine learning candidate value and the historical data estimate are output in parallel, and the insufficient basis for dynamic weights is recorded and experimental verification is required. When the sum of the two confidence scores is 0, fusion is not performed.

[0154] Furthermore, for continuous numerical performance metrics, when the prediction reliability level is high or medium, valid historical data estimates exist, and the dynamic weight calculation is based on complete data, the fused prediction value equals the sample-level weight multiplied by the machine learning base prediction value plus 1 minus the sample-level weight multiplied by the historical data estimate. When no valid historical data estimate exists, numerical fusion is not performed, and the machine learning prediction is used as a candidate value. When the prediction reliability level for continuous numerical performance is low and valid historical data estimates exist, a single fused value is not given. Instead, the machine learning base prediction value and the historical data estimate are output side-by-side, forming an experimental verification interval. This interval is not a statistical confidence interval and should not be used to conclude that the performance has met the target. For ordered hierarchical performance metrics, the probability of the c-th valid level output by the ordered classification model is the machine learning probability, and the similarity-weighted probability formed by historical recipes is the historical weighted probability. When the reliability level is high or medium and valid historical data exists, the fusion probability equals the sample-level weight multiplied by the machine learning probability plus 1 minus the sample-level weight multiplied by the historical weighted probability. The final level is the valid level with the highest fusion probability. When the reliability level is low and valid historical data exists, the highest machine learning probability level and the highest historical weighted probability level are output in parallel. If they are inconsistent, all valid levels between the two levels constitute the set of levels to be verified, and no single reliability level is given. When no valid historical data exists, only machine learning candidate levels are output. All the above low reliability outputs are accompanied by mandatory experimental verification prompts.

[0155] Furthermore, when the prediction reliability level is high or medium, a fused prediction value exists, and the system has established numerical correction rules applicable to the current feature range and independently verified based on historical data or control experiments, the corrected prediction value equals the fused prediction value plus the correction amount. For continuous numerical performance indicators with physical lower limits, physical upper limits, or enterprise-specified output ranges, the correction result is restricted to the corresponding valid interval; for example, the lower limit of a non-negative performance indicator is set to 0. The valid interval is read from the performance indicator configuration file. For ordered hierarchical performance indicators, the correction rule applies to the fusion probability of each valid level. Let the fusion probability of the c-th valid level be the fusion probability, and the verified level correction amount be the level correction amount. Then, the corrected probability equals the larger value between the sum of the level fusion probability and the level correction amount and 0, divided by the sum of the non-negative correction probabilities corresponding to each valid level. When the sum of the non-negative correction probabilities corresponding to each valid level is 0, level probability correction is not performed; instead, the system reverts to the fusion probability before correction and outputs an abnormal level correction rule flag. When the sum of the non-negative correction probabilities corresponding to each valid level is not 0, the final level is the valid level with the highest corrected probability. When no validated rank correction rule exists, the fusion probability and its corresponding highest probability rank are retained. In one implementation, the numerical correction rule is established based on at least 20 sets of measured data from formulations with consistent test methods and conditions, and validated using independent validation data. When the validation set mean absolute error decreases by at least 5% relative to the uncorrected result after applying the correction rule, and the performance change direction does not contradict the preset monotonicity rule, the numerical correction rule is deemed to have passed validation. Rules that fail validation may not be used to modify fusion prediction values. For correction rules of ordered rank performance, the accuracy and macro-average F1 value before and after correction are evaluated using independent validation data. When the accuracy or macro-average F1 value after correction increases by at least 0.03 relative to before correction, and does not violate the preset rank order and monotonicity rule, the rank correction rule is deemed to have passed validation. Rank correction rules that fail validation may not be used to modify fusion probabilities. When no validated numerical correction rule exists, high or medium reliability results retain the fused prediction value; when low reliability exists but valid historical data exists, machine learning estimates, historical estimates, and their unvalidated intervals or level sets are retained, without compressing them into a single final value; when low reliability exists but no valid historical data exists, machine learning candidate values ​​are retained.

[0156] Furthermore, the system provides three switchable prediction modes. The Explanation mode utilizes historically similar formulations and performance-specific mechanistic features to generate qualitative trends and experimental hints, without outputting definitive values ​​not calculated by a machine learning model or validated rules. The Quick mode calls the corresponding performance's machine learning model to output basic predicted values ​​and training range coverage status, without performing historical data fusion or large language model mechanism description generation. The Mechanism Enhancement mode, building upon the Quick mode, further performs historical data estimation, out-of-distribution identification, reliability level determination, and deterministic result processing, and generates mechanism descriptions from the large language model. All three modes share the same set of logic for formulation analysis, paint type identification, absolute ratio conversion, pre-validation rationality checks, and performance-specific mechanistic feature construction, and use the same performance indicator names, units of measurement, and basic JSON fields. In the Explanation mode, the numerical prediction field is set to empty; in the Fast mode, the fields for historical data estimation, fusion or interval results, and large language model description are set to empty; the Mechanism Enhancement mode outputs machine learning basic prediction, historical data estimation, high or medium reliability fusion results, or low reliability double values ​​and intervals or candidate level sets, and simultaneously outputs out-of-distribution labels, prediction reliability levels, mechanism descriptions, and experimental verification requirements.

[0157] Furthermore, in the mechanism enhancement mode, the main influencing factors are determined through the model interpretation module. For regression models, the contribution of each input feature in the current test formulation to the prediction result is calculated using sample-level SHAP values, and the top 5 features are selected as the main influencing factors according to the absolute value of the SHAP values ​​from largest to smallest. For ordered hierarchical models, the category SHAP value corresponding to the final predicted level is used. When sample-level SHAP values ​​cannot be calculated, the global feature importance of the model can be used as a substitute, but it should be clearly marked as global importance in the output results and should not be expressed as a deterministic local contribution of the current test formulation. The large language model receives fused predicted values ​​or fused levels, low reliability double values ​​and the set of intervals to be verified or candidate levels, predicted reliability level, out-of-distribution markers, out-of-distribution causes, and experimental verification prompts, and constructs structured prompt words by combining paint type, performance indicators, test methods, test conditions, performance-specific mechanism characteristics, and main influencing factors, generating only explanatory information. The explanatory information includes main favorable factors, main unfavorable factors, explanation of performance formation mechanism, explanation of out-of-distribution causes, risk warnings, and experimental verification suggestions. Large language models must not generate or modify predicted values, prediction levels, intervals to be verified, candidate level sets, prediction reliability levels, or out-of-distribution labels. The text validation module checks the large language model output for any tendency to modify predicted values, contradictions with deterministic calculation results, performance-specific mechanistic characteristics, and preset monotonicity rules, and for any missing necessary out-of-distribution explanations or experimental verification prompts. When the large language model output passes text validation, the explanation information is merged with the deterministic prediction result; when it fails text validation, the deterministic prediction result is retained, and the validation error information is fed back to the large language model to regenerate the explanation text, allowing for two regenerations; if it still fails validation after two regenerations, the explanation text generated by the large language model is not output, only the deterministic prediction result and templated experimental verification prompts are output. The system ultimately outputs the integrated results according to a preset JSON structure. The integrated results include at least the formula identifier, paint type and prediction mode, formula composition and unified absolute quality score, test methods and conditions, theoretical parameters and specific performance mechanism characteristics, machine learning-based prediction results, historical data estimation results and nearest-neighbor composition similarity, high or medium reliability fusion prediction results or low reliability double values, verification intervals and candidate level sets, prediction reliability level, out-of-distribution markers and reasons for out-of-distribution, main influencing factors determined by the model interpretation module, a mechanism explanation of the large language model, and experimental verification suggestions and limitations on result usage. The system can also generate single performance descriptions, multi-performance summary tables, or prediction reports based on the structured results.

[0158] Example 1: Performance Prediction of Epoxy Primer Formulation. An epoxy primer formulation was input, with the main components comprising 32% 601 epoxy resin liquid, 0.5% anti-settling agent, 1% organic bentonite, 4.4% petroleum-derived xylene, 5% titanium dioxide, 0.1% carbon black, 56% low oil-absorbing powder, and 1% polyamide wax. The curing agent comprised 25% D119 curing agent, 28% polyamide resin, 1% epoxy curing accelerator, 35% petroleum-derived xylene, and 11% n-butanol, with a main-to-solid ratio of 9:1. The test conditions were: a sandblasted carbon steel plate substrate with a surface treatment grade of Sa2.5, a wet film thickness of 130±15 micrometers, and a dry film thickness of 80±10 micrometers. The test plates were cured for 7 days at 23±2 degrees Celsius and 50±5% relative humidity. The target paint type was determined to be an epoxy primer. A candidate pool of performance characteristics was constructed, with candidate feature sources including formulation composition characteristics, theoretical parameters, general mechanism characteristics, performance-specific mechanism characteristics, test conditions, key feature missing markers, and combined features. Theoretical parameters yielded a volume solids content of 61%, a mass solids content of 80%, a pigment-to-binder ratio of 2.6, a pigment volume concentration of 51.82%, an epoxy system reaction equivalence ratio of 0.98, a volatile organic compound content of 345.32 g / L, and a critical pigment volume concentration of 65.38%. Candidate features were statistically screened, grouped by basic formulation series, raw material batches, and collection time. Training and validation datasets were separated by maintaining group and time isolation. Statistical correlation indices were calculated, and repeated cross-validation was performed. The frequency of selection and the degree of consistency in correlation direction were statistically analyzed to determine the comprehensive screening score. Candidate features meeting preset admission and stability thresholds were retained. Constraint verification was performed on the retained candidate features after statistical screening. Mechanism consistency verification was performed based on raw material functional categories and reaction relationships; dimensional consistency verification was performed based on dimensions and value ranges; influence direction verification was performed based on preset monotonicity rules; collinearity checks and ablation verification were performed to obtain the effective feature set. Based on the effective feature set, an ordered classification model corresponding to the epoxy primer adhesion performance was invoked to output the cross-cut adhesion level. The prediction results are used to illustrate the prediction process and structured output method of this invention, and still need to be verified through board fabrication and corresponding performance tests.

[0159] Example 2: Performance Prediction of Acrylic Polyurethane Topcoat Formulation. An acrylic polyurethane topcoat formulation was input, with the main components comprising 48% acrylic resin, 18% titanium dioxide, 10% precipitated barium sulfate, 3% matting agent, 5% colorant, 1% dispersant, 0.8% organobentonite, 0.3% defoamer, 0.3% leveling agent, 6% butyl acetate, and 7.6% xylene. The curing agent comprised 75% HDI curing agent, 15% butyl acetate, and 10% xylene. The mixing ratio of main component to curing agent was 12:1. Testing conditions included a 60-degree gloss measurement angle, a dry film thickness of 50±5 micrometers, and curing of the test panels for 7 days at 23±2 degrees Celsius and 50±5% relative humidity. The target paint type was determined to be an acrylic polyurethane topcoat. A candidate pool of performance characteristics was constructed. Theoretical parameters calculated showed a main-to-solids ratio of 12:1, volumetric solids content of 0.54, mass solids content of 73%, pigment-to-binder ratio of 1.91, pigment volume concentration of 33.37%, equivalence ratio of 1.26, volatile organic compound content of 410.18 g / L, and critical pigment volume concentration of 55.05%. Statistical screening and constraint verification were performed on the candidate characteristics to obtain a set of effective features. Based on the effective feature set, a regression model corresponding to gloss performance was invoked to output the predicted gloss value. This embodiment illustrates a unified process of analysis, verification, theoretical parameter calculation, and performance prediction, automatically distributing indicators, weights, and parameter calibers according to paint type, achieving unified support for multiple paint types.

[0160] Example 3: Out-of-Distribution Labeling and Low-Reliability Output Control. A low-gloss acrylic polyurethane topcoat formulation is input, with a matting agent content of 12%. The highest matting agent content in historical training samples was 8%. After conversion according to a 12:1 main-to-solid ratio, the absolute mass fraction of matting agent in the mixed coating covers a range of approximately 1.85% to 7.38%. The absolute mass fraction of matting agent in the current tested formulation is approximately 11.08%, exceeding the training upper limit by 50%. After constructing a performance feature candidate pool, statistical screening and constraint verification are performed on the candidate features. Based on the effective feature set, the gloss performance regression model is invoked, outputting the basic gloss prediction value and historical data estimates. Since gloss performance is labeled as out-of-distribution, the prediction reliability level is low. An out-of-distribution warning message is output, and the performance prediction of gloss performance is terminated, indicating that it must be verified through panel experiments and cannot replace experimental measured values.

[0161] Example 4: Reliability Grading and Grade Fusion When the Reaction Equivalent Ratio Exceeds the Training Range. An epoxy primer formulation was input, and the calculated reaction equivalent ratio was 0.82, lower than the lower limit of the reaction equivalent ratio coverage range of 0.90 to 1.10 in the hardness model training samples, exceeding the range by 8.9%. After constructing a performance feature candidate pool, statistical screening and constraint verification were performed on the candidate features, and the reaction equivalent ratio feature was marked as out of distribution. Based on the effective feature set, the ordered classification model corresponding to the hardness performance was invoked, and the hardness grade was output. Since the reaction equivalent ratio only slightly exceeded the limit, the predicted reliability grade was medium. The dynamic weight module calculated the weights by comprehensively considering model uncertainty, joint distribution density, and historical nearest neighbor dispersion, and output the hardness grade after fusion. This result is used to illustrate the out-of-distribution identification and grade-based performance fusion process, and still needs to be verified through board fabrication and pencil hardness tests.

[0162] Accordingly, such as Figure 2 As shown, a second aspect of the present invention provides a coating formulation performance prediction system, which predicts the performance of coating formulations based on the above-described prediction method, including... Data acquisition module 1 is used to acquire the coating formula to be tested and determine the target paint type to which the coating formula to be tested belongs; Candidate pool construction module 2 is used to construct a performance feature candidate pool for the predicted performance of the coating formulation to be tested. The performance feature candidate pool is a set of candidate features, including at least the formulation composition features determined based on the coating formulation to be tested, theoretical parameters calculated from the coating formulation to be tested, general mechanism features applicable to multiple performance indicators, and performance-specific mechanism features corresponding to the performance to be tested, as well as at least one of test conditions, key feature missing markers, and combined features. The screening and verification module 3 is used to acquire historical formula test data corresponding to the target paint type and the performance to be tested. Based on the historical formula test data, the candidate features in the performance feature candidate pool are first statistically screened, and then the candidate features retained after the statistical screening are constrained and verified to obtain a subset of candidate features corresponding to the performance to be tested. The subset of candidate features is used as the effective feature set corresponding to the performance to be tested. The statistical screening is to calculate the statistical correlation index between the candidate features and the performance to be tested based on the historical formula test data and retain or delete the candidate features accordingly. The constraint verification is to delete candidate features that do not conform to the preset coating performance mechanism rules according to the preset coating performance mechanism rules. The performance prediction module 4 is used to call the machine learning model corresponding to the performance to be tested based on the effective feature set, and to perform performance prediction on the coating formulation to be tested, so as to obtain the performance prediction result of the coating formulation to be tested.

[0163] Accordingly, a third aspect of the present invention provides an electronic device, comprising: at least one processor; and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described coating formulation performance prediction method.

[0164] Accordingly, a fourth aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described method for predicting the performance of coating formulations.

[0165] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0166] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0167] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0168] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0169] 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 it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting the performance of coating formulations, characterized in that, Includes the following steps: S1, Obtain the coating formula to be tested, and determine the target paint type to which the coating formula to be tested belongs; S2, for the predicted performance of the coating formulation to be tested, a performance feature candidate pool is constructed. The performance feature candidate pool is a set of candidate features, including at least the formulation composition features determined based on the coating formulation to be tested, theoretical parameters calculated from the coating formulation to be tested, general mechanism features applicable to multiple performance indicators, and performance-specific mechanism features corresponding to the performance to be tested, as well as at least one of test conditions, key feature missing markers, and combined features. S3, obtain historical formula test data corresponding to the target paint type and the performance to be tested, perform statistical screening on the candidate features in the performance feature candidate pool based on the historical formula test data, and then perform constraint verification on the candidate features retained after the statistical screening to obtain a subset of candidate features corresponding to the performance to be tested, and use the subset of candidate features as the effective feature set corresponding to the performance to be tested. The statistical screening is to calculate the statistical correlation index between candidate features and the performance to be tested based on the historical formula test data, and retain or delete candidate features accordingly. The constraint verification is to delete candidate features that do not conform to the preset coating performance mechanism rules according to the preset coating performance mechanism rules. S4. Based on the effective feature set, call the machine learning model corresponding to the performance to be tested to predict the performance of the coating formulation to be tested, and obtain the performance prediction result of the coating formulation to be tested.

2. The method for predicting the performance of coating formulations according to claim 1, characterized in that, Step S2, which involves constructing a candidate pool of performance features for the predicted performance of the coating formulation to be tested, includes: S21, based on the coating formulation to be tested and the target paint type, determine the candidate feature sources corresponding to the performance to be tested. The candidate feature sources include formulation composition features, theoretical parameters, general mechanism features and performance-specific mechanism features, as well as test conditions, key feature missing markers and combination features. The formulation composition features are determined based on the unique raw material identifier and addition ratio of the raw materials in the coating formulation to be tested. The unique raw material identifier is the identification information used to uniquely identify a raw material in a pre-set raw material identifier system. S22, Based on the candidate feature source and the unique raw material identifier, a fixed-dimensional candidate feature column is constructed, wherein the candidate features corresponding to the formulation composition features correspond one-to-one with the unique raw material identifier, and the theoretical parameters, the general mechanism features, and the performance-specific mechanism features correspond to preset feature identifiers respectively; S23, exclude candidate features from the candidate feature column that are related to the measured value of the performance to be tested. The relationship includes direct relationship and indirect relationship. The direct relationship is that the candidate feature itself is the measured value of the performance to be tested or its derived statistics. The indirect relationship is that the candidate feature can uniquely determine the value of the measured value of the performance to be tested. S24, the test conditions, key feature missing markers, and combined features generated according to preset feature construction rules corresponding to the coating formulation to be tested are included in the candidate feature column and summarized into the performance feature candidate pool; the key feature missing marker is used to characterize the missing data required to calculate the formulation composition features, theoretical parameters, general mechanism features or performance-specific mechanism features, or the state that all raw materials corresponding to a certain raw material functional category in the coating formulation to be tested are not included in the coating formulation to be tested.

3. The method for predicting the performance of coating formulations according to claim 2, characterized in that, The construction of a fixed-dimensional candidate feature column in step S22 further includes: S2211, Identify new raw materials in the coating formulation to be tested that have not appeared in the modeling sample corresponding to the historical formulation test data; S2212, determine the functional category of the new raw material in the preset raw material functional category system, wherein the preset raw material functional category system is a pre-set system for classifying raw materials according to their functions; S2213, determine whether the functional category belongs to the raw material functional category related to the performance to be tested; S2214, if the functional category belongs to the raw material functional category related to the performance to be tested, then the mass percentage of the new raw material in the coating formulation to be tested is calculated as an out-of-distribution identification statistic; the mass percentage is the absolute mass fraction of the new raw material in the mixed coating; the out-of-distribution identification statistic is not used as an input feature of the machine learning model; S2215, compare the out-of-distribution identification statistics with a preset trigger threshold. If the out-of-distribution identification statistics reach the preset trigger threshold, mark the performance to be tested as out-of-distribution, output out-of-distribution warning information, and terminate the performance prediction of the performance to be tested.

4. The method for predicting the performance of coating formulations according to claim 2, characterized in that, The construction of a fixed-dimensional candidate feature column in step S22 further includes: S2221, For known raw materials not included in the coating formulation to be tested, determine the functional category of the known raw materials in the pre-set raw material functional category system; S2222, determine whether the functional category is completely missing in the coating formulation to be tested, wherein the complete absence means that all raw materials corresponding to the functional category are not included in the coating formulation to be tested; S2223, if the functional category is completely missing in the coating formulation to be tested, a key feature missing marker is generated. The key feature missing marker is used to include the candidate feature column as an independent candidate feature in step S24. The key feature missing marker is an identifier indicating that all raw materials corresponding to the functional category are not included in the coating formulation to be tested. S2224, if the functional category is not entirely missing in the coating formulation to be tested, then the candidate feature corresponding to the known raw material is set as a null value marker, and the null value marker is a preset sentinel value that is different from the effective numerical range.

5. The method for predicting the performance of coating formulations according to claim 1, characterized in that, Step S3, which involves statistically filtering candidate features in the performance feature candidate pool based on the historical formula test data, includes: S311, the historical formula test data are grouped according to the basic formula series, raw material batch, and collection time, and the training dataset and validation dataset are divided while maintaining group isolation and time isolation; the basic formula series is a set of formulas with the same film-forming resin system and curing agent system; the grouping is to group historical samples with the same basic formula series identifier and the same raw material batch identifier into the same historical sample group; the group isolation is that historical samples within the same historical sample group do not cross the training dataset and the validation dataset, and the time isolation is that historical samples with later collection times are not included in the training dataset; S312, Calculate the statistical correlation index between the candidate feature and the performance to be tested based on the training dataset, and perform repeated cross-validation on the candidate feature based on the validation dataset, and count the frequency of the candidate feature being selected and the degree to which the correlation direction remains consistent in the repeated cross-validation; the statistical correlation index is an indicator characterizing the degree of correlation or importance between the candidate feature and the performance to be tested, and the correlation direction is a positive or negative correlation between the candidate feature and the performance to be tested; S313, determine the comprehensive screening score based on the statistical correlation index, the selected frequency and the degree of consistency of the correlation direction, retain candidate features that reach the preset admission threshold and the preset stability threshold, and delete candidate features that do not reach the preset admission threshold or the preset stability threshold. S314, if a candidate feature belongs to a preset knowledge-forced retention feature set, then even if the preset admission threshold or the preset stability threshold is not reached, it is still retained in the candidate feature subset and marked as a knowledge-forced retention feature. The missing state and ablation evaluation result of the knowledge-forced retention feature are recorded. The knowledge-forced retention feature set is a set of candidate features that are predetermined according to the coating performance formation mechanism, have a necessary influence on the performance to be tested, and cannot be replaced by other candidate features.

6. The method for predicting the performance of coating formulations according to claim 5, characterized in that, Step S312, which involves calculating the statistical correlation index between the candidate features and the performance to be tested based on the training dataset, and performing repeated cross-validation on the candidate features based on the validation dataset, includes: S3121, Based on the training dataset, calculate the mutual information, permutation importance or sample-level contribution between the candidate features and the performance to be tested, and use the calculation results as the statistical correlation index; S3122, Based on the validation dataset, perform repeated cross-validation on the candidate features, record whether the candidate feature is selected in each cross-validation, and record the correlation direction between the candidate feature and the performance to be tested when the candidate feature is selected; S3123, Based on the records of multiple cross-validations, calculate the frequency of the candidate feature being selected and the degree to which the association direction remains consistent in the repeated cross-validations; S3124, for the candidate features retained in step S313, perform ablation verification on independent verification data, retain candidate features that reduce the prediction error of the machine learning model or improve the grade evaluation index, and delete candidate features that increase the prediction error or worsen the grade evaluation index; the grade evaluation index is an indicator used to evaluate the accuracy of the machine learning model in classifying the performance to be tested; the independent verification data is historical formula test data that has not participated in the corresponding screening and verification.

7. The method for predicting the performance of coating formulations according to claim 5, characterized in that, Step S313, which involves determining the comprehensive screening score based on the statistical correlation indicators, the frequency of selection, and the degree of consistency between the correlation direction, includes: S3131, the statistical correlation index is determined as the prediction contribution item, the selected frequency is determined as the selection stability item, the degree of consistency of the correlation direction is determined as the directional stability item, the coating performance mechanism consistency result obtained by performing a pre-set coating performance mechanism rule verification on the candidate features is determined as the coating performance mechanism consistency item, and the redundancy between the candidate features and the selected candidate features is determined as the redundancy item; the coating performance mechanism consistency item is a scoring item used to calculate the comprehensive screening score, and the coating performance mechanism consistency result is the degree of consistency between the candidate features and the pre-set coating performance mechanism rules; S3132, the prediction contribution item, the selection stability item, the directional stability item, the coating performance mechanism consistency item and the redundancy item are weighted and summed according to the preset weighting coefficients to obtain the comprehensive screening score of the candidate feature; S3133, compare the comprehensive screening score with a preset admission threshold, and compare the selected frequency with a preset stability threshold. Retain candidate features that simultaneously reach the preset admission threshold and the preset stability threshold, and delete candidate features that do not reach the preset admission threshold or the preset stability threshold.

8. The method for predicting the performance of coating formulations according to claim 5, characterized in that, Step S3 involves constraining and validating the candidate features in the performance feature candidate pool based on the historical formula test data, including: S321, For the candidate features retained after the statistical screening, perform a mechanism consistency check based on the raw material functional category and reaction relationship, and delete candidate features that are inconsistent with the preset coating performance mechanism rules. The preset coating performance mechanism rules are the allowed correlation between candidate features and the performance to be tested, which are predetermined based on the coating performance formation mechanism. S322, for the candidate features retained after the mechanism consistency verification, according to whether the dimension of the candidate feature belongs to the set of allowed dimensions corresponding to the performance to be tested, and whether the value range of the candidate feature is within the preset value range, delete the candidate features whose dimension does not belong to the set of allowed dimensions or whose value range exceeds the preset value range. S323, For the candidate features retained after the dimensional consistency check, perform an influence direction check according to the preset monotonicity rule, and delete the candidate features whose influence direction is inconsistent with the preset monotonicity rule. S324, For the candidate features retained after the influence direction verification, perform collinearity check and ablation verification. The ablation verification is a final confirmatory ablation verification performed on the candidate features retained after the aforementioned steps in the constraint verification. Candidate features retained on independent verification data that reduce the prediction error of the machine learning model or improve the level evaluation index for evaluating the accuracy of the machine learning model in classifying the performance under test are used as a subset of candidate features after constraint verification. The collinearity check is to calculate the correlation coefficient between candidate features, and when the correlation coefficient is higher than a preset correlation coefficient threshold, delete the candidate features with high redundancy with the retained candidate features. The independent verification data is historical formula test data that did not participate in the corresponding screening and verification.

9. The method for predicting the performance of coating formulations according to claim 8, characterized in that, Step S321, which involves performing a mechanism consistency check based on the functional categories of raw materials and reaction relationships, includes: S3211, Determine the functional category of the raw material corresponding to the candidate feature in the preset raw material functional category system; S3212, Determine the reaction relationship of the raw materials corresponding to the candidate features in the coating formulation to be tested; S3213, Based on the preset coating performance mechanism rules, determine whether the functional category and the reaction relationship belong to an allowable combination related to the performance to be tested; S3214, if the functional category and the response relationship do not belong to the allowed combination, then delete the candidate feature; if the functional category and the response relationship belong to the allowed combination, then retain the candidate feature. S3215, based on the preset raw material compatibility rule library, determine whether there is a prohibited combination between the functional category and reaction relationship of the raw material corresponding to the candidate feature and the functional category and reaction relationship of other raw materials in the coating formulation to be tested; if there is a prohibited combination, delete all candidate features involved in the prohibited combination.

10. The method for predicting the performance of coating formulations according to claim 8, characterized in that, Step S323, which involves performing influence direction verification according to preset monotonicity rules, includes: S3231, determine the correlation direction between the candidate feature and the performance to be tested; S3232, Read the preset monotonicity rule corresponding to the performance to be tested; S3233, determine whether the association direction is consistent with the preset monotonicity rule; S3234, if the correlation direction is inconsistent with the preset monotonicity rule, then the candidate feature is deleted; if the correlation direction is consistent with the preset monotonicity rule, then the candidate feature is retained, and the correlation direction is recorded as the expected influence direction of the candidate feature, and the feature identifier of the candidate feature and its corresponding expected influence direction are recorded; the expected influence direction is the allowed positive or negative correlation between the candidate feature and the performance to be tested.

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