A non-pneumatic tire three-directional stiffness prediction method based on an SSA-XGBoost interpretable model

Abstract

This invention discloses a method for predicting the triaxial stiffness of non-pneumatic tires based on an SSA-XGBoost interpretable model. The method first establishes a parametric model of the non-pneumatic tire and uses experimental design methods to obtain a small amount of mapping data between structural parameters and radial, lateral, and longitudinal stiffness, constructing a small-sample training set. Second, an XGBoost regression prediction model is constructed, and a sparrow search algorithm is introduced to adaptively optimize key hyperparameters such as the learning rate and tree depth, improving prediction accuracy and generalization ability under small sample conditions. Finally, the prediction results are additively interpreted using the SHAP game theory method, quantifying the contribution of each design variable to the triaxial stiffness. This invention effectively solves the problems of high computational cost of traditional finite element simulation, low accuracy of conventional surrogate models under small sample conditions, and lack of physical interpretability, achieving rapid and accurate prediction and design guidance of non-pneumatic tire stiffness characteristics.

Description

Technical Field

[0001] This invention relates to the field of non-pneumatic tire performance prediction technology, and in particular to a method for predicting the triaxial stiffness of non-pneumatic tires based on the SSA-XGBoost interpretable model. Background Technology

[0002] Non-pneumatic tires are increasingly widely used due to their advantages such as maintenance-free operation, no risk of tire blowout, and high load-bearing capacity. Their radial, lateral, and longitudinal stiffness are core mechanical performance indicators that directly affect vehicle safety and comfort. Currently, stiffness prediction mainly relies on finite element simulation or physical testing. Finite element simulation offers high accuracy but is time-consuming and expensive, resulting in long design iteration cycles; physical testing requires the fabrication of numerous samples, leading to significant R&D investment.

[0003] With the development of machine learning technology, researchers have attempted to apply it to tire stiffness prediction. However, existing technologies have significant drawbacks: 1) Data dependency: Traditional algorithms require a large amount of high-precision data, but obtaining large-scale data in the early stages of design is impractical; 2) Parameter tuning challenges: High-performance algorithms such as XGBoost have many hyperparameters, making manual parameter tuning inefficient and prone to getting trapped in local optima; 3) Poor model interpretability: Prediction results based on black-box models are difficult to interpret, making it impossible to clarify the influence mechanism of each structural parameter and directly guide product optimization.

[0004] The prediction method based on response surface methodology disclosed in Chinese patent application CN118332776A, "A Prediction Method for the Performance of Spoke-Type Non-Pneumatic Tires, Its Establishment Method and Application," has limited model expressive power and is difficult to accurately capture the highly nonlinear mapping relationship between the complex structural parameters of non-pneumatic tires and triaxial stiffness, especially with insufficient accuracy under small sample conditions.

[0005] The prediction method based on a BP neural network disclosed in Chinese patent application CN119720628A, "A Gradient Negative Poisson's Ratio Non-pneumatic Tire Stiffness Prediction Method," suffers from several drawbacks. Its model performance is heavily influenced by initial weights, making it prone to getting trapped in local optima. Furthermore, its hyperparameter tuning relies heavily on experience, and it also faces the problem of unstable generalization ability with small sample data. Both of these methods lack physical interpretability in their prediction results, failing to clearly reveal the influence mechanism and contribution degree of each structural design parameter on a specific stiffness, thus making it difficult to directly and effectively guide designers in structural optimization. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting the triaxial stiffness of non-pneumatic tires based on the SSA-XGBoost interpretable model, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting the triaxial stiffness of a non-pneumatic tire based on an SSA-XGBoost interpretable model, comprising the following steps: S1. Obtain the structural design parameters of the non-pneumatic tire and construct a parametric finite element simulation model; use the experimental design method to extract sample points in the design space, and obtain the radial, lateral and longitudinal stiffness response values ​​corresponding to each sample point through finite element simulation calculation, and construct a small sample original dataset containing design variables and three-dimensional stiffness labels. S2. Preprocess the original small sample dataset and divide it into training and test sets; S3. Construct a stiffness prediction benchmark model based on the XGBoost algorithm and determine the hyperparameter space of the model to be optimized. S4. The XGBoost model is optimized for hyperparameters using the sparrow search algorithm. The cross-validation prediction error of the training set is used as the fitness function to iteratively search for the global optimal combination of hyperparameters. S5. Construct the final triaxial stiffness prediction model using the global optimal hyperparameter combination, and introduce the SHAP interpreter to train the model, quantifying the contribution of each structural design parameter to the stiffness prediction result. S6. Input the structural design parameters of the non-pneumatic tire to be tested, use the trained model to output the predicted triaxial stiffness value, and combine the SHAP value to output the feature importance analysis results to guide the structural optimization of the non-pneumatic tire.

[0008] Preferably, in step S1, the construction of the parametric finite element simulation model and the small sample original dataset specifically includes: S101. Spoke thickness, spoke curvature, hub radius, shear band modulus, and tread depth are selected as key structural design variables. S102. The optimal Latin hypercube sampling method is used to sample within the range of values ​​of each design variable to generate a preset number of sample combinations. S103. For each sample combination, apply radial, lateral, and longitudinal load conditions respectively, calculate the corresponding radial stiffness, lateral stiffness, and longitudinal stiffness using a finite element solver, and establish a mapping database between input characteristics and output response.

[0009] Preferably, in step S2, the preprocessing of the small sample original dataset includes: S201. Perform outlier detection on the original dataset and remove outlier samples that cause the simulation to fail to converge due to mesh distortion. S202. Normalize the structural design variables and stiffness response values, and map the data to the [0,1] interval to eliminate the influence of different dimensions on model training.

[0010] Preferably, in step S3, the hyperparameter space of the model to be optimized includes at least: learning rate, maximum tree depth, subsample sampling rate, column sampling rate, and regularization weights; The XGBoost model uses the squared error loss function.

[0011] Preferably, in step S4, the process of using the Sparrow Search algorithm to optimize the hyperparameters of the XGBoost model includes: S401. Population initialization: Define the position vector of each individual in the sparrow population as a set of XGBoost hyperparameter combinations; S402, Fitness Calculation: Substitute the current hyperparameter combination into the XGBoost model for K-fold cross-validation, and calculate the root mean square error of the validation set as the fitness value of the individual. S403, Position Update: For the discoverer, a global search is performed within the search space; for the joiner, a local search is performed following the discoverer; for the alerter, when it realizes that it has entered a local optimum, it jumps to other positions in the search space for random exploration. S404, Termination of Iteration: When the preset maximum number of iterations is reached or the fitness value no longer decreases significantly, output the hyperparameter combination corresponding to the global optimal fitness.

[0012] Preferably, in step S5, the introduction of the SHAP interpreter to train the model and quantify its contribution specifically includes: S501. Based on the Shapley value theory of game theory, calculate the SHAP value of each structural design parameter. The SHAP value represents the positive or negative marginal contribution of the parameter to the stiffness prediction result when it deviates from the benchmark value. S502. Based on the average absolute value of the SHAP values ​​of all samples, generate a feature importance ranking chart to identify key design parameters that affect the stiffness of non-pneumatic tires in a specific direction. S503. Generate a SHAP dependency graph to visualize the nonlinear correlation between key design parameters and stiffness values.

[0013] Preferably, in step S6, the structural optimization of the non-pneumatic tire specifically includes: S601. If the predicted stiffness in a certain direction is less than the design target value, then according to the SHAP feature importance ranking chart, select the structural parameter that contributes the most to the SHAP value for adjustment. S602. Based on the parameter influence trend reflected in the SHAP dependency graph, determine the specific adjustment direction of the structural parameters.

[0014] Preferably, the parametric modeling and data acquisition module is used to acquire the structural design parameters of the non-pneumatic tire and construct a small sample dataset containing design variables and triaxial stiffness values ​​through optimal Latin hypercube sampling and finite element simulation. The data preprocessing module is used to clean, normalize, and divide the dataset into training and test sets. The intelligent optimization module is used to initialize the sparrow search algorithm and adaptively optimize the key hyperparameters of the XGBoost model globally using the prediction error of the XGBoost model as the fitness function. The prediction model building module is used to receive the optimal hyperparameters output by the intelligent optimization module and train to generate a high-precision triaxial stiffness prediction model for non-pneumatic tires. The interpretability analysis module is used to calculate and output the SHAP values ​​of each structural parameter, the feature importance ranking graph, and the dependency graph; The results output module is used to receive new tire geometry parameters input by the user and output triaxial stiffness prediction values ​​and structural optimization suggestions.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention combines optimal Latin hypercube sampling with the high-performance XGBoost algorithm to achieve high-precision prediction even with small sample sizes.

[0016] By leveraging the global optimization capability of the sparrow search algorithm, the optimal hyperparameters for XGBoost can be automatically found, thereby improving model performance and debugging efficiency.

[0017] By introducing SHAP value quantitative analysis, the contribution of each structural parameter to stiffness is revealed, providing clear guidance for optimized design. Attached Figure Description

[0018] Figure 1 A flowchart of a non-pneumatic tire triaxial stiffness prediction method based on an SSA-XGBoost interpretable model provided in an embodiment of the present invention.

[0019] Figure 2 This is a structural block diagram of the non-pneumatic tire triaxial stiffness prediction system based on the SSA-XGBoost interpretable model provided in this embodiment of the invention. Detailed Implementation

[0020] 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 of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0021] Please see Figures 1 to 2 This invention provides a technical solution: a method for predicting the triaxial stiffness of a non-pneumatic tire based on an SSA-XGBoost interpretable model, comprising: S1. Parametric Modeling and Small Sample Dataset Construction: Determine key structural design parameters (such as spoke thickness, curvature, etc.) and establish a parametric model in finite element software; use the optimal Latin hypercube sampling method to extract 30-100 sets of samples in the design space; through finite element simulation, calculate the stiffness values ​​of each set of samples under radial, lateral, and longitudinal loads to form a "feature-label" dataset.

[0022] S2. Data preprocessing: Clean up outlier data and normalize all features and labels to eliminate the influence of units. Then, divide the dataset into training and test sets.

[0023] S3. Constructing the XGBoost prediction model and defining the hyperparameter space: Initialize the XGBoost regression model and set the hyperparameters to be optimized and their search space, including the learning rate and the maximum tree depth.

[0024] S4. Intelligent Hyperparameter Optimization Based on Sparrow Search Algorithm: The hyperparameter combination of XGBoost is mapped to the position of individual sparrows; the root mean square error of the K-fold cross-validation of the XGBoost model on the training set is used as the fitness value; the position update rules of the discoverer, joiner and warning in the sparrow search algorithm are iteratively executed to automatically find the globally optimal hyperparameter combination.

[0025] S5. Training an interpretable stiffness prediction model: Retrain the XGBoost model using the optimal hyperparameters obtained through optimization; then introduce the SHAP interpreter, which calculates the SHAP value of each structural parameter for each prediction sample based on the Shapley value of game theory, thereby quantifying the contribution of each parameter.

[0026] S6. Stiffness Prediction and Optimization Decision Support: For a new combination of design parameters, the trained model can instantly output the predicted values ​​of three-dimensional stiffness. At the same time, the system provides feature importance ranking and feature dependency graph based on SHAP values, clearly indicating which parameter should be adjusted first and how to adjust it in order to achieve the target stiffness, thus realizing a closed loop from "prediction" to "interpretation" and then to "guidance".

[0027] Example 1: A method for predicting the triaxial stiffness of non-pneumatic tires based on an SSA-XGBoost interpretable model This embodiment provides a method for predicting the triaxial stiffness of non-pneumatic tires based on the SSA-XGBoost interpretable model, such as... Figure 1 As shown, the specific steps are as follows: S100. Construct a small sample dataset.

[0028] S101. Determine design variables: Select structural parameters that have a significant impact on stiffness characteristics as design variables, such as spoke thickness, spoke curvature, hub radius, shear band modulus, and tread depth.

[0029] S102. Parametric Modeling and Simulation: A parametric model of a non-pneumatic tire is established in finite element software, enabling automated driving of geometric parameters and batch simulation. The spoke structure can be simplified (e.g., set as a tensile shell element) to improve simulation efficiency.

[0030] S103. Small sample sampling: Use the optimal Latin hypercube sampling method to sample within the design space and generate N sets of sample points (N is recommended to be 30 to 100).

[0031] S104. Perform finite element simulation calculations for each sample point under radial compression, lateral sway, and longitudinal torsion conditions to obtain the corresponding radial stiffness, lateral stiffness, and longitudinal stiffness response values.

[0032] S105. Constructing the dataset: Combine the N sets of design variables and their corresponding stiffness values ​​into a matrix to form a small sample original dataset containing input features and output labels.

[0033] S200, Data Preprocessing and Partitioning.

[0034] S201. Data cleaning: Remove invalid samples that do not converge or have abnormal results.

[0035] S202. Data Normalization: Normalize all variables and stiffness values, mapping them to the [0,1] interval to eliminate interference from different units of measurement during model training. The normalization formula is as follows:

[0036] in, The original data values, and These are the minimum and maximum values ​​of the feature in the training set, respectively.

[0037] S203. Dataset partitioning: Divide the data into training set and test set according to a preset ratio (e.g., 7:3).

[0038] S300: The XGBoost model is optimized using the Sparrow Search Algorithm (SSA).

[0039] S301, learning rate (learning_rate), maximum depth of the tree (max_depth), subsample rate of samples (subsample), subsample rate of columns by tree (colsample_bytree), L1 regularization term (lambda), L2 regularization term (alpha), etc.

[0040] S302, Initialize the SSA population: Map the position vector of each sparrow to a set of XGBoost hyperparameter combinations.

[0041] S303, Train the XGBoost model with the current hyperparameter combination, and use K-fold cross-validation (for example, K = 5) to calculate the root mean square error (RMSE) of the validation set as the individual fitness value. The smaller the RMSE, the better the model performance.

[0042] S304, Update the position of the sparrow population: Responsible for exploring potential better regions, and the update formula is as follows: ; where, X i t is the position of the i-th discoverer in the t-th generation, α is a random number within (0, 1], iter max is the maximum number of iterations. When the warning value R2 < ST, the discoverer will randomly move to a safe position.

[0043] 1. Update of the discoverer: The discoverer leads the global search and is responsible for exploring potential better regions; 2. Update of the joiner: The joiner follows the discoverer for local search, and its position update formula is related to the state of the discoverer. When the i-th sparrow is the optimal individual, its update method is different to avoid falling into local optimality; 3. Update of the early warning sparrow: Preset a certain proportion (such as 10% - 20%) of the sparrows as early warning sparrows. When they detect a danger signal (such as falling into local optimality), they will randomly jump to other positions in the search space; S305, Judge the termination condition: Repeat steps S303 - S304, and terminate the iteration when the maximum number of iterations is reached or the fitness value no longer decreases significantly.

[0044] S306, Obtain the global optimal solution: Output the global optimal hyperparameter combination.

[0045] S400, Build and train the final prediction model.

[0046] S401, Model initialization: Initialize the XGBoost model with the optimal hyperparameter combination.

[0047] S402. Model Training: Train the model on the full training set, with radial, lateral and longitudinal stiffness as multi-task learning objectives, or build independent prediction models for each.

[0048] S403. Model Evaluation: Evaluate the predictive performance of the model on the test set and verify the model accuracy by calculating indicators such as the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). S404. Introduce the SHAP interpreter: Based on the Shapley value theory, calculate the SHAP value of each design variable.

[0049] S500, stiffness prediction and interpretability analysis.

[0050] S501, Stiffness Prediction: Input the structural design parameters of the non-pneumatic tire under test, and use the trained SSA-XGBoost model to output the predicted values ​​of radial, lateral, and longitudinal stiffness. The entire process takes only milliseconds, which is thousands of times more efficient than finite element simulation.

[0051] S502, Feature Importance Ranking: Based on the average of the absolute values ​​of the SHAP values ​​of all samples, a feature importance ranking chart is generated. This ranking chart clearly shows the comprehensive contribution of each structural parameter to stiffness performance, helping engineers quickly identify key design variables.

[0052] S503, Univariate Influence Analysis: Through the SHAP Dependence Plot, the nonlinear relationship between a key design parameter and stiffness value is visualized, showing the positive and negative influence trends of parameter values ​​on the results.

[0053] S504. Provide optimization suggestions: Based on the above analysis results, provide quantitative guidance for the optimization of non-pneumatic tire structures. For example, if it is necessary to improve lateral stiffness, engineers can prioritize adjusting the "spoke angle" parameter, which contributes the most to the SHAP value, and determine the direction of adjustment based on the dependency graph.

[0054] Example 2: Triaxial Stiffness Prediction System for Non-Pneumatic Tires Based on SSA-XGBoost Interpretable Model The present invention also provides a system for implementing the above method, the system comprising: 1. Used to construct a parametric non-pneumatic tire finite element model, and obtain and store a small sample dataset containing structural design parameters and triaxial stiffness labels through optimal Latin hypercube sampling and finite element simulation calculation.

[0055] 2. Data preprocessing module: This module cleans and normalizes the raw simulation data, and divides the data into training and test sets according to a set ratio, providing standardized input data for subsequent model training.

[0056] 3. Intelligent Optimization Module: Used to initialize the Sparrow Search algorithm, set the fitness function, traverse the search space, and output the globally optimal hyperparameter combination of the XGBoost model.

[0057] 4. Prediction Model Building Module: Used to initialize the XGBoost model based on the optimization results, complete model training using the training set, and evaluate performance on the test set.

[0058] 5. Interpretability Analysis Module: Used to calculate the SHAP value of each design variable, generate feature importance ranking plots and SHAP dependency plots, and quantify and explain the influence mechanism of each parameter on the prediction results.

[0059] Results output module: Provides users with an interactive interface for inputting the structural parameters of the non-pneumatic tire under test, receiving and displaying the system's output triaxial stiffness prediction values ​​and interpretability analysis reports, providing a scientific basis for engineers' structural optimization decisions.

[0060] As is known from common technical knowledge, this invention can be implemented through other embodiments that do not depart from its spirit or essential characteristics. Therefore, the disclosed embodiments described above are merely illustrative and not exhaustive. All modifications within the scope of this invention or its equivalents are included in this invention.

Claims

1. A method for predicting the triaxial stiffness of a non-pneumatic tire based on an SSA-XGBoost interpretable model, characterized in that: Includes the following steps: S1. Obtain the structural design parameters of the non-pneumatic tire and construct a parametric finite element simulation model; use the experimental design method to extract sample points in the design space, and obtain the radial, lateral and longitudinal stiffness response values ​​corresponding to each sample point through finite element simulation calculation, and construct a small sample original dataset containing design variables and three-dimensional stiffness labels. S2. Preprocess the original small sample dataset and divide it into training and test sets; S3. Construct a stiffness prediction benchmark model based on the XGBoost algorithm and determine the hyperparameter space of the model to be optimized. S4. The XGBoost model is optimized for hyperparameters using the sparrow search algorithm. The cross-validation prediction error of the training set is used as the fitness function to iteratively search for the global optimal combination of hyperparameters. S5. Construct the final triaxial stiffness prediction model using the global optimal hyperparameter combination, and introduce the SHAP interpreter to train the model, quantifying the contribution of each structural design parameter to the stiffness prediction result. S6. Input the structural design parameters of the non-pneumatic tire to be tested, use the trained model to output the predicted triaxial stiffness value, and combine the SHAP value to output the feature importance analysis results to guide the structural optimization of the non-pneumatic tire.

2. The method for predicting the triaxial stiffness of a non-pneumatic tire based on an SSA-XGBoost interpretable model according to claim 1, characterized in that: In step S1, the construction of the parametric finite element simulation model and the small sample original dataset specifically includes: S101. Spoke thickness, spoke curvature, hub radius, shear band modulus, and tread depth are selected as key structural design variables. S102. The optimal Latin hypercube sampling method is used to sample within the range of values ​​of each design variable to generate a preset number of sample combinations. S103. For each sample combination, apply radial, lateral, and longitudinal load conditions respectively, calculate the corresponding radial stiffness, lateral stiffness, and longitudinal stiffness using a finite element solver, and establish a mapping database between input characteristics and output response.

3. The method for predicting the triaxial stiffness of a non-pneumatic tire based on an SSA-XGBoost interpretable model according to claim 2, characterized in that: In step S2, the preprocessing of the small sample original dataset includes: S201. Perform outlier detection on the original dataset and remove outlier samples that cause the simulation to fail to converge due to mesh distortion. S202. Normalize the structural design variables and stiffness response values, and map the data to the [0,1] interval to eliminate the influence of different dimensions on model training.

4. The method for predicting the triaxial stiffness of a non-pneumatic tire based on an SSA-XGBoost interpretable model according to claim 1, characterized in that: In step S3, the hyperparameter space of the model to be optimized includes at least: learning rate, maximum tree depth, subsample sampling rate, column sampling rate, and regularization weights; The XGBoost model uses the squared error loss function.

5. The method for predicting the triaxial stiffness of a non-pneumatic tire based on an SSA-XGBoost interpretable model according to claim 1, characterized in that: In step S4, the hyperparameter optimization of the XGBoost model using the sparrow search algorithm specifically includes: S401. Population initialization: Define the position vector of each individual in the sparrow population as a set of XGBoost hyperparameter combinations; S402, Fitness Calculation: Substitute the current hyperparameter combination into the XGBoost model for K-fold cross-validation, and calculate the root mean square error of the validation set as the fitness value of the individual. S403, Position Update: For the discoverer, a global search is performed within the search space; for the joiner, a local search is performed following the discoverer; for the alerter, when it realizes that it has entered a local optimum, it jumps to other positions in the search space for random exploration. S404, Termination of Iteration: When the preset maximum number of iterations is reached or the fitness value no longer decreases significantly, output the hyperparameter combination corresponding to the global optimal fitness.

6. The method for predicting the triaxial stiffness of a non-pneumatic tire based on an SSA-XGBoost interpretable model according to claim 1, characterized in that: In step S5, the introduction of the SHAP interpreter to train the model and quantify its contribution specifically includes: S501. Based on the Shapley value theory of game theory, calculate the SHAP value of each structural design parameter. The SHAP value represents the positive or negative marginal contribution of the parameter to the stiffness prediction result when it deviates from the benchmark value. S502. Based on the average absolute value of the SHAP values ​​of all samples, generate a feature importance ranking chart to identify key design parameters that affect the stiffness of non-pneumatic tires in a specific direction. S503. Generate a SHAP dependency graph to visualize the nonlinear correlation between key design parameters and stiffness values.

7. The method for predicting the triaxial stiffness of a non-pneumatic tire based on an SSA-XGBoost interpretable model according to claim 1, characterized in that: In step S6, the structural optimization of the non-pneumatic tire specifically includes: S601. If the predicted stiffness in a certain direction is less than the design target value, then according to the SHAP feature importance ranking chart, select the structural parameter that contributes the most to the SHAP value for adjustment. S602. Based on the parameter influence trend reflected in the SHAP dependency graph, determine the specific adjustment direction of the structural parameters.

8. The method for predicting the triaxial stiffness of a non-pneumatic tire based on an SSA-XGBoost interpretable model according to claim 1, characterized in that: The parametric modeling and data acquisition module is used to obtain the structural design parameters of non-pneumatic tires. It constructs a small sample dataset containing design variables and triaxial stiffness values ​​through optimal Latin hypercube sampling and finite element simulation. The data preprocessing module is used to clean, normalize, and divide the dataset into training and test sets. The intelligent optimization module is used to initialize the sparrow search algorithm and adaptively optimize the key hyperparameters of the XGBoost model globally using the prediction error of the XGBoost model as the fitness function. The prediction model building module is used to receive the optimal hyperparameters output by the intelligent optimization module and train to generate a high-precision triaxial stiffness prediction model for non-pneumatic tires. The interpretability analysis module is used to calculate and output the SHAP values ​​of each structural parameter, the feature importance ranking graph, and the dependency graph; The results output module is used to receive new tire geometry parameters input by the user and output triaxial stiffness prediction values ​​and structural optimization suggestions.

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