Automobile tire modeling method, system and storage medium

Abstract

The application relates to the technical field of modeling, in particular to a tire modeling method and system and a storage medium, which comprises the following steps: step 1, acquiring tire contour data; step 2, extracting tire cross-section image features: extracting feature vectors of two-dimensional tire cross-section images based on point cloud images, and calculating the distance between the feature vectors; judging the similarity between images based on the distance, and segmenting tire point clouds into tread point clouds and groove point clouds according to the similarity; step 3, constructing a tread point cloud mapping array; step 4, fitting a pattern boundary curve; step 5, determining tire material layer distribution: combining the geometric features obtained from the tread point cloud mapping array, and using a DeepLabV3+ network structure to segment the material layers of the tire, so as to obtain the distribution of the tire material layers; and step 6, training and verifying the model, and obtaining a tire finite element model after verification. The application improves the precision of the tire finite element model.

Description

Technical Field

[0001] This invention relates to the field of modeling technology, and specifically to a method, system and storage medium for modeling automobile tires. Background Technology

[0002] In the field of vehicle technology, tires, as the sole medium of contact between a vehicle and the ground, directly affect the vehicle's handling, safety, and comfort. Therefore, accurate tire modeling to predict its mechanical properties under different operating conditions has always been a research hotspot in vehicle engineering.

[0003] Existing tire modeling methods primarily rely on experimental testing and data analysis, using extensive experimental data to fit the mechanical properties of tires. However, this method is not only time-consuming and labor-intensive, but also struggles to comprehensively consider performance changes under different wear conditions. In recent years, with the rapid development of computer technology, finite element simulation technology has gradually become an important tool for tire modeling. Through finite element simulation, the stress conditions of tires under different operating conditions can be simulated, thereby predicting their mechanical properties.

[0004] However, existing finite element method (FEM) simulation techniques for tires still have some limitations, particularly in considering the tire vulcanization process and tire wear. During the vulcanization process, the tire's profile and material layers undergo deformation due to high temperature and pressure. This deformation not only affects the tire's geometry but also alters its internal stress distribution and material properties. Ignoring this factor during finite element simulation will lead to significant discrepancies between the simulation results and actual conditions, thus reducing the simulation's accuracy.

[0005] Furthermore, tires experience wear during use, and the degree of wear directly affects their mechanical properties. While existing tire modeling methods have begun to consider the impact of tire wear on mechanical properties, they often identify wear characteristics only after the tire model has been built. Although this method can reflect performance changes after tire wear to some extent, it cannot address the impact of wear on tire modeling at its source, and therefore cannot obtain a completely accurate tire dynamics model.

[0006] Therefore, it is necessary to develop a new method, system, and storage medium for modeling automobile tires. Summary of the Invention

[0007] The purpose of this invention is to provide a method, system, and storage medium for modeling automobile tires, which can improve the accuracy of automobile tire finite element models.

[0008] In a first aspect, the automobile tire modeling method of the present invention includes the following steps:

[0009] Step 1. Obtain tire contour data: Scan the tire to obtain point cloud images of the inner and outer contours of the tire;

[0010] Step 2. Extract tire cross-section image features: Extract feature vectors from the two-dimensional tire cross-section image based on the point cloud image, and calculate the distance between the feature vectors; determine the similarity between images based on the distance, and segment the tire point cloud into tread point cloud and tread groove point cloud according to the similarity;

[0011] Step 3. Constructing the tread point cloud mapping matrix: The tread basis function curve is fitted with NURBS spline curves to construct a tread point cloud mapping matrix that maps the tread point cloud onto the surface of the tire model.

[0012] Step 4: Fitting the pattern boundary curve: After segmenting the pattern groove point cloud, a multi-segment dynamically optimized straight-line circular arc approximation method is used to fit the tangent curve of each pattern boundary.

[0013] Step 5. Determine the tire material layer distribution: Use a DeepLabV3+ network structure to segment the tire material layers to obtain the distribution of the tire material layers, thus constructing a preliminary model of the car tire;

[0014] Step 6. Training and Validating the Model: The preliminary model of the car tire is trained and validated using tire image samples, and the finite element model of the car tire is obtained after successful validation.

[0015] Optionally, in step 1, a 3D scanner is used to perform a 3D scan of the tire to obtain a point cloud map of the tire's inner and outer contours. The 3D scanner has a resolution of 0.1 mm or higher. Using a high-resolution 3D scanner to scan the tire ensures that the acquired point cloud map has high precision and detail, providing a reliable data foundation for subsequent tire modeling. This high-precision data acquisition method helps improve the accuracy and realism of the tire model.

[0016] Optionally, in step 2, based on the point cloud image, an AlexNet network is used to extract image features from the two-dimensional tire cross-section image and establish a feature vector. Using the AlexNet network to extract the feature vector of the two-dimensional tire cross-section image can fully utilize the deep learning capabilities of the network to extract rich feature information from the image.

[0017] Optionally, the hierarchical structure of the AlexNet network includes features from low to high levels, specifically including edges, textures, shapes, and complex objects. This helps to more accurately segment the tire point cloud and improve the detail representation of the tire model.

[0018] Optionally, in step 5, the DeepLabV3+ network structure includes an encoder and a decoder. The encoder uses a lightweight MobileNet V3_Large as its backbone network and mines basic features through a dilated spatial pyramid pooling module. The decoder restores the high-level semantic information extracted by the encoder to the scale of the original image to reconstruct the edges and details of the tire material layer. Using the DeepLabV3+ network structure to segment the tire material layer can fully utilize the deep learning and semantic segmentation capabilities of the DeepLabV3+ network. Through the collaboration of the encoder and decoder, feature information of the tire material layer can be extracted efficiently, and a tire material layer model with clear edges and details can be reconstructed. In addition, using the lightweight MobileNet V3_Large as the backbone network can also improve the model's running efficiency and real-time performance.

[0019] Optionally, in step 5, before dividing the material layers of the tire, the following operations are also performed:

[0020] The low-dimensional feature map extracted by the backbone network is concatenated with the high-dimensional feature map obtained through a four-fold upsampling operation. This concatenation integrates spatial information about the tire surface texture, edge lines, and seams, as well as channel information related to corresponding brightness, color variations, and texture features. Before tire material layer segmentation, this concatenation and fusion of low-dimensional and high-dimensional feature maps fully utilizes feature information at different scales, improving the accuracy and robustness of tire material layer segmentation. This fusion method helps capture detailed information about the tire surface texture, edge lines, seams, and corresponding brightness, color variations, and texture features, thereby generating a more realistic tire model.

[0021] Optionally, in step 6, the tire image samples are actual tire image samples. Using actual tire image samples for model training and validation ensures the similarity and accuracy between the tire model and a real tire. This modeling approach based on real data helps improve the practicality and reliability of the tire model, providing strong support for tire design and optimization.

[0022] Optionally, in step 6, the actual tire image samples are divided into a training set and a validation set. The preliminary model is trained using the training set and validated using the validation set. The model performance is comprehensively evaluated using the loss function value, mean intersection-over-union ratio (MIU), and accuracy. After successful validation, the finite element model of the automobile tire is obtained. Dividing the actual tire image samples into training and validation sets, and using evaluation metrics such as loss function value, MTU, and accuracy to comprehensively evaluate model performance, ensures the accuracy and reliability of the tire model. Simultaneously, the validated tire finite element model provides a reliable foundation for subsequent tire simulation analysis and optimization design. This modeling and validation method based on actual tire data helps improve the efficiency and accuracy of tire design and optimization.

[0023] Secondly, the present invention provides an automobile tire modeling system, which includes a controller and a memory. The memory stores a computer-readable program, which, when invoked by the controller, can execute the steps of the automobile tire modeling method described in the present invention.

[0024] Thirdly, the present invention provides a storage medium storing a computer-readable program that, when invoked, can execute the steps of the automobile tire modeling method described in the present invention.

[0025] The beneficial effects of this invention are:

[0026] (1) This invention uses a physical tire for modeling. The physical tire can fully reflect the deformation of the tire's contour and material layers during the vulcanization process, which is something that traditional design parameters cannot fully capture. Therefore, using a physical tire for modeling makes the finite element model of the car tire closer to the physical characteristics of the actual tire, thereby significantly improving the accuracy and realism of the simulation.

[0027] (2) This invention utilizes a convolutional neural network to extract features from actual two-dimensional tire cross-sectional images. By calculating the distance between the feature vectors of the images, the similarity between the images is determined, thereby improving the accuracy of the actual tire cross-sectional profile. This technique not only improves the efficiency of establishing finite element models of automobile tires but also makes the simulation results more accurate and reliable.

[0028] (3) This invention uses a DeepLabV3+ network structure to segment the material layers of the tire, which can accurately obtain the material layer distribution of the tire. This technology provides key data support for the accurate establishment of the finite element model of automobile tires, enabling the finite element model of automobile tires to more accurately reflect the internal material structure and mechanical properties of the tire.

[0029] In summary, this invention, by using physical tires for modeling and combining advanced deep learning technology, significantly improves the accuracy and realism of finite element simulation of automobile tires, providing strong technical support for tire design, optimization, and performance evaluation. This innovative achievement not only reduces R&D costs and time but also promotes the continuous progress and development of tire modeling and simulation technology. Attached Figure Description

[0030] Figure 1 This is a flowchart of the automobile tire modeling method described in the embodiments of this application;

[0031] Figure 2 This is a schematic diagram of image synthesis in an embodiment of this application;

[0032] Figure 3 This is a flowchart of the image retrieval process in an embodiment of this application;

[0033] Figure 4 This is a schematic diagram of the DeepLabV3+ network structure in the embodiments of this application;

[0034] Figure 5 This is a schematic diagram of the key semantic category labels of the tire tread rubber dataset in the embodiments of this application;

[0035] Figure 6 This is a graph showing the changes in the loss function values ​​of the training set and validation set with the number of training rounds in the embodiments of this application.

[0036] Figure 7 This is a graph showing the average intersection-union ratio (IU) of the validation set as a function of the number of training rounds in the embodiments of this application.

[0037] Figure 8 This is a graph showing the change in the accuracy of the validation set with the number of training rounds in the embodiments of this application.

[0038] Figure 9 This is a schematic diagram of the automobile tire modeling system described in the embodiments of this application;

[0039] In the diagram: 1-Memory, 2-Controller. Detailed Implementation

[0040] The embodiments of the present invention will be described below with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention and not for limiting the scope of protection of the present invention.

[0041] like Figure 1 As shown in the embodiments of this application, a method for modeling automobile tires includes the following steps:

[0042] Step 1. Obtain tire contour data: Scan the tire to obtain point cloud maps of the tire's inner and outer contours.

[0043] Step 2. Extract tire cross-section image features: Extract feature vectors from the two-dimensional tire cross-section image based on the point cloud image, and calculate the distance between the feature vectors; determine the similarity between images based on the distance, and segment the tire point cloud into tread point cloud and tread groove point cloud according to the similarity.

[0044] Step 3. Construct the tread point cloud mapping matrix: Use NURBS spline curves to fit the tread basis function curves to construct a tread point cloud mapping matrix that maps the tread point cloud onto the surface of the tire model.

[0045] Step 4: Fitting the pattern boundary curve: After segmenting the pattern groove point cloud, a multi-segment dynamically optimized straight-line circular arc approximation method is used to fit the tangent curve of each pattern boundary.

[0046] Step 5. Determine the tire material layer distribution: Use a DeepLabV3+ network structure to segment the tire material layers and obtain the distribution of the tire material layers, thus constructing a preliminary model of the car tire.

[0047] Step 6. Training and Validating the Model: Use tire image samples to train and validate the preliminary model of the car tire, and obtain the finite element model of the car tire after successful validation.

[0048] In one possible embodiment, acquiring tire profile data specifically involves:

[0049] Use a 3D scanner to perform a 3D scan of the tire to obtain a point cloud image of the tire's inner and outer contours. To ensure high accuracy of the point cloud data, it is recommended to use a high-resolution 3D scanner with a resolution of 0.1 mm or higher to ensure that the tire's detailed features can be captured.

[0050] In one possible embodiment, the tire cross-section image features are extracted, specifically as follows:

[0051] To compare a 2D tire cross-section image with the actual tire's outer contour, the AlexNet network was used to extract image features from the 2D tire cross-section image and construct feature vectors. In extracting image features, the hierarchical structure of the AlexNet network includes features from low to high levels, including detailed information such as edges, textures, shapes, and complex objects. During the image feature extraction process, the first few layers of the AlexNet network extract low-level edge and texture features, the middle layers capture contours and shapes, and the last few layers extract higher-level semantic features of complex objects.

[0052] When constructing feature vectors, multiple dimensions are included, such as activation values ​​processed by convolutional and pooling layers. The feature vector set includes edge features, texture features, local structural features, and geometric shape features of the image. The extracted feature vectors can comprehensively represent the key information of the two-dimensional tire cross-sectional image, and these feature vectors are used to represent the corresponding image. The similarity between images is determined by calculating the distance between feature vectors, and then the tire point cloud is segmented into tread point cloud and tread groove point cloud based on the similarity.

[0053] like Figure 2 As shown in the figure, A represents the synthesized image region, B represents the image to be synthesized, and A' and B' are the parts of the overlapping region belonging to image A and image B, respectively. In the overlapping region, the smaller the difference in feature information between the two images, the higher the similarity, and vice versa.

[0054] In one possible implementation, the distance between feature vectors is calculated as follows:

[0055]

[0056] In the formula, d(x,y) is the distance between feature vectors; i is the dimension of the feature vectors of the image, i = 1, 2, ..., m, where m is the total number of dimensions of the feature vectors. i Let y be the feature vector of the image to be retrieved. i The image feature vectors are from the image database (i.e., the multiple images obtained through scanning in step 1). The distance between the images is obtained by comparing the distance between the image to be retrieved and the feature vectors in the image database. The smaller the distance, the higher the similarity.

[0057] D j =qT j (2)

[0058] Let the total number of images in the image database be N, q be the feature vector of the feature region of the image to be retrieved, and T be... j Let j = 1, 2, ..., N, D, be the feature vector of the image segment corresponding to the feature region of the image to be retrieved in the j-th image in the image database. j The distance difference between the feature vector of the image to be retrieved and the feature vector of the j-th image in the image database is used to sort D. jThe values ​​are compared, and n similar images are found and output. The purpose of finding and outputting n similar images is to find the image segment most similar to the image to be retrieved, so as to compare and enhance the accuracy of local details of the image to be retrieved, thereby improving the accuracy of image processing results. The image features in the image database are extracted using the trained finite element model of automobile tires and a vector index library is established. The feature vector of the image to be retrieved is extracted through the AlexNet network. The n similar images to the image to be retrieved are calculated using formula (2). Then, the similarity matching degree can be calculated by comparing the distances of the n images calculated by formula (1).

[0059] like Figure 3 As shown, in one possible embodiment, the neighborhood retrieval process is as follows: Input the image to be retrieved; use the trained AlexNet network to extract the feature vectors of each image in the image database, perform PCA (principal component analysis) dimensionality reduction processing, and establish a two-dimensional tire cross-section image database; calculate the Euclidean distance matching feature vector, and after retrieval, place the image to be retrieved in the specified area according to the specified image size. Then, use the Dijkstra algorithm to stitch the new and old images together to ensure a smooth transition between the new and old images and reduce the potential boundary inconsistency problem in the images.

[0060] In one possible embodiment, determining the distribution of the tire material layers specifically involves:

[0061] To accurately determine the material distribution of each layer of a tire, a DeepLabV3+ network structure was proposed, and the training dataset was optimized.

[0062] like Figure 4As shown, the DeepLabV3+ network structure consists of two parts: an encoder and a decoder. The encoder first extracts basic visual features, also known as low-dimensional feature maps, through a backbone network. These features include, but are not limited to, edge features, texture features, color features, and shape features. Through multi-layered processing by a convolutional neural network, these feature maps contain preliminary structural and texture information of the image. Low-level convolutional kernels (such as 3x3 convolutions) can capture local edge and texture information, while mid-to-high-level convolutional kernels can recognize more complex shape and structural information. In this process, to meet computational efficiency and segmentation performance requirements, the original backbone network Xception is improved to the more lightweight MobileNet V3_Large. MobileNet V3_Large utilizes depthwise separable convolutions to further enhance feature extraction efficiency and reduce computational load while maintaining accuracy requirements. Furthermore, the Spatial Pyramid Pooling (ASPP) module is used to deeply mine these basic features. In this process, more detailed feature information is extracted through 1×1 convolution; a series of 3×3 dilated convolutions with different dilation rates are used to detect feature information at different scales, thereby effectively capturing and fusing multi-scale information and enhancing the ability to identify and extract objects of different sizes in the image; and global average pooling is used to capture the global contextual information of the image.

[0063] Furthermore, these fundamental features are further explored using the dilated spatial pyramid pooling module. This module effectively captures multi-scale information in the image through convolution operations at different scales (i.e., different dilation rates). Specifically, 1×1 convolutions extract more detailed feature information. This detailed feature information includes the particle size of tire rubber and subtle surface texture variations, which can improve feature resolution in local areas. A series of 3×3 dilated convolutions with different dilation rates are used to detect feature information at different scales. By selecting multiple different dilation rates (e.g., 1, 2, 4, 8), information from details to the overall image can be captured comprehensively; however, generally, choosing 3-4 different dilation rates is most suitable to achieve a balanced feature fusion effect.

[0064] Global average pooling captures the global contextual information of an image. In tire images, this global contextual information manifests as the overall material distribution and large-scale structural information. Specifically, global average pooling comprehensively considers the average feature values ​​of all pixels in the image, including global information at different locations, thereby improving the model's understanding of the overall structure and segmentation accuracy.

[0065] The high-level semantic information extracted by the encoder is restored to the scale of the original image to accurately reconstruct the edges and details of objects. This process first effectively concatenates the low-dimensional feature map extracted by the backbone network with the high-dimensional feature map obtained through a four-fold upsampling. This fuses spatial information including tire surface texture, edge lines, seams, etc., with corresponding channel information such as brightness, color variations, and texture features. This enhances the ability to recognize the edges and details of objects such as tire tread patterns, tire body layers, and tire defects in the image, thereby improving the accuracy of semantic segmentation. Secondly, the number of channels in the output feature map is adjusted using a 3×3 convolution to match the number of target categories, and a four-fold upsampling is used to output a segmentation result with the same size as the original image. In this way, the decoder can remap the deep features extracted by the convolutional neural network back to the resolution of the original image, while ensuring that edges and details in the image are accurately restored, ultimately improving the overall effect and accuracy of semantic segmentation.

[0066] In one possible implementation, training and validating the model specifically involves:

[0067] Semantic segmentation training requires a large number of image samples with pixel-level labels (8-bit grayscale images). By cutting tires, a tire cross-section sample set was obtained and manually labeled. Detailed annotations were provided for 15 different semantic categories of tread rubber, including rubber elements such as the inner liner, carcass, belts, crown belt, tread, and tread trim. Figure 5 As shown, each category is equipped with a unique identifier ID and corresponding RGB color code for easy identification and application. The sample set consists of 2975 images for training, 500 images for validation, and 1525 images for testing.

[0068] like Figure 6 As shown in the figure, in the initial stage, the loss function value rapidly decreased to approximately 0.174 (after about 15 rounds), then continued to decrease at a slower rate and tended to converge, with the final training loss being approximately 0.075. This indicates that the finite element model of the car tire effectively learned and gradually approached its optimal performance. The validation set loss also showed a decreasing trend, eventually stabilizing at around 0.101, demonstrating the good generalization ability of the finite element model of the car tire on unseen data.

[0069] like Figure 7 and Figure 8 As shown, the mean crossover ratio and accuracy on the validation set reached 74.65% and 94.74%, respectively, highlighting the superior performance of the DeepLabV3+ model in processing images of tire tread rubber material layers.

[0070] like Figure 9As shown in the embodiments of this application, a car tire modeling system includes a controller 2 and a memory 1. The memory 1 stores a computer-readable program, which, when called by the controller, can execute the steps of the car tire modeling method as described in the embodiments of this application.

[0071] In this embodiment of the application, a storage medium stores a computer-readable program that, when invoked, can execute the steps of the automobile tire modeling method described in this embodiment of the application.

[0072] In embodiments of this application, the storage medium may be a tangible storage medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. The storage medium may be a machine-readable signal storage medium or a machine-readable storage medium. The storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0073] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for modeling automobile tires, characterized in that, Includes the following steps: Step 1. Obtain tire contour data: By scanning the tire, obtain the point cloud map of the inner and outer contours of the tire; Step 2. Extract tire cross-section image features: Extract feature vectors from the two-dimensional tire cross-section image based on the point cloud image, calculate the distance between the feature vectors, determine the similarity between images based on the distance, and segment the tire point cloud into tread point cloud and tread groove point cloud according to the similarity. Step 3. Constructing the tread point cloud mapping array: Using the NURBS algorithm, the basis function curve of the tread is fitted to a NURBS curve. Based on the NURBS curve, the mapping relationship between the tread point cloud and the tire model surface is established. The mapped point cloud data is organized into a preset data structure to form the tread point cloud mapping array. Step 4. Fitting the pattern boundary curve: The segmented pattern groove point cloud is approximated by a multi-segment dynamically optimized straight-line circular arc approach to achieve tangent curve fitting for each pattern boundary. The structural information in the tread point cloud mapping array is used to assist in locating the pattern boundary. Step 5. Determine the tire material layer distribution: Combining the geometric features obtained from the tread point cloud mapping array, the tire material layers are segmented using an algorithm based on the DeepLabV3+ network structure to obtain the distribution of the tire material layers and construct a preliminary model of the car tire; wherein, the DeepLabV3+ network structure includes an encoder and a decoder, the encoder uses a lightweight MobileNet V3_Large as the backbone network, and mines basic features through a hollow spatial pyramid pooling module; Step 6. Training and Validating the Model: The preliminary model of the car tire is trained and validated using tire image samples, and the finite element model of the car tire is obtained after successful validation. Before dividing the material layers of the tire in step 5, the following operations are performed: The low-dimensional feature map extracted by the backbone network is concatenated with the high-dimensional feature map obtained by a four-fold upsampling operation, and the spatial information including the texture, edge lines, and seams of the tire surface, as well as the corresponding channel information of brightness, color changes and texture features are fused.

2. The automobile tire modeling method according to claim 1, characterized in that, In step 1, a 3D scanner is used to perform a 3D scan on the tire to obtain a point cloud map of the tire's inner and outer contours.

3. The automobile tire modeling method according to claim 1, characterized in that, In step 2, based on the point cloud map, the AlexNet network is used to extract image features of the two-dimensional tire cross-section image and establish a feature vector.

4. The automobile tire modeling method according to claim 3, characterized in that, The hierarchical structure of the AlexNet network includes features from low to high levels, specifically including edges, textures, shapes, and complex objects.

5. The automobile tire modeling method according to claim 1, characterized in that: The decoder restores the high-level semantic information extracted by the encoder to the scale of the original image in order to reconstruct the edges and details of the tire material layers.

6. The automobile tire modeling method according to claim 1, characterized in that: In step 6, the tire image sample is an actual tire image sample.

7. The automobile tire modeling method according to claim 6, characterized in that: In step 6, the actual tire image samples are divided into a training set and a validation set. The preliminary model is trained using the training set and validated using the validation set. The model performance is comprehensively evaluated by the loss function value, average crossover ratio, and accuracy. After successful validation, the finite element model of the automobile tire is obtained.

8. A vehicle tire modeling system, characterized in that: It includes a controller (2) and a memory (1), wherein the memory (1) stores a computer-readable program that, when invoked by the controller (2), can perform the steps of the automobile tire modeling method as described in any one of claims 1 to 7.

9. A storage medium, characterized in that: It contains a computer-readable program that, when invoked, can perform the steps of the automobile tire modeling method as described in any one of claims 1 to 7.

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