JP3054251B2 - A method for measuring the continuous road height in the longitudinal direction of the road using a profile meter - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring a continuous road surface height in a longitudinal direction of a road surface using a profile meter.

[0002]

2. Description of the Related Art Currently, in Japan, a vehicle equipped with a measuring device based on the principle of a three-point profile meter is run to measure the amount of vertical irregularity on a road surface, and the measured values in a certain section are statistically processed. It is common to find the standard deviation and use it as an index for pavement road surface flatness. Devices for measuring the flatness of a pavement road surface are roughly classified into a profile type and a response type. A measuring device using the principle of a three-point profile meter targets a static shape of a pavement surface, and belongs to the former. On the other hand, the latter response-type device attempts to evaluate the state of a pavement road surface by measuring the dynamic characteristics of a vehicle traveling on the road surface. Regardless of which type of device is used, the index obtained depends on the structure of the device itself and the measurement method.

[0003] For this reason, the International Roughness Index (IRI) has been proposed in order to disregard the individual characteristics of the measuring device and evaluate the road surface condition based on the behavior of the traveling vehicle. That is, a virtual vehicle called a quarter car or a half car, which is not limited to a specific measuring device, and a traveling method thereof are determined, and an arbitrary road surface is to be evaluated under the same preconditions. In recent years, mainly through the efforts of road traffic officials in the United States and Europe, simulation algorithms have been developed that can calculate the IRI of a given road surface given a given road profile.

[0004]

However, in order to grasp the flatness of the pavement road surface, there are three methods used in Japan.
With a point-type profile meter, it was extremely difficult to determine the actual profile of the road surface.

[0005]

According to the present invention, the gradient change rate of a minute section at a profile meter measurement point that cannot be measured is replaced with a profile meter gradient change rate (a road surface gradient change rate obtained by a profile meter). Then, the road surface height at the continuous profile meter measurement points is obtained.

[0006]

Hereinafter, the present invention will be described in detail with reference to the drawings. FIG. 1 is a schematic cross-sectional view in a longitudinal direction (vehicle running direction) of a pavement road surface (hereinafter sometimes simply referred to as a road surface). In Figure 1, lambda: distance road height measurement points, P _i: i-th (FIG. 1, i = -1~ (n + 1) ) road surface height measurement points, R _i: a measurement point road height at P _i, S _i-1 ⁱ : Road surface gradient from measurement point P _i-1 to measurement point P _i (= (R _i −R _i-1 ) / λ) S ^* : On the left (on the drawing) of measurement point P ₀ Road surface gradient α _{i in the} section (from P ₋₁ to P ₀ ): the road surface gradient change rate at the measurement point P _i . Road height R _n at the measuring point P _n is expressed by the following Equation 2. R _n = R _n-1 + λS _n-1 ⁿ (2)

Further, the road surface gradient between two adjacent measurement points (interval λ) is expressed by Equation 3, respectively. _{^{S 0 1 = S * + λα}} 0 S 1 2 = S 0 1 + λα 1 ····· S n-1 n = S n-2 n-1 + λ α n-1 ··· (3) the formula When both sides of 3 are added, the road surface gradient S _n-1 ⁿ is expressed by Expression 4. S _n-1 ⁿ = S ^* + λ (α ₀ +... + Α _n-1 ) (4) When Expression 4 is substituted for S _n-1 ⁿ in Expression 2, Expression 5 is obtained.

(Equation 5) Equation 5 is also expressed as Equation 6.

(Equation 6)

As shown in FIG. 2A, the measurement point P _a
And P _b of the road surface height (R _a, R _b) Assuming equal,
As shown in FIG. 2 (B), the road height at each measurement point can be specified by the vertical distance from the "reference level of displacing" through the points of the road surface height measurement points P _a and P _b . FIG.
In the case of, S ^* can be obtained by Expression 7 or Expression 8.

(Equation 7)

(Equation 8) Each measurement points a and b _{P a} and sequence number indicating the _{P b} (i.e.
In the above Pi, i is a or b). Where 0 <
a <b. Therefore, the road height R of the measurement point P _a and P _b
a and R _b are obtained by Expression 9 obtained by replacing S ^* in Expression 6 with Expression 7 or Expression 8.

(Equation 9) In Equation 9, the second term on the right side is a constant value, and R _a (or R _b ) and R ₀ are in an interpolating relationship. When the road surface height R _a and R _b at the measuring point P _a and P _b are assumed both the road surface height 0, the road height R _n of measuring points P _n is calculated by Equation 10 or Equation 11.

(Equation 10)

[Equation 11] In Equations 10 and 11, n = a + 1, a + 2,.
, B. that's all

Incidentally, in order to obtain the vertical profile of the road surface, it is necessary to obtain a series of road surface heights for each minute section λ (for example, 10 cm). For this purpose, the road surface gradient change rate (α) for each minute section λ is required. ). However, the length of a three-point profile meter that is currently widely used is 300 cm (span 150 cm × 2), and the rate of change in the profile meter gradient obtained by this profile meter is small for each minute section λ defined by the span L. (Ie, every 10 cm defined by a span of 150 cm). Therefore, 1 was determined using a 300 cm long profile meter currently used.
By the rate of change of the profile gradient every 0 cm, the minute section 1
Road surface gradient change rate (α) every 10 cm defined at 0 cm
If can be approximated, it is possible to obtain a road profile that can be used practically.

Hereinafter, referring to FIG. 3, the road surface gradient change rate (α) of the minute section λ is calculated as a reference length 2L (L is, for example, 150c).
The approximation (or replacement) with the gradient change rate for each λ obtained by the profile meter of m) will be described with reference to FIG.

Assuming that the road surface gradient in the second half (R to M) of the profile meter shown in FIG. 3 is S ₀ , and the road surface gradient change rate in the first half (M to F) with respect to the second half is A, The road surface gradient is S ₀ + AL. Therefore,
The road surface height increment from the midpoint P of the second half of the profile meter to the center M of the profile meter is S ₀ L / 2, while the road surface from the midpoint M of the profile meter to the midpoint Q of the first half of the profile meter. High increment is (S ₀ + AL) L
/ 2. The increment from the midpoint P to the midpoint Q, the measurement interval of the profilometer (e.g., 10 cm) road surface gradient of the small sections λ is (S _{1 ^2,} S ^{2 3} illustrated. ···, S ₁₄ ¹⁵⁾
And the minute section gradient change rate α _i
Can be represented by _{S 0 L / 2 + (S} 0 + AL) L / 2 = S 0 λ / 2 + S 1 2 λ + ··· + S k-1 k λ + (S 0 + AL) λ / 2 ··· (12 Here, the last measurement point is represented by k for generalization, but in the case of FIG. 3, k = 15. S _{0 in} Equation 12
2 of the denominator of λ / 2 and (S ₀ + AL) λ / 2 are
This is because the middle points P and Q are located at the center of the minute section λ.

Further, the gradient of each minute section (which is generalized by S _i ^{i + 1} ) can be expressed as in Equation 13 using the gradient of the immediately preceding minute section and the rate of change of the minute section thereafter. it can. That is, S _i ^{i + 1} = S _i-1 ⁱ + λ α _i = S ₀ + λ (α _l +... + Α _i ) (13) If Expression 13 is used, Expression 12 is as follows. Can be rewritten. _{S 0 L / 2 + (S} 0 + AL) L / 2 = S 0 λ / 2 + λ (S 0 + λα 1) + λ (S 0 + λ (α 1 + α 2) + λ (S 0 + λ ( α ₁ + α ₂ + α ₃ )... + λ (S ₀ + λ (α ₁ + α ₂ +... + α _k−1 ) + λ (S ₀ + λ (α ₁ + α ₂ +... + α) _k-1 + α _k ) + (S ₀ + AL) λ / 2 (14) By solving the equation (14) for A, the equation (15) or the equation (1) is obtained.
Get 6

(Equation 15)

(Equation 16) The relationship between the gradient change rate A of the profile meter and the minute section gradient change rate α has been clarified by Expression 15 or Expression 16. However, in Equation 16, even if the profile meter gradient change rate A is obtained by measurement, the k minute section gradient change rates α cannot be determined. In theory, the following describes two methods for achieving a consistent solution and their respective problems.

For example, as a first method, if a profile meter having a span L equal to a desired minute section λ can be prepared (ie, if k = L / λ = 1), Equation 16
From A = α ₁ next, there is no any problem in theory. However, it is practically impossible to measure the amount of vertical unevenness of the road surface using a small profile meter having a span equal to λ. The span (base line length) of the best profile meter currently used is 300 cm, and the minimum measurement interval of the currently best profile meter is 10 c.
m, the reference length is 300 cm (L = 150 cm), and λ must be 150 cm in order to set R = 1, which cannot reproduce a practically sufficient road surface shape. Further, as a problem of the first method, there is accumulation of measurement errors.

Next, the second method will be described. Formula 1
Rewriting 5 or 16 gives equation 17 or 18

[Equation 17]

(Equation 18) Therefore, if the (k-1) pieces of alpha _i from the first measurement point to the (k-1) th measurement point is known, alpha _k of the k-th measurement point can be determined immediately. In the first measurement of the target section for which the profile is to be drawn, if the above (k-1) α _i are given as initial values, the k-th minute section (measurement interval) newly appearing for each measurement point thereafter α _{k with} respect to λ can be sequentially _obtained by Expression 15. This method is compared with the first method (where the span of the profile meter is equal to a minute section) and the minimum measurement interval (1
It is much better in that all measurements at 0 cm) can be used continuously. However, the fact that it is necessary to provide (k-1) initial values at the time of the first measurement is a serious limitation in practical use. In addition, the problem of accumulation of measurement errors exists to a greater or lesser extent as in the first method.

That is, if the theoretical consistency is not impaired, either the measurement accuracy is sacrificed or the practicality is reduced, and the difficult problem of accumulating measurement errors is avoided. Can not do. Based on the above considerations,
We introduce the following assumptions. α ₁ = α ₂ =... = α _k = α This assumption is based on the assumption that, in FIG. 3, the rate of change of the profile meter gradient at the midpoint M (change of the gradient from the second half to the first half of the profile meter) is k. Gradient change rate (α
_{1 to} a _k ). Applying the above assumption to Equation 15 or Equation 16 yields α = A.

On the other hand, the displacement of the midpoint M, which is the measured value of the profile meter (ie, the rear end and the front end R of the profile meter)
And displacement) D from a straight line connecting the road height at the F, D = R _M - is _{(R R + R F) /} 2 ··· (19), _{further, A = {(R F -R} M _{) / L - (R M -R} R) / L} L = (R R -2R M + R F) / L 2 = - (2 / L 2) {R M - (R R + R F) / 2} ·・ ・ (20) Further, from Expressions 19 and 20, A = −2D / L ² (21) Applying the above assumption (α = A) to Equations 10 and 11, yields Equations 22 and 23, respectively.

(Equation 22)

(Equation 23) Here, n = a, a + 1, a + 2,..., B.

[0017]

As described above, according to the present invention,
The road surface height at each measurement point is obtained by replacing the gradient change rate of the minute section defined by the minimum measurement interval (minute section) of the profile meter with the profile meter slope change rate of each minute section, and is currently used in Japan. The continuous road surface height in the longitudinal direction of the road surface can be accurately obtained using the profile meter (base line length 2L = 3 m is normal) as it is.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining a premise of an embodiment of the present invention.

FIG. 2 is a diagram illustrating a premise of an embodiment of the present invention.

FIG. 3 is a diagram illustrating an embodiment of the present invention.

Claims (1)

(57) [Claims] (A) moving a three-point profile meter in a longitudinal direction of a road surface and measuring a profile meter gradient change rate at predetermined measurement intervals shorter than a reference length of the three-point profile meter; The rate of change of the profile meter gradient is Here, R _n : road surface height at the n-th measurement point R _n-1 : road surface height at the (n-1) -th measurement point λ: measurement interval of the profile meter a: measurement point at the front end of the measurement section b: Measurement method at the rear end of the measurement section α _i : a method of substituting α _i of the gradient change rate in the i-th minute section to measure the road surface height at predetermined intervals in the longitudinal direction of the road surface.