Pavement longitudinal section Gaussian filtering method fused with Newton's theorem

Abstract

The invention discloses a road surface longitudinal section Gaussian filtering method fused with the Newton's theorem. Comprising the following steps: (1) determining a sampling interval and a cut-off wavelength; (2) determining the length of a Gaussian template according to the Nyquist sampling theorem; (3) judging and supplementing boundary points; (4) calculating related parameters and obtaining a final Gaussian template; and (5) performing low-pass and high-pass Gaussian filtering. The efficient and accurate method is provided for road longitudinal section contour filtering, IRI insensitive wavelength components can be effectively weakened, the original contour of a specified wave band is reserved to the maximum extent, the method is not limited by sampling intervals, the precision of international flatness index calculation is improved, and the method has important significance in road surface flatness detection.

Description

Technical Field

[0001] The invention relates to the field of road surface flatness detection, and in particular to a filtering method for a road longitudinal section profile. Background Art

[0002] The roughness of the road surface not only affects the driving comfort, but also has a certain impact on driving safety. It is an important indicator for highway quality evaluation and road construction acceptance. Among them, the International Roughness Index (IRI) is the most widely used index in the world to characterize the longitudinal road surface roughness.

[0003] The International Roughness Index is closely related to the wavelength of the road surface. Studies have shown that the wavelengths contributing to IRI are mainly concentrated in the range of 1.3~29.4m. The longitudinal section wavelengths beyond this range will affect the calculation of IRI. Therefore, before calculating IRI, it is usually necessary to filter the original longitudinal section profile to weaken the longitudinal section wavelength components that are insensitive to IRI. Therefore, domestic and foreign scholars have conducted relevant research on road longitudinal section profile filtering.

[0004] Zhang Liguang and others from Wuhan University of Technology published a paper titled "Research and Implementation of Automatic Road Roughness Detection System" in the Journal of Wuhan University of Technology. In the preprocessing process, a moving average filter was used to reduce the tire inclusion effect, but it did not filter and reduce the longitudinal section wavelength components to which IRI is insensitive.

[0005] In a paper titled "Calculation Principle and Test Evaluation of Three-Dimensional Line Laser International Flatness Index" published in the Journal of Tsinghua University, Runhua Wu et al. from Tsinghua University built an anti-motion smoothing filter into the three-dimensional vehicle-mounted laser profiler they designed, which effectively reduced the impact of high-frequency noise below 1m and low-frequency noise above 30m, but caused a slight amplification of the signal in the 1-30m frequency band.

[0006] In response to the above-mentioned problem of signal distortion caused by weakening sensitive wavelength components, the present invention discloses a pavement longitudinal section Gaussian filtering method integrating Nyssa's theorem. This method is not limited by the sampling interval, can effectively weaken the longitudinal section wavelength components that are insensitive to IRI, and retain the true contour of the specified band. Summary of the invention

[0007] In view of the above problems, the present invention discloses a road longitudinal section Gaussian filtering method integrating Nyssa's theorem, which weakens the IRI-insensitive longitudinal section wavelength component while retaining the true contour of the data as much as possible, and ultimately serves the road surface flatness detection of calculating IRI.

[0008] A road longitudinal section Gaussian filtering method integrating Nyssa's theorem comprises the following steps:

[0009] (1) Enter the profile data sampling interval and set the wavelength range

[0010] (2) Determine the Gaussian template length using the theory of the least sampling points to determine the most accurate waveform

[0011] (3) Determine whether the filtering point is a boundary point and fill in the points involved in the boundary point filtering

[0012] (4) Calculate relevant parameters to obtain the final Gaussian template

[0013] (5) Perform Gaussian filtering to obtain the filtered longitudinal section profile

[0014] Preferably, in step (1), The rate of profile data By sampling at equal intervals, the discrete contour data can be expressed as:

[0015] (1)

[0016] in is a discrete contour; is the sampling frequency; is the number of discrete points. If you want to transform the original contour into Complete determination requires:

[0017] (2)

[0018] in is the number of periodic waves per length of the real profile. When the sine curve is defined as a function of length, its spatial frequency is actually the wave number, which is the reciprocal of the wavelength. Therefore, when studying the specified wavelength of the real profile, it is only necessary to satisfy:

[0019] (3)

[0020] in is the sampling interval of the samples, and is the limit of the wavelength range that you want to study.

[0021] Preferably, in step (2), when the Nyquist sampling theorem is used to determine the Gaussian template length, the following conditions must be met:

[0022] (4)

[0023] in is the cut-off wavelength of the filter, is the sampling interval of the longitudinal elevation data, In fact, it is the length of the discrete Gaussian template.

[0024] Preferably, the boundary point in step (3) refers to when the filter point is located on the left or right side of the entire longitudinal section, the length of the points around the point that need to participate in the filtering calculation has exceeded the range of the entire longitudinal section data. For the above boundary points, the present invention uses the value of the starting point or the end point to fill the value of the left or right boundary point respectively.

[0025] Preferably, in step (4), a Gaussian function is used to calculate the The Gaussian function value of the point must satisfy the following formula:

[0026] (5)

[0027] Where y is the elevation of the longitudinal section; is the current filtering point; and The filter point The mean and sample standard deviation of y are calculated by summing the values ​​of the Gaussian function at each elevation point in y, and then dividing the value of each point by this sum to obtain the first Gaussian template of points:

[0028] (6)

[0029] Preferably, the Gaussian filter model described in step (5) is:

[0030] (7)

[0031] (8)

[0032] in is the value after Gaussian low-pass filtering of the longitudinal section, It is the value after Gaussian high-pass filtering of the longitudinal section.

[0033] Compared with the prior art, the present invention adopts the above technical solution and has the following significant improvements:

[0034] (1) No sampling interval limitation: Traditional methods are limited by the sampling interval and cannot accurately filter data with a smaller sampling interval. In the present invention, the sampling interval is an adjustable input parameter without any limitation.

[0035] (2) Preserving the authenticity of contour data: Compared with traditional filtering methods that cause data to deviate from the true contour after filtering, the present invention can suppress non-sensitive bands to the greatest extent while retaining sensitive bands, and can obtain higher calculation accuracy after filtering. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a specific flow chart of the present invention

[0037] Figure 2 The present invention uses Nyssin's theorem to determine the wavelength principle diagram

[0038] Figure 3 It is a schematic diagram of boundary point processing of the present invention.

[0039] Figure 4 This is the filtering result diagram of the present invention.

[0040] Figure 5 This is a comparison diagram of the power spectrum density of the filtering results of the present invention. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, preferred embodiments are given below and the specific implementation of the present invention is further described in detail in conjunction with the accompanying drawings.

[0042] Example:

[0043] Combination Figure 1 , the specific process of this embodiment is described. Taking the measured elevation data of the longitudinal section of the Long-Term Pavement Performance (LTPP) study in the United States as an example, this example provides a Gaussian filtering method for the longitudinal section of the road surface integrating the Nyssa theorem, including the following steps:

[0044] (1) Combination Figure 2 , explaining the process of determining the Gaussian template length. The selected LTPP data sampling interval is 25 mm, and the data segment length is 152.4 m. In order to retain the data of the 1.3-29.4 m segment length, the cutoff wavelength limits of 1.3 and 29.4 are respectively substituted into formula (4), retaining the integer part of the calculation result, and the Gaussian template lengths of 26 and 588 are obtained respectively.

[0045] (2) Combination Figure 3 , which explains the process of boundary point judgment and filling. If the total length of the data is , in formula (6) when or , fill all left boundary points with the value of the starting point 3.875, and fill all right boundary points with the value of the ending point 7.495.

[0046] (3) Taking the first point as an example, when the cutoff wavelength is 1.3 m, the values ​​of the 53 points involved in the filtering of this point are substituted into formula (6) to obtain the Gaussian template of the first point.

[0047] (4) Combination Figure 4 , illustrating the filtering result of this embodiment. Substituting the obtained Gaussian template into formula (7) and formula (8) respectively, the Gaussian low-pass and Gaussian high-pass filtering results are obtained.

[0048] (5) Combination Figure 5 , illustrating the power spectrum density results of this embodiment. Performing power spectrum density (PSD) analysis on the original profile data and the filtered data, it can be seen that the bands with wavelengths less than 1.3m and greater than 29.4m are significantly weakened, while the bands with wavelengths in the range of 1.3-29.4m are almost not affected at all, and the real profile is retained to the maximum extent during the filtering process.

[0049] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the implementation modes, and they can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A road longitudinal section Gaussian filtering method integrating Nyssian theorem is characterized by: The steps include: (1) Input the profile data sampling interval and expected cutoff wavelength; (2) Determine the Gaussian template length using the Nyquist sampling theorem; (3) Determine whether the filtering point is a boundary point and fill in the points involved in the boundary point filtering; (4) Calculate relevant parameters to obtain the final Gaussian template; (5) Perform Gaussian filtering to obtain the filtered longitudinal section profile.

2. The road longitudinal section Gaussian filtering method integrating Nyssa's theorem according to claim 1 is characterized in that: In step (1), The rate of profile data By sampling at equal intervals, the discrete contour data can be expressed as: （1） in is a discrete contour; is the sampling frequency; is the number of discrete points; if you want to use discrete sampling values ​​to convert the original contour Complete determination requires: （2） in is the number of periodic waves per length of the real profile; when the sine curve is defined as a function of length, its spatial frequency is actually the wave number, which is the reciprocal of the wavelength; therefore, when studying the specified wavelength of the real profile, it is only necessary to satisfy: （3） in is the sampling interval of the samples, and is the limit of the wavelength range that you want to study.

3. The road longitudinal section Gaussian filtering method integrating Nyssa's theorem according to claim 1 is characterized in that: In step (2), the following conditions must be met when using the Nyquist sampling theorem to determine the Gaussian template length: （4） in is the cut-off wavelength of the filter, is the sampling interval of the longitudinal elevation data, In fact, it is the length of the discrete Gaussian template.

4. The road longitudinal section Gaussian filtering method integrating Nyssa's theorem according to claim 1 is characterized in that: The boundary point described in step (3) is when the filter point is located on the left or right side of the entire longitudinal section, and the length of the points around the point that need to participate in the filtering calculation has exceeded the range of the entire longitudinal section data; for the above-mentioned boundary point, the present invention uses the value of the starting point or the end point to fill in the value of the left or right boundary point respectively.

5. The road longitudinal section Gaussian filtering method integrating Nyssa's theorem according to claim 1 is characterized in that: In step (4), the Gaussian function is used to calculate the The Gaussian function value of the point must satisfy the following formula: （5） Where y is the elevation of the longitudinal section; is the current filtering point; and The filter point The mean and sample standard deviation of the calculated Gaussian function at each elevation point in y are summed, and the value of each point is divided by this sum to obtain the first Gaussian template of points: （6）。 6. The road longitudinal section Gaussian filtering method integrating Nyssa's theorem according to claim 1 is characterized in that: The Gaussian filter model described in step (5) is: （7） （8） in is the value after Gaussian low-pass filtering of the longitudinal section, It is the value after Gaussian high-pass filtering of the longitudinal section.

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