A method for filtering road surface longitudinal profile based on nae's theorem

Abstract

The application discloses a road surface longitudinal section Gaussian filtering method fusing Nyquist theorem. The method comprises the following steps: (1) determining a sampling interval and a cutoff wavelength; (2) determining a Gaussian template length according to Nyquist sampling theorem; (3) judging and completing boundary points; (4) calculating relevant parameters and obtaining a final Gaussian template; and (5) low-pass and high-pass Gaussian filtering. The application provides an efficient and accurate method for road longitudinal section profile filtering, can effectively weaken IRI insensitive wavelength components, maximally retains original profiles of specified wavelength bands, is not limited by a sampling interval, improves the precision of international roughness index calculation, and has important significance in road roughness detection.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of road surface flatness detection, in particular to a road longitudinal profile filtering method. BACKGROUND

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

[0003] The international roughness index is closely related to the road surface wavelength. Research shows that the wavelengths contributing to IRI mainly concentrate in the interval of 1.3-29.4m, and the longitudinal profile wavelengths beyond this range will affect the calculation of IRI. Therefore, before calculating IRI, the original longitudinal profile usually needs to be filtered to weaken the longitudinal profile wavelength components that are insensitive to IRI. Therefore, scholars at home and abroad have carried out relevant research on road longitudinal profile filtering.

[0004] Zhang Liguang et al. of Wuhan University of Technology published a paper entitled "Research and Implementation of Road Surface Flatness Automatic Detection System" in the journal of Wuhan University of Technology. In the preprocessing process, a moving average filter was used to weaken the tire containment effect, but it did not filter the longitudinal profile wavelength components that are insensitive to IRI.

[0005] Ruhunhua et al. of Tsinghua University published a paper entitled "Three-dimensional line laser international roughness index calculation principle and test evaluation" in the journal of Tsinghua University. In the three-dimensional vehicle-mounted laser profilometer designed by them, a reverse moving smoothing filter is built in, which effectively reduces the influence of high-frequency noise below 1m and low-frequency noise above 30m, but causes a slight amplification of the signal in the frequency band of 1-30m.

[0006] In view of the problem that the above-mentioned weakening of the sensitive wavelength component will cause signal distortion, the present application discloses a road longitudinal profile Gaussian filtering method fusing Nyquist theorem, which is not limited by sampling interval, can effectively weaken the longitudinal profile wavelength components that are insensitive to IRI, and retain the true profile of the specified band. SUMMARY

[0007] The present application discloses a road longitudinal profile Gaussian filtering method fusing Nyquist theorem, which weakens the longitudinal profile wavelength components that are insensitive to IRI as much as possible while retaining the true profile of the data, and finally serves the road surface flatness detection for calculating IRI.

[0008] A road longitudinal profile Gaussian filtering method fusing Nyquist theorem, comprising the following steps:

[0009] (1) Input the sampling interval of profile data, set the wavelength range

[0010] (2) Determine the length of Gaussian template by the least sampling points

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

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

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

[0014] Preferably, in step (1), the profile data is sampled at an equal interval at a rate of The discrete profile data can be expressed as:

[0015] (1)

[0016] Wherein is the discrete profile; is the sampling frequency; is the number of discrete points. If the original profile is to be completely determined by discrete sampling values, it must satisfy:

[0017] (2)

[0018] Wherein is the period wave number of the real profile per length. When the sinusoidal 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 only needs to satisfy:

[0019] (3)

[0020] Wherein is the sampling interval of the sample, and is the limit value of the wavelength range to be studied.

[0021] Preferably, in step (2), when determining the length of the Gaussian template by using the Nyquist sampling theorem, it needs to satisfy:

[0022] (4)

[0023] Wherein is the cutoff wavelength of the filter, is the sampling interval of the vertical profile elevation data, is actually the length of the discrete Gaussian template.

[0024] Preferably, the boundary point in step (3) refers to the point that when the filtering point is located at the left or right side of the whole profile, the length of the points needed to participate in the filtering calculation around this point has exceeded the range of the whole profile data. For the above-mentioned boundary point, the value of the starting point or the terminal point is used to fill in the value of the left or right boundary point, respectively.

[0025] Preferably, in step (4), the Gaussian function value of the i-th point is calculated by the following formula:

[0026] (5)

[0027] Wherein y is the profile elevation; is the current filtering point; and is the mean and sample standard deviation of the filtering point The values of the Gaussian function of each elevation point in y are summed up, and the value of each point is divided by the sum, respectively, to obtain the Gaussian template of the i-th point:

[0028] (6)

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

[0030] (7)

[0031] (8)

[0032] Wherein is the value of the profile Gaussian low-pass filtering, is the value of the profile Gaussian high-pass filtering.

[0033] Compared with the prior art, the technical scheme has the following significant progress:

[0034] (1) No sampling interval limit: the traditional method is limited by the sampling interval, and cannot accurately filter the data with small sampling interval. In the present application, the sampling interval is an adjustable input parameter, and there is no any limit.

[0035] (2) Retaining the authenticity of the profile data: compared with the traditional filtering method, the present application can inhibit the non-sensitive band to the greatest extent, retain the sensitive band, and obtain higher calculation accuracy after filtering. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 is the specific flowchart of the present application

[0037] ​​Figure 2 is the principle diagram of wavelength determined by Nyquist theorem

[0038] Figure 3 is the schematic diagram of boundary point processing of the present application.

[0039] Figure 4 is the filter result diagram of the present application

[0040] Figure 5 is the filter result power spectrum density comparison diagram of the present application DETAILED DESCRIPTION

[0041] In order to make the objects, technical solutions and advantages of the present application clearer, the following preferred embodiments are combined with the drawings to further describe the specific implementation of the present application in detail.

[0042] Embodiment:

[0043] The specific process of the present embodiment is described in combination with Figure 1 , taking the measured elevation data of the vertical section of the Long-Term Pavement Performance (LTPP) of the United States as an example, the present example provides a pavement vertical section Gaussian filtering method fusing Nyquist theorem, including the following steps:

[0044] (1) The process of determining the length of the Gaussian template is described in combination with Figure 2 . The sampling interval of the selected LTPP data is 25 mm, and the data segment length is 152.4 m. In order to retain the data with a segment length of 1.3-29.4 m, the cut-off wavelengths of 1.3 and 29.4 are respectively brought into formula (4), and the integer part of the calculation result is retained, respectively obtaining the length of the Gaussian template of 26 and 588.

[0045] (2) The process of boundary point judgment and filling is described in combination with Figure 3 . If the total length of the data is , when or in formula (6), the left boundary point is filled with the value of the starting point 3.875, and the right boundary point is filled with the value of the ending point 7.495.

[0046] (3) Taking the first point as an example, when the cut-off wavelength is 1.3 m, the values of the 53 points participating in the filtering of the point are brought into formula (6), and the Gaussian template of the first point is obtained.

[0047] (4) The filtering result of the present embodiment is described in combination with Figure 4 . The obtained Gaussian template is respectively brought into formula (7) and formula (8), and the Gaussian low-pass and high-pass filtering results are obtained.

[0048] (5) The filtering result of the present embodiment is described in combination withFigure 5 The power spectral density (PSD) results of the present example are illustrated in FIG. 14. The original profile data and the filtered data were analyzed using power spectral density (PSD) analysis. It can be seen that the wavelengths less than 1.3 m and greater than 29.4 m were significantly attenuated, while the wavelengths in the range of 1.3-29.4 m were hardly affected at all, and the filtering process maximized the preservation of the true profile.

[0049] While embodiments of the application have been disclosed in connection with the above specification, it will be apparent to those skilled in the art that numerous modifications can be made thereto without departing from the general concept of the application. Accordingly, it is intended that all such modifications be included within the scope of the claims and their equivalents.

Claims

1. A method of filtering a road profile using a Gaussian filter with the fusion of the Naeiss theorem, characterized in that, Comprising the following steps: (1) input profile data sampling interval, desired cut-off wavelength; At a rate of 1 / 1000 of the profile data is equally spaced sampled, the discrete profile data can be represented as: （1） wherein is the discrete profile; is the sampling frequency; is the number of discrete points; if one wants to determine the original profile completely from the discrete sampled values, one has to satisfy: （2） wherein is the period wave number per length of the real profile; when the sinusoid is defined as a function of length, its spatial frequency is actually the wave number, which is the inverse of the wavelength; thus, when studying a specified wavelength of the real profile, it is only necessary to satisfy: （3） wherein is the sampling interval of the sample, and is the limit of the wavelength range to be investigated; (2) determine the length of the Gaussian template using the Nyquist sampling theorem; When determining the length of the Gaussian template using the Nyquist sampling theorem, the following needs to be met: （4） wherein is a cut-off wavelength of the filter, is a sampling interval of the profile elevation data, is actually the length of the discrete Gaussian template; (3) judge whether the filtering point is a boundary point, and supplement the points participating in the filtering of the boundary point; The boundary point is when the filtering 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-mentioned boundary point, the value of the starting point or the terminal point is used to supplement the value of the left or right boundary point; (4) Calculate the Gaussian function value of the point, sum the Gaussian function value of the elevation point, and normalize to obtain the Gaussian template finally. point Gaussian function value, sum the Gaussian function value of the elevation point, and normalize to obtain the Gaussian template finally. The Gaussian function is used to calculate the Gaussian function value of the i-th point The following formula must be satisfied when calculating the Gaussian function value of the i-th point （5） where y is the profile elevation; is the current filter point; and is the filter point the mean and sample standard deviation; sum the values of the Gaussian function for each elevation point of , and divide each point's value by this sum separately to obtain the Gaussian template for the point. （6） (5) Gaussian filtering to obtain the filtered longitudinal section profile; The model of the Gaussian filtering is: （7） （8） wherein is the value after longitudinal profile Gaussian low-pass filtering, is the value after longitudinal profile Gaussian high-pass filtering.

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