Asphalt pavement skid resistance index analysis method based on multivariate quadratic polynomial

Abstract

The invention discloses an asphalt pavement anti-slide performance index analysis method based on a multivariate quadratic polynomial. The method comprises the following steps: S1, extracting a pavement macroscopic texture average structure depth of a three-dimensional texture morphology rough characteristic; s2, extracting a contour single-peak average interval and a contour root-mean-square wavelength of the three-dimensional texture morphology rough characteristic; s3, extracting shape indexes of three-dimensional texture morphology roughness characteristics, wherein the shape indexes include contour skewness, hump degree, apparent anisotropy and three-dimensional morphology fractal dimension; s4, establishing a multivariate quadratic polynomial to solve a BPN regression model; and S5, establishing a multivariate quadratic polynomial to solve an SFC regression model. According to the method, the relationship between the texture roughness characteristic index and the pavement skid resistance is discussed from two perspectives of theoretical analysis and empirical regression by adopting a tribology theory and a multiple regression analysis method. A system for evaluating the skid resistance of the pavement based on the texture roughness characteristic is further established, and a new method and thought are provided for evaluating the skid resistance of the asphalt pavement.

Description

Technical Field

[0001] The invention relates to the field of anti-skid performance indexes of asphalt pavements, and in particular to an analysis method for anti-skid performance indexes of asphalt pavements based on multivariate quadratic polynomials. Background Art

[0002] Frequent traffic accidents have prompted people to investigate and analyze the anti-skid performance of pavement and traffic accidents, and to explore and understand the formation mechanism of pavement anti-skid force and its influencing factors. Only by fully understanding the formation mechanism of pavement anti-skid force can we further explore feasible measures to reduce traffic accident rates and protect the lives and property of traffic participants. The pavement friction system is different from the traditional mechanical friction system. The friction system involves multiple aspects such as the pavement itself, the vehicle itself, the traffic user group, the traffic management group, and the climate environment. The situation is changeable and the influencing factors are complex. However, when studying the anti-skid performance of the pavement under the background that the tire body factors are fixed, the rough characteristics of its texture morphology should be considered.

[0003] Therefore, the relationship between texture roughness characteristics and pavement anti-skid performance was discussed from the perspectives of theoretical analysis and empirical regression using tribology theory and multiple regression analysis. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes an analysis method for the anti-skid performance index of asphalt pavement based on multivariate quadratic polynomials.

[0005] A method for analyzing the anti-skid performance index of an asphalt pavement based on a multivariate quadratic polynomial comprises the following steps:

[0006] S1: Average structural depth of pavement macro texture for extracting roughness characteristics of three-dimensional texture morphology;

[0007] S2: Extract the average spacing of single peaks and the root mean square wavelength of the three-dimensional texture roughness characteristics;

[0008] S3: Extract shape indicators of roughness characteristics of three-dimensional texture morphology: contour skewness, hump, apparent anisotropy, and three-dimensional morphology fractal dimension;

[0009] S4: Introduce the independent variable of mineral material type, eliminate the independent variables with poor significance through the regression model effect, and establish a multivariate quadratic polynomial to solve the BPN regression model;

[0010] S5: Establish a multivariate quadratic polynomial to solve the SFC regression model through the steps of the BPN regression model.

[0011] Furthermore, a method for analyzing the anti-skid performance index of an asphalt pavement based on a multivariate quadratic polynomial, the step S1 comprises the following sub-steps:

[0012] S11: Delaunay triangulation method is used to reconstruct the road surface texture in three dimensions, and wavelet decomposition is used to eliminate the cross-section point cloud. The reconstructed cross-section points are on the same horizontal plane;

[0013] S12: simulate the MTD volume filling method for the 3D surface, reconstruct the distance between the texture and the ideal road surface, and set the ideal plane to cover 95% of the texture point cloud;

[0014] S13: Using the triangular mesh model volume calculation method, the ratio of the structural depth volume of the area to be measured to the area of ​​the area to be measured is calculated as the MTD index.

[0015] Furthermore, a method for analyzing the anti-skid performance index of an asphalt pavement based on a multivariate quadratic polynomial is characterized in that step S13 includes the following sub-steps:

[0016] S131: Let plane XOY be the projection plane, let any triangle in the triangular mesh model be t, let the convex pentahedron enclosed by the projection plane be the projection volume Pt ​​of the triangle, and let the volume of the convex pentahedron be the projection volume Vt of the triangle;

[0017] S132: A convex pentahedron is divided into a triangular prism and two tetrahedrons. For any tetrahedron, the volume calculation formula is:

[0018]

[0019] Wherein, V((x1, y1, z1), (x2, y2, z2), (x3, y3, z3), (x4, y4, z4)) represents the volume of any tetrahedron, and the three-dimensional coordinates of the four vertices of any tetrahedron represent (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y4, z4) respectively;

[0020] S133: Let the triangle face set of the triangular mesh model be A, the projection triangle of each triangle face on the projection plane be tp, the convex polyhedron formed by the triangle face t and the projection plane be Pt, and determine all other triangle facets intersecting with it as the intersection triangle face set At;

[0021] S134: Obtain the projection volume Vt of the triangular facet, and determine whether to add or subtract in the triangular network model:

[0022] If the sign of the projection volume Vt of the triangle is positive, the projection volume Vt of the triangle is added when calculating the volume of the triangular mesh model;

[0023] If the projected volume Vt of the triangle is negative, the projected volume Vt of the triangle is subtracted when calculating the volume of the triangular mesh model;

[0024] S135: The volume of the convex polyhedron enclosed by all triangular facets and the projection plane is added to obtain the volume of the triangular mesh model. The texture elevation value is flipped symmetrically according to the projection plane. The elevation formula for calculating the road surface macro texture is:

[0025]

[0026] Among them, z(x, y) represents the macro texture elevation function, x and y represent the coordinate values, and T represents the elevation value corresponding to the texture point cloud that the ideal plane needs to cover 95%;

[0027] S136: According to the volume filling principle of the sand spreading method, the average structural depth index MTDst of the road surface macro texture is calculated by the structural depth filling volume of the area to be tested and the area of ​​the area to be tested. The formula is:

[0028]

[0029] Among them, MTD st represents the average structural depth index of the pavement macro texture, n represents the number of cross sections, N represents the number of cross section elements, a represents the longitudinal accuracy, b represents the lateral accuracy, i represents the sampling point variable, t represents the total number of sampling points, and Vt represents the projected volume of the triangular patch.

[0030] Furthermore, a method for analyzing the anti-skid performance index of an asphalt pavement based on a multivariate quadratic polynomial is characterized in that step S2 includes the following sub-steps:

[0031] S21: Get the projection length of the distance between the highest points of two adjacent single peaks on the midline and calculate the average value. The formula is:

[0032]

[0033] Among them, S represents the average single-peak spacing of the profile, S0 represents the distance between the Oth adjacent single-peak peak points, p represents the total number of adjacent single-peak peak points, and O represents the adjacent single-peak peak point variable;

[0034] S22: Get the profile RMS deviation and profile RMS slope, and calculate the profile RMS wavelength. The formula is:

[0035]

[0036] Among them, Δ q represents the RMS slope of the profile, m represents the length in the x direction, n1 represents the length in the y direction, and R q represents the profile root mean square deviation, λ q Represents the profile rms wavelength.

[0037] Furthermore, a method for analyzing the anti-skid performance index of an asphalt pavement based on a multivariate quadratic polynomial is characterized in that S3 comprises the following sub-steps:

[0038] S31: Get the average value of the cube of the contour offset within the sampling range. The formula is:

[0039]

[0040] Among them, S k represents the profile skewness, R q represents the root mean square deviation of the profile, represents the macro texture elevation function, i1 = 1, 2...n1, j = 1, 2...m;

[0041] S32: Get the sharpness of the change in the profile surface distribution. The formula is:

[0042]

[0043] Among them, K u represents the hump, u4 and u2 represent the fourth-order and second-order central moments of the surface morphology, respectively;

[0044] S33: Obtain the difference in shape in different directions. The formula is:

[0045]

[0046] Among them, Ka represents the apparent anisotropy, P x (x,y) and P y (x, y) represents the roughness characteristic parameters of the two-dimensional topography along the x and y directions, respectively;

[0047] S34: Obtain a comprehensive characterization index of surface roughness characteristics, the formula is:

[0048] N L ∝L -D ;

[0049]

[0050] Among them, N L Represents the value corresponding to the number of different scales L, L -D represents the negative dimension of scale L, DD represents the three-dimensional fractal dimension, n2 represents the midpoint of scale L,

[0051] Furthermore, a method for analyzing the anti-skid performance index of an asphalt pavement based on a multivariate quadratic polynomial is characterized in that S4 comprises the following sub-steps:

[0052] S41: Establish the initial BPN synthesis matrix, the formula is:

[0053] M1=[MTD1,S k ,S k 1,λ q ,K a 1,K u 1,DD,S,S1];

[0054] Among them, M1 represents the initial BPN synthesis matrix, MTD1 represents the average structural depth index of the microscopic road surface macro texture, and S k 1 represents the microscopic profile skewness, K a 1 represents the apparent anisotropy at the microscopic level, K u 1 represents the microscopic hump degree, S1 represents the average spacing of the single peaks of the microscopic profile;

[0055] S42: Introduce virtual independent variables X and Y to characterize the material of the mixture:

[0056] When X=1, it indicates that the material of the mixture is limestone;

[0057] When X=0, it indicates that the material of the mixture is other materials;

[0058] When X=0, Y=0, it indicates that the material of the mixture is basalt;

[0059] S43: Delete the less significant independent variables one by one, and finally retain X, MTD1, Sk1 and λ according to the goodness of fit and factor test probability. q The four independent variables together form the BPN synthesis matrix, the formula is:

[0060] M1=[X,MTD1,S k 1, λ q ];

[0061] Among them, M1 represents the BPN synthesis matrix, MTD1 represents the average structural depth of the microscopic road surface macro texture, and λ q represents the RMS wavelength of the profile, S k 1 represents the microscopic texture profile skewness, and X represents a dummy independent variable;

[0062] S44: Construct a multivariate quadratic polynomial to solve the BPN regression model. The formula is:

[0063]

[0064] B1=[-93.578275.868-34.2397.037]

[0065] C1=42.444;

[0066] Among them, BPN represents the BPN regression model, M1 represents the BPN synthesis matrix, M2 represents the synthesis matrix, A1, B1, and C1 represent the quadratic term coefficient matrix, linear term coefficient matrix, and constant term of the BPN binary multivariate polynomial, respectively.

[0067] Furthermore, a method for analyzing the anti-skid performance index of an asphalt pavement based on a multivariate quadratic polynomial, said S5 comprises the following sub-steps:

[0068] S51: Introduce virtual independent variables X and Y, exclude independent variables with poor significance through the regression model effect, and establish a synthetic matrix. The formula is:

[0069] M2=[MTDλ q S k 1 XY];

[0070] Where M2 represents the synthesis matrix, MTD represents the average construction depth of the pavement macro texture, and λ q represents the RMS wavelength of the profile, S k 1 represents the microscopic texture profile skewness, and X and Y represent dummy independent variables;

[0071] S52: Establish a multivariate quadratic polynomial to solve the SFC regression model. The formula is:

[0072]

[0073] B2=[0.265-0.104-0.668-0.586-0.200];

[0074] C2=0.857;

[0075] Among them, DF 60 represents the SFC regression model, M2 represents the synthetic matrix, A, B, and C represent the quadratic term coefficient matrix, linear term coefficient matrix, and constant term of the SFC bivariate multivariate polynomial, respectively.

[0076] The beneficial effects of the present invention are: a method for analyzing the anti-skid performance index of asphalt pavement based on multivariate quadratic polynomials, which extracts a total of 6 indicators of surface three-dimensional texture morphology roughness characteristics from three aspects of height correlation evaluation, wavelength correlation evaluation and shape correlation evaluation, and further establishes an evaluation system for the anti-skid performance of pavement based on texture roughness characteristics, providing a new method and idea for the evaluation of the anti-skid performance of asphalt pavement. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 It is a schematic diagram of pavement texture depth calculation.

[0078] Figure 2 It is a schematic diagram of tetrahedral coordinates.

[0079] Figure 3 It is a flowchart for identifying adjacent triangles.

[0080] Figure 4 is a schematic diagram of the unimodal average spacing S of the contour.

[0081] Figure 5 It is the BPN significance relationship diagram.

[0082] Figure 6 It is the SFC significance relationship diagram. DETAILED DESCRIPTION

[0083] The present invention is further described below, but the protection scope of the present invention is not limited to the following description.

[0084] The height-related index is an evaluation parameter related to the height direction of the road surface, which is used to evaluate the height characteristics of the surface. It directly affects the hysteresis energy loss of tire elastic deformation, the drainage capacity of road surface water, etc., thus affecting the anti-skid performance of the road surface.

[0085] (1) Surface roughness characteristics height-related indicators

[0086] Average structural depth index of pavement macro texture

[0087] Mean texture depth (MTD) refers to the arithmetic mean of the sum of the distances from each contour point to the contour peak line within the sampling range. Its traditional measurement uses the sand-laying method. The specific calculation is shown in formula (1-1). The calculation of discrete surface morphology is shown in formula (1-2).

[0088] Among them, the line of profile peaks refers to the line parallel to the reference line and passing through the highest point of the profile. At the same time, this indicator can also be expressed by volume parameters. Taking the sand spreading method as an example, a certain volume V of sand is placed on the road surface measurement position, and then the sand is carefully spread evenly into a circle with an area of ​​S. The average construction depth MTP can be expressed by the volume method as formula (1-3).

[0089] The calculation principles of the two methods (1-1) and (1-3) are exactly the same. The contour peak line is actually the upper surface of the sand after expansion in the sand paving method. The space between the peak line and the contour line is filled with sand. Due to the influence of the sand particle size, the sand cannot enter the micro-structural morphology area. Therefore, the scale corresponding to the test results of this method is the macro-texture morphology scale, which cannot reflect the micro-texture morphology characteristics of the road surface.

[0090]

[0091] In the formula, zp (x, y) represents the maximum value corresponding to the peak line of the spatial morphology.

[0092] Traditional detection methods are greatly affected by human factors and have large errors. Therefore, 3D laser is introduced to conduct comprehensive detection of the road surface structure depth to obtain the anti-skid performance of the road surface. The 3D laser continuously scans the surrounding environment and records the distance information from the sensor to each point on the road surface. It processes and analyzes these distance data to generate 3D point cloud data of the road surface, and then calculates the road surface structure depth based on the point cloud data.

[0093] The Delaunay triangulation method is used to complete the three-dimensional reconstruction of the road surface texture. After wavelet decomposition and reconstruction, the cross-sectional point cloud has eliminated the posture and is on the same horizontal plane. Based on this three-dimensional surface without posture and macro deformation, the MTD volume filling method is simulated to calculate the distance between the reconstructed texture and the ideal road surface. Considering that some excessively high textures will not be included in the actual sand paving method, such as Figure 1 As shown in the figure, the ideal plane only needs to cover 95% of the texture point cloud. On this basis, a MTD calculation model based on the road surface texture three-dimensional point cloud is proposed. The calculation method of the volume of any triangular mesh model is used. The ratio of the depth volume of the area to be tested to the area of ​​the area to be tested is the required MTD index.

[0094] For the convenience of calculation, plane XOY is used as the projection plane, and the convex pentahedron formed by any triangle patch t and the projection plane in the triangular mesh model is called the projection volume Pt ​​of the triangle patch, and the volume of the convex pentahedron is called the projection volume Vt of the triangle patch. The projection volume of the triangle patch is a convex pentahedron, which can be divided into a triangular prism and two tetrahedrons, and the sum of their volumes is the volume of the convex pentahedron.

[0095] If the space area of ​​all triangular facets enclosed by the triangular mesh is closed, the volume of the triangular network model can be calculated by the sum of the projected volumes of each triangular facet. For any tetrahedron, such as Figure 2 As shown, if the three-dimensional coordinates of the four vertices are (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y4, z4), the volume can be calculated according to formula 1-4.

[0096]

[0097] In the calculation of the triangle patch projection volume, if the volume sign is positive, the projection volume of the triangle patch is added when calculating the volume of the triangular mesh model; otherwise, the projection volume of the triangle patch is subtracted.

[0098] For any triangle facet, in order to obtain the signed volume of the polyhedron projected by the triangle facet, it is necessary to determine all other triangle facets that intersect with it, that is, the set of intersecting triangle facets At. In the triangle mesh model, let the triangle face set of the triangle mesh model be A, and the projection triangle of each triangle facet t(tòA) on the projection plane is tp, and the convex polyhedron enclosed by t and the projection plane is Pt.

[0099] like Figure 3 As shown, in the process of determining the intersection of the projected triangles of two triangular facets, if the above method cannot be used to determine the intersection, it is determined that the adjacent triangular facets are partially or completely located in the convex polyhedron enclosed by the triangular facets and the projection plane.

[0100] The volume of the triangular mesh model is the algebraic sum of the volumes of the convex polyhedron enclosed by all triangular faces and the projection plane. After the texture elevation value is flipped symmetrically according to the projection plane, the elevation expression actually used to calculate the macro texture of the road surface is shown in Formula 2-5.

[0101]

[0102] According to the principle of volume filling by the sand spreading method, after obtaining the structural depth filling volume of the area to be tested, its ratio to the area of ​​the area to be tested is the required average structural depth index. For any asphalt pavement area to be tested, the average structural depth index MTDst of its pavement macro texture can be calculated.

[0103]

[0104] Among them, n is the number of cross sections, N is the number of cross section elements, a is the longitudinal accuracy, and b is the lateral accuracy.

[0105] (2) Surface roughness characteristic wavelength-related indicators

[0106] In addition to the height direction, the spacing and distribution of the pavement texture structure in the horizontal direction are also key factors affecting the anti-skid performance. The traditional pavement morphology characteristic parameters are mainly based on height-related indicators, and rarely involve the lateral direction. Fwa et al. deliberately set the road surface aggregates into different gaps through indoor experiments to construct different wavelength characteristics. The results show that the wavelength characteristics of the road surface aggregates in the horizontal direction have a significant effect on their friction. Unfortunately, in this document, the author only set different gaps between minerals through experiments and gave a qualitative description that the wavelength characteristics will affect the anti-skid performance of the pavement. There is no calculation method for wavelength-related indicators for different texture morphologies. In order to quantitatively describe the roughness characteristics of the pavement texture morphology in the wavelength direction, the study will further carry out the study of indicators related to the wavelength in the horizontal direction of the three-dimensional pavement morphology.

[0107] 1) The average unimodal spacing S of the contour

[0108] In three-dimensional texture morphology, the average single peak spacing S of the contour is defined as the average value of the single peak spacing of the contour within the sampling length (the projection length of the distance between the highest points of two adjacent single peaks on the midline), formula (2-7), as shown in Figure 4 As shown, for three-dimensional space, the corresponding length average value needs to be replaced by the area average value. The statistical significance of the average spacing S of the single peaks of the profile is clear, and it is also the main evaluation parameter of the lateral information of the profile surface. The difference from the average spacing Sm of the micro-roughness is that the average spacing S of the single peaks of the profile indicates the peak density of the profile, which is of great significance for evaluating the stability and wear resistance of the profile.

[0109]

[0110] 2) Profile root mean square wavelength λ q

[0111] Profile RMS wavelength λ q is the profile root mean square deviation Rq and the profile root mean square slope Δ q 2π times the ratio, see formulas (1-8) and (1-9), the profile root mean square wavelength λ q It has good stability and is a measure of the average spacing between peaks or valleys of the topographic profile within the sampling range. It is related to the amplitude of the peaks or valleys of the profile surface and their respective spatial frequencies.

[0112]

[0113] (3) Surface roughness characteristics and shape related indicators

[0114] The first two evaluation parameters take into account the roughness characteristics of the morphology from their respective levels, and can only locally reflect certain aspects of the contour characteristics. Texture morphologies with the same height and wavelength characteristics may also have different anti-slip properties due to the different shapes of peaks or valleys on their morphological surfaces. Therefore, on the basis of the first two evaluation parameters, shape-related indicators are further introduced. Most of them are derived by further analyzing the surface structure geometry using theories and methods based on probability statistics.

[0115] 1) Profile skewness Sk

[0116] The profile skewness Sk refers to the average value of the cube of the profile offset within the sampling range, i.e., Equation (1-10). This index uses the profile reference line as a reference to measure the degree of asymmetry of the amplitude distribution of the topography profile deviating from the reference line, and is affected by discrete peaks or valleys. When Sk = 0, it indicates that the profile line is symmetrically distributed with respect to the reference line; when Sk < 0, it means that the profile valleys are sharp and narrow while the profile peaks are smooth and wide; when Sk > 0, it indicates that the profile valleys are wide and flat while the profile peaks are sharp and narrow. This index can well distinguish the shape of the surface topography profile and can reflect the support ability and stability of the profile.

[0117]

[0118] 2) Kurtosis Ku

[0119] The kurtosis Ku is similar to the profile skewness Sk and represents the sharpness of the change in the profile surface distribution. It is the ratio of the fourth central moment to the square of the second central moment of the profile surface amplitude, as shown in Equation (1-11). The kurtosis Ku is based on the surface shape of the normal distribution. When the offsets of the topography profile satisfy the condition of an ideal random normal distribution, Ku = 3; when the Ku value is greater than 3, it indicates that the amplitude distribution of the profile surface is steep, called a leptokurtic surface; when the Ku value is less than 3, the profile surface is called a platykurtic surface, and at this time the profile surface distribution is relatively flat.

[0120]

[0121] In the formula, u4 and u2 are the fourth and second central moments of the surface topography respectively.

[0122] 3) Apparent anisotropy degree Ka

[0123] To describe the degree of difference in the shape of the topography in different directions, the apparent anisotropy degree index is given. The apparent anisotropy degree Ka reflects the degree of difference in the geometric roughness characteristics of the surface topography in different directions. The calculation of Ka includes two parameters, P x (x,y) and P y (x,y). They respectively represent the roughness characteristic parameters of the two-dimensional topography in the x and y directions, and their ratio is used to reflect the anisotropy degree of the topography. The roughness characteristic parameters of the two-dimensional topography here specifically refer to the root mean square slope Δ q of the profile. The calculation formula of Ka is shown in (1-12).

[0124]

[0125] When Ka = 1, it indicates that the surface is isotropic; when 0 < Ka < 1, it shows that the surface is anisotropic, and as the value of Ka decreases, the degree of anisotropy becomes more obvious.

[0126] 4) Three-dimensional topography fractal dimension DD

[0127] In order to better characterize the roughness characteristics of pavement morphology profile information, a standard index for comprehensive evaluation of surface roughness characteristics is further introduced. The fractal box dimension of the three-dimensional texture morphology of asphalt pavement is used as a comprehensive characterization index for evaluating its surface roughness characteristics to describe its influence on the anti-skid performance of the pavement. The fractal dimension of the three-dimensional texture morphology is denoted as DD, and its calculation is shown in Formula 1-14.

[0128] N L ∝L -D (1-13)

[0129]

[0130] When calculating the box fractal dimension, choosing a variety of different measurement scales L will produce multiple corresponding values. In a two-dimensional coordinate system, with 1 / logL as the horizontal coordinate and logNL as the vertical coordinate, we can get the discrete points of logNL-1 / logL in the two-dimensional coordinate system, fit the discrete points into a straight line, and use the least squares method to solve the slope of the line, which is the fractal dimension DD.

[0131] (2) Establishment of anti-slip model based on two-dimensional texture information characteristics

[0132] The texture roughness characteristics mainly include the texture information roughness characteristics based on two-dimensional images and the texture morphology roughness characteristics based on the three-dimensional surface morphology structure. Through the correlation analysis between the texture indices, it can be seen that the two-dimensional texture information index cannot truly reflect the distribution of the morphology structure in the three-dimensional space, which makes the correlation between the two-dimensional texture information index and the anti-skid performance index poor. Since the two-dimensional texture information index is easy to obtain, the solution constraints are low, and it has strong anti-interference ability to changes in the operating environment. First, starting from the two-dimensional texture information index, using SAS software programming, try to use a multivariate regression model to establish a relationship model between it and the anti-skid performance of the road surface. The results of the model establishment are shown in Tables 1-1 and

[0133] Table 1-2.

[0134] Table 1-1 Multiple linear regression model analysis results

[0135] Model Dependent Variable Independent Variable <![CDATA[Adjust R 2 > 1 BPN R. ASM 0.028 2 SFC R. ASM 0.023

[0136] Table 1-2 Analysis results of quadratic polynomial regression model

[0137] Model Dependent Variable Independent Variable <![CDATA[Adjust R 2 > 1 BPN R. ASM 0.109 2 SFC R. ASM 0.143

[0138] Tables 1-3 and 2-4 respectively give the goodness of fit test results of the multivariate linear and quadratic polynomial regression models between the two-dimensional texture information roughness characteristic index and the pavement anti-skid performance index. The value range of the determination coefficient R2 is 0 to 1. The closer its value is to 1, the higher the goodness of fit of the regression equation to the data point. From the analysis results of Tables 1-3 and 2-4, it can be seen that whether it is a multivariate linear regression model or a multivariate quadratic polynomial regression model, it is difficult to obtain a good fitting effect when used to fit the relationship model between the two-dimensional texture information index and the pavement anti-skid performance index. This phenomenon once again shows that the two-dimensional texture information index reflects the projection of the morphology on the horizontal plane, not the distribution of the actual texture morphology in three-dimensional space. It is difficult to complete the establishment of the pavement anti-skid model if the two-dimensional texture information roughness characteristic index is simply used alone.

[0139] (3) Establishment of anti-slip model based on three-dimensional texture morphology characteristics

[0140] Depend on Figures 5-6 It can be seen that the indicators that have a significant linear relationship with BPN are MTD, MTD1, S1, λ q 1; The indicators that have significant linear relationships with the SFC index include MTD, S1, and λ q 1. The significance level of the partial coefficients of these indicators is less than 0.05. It can be considered that there is a significant linear relationship between these independent variables and their respective dependent variables. The variance inflation factor VIF is used to identify the multicollinearity problem between the independent variables. The larger the VIF value, the more serious the multicollinearity between the independent variables. Usually, when the VIF value is greater than or equal to 10, it means that there is a serious multicollinearity problem between the independent variables in the model. It can be seen from the VIF values ​​in Tables 1-6 and 1-7 that the VIF of the two indicators MTD and MTD1 is too large, and there are still serious multicollinearity problems between the various texture morphology indicators. The existence of multicollinearity will bring many influences to the establishment of the model, such as the difficulty in estimating the partial regression coefficient, the increase in the estimated variance of the partial regression coefficient with the increase in the correlation of the independent variables, and the insignificant results of the partial regression coefficient hypothesis test. In order to further achieve the purpose of dimensionality reduction and eliminate multicollinearity, the correlation analysis between the indicators is used to determine the selection of each indicator. The results of the correlation analysis are shown in Table 1-3.

[0141] Table 1-3 Correlation analysis of coefficients between texture morphology indicators

[0142] <![CDATA[λ q 1]]> MTD1 Sk Sk1 <![CDATA[λ q ]]> Ka1 Ku1 DD S S1 MTD λq1 1.00 0.13 0.18 -0.18 0.04 -0.18 -0.25 -0.11 0.40 0.63 -0.03 MTD1 0.13 1.00 0.00 -0.22 0.36 0.09 -0.38 0.04 -0.03 -0.48 0.84 <![CDATA[S k ]]> 0.18 0.00 1.00 -0.05 0.14 -0.15 0.05 -0.03 -0.01 -0.16 -0.03 <![CDATA[S k 1]]> -0.18 -0.22 -0.05 1.00 -0.10 -0.03 -0.17 -0.02 -0.03 0.27 0.08 λq 0.04 0.36 0.14 1.04 1.00 0.03 -0.05 0.51 0.17 -0.21 -0.30 <![CDATA[K a 1]]> -0.18 0.09 -0.15 -0.03 0.03 1.00 0.04 0.02 0.29 0.17 -0.07 <![CDATA[K u 1]]> -0.25 -0.38 0.05 -0.22 -0.05 0.04 1.00 0.21 -0.34 0.26 0.33 DD -0.11 0.04 -0.03 -0.02 0.51 0.02 0.21 1.00 -0.14 -0.17 0.05 S 0.40 -0.03 -0.01 -0.03 -0.17 0.29 -0.34 -0.14 1.00 0.10 -0.21 S1 0.63 -0.48 -0.16 0.27 -0.21 0.17 0.26 -0.17 0.10 1.00 0.14 MTD -0.03 0.84 -0.03 0.08 -0.30 -0.07 0.33 0.05 -0.21 0.14 1.00

[0143] The analysis results in Table 1-8 show that the correlation coefficient between MTD1 and MTD is as high as 0.837, λ q The correlation coefficient between MTD1 and S1 is also 0.631, and the overall |r|>0.5 is satisfied, indicating that MTD1 and MTD, λq There is multicollinearity between the 1 and S1 indicators. Therefore, before further model regression analysis, the indicators should be selected and deleted to minimize the adverse effects of multicollinearity between indicators. The significance analysis results in Tables 1-6 and 1-7 show that the correlation between the MTD1 indicator and BPN is more significant, and the correlation between the MTD indicator and SFC is more significant. q 1. Whether it is the same BPN or SFC, the correlation of S1 index is more significant. Therefore, for the establishment of BPN index model, it is necessary to consider excluding MTD and λ. q 1 Two indicators, MTD1 and S1 are retained; for the establishment of the SFC indicator model, MTD1 and λ should be considered to be eliminated q 1. Keep MTD and S1.

[0144] 2) Multivariate quadratic polynomial regression model analysis

[0145] In order to facilitate analysis, different three-dimensional texture morphology indicators are first integrated into a synthetic vector. For example, for the BPN indicator, MTD1, S1, Sk, Sk1, λ q The indexes are synthesized and recorded as SFC index. The multivariate quadratic polynomial regression model can be expressed as formula (1-20).

[0146] F=MAM T +BM T +C (1-20)

[0147] In the formula, F is the anti-slip performance index, specifically BPN or SFC; M is the synthetic vector of the evaluation index, M1 or M2, etc.; A, B, and C are the quadratic coefficient matrix, linear coefficient matrix, and constant term of the model, respectively, where matrix A is a symmetric square matrix. The following will use the statistical analysis software SAS to perform quadratic polynomial regression analysis on the two indicators BPN and SFC.

[0148] 1. Establishment of BPN regression model by solving multivariate quadratic polynomial

[0149] First, as many three-dimensional texture morphology indicators as possible are included in the synthesis matrix M. For the BPN indicator, the initial synthesis matrix M1 = [MTD1, S k ,S k 1,λ q ,K a 1,K u 1, DD, S, S1], a total of 9 indicators. The model summary results and factor test results are shown in Tables 1-4 and 1-5.

[0150] Table 1-4 Summary results of 9-index multivariate binomial solution BPN model

[0151]

[0152] Table 1-5 Results of the BPN factor test using the 9-index multivariate binomial solution

[0153]

[0154] Generally, the more independent variables there are, the better the model fit is. The results in Table 1-9 show that although the selection of three-dimensional texture morphology indicators has been considered as much as possible. However, the determination coefficient (R2) is only 0.6530, and the average residual sum of squares is as high as 59.9731, indicating that the model fit is still in need of further improvement. The factor test is a joint test of all parameters containing each factor. Further observation of the factor analysis results in Table 1-10 shows that, except for the MTD1 indicator, the probability P of the F test of other independent variable factors is greater than the significance level of 0.05, indicating that the significance level of the model parameters is poor.

[0155] The establishment of the regression model did not achieve satisfactory results. The reason may be that in addition to the key factor of texture morphology, there are other key factors, such as mineral material types, that affect the anti-skid performance index. In the process of testing the anti-skid performance of the pavement, the outside world needs to do work on the pavement, and this work will be lost due to friction during the test. The anti-skid performance can be evaluated based on the size of the loss. Even for surfaces with exactly the same three-dimensional texture morphology, the work lost due to friction will be different in the process of doing work due to the different hardness and wear resistance of the material. Therefore, it is not possible to achieve satisfactory results to establish an anti-skid performance model by relying solely on the three-dimensional texture morphology index without combining the material composition of the specific object itself. To this end, the study introduces virtual independent variables to characterize the different materials of the mixture. Considering that the asphalt mixture selected in the experimental plan is divided into three materials, namely, three levels, it is necessary to introduce two virtual independent variables, namely, X and Y. When X=1, it indicates that the material of the mixture is limestone; when X=0, it indicates that the material of the mixture is other materials; when X=0, Y=0, it indicates that the material of the mixture is basalt.

[0156] After introducing two virtual independent variables X and Y, combined with the 9 independent variables in Table 1-10, the independent variables with poor significance are deleted one by one, and the analysis is performed step by step until a satisfactory regression effect is obtained. The good regression effect is mainly reflected in three aspects: the overall goodness of fit is better, that is, the closer the R2 value is to 1, the better; the probability of model parameter estimation test P<0.05, that is, the model equation meets the significance level; the probability of factor test P<0.05, that is, there is a significant regression relationship between each explanatory variable and the explained variable in the model. Through step-by-step analysis, X, MTD1, Sk1 and λ are finally retained. q The four independent variables together form the M1 composite matrix, that is, M1 = [X, MTD1, S k 1, λ q ]. The results of regression analysis and parameter test are shown in Table 1-6, Table 1-7 and Table 1-8. At this time, the results of parameters A, B and C in the multivariate quadratic polynomial regression model are shown in Formula 1-21.

[0157]

[0158] Where, M1 = [X MTD1 S k 1λ q ]

[0159]

[0160] B1=[-93.578 275.868-34.239 7.037]

[0161] C1=42.444

[0162] Table 1-6 Summary results of multivariate binomial solution BPN model

[0163]

[0164] Table 1-7 Multivariate binomial solution BPN model parameter estimation and test

[0165]

[0166] Table 1-8 Multivariate binomial solution BPN model factor test

[0167]

[0168] As can be seen from Table 1-6, the coefficient of determination (R2) of the model is 0.8038, and the average residual sum of squares is 19.4315, indicating that the data points can be densely gathered near the regression line, that is, the model fit is good. The results of Table 1-7 show that the P values ​​of the linear term, square term, cross term and overall F test of the regression model are P<0.0001, P=0.0033, P<0.0001, and P<0.0001, respectively, all lower than 0.05, indicating that the quadratic polynomial relationship between the explained variable and the explanatory variable of the model is significant, that is, the regression equation model relationship is significant. Further joint tests are performed on all parameters of each factor in the model to comprehensively analyze the significance of the overall regression coefficient of each factor. The results of the factor test in Table 1-8 show that the probability values ​​of the F test for all factor items are P<0.0001, and their probability values ​​P are all less than 0.05, indicating that the overall regression coefficient of each factor is highly significant. The above results show that the multivariate quadratic polynomial regression model is highly significant and can well reflect the relationship between the anti-slip performance index BPN and the three-dimensional texture morphology index. Therefore, X, MTD1, Sk1 and λ are finally retained. q The four indicators together form a composite matrix M1. A relationship model between the anti-slip performance index BPN and the multivariate quadratic polynomial of the composite matrix is ​​established to describe the performance relationship between the anti-slip performance index BPN and the three-dimensional texture morphology index.

[0169] 2. Establishment of SFC regression model by solving multivariate quadratic polynomial

[0170] According to the idea of ​​establishing the BPN regression model in the previous article, by gradually screening and eliminating each independent variable indicator, X, Y, MTD, Sk1, λ are finally retained. q The five indicators together form a composite matrix M2. On the basis of the composite matrix M2, the optimal multivariate quadratic polynomial model between SFC and different indicators is established. The regression analysis and parameter test results of the model are shown in Table 1-9, Table 1-10 and Table 1-11 respectively. The solution results of each coefficient in the model are shown in Formula 1-22.

[0171]

[0172] Where, M2 = [MTD λ q S k 1 XY]

[0173]

[0174] B2=[0.265 -0.104 -0.668 -0.586 -0.200]

[0175] C2=0.857

[0176] Table 1-9 Summary results of multivariate binomial solution to SFC model

[0177]

[0178] Table 1-10 Multivariate binomial solution SFC model parameter estimation and test

[0179]

[0180] Table 1-11 Multivariate binomial solution SFC model factor test

[0181]

[0182]

[0183] In Table 1-9, the coefficient of determination R2 of the model is as high as 0.9269, and its average residual sum of squares is only 0.0006. These data are sufficient to show that the multivariate quadratic polynomial model has a high goodness of fit and a small residual when used for regression fitting. From the results of model parameter estimation and testing in Table 1-10, it can be seen that the P values ​​of the model's linear term, square term, cross term, and overall F test of the regression model are P<0.0001, P=0.1285, P<0.0001, and P<0.0001, respectively.

[0184] Although the probability value of the square term of the model does not meet the requirement of being lower than 0.05, the test results at the overall level of the model show that its probability value P<0.0001 is highly significant, indicating that although the square term of the explanatory variable in the model is not significant, from the overall level of the model, the quadratic polynomial relationship between the explained variable and the explanatory variable is significant, and the regression equation model relationship is significant, that is, the quadratic polynomial relationship model as a whole can be used to simulate the changing relationship between the explained variable and the explanatory variable. The factor test in Table 1-11 comprehensively analyzes the significance of the overall regression coefficient of each factor. The results show that for all factor terms, their probability values ​​P meet the requirement of being less than 0.05, indicating that the overall regression coefficient of each factor is highly significant. The analysis results of the data in the above three tables show that the multivariate quadratic polynomial can well reflect the relationship between the anti-slip performance index SFC and the two-dimensional texture morphology index. Therefore, MTD and λ are finally retained. q, Sk1, X, and Y together form a synthetic matrix M2. A relationship model between the anti-skid performance index SFC and the multivariate quadratic polynomial of the synthetic matrix is ​​established to describe the performance relationship between the anti-skid performance index SFC and the three-dimensional texture morphology index. By comparing the model relationship between the two indicators SFC and BPN, it is not difficult to find that compared with the BPN indicator model, the SFC model has an additional independent variable indicator Y. In the components that make up the synthetic matrix, the X and Y indicators are used to distinguish the materials of the mixture. This also shows that compared with SFC, the BPN indicator has relatively loose requirements for stone classification. The reason for this may be due to the different test speeds of the two indicators SFC and BPN, which determines that the severity of the impact and wear of the test equipment on the stone is different.

[0185] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for analyzing the anti-skid performance index of asphalt pavement based on multivariate quadratic polynomials, characterized in that: The following steps are involved: S1: Average structural depth of pavement macro texture for extracting roughness characteristics of three-dimensional texture morphology; S2: Extract the average spacing of single peaks and the root mean square wavelength of the three-dimensional texture roughness characteristics; S3: Extract shape indicators of roughness characteristics of three-dimensional texture morphology: contour skewness, hump, apparent anisotropy, and three-dimensional morphology fractal dimension; S4: Introduce the independent variable of mineral material type, eliminate the independent variables with poor significance through the regression model effect, and establish a multivariate quadratic polynomial to solve the BPN regression model; S5: Establish a multivariate quadratic polynomial to solve the SFC regression model through the steps of the BPN regression model.

2. The method for analyzing the anti-skid performance index of asphalt pavement based on multivariate quadratic polynomial according to claim 1 is characterized in that: The step S1 comprises the following sub-steps: S11: Delaunay triangulation method is used to reconstruct the road surface texture in three dimensions, and wavelet decomposition is used to eliminate the cross-section point cloud. The reconstructed cross-section points are on the same horizontal plane; S12: simulate the MTD volume filling method for the 3D surface, reconstruct the distance between the texture and the ideal road surface, and set the ideal plane to cover 95% of the texture point cloud; S13: Using the triangular mesh model volume calculation method, the ratio of the structural depth volume of the area to be measured to the area of ​​the area to be measured is calculated as the MTD index.

3. The method for analyzing the anti-skid performance index of asphalt pavement based on multivariate quadratic polynomial according to claim 2 is characterized in that: The step S13 includes the following sub-steps: S131: Let plane XOY be the projection plane, let any triangle in the triangular mesh model be t, let the convex pentahedron enclosed by the projection plane be the projection volume Pt ​​of the triangle, and let the volume of the convex pentahedron be the projection volume Vt of the triangle; S132: A convex pentahedron is divided into a triangular prism and two tetrahedrons. For any tetrahedron, the volume calculation formula is: Wherein, V((x1, y1, z1), (x2, y2, z2), (x3, y3, z3), (x4, y4, z4)) represents the volume of any tetrahedron, and the three-dimensional coordinates of the four vertices of any tetrahedron represent (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y4, z4) respectively; S133: Let the triangle face set of the triangular mesh model be A, the projection triangle of each triangle face on the projection plane be tp, the convex polyhedron formed by the triangle face t and the projection plane be Pt, and determine all other triangle facets intersecting with it as the intersection triangle face set At; S134: Obtain the projection volume Vt of the triangular facet, and determine whether to add or subtract in the triangular network model: If the sign of the projection volume Vt of the triangle is positive, the projection volume Vt of the triangle is added when calculating the volume of the triangular mesh model; If the projected volume Vt of the triangle is negative, the projected volume Vt of the triangle is subtracted when calculating the volume of the triangular mesh model; S135: The volume of the convex polyhedron enclosed by all triangular facets and the projection plane is added to obtain the volume of the triangular mesh model. The texture elevation value is flipped symmetrically according to the projection plane. The elevation formula for calculating the road surface macro texture is: Among them, z(x, y) represents the macro texture elevation function, x and y represent the coordinate values, and T represents the elevation value corresponding to the texture point cloud that the ideal plane needs to cover 95%; S136: According to the volume filling principle of the sand spreading method, the average structural depth index MTDst of the road surface macro texture is calculated by the structural depth filling volume of the area to be tested and the area of ​​the area to be tested. The formula is: Among them, MTD st represents the average structural depth index of the pavement macro texture, n represents the number of cross sections, N represents the number of cross section elements, a represents the longitudinal accuracy, b represents the lateral accuracy, i represents the sampling point variable, t represents the total number of sampling points, and Vt represents the projected volume of the triangular patch.

4. The method for analyzing the anti-skid performance index of asphalt pavement based on multivariate quadratic polynomial according to claim 1 is characterized in that: The step S2 comprises the following sub-steps: S21: Get the projection length of the distance between the highest points of two adjacent single peaks on the midline and calculate the average value. The formula is: Among them, S represents the average single-peak spacing of the profile, S0 represents the distance between the Oth adjacent single-peak peak points, p represents the total number of adjacent single-peak peak points, and O represents the adjacent single-peak peak point variable; S22: Get the profile RMS deviation and profile RMS slope, and calculate the profile RMS wavelength. The formula is: Among them, Δ q represents the RMS slope of the profile, m represents the length in the x direction, n1 represents the length in the y direction, and R q represents the profile root mean square deviation, λ q Represents the profile rms wavelength.

5. The method for analyzing the anti-skid performance index of asphalt pavement based on multivariate quadratic polynomial according to claim 1 is characterized in that: The S3 comprises the following sub-steps: S31: Get the average value of the cube of the contour offset within the sampling range. The formula is: Among them, S k represents the profile skewness, R q represents the root mean square deviation of the profile, represents the macro texture elevation function, i1 = 1, 2...n1, j = 1, 2...m; S32: Get the sharpness of the change in the profile surface distribution. The formula is: Among them, K u represents the hump, u4 and u2 represent the fourth-order and second-order central moments of the surface morphology, respectively; S33: Obtain the difference in shape in different directions. The formula is: Among them, Ka represents the apparent anisotropy, P x (x,y) and P y (x, y) represents the roughness characteristic parameters of the two-dimensional topography along the x and y directions, respectively; S34: Obtain a comprehensive characterization index of surface roughness characteristics, the formula is: N L ∝L -D ; Among them, N L Represents the value corresponding to the number of L at different scales, L -D represents the negative dimension of scale L, DD represents the three-dimensional fractal dimension, n2 represents the midpoint of scale L, 6. The method for analyzing the anti-skid performance index of asphalt pavement based on multivariate quadratic polynomial according to claim 1 is characterized in that: The S4 comprises the following sub-steps: S41: Establish the initial BPN synthesis matrix, the formula is: M1=[MTD1,S k ,S k 1,λ q ,K a 1,K u 1,DD,S,S1]; Among them, M1 represents the initial BPN synthesis matrix, MTD1 represents the average structural depth index of the microscopic road surface macro texture, S k 1 represents the microscopic profile skewness, K a 1 represents the apparent anisotropy at the microscopic level, K u 1 represents the microscopic hump degree, S1 represents the average spacing of the single peaks of the microscopic profile; S42: Introduce virtual independent variables X and Y to characterize the material of the mixture: When X=1, it indicates that the material of the mixture is limestone; When X=0, it indicates that the material of the mixture is other materials; When X=0, Y=0, it indicates that the material of the mixture is basalt; S43: Delete the less significant independent variables one by one, and finally retain X, MTD1, Sk1 and λ according to the goodness of fit and factor test probability. q The four independent variables together form the BPN synthesis matrix, the formula is: M1=[X,MTD1,S k 1,λ q ]; Among them, M1 represents the BPN synthesis matrix, MTD1 represents the average structural depth of the microscopic road surface macro texture, and λ q represents the RMS wavelength of the profile, S k 1 represents the microscopic texture profile skewness, and X represents a dummy independent variable; S44: Construct a multivariate quadratic polynomial to solve the BPN regression model. The formula is: B1＝[-93.578 275.868-34.239 7.037] C1＝42.444； Among them, BPN represents the BPN regression model, M1 represents the BPN synthesis matrix, M2 represents the synthesis matrix, A1, B1, and C1 represent the quadratic term coefficient matrix, linear term coefficient matrix, and constant term of the BPN binary multivariate polynomial, respectively.

7. The method for analyzing the anti-skid performance index of asphalt pavement based on multivariate quadratic polynomial according to claim 1 is characterized in that: The S5 comprises the following sub-steps: S51: Introduce virtual independent variables X and Y, exclude independent variables with poor significance through the regression model effect, and establish a synthetic matrix. The formula is: M2=[MTD λ q S k 1 X Y]; Where M2 represents the synthesis matrix, MTD represents the average construction depth of the pavement macro texture, and λ q represents the RMS wavelength of the profile, S k 1 represents the microscopic texture profile skewness, and X and Y represent dummy independent variables; S52: Establish a multivariate quadratic polynomial to solve the SFC regression model. The formula is: B2＝[0.265 -0.104 -0.668 -0.586 -0.200]； C2＝0.857； Among them, DF 60 represents the SFC regression model, M2 represents the synthetic matrix, A, B, and C represent the quadratic term coefficient matrix, linear term coefficient matrix, and constant term of the SFC bivariate multivariate polynomial, respectively.

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