Fast calculation method of laser scattering intensity distribution of asphalt pavement based on scale decomposition

Abstract

The present invention discloses a method for fast calculation of laser scattered light intensity distribution of asphalt pavement based on scale decomposition, which includes the following steps: modeling the asphalt pavement using fractal structure; performing scale decomposition and unit segmentation using self-similarity; calculating the unit scattering field using Kirchhoff approximation method combined with finite element method; establishing a shielding function using geometric coordinate relationship, superimposing small-scale unit scattering field vectors to obtain the laser scattered light intensity distribution of the asphalt pavement; and using parallel calculation for small-scale unit scattering fields to improve calculation efficiency. The method introduces a scale decomposition method into the calculation of scattered light intensity of asphalt pavement, solves the problem of huge amount of calculation caused by the road surface roughness level being much larger than the laser wavelength, improves the calculation speed, and at the same time improves the calculation accuracy, and is suitable for the calculation of laser scattered light intensity distribution of asphalt pavement with large roughness.

Description

Technical Field

[0001] The invention belongs to the technical field of laser scattering, and in particular to a method for quickly calculating the intensity distribution of laser scattering of an asphalt pavement based on scale decomposition. Background Art

[0002] The research on the scattering characteristics of the road surface is gradually increasing. On the one hand, according to the design specifications of national highways, vehicles have strict requirements on the roughness of the road surface. The roughness of the road surface is related to the safety of the car when starting, braking, going uphill and downhill, and driving at high speed. The scattering characteristics of the road surface can reflect the roughness of the road surface and ensure driving safety. On the other hand, with the rise of assisted driving and autonomous driving technology, the application of various types of vehicle-mounted environmental perception sensors is becoming more and more popular. The scattering characteristics of the road surface directly affect their detection performance. Therefore, the research on the scattering characteristics of the road surface has received more and more attention. With the popularization of optical sensors such as cameras and lidar in vehicle-mounted applications, the research on optical bands, especially laser scattering characteristics, has received particular attention in recent years, but the research on the laser scattering characteristics of asphalt pavements is relatively lacking.

[0003] In previous studies, Gaussian distribution functions are often used to simulate rough surface profile features, and Kirchhoff approximation is used to describe the road surface scattering characteristics. Generally speaking, the roughness of actual asphalt pavement is mostly in the millimeter order, far exceeding the laser wavelength order, and the light wave scattering process is more complicated. It is difficult to accurately describe the laser scattering characteristics of the road surface using the original model. The problems of huge calculation amount and low calculation accuracy have not been effectively solved. Summary of the invention

[0004] The purpose of the present invention is to provide a method for quickly calculating the laser scattered light intensity distribution of asphalt pavement based on scale decomposition.

[0005] The technical solution to achieve the purpose of the present invention is: a method for quickly calculating the intensity distribution of laser scattered light on an asphalt pavement based on scale decomposition, comprising the following steps:

[0006] Step 1, modeling the asphalt pavement using fractal structure;

[0007] Step 2, using self-similarity to perform scale decomposition and unit segmentation;

[0008] Step 3, using Kirchhoff approximation method combined with finite element method to calculate the unit scattered field;

[0009] Step 4: Use the geometric coordinate relationship to establish a shielding function, and superimpose the small-scale unit scattering field vectors to obtain the laser scattering light intensity distribution of the asphalt pavement.

[0010] Preferably, the actual asphalt pavement is modeled using a one-dimensional WM fractal structure model function.

[0011] Preferably, the analytical expression of the one-dimensional WM fractal model function is:

[0012]

[0013] Where C is the amplitude control factor

[0014]

[0015] δ represents the root mean square height of the rough surface, b is the step frequency scale factor, D represents the fractal dimension, N represents the number of harmonics, which can be determined by the frequency of the incident wave, and K 0 b N-1 = k, where k = 2π / λ, λ is the incident wavelength, K 0 is the spatial fundamental wave number, Represents random phase.

[0016] Preferably, the specific method of step 2 for performing scale decomposition and unit segmentation by using self-similarity is:

[0017] The asphalt rough surface is divided into two cosine quantities of different scales and the result of superposition includes a large-scale surface and a small-scale surface. The large-scale surface is the surface contour scale of the actual asphalt pavement, and the small-scale surface is the rough surface that meets Kirchhoff's approximation conditions.

[0018] Preferably, step 3 of calculating the unit scattered field by using Kirchhoff approximation method combined with finite element method comprises the following steps:

[0019] Step 3.1, establish the corresponding small-scale unit scattering model and set the boundary conditions in combination with the finite element method;

[0020] The established small-scale unit scattering model includes an air layer and an asphalt layer. The intersection of the two is the asphalt road surface contour, and the outermost layer is an ideal boundary that can absorb all outgoing waves.

[0021] Assume that the incident light is emitted from infinity and is set as a plane wave. The light wave vector is divided into two components, S and P. The incident wave vector is:

[0022]

[0023] in, is the plane wave electric field unit vector, is the incident wave vector, are the source point and the field point respectively, is the unit vector of the incident wave p light direction, is the unit vector of the incident wave s light direction, A pi A si represents unit amplitude in both directions;

[0024] Step 3.2, mesh the small-scale unit scattering model in step 3.1, the mesh size is one eighth of the wavelength, and free triangle mesh is used for the air layer and the asphalt layer.

[0025] Step 3.3, derive the numerical integration formula of scattered light intensity under the one-dimensional WM fractal model in combination with the Stratton-Chu equation, and use the numerical integration formula of scattered light intensity to calculate the unit scattered field.

[0026] Preferably, the numerical integration formula of scattered light intensity under the one-dimensional WM fractal model is:

[0027]

[0028] Among them, r is the distance from the field point to the source point, x is the horizontal coordinate value, is the incident wave vector, f(x) is the height value at different horizontal positions of the fractal surface, f′(x) represents the slope of the surface element at the horizontal coordinate x in the one-dimensional WM model function, θ i and θ s Respectively represent the scattering angle and incident angle in the scattering system, A, B, C, D are vectors, specifically expressed as follows:

[0029]

[0030]

[0031]

[0032]

[0033] Among them, r s ,r p is the reflection coefficient, are the wave vectors of the incident wave and the scattered wave, is the local unit normal vector, is the reflected wave vector, is the unit vector of the incident wave p light direction, is the unit vector of the incident wave s light direction, A pi A si Represents unit amplitude in both directions.

[0034] Preferably, the masking function is established as:

[0035]

[0036] The sample point is any point on the rough curve, and the intersection point refers to the point where the incident wave vector intersects the rough curve in the direction of the wave vector.

[0037] Preferably, the laser scattered light intensity distribution of the asphalt pavement is:

[0038]

[0039] in represents the total scattered field of asphalt pavement, Represents the scattered field of each surface element, and M represents the total number of small-scale units divided.

[0040] Preferably, step 3 utilizes GPU technology and uses the Parallel Computing Toolbox of matlab to perform parallel computing via COMSOL LiveLink with matlab.

[0041] Compared with the prior art, the present invention has the following significant advantages:

[0042] The present invention establishes an asphalt pavement model based on fractal theory, performs scale decomposition based on the self-similarity of the fractal structure, calculates the scattering far-field vector value of the small-scale unit based on the Kirchhoff approximation combined with the finite element method, constructs a shielding function using geometric relationships and performs unit scattering field superposition to obtain a total scattering field, breaking through the barrier of calculating laser scattering characteristics of a strong rough road surface, making the calculation results more referenceable and more accurate. Due to the advantages of the model, the configuration requirements for the computer can be reduced, and the calculation efficiency is greatly improved. The method described in the present invention introduces a scale decomposition method in the calculation of the scattered light intensity of the asphalt pavement, solves the problems of huge calculation amount and low calculation accuracy in the calculation of laser scattering of the asphalt pavement, and realizes efficient and rapid calculation of the distribution of laser scattering light intensity of the asphalt pavement, which has great reference value for the research on the laser scattering echo characteristics of the surface with large surface undulations. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The present invention is a flow chart of a method for quickly calculating the laser scattered light intensity distribution of an asphalt pavement based on scale decomposition.

[0044] Figure 2 This is a one-dimensional asphalt pavement fractal structure model diagram of a method for quickly calculating the laser scattering light intensity distribution of an asphalt pavement based on scale decomposition of the present invention.

[0045] Figure 3 It is a schematic diagram of scale decomposition and unit segmentation of an asphalt pavement model according to a method for fast calculation of laser scattered light intensity distribution of an asphalt pavement based on scale decomposition of the present invention.

[0046] Figure 4 The schematic diagram of the geometric relationship of the shielding function of the method for fast calculation of laser scattered light intensity distribution of asphalt pavement based on scale decomposition of the present invention is shown.

[0047] Figure 5 Schematic diagram of rough curve generation for the one-dimensional WM fractal model function. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with the accompanying drawings.

[0049] like Figure 1 As shown, a method for quickly calculating the laser scattered light intensity distribution of asphalt pavement based on scale decomposition comprises the following steps:

[0050] Step 1: Obtain the statistical parameters of the roughness of the asphalt pavement model, such as Figure 2 As shown in the figure, the actual asphalt pavement is modeled using the one-dimensional WM fractal structure model function. The analytical formula of the one-dimensional WM fractal model function is:

[0051]

[0052] Where C is the amplitude control factor

[0053]

[0054] δ represents the root mean square height of the rough surface, b is the step frequency scale factor, D represents the fractal dimension, N represents the number of harmonics, which can be determined by the frequency of the incident wave, and K 0 b N-1 = k, where k = 2π / λ, λ is the incident wavelength, K 0 is the spatial fundamental wave number, represents a random phase, taking [-π,π].

[0055] Step 2: During the calculation process, it is assumed that the asphalt rough surface is composed of the superposition of multiple scale cosine quantities.

[0056]

[0057] In order to simplify the calculation, the scale in the present invention is that the entire asphalt rough surface is divided into two cosine quantities of different scales and the result of superposition. The large-scale surface is the surface contour scale of the actual asphalt pavement, which is macroscopic and determines the scattering direction of the scattering field; the small-scale surface is a rough surface that meets the Kirchhoff approximation condition, which is at the microscopic level and uses the Kirchhoff approximation to calculate the scattering field and determines the intensity of the entire scattering field. Figure 3 As shown in Figure 1, the entire asphalt pavement model can be viewed as countless small-scale surfaces combined along a large-scale contour.

[0058] Fractal structures have self-similarity, that is, the structural shape of an object does not change as the size of the surface scale is enlarged or reduced. This is an inherent property. The structural outline of a small-scale surface is the same as that of a large-scale surface, but the scale is different.

[0059] When calculating, if Figure 3 As shown in the figure, the asphalt pavement model to be solved is divided into multiple small units at equal intervals. If the intervals are small enough, the large-scale surface is close to a plane, and only the structural outline of the small-scale surface is retained. Only the small-scale surface contributes to the calculation. Therefore, this series of units is defined as small-scale units, and the scattering field of each unit is calculated. Then, the scattering field is superimposed on the large-scale surface according to the geometric relationship, and the small-scale units are numbered 1, 2, ..., M.

[0060] Step 3, using Kirchhoff approximation method combined with finite element method to calculate the unit scattered field, this step includes:

[0061] Step 3.1, combine the finite element method to establish the corresponding small-scale unit scattering model and set the boundary conditions.

[0062] Establish the corresponding scattering model as Figure 4 As shown in the figure, it includes the air layer and the asphalt layer. The intersection of the two is the asphalt road profile. The outermost layer is an ideal boundary that can absorb all outgoing waves to reduce calculation errors. The incident light is set to be emitted from infinity and can be set to a plane wave. The light wave vector can be divided into two components, S and P. The incident wave vector is

[0063]

[0064] in, is the plane wave electric field unit vector, is the incident wave vector, are the source point and the field point respectively, is the unit vector of the incident wave p light direction, is the unit vector of the incident wave s light direction, and A pi A si Represents unit amplitude in both directions.

[0065] Step 3.2, meshing is performed according to the scattering model in step 3.1. The small-scale units are further meshed by surface elements. The solution of the electromagnetic field generally requires at least 5 grids within a wavelength. To improve the calculation accuracy, the mesh size is one eighth of the wavelength. Free triangle meshes are used for the air layer and the asphalt layer.

[0066] Specific calculation process using PARDISO direct solver: Combined with the Stratton-Chu equation, the numerical integration formula of scattered light intensity under the one-dimensional WM fractal model is derived:

[0067]

[0068] Among them, r is the distance from the field point to the source point, x is the horizontal coordinate value, is the incident wave vector, f(x) is the height value at different horizontal positions of the fractal surface, f′(x) is the slope of the surface element at that point, θ i and θ s Respectively represent the scattering angle and incident angle in the scattering system, A, B, C, D are vectors, specifically expressed as follows:

[0069]

[0070]

[0071]

[0072]

[0073] Among them, r s ,r p is the reflection coefficient, are the wave vectors of the incident wave and the scattered wave, is the local unit normal vector, is the reflected wave vector. is the unit vector of the incident wave p light direction, is the unit vector of the incident wave s light direction, and A pi A si Represents unit amplitude in both directions.

[0074] Step 4: Construct the masking function S(θ i ), superimpose the small-scale unit scattering vector field, this step includes:

[0075] Step 4.1, when the light illuminates the entire asphalt surface, the large-scale surface plays a role in changing the scattering direction. If only single scattering is considered, the shielding function S(θ i ),like Figure 5 shown.

[0076]

[0077] Generate a rough curve based on the one-dimensional WM fractal model function generated in step 1, and select any point on the rough curve (such as Figure 5 The x1, x2, etc. in the figure are used as sample points to determine the shielding condition at this sample point. The intersection point refers to the point where the incident wave vector intersects the rough curve in the direction of the wave vector. When the incident wave vector has only one intersection point with the undulating surface, the sample point at the intersection must be in a non-shielded state; when the incident wave vector has only multiple intersection points with the undulating surface, only the sample point at the first intersection point is in a non-shielded state, and the sample points at the remaining intersection points are in a shielded state.

[0078] Step 4.2, superimpose the scattered field vectors of each unit.

[0079]

[0080] in represents the total scattered field of asphalt pavement, Represents the scattered field of each surface element, and M represents the total number of small-scale units divided.

[0081] The small-scale unit modeling and scattered field solution in step 3 use GPU technology and MATLAB's Parallel Computing Toolbox through COMSOL LiveLink with MATLAB to improve computational efficiency.

Claims

1. A fast calculation method for laser scattered light intensity distribution of asphalt pavement based on scale decomposition, characterized in that: The following steps are involved: Step 1, modeling the asphalt pavement using fractal structure; Step 2, using self-similarity to perform scale decomposition and unit segmentation; Step 3, using Kirchhoff approximation method combined with finite element method to calculate the unit scattered field, including the following steps: Step 3.1, establish the corresponding small-scale unit scattering model and set the boundary conditions in combination with the finite element method; The established small-scale unit scattering model includes an air layer and an asphalt layer. The intersection of the two is the asphalt road surface contour, and the outermost layer is an ideal boundary that can absorb all outgoing waves. Assume that the incident light is emitted from infinity and is set as a plane wave. The light wave vector is divided into two components, S and P. The incident wave vector is: in, is the plane wave electric field unit vector, is the incident wave vector, are the source point and the field point respectively, is the unit vector of the incident wave p light direction, is the unit vector of the incident wave s light direction, A pi A si represents unit amplitude in both directions; Step 3.2, mesh the small-scale unit scattering model in step 3.

1. The mesh size is one eighth of the wavelength. Free triangle mesh is used for the air layer and asphalt layer. Step 3.3, derive the numerical integration formula of scattered light intensity under the one-dimensional WM fractal model in combination with the Stratton-Chu equation, and use the numerical integration formula of scattered light intensity to calculate the unit scattered field; wherein, the numerical integration formula of scattered light intensity under the one-dimensional WM fractal model is specifically: Among them, r is the distance from the field point to the source point, x is the horizontal coordinate value, is the incident wave vector, f(x) is the height value at different horizontal positions of the fractal surface, f′(x) represents the slope of the surface element at the horizontal coordinate x in the one-dimensional WM model function, θ i and θ s Respectively represent the scattering angle and incident angle in the scattering system, A, B, C, D are vectors, specifically expressed as follows: Among them, r s ,r p is the reflection coefficient, are the wave vectors of the incident wave and the scattered wave, is the local unit normal vector, is the reflected wave vector, is the unit vector of the incident wave p light direction, is the unit vector of the incident wave s light direction, A pi A si represents unit amplitude in both directions; Step 4: Use the geometric coordinate relationship to establish a shielding function, and superimpose the small-scale unit scattering field vectors to obtain the laser scattering light intensity distribution of the asphalt pavement.

2. The method for rapid calculation of laser scattered light intensity distribution of asphalt pavement based on scale decomposition according to claim 1 is characterized in that: The actual asphalt pavement is modeled using one-dimensional WM fractal structure model function.

3. The method for rapid calculation of laser scattered light intensity distribution of asphalt pavement based on scale decomposition according to claim 1 or 2, characterized in that: The analytical expression of the one-dimensional WM fractal model function is: Where C is the amplitude control factor δ represents the root mean square height of the rough surface, b is the step frequency scale factor, D represents the fractal dimension, N represents the number of harmonics, N can be determined by the frequency of the incident wave, K0b N-1 =k, where k = 2π / λ, λ is the incident wavelength, K0 is the spatial fundamental wave number, Represents random phase.

4. The method for rapid calculation of laser scattered light intensity distribution of asphalt pavement based on scale decomposition according to claim 1 is characterized in that: Step 2 The specific method of using self-similarity to perform scale decomposition and unit segmentation is: The asphalt rough surface is divided into two cosine quantities of different scales and the result of superposition includes a large-scale surface and a small-scale surface. The large-scale surface is the surface contour scale of the actual asphalt pavement, and the small-scale surface is the rough surface that meets Kirchhoff's approximation conditions.

5. The method for rapid calculation of laser scattered light intensity distribution of asphalt pavement based on scale decomposition according to claim 1 is characterized in that: The masking function established is: The sample point is any point on the rough curve, and the intersection point refers to the point where the incident wave vector intersects the rough curve in the direction of the wave vector.

6. The method for rapid calculation of laser scattered light intensity distribution of asphalt pavement based on scale decomposition according to claim 5 is characterized in that: The laser scattered light intensity distribution of asphalt pavement is: in represents the total scattered field of asphalt pavement, Represents the scattered field of each surface element, and M represents the total number of small-scale units divided.

7. The method for rapid calculation of laser scattered light intensity distribution of asphalt pavement based on scale decomposition according to claim 1 is characterized in that: Step 3 uses GPU technology and MATLAB's Parallel Computing Toolbox to perform parallel computing through COMSOL LiveLink with MATLAB.

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