A data-driven adaptive parameterization modeling method for automobile roof lines
By employing a data-driven, two-layer optimization strategy and segmented parametric modeling, the adaptability and accuracy issues of existing automotive roofline modeling technologies are resolved, achieving efficient and accurate reconstruction of the automotive roofline and model simplicity.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2026-04-03
- Publication Date
- 2026-07-03
AI Technical Summary
Existing parametric modeling techniques for vehicle body geometry are difficult to adapt to complex features and struggle to achieve an optimal balance between fitting accuracy and model complexity, resulting in low efficiency and poor reconstruction accuracy.
A data-driven, two-layer optimization strategy is adopted. By segmented parametric modeling and normalized coordinate system, the number and location of control points and the type of reconstructed model are automatically determined. Heuristic algorithms such as particle swarm optimization are used to optimize control variables, thereby achieving adaptive parameterization of the model.
It significantly improves the reconstruction accuracy of the car roofline and the model generalization ability, achieving an optimal balance between fitting accuracy and model complexity, and improving the consistency and efficiency of modeling.
Smart Images
Figure CN122333633A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of vehicle body development and design technology, and in particular relates to a data-driven adaptive parametric modeling method for vehicle roofline. Background Technology
[0002] The roofline of a car is a key geometric feature that determines its aerodynamic performance and aesthetic styling. In modern automotive R&D processes, establishing high-precision, low-dimensional parametric models is a prerequisite for achieving automated aerodynamic optimization. However, existing parametric modeling technologies for vehicle geometry face the following technical bottlenecks when dealing with large-scale, heterogeneous vehicle data sets:
[0003] First, the model structure is rigid and struggles to adapt to complex features. Traditional parametric methods (such as CST-like function transformations, Bézier curves, or B-splines) typically rely on engineers' experience to pre-determine the number and location of control points. This a priori, fixed structure cannot adapt to the differences in geometric feature distributions among different vehicle models. For regions with drastic curvature changes, a fixed distribution of control points often leads to underfitting; while for flat regions, too many control points result in parameter redundancy.
[0004] Second, the trade-off between model complexity and fitting accuracy relies on manual trial and error. When constructing a parametric model, the choice of the number of control points and the model type is crucial. Too few control points lead to poor fitting accuracy, while too many result in overfitting and significantly increase the computational cost of subsequent optimization. Current technologies lack a mechanism to automatically determine the optimal model structure based on data characteristics, often requiring designers to repeatedly try and fail, which is inefficient and makes it difficult to guarantee the most cost-effective parametric solution from a global perspective. Summary of the Invention
[0005] Purpose of the invention: The purpose of this invention is to provide a data-driven adaptive parametric modeling method for automotive roofline, which aims to solve the problems in existing automotive generative design technologies where the parametric model structure relies on human experience and pre-set parameters, and where it is difficult to achieve the optimal balance between fitting accuracy and model complexity.
[0006] Technical solution: To achieve the above objectives, the adaptive parametric modeling method for automobile roofline described in this invention includes the following steps: (1) Obtain the side view top profile coordinate data of multiple real vehicles, divide the side view top profile into the front guide section and the rear main body section along the longitudinal direction of the vehicle; establish a normalized coordinate system for each segment, and then discretize the top profile curve in each segment into several sampling points according to the preset sampling density, obtain the two-dimensional coordinate data of each sampling point in the corresponding coordinate system, and form the bottom sample database. (2) Define the control variables for parametric modeling. The control variables include the spatial location of the control points in the normalized coordinate system, the number of control points, and the type of reconstructed model. (3) Based on the underlying sample database, a two-layer optimization strategy is adopted to perform global iterative optimization of the control variables of the front guidance section and the rear main body section to obtain the optimal control variables that make the comprehensive evaluation index optimal, and thus obtain the optimal parameterized reconstruction model. The two-layer optimization strategy includes outer-layer structure optimization and inner-layer parameter optimization. Outer-layer structure optimization refers to traversing the number of control points and the type of reconstructed model in a preset discrete space to generate multiple candidate model structures. Inner-layer parameter optimization refers to using a piecewise optimization strategy to search for the optimal spatial distribution of control points in a continuous space for each candidate model structure, obtaining the parameterized reconstructed model after inner-layer optimization, and calculating its corresponding overall sample reconstruction error.
[0007] Optionally, in step (1), the side-view roofline is taken from the outer contour projection line of the longitudinal symmetry center plane of the vehicle body on the side view of the vehicle body. The data range of the side-view roofline is defined as a continuous geometric curve starting from the front edge of the car hood, extending through the front windshield, roof, and rear windshield to the rear end point of the vehicle. The front guide section and the rear main body section are divided by the starting feature point of the windshield.
[0008] Optionally, the normalized coordinate system in step (1) is constructed by mapping the lateral physical length of each segment to the [0,1] interval.
[0009] Optionally, in step (2), the number of control points in the front guide section is limited to the range of [2,5], and the number of control points in the rear main section is limited to the range of [4,9].
[0010] Optionally, in step (2), the starting endpoint x-coordinate of the front guide segment and the rear main segment in the normalized coordinate system is fixed at 0, and the ending endpoint x-coordinate is fixed at 1; the spatial position of the control point in the normalized coordinate system is limited to the interval [0.01, 0.99].
[0011] Optionally, the reconstructed model type in step (2) includes one or more of the following: radial basis function interpolation model, cubic spline interpolation model, piecewise cubic Hermitian interpolation model, and modified Akima piecewise cubic Hermitian interpolation model.
[0012] Optionally, the overall sample reconstruction error in step (3) refers to the root mean square error (RMSE) between the parameterized reconstruction model of all samples and the original top-shaped curve collected in step (1).
[0013] Optionally, in step (3), the first stage of the segmented optimization strategy is to fix the control variables of the rear main body segment, use the minimization of the overall sample reconstruction error as the fitness function, and use a heuristic optimization algorithm to optimize the front guiding segment; the second stage of the segmented optimization strategy is to fix the control variables of the optimized front guiding segment, use the minimization of the overall sample reconstruction error as the fitness function, and use a heuristic optimization algorithm to optimize the rear main body segment.
[0014] Optionally, the heuristic optimization algorithm in step (3) is a particle swarm optimization algorithm (PSO), a genetic algorithm (GA), or a differential evolution algorithm (DE).
[0015] Optionally, in step (3), a comprehensive evaluation index is constructed. From all the parameterized reconstruction models that have undergone inner-layer optimization, the control variable with the smallest comprehensive evaluation index is selected as the optimal control variable. The expression for the comprehensive evaluation index is: , in, As a comprehensive evaluation indicator; The overall sample reconstruction error characterizes the model's fitting accuracy. This is the model complexity penalty coefficient, used to adjust the weights of accuracy and complexity; This represents the number of normalized control points currently deployed in the segment.
[0016] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: By segmenting and parametrically modeling the roofline of a car, this invention effectively characterizes the geometric differences between the front guide region and the rear main body region of the roofline, significantly improving the reconstruction accuracy and generalization ability of complex car body curves; by introducing normalized control points and a two-layer optimization strategy including a complexity penalty term, this invention achieves fully automatic adaptive determination of model type, number of control points, and their spatial distribution; it effectively solves the problem of traditional methods relying on manual experience to pre-set model structures, achieving the optimal balance between fitting accuracy and model complexity, effectively avoiding overfitting, and improving the consistency of modeling; the general parametric reconstruction model established by this invention has the characteristics of low parameter dimension, clear physical semantics, and unified expression form, making it easy to combine with aerodynamic simulation, optimization design, and data-driven design processes, and has high engineering application value. Attached Figure Description
[0017] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of the extraction and physical segmentation of the roofline features of a car in this invention; Figure 3 This is a schematic diagram of the construction of the normalized coordinate system for the front guide section of the car roofline in this invention; Figure 4This is a schematic diagram of the construction of the normalized coordinate system for the rear main body segment of the car roofline in this invention; Figure 5 This is a comparison of the geometric feature reconstruction and local fitting residuals before and after optimization of typical sample 1 in this invention; Figure 6 This is a comparison of the geometric feature reconstruction and local fitting residuals before and after optimization of typical sample 50 in this invention; Figure 7 This is a comparison of the geometric feature reconstruction and local fitting residuals of a typical sample 100 before and after optimization in this invention. Detailed Implementation
[0018] The technical solution of the present invention will be further described below with reference to the accompanying drawings.
[0019] like Figure 1 As shown, this embodiment of the invention provides a data-driven adaptive parametric modeling method for automotive roofline, comprising the following steps: (1) Obtain the side view top profile coordinate data of multiple real vehicles, divide the side view top profile into the front guide section and the rear main body section along the longitudinal direction of the vehicle; establish a normalized coordinate system for each segment, and then discretize the top profile curve in each segment into several sampling points according to the preset sampling density, obtain the two-dimensional coordinate data of each sampling point in the corresponding coordinate system, and form the bottom sample database. The side-view roofline is taken from the outer contour projection line of the longitudinal symmetry center plane of the vehicle body on the side view of the vehicle body. The data range of the side-view roofline is defined as a continuous geometric curve starting from the front edge of the car hood, passing through the front windshield, roof, and rear windshield, and extending to the rear end point of the vehicle. A normalized coordinate system is established by mapping the lateral physical length of each segment to a coordinate system. Interval construction; The front guide section and the rear main body section are divided by the starting feature point of the front windshield; Specifically, 100 sets of 3D shape data for hatchback vehicles were acquired, and the side profile of each vehicle was extracted using a Rhino script. The top profile feature curve was then extracted along the top outer contour of each sample image. For example... Figure 2 As shown, the side-view roofline is divided into a front guide section and a rear main section, with the geometric inflection point between the rear edge of the hood and the bottom of the windshield as the boundary. The dividing point of the two sections is then moved to the origin of the coordinate system to unify the coordinate reference. Figure 3 and Figure 4 As shown, the lateral physical length of each segment is mapped to... A normalized coordinate system is constructed for each interval. Finally, the side-view top profile line is discretized into 1000 sampling points, and the two-dimensional coordinates of all sampling points are obtained in Rhino using a script, serving as the underlying sample database for subsequent calculations and reconstructions.
[0020] (2) Define the control variables for parametric modeling. The control variables include the spatial location of the control points in the normalized coordinate system, the number of control points, and the type of reconstructed model. The starting point x-coordinate of the front guide section and the rear main body section is fixed at 0 and the ending point x-coordinate is fixed at 1 in the normalized coordinate system; only the spatial position of the internal control point located between the starting point and the ending point is iteratively optimized, that is, the control point cannot be taken as the endpoint. The range of control points for the front guide section is limited to: The range of control points for the interval and the main body section is limited to a certain value. The range of values for the spatial location of control points in the normalized coordinate system is limited to the interval. The interval is used to avoid the control points being too concentrated or the boundaries being degraded; The reconstructed model types include one or more of the following: radial basis function interpolation model (RBF), cubic spline interpolation model (Spline), piecewise cubic Hermite interpolation model (Pchip), and modified Akima piecewise cubic Hermite interpolation model (Makima).
[0021] The RBF model expression is: , in, This represents the number of normalized control points currently deployed in the segment. For the first The center coordinates of each control point; For the first The weight coefficients corresponding to the kernel function of each control point; The location of the point to be reconstructed in the normalized coordinate system; The selected radial basis kernel function is chosen from one or more of the following: cubic kernel function, Gaussian kernel function, multiple quadratic kernel function, or inverse multiple quadratic kernel function.
[0022] The expression for the cubic kernel function is: , Where 𝑟 is the distance between the point to be reconstructed and the control point.
[0023] The Gaussian kernel function expression is: , Where 𝜎 is the scale parameter; It is a natural exponential function used to implement a weight distribution that decays exponentially with increasing distance.
[0024] The expression for the quadratic kernel function is: , in, The shape parameter is used to adjust the smoothness of the kernel function and the overall response amplitude.
[0025] The expression for the inverse quadratic kernel function is: , The expression for the Spline model is: , , in, In the control point interval cubic polynomial; coefficients , , , The determination is based on the constraints that the function values are continuous, the first derivative is continuous, and the second derivative is continuous at all control points. For the first The x-coordinates of the known control points.
[0026] The expression for the Makima model is: , in, For normalized variables, , For the side view top profile line at the control point The corresponding ordinate value; , , , For cubic Hermitian basis functions, , , , , Control points The derivative at the control point is calculated by weighting the slopes of the secant lines of four adjacent intervals to suppress oscillations in the interpolation results at points of data abrupt change; the four adjacent intervals refer to intervals centered on the control point. As the boundary, there are two sub-intervals that are sequentially adjacent along the parameter direction on the left and two sub-intervals that are sequentially adjacent along the parameter direction on the right.
[0027] The Pchip model expression is: , The model form is consistent with the Makima model, but the derivative... The determination that the conformal condition is met is as follows: if the data is at the control point If the value is a local extremum, then Otherwise, the derivative It is determined by the harmonic mean of the slopes of the secant lines of adjacent intervals to ensure the monotonicity of the interpolation curve within the monotonic interval.
[0028] (3) A two-layer optimization strategy is adopted to perform global iterative optimization of the control variables of the front guide section and the rear main body section to obtain the optimal control variables that make the comprehensive evaluation index optimal; the two-layer optimization strategy includes outer layer structure optimization and inner layer parameter optimization. Outer structure optimization refers to traversing the number of control points and reconstructing the model type within a preset discrete space to generate multiple candidate model structures, which are the initial models. Inner layer parameter optimization refers to using a piecewise optimization strategy to search for the optimal spatial distribution of control points in a continuous space for each candidate model structure, and calculating the corresponding overall sample reconstruction error, that is, the root mean square error (RMSE) of the parameterized reconstruction model of all samples and the original top-shaped curve collected in step (1). In the segmented optimization strategy, the first stage is to fix the control variables of the latter main body segment, use the minimization of the overall sample reconstruction error as the fitness function, and use a heuristic optimization algorithm to optimize the former guiding segment; the second stage is to fix the optimized former guiding segment control variables, use the minimization of the overall sample reconstruction error as the fitness function, and use a heuristic optimization algorithm to optimize the latter main body segment.
[0029] Heuristic optimization algorithms include Particle Swarm Optimization (PSO), Genetic Algorithm (GA), or Differential Evolutionary Algorithm (DE). The population size of the Particle Swarm Optimization (PSO) algorithm is set to 40, the maximum number of iterations is set to 60, and its velocity and position update formulas are as follows: , , in, Number the particles; Number the dimensions of the decision variables; This represents the number of iterations. express In the nth iteration The particle in the first Velocity components in the dimension; Inertial weights; express In the nth iteration The particle in the first Velocity components in the dimension; for In the nth iteration The particle in the first Position on the dimension; For the first The particle up to the [number]th The iteration is at the... The individual's historical best position on the dimension; For the first The particle up to the [number]th The iteration is at the... The globally optimal position in the dimension; , These are individual learning factors and group learning factors, respectively. , A random number uniformly distributed within the interval [0,1]. for In the nth iteration The particle in the first Position on the dimension.
[0030] The inner layer parameter optimization process applies fixed boundary constraints: for the front guide segment and the rear main segment, the x-coordinate of the starting endpoint in the normalized coordinate system is fixed at 0, and the x-coordinate of the ending endpoint is fixed at 1; the segmented optimization strategy only iteratively optimizes the spatial position of the internal control points located between the starting endpoint and the ending endpoint.
[0031] Model optimization decision: Construct a comprehensive evaluation index that includes the overall sample reconstruction error and the model complexity penalty term. From all candidate model structures that have undergone inner-layer optimization, select the control variable with the best comprehensive evaluation index as the optimal control variable to obtain the corresponding optimized model.
[0032] The expression for the comprehensive evaluation index is: , in, As a comprehensive evaluation indicator; The overall sample reconstruction error characterizes the model's fitting accuracy. This is the model complexity penalty coefficient, used to adjust the weights of accuracy and complexity, and is set to 0.01; This represents the number of normalized control points currently deployed in the segment. From all the parameterized reconstruction models that have undergone inner-layer optimization, the control variable with the best comprehensive evaluation index is selected as the optimal control variable; wherein, the smaller the comprehensive evaluation index, the better the comprehensive evaluation index, that is, the better the overall performance of the model in terms of fitting accuracy and complexity.
[0033] The comparison results of the control variables before and after optimization of the front guide segment are shown in Table 1.
[0034] Table 1
[0035] The comparison results of the control variables before and after optimization of the rear main body section are shown in Table 2.
[0036] Table 2
[0037] (4) Parametric feature extraction and modeling: Based on the optimal control variables, the optimal parametric reconstruction model is constructed, which is the general parametric reconstruction model used to generate the roofline of the car. In this general parametric reconstruction model, only the ordinate parameters of each control point need to be adjusted to achieve rapid fitting and reconstruction of the roofline of different car models.
[0038] (5) Parametric model verification: By reconstructing all top profile lines in the sample database, the overall reconstruction error and comprehensive evaluation index between the original profile lines and the reconstructed profile lines are compared to verify the reconstruction accuracy and stability of the established model under diverse vehicle conditions.
[0039] The comparison results of the overall sample reconstruction error and comprehensive evaluation index before and after the optimization of the control variables of the front guiding section are shown in Table 3.
[0040] Table 3
[0041] The comparison results of the overall sample reconstruction error and comprehensive evaluation index before and after the optimization of the control variables of the rear main body section are shown in Table 4.
[0042] Table 4
[0043] As shown in the table, compared with the initial model, the optimized parametric reconstruction model shows a significant reduction in the overall reconstruction error and comprehensive evaluation index of both the leading section and the main body section. Further, combined with... Figures 5 to 7 Qualitative analysis was performed on the comparison of geometric features and local residuals before and after optimization of typical samples (samples 1, 50, and 100). The optimized reconstruction curves more closely fit the real top-shaped line model in terms of morphology, especially showing excellent adaptability in the curvature change region. At the same time, the local fitting residual amplitudes at each sampling position were greatly converged, verifying that the method of the present invention significantly improves the reconstruction accuracy while ensuring the simplicity of the model.
Claims
1. A data-driven adaptive parametric modeling method for automobile roofline, characterized in that, Includes the following steps: (1) Obtain the side view top profile coordinate data of multiple real vehicles, divide the side view top profile into the front guide section and the rear main body section along the longitudinal direction of the vehicle; establish a normalized coordinate system for each segment, and then discretize the top profile curve in each segment into several sampling points according to the preset sampling density, obtain the two-dimensional coordinate data of each sampling point in the corresponding coordinate system, and form the bottom sample database. (2) Define the control variables for parametric modeling. The control variables include the spatial location of the control points in the normalized coordinate system, the number of control points, and the type of reconstructed model. (3) Based on the underlying sample database, a two-layer optimization strategy is adopted to perform global iterative optimization of the control variables of the front guidance section and the rear main body section to obtain the optimal control variables that make the comprehensive evaluation index optimal, and thus obtain the optimal parameterized reconstruction model. The two-layer optimization strategy includes outer-layer structure optimization and inner-layer parameter optimization. Outer-layer structure optimization refers to traversing the number of control points and the type of reconstructed model in a preset discrete space to generate multiple candidate model structures. Inner-layer parameter optimization refers to using a piecewise optimization strategy to search for the optimal spatial distribution of control points in a continuous space for each candidate model structure, obtaining the parameterized reconstructed model after inner-layer optimization, and calculating its corresponding overall sample reconstruction error.
2. The data-driven adaptive parametric modeling method for automotive roofline according to claim 1, characterized in that, In step (1), the side-view roofline is taken from the outer contour projection line of the longitudinal symmetry center plane of the vehicle body on the side view of the vehicle body. The data range of the side-view roofline is defined as a continuous geometric curve starting from the front edge of the car hood, extending through the front windshield, roof, and rear windshield to the rear end point of the vehicle. The front guide section and the rear main body section are divided by the starting feature point of the front windshield.
3. The data-driven adaptive parametric modeling method for automotive roofline according to claim 1, characterized in that, In step (1), the normalized coordinate system is constructed by mapping the horizontal physical length of each segment to the [0,1] interval.
4. The data-driven adaptive parametric modeling method for automotive roofline according to claim 1, characterized in that, In step (2), the number of control points in the front guide section is limited to the range of [2,5], and the number of control points in the rear main body section is limited to the range of [4,9].
5. The data-driven adaptive parametric modeling method for automotive roofline according to claim 1, characterized in that, In step (2), the starting point x-coordinate of the front guide segment and the rear main segment in the normalized coordinate system is fixed at 0, and the ending point x-coordinate is fixed at 1; the spatial position of the control point in the normalized coordinate system is limited to the interval [0.01, 0.99].
6. The data-driven adaptive parametric modeling method for automotive roofline according to claim 1, characterized in that, The reconstructed model type in step (2) includes one or more of the following: radial basis function interpolation model, cubic spline interpolation model, piecewise cubic Hermitian interpolation model, and modified Akima piecewise cubic Hermitian interpolation model.
7. The data-driven adaptive parametric modeling method for automotive roofline according to claim 1, characterized in that, In step (3), the overall sample reconstruction error refers to the root mean square error (RMSE) between the parameterized reconstruction model of all samples and the original top-shaped curve collected in step (1).
8. The data-driven adaptive parametric modeling method for automotive roofline according to claim 1, characterized in that, In step (3), the first stage of the segmented optimization strategy is to fix the control variables of the rear main body segment, use the minimization of the overall sample reconstruction error as the fitness function, and use a heuristic optimization algorithm to optimize the front guiding segment; the second stage of the segmented optimization strategy is to fix the control variables of the optimized front guiding segment, use the minimization of the overall sample reconstruction error as the fitness function, and use a heuristic optimization algorithm to optimize the rear main body segment.
9. The data-driven adaptive parametric modeling method for automobile roofline according to claim 8, characterized in that, The heuristic optimization algorithm in step (3) is Particle Swarm Optimization (PSO), Genetic Algorithm (GA), or Differential Evolution Algorithm (DE).
10. The data-driven adaptive parametric modeling method for automotive roofline according to claim 1, characterized in that, In step (3), a comprehensive evaluation index is constructed. From all the parameterized reconstruction models that have undergone inner-layer optimization, the control variable with the smallest comprehensive evaluation index is selected as the optimal control variable. The expression for the comprehensive evaluation index is: ， in, As a comprehensive evaluation indicator; The overall sample reconstruction error characterizes the model's fitting accuracy. This is the model complexity penalty coefficient, used to adjust the weights of accuracy and complexity; This represents the number of normalized control points currently deployed in the segment.