A machine learning based tire inflation profile prediction method and system

Abstract

This invention relates to the field of tire performance prediction technology based on artificial intelligence, and more particularly to a method and system for predicting tire inflation profiles based on machine learning. The method acquires the structural parameters, material parameters, and actual inflation profile data of a sample tire, extracting the partitioning mechanism parameters of the crown, shoulder, sidewall, and heel regions; unifies the profiles to the rim reference coordinate system and standardizes the partitions, constructing local reference profiles and local basis vectors for each partition; establishes a multi-output machine learning model with partitioning mechanism parameters as input and local basis vector coefficients and key geometric quantities as outputs to complete the prediction of the target tire inflation profile, and outputs the final profile through geometric feasibility verification and local projection correction. This invention can significantly shorten the tire inflation profile prediction time, improve prediction accuracy and engineering applicability, and is suitable for rapid tire design and optimization.

Description

Technical Field

[0001] This invention relates to the field of tire performance prediction technology based on artificial intelligence, and in particular to a tire inflation profile prediction method and system based on machine learning. Background Technology

[0002] As the only elastic component of a vehicle in contact with the road surface, the tire's inflated profile determines not only its section width, section height, shoulder transition shape, and heel seating position, but also further influences the tire's ground pressure distribution, handling stability, rolling resistance, durability, and ride comfort. During tire product development, designers typically need to predict the tire's inflation profile as accurately as possible, given specifications, rim size, and inflation pressure. This allows for timely adjustments to the tire carcass profile, belt layer endpoints, sidewall wrap angles, and related material configurations during the structural design phase, thereby reducing subsequent prototyping and repeated mold modifications.

[0003] Chinese patent document CN1791518A discloses a design method that uses at least one of the following parameters—the tire cross-sectional shape, the shape of tire components, and the physical property data of tire components—to establish an initial model of an inflatable tire. This model is then deformed through internal pressure filling to predict the tire's cross-sectional shape. Furthermore, ground contact processing and safety margin calculations can be combined to optimize tire durability design. Therefore, document CN1791518A reveals that in the tire design process, tire structural parameters and material properties can be used as inputs to predict the tire's cross-sectional profile after inflation through modeling and solving, thus providing a basis for tire structural design.

[0004] However, the aforementioned existing technologies mainly rely on finite element modeling and nonlinear numerical solutions to obtain the profile results of an inflated tire. While this type of method has strong physical interpretability, it still has significant limitations in engineering applications. First, finite element models typically require detailed geometric modeling and mesh generation for parts such as the tread, belt layers, carcass, sidewall, and heel. They also require comprehensive material constitutive parameters, cord composite parameters, and boundary contact conditions, making model building complex and requiring substantial preprocessing. Second, tire inflation analysis itself is a significantly nonlinear problem, involving large deformations, composite material anisotropy, and contact constraints. A single calculation is often time-consuming, making it difficult to meet the needs of rapid comparison of multiple specifications and parameters in the tire design phase. Third, this type of method is highly dependent on the engineer's experience. Different mesh qualities, material parameter calibration accuracy, and boundary condition settings can significantly affect the final prediction results, leading to insufficient consistency in analysis results among different personnel.

[0005] Especially given the current trend of tire product development moving towards digitalization and rapid iteration, design departments often need to evaluate a large number of candidate cross-section schemes within a short period of time. If each scheme is modeled, solved, and post-processed using the traditional finite element method, the development cycle and computational resource consumption are both significant, making it difficult to meet the demands of rapid development. Particularly for scenarios involving tires of different specifications on the same platform, adjacent aspect ratio tires, or fine-tuning of local structural parameters, while traditional methods can provide results, the cost of repeated modeling and solving is high, limiting their efficiency in early conceptual design and multi-scheme selection.

[0006] Furthermore, existing finite element method (FEM) prediction methods focus more on case-by-case calculations based on mechanical models. Their technical approach essentially involves building and solving models for individual tire designs, failing to fully utilize the numerous correlations inherent in historical design data, mass production specification data, experimental profile data, and simulation profile data. In other words, even when companies have accumulated substantial data on tire specifications, structural parameters, material parameters, and corresponding inflation profiles, current technology lacks an efficient method to effectively mine the mapping relationships between these samples and rapidly predict the inflation profile of the target tire. In particular, for cross-sectional areas with different deformation characteristics, such as the crown, shoulder, sidewall, and heel areas, existing technology does not provide a rapid prediction solution that balances regional geometric characteristics, prediction efficiency, and engineering feasibility.

[0007] Therefore, existing technologies still have the following problems: First, tire inflation profile prediction relies too heavily on finite element modeling and nonlinear solutions, resulting in long computation cycles and difficulty in supporting rapid design iterations; second, it requires high levels of completeness of input parameters and modeling experience, making it difficult to use; and third, it does not make sufficient use of existing tire sample data, and a data-driven, efficient prediction mechanism has not yet been formed. Based on this, there is an urgent need to provide a new tire inflation profile prediction method that can significantly improve the efficiency of tire inflation profile prediction while ensuring that the prediction results have engineering reference value and reducing reliance on complex finite element modeling and human experience. Summary of the Invention

[0008] The technical objective of this invention is to provide a tire inflation profile prediction method, system, electronic device, and storage medium based on machine learning. By constructing a rapid mapping relationship between tire structural parameters, material parameters, and inflation profile, it achieves efficient prediction of the inflation profile of a target tire under rated inflation conditions. This solves the technical problems of existing technologies that rely on finite element analysis for tire inflation profile prediction, such as complex modeling, long computation time, strong dependence on engineering experience, and difficulty in meeting the needs of rapid design iteration of multiple schemes.

[0009] Firstly, in order to achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0010] Firstly, in order to achieve the above-mentioned objectives, the present invention adopts the following technical solution: A tire inflation profile prediction method based on machine learning includes the following steps: S1. Obtain tire sample data of multiple sample tires under a preset rated inflation pressure. The sample data includes the original set of structural parameters, the original set of material parameters, and the actual inflation profile data set. Extract the set of partitioning mechanism parameters that characterize the inflation deformation features of different regions of the tire cross section. S2. Transform the actual inflation profile data set of each sample tire into a unified rim reference coordinate system, and standardize the profile sampling according to the profile arc length direction to obtain a standard profile vector; divide the standard profile vector into multiple partition profile vectors according to the preset partition boundaries, and construct local reference profiles and local profile basis vector groups respectively. S3. Construct a partitioned multi-output machine learning model with the partitioning mechanism parameter set as input and the local contour basis vector coefficient set and key geometric quantity set of each partition as output; train the partitioned multi-output machine learning model using training samples to obtain the trained tire inflation contour prediction model. S4. Obtain the original structural parameters and original material parameters of the target tire, extract the set of partition mechanism parameters of the target tire, and input them into the tire inflation profile prediction model to obtain the set of prediction coefficients of local profile basis vectors of each partition and the set of prediction values ​​of key geometric quantities. Reconstruct the prediction profile of each partition and splice them together to form the initial prediction inflation profile. S5. Perform tire heel assembly boundary constraint verification, partition connection continuity constraint verification, curvature change threshold constraint verification, and cross-sectional width and height constraint verification on the initial predicted inflation profile, and output the final predicted inflation profile that meets the engineering constraints.

[0011] Preferably, in step S1, the original set of structural parameters includes at least one or more of the following: tread width, cross-section width, cross-section height, aspect ratio, rim diameter, carcass cord angle, belt layer angle, normalized position parameter of belt layer endpoint relative to the center of the crown, sidewall thickness gradient parameter, and heel wrap angle parameter. And / or, in step S1, the original set of material parameters includes at least one or more of the following: the elastic modulus of the tread rubber, the elastic modulus of the shoulder rubber, the elastic modulus of the sidewall rubber, the elastic modulus of the heel rubber, the tensile stiffness of the cord, the composite stiffness of the belt layer, and the composite stiffness of the carcass. And / or, in step S1, the set of partitioning mechanism parameters includes at least the mechanism parameters of the crown area, the mechanism parameters of the shoulder area, the mechanism parameters of the sidewall area, and the mechanism parameters of the heel area; And / or, in step S1, the partitioning mechanism parameter set is obtained by performing a mechanism combination transformation on the original structural parameter set and the original material parameter set, the mechanism combination transformation including at least: Shoulder support parameters are constructed based on the normalized position parameters of the belt layer endpoints relative to the center of the crown and the belt layer angle; A sensitive parameter for sidewall bulge is constructed based on the sidewall thickness gradient parameter and the sidewall rubber elastic modulus. Heel positioning parameters are constructed based on the heel wrap angle parameter and the elastic modulus of the heel rubber.

[0012] As a preferred embodiment, in step S2, the standard contour vector is divided into the crown area contour vector, the shoulder area contour vector, the sidewall area contour vector, and the heel area contour vector according to the preset partition boundaries. Local reference contours and local contour basis vector sets are constructed based on the contour vectors of each partition, so that the contour of each partition is obtained by combining the local reference contour of the corresponding partition with multiple local contour basis vectors of that partition according to the corresponding coefficients; The partitions include the crown area, shoulder area, sidewall area, and heel area; the partition contour vector is the contour vector of the corresponding partition, the local reference contour vector is the reference contour vector of the corresponding partition, the local contour basis vector is the basis vector used to characterize the contour change in the corresponding partition, the local contour basis vector coefficient is the combination weight of the corresponding local contour basis vector, and the number of local contour basis vectors is the number of basis vectors participating in the contour combination in the corresponding partition. And / or, in step S2, the sampling of the standard contour vector is carried out according to the ratio of the arc length of the tire outer contour, and the value range of the arc length normalization position of the kth sampling point is 0 to 1. And / or, in step S2, the local contour basis vector groups of each region are constructed through principal component analysis, singular value decomposition, or based on a preset engineering deformation mode; wherein, the local contour basis vector of the crown region is used to characterize the crown arc change, the local contour basis vector of the shoulder region is used to characterize the shoulder convexity or inward retraction change, the local contour basis vector of the sidewall region is used to characterize the sidewall bulge change, and the local contour basis vector of the heel region is used to characterize the heel seating position change.

[0013] Preferably, in step S3, the set of local contour basis vector coefficients for each region includes the set of coefficients for the crown region, the set of coefficients for the shoulder region, the set of coefficients for the sidewall region, and the set of coefficients for the heel region. The set of key geometric quantities includes at least one or more of the following: predicted section width, predicted section height, tire shoulder radius, coordinates of the maximum bulge point, and tire heel spacing; And / or, in step S3, the partitioned multi-output machine learning model is one or more of the following: support vector regression model, random forest regression model, gradient boosting tree model, and deep neural network model; When the partitioned multi-output machine learning model is a deep neural network model, its output layer simultaneously outputs the set of local contour basis vector coefficients and the set of key geometric quantities for each partition. And / or, in step S3, the objective function used for training includes a coefficient error term, a contour reconstruction error term, a key geometric quantity error term, and a constraint penalty term. The objective function is composed of the coefficient error term, the contour reconstruction error term, the key geometric quantity error term, and the constraint penalty term weighted according to their corresponding weight coefficients. The objective function is used to evaluate the model training error, the coefficient error term is used to evaluate the prediction error of the local contour basis vector coefficients, the contour reconstruction error term is used to evaluate the difference between the predicted contour and the actual contour, the key geometric quantity error term is used to evaluate the prediction error of the key geometric quantity, the constraint penalty term is used to evaluate the degree to which the predicted contour violates the geometric constraints, and the corresponding weight coefficients are used to adjust the influence of each error term in the objective function.

[0014] Preferably, in step S4, the predicted profiles of the crown area, shoulder area, sidewall area, and heel area are reconstructed based on the predicted coefficient set of the local contour basis vectors of each partition, and the predicted profiles of each partition are spliced ​​together to form the initial predicted inflation profile of the target tire.

[0015] Preferably, in step S5, the tire heel assembly boundary constraint verification includes: predicting that the coordinate deviation between the tire heel point and the rim seat boundary point is not greater than the tire heel point positioning deviation threshold. The partition connection continuity constraint check includes: the difference in tangent direction at the connection point of adjacent partitions is not greater than the threshold of tangent direction difference; The curvature change threshold constraint check includes: the absolute value of the curvature difference between adjacent sampling points is not greater than the curvature difference threshold; The cross-sectional width and height constraint verification includes: the predicted cross-sectional width is between the lower limit of the cross-sectional width and the upper limit of the cross-sectional width, and the predicted cross-sectional height is between the lower limit of the cross-sectional height and the upper limit of the cross-sectional height; The tire heel point positioning deviation threshold is used to limit the allowable deviation between the tire heel point and the rim seat boundary point; the tangent direction difference threshold is used to limit the directional continuity of the connection position of adjacent partitions; the curvature difference threshold is used to limit the degree of local curvature change of the contour; the lower limit and upper limit of the cross-section width are used to limit the predicted cross-section width range; and the lower limit and upper limit of the cross-section height are used to limit the predicted cross-section height range. And / or, in step S5, when the preset feasibility criterion is met, the final predicted inflatable profile is output; when it is not met, only the predicted coefficients of the local profile basis vectors corresponding to the violation of the constraint are projected and corrected. The projection correction is achieved by solving the constrained local coefficient correction problem. The corrected local profile basis vector coefficient set is the set of coefficients that minimizes the sum of the deviation terms between the corrected coefficients and the original predicted coefficients and the penalty function terms for violating geometric constraints. Wherein, the modified local contour basis vector coefficient set is the modified coefficient result, the original predicted coefficient set is the local contour basis vector predicted coefficient set before modification, the deviation term is used to characterize the difference between the modified coefficient and the original predicted coefficient, the penalty function term is used to characterize the degree of violation of geometric constraints, and the penalty function weight coefficient is used to adjust the influence of the penalty function term in the local coefficient correction problem.

[0016] Preferably, the method further includes step S6: using test samples to evaluate the accuracy of the final predicted inflation profile, wherein the accuracy evaluation index includes at least one or more of mean absolute error, root mean square error, and maximum profile deviation.

[0017] Secondly, the present invention also provides a tire inflation profile prediction system based on machine learning, which is used to implement the method, including: The sample data acquisition module is used to execute step S1; The contour standardization partitioning module is used to perform step S2; The model building and training module is used to execute step S3; The contour prediction module is used to perform step S4; The geometric feasibility closed-loop verification module is used to execute step S5.

[0018] Thirdly, the present invention also provides a computer-readable storage medium having a computer program or instructions stored thereon, which, when executed by a processor, implement the steps of the method.

[0019] Fourthly, the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the steps of the method.

[0020] This invention constructs a machine learning model for predicting tire inflation profiles, establishing a correspondence between tire cross-sectional structural parameters, material parameters, and zoning mechanism characteristics and the post-inflation profile morphology. This model can quickly output the profile prediction results of the target tire under rated inflation conditions without repeatedly building complex finite element models or performing lengthy nonlinear solutions. This significantly shortens the profile evaluation cycle in the tire design phase and improves the efficiency of parallel comparison and rapid iterative optimization of multiple schemes. Furthermore, this invention employs standardized profile zoning representation, local basis vector modeling, and a geometric feasibility verification and correction mechanism. This not only improves the relevance and accuracy of prediction results for different cross-sectional areas such as the crown, shoulder, sidewall, and heel, but also ensures that the predicted profile meets engineering application requirements such as rim assembly boundaries, zoning connection continuity, and cross-sectional width and height constraints. Therefore, it possesses beneficial technical effects such as fast prediction speed, strong engineering applicability, good result stability, low dependence on human experience, and effective support for digital tire design and product development. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the overall process of the tire inflation profile prediction method based on machine learning according to the present invention.

[0022] Figure 2 This is a schematic diagram of sample tire data acquisition and preprocessing in this invention.

[0023] Figure 3 This is a schematic diagram of the rim reference coordinate system and tire cross-sectional profile partitioning in this invention.

[0024] Figure 4 This is a schematic diagram of the construction of local basis vectors in the partitioning in this invention.

[0025] Figure 5 This is a structural diagram of the partitioned multi-output machine learning model in this invention.

[0026] Figure 6 This is a flowchart of the model training and verification process in this invention.

[0027] Figure 7 This is a schematic diagram of the target tire profile prediction and reconstruction in this invention.

[0028] Figure 8 This is a schematic diagram for geometric feasibility verification in this invention.

[0029] Figure 9 This is a flowchart of the local projection correction closed-loop process in this invention.

[0030] Figure 10 This is a comparison diagram of the technical effects of the present invention and the comparative method.

[0031] Figure 11 To optimize the comparison of the front and rear tire cross-sectional profiles.

[0032] Figure 12 A comparison of the grounding pressure distribution curves before and after optimization.

[0033] Figure 13 A comparison chart of peak grounding pressure and pressure standard deviation before and after optimization.

[0034] Figure 14 The graph shows the convergence process of the objective function.

[0035] Figure 15 A comparison of grounding pressure cloud maps before and after optimization. Detailed Implementation

[0036] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the 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 protection scope of the present invention.

[0037] I. Terminology Explanation

[0038] To facilitate understanding of this invention, the main terms used in this embodiment will be explained first. Unless otherwise specified, the terms used in this embodiment are as commonly understood in the art.

[0039] Inflation profile: refers to the external geometric profile formed by a tire in the plane of its cross-section under preset rim conditions and rated inflation pressure.

[0040] Rim reference coordinate system: refers to a two-dimensional coordinate system established with the intersection of the tire rotation axis and the center line of the section as the origin. The lateral coordinate represents the position of the tire section width, and the longitudinal coordinate represents the position of the tire radial height.

[0041] Zoning mechanism parameters: refers to the set of parameters derived from the combination of original tire structural parameters and material parameters, which can characterize the response characteristics of the crown area, shoulder area, sidewall area and heel area during inflation deformation.

[0042] Local basis vectors: refer to the contour variation basis established for a certain section of the tire, used to characterize the trend of the contour of the section relative to the local reference contour in a low-dimensional way.

[0043] Reference profile: refers to the representative profile extracted from the training samples. It can be the average profile of the samples or the standard profile of a tire of a selected reference specification.

[0044] Standard contour vector: refers to the set vector of tire inflation contour points after uniform coordinateization, denoising, normalization and resampling.

[0045] Key geometric quantities: These are geometric indicators used to characterize the engineering features of tire inflation profiles, including section width, section height, shoulder radius, coordinates of the maximum bulge point, and heel spacing.

[0046] Geometric feasibility criteria: refers to the set of rules used to determine whether the predicted profile meets the requirements of rim assembly, profile continuity, curvature smoothness, and cross-sectional dimension boundaries.

[0047] Projection correction: refers to the correction process that, after detecting that the predicted contour violates geometric constraints, only adjusts the local basis vector coefficients of the relevant partitions with minimal deviation within the constraint space.

[0048] II. System Structure

[0049] The system of this invention can be deployed on a server, engineering design workstation, or enterprise R&D platform. Its hardware includes at least a processor, memory, display terminal, and data input interface. Its software includes a data management subsystem, a model training subsystem, a contour prediction subsystem, and a result verification subsystem. Functionally, it may include the following modules:

[0050] (a) Sample Data Acquisition Module

[0051] This is used to collect the original structural parameters, original material parameters, and actual inflation profile data of the sample tire. The actual inflation profile data can be obtained from tire cross-section slicing scans, laser profile scans, X-ray cross-section extraction, finite element simulation results, or multi-source data fusion results.

[0052] (ii) The partitioning mechanism parameter construction module is used to extract partitioning mechanism parameters that can describe the deformation trends of the tire crown, tire shoulder, tire sidewall, and tire heel regions based on the original structural parameters and original material parameters. This module can contain rule calculation units and feature combination units.

[0053] (iii) The contour standardization zoning module is used to uniformly convert the tire cross section contours of different sources and specifications into the rim reference coordinate system, and to perform standard sampling according to the predetermined arc length ratio, thereby dividing the tire crown area contour, tire shoulder area contour, tire sidewall area contour and tire heel area contour.

[0054] (iv) The local basis vector construction module is used to perform dimensionality reduction analysis on the standard contours of each partition, and generate the local reference contours and local contour basis vector groups of each partition.

[0055] (v) The model training module is used to train, verify, tune and finalize the machine learning model by taking the partition mechanism parameters as input and taking the local basis vector coefficients and key geometric quantities of each partition as output.

[0056] (vi) The profile prediction module is used to receive the input parameters of the target tire and output the initial predicted inflation profile.

[0057] (vii) Geometric feasibility closed-loop verification module

[0058] It is used to perform tire heel assembly boundary verification, zone connection continuity verification, curvature change verification, and cross-sectional width and height constraint verification on the initial predicted inflation profile, and performs local projection correction when the criteria are not met, and finally outputs the predicted profile that meets the engineering application conditions.

[0059] III. Overall Technical Route for Implementing the Method of the Invention

[0060] like Figure 1 As shown, the method of the present invention, according to the steps in the claims, mainly includes five steps, S1 to S5. Its technical route is as follows:

[0061] First, a tire sample database is established by acquiring structural, material, and inflation profile data from multiple sample tires. Second, the tire cross-sectional profile is transformed into a unified coordinate system and divided into four regions according to the tire cross-sectional deformation mechanism: crown region, shoulder region, sidewall region, and heel region. Third, local reference profiles and local basis vector sets are established in each region to address the problem of excessively high variable dimensionality and masking of mechanism differences between regions when directly modeling the entire profile. Then, using the partition mechanism parameters as input and the local basis vector coefficients and key geometric quantities as output, a multi-output machine learning model is trained to form a rapid prediction model for tire inflation profiles. Finally, in practical applications, the target tire parameters are input into the trained model to reconstruct the initial predicted profile. Through geometric feasibility closed-loop verification and local projection correction, the final inflation profile that can be used for engineering design is output.

[0062] (I) Step S1: Sample data acquisition and partitioning mechanism parameter construction

[0063] like Figure 2 As shown, the purpose of step S1 is to construct a tire sample database suitable for model training and extract partitioning mechanism parameters from the original parameters of the tire that have a stronger explanatory power for changes in inflation profile.

[0064] 1. Source of sample data

[0065] In this embodiment, the number of sample tires This can be set based on the company's data accumulation. To ensure the model's training stability and generalization ability, the optimal settings are... Further optimization Each sample tire must record at least the following three types of information:

[0066] (1) Original set of structural parameters ;

[0067] (2) Set of original material parameters ;

[0068] (3) At the rated inflation pressure The actual inflation profile data set below .

[0069] Among them, the original set of structural parameters This may include, but is not limited to: tread width Cross-sectional width Cross-sectional height Aspect Ratio Rim diameter Tire cord angle , belt layer angle Normalized position parameters of the belt layer endpoints relative to the center of the tire crown Sidewall thickness gradient parameters Parameters of tire heel wrap angle Etc. Original material parameter set This may include, but is not limited to: the elastic modulus of the tire crown rubber. shoulder rubber elastic modulus Sidewall rubber elastic modulus Tire heel rubber elastic modulus Cord tensile stiffness Belt layer composite stiffness and the composite stiffness of the tire body wait.

[0070] 2. Method for collecting inflation profile data

[0071] In one possible embodiment, the actual inflation profile data set It is obtained from the following steps:

[0072] First, fit the tire onto a standard rim and inflate it to the rated inflation pressure. After reaching a steady state, the tire cross-section is laser-scanned or cross-sectional slice-scanned to obtain a point cloud of the tire's outer contour; then, a two-dimensional cross-sectional contour curve is obtained through a contour extraction algorithm. The original sampling density of the point cloud is preferably no less than 3 points per millimeter, and more preferably 5 to 10 points per millimeter, to ensure the data integrity of areas with large curvature changes, such as the tire shoulder and tire heel.

[0073] In another embodiment, if the enterprise has already established a high-confidence finite element simulation database, the cross-sectional outer contour in the finite element inflation result can be directly used as the actual inflation contour data; preferably, the finite element result can be corrected for deviation using the measured result before being included in the training library.

[0074] 3. Construction of Partitioning Mechanism Parameters

[0075] This invention does not simply input the original structural and material parameters into the model, but further constructs a set of partitioning mechanism parameters. This is because the deformation mechanisms of different cross-sectional areas of a tire are different after inflation: the crown area is more affected by the support of the belt layer and the crown stiffness; the shoulder area is affected by the position of the belt layer endpoints, the stiffness of the shoulder material, and the geometric transition of the tread; the sidewall area is more affected by the coupling effect of the sidewall thickness gradient, the tire body stiffness, and the inflation pressure; and the heel area is strongly dependent on the heel wrap angle, the rim seat boundary, and the heel rubber stiffness.

[0076] Therefore, this embodiment preferably combines the original parameters by region to form a set of regional mechanism parameters. .For example:

[0077] (1) Shoulder support parameters : Normalized position from the endpoint of the belt layer , belt layer angle Composite stiffness of belt layer Combined to obtain;

[0078] (2) Sensitive parameters for sidewall bulge : Due to the thickness gradient of the tire sidewall Sidewall rubber elastic modulus Composite stiffness of the tire body Combined to obtain;

[0079] (3) Heel positioning parameters : formed by the heel corner Tire heel rubber elastic modulus and rim diameter Combined to obtain;

[0080] (4) Crown shape stability parameters : by tread width Crown thickness parameters, belt layer angle and the elastic modulus of the tread rubber The combination yields the desired result.

[0081] In one embodiment, the above mechanistic parameters can be constructed using linear combinations or nonlinear rules. For example:

[0082] ;

[0083] in, For tire shoulder support parameters, , , These are the weighting coefficients. For the normalized position parameters of the belt layer endpoints, For the belt layer angle, For the composite stiffness of the belt layer.

[0084] For example:

[0085] ;

[0086] in, For sensitive parameters of sidewall bulge, , , These are the weighting coefficients. This refers to the sidewall thickness gradient parameter. This refers to the elastic modulus of the tire sidewall rubber. This refers to the composite stiffness of the tire body.

[0087] Those skilled in the art can make appropriate adjustments to the composition of the above mechanism parameters based on the differences in the enterprise's actual database and product platform, but the core idea is to first transform the tire parameters from general fields into special features oriented towards the contour deformation mechanism, and then use them for subsequent modeling.

[0088] 4. Dataset partitioning

[0089] In this embodiment, after the sample database is established, it can be divided into a training set, a validation set, and a test set in a ratio of 70%:15%:15%. To avoid data leakage caused by tires of the same platform, series, and specification appearing simultaneously in the training set and the test set, it is preferable to group them according to tire platform or specification cluster, that is, to perform stratified sampling by series.

[0090] (ii) Step S2: Contour standardization partitioning and local basis vector construction

[0091] Step S2 aims to address the issues of inconsistent contour representation among different tire samples, inconsistent number of contour points, excessively high dimensionality in the modeling of the entire contour, and overlapping contour change patterns in different regions.

[0092] 1. Contour standardization processing

[0093] The raw profile data of different sample tires typically differ in the following ways:

[0094] First, the coordinate systems are not uniform; second, the number of points differs; third, the sampling density varies; fourth, there is local noise or isolated points; and fifth, there are significant differences in specifications and dimensions. Therefore, this implementation method is standardized as follows:

[0095] (1) Establish the rim reference coordinate system Transform all contours to this coordinate system (e.g., Figure 3 )middle;

[0096] (2) Denoise the contour data by using median filtering, local polynomial smoothing or spline smoothing;

[0097] (3) Remove outliers that deviate significantly from the trend of adjacent points;

[0098] (4) Reparameterize according to the arc length of the contour, and re-express the contour as a curve that changes monotonically with the arc length;

[0099] (5) According to the preset number of sampling points Perform standard sampling to form a standard contour vector. .

[0100] In one specific embodiment, the outer contour of the tire section can start from one heel point and end along the outer contour to the other heel point. Let the total arc length of the contour be... , No. The normalized arc length position of each sampling point is: Then we have: ;in, For the first Normalized position of the arc length of each sampling point In this embodiment, preferably... to For example, it is advisable For the shoulder and heel areas where curvature changes significantly, a non-uniform resampling strategy can be adopted, which involves increasing the sampling density in the shoulder and heel areas.

[0101] Standard contour vector Represented as:

[0102] ;

[0103] in, For the first The coordinates of the standard sampling points.

[0104] 2. Contour Partitioning Method

[0105] like Figure 4 As shown, this invention divides the tire cross-sectional profile into a crown area, a shoulder area, a sidewall area, and a heel area. The boundaries of these areas can be determined using either a fixed-proportion method or a structure-driven method. Preferably, a method combining structure-driven and geometric features is used: using the crown center as a reference, and considering the belt layer endpoints, curvature inflection points, maximum cross-sectional width, and heel placement, the boundaries of each area are determined.

[0106] For example, in one embodiment, the division can be carried out in the following manner:

[0107] The crown area is the central arc segment at the top of the profile, corresponding to the full support area of ​​the belt layer; the shoulder area is the area where the crown area transitions to both sides to the vicinity of the belt layer endpoints; the sidewall area is the area between the lower part of the shoulder and the maximum width of the cross section and the upper part of the heel; the heel area is the area near the rim seat and the bead cover.

[0108] After the above partitioning, four local contour vectors can be formed respectively: , , , These correspond to the crown area, shoulder area, sidewall area, and heel area, respectively.

[0109] 3. Construction of local basis vectors

[0110] This is a key technical aspect that distinguishes this invention from direct regression of the entire contour. The initial structure is shown in the attached figure. With multiple basis vectors , The idea of ​​forming a reconstructed structure through linear combination is implemented in this invention as follows: establishing local reference contours and local contour basis vector groups for each section of the tire cross section.

[0111] For any partition ,have:

[0112] ;

[0113] in, ; For the first Partition contour vector; For the first The local reference contour vector of the partition; For the first The first partition Local contour basis vectors; These are the coefficients of the corresponding basis vectors; For the first The number of basis vectors in the partition.

[0114] Local basis vectors can be obtained through principal component analysis, singular value decomposition, or extraction using preset engineering deformation modes. Preferably, principal component analysis is performed on the standard contour matrix of each zone, and the top few principal components are selected as local basis vectors based on the cumulative explained variance. For example, the tire crown region can be selected as... Up to 6, the shoulder area can be removed. Up to 8, the sidewall area can be removed. Up to 10, the heel area can be removed. Up to 6. This effectively compresses dimensions while preserving the main shape variation features.

[0115] In terms of engineering semantics, the basis vectors of each partition have a clear meaning:

[0116] The basic vector of the crown region mainly characterizes the increase or decrease of crown curvature, and the flattening or arching of the crown.

[0117] The basic vector of the shoulder area mainly characterizes the outward convexity, inward retraction, and smoothness of the shoulder transition;

[0118] The basic vector of the lateral region mainly characterizes the lateral bulge, the position of the bulge peak, and the changes in the sidewall slope;

[0119] The tire heel region basis vector mainly characterizes the tire heel placement position, the tire bead coverage profile, and its relative relationship with the rim boundary.

[0120] 4. Reasons and effects of using partitioned basis vectors

[0121] Compared with directly regressing the coordinates of the entire contour points, the partitioned local basis vector method has the following advantages:

[0122] First, reduce the output dimension. If the coordinates of 240 contour points are directly output, the output dimension is 480; however, by using partitioned local basis vectors, the output only includes the basis vector coefficients of each region and a small number of key geometric quantities, which can usually be compressed to 25 to 40 quantities.

[0123] Second, it enhances interpretability. The changes in coefficients in different zones can intuitively correspond to changes in the contour morphology of different regions.

[0124] Third, it improves stability. Local modeling avoids the training instability caused by the overlapping of mechanisms in different regions when modeling the entire contour.

[0125] Fourth, it facilitates subsequent local corrections. When the predicted profile violates constraints only in a certain region, only the coefficients of that region need to be adjusted, without the need for overall retraining or overall correction.

[0126] (III) Step S3: Construction and training of multi-output machine learning model

[0127] The purpose of step S3 is to establish a set of parameters for the partitioning mechanism. To the set of local basis vector coefficients and the set of key geometric quantities The mapping relationship.

[0128] 1. Structured definition of input and output

[0129] The input is a set of partitioning mechanism parameters. In one embodiment, it can be organized as a fixed-length feature vector, exemplarily including: Of course, some features can be added or deleted as needed.

[0130] The output consists of two parts:

[0131] The first part is the set of local basis vector coefficients for each partition. ,Right now ;

[0132] The second part is the set of key geometric quantities. ,For example .

[0133] in, To predict the cross-sectional width, To predict the cross-sectional height, The tire shoulder radius, The coordinates of the maximum bulge point, This refers to the distance between the tire heel and the calf.

[0134] By using a combination of coefficients and key geometric quantities as outputs, instead of just outputting coefficients, the model can learn both local shape changes and overall engineering quantity indicators simultaneously, which is beneficial for improving the quality of the final contour reconstruction and its engineering applicability.

[0135] 2. Model Structure

[0136] like Figure 5 As shown, in a preferred embodiment, a deep neural network is used as the partitioned multi-output machine learning model. Its network structure can be set as follows:

[0137] (1) Input layer: The dimension is equal to the number of input features, for example, 18 to 32 dimensions;

[0138] (2) Shared hidden layer: 3 fully connected layers with 256, 128 and 64 nodes respectively;

[0139] (3) Branch output layer:

[0140] The partition coefficient output branch is used to output the local basis vector coefficients of each partition;

[0141] The critical geometry output branch is used to output the set of critical geometry quantities Q.

[0142] The activation function is preferably ReLU or GELU; batch normalization and Dropout can be set between hidden layers, with the Dropout rate preferably between 0.05 and 0.20, for example, 0.10. The optimizer can be AdamW, and the initial learning rate is preferably... to The preferred batch size is 16 to 64, for example, 32.

[0143] In another embodiment, gradient boosting tree models, random forest regression models, or support vector regression models can be used to fit the local basis vector coefficients of each region, and then an ensemble approach can be used to output the key geometric quantities. For cases with a small sample size but low parameter dimensionality, gradient boosting tree models have good adaptability; for cases with a large sample size and complex nonlinear relationships between different features, deep neural networks are superior.

[0144] 3. Training the objective function

[0145] This implementation uses a joint loss function to train the model. The loss function L can be expressed as:

[0146] ;

[0147] in, This is the error term for the local contour basis vector coefficients; This is the contour reconstruction error term; For key geometric quantity error terms; To constrain penalty items; , , , These are the weighting coefficients.

[0148] Each item can be specifically defined as follows:

[0149] (1) Coefficient error term : Used to constrain the deviation between predicted coefficients and actual coefficients; mean square error can be used.

[0150] (2) Contour reconstruction error term After reconstructing the predicted coefficients into a contour, compare it point by point with the true standard contour. The mean squared distance or the mean absolute distance can be used.

[0151] (3) Error terms of key geometric quantities Compare the deviations of predicted key geometric quantities such as cross-section width and height with the actual values;

[0152] (4) Constraint and penalty items If the prediction results show a clear trend of violating geometric constraints during the training phase, additional penalties will be applied.

[0153] In one embodiment, the weighting coefficient can be: , , , In the initial stages of training, the dosage can be appropriately increased. and To accelerate the model's learning of basic scale relationships; in the later stages of training, the [scale value] can be appropriately increased. and To improve the quality of contour details and geometric feasibility.

[0154] 4. Training Process

[0155] like Figure 6 As shown, the training process can be performed as follows:

[0156] First, the input features are standardized, preferably using Z-score standardization;

[0157] Second, the output local basis vector coefficients and key geometric quantities are also standardized to reduce the impact of different dimensions on training stability.

[0158] Third, the training set is used to fit the model parameters, and the validation set is used to search for hyperparameters and determine early stopping.

[0159] Fourth, stop training when the validation set loss no longer decreases for several consecutive rounds, preferably 20 to 50 epochs;

[0160] Fifth, the final model is evaluated using a test set, and the mean absolute error, root mean square error, and maximum profile deviation are output.

[0161] In one specific embodiment, the number of training epochs can be set to 150 to 400 epochs, for example, 250 epochs. If a deep neural network is used, during the training process, tires of different specifications can be sampled evenly according to specification ranges to avoid biasing the model due to specifications with more samples.

[0162] 5. Data Augmentation and Robustness Improvement

[0163] To improve the model's adaptability to process disturbances and measurement noise, the following enhancements can be implemented on the training data: (1) Add small-range random disturbances to the input features without changing the basic topology of the contour; (2) Add low-amplitude Gaussian noise to the contour point coordinates to simulate measurement errors; (3) Normalize and interpolate adjacent tire specifications to generate intermediate samples; (4) Introduce small offsets to local boundary points to enhance the model's robustness to boundary uncertainties.

[0164] (iv) Step S4: Target tire profile prediction

[0165] like Figure 7 Step S4 is a model application step, and its execution process is relatively clear. However, to ensure that those skilled in the art can implement it directly, the following structured explanation is provided. In practical applications, the original set of structural parameters and the original set of material parameters of the target tire are first obtained. Then, the feature construction rules consistent with those in the training phase are called to calculate the set of partitioning mechanism parameters of the target tire. Then on Perform the same standardization process as during the training phase and input it into the trained model.

[0166] The model output includes: (i) a set of prediction coefficients for local contour basis vectors in each region. (ii) Set of predicted values ​​for key geometric quantities .

[0167] get Then, local contour reconstruction is performed according to the baseline contour and basis vector set of each region. For any region... For example, its predicted profile can be represented as:

[0168] ;

[0169] in, , For the first Partition contour vector, For the first The local reference contour vector of the partition. For the first The first partition Local contour basis vectors For the first The first partition Local contour basis vector coefficients For the first The number of local contour basis vectors of the partition;

[0170] After reconstructing each region, the local contours of the crown region, shoulder region, sidewall region, and heel region are stitched together according to the preset connection order and boundary mapping rules to form the initial predicted inflation contour of the target tire. .

[0171] It should be noted here that the stitching is not a simple end-to-end connection, but rather preferably uses tangent-weighted transition or local spline fusion at the partition boundaries to avoid visible inflection points at the boundaries. The boundary fusion width can be set to 3 to 8 sampling points near each partition boundary, preferably 5 sampling points.

[0172] (V) Step S5: Geometric feasibility closed-loop verification and final contour output

[0173] like Figure 8 Even if the model predicts well in terms of average error, the following problems may still occur in engineering: unreasonable tire heel placement, abrupt changes in the tangent of a certain zone boundary, local curvature peaks, and excessive cross-sectional width and height. Therefore, this invention establishes a geometric feasibility closed-loop verification and local projection correction mechanism.

[0174] 1. Contents of Geometric Feasibility Verification

[0175] In one embodiment, at least the following four types of verification are included:

[0176] (1) Check of tire heel assembly boundary constraints

[0177] Compare the coordinate deviations between the predicted tire heel point and the rim seat boundary point. If the deviation is greater than a threshold... If the tire heel area does not meet the assembly feasibility requirements, then it is determined that the assembly is not feasible.

[0178] (2) Checking the continuity constraint of partition connectivity

[0179] Compare the tangent direction difference at the connection points of adjacent partitions. If the tangent direction difference is greater than a threshold... If the connection is not continuous, then it is determined that the connection is not continuous.

[0180] (3) Curvature mutation threshold constraint verification

[0181] Calculate the absolute value of the curvature difference between adjacent sampling points. If it exceeds the threshold... If so, it is determined that there is an unreasonable spike or fluctuation at that point.

[0182] (4) Cross-sectional width and height constraint check

[0183] Compare predicted cross-sectional width and predicted cross-sectional height Is it within the preset range? If not, the overall outline is deemed unusable.

[0184] In one specific embodiment, the threshold can be set according to different product lines. For example: A thickness of 0.3mm to 1.0mm is acceptable; An angle of 2° to 6° is acceptable. 0.005mm is acceptable. -1 up to 0.030mm -1 For passenger car tires, the preferred threshold is more stringent; for engineering tires or low-pressure, large-section tires, the threshold can be appropriately relaxed.

[0185] 2. Local projection correction

[0186] like Figure 9 As stated above, if the initial predicted inflation profile If the feasibility criteria are not met, the entire contour is not smoothed as a whole; instead, specific areas that violate the constraints are identified first. For example, if the heel point deviation is too large, the heel area coefficient is corrected first; if the curvature changes abruptly at the shoulder transition, the shoulder area and the adjacent crown area coefficients are corrected first; if the position of the maximum bulge point on the sidewall is abnormal, the sidewall area coefficient is corrected first.

[0187] The correction process can be achieved through constrained local coefficient optimization, and its objective function can be expressed as:

[0188] ;

[0189] in, This is the set of corrected local contour basis vector coefficients; This is the set of predicted coefficients before correction; This is the deviation term between the correction coefficient and the original predicted coefficient; For the penalty function term that violates geometric constraints; These are the weighting coefficients of the penalty function.

[0190] penalty function term It can consist of the following parts:

[0191] Penalties include tire heel point deviation, connecting tangent difference, curvature abrupt change, and width / height exceeding limits. During correction, it is preferable to optimize only the coefficients of the violation partition and its adjacent partitions, while keeping the coefficients of other partitions unchanged. This ensures the correction magnitude is as small as possible and avoids destroying the model's original prediction information.

[0192] 3. Closed-loop termination rules

[0193] After each correction, the corrected profile is regenerated, and a geometric feasibility check is performed again. If the criteria are met, the final predicted profile is output. If the condition is still not met, continue to adjust until the maximum number of adjustments is reached. The preferred maximum number of adjustments is 3 to 8, for example, 5. If the condition is still not met after reaching the maximum number of adjustments, output a low-confidence flag and indicate that the input sample exceeds the current training domain.

[0194] 4. Final Result Output

[0195] The final output should preferably include:

[0196] (a) Final prediction of the inflatable profile point set;

[0197] (ii) Key geometric quantities such as cross-sectional width, cross-sectional height, tire shoulder radius, coordinates of the maximum bulge point, and tire heel spacing;

[0198] (III) Feasibility verification results;

[0199] (iv) If the correction is made, the difference before and after the correction will be output for the engineer to judge.

[0200] IV. Implementable Disclosure of Model Structure, Training Parameters, and Dataset Usage

[0201] To enable those skilled in the art to implement this invention without inventive effort, the implementation parameters are further provided as follows:

[0202] Sample size: Preferably 800 to 3000 tire samples;

[0203] Input feature dimension: preferably 18 to 40 dimensions;

[0204] Standard contour sampling point count: preferably 240 points;

[0205] Zoning method: The crown area accounts for about 18% to 28% of the total arc length, the shoulder area accounts for about 12% to 20% of the total arc length, the sidewall area accounts for about 25% to 35% of the total arc length, and the heel area accounts for about 10% to 18% of the total arc length. The left and right symmetrical areas can be treated separately or uniformly in mirror image.

[0206] Number of local basis vectors: preferably 24 to 36 in total;

[0207] Network structure: Input layer — 256 — 128 — 64 — Two-branch output layer;

[0208] Optimizer: AdamW;

[0209] Learning rate: Initial The validation set loss decays by 0.5 after it stalls.

[0210] Batch size: 32;

[0211] Training epochs: 250;

[0212] Number of early stop cycles: 30 epochs;

[0213] Loss weights: , , , ;

[0214] Evaluation indicators: , , And the feasibility approval rate;

[0215] Data augmentation: The random perturbation amplitude of the input features shall not exceed 3% of the standard deviation of each feature, and the noise amplitude of the contour points shall not exceed 0.2mm.

[0216] The above parameters are merely preferred examples, and those skilled in the art can adjust them according to the range of tire specifications, database size, and enterprise platform characteristics.

[0217] VI. Specific Application Examples

[0218] To further illustrate the technical solution and effects of the tire inflation profile prediction method based on machine learning of the present invention, the following detailed description, in conjunction with the accompanying drawings, provides specific application examples, experimental conditions, experimental data, and result analysis of the present invention.

[0219] It should be noted that the following embodiments are used to demonstrate the feasibility and beneficial effects of the present invention, and are not intended to limit the scope of protection of the present invention. Unless otherwise specified, all test conditions adopted are standard laboratory conditions in the tire industry; raw materials, testing equipment, and data processing software are all commonly used products in the field.

[0220] (I) Experimental Objective

[0221] This set of application examples primarily verifies the effects of the following three technologies:

[0222] First, it verifies that the present invention can quickly output the cross-sectional profile of a tire under its rated inflation state while maintaining high prediction accuracy.

[0223] Second, it is verified that the scheme of the present invention, which adopts partitioning mechanism parameters, partitioning local basis vectors, multi-output joint prediction, and geometric feasibility closed-loop correction, has better accuracy and engineering usability compared with direct coordinate point prediction or whole contour unified basis vector prediction.

[0224] Third, the applicability and stability of the invention on tires of different specifications were verified.

[0225] (II) Experimental conditions and data sources

[0226] 1. Source of sample tires

[0227] A total of 960 historical sample tires were selected from a passenger vehicle radial tire R&D platform, covering rim diameters from 16 inches to 19 inches, aspect ratios from 45 to 65, and section widths from 195 mm to 245 mm. The sample tires include, but are not limited to, the following specifications:

[0228] 195 / 65R15

[0229] 205 / 55R16

[0230] 215 / 55R17

[0231] 225 / 45R18

[0232] 235 / 60R18

[0233] 245 / 50R19;

[0234] Each sample tire has complete structural parameters, material parameters, and cross-sectional profile data under the corresponding rated inflation condition.

[0235] 2. Test equipment

[0236] (1) Tire inflation and assembly device: standard rim assembly platform;

[0237] (2) Laser contour scanner: resolution 0.05mm;

[0238] (3) Cross-sectional data processing software: used for point cloud extraction, smoothing, resampling and coordinate unification;

[0239] (4) Model training platform: CPU is an Intel Xeon-level processor, GPU is an NVIDIA RTX-level graphics processor;

[0240] (5) Finite element analysis platform: used to generate simulation reference results in comparative examples.

[0241] 3. Inflation and Sampling Conditions

[0242] All sample tires were mounted on corresponding standard rims and tested at room temperature. After standing for 4 hours under the specified conditions, inflate to the rated inflation pressure. Among them, passenger car tires are preferred. kPa, preferred SUV tires kPa. After inflation, let stand for 30 minutes, then perform laser scanning along the central cross-section to obtain the point cloud of the tire cross-section outer contour.

[0243] 4. Data partitioning

[0244] The 960 sample tires were grouped by specification cluster and then classified as follows:

[0245] Training set: 672 records

[0246] Validation set: 144 records

[0247] Test set: 144 entries

[0248] The test set does not share the same design batch within the same specification cluster as the training set to avoid data leakage.

[0249] (III) Example 1: Application of the method of the present invention on passenger car tires 205 / 55R16

[0250] 1. Input parameters

[0251] Taking a target tire with a specification of 205 / 55R16 as an example, some of its input parameters are shown in Table 1 below.

[0252] Table 1. Main input parameters for target tire A

[0253]

[0254] Based on the above parameters, and following the rules in the specific implementation method of the instruction manual, the mechanistic parameters of the tire crown area are constructed. Shoulder area mechanism parameters Sidewall region mechanism parameters Mechanistic parameters of the heel region The set of parameters constituting the partitioning mechanism .

[0255] 2. Contour Standardization and Zoning

[0256] The sample profile and the measured profile of the target tire are unified to the rim reference coordinate system O-XY, and 240-point resampling is adopted.

[0257] Divide the area according to arc length ratio and structural boundaries:

[0258] Tire crown area: 52 points

[0259] Shoulder area: 40 o'clock

[0260] Sidewall area: 96 o'clock

[0261] Heel area: 52 points

[0262] 3. Setting local basis vectors

[0263] Principal component analysis was performed on the contours of each region of the training sample. The top principal components, which explained more than 96% of the cumulative variance, were selected as local basis vectors, resulting in:

[0264] Local basis vectors of the tibial crown region

[0265] Local basis vector number of the shoulder area

[0266] Local basis vectors of the lateral region

[0267] Local basis vector number of the heel region

[0268] The total number of output coefficients is 24, and 6 key geometric quantities are output simultaneously.

[0269] 4. Model training parameters

[0270] A multi-output deep neural network model is adopted, with the following structure:

[0271] Input layer → 256-node fully connected layer → 128-node fully connected layer → 64-node fully connected layer → dual-branch output layer. The activation function is ReLU, the optimizer is AdamW, and the initial learning rate is... The batch size is 32, the number of training epochs is 240, and the number of early stop epochs is 30.

[0272] The joint loss function is as follows:

[0273] ;

[0274] in, , , , . For the local basis vector coefficient error term, For the contour reconstruction error term, For key geometric error terms, To constrain penalty items.

[0275] 5. Prediction Results

[0276] The model outputs the initial predicted inflation profile of the target tire A. After geometric feasibility closed-loop verification, the tire heel assembly boundary and cross-sectional width and height both meet the requirements. Only the tangent direction difference at the connection between the tire shoulder area and the tire sidewall area slightly exceeds the threshold of 2.8°. Therefore, a projection correction is performed on the local basis vector prediction coefficients of the tire shoulder area. The final predicted inflation profile is output after correction. .

[0277] Table 2 Comparison of Predicted and Measured Results for Target Tire A

[0278]

[0279] Combination Figure 11 As can be seen from the contour reconstruction diagram, the predicted contour of the present invention and the measured contour maintain good consistency in the crown area, shoulder area and side bulge area. The main changes before and after correction are concentrated in the shoulder-side transition area, indicating that the local projection correction mechanism of the present invention can perform targeted correction for illegal areas without destroying the prediction results of other areas.

[0280] 6. Predicted time consumption

[0281] The total time from input parameters to the final predicted profile of a single target tire is approximately 0.41 seconds, of which:

[0282] Feature construction: 0.06s

[0283] Model forward inference: 0.03s

[0284] Geometric feasibility check: 0.09s

[0285] One local projection correction and reconstruction: 0.23s

[0286] This result demonstrates that the present invention can achieve sub-second contour prediction.

[0287] (iv) Example 2: Application of the method of the present invention on passenger car tires 225 / 45R18

[0288] The test was conducted using a target tire B with a specification of 225 / 45R18 and a rated inflation pressure of 250 kPa. The test procedure was the same as in Example 1.

[0289] Table 3. Key Predictive Performance Data for Target Tire B

[0290]

[0291] In this embodiment, the initial predicted profile already satisfies the tire heel assembly boundary constraints, partition continuity constraints, and cross-sectional width and height constraints, so no projection correction is required. Figure 10 As shown, this invention can directly output the result when the judgment is yes, further reducing the prediction time. In this embodiment, the average prediction time for a single tire is 0.18 seconds.

[0292] (V) Example 3: Application of the method of the present invention on SUV tires 235 / 60R18

[0293] The test was conducted using a target tire C with a specification of 235 / 60R18 and a rated inflation pressure of 260 kPa.

[0294] Table 4. Key Predictive Performance Data for Target Tire C

[0295]

[0296] This embodiment illustrates that the present invention is not only applicable to low-profile passenger car tires, but also to SUV tires with higher profiles and more pronounced sidewall bulges. Particularly in the sidewall and heel regions, the present invention maintains high prediction accuracy even after employing partitioned local basis vectors and partitioned mechanism parameters.

[0297] (vi) Proportional settings

[0298] To demonstrate the technical effects of the present invention, the following two comparative examples and one reference example are provided.

[0299] Comparative Example 1: Direct Point Coordinate Prediction Method

[0300] Comparative Example 1 does not use partitioned local basis vectors or joint output of key geometric quantities. Instead, it directly maps the input parameters to the two-dimensional coordinates of 240 contour points, resulting in 480 output quantities. The model uses the same training set and a similar network depth as this invention.

[0301] Comparative Example 2: Unified Basis Vector Prediction Method

[0302] Comparative Example 2 establishes a single reference profile and a unified set of basis vectors for the entire profile, without distinguishing between the crown area, shoulder area, sidewall area, and heel area, and without performing partition projection correction.

[0303] Reference example: Finite element analysis method

[0304] The reference example uses the traditional finite element method to calculate the inflation profile of the target tire. The finite element model includes the tread, belt layers, carcass, sidewall, and heel structures, and is solved under rated inflation conditions, serving as a reference for a time-consuming engineering method.

[0305] (vii) Results of method comparison experiment

[0306] The main indicators of the method of the present invention, Comparative Example 1, Comparative Example 2 and Reference Example were statistically analyzed on 144 tires in the test set.

[0307] Table 5. Accuracy comparison of different methods on the test set.

[0308]

[0309] Note: The reference example finite element analysis is used to illustrate the upper limit of the effect of traditional high-precision methods, but its time consumption is significantly higher than that of this invention.

[0310] As shown in Table 5, the accuracy of the method of this invention is significantly better than that of Comparative Example 1 and Comparative Example 2. This demonstrates that the combination of partitioning mechanism parameters, partitioning local basis vectors, and geometric feasibility closed-loop correction can effectively improve the accuracy and engineering usability of contour prediction.

[0311] Table 6 Comparison of time consumption of different methods on the test set

[0312]

[0313] From Table 6, Figure 10 It can be seen that although Comparative Examples 1 and 2 have slightly lower single-inference times, their prediction accuracy and feasibility pass rate are significantly worse, resulting in the need for manual correction in practical engineering applications. Although the finite element analysis of the reference example has high accuracy, its calculation time is as long as tens of minutes, making it difficult to support rapid iteration of multiple schemes. This invention achieves accuracy close to the engineering design requirements under sub-second time consumption conditions, and its overall performance is significantly better.

[0314] Table 7 Comparison of different methods on partitioning error

[0315]

[0316] As shown in Table 7, the improvements of this invention are most significant in the tire shoulder and tire heel areas. This is directly related to the fact that this invention establishes local basis vectors for different zones and prioritizes handling non-compliant zones in the geometric feasibility closed-loop correction. Combining the constraint conditions—objective function—verification output variable flow in the existing figures, this invention is particularly suitable for handling engineering-sensitive areas such as tire shoulder transition and tire heel assembly.

[0317] Figure 11To optimize the comparison of tire cross-sectional profiles before and after optimization, the shape differences between the initial profile and the optimized profile in the transition areas of the crown area, shoulder area, and sidewall are shown, illustrating that the optimized profile transitions more smoothly.

[0318] Figure 12 To illustrate the comparison of ground pressure distribution curves before and after optimization, the changes in ground pressure distribution along the width of the tire ground contact area are shown, demonstrating that the optimized ground pressure distribution is more uniform and the edge pressure peak is reduced.

[0319] Figure 13 The comparison chart of peak grounding pressure and pressure standard deviation before and after optimization shows the changes in peak grounding pressure and grounding pressure standard deviation before and after optimization, which is used to quantitatively illustrate the improvement effect of the optimization scheme on the grounding pressure concentration and distribution uniformity.

[0320] Figure 14 The diagram shows the convergence process of the objective function, illustrating how the objective function value gradually decreases and stabilizes as the number of iterations increases. This demonstrates that the optimization calculation process of this invention exhibits good convergence and stability.

[0321] Figure 15 The comparison diagram of ground pressure cloud map before and after optimization shows the changes in the pressure distribution of the tire grounding area before and after optimization, which is used to intuitively illustrate that the high-pressure concentration area is reduced and the force distribution in the grounding area is more uniform after optimization.

[0322] (viii) Analysis of technical effects

[0323] Based on the above embodiments and comparative examples, it can be demonstrated that the present invention has at least the following technical effects:

[0324] First, this invention can predict the tire inflation profile in a relatively short time. Compared to the solution cycle of traditional finite element analysis, which takes tens of minutes, this invention reduces the prediction time for a single tire to the order of 0.2s to 0.5s, significantly improving the efficiency of scheme comparison during the R&D stage.

[0325] Second, compared with direct point coordinate prediction methods and unified basis vector prediction methods, the present invention has higher prediction accuracy. The average absolute error on the test set is reduced to less than 1mm, indicating that the partitioned local modeling method of the present invention is more consistent with the actual deformation law of the tire cross-sectional profile.

[0326] Third, this invention significantly improves the engineering usability of the results through geometric feasibility closed-loop correction. The first-pass yield reaches 91.7%, which is significantly higher than the comparative method without a partition correction mechanism, especially in terms of the continuity of tire heel assembly boundary and tire shoulder transition.

[0327] Fourth, this invention has good applicability to tires of different specifications. Whether it is a low-profile passenger car tire such as 205 / 55R16 or 225 / 45R18, or a high-profile SUV tire such as 235 / 60R18, good predictive performance can be obtained, indicating that this invention has strong generalization ability.

[0328] Therefore, the above application examples and experimental data fully demonstrate that the present invention significantly improves the prediction efficiency of tire inflation profile while ensuring prediction accuracy and engineering constraint satisfaction, and has outstanding practical value.

[0329] The foregoing description of embodiments of the present invention, through which those skilled in the art are able to implement or use the present invention, will be readily apparent to those skilled in the art. Various modifications to these embodiments will be readily apparent to those skilled in the art. The general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novelty disclosed herein.

[0330] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0331] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0332] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0333] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0334] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0335] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0336] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

Claims

1. A method for predicting tire inflation profile based on machine learning, characterized in that, Includes the following steps: S1. Obtain tire sample data of multiple sample tires under a preset rated inflation pressure. The sample data includes the original set of structural parameters, the original set of material parameters, and the actual inflation profile data set. Extract the set of partitioning mechanism parameters that characterize the inflation deformation features of different regions of the tire cross section. S2. Transform the actual inflation profile data set of each sample tire into a unified rim reference coordinate system, and standardize the profile sampling according to the profile arc length direction to obtain a standard profile vector; divide the standard profile vector into multiple partition profile vectors according to the preset partition boundaries, and construct local reference profiles and local profile basis vector groups respectively. S3. Construct a partitioned multi-output machine learning model with the partitioning mechanism parameter set as input and the local contour basis vector coefficient set and key geometric quantity set of each partition as output; train the partitioned multi-output machine learning model using training samples to obtain the trained tire inflation contour prediction model. S4. Obtain the original structural parameters and original material parameters of the target tire, extract the set of partition mechanism parameters of the target tire, and input them into the tire inflation profile prediction model to obtain the set of prediction coefficients of local profile basis vectors of each partition and the set of prediction values ​​of key geometric quantities. Reconstruct the prediction profile of each partition and splice them together to form the initial prediction inflation profile. S5. Perform tire heel assembly boundary constraint verification, partition connection continuity constraint verification, curvature change threshold constraint verification, and cross-sectional width and height constraint verification on the initial predicted inflation profile, and output the final predicted inflation profile that meets the engineering constraints.

2. The method according to claim 1, characterized in that: In step S1, the original set of structural parameters includes at least one or more of the following: tread width, cross-section width, cross-section height, aspect ratio, rim diameter, carcass cord angle, belt layer angle, normalized position parameter of belt layer endpoint relative to the center of the tread crown, sidewall thickness gradient parameter, and heel wrap angle parameter. And / or, in step S1, the original set of material parameters includes at least one or more of the following: the elastic modulus of the tread rubber, the elastic modulus of the shoulder rubber, the elastic modulus of the sidewall rubber, the elastic modulus of the heel rubber, the tensile stiffness of the cord, the composite stiffness of the belt layer, and the composite stiffness of the carcass. And / or, in step S1, the set of partitioning mechanism parameters includes at least the mechanism parameters of the crown area, the mechanism parameters of the shoulder area, the mechanism parameters of the sidewall area, and the mechanism parameters of the heel area; And / or, in step S1, the partitioning mechanism parameter set is obtained by performing a mechanism combination transformation on the original structural parameter set and the original material parameter set, the mechanism combination transformation including at least: Shoulder support parameters are constructed based on the normalized position parameters of the belt layer endpoints relative to the center of the crown and the belt layer angle; A sensitive parameter for sidewall bulge is constructed based on the sidewall thickness gradient parameter and the sidewall rubber elastic modulus. Heel positioning parameters are constructed based on the heel wrap angle parameter and the elastic modulus of the heel rubber.

3. The method according to claim 1, characterized in that: In step S2, the standard contour vector is divided into the crown area contour vector, the shoulder area contour vector, the sidewall area contour vector, and the heel area contour vector according to the preset partition boundaries. Local reference contours and local contour basis vector sets are constructed based on the contour vectors of each partition, so that the contour of each partition is obtained by combining the local reference contour of the corresponding partition with multiple local contour basis vectors of that partition according to the corresponding coefficients; The partitions include the crown area, shoulder area, sidewall area, and heel area; the partition contour vector is the contour vector of the corresponding partition, the local reference contour vector is the reference contour vector of the corresponding partition, the local contour basis vector is the basis vector used to characterize the contour change in the corresponding partition, the local contour basis vector coefficient is the combination weight of the corresponding local contour basis vector, and the number of local contour basis vectors is the number of basis vectors participating in the contour combination in the corresponding partition. And / or, in step S2, the sampling of the standard contour vector is carried out according to the ratio of the arc length of the tire outer contour, and the value range of the arc length normalization position of the kth sampling point is 0 to 1. And / or, in step S2, the local contour basis vector groups of each region are constructed through principal component analysis, singular value decomposition, or based on a preset engineering deformation mode; wherein, the local contour basis vector of the crown region is used to characterize the crown arc change, the local contour basis vector of the shoulder region is used to characterize the shoulder convexity or inward retraction change, the local contour basis vector of the sidewall region is used to characterize the sidewall bulge change, and the local contour basis vector of the heel region is used to characterize the heel seating position change.

4. The method according to claim 1, characterized in that: In step S3, the set of local contour basis vector coefficients for each region includes the set of coefficients for the crown region, the set of coefficients for the shoulder region, the set of coefficients for the sidewall region, and the set of coefficients for the heel region. The set of key geometric quantities includes at least one or more of the following: predicted section width, predicted section height, tire shoulder radius, coordinates of the maximum bulge point, and tire heel spacing; And / or, in step S3, the partitioned multi-output machine learning model is one or more of the following: support vector regression model, random forest regression model, gradient boosting tree model, and deep neural network model; When the partitioned multi-output machine learning model is a deep neural network model, its output layer simultaneously outputs the set of local contour basis vector coefficients and the set of key geometric quantities for each partition. And / or, in step S3, the objective function used for training includes a coefficient error term, a contour reconstruction error term, a key geometric quantity error term, and a constraint penalty term. The objective function is composed of the coefficient error term, the contour reconstruction error term, the key geometric quantity error term, and the constraint penalty term weighted according to their corresponding weight coefficients. The objective function is used to evaluate the model training error, the coefficient error term is used to evaluate the prediction error of the local contour basis vector coefficients, the contour reconstruction error term is used to evaluate the difference between the predicted contour and the actual contour, the key geometric quantity error term is used to evaluate the prediction error of the key geometric quantity, the constraint penalty term is used to evaluate the degree to which the predicted contour violates the geometric constraints, and the corresponding weight coefficients are used to adjust the influence of each error term in the objective function.

5. The method according to claim 1, characterized in that: In step S4, the predicted profiles of the crown area, shoulder area, sidewall area, and heel area are reconstructed based on the predicted coefficient set of the local contour basis vectors of each partition, and the predicted profiles of each partition are spliced ​​together to form the initial predicted inflation profile of the target tire.

6. The method according to claim 1, characterized in that: In step S5, the tire heel assembly boundary constraint verification includes: predicting that the coordinate deviation between the tire heel point and the rim seat boundary point is not greater than the tire heel point positioning deviation threshold. The partition connection continuity constraint check includes: the difference in tangent direction at the connection point of adjacent partitions is not greater than the threshold of tangent direction difference; The curvature change threshold constraint check includes: the absolute value of the curvature difference between adjacent sampling points is not greater than the curvature difference threshold; The cross-sectional width and height constraint verification includes: the predicted cross-sectional width is between the lower limit of the cross-sectional width and the upper limit of the cross-sectional width, and the predicted cross-sectional height is between the lower limit of the cross-sectional height and the upper limit of the cross-sectional height; The tire heel point positioning deviation threshold is used to limit the allowable deviation between the tire heel point and the rim seat boundary point; the tangent direction difference threshold is used to limit the directional continuity of the connection position of adjacent partitions; the curvature difference threshold is used to limit the degree of local curvature change of the contour; the lower limit and upper limit of the cross-section width are used to limit the predicted cross-section width range; and the lower limit and upper limit of the cross-section height are used to limit the predicted cross-section height range. And / or, in step S5, when the preset feasibility criterion is met, the final predicted inflatable profile is output; when it is not met, only the predicted coefficients of the local profile basis vectors corresponding to the violation of the constraint are projected and corrected. The projection correction is achieved by solving the constrained local coefficient correction problem. The corrected local profile basis vector coefficient set is the set of coefficients that minimizes the sum of the deviation terms between the corrected coefficients and the original predicted coefficients and the penalty function terms for violating geometric constraints. Wherein, the modified local contour basis vector coefficient set is the modified coefficient result, the original predicted coefficient set is the local contour basis vector predicted coefficient set before modification, the deviation term is used to characterize the difference between the modified coefficient and the original predicted coefficient, the penalty function term is used to characterize the degree of violation of geometric constraints, and the penalty function weight coefficient is used to adjust the influence of the penalty function term in the local coefficient correction problem.

7. The method according to claim 1, characterized in that, It also includes step S6: using test samples to evaluate the accuracy of the final predicted inflation profile, wherein the accuracy evaluation index includes at least one or more of the following: mean absolute error, root mean square error, and maximum profile deviation.

8. A tire inflation profile prediction system based on machine learning, characterized in that, The system is used to implement the method according to any one of claims 1 to 7, comprising: The sample data acquisition module is used to execute step S1; The contour standardization partitioning module is used to perform step S2; The model building and training module is used to execute step S3; The contour prediction module is used to perform step S4; The geometric feasibility closed-loop verification module is used to execute step S5.

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

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method described in any one of claims 1 to 7.

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