A method and system for predicting tire rolling resistance performance

Abstract

The application discloses a kind of tire rolling resistance performance prediction method and system, including the data of historical tire is obtained, data set is constructed;And pre-processing, form numerical data set;Establish initial multiple regression model;To initial model or modified model, execute model diagnosis procedure;When any diagnosis item does not pass, execute correction operation, and based on the model after modification re-executes model diagnosis procedure, until all diagnosis items of model diagnosis procedure pass or satisfy preset engineering concession condition, obtain final regression model;To its inverse transformation processing, obtain the final real coefficient model of original variable.Design parameters of the tire to be measured are received, and the final real coefficient model is used to output the rolling resistance performance prediction result.The application realizes efficient, low-cost and statistically robust and reliable prediction of tire rolling resistance performance under the premise of not relying on physical sample tire test and complex finite element simulation through closed-loop model diagnosis and correction mechanism.

Description

Technical Field

[0001] This invention relates to the field of tire testing technology, and in particular to a method and system for predicting tire rolling resistance performance. Background Technology

[0002] As the only component of a vehicle in contact with the road surface, tire performance is crucial to a vehicle's fuel economy, handling, and safety. Among numerous performance indicators, rolling resistance is a key focus for OEMs due to its direct correlation with fuel and electricity consumption. Studies show that rolling resistance accounts for approximately 10%-15% of the total resistance of passenger car tires, and even higher for commercial vehicle tires, reaching up to 50%. A 10% reduction in rolling resistance coefficient can save approximately 3% of fuel for both passenger cars and trucks. Therefore, reducing rolling resistance is a key technology for improving vehicle energy efficiency, reducing CO2 emissions, and meeting increasingly stringent regulations.

[0003] How to improve rolling resistance performance through material innovation, tread pattern innovation, and structural optimization, and how to effectively and quickly evaluate the quality of tire rolling resistance performance, has become an important technical problem that the tire industry urgently needs to solve.

[0004] Currently, the main method for evaluating tire rolling resistance performance is physical testing, such as indoor drum tests, performed according to standards like ISO 28580, GB / T 15082, and SAE J2452. While this method serves as an industry benchmark and yields relatively accurate results, it has significant drawbacks: it requires manufacturing finished tires for actual tire testing, resulting in high costs, long lead times, high resource consumption, and slow design feedback.

[0005] To overcome the limitations of physical experimental testing, numerical simulation methods such as finite element analysis (FEA) have been introduced into the field of tire performance prediction. FEA can simulate the complex mechanical behavior and heat generation process of a tire during rolling. Theoretically, as long as the model accuracy and algorithm are good enough, it can accurately predict rolling resistance performance. However, FEA requires high-precision models, accurate material properties, complex contact algorithms, and a large amount of computational resources. Its computational and time costs are also high, making it difficult to meet the needs of rapid design and optimization. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the existing technology. To achieve the above objective, a method and system for predicting tire rolling resistance performance are adopted to solve the problems mentioned in the background technology.

[0007] The technical solution provided in the first aspect is: a method for predicting tire rolling resistance performance, including the following steps: Obtain historical tire design parameters and corresponding measured rolling resistance data to construct a dataset; The design parameters in the dataset are preprocessed to form a numerical dataset suitable for regression analysis; Based on the numerical dataset, an initial multiple regression model is established with rolling resistance performance index as the dependent variable and design parameters as the independent variables. A model diagnostic procedure is performed on the initial model or the modified model. The model diagnostic procedure includes nonlinearity diagnosis, multicollinearity test, residual test, and generalization ability diagnosis. When any diagnostic item of the model diagnostic procedure fails, the correction operation corresponding to the diagnostic item is executed, and the model diagnostic procedure is re-executed based on the corrected model until all diagnostic items of the model diagnostic procedure pass or meet the preset engineering concession conditions to obtain the final regression model; and the model is then subjected to inverse transformation to obtain the final true coefficient model of the original variables.

[0008] The design parameters of the tire to be tested are received, and the rolling resistance performance prediction results are output using the final true coefficient model.

[0009] As a further aspect of the present invention: the preprocessing of the design parameters in the dataset specifically includes: The numerical variables in the design parameters are normalized. One-hot encoding is performed on the categorical variables in the design parameters; The normalization process is performed before the one-hot encoding process.

[0010] As a further aspect of the present invention, it also includes: Initial tests are performed on the initial model, including overall significance test (F test), goodness-of-fit test (R² and adjusted R² test), regression coefficient significance test (t test), and multicollinearity test; If the initial test fails, the correction operation will proceed directly.

[0011] As a further aspect of the present invention: the multicollinearity test includes: Calculate the variance inflation factor (VIF) values ​​for each independent variable; When the variance inflation factor (VIF) value of any independent variable is greater than 10, the multicollinearity test is deemed to have failed. The corresponding corrective actions include deleting independent variables with high VIF values, using Cook distance to remove outliers and strong influence points, and using ridge regression, stepwise regression, or variable orthogonalization to deal with multicollinearity.

[0012] As a further aspect of the present invention: the residual test includes: The residual normality test is used to determine whether the residuals follow a normal distribution. The residual independence test is used to determine whether the residuals are autocorrelated. The residual variance test is used to determine whether the residual variance is constant. When the residual normality test, residual independence test, or residual variance test fails, the correction operation includes: using the Cook distance method to detect outliers and strong influence points in the dataset, removing the detected outliers and strong influence points, and correcting the model with heteroscedasticity robust standard error HC3; if the residual variance test and autocorrelation test both fail, then the Newey-West robust standard error HAC method is used for correction.

[0013] As a further aspect of the present invention: the nonlinear diagnosis includes: Perform a RESET test to check for any missing higher-order terms or interaction terms; If the p-value of the RESET test is less than the preset threshold, then higher-order terms and / or interaction terms are introduced into the model. If the introduced higher-order terms and / or interaction terms pass the regression coefficient significance test and have a significant effect, they are retained; When higher-order terms and / or interaction terms are introduced into the model, and the RESET test passes, but multiple variables show an increase in variance inflation factor (VIF), variable orthogonalization (Gram-Schmidt strict orthogonalization) can be used. The squared terms and interaction terms are regressed against the original variables, and the residuals are taken as new variables. This ensures that the nonlinear terms are linearly independent of the original variables, thus solving the multicollinearity problem in the multinomial model.

[0014] As a further aspect of the present invention: the generalization ability diagnosis includes: Once the nonlinearity diagnosis, multicollinearity test, and residual test are all passed, the corrected regression model is obtained. If the dataset sample size is ≤50, this modified regression model is the final regression model; If the dataset sample size is greater than 50, the k-fold cross-validation method is used to diagnose the generalization ability and stability of the model. If the difference between the mean R² of k-fold cross-validation and the R² of the original model is ≤ 0.05, and the coefficient of variation (CV) of the mean MAE, RMSE, and MAPE is less than the preset threshold, then the model is considered stable and has strong generalization ability, and is used as the final regression model.

[0015] As a further aspect of the present invention: the preset engineering concession conditions include the following conditions being satisfied simultaneously: The overall goodness of fit of the model is R² greater than 0.85; The p-value of the RESET test is greater than or equal to the preset threshold; The p-values ​​for the significance test of the regression coefficients of the independent variables after robust standard errors are less than 0.05; The signs of the coefficients of each independent variable are consistent with common sense in engineering physics. Furthermore, when all the above conditions are met, the variance inflation factor (VIF) value of individual independent variables in the multicollinearity diagnosis is allowed to be greater than 10 and less than 20.

[0016] As a further aspect of the present invention: the final regression model uses tire rolling resistance FR as the dependent variable and includes at least the following independent variables: tire test load FZ or tire standard load FZS, tire tread compound heat generation index ZP, and the square of tire tread groove depth GD. 2 =FZ² or FZS² of the tire test load or tire standard load, ZP² of the tire tread compound heat generation index, and ZP·FZ or ZP·FZS of the interaction between the tire tread compound heat generation index and the tire test load or tire standard load.

[0017] The second aspect provides a technical solution as follows: a prediction system employing a tire rolling resistance performance prediction method as described in any of the above claims, characterized in that it includes: The data acquisition module is used to acquire historical tire design parameters and corresponding measured rolling resistance data to build a dataset; The data preprocessing module is used to preprocess the design parameters in the dataset to form a numerical dataset suitable for regression analysis. The model building and diagnostic module is used to establish an initial multiple regression model based on the numerical dataset, with rolling resistance performance index as the dependent variable and design parameters as the independent variables. It then executes a model diagnostic procedure on the initial or modified model, which includes at least nonlinearity diagnosis, multicollinearity test, residual test, and generalization ability diagnosis. If any diagnostic item in the model diagnostic procedure fails, a correction operation corresponding to that item is performed, and the model diagnostic procedure is re-executed based on the modified model until all diagnostic items pass or preset engineering concession conditions are met, thus obtaining the final regression model. Finally, the module performs an inverse transformation on the model to obtain the final true coefficient model of the original variables. The prediction output module is used to receive the design parameters of the tire under test and output the rolling resistance performance prediction results using the final true coefficient model.

[0018] Compared with the prior art, the present invention has the following technical advantages: Using the above technical solution, a dataset is constructed by acquiring historical tire design parameters and corresponding measured rolling resistance data. The design parameters in the dataset are preprocessed to form a numerical dataset suitable for regression analysis. Then, based on this numerical dataset, an initial multiple regression model is established with rolling resistance performance as the dependent variable and design parameters as independent variables. Next, a model diagnostic procedure is executed on the initial or modified model, including nonlinearity diagnosis, multicollinearity test, residual test, and generalization ability diagnosis. When any diagnostic item fails, a correction operation corresponding to that item is performed, and the model diagnostic procedure is re-executed based on the corrected model. This process is iterated until all diagnostic items pass or the preset engineering concession conditions are met, resulting in the final regression model. This model is then inversely transformed to obtain the final true coefficient model of the original variables. Finally, the design parameters of the tire to be tested are received, and the rolling resistance performance prediction results are output using this final true coefficient model.

[0019] By constructing a closed-loop model diagnosis and correction system that includes nonlinearity diagnosis, multicollinearity testing, residual testing, and generalization ability diagnosis, a reliable predictive model with high goodness of fit and residuals satisfying classical regression assumptions can be quickly established in the early stages of product design, based solely on existing historical test data or finite element analysis results. Compared to physical experimental testing, it eliminates the need for manufacturing prototype tires and conducting actual tire tests, significantly shortening the design feedback cycle and reducing development costs. Compared to finite element simulation, it eliminates the need for high-precision modeling and massive computational resources, significantly improving evaluation efficiency. Furthermore, by introducing pre-defined engineering concession conditions, it retains effective models with practical engineering value even when individual statistical indicators do not reach theoretical optimality, balancing statistical rigor with engineering practicality. This enables tire companies to achieve design, prediction, and real-time feedback during product solution iteration and optimization. Attached Figure Description

[0020] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings: Figure 1 This is a schematic diagram illustrating the steps of the performance prediction method according to an embodiment of this application; Figure 2 This is a flowchart illustrating the performance prediction method according to an embodiment of this application. Figure 3 This is a schematic diagram illustrating the analysis of k-fold cross-validation results in an embodiment of this application.

[0021] Terminology Explanation: ZP: Tire tread compound heat generation index P: Standard tire pressure or test tire pressure TM: Tire crown thickness at the tire section TN: Tire section shoulder thickness TZ: Tire section bead thickness OD: Tire outer diameter CD: Diameter at the maximum width of the tire section TD: Tire contact diameter SW: Maximum tire section width SH: Tire section height TW: Tire fit width HW: Tire tread width HH: Vertical height from the center of the tire tread to the shoulder point HR: Tire tread center crown radius GD: Tire tread groove depth WT: Standard tire weight FZ: Tire test load FZS: Standard Tire Load FR: Tire rolling resistance RRC: Tire Rolling Resistance Coefficient Detailed Implementation The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Please refer to Figure 1 and Figure 2 In this embodiment of the invention, a method for predicting tire rolling resistance performance is provided for quickly and cost-effectively evaluating the rolling resistance performance of a tire during the product design phase. The method specifically includes the following steps: Step S1: Data Acquisition and Preprocessing S11. Obtain historical tire design parameters and corresponding measured rolling resistance data to construct a dataset.

[0023] Specifically, tire design parameters and corresponding measured rolling resistance data are collected from tire manufacturers' design databases, experimental testing databases, or finite element analysis results. The collected design parameters can cover one or more of the following four categories: structural parameters, tread parameters, compound parameters, and environmental parameters. For example, structural parameters may include tire outer diameter OD, tire section diameter at maximum width CD, tire contact diameter TD, tire maximum section width SW, tire section height SH, tire contact width TW, tire crown thickness TM, tire shoulder thickness TN, tire bead thickness TZ, and tire standard weight WT; tread parameters may include tire tread horizontal width HW, tire tread center to shoulder height HH, tire tread center crown radius HR, and tire tread groove depth GD; compound parameters may include tire tread compound heat generation index ZP; and environmental parameters may include tire standard or test tire pressure P, tire test load FZ, and tire standard load FZS. The collected measured rolling resistance data includes tire rolling resistance FR and / or tire rolling resistance coefficient RRC.

[0024] In a specific example, an initial dataset containing 397 tire product data points was collected. Each data point includes the following parameter fields: aspect ratio, tread pattern type, belt layer structure, ZP, P, TM, TN, TZ, OD, CD, TD, SW, SH, TW, HW, HH, HR, GD, WT, FZS, FZ, FR, and RRC. The resulting 397 rolling resistance data points are shown in the table below (showing the first 20 rows):

[0025]

[0026] S12. Preprocess the design parameters in the dataset to form a numerical dataset suitable for regression analysis.

[0027] The preprocessing process includes data cleaning, variable splitting, and quantification.

[0028] Data cleaning includes: missing value handling (deleting samples containing missing values ​​or imputing with mean / median), outlier detection and handling (identifying and removing outlier samples based on the 3σ principle or box plots), and duplicate value removal.

[0029] After data cleaning, the design parameters are decomposed into variables: numerical variables and categorical variables are identified and distinguished. For example, parameters such as ZP, P, TM, TN, TZ, OD, CD, TD, SW, SH, TW, HW, HH, HR, GD, WT, FZS, FZ, FR, and RRC are numerical variables; while flatness ratio, pattern type, and belt layer structure are categorical variables.

[0030] For numerical variables, normalization is performed. The purpose of normalization is to eliminate large differences in dimensions and magnitudes between tire design parameters (for example, the outer diameter (OD) of an all-steel radial tire is typically on the order of 700-1200 mm, while the tread groove depth (GD) is typically on the order of 10-22 mm, a difference of hundreds of times), making different features comparable and ensuring the fairness and stability of subsequent model training. Normalization can be performed using Z-Score standardization or Min-Max Scaling methods.

[0031] For categorical variables, one-hot encoding is used. The reason for using one-hot encoding is that this encoding method does not force the assumption of a linear relationship between categories, does not use dependent variable information, and avoids data leakage and endogeneity issues; at the same time, one-hot encoding is a linear structure, which is naturally compatible with regression models and can ensure that the transformed data does not affect the validity of subsequent tests.

[0032] It is important to note that when both normalization and one-hot encoding are required, normalization must be performed before one-hot encoding. If normalization is performed after one-hot encoding, the encoded values ​​that were originally 0 or 1 will be normalized to other scales, causing the classification features to lose their clear physical meaning.

[0033] Step S2: Establish the initial multiple regression model Using the preprocessed dataset, an initial multiple regression model is established with rolling resistance performance index as the dependent variable and design parameters as the independent variables.

[0034] Specifically, after one-hot encoding, data needs to be concatenated in the column direction to incorporate the generated dummy variables into the original dataset, while deleting the original categorical variables (and one of the dummy variables) to avoid information duplication and multicollinearity, ultimately forming a numerical dataset that can be used for multiple regression.

[0035] The results of the dataset processing are shown in the table below (showing the first 20 rows):

[0036] In a specific example, tire rolling resistance FR is selected as the dependent variable, and the other preprocessed design parameters are used as independent variables to establish an initial multiple regression model.

[0037] Step S3: Model Diagnosis and Correction – Closed-Loop Iterative Process S31. Perform a model diagnostic procedure on the initial model or the modified model. The model diagnostic procedure includes nonlinearity diagnosis, multicollinearity test, residual test, and generalization ability diagnosis.

[0038] Initial tests were performed on the initial model, including overall significance test (F-test), goodness-of-fit test (R² and adjusted R² tests), regression coefficient significance test (t-test), and multicollinearity test. The results are shown in the table below. It can be seen that the initial t-test and multicollinearity test failed.

[0039] The multicollinearity test is used to examine whether there is a high linear correlation among independent variables. Specifically, the variance inflation factor (VIF) value of each independent variable is calculated. If the VIF value of any independent variable is greater than 10, the multicollinearity test is considered to have failed.

[0040] Residual tests are used to verify whether the basic assumptions of the regression model are met. Residual diagnostics include: residual normality tests (to determine if the residuals follow a normal distribution, using the Jarque-Bera test / QQ plot), residual independence tests (to determine if the residuals are autocorrelated, using the Durbin-Watson test), and residual variance tests (to determine if the residuals exhibit heteroscedasticity, using the Breusch-Pagan test / residual-fit value scatter plot). When the residual-fit value scatter plot shows a clear curvilinear trend, it indicates that the model may have a functional specification bias or a nonlinear relationship; if it shows a funnel-shaped distribution, it suggests that the model has heteroscedasticity.

[0041] Nonlinear diagnosis uses the RESET test to determine whether it is reasonable to use a linear model to fit the data. If the test fails, it means that the model has missed higher-order terms or interaction terms.

[0042] Generalization ability diagnosis: After passing nonlinearity diagnosis, multicollinearity test, and residual test, a modified regression model is obtained. When the dataset sample size is ≤50, this modified regression model is the final regression model. When the dataset sample size is >50, preferably ≥200, k-fold cross-validation can be used to diagnose the generalization ability and stability of the model, usually k=5 or 10; when the difference between the mean R² of k-fold cross-validation and the R² of the original model is ≤0.05 (5%), and the coefficient of variation (CV) of the mean MAE, RMSE, and MAPE is less than the preset threshold, the model is considered stable and has strong generalization ability, and can be used as the final regression model.

[0043] S32. When any diagnostic item of the model diagnostic program fails, the correction operation corresponding to the diagnostic item is executed, and the model diagnostic program is re-executed based on the corrected model until all diagnostic items of the model diagnostic program pass or meet the preset engineering concession conditions, and the final regression model is obtained. S33. Perform an inverse transformation on the model to obtain the final true coefficient model of the original variables.

[0044] The coefficients in the final regression model are calculated based on the collected specific dataset after standardization and orthogonalization. In practical applications, for simplicity, the final regression model is subjected to inverse transformation. Through orthogonal transformation decoupling and standardization of dimensions, the final true coefficient model of the original variables is obtained.

[0045] The specific correction operations for each diagnostic item include: (1) For cases where the multicollinearity test fails, the corrective actions include: deleting independent variables with high VIF values, using Cook distance to remove outliers and strong influence points, and using ridge regression, stepwise regression, or variable orthogonalization to treat multicollinearity.

[0046] (2) If the residual normality test, independence test or heteroscedasticity test fails, the correction operation includes: using the Cook distance method to detect outliers and strong influence points in the dataset, and removing the detected outliers and strong influence points; and correcting the model with heteroscedasticity robust standard error HC3; if the heteroscedasticity and autocorrelation tests fail, the Newey-West robust standard error HAC method is used for correction.

[0047] (3) For nonlinear diagnosis, perform RESET test to check whether higher-order terms or interaction terms are missing; if the p value of RESET test is less than the preset threshold (e.g., 0.05), higher-order terms and / or interaction terms are introduced into the model; if the introduced higher-order terms and / or interaction terms pass the regression coefficient significance test (t test) and have a significant effect, they are retained.

[0048] (4) When higher-order terms and / or interaction terms are introduced into the model, the RESET test passes, but the variance inflation factor (VIF) of multiple variables increases. In this case, variable orthogonalization (Gram-Schmidt strict orthogonalization) can be used to regress the squared terms and interaction terms against the original variables and take the residuals as new variables. This will ensure that the nonlinear terms are not linearly independent of the original variables and solve the multicollinearity problem of the polynomial model.

[0049] After correction, the model diagnostic procedure in step S31 is re-executed, and this process is repeated until all diagnostic items pass or meet the preset engineering concession conditions.

[0050] The preset engineering concession conditions refer to the fact that, considering the existence of certain errors in the original data in actual engineering applications, when individual diagnostic indicators do not reach the theoretical optimal standard, concessions can be made by comprehensively considering other test results. Specifically, when the VIF value of an individual independent variable in multicollinearity diagnosis is greater than 10 and less than 20, but all of the following conditions are met, it can be determined that the engineering concession conditions are met: the overall model fit R² is greater than 0.85; the p-value of the RESET test is greater than or equal to the preset threshold (e.g., 0.05); the p-value of the significance test of the regression coefficients of each independent variable is less than 0.05; and the sign of the coefficients of each independent variable is consistent with common sense in engineering physics.

[0051] After multiple diagnostic and revision iterations, the model retains only the following independent variables: tire standard load FZS, tire tread compound heat generation index ZP, and the square of tire tread groove depth GD. 2 The square of the tire standard load FZS², the square of the tire tread compound heat generation index ZP², and the interaction term ZP·FZS between the tire tread compound heat generation index and the tire standard load.

[0052] The diagnostic results show that the model has a high goodness of fit, is highly significant overall, and passes nonlinearity diagnosis, multicollinearity test, residual test, and generalization ability diagnosis. The model is robust overall and has high prediction accuracy, yielding the final regression model. The test results are shown in the table below:

[0053] Step S4: Model Application – Performance Prediction S41, Receive the design parameters of the tire to be tested.

[0054] The tire to be tested can be a tire in a new product design or a tire to be evaluated in an improved product design. The input design parameters should correspond to the independent variables in the final regression model.

[0055] S42. Utilize the final regression model to output the rolling resistance performance prediction results.

[0056] When numerical variables are normalized during model building, in the prediction stage, the design parameters of the tire to be tested must first be substituted into the mean and standard deviation of the original training dataset for the same normalization process before being input into the model for prediction.

[0057] In a specific example, the final regression model obtained is: FR=129.66 12.18×ZP+13.35×GD²+24.01×FZS+30.55×ZP²+13.48 × FZS² 20.71×ZP×FZS Where FR is the tire rolling resistance, in Newtons (N); FZS is the tire standard load; ZP is the tire tread compound heat index; GD 2 ZP² is the square of the tire tread groove depth; ZP² is the square of the tire tread compound heat index; FZS² is the square of the tire standard load; ZP×FZS is the product of the tire tread compound heat index and the tire standard load.

[0058] The influence directions of the independent variables in this model are as follows: linear influence: FZS has a significant positive influence on FR, and ZP has a significant negative influence on FR; nonlinear influence: GD², ZP², and FZS² have significant positive influences on FR; the interaction term ZP×FZS has a significant negative influence on FR.

[0059]

[0060] When the tire rolling resistance coefficient (RRC) needs to be obtained, it can be calculated using the following formula: RRC = (FR / (FZS × 0.85)) × 1000 The unit of RRC is N / kN.

[0061] The method described in this embodiment integrates a closed-loop diagnostic and correction mechanism—combining multicollinearity testing, residual testing, nonlinearity diagnosis, and generalization capability diagnosis—into the modeling process. This enables the rapid construction of a statistically robust and engineering-usable rolling resistance prediction model using historical data, without the need for manufacturing prototype tires or relying on complex finite element simulations. This model can be used at any stage of tire product design; inputting design parameters instantly yields predicted rolling resistance performance, effectively shortening the design feedback cycle and reducing development costs.

[0062] Example 2 Pre-screening for initial testing: Based on Example 1, a pre-screening step of initial testing is further added after the initial regression model is established and before the model diagnostic procedure is executed.

[0063] Specifically, after establishing the initial regression model, initial tests are performed on the initial model. These initial tests include overall significance test (F-test), goodness-of-fit test (R² and adjusted R² tests), regression coefficient significance test (t-test), and multicollinearity test. The initial tests include the following four items: (1) Overall significance test: The F-test is used to test whether the linear relationship between the dependent and independent variables in the regression model is significant as a whole. When the p-value of the F-test is less than 0.05, the model is considered to be significant as a whole, and the established linear relationship is statistically significant.

[0064] (2) Goodness-of-fit test: R² (coefficient of determination) or adjusted R² is used to measure the goodness of fit of the model to the data. When R² or adjusted R² is greater than 0.85, it indicates that the model has good explanatory power.

[0065] (3) Significance test of regression coefficients: The t-test is used to test whether the influence of each independent variable on the dependent variable is significant. When the p-value of the t-test for a certain independent variable is less than 0.05, it is determined that the independent variable has a significant influence on the dependent variable.

[0066] (4) Multicollinearity test: Calculate the variance inflation factor (VIF) value of each independent variable. When the VIF value of an independent variable is greater than 10, it is determined that there is a multicollinearity problem.

[0067] If any test item fails in the initial test, there is no need to wait for a full diagnosis; the process can proceed directly to the correction phase, thereby improving overall modeling efficiency. For example, if the initial test finds that the t-test p-values ​​of certain categorical variables (such as flatness, pattern type, and banded layer structure) are much greater than 0.05, and the VIF values ​​are too high, these variables can be removed directly in the initial stage. After correcting the model, the initial test can be repeated until it passes before proceeding to the full model diagnosis procedure.

[0068] This embodiment adds an initial screening step, which can quickly identify and remove obviously invalid or severely collinear independent variables in the early stages of modeling, thereby reducing the number of subsequent comprehensive diagnoses and iterative corrections and further improving the execution efficiency of the method.

[0069] Example 3 Linkage between residual testing and nonlinear processing: Based on Example 1, the linkage triggering mechanism between residual diagnosis and nonlinear diagnosis is further explained in detail.

[0070] The specific execution process of residual inspection is as follows: First, perform a residual normality test. A preliminary assessment can be made by plotting a residual QQ plot. If the residual points are approximately distributed along the diagonal, it preliminarily indicates that the residuals follow a normal distribution. Further, an Omnibus test or Jarque-Bera test can be performed for quantitative assessment. When the p-value of the test result is greater than 0.05, the null hypothesis that the residuals follow a normal distribution cannot be rejected at the 5% significance level, and the residual normality test is passed.

[0071] Secondly, an independence test of the residuals was performed. The Durbin-Watson test (DW test) was used to test whether there was first-order autocorrelation in the residuals. The DW statistic ranges from 0 to 4. When the DW value is between 1.8 and 2.2, it indicates that there is no significant first-order autocorrelation in the residuals, and the independence test of the residuals is passed.

[0072] Finally, perform a residual variance test. This is done by plotting a scatter plot of residuals versus fitted values. Ideally, the scatter plot should show a uniform distribution, without a distinct funnel shape (i.e., the residuals diverge as the fitted values ​​increase) or a curved pattern.

[0073] When the residual normality test or residual variance test fails, it indicates that there may be outliers or strongly influential points in the dataset. The corrective action taken in this case is to use the Cook distance method to detect outliers and strongly influential points in the dataset. The Cook distance value is calculated for each data sample, and outliers and strongly influential points whose Cook distance values ​​are significantly greater than those of other samples are marked and removed to optimize the dataset quality.

[0074] More importantly, when the residual-fit value scatter plot exhibits a funnel-shaped or curved pattern in the residual variance test, this not only indicates heteroscedasticity but may also suggest that the model has missed important nonlinear relationships. In this case, triggering the nonlinearity diagnostic procedure includes: The first step is to perform a RESET test to systematically check whether the model has missed any higher-order terms (such as square terms, cube terms, etc.) or interaction terms. If the p-value of the RESET test is greater than or equal to a preset threshold (e.g., 0.05), it indicates that there are no missed higher-order nonlinear relationships, and no further processing is required. If the p-value of the RESET test is less than the preset threshold (e.g., 0.05), it indicates that the model has a specification error, and higher-order terms or interaction terms need to be introduced.

[0075] The second step involves introducing potential higher-order terms into the model based on engineering experience and tire physics. For example, considering that the effect of tire tread depth on rolling resistance may not be a simple linear relationship, and the rate of influence on rolling resistance may differ depending on the tread depth, a square term GD² for tread depth is introduced into the model. If the modified model still fails the RESET test, further square terms and / or interaction terms need to be added, such as: the square of tire test load or tire standard load FZ² or FZS², the square of tire tread compound heat generation index ZP², and the interaction term ZP·FZ or ZP·FZS between tire tread compound heat generation index and tire test load or tire standard load.

[0076] The third step is to perform a t-test on the introduced higher-order terms or interaction terms. If the p-value is less than 0.05, it indicates that the higher-order term has a significant impact on the dependent variable, and it is retained; otherwise, it is removed to maintain the simplicity of the model.

[0077] This embodiment establishes a logical triggering relationship between residual diagnosis and nonlinear diagnosis, enabling the model to not only handle routine data quality issues (outliers) but also automatically detect and correct deviations in the model's formal specifications (omissions of nonlinear relationships). The final model can satisfy classical regression assumptions and accurately depict the true influence patterns between variables.

[0078] Example 4 Application of engineering concessions: This embodiment provides a specific scenario to illustrate the judgment logic of preset engineering concession conditions in practical applications.

[0079] In the process of constructing a prediction model for tire rolling resistance performance, due to the inherent high correlation between tire design parameters (for example, tire outer diameter, section width, and contact diameter usually change in tandem), it is often difficult to completely eliminate multicollinearity among independent variables.

[0080] In the first round of model diagnosis and correction, assuming that after variable selection and stepwise regression, the current model contains five independent variables: FZ, GD, ZP, TZ, and GD², the VIF values ​​of each variable are calculated as follows: VIF of FZ is 4.2, VIF of GD is 6.8, VIF of ZP is 3.5, VIF of TZ is 10.3, and VIF of GD² is 8.1.

[0081] According to the standard judgment criteria, the VIF value of TZ is 10.3, which is greater than 10. Therefore, it should be judged that the multicollinearity test has not been passed, and the TZ variable needs to be deleted or further regularized.

[0082] However, directly removing the TZ variable would decrease the model's explanatory power and prediction accuracy due to its physical impact on rolling resistance performance. Therefore, a comprehensive evaluation of the engineering concession conditions is initiated. If the model satisfies: The overall goodness of fit of the model is R² greater than 0.85; The p-value of the RESET test is greater than or equal to a preset threshold (e.g., 0.05). The p-values ​​for the significance test of the regression coefficients of the independent variables after robust standard errors are less than 0.05; The signs of the coefficients of each independent variable are consistent with common sense in engineering physics; Furthermore, when all the above conditions are met, only the variance inflation factor (VIF) of a few independent variables is greater than 10 and less than 20. Therefore, it can be comprehensively determined that the model meets the preset engineering concession conditions, the multicollinearity diagnosis concession is passed, and the current model is the final regression model.

[0083] This embodiment clarifies the specific criteria for determining engineering concession conditions, making the method more adaptable and flexible in practical engineering applications, and avoiding the loss of effective predictive models that perform well in practical applications due to an excessive pursuit of the perfection of statistical theoretical indicators.

[0084] Example 5 The composition of the independent variables in the final model: This embodiment specifically defines the composition of the independent variables in the final regression model.

[0085] Based on the model construction, diagnosis, and correction process provided in Examples 1 to 3 above, the final regression model obtained uses tire rolling resistance FR as the dependent variable and includes at least the following independent variables: tire test load FZ or tire standard load FZS, tire tread compound heat generation index ZP, and the square of tire tread groove depth GD. 2 =FZ² or FZS² of the tire test load or tire standard load, ZP² of the tire tread compound heat generation index, and ZP·FZ or ZP·FZS of the interaction between the tire tread compound heat generation index and the tire test load or tire standard load.

[0086] In a specific example, when the tire test load FZS is selected as the load parameter, after a complete diagnostic and correction process, the fitting formula is obtained as follows: FR=129.66 12.18×ZP+13.35×GD²+24.01×FZS+30.55×ZP²+13.48 × FZS² 20.71×ZP×FZS The following is a list of significant factors influencing FR:

[0087] Real-world example: The error between the FR prediction results and the actual values ​​is shown in the table below (showing the first 20 rows):

[0088] In another specific example, when the tire test load FZ is selected as the load parameter, the fitting formula is obtained after the same diagnostic and correction process: FR = 129.79 12.19×ZP+13.58 × GD²+24.26 × FZ+26.65 × ZP²+12.34 ×FZ² 14.53×ZP×FZ List of significant factors influencing FR:

[0089] Real-world example: The error between the FR prediction result and the actual value is shown below (first 20 lines displayed):

[0090] The above analytical steps are also applicable to the prediction of other tire performance characteristics, and even the prediction of variables in other engineering applications.

[0091] The goodness-of-fit R² of both formulas exceeds 0.97, indicating extremely high prediction accuracy. While the former formula's prediction performance is slightly lower than the latter, its independent variable FZS is the tire standard load, a specification parameter directly obtainable during the design phase without the need for physical experiments. Therefore, it is more suitable for use in the new product concept design stage.

[0092] It should be noted that the coefficients in the above formula (such as 12.18, 13.15, etc.) are values ​​obtained by regression calculation based on the specific dataset collected. When the dataset is updated or expanded, the modeling process of this method is re-executed, and the obtained coefficient values ​​may fluctuate within a reasonable range, but the significance level and influence direction of each independent variable should remain stable.

[0093] This embodiment reveals the key design parameters (standard load, tread groove depth, and tread compound heat generation index) that affect tire rolling resistance by limiting the core independent variables included in the final model. It also introduces the square term of tread groove depth, the square term of standard load, the square term of tread compound heat generation index, and the interaction term of tread compound heat generation index and standard load to characterize their nonlinear influence, so that the model can have high interpretability and prediction accuracy while maintaining simplicity.

[0094] Example 6 This embodiment is based on the steps that failed the RESET test, and adds square terms and interaction terms to continue the correction and iteration.

[0095] Step 1: After multiple diagnostic and iterative corrections, only 5 independent variables were retained in the model: ZP, TZ, GD, FZS, and GD². The overall R-squared value of the model was [value missing]. 2 The p-value reached 0.965, with all variables' p-values ​​approaching 0.000 and VIF values ​​also close to <10. However, the RESET test p-value (0.0000 < 0.05) failed. Specific parameters are shown in the table below:

[0096] Specifically, this involves adding square terms and interaction terms: ZP², FZS², and ZP. After FZS iterations, the calculation results are as follows: Overall RV of the model 2The p-value reached 0.977, and all variables' p-values ​​approached 0.000. The RESET p-value was 0.1026 > 0.05, indicating the test passed. However, several variables showed increased VIF values, and heteroscedasticity and autocorrelation were also observed. The parameters are shown in the table below:

[0097] Step 2: Based on the above steps, the model is further refined. Specifically, the Newey-West robust standard error (HAC) method is used to correct heteroscedasticity and autocorrelation issues, and variable orthogonalization is used to address the problem of excessively high VIF values. The following analysis results are shown in the table below:

[0098] Based on the results in the table above, we can conclude that: The goodness of fit was R² = 0.977, and the adjusted R² = 0.977, which means that it explained 97.7% of the rolling resistance variation. Overall significance: F-statistic = 3794, p = 1.64e-292, indicating the model is highly significant overall; after orthogonalization, the VIF value drops below 5, thus passing the multicollinearity test; the RESET test is passed; JB = 0.861 > 0.05, indicating the residuals are approximately normally distributed; residual variance and autocorrelation have been corrected. The average residual rate is 3.59%, and the maximum residual rate is 12.95%. This demonstrates the model's overall robustness and high predictive accuracy.

[0099] Step 3: If the sample size is >50, the generalization ability of the models that have passed the comprehensive diagnosis can be diagnosed using the k-fold cross-validation method, k=5. The validation results are as follows:

[0100] According to the table above: like Figure 3 As shown in the figure, the diagram illustrates the analysis of the k-fold cross-validation results; the figure shows the analysis results when k=5.

[0101] The mean ± standard deviation of R² is 0.9756 ± 0.0063. The mean is close to the full sample R² (0.977), indicating that the model has strong generalization ability and is not overfitting.

[0102] Mean absolute error (MAE): 4.4089 ± 0.30243, coefficient of variation (CV) = 6.86% < 10%. The average prediction error of the model fluctuates very little, and the prediction bias is stable and controllable.

[0103] The root mean square error (RMSE) was 5.5809 ± 0.3760, and the coefficient of variation (CV) was 6.74% < 10%. The overall prediction error of the model was low and the fluctuation was minimal.

[0104] The mean absolute percentage error (MAPE) is 3.63% ± 0.24%, with a mean of <10%, and the coefficient of variation (CV) is 6.61% <10%. The model's relative prediction accuracy is highly consistent across different data subsets, with no significant subsample bias.

[0105] Note: Calculation of coefficient of variation for each indicator: CV = standard deviation / mean × 100% Step 4: Obtain the final regression model formula through comprehensive diagnosis and generalization ability diagnosis: FR = 129.66 12.18×ZP+13.35×GD²+24.01×FZS+30.55×ZP²+13.48×FZS² 20.71×ZP×FZS The error between the FR prediction result and the actual value is shown in the table below (showing the first 20 rows):

[0106] The significance of the factors influencing FR is shown in the table below:

[0107] Based on the above steps, the specific steps for engineering application are as follows: This embodiment reveals the key design parameters (standard tire load and tread compound heat generation index) that affect tire rolling resistance by limiting the core independent variables included in the final model. It also introduces the square terms of standard load, tread groove depth, and tread compound heat generation index, as well as the interaction term between tread compound heat generation index and standard load, to characterize their nonlinear influence. This makes the model more concise while having high interpretability and prediction accuracy.

[0108] It should be noted that the coefficients in the above formula (such as -12.18, 13.35, etc.) are calculated based on the specific dataset collected and after regression and orthogonalization. When the dataset is updated or expanded, the modeling process of this method is re-executed, and the obtained coefficient values ​​may fluctuate within a reasonable range, but the significance level and influence direction of each independent variable remain stable.

[0109] Step 5: Obtain the final true coefficient model through orthogonal and standardized inverse transforms. The final regression model obtained above is decoupled by orthogonal transformation and its dimensionality is restored by standardization to obtain the true coefficient model of the original variables.

[0110] The formula is as follows: Original variable coefficients = (orthogonality coefficients × orthogonal transformation matrix) / standard deviation of the variable

[0111] Orthogonal transformation matrix Orthogonal space regression coefficients : Standard deviation of the j-th original variable Coefficients of the original variables Coefficients of the original constant term

[0112] The following final true coefficient model for rolling resistance FR is obtained through the inverse transformation of the above formula. Theoretically, the inverse transformation has no impact on the FR prediction result. However, considering the difference in the units of the original variables, the coefficients after the inverse transformation need to retain as many decimal places as possible to restore the true calculation result: FR = 213.680356474 - 2.438737126×ZP + 0.139976858×GD 2 + 0.030653355×FZS + 0.008269479×ZP² + 0.000002348×FZS² - 0.000152335×ZP·FZS The error between the FR prediction results and the actual values ​​is shown in the table below (showing the first 20 rows):

[0113] Example 7 This embodiment provides a prediction system for implementing the method described in any of the above embodiments. The system includes the following functional modules: The data acquisition module is used to acquire historical tire design parameters and corresponding measured rolling resistance data to build a dataset. This module can interface with tire companies' product data management systems, laboratory information management systems, or finite element analysis platforms to extract the required parameter and test data.

[0114] The data preprocessing module is used to preprocess the design parameters in the dataset to form a numerical dataset suitable for regression analysis. This module specifically performs the following functions: data cleaning (missing value handling, outlier detection and handling, duplicate value removal); normalization of numerical variables (such as Z-Score standardization or Min-Max Scaling); one-hot encoding of categorical variables; and data concatenation and integration. When both normalization and one-hot encoding are required, this module ensures that normalization is performed before one-hot encoding.

[0115] The model building and diagnostic module performs the following core functions: Based on the numerical dataset, it establishes an initial multiple regression model with rolling resistance performance index as the dependent variable and design parameters as the independent variables, and executes a model diagnostic procedure on the initial model or the modified model. The model diagnostic procedure includes at least nonlinearity diagnosis, multicollinearity test, residual test, and generalization ability diagnosis. When any diagnostic item of the model diagnostic procedure fails, it performs the correction operation corresponding to the diagnostic item, and re-executes the model diagnostic procedure based on the modified model until all diagnostic items of the model diagnostic procedure pass or meet the preset engineering concession conditions to obtain the final regression model. Then, it performs inverse transformation to obtain the final true coefficient model of the original variables.

[0116] The prediction output module receives the design parameters of the tire under test and outputs the predicted rolling resistance performance results using the final true coefficient model. The prediction results may include the predicted value of the tire rolling resistance FR and / or the predicted value of the tire rolling resistance coefficient RRC.

[0117] This system can be deployed on computers, servers, or cloud platforms. Through the collaborative work of its modules, it enables rapid prediction of tire rolling resistance performance. When the data acquisition module receives new test data, the model building and diagnostic module can re-execute the modeling and diagnostic process to update and optimize the model, thereby continuously improving prediction accuracy.

[0118] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention. The scope of the invention is defined by the appended claims and their equivalents, all of which should be included within the scope of protection of the invention.

Claims

1. A method for predicting tire rolling resistance performance, characterized in that, Includes the following steps: Obtain historical tire design parameters and corresponding measured rolling resistance data to construct a dataset; The design parameters in the dataset are preprocessed to form a numerical dataset suitable for regression analysis; Based on the numerical dataset, an initial multiple regression model is established with rolling resistance performance index as the dependent variable and design parameters as the independent variables. A model diagnostic procedure is performed on the initial model or the modified model. The model diagnostic procedure includes nonlinearity diagnosis, multicollinearity test, residual test, and generalization ability diagnosis. When any diagnostic item of the model diagnostic program fails, the correction operation corresponding to the diagnostic item is executed, and the model diagnostic program is re-executed based on the corrected model until all diagnostic items of the model diagnostic program pass or meet the preset engineering concession conditions, and the final regression model is obtained. Then, an inverse transformation is performed on it to obtain the final true coefficient model of the original variables. The design parameters of the tire to be tested are received, and the rolling resistance performance prediction results are output using the final true coefficient model.

2. The method for predicting tire rolling resistance performance according to claim 1, characterized in that, The preprocessing of the design parameters in the dataset specifically includes: The numerical variables in the design parameters are normalized. One-hot encoding is performed on the categorical variables in the design parameters; The normalization process is performed before the one-hot encoding process.

3. The method for predicting tire rolling resistance performance according to claim 1, characterized in that, Also includes: Initial tests are performed on the initial model, including overall significance test, goodness-of-fit test, regression coefficient significance test, and multicollinearity test; If the initial test fails, the correction operation will proceed directly.

4. The method for predicting tire rolling resistance performance according to claim 1, characterized in that, The multicollinearity test includes: Calculate the variance inflation factor (VIF) values ​​for each independent variable; When the variance inflation factor (VIF) value of any independent variable is greater than 10, the multicollinearity test is deemed to have failed. The corresponding corrective actions include deleting independent variables with high VIF values, using Cook distance to remove outliers and strong influence points, and using ridge regression, stepwise regression, or variable orthogonalization to deal with multicollinearity.

5. The method for predicting tire rolling resistance performance according to claim 1, characterized in that, The residual test includes: The residual normality test is used to determine whether the residuals follow a normal distribution. The residual independence test is used to determine whether the residuals are autocorrelated. The residual variance test is used to determine whether the residual variance is constant. When the residual normality test, residual independence test, or residual variance test fails, the correction operation includes: using the Cook distance method to detect outliers and strong influence points in the dataset, removing the detected outliers and strong influence points, and correcting the model with heteroscedasticity robust standard error HC3; if the residual variance test and autocorrelation test both fail, then the Newey-West robust standard error HAC method is used for correction.

6. The method for predicting tire rolling resistance performance according to claim 1, characterized in that, The nonlinear diagnosis includes: Perform a RESET test to check for any missing higher-order terms or interaction terms; If the p-value of the RESET test is less than the preset threshold, then higher-order terms and / or interaction terms are introduced into the model. If the introduced higher-order terms and / or interaction terms pass the regression coefficient significance test and have a significant effect, they are retained; When higher-order terms and / or interaction terms are introduced into the model, and the RESET test passes, but multiple variables show an increase in variance inflation factor (VIF), variable orthogonalization (Gram-Schmidt strict orthogonalization) can be used. The squared terms and interaction terms are regressed against the original variables, and the residuals are taken as new variables. This ensures that the nonlinear terms are linearly independent of the original variables, thus solving the multicollinearity problem in the multinomial model.

7. The method for predicting tire rolling resistance performance according to claim 1, characterized in that, The generalization ability diagnosis includes: Once the nonlinearity diagnosis, multicollinearity test, and residual test are all passed, the corrected regression model is obtained. If the dataset sample size is ≤50, this modified regression model is the final regression model; If the dataset sample size is greater than 50, the k-fold cross-validation method is used to diagnose the generalization ability and stability of the model. If the difference between the mean R² of k-fold cross-validation and the R² of the original model is ≤ 0.05, and the coefficient of variation (CV) of the mean MAE, RMSE, and MAPE is less than the preset threshold, then the model is considered stable and has strong generalization ability, and is used as the final regression model.

8. The method for predicting tire rolling resistance performance according to claim 1, characterized in that, The preset engineering concession conditions include the following conditions being met simultaneously: The overall goodness of fit of the model is R² greater than 0.85; The p-value of the RESET test is greater than or equal to the preset threshold; The p-values ​​for the significance test of the regression coefficients of the independent variables after robust standard errors are less than 0.05; The signs of the coefficients of each independent variable are consistent with common sense in engineering physics. Furthermore, when all the above conditions are met, the variance inflation factor (VIF) value of individual independent variables in the multicollinearity diagnosis is allowed to be greater than 10 and less than 20.

9. The method for predicting tire rolling resistance according to claim 1, characterized in that, The final regression model uses tire rolling resistance FR as the dependent variable and includes at least the following independent variables: tire test load FZ or tire standard load FZS, tire tread compound heat index ZP, and the square of tire tread groove depth GD. 2 =FZ² or FZS² of the tire test load or tire standard load, ZP² of the tire tread compound heat generation index, and ZP·FZ or ZP·FZS of the interaction between the tire tread compound heat generation index and the tire test load or tire standard load.

10. A prediction system employing the tire rolling resistance performance prediction method as described in any one of claims 1 to 9, characterized in that, include: The data acquisition module is used to acquire historical tire design parameters and corresponding measured rolling resistance data to build a dataset; The data preprocessing module is used to preprocess the design parameters in the dataset to form a numerical dataset suitable for regression analysis. The model building and diagnostic module is used to establish an initial multiple regression model based on the numerical dataset, with rolling resistance performance index as the dependent variable and design parameters as the independent variables. It then executes a model diagnostic procedure on the initial or modified model, which includes at least nonlinearity diagnosis, multicollinearity test, residual test, and generalization ability diagnosis. If any diagnostic item in the model diagnostic procedure fails, a correction operation corresponding to that item is performed, and the model diagnostic procedure is re-executed based on the modified model until all diagnostic items pass or preset engineering concession conditions are met, thus obtaining the final regression model. Finally, the module performs an inverse transformation on the model to obtain the final true coefficient model of the original variables. The prediction output module is used to receive the design parameters of the tire under test and output the rolling resistance performance prediction results using the final true coefficient model.

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