CN114016360B - Road surface damage detection method based on epicycloid model - Google Patents
Road surface damage detection method based on epicycloid model Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
- E01C—CONSTRUCTION OF, OR SURFACES FOR, ROADS, SPORTS GROUNDS, OR THE LIKE; MACHINES OR AUXILIARY TOOLS FOR CONSTRUCTION OR REPAIR
- E01C23/00—Auxiliary devices or arrangements for constructing, repairing, reconditioning, or taking-up road or like surfaces
- E01C23/01—Devices or auxiliary means for setting-out or checking the configuration of new surfacing, e.g. templates, screed or reference line supports; Applications of apparatus for measuring, indicating, or recording the surface configuration of existing surfacing, e.g. profilographs
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/15—Correlation function computation including computation of convolution operations
Abstract
The invention discloses a pavement damage detection method based on an epicycloid model, which comprises the steps of constructing a standard epicycloid model; the route of the circle O in the model for completing one arch is L0, and the motion trail of the point R on the circle is A0; for the road section to be detected with damage, recording the motion route of the circle O as L1, and the epicycloid track of R on the L1 as A1; comparing the data difference in the spatial position of the point R in A1 with that in A0 under the same angle t, and marking the difference as a damaged point bi; calculating the distance positions between all the damaged points bi and the original point, and marking the distance positions on L0; comparing the elevation data of A0 with the elevation data of A0; and (5) re-selecting a route on the residual damaged pavement, marking as L1, and repeating the steps until all the pavement areas are measured. The invention can more accurately measure the damage condition of the road surface by supplementing the actual measurement and the scientific calculation, and has more operability and practical significance compared with the traditional calculation method.
Description
Technical Field
The invention relates to a pavement damage detection method in the field of road engineering, in particular to a pavement damage detection method based on an epicycloid model.
Background
In the rapid development of transportation, too much traffic brings great prosperity and great challenges to the transportation road. Under a large amount of transportation loads, the road surface often has the problems of cracking, slipping, sinking and the like. Therefore, maintenance of the constructed transportation road is always critical, and the requirement for a road pavement detection method is also provided.
At present, the most common method of manual detection is the most wasteful and time-consuming method, so that the detection of road surface damage by using the techniques such as laser detection, image recognition, and acoustic detection is becoming the mainstream identification and detection method in terms of efficiency and manpower. However, these methods are often too complex, the required data are often difficult to collect and process, and high practical costs are required, the laser detection is most accurate but the equipment cost and operation requirements are often too high, and the image recognition technology is advanced enough. However, there are problems of being limited by data processing technology and image analysis means, and the means of sound wave detection also has practical troubles of transmission medium and conduction efficiency, and these methods are undoubtedly more advanced and faster than manual measurement, and more accurate and more efficient, but have the same problems. Therefore, a more scientific and accurate measurement method is needed to effectively solve the various problems at present.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a simpler and more convenient road surface damage detection method based on an epicycloid model so as to realize more convenient detection and auxiliary repair of road surface damage.
The technical scheme is as follows: the invention provides a pavement damage detection method based on an epicycloid model, which specifically comprises the following steps:
(1) Constructing an epicycloid model;
(2) The route of the circle O in the standard epicycloid model for completing one arch is L0, and the motion trail of a point R on the circle is A0;
(3) For the road section to be detected with damage, the movement route of the circle O is marked as L1, and the epicycloid track of R on the L1 is A1;
(4) At the same angle ti, compare the spatial positions of the R points in A1 and A0 (x) A1 ，y A1 ) And (x) A0 ，y A0 ) The difference in data is denoted as a breakage point bi; and the rotation angle ti of the circle O at this time is recorded, whereinI is a positive integer;
(5) Calculating the distance positions between all the damaged points bi and the original point, and marking the distance positions on the L1; comparing the elevation data of A0 with the elevation data of A1;
(6) And (6) re-selecting a route on the residual damaged pavement, marking as L2, and repeating the steps (3) to (5) until all the pavement areas are measured.
Further, the construction process of the epicycloid model in the step (1) is as follows:
setting a circle O, wherein r is the radius of the circle O, and t is the angle swept by the radius when the circle O moves; r is a point on the circle, and when the circle O rolls towards the fixed direction along the straight line L0 for the distance of the perimeter, the point R on the circle O moves to form a section of track A0 in the process, which is called as an arch; the position relation between the circle O and the point R on the circle O is a standard epicycloid model;
establishing a plane rectangular coordinate system by taking the initial position of the point R as an origin and the L0 as an X axis, and regarding the mathematical expression of the track A0 drawn by the plane rectangular coordinate system, namely the coordinate (X) of each point on the A0 A0 ，y A0 ) The way in which the parametric equations are used is expressed as:
wherein x is A0 y A0 Rolling a circle O by a perimeter, wherein in the process of rotating the angle from 0 to 2 pi, a point R on the circle moves to the spatial position of one arch; r is the radius of the circle O, t is the angle of rotation of the circle O, and t ranges from [0:2 pi]In the meantime.
Further, the coordinate x of the point of A0 in the step (2) A0 ，y A0 The relationship between them is:
coordinates (x) of point R A0 ，y A0 ) Is related to the radius of the circle O only, and to the angle t the circle is rotated through, independently of other factors.
Further, the distance between the breakage specific point bi and the origin in the step (5) is:
di＝ti×r (3)
wherein di is the distance between the damaged point bi and the origin, ti is the rotation angle t of the circle O corresponding to the damaged point, and i is a positive integer.
Further, the comparing the elevation data of A0 with the elevation data of A1 in step (5) is as follows:
subtracting the A1 elevation from the A0 elevation to obtain the elevation difference of the damaged part:
Δ y = damaged road surface elevation-undamaged road surface elevation = y A1 -y A0 ；
Wherein, when the value of the delta y is a negative value, the elevation of the damaged road surface is lower than that of the undamaged road surface; if delta y is a positive value, the elevation of the damaged road surface is higher than that of the undamaged road surface; the A0 elevation refers to the altitude of each point on the track A0 moved by the point R on the L0 to the horizontal ground; the elevation of A1 refers to the poster height of each point on the track A0 moved by the point R on L1 to the horizontal ground.
Has the beneficial effects that: compared with the prior art, the invention has the beneficial effects that: the invention provides a new idea and method for calculating the road surface damage from a classical epicycloid model, and the damage condition of the road surface can be more accurately measured by complementing actual measurement and scientific calculation.
Drawings
FIG. 1 is a schematic view of an epicycloidal model of the invention when the road surface is not damaged;
FIG. 2 is a schematic diagram of a broken road segment according to an embodiment of the present invention;
FIG. 3 is a data model diagram of the present invention for this embodiment;
FIG. 4 is a schematic view of an epicycloidal model of the invention in a state of road surface damage;
FIG. 5 is a schematic diagram of a method for detecting road surface damage according to an embodiment of the present invention;
fig. 6 is a schematic diagram of the final result of the road surface damage detection method according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a road surface damage detection method based on an epicycloid model, and as shown in figure 1, a circle O is set, r is the radius of the circle O, and t is the angle swept by the radius when the circle O moves. When there is a point R on the circle, and the circle O rolls along the straight line L0 to a fixed distance of its perimeter, the point R thereon moves out a track A0 in the process, and the length of this standard track is called "one arch".
Establishing a plane rectangular coordinate system by taking the initial position of the point R as an origin and the L0 as an X axis, and mathematically expressing the locus A0 stroked by the plane rectangular coordinate system to obtain the coordinate (X) of each point on the A0 A0 ，y A0 ) The way in which the parametric equations are used is expressed as:
wherein x is A0 y A0 Rolling a circle O by a perimeter, wherein in the process of rotating the angle from 0 to 2 pi, a point R on the circle moves to the spatial position of one arch; r is the radius of the circle O, t is the angle of rotation of the circle O, t ranges from [0:2 pi]In the meantime.
Obtaining x by a ginseng elimination method A0 y A0 The relationship between (A) and (B) is as follows:
as can be seen from the above equations (1) and (2), the coordinates (x) of the point R A0 ，y A0 ) Is dependent only on the radius of the circle O and on the angle t over which the circle turns, and not on other factors.
When the circle runs "one arch" in a straight line in the horizontal plane, the moving locus of the point R is always as described in the above formula. The positional relationship between the circle O and the point R on the circle O in the present invention is a standard epicycloidal model. When the road section is broken, the broken part is taken as a special broken line or curve in the form of linear vertical section, and the circle O rolls on the road lineIn motion, the motion locus of R, namely the space position (x) of R, different from that of the epicycloid model appears A0 ，y A0 ) The change is compared with the data difference before and after the change, and accordingly, the position of the road surface where the damage occurs is judged.
As shown in fig. 2, a damaged road section 1 to be measured in one embodiment of the present invention has a length of 2.2m and a width of 1.7m; irregular pavement damage exists in the center of the road section, the damage length is 83cm, the width is 62cm, and 1.8 cm-2.2 cm of pits are distributed on the pavement, and the pavement is measured by adopting the pavement damage method.
As shown in fig. 3, a route is selected at an undamaged road surface on the road section 1 to be measured, and is marked as L0, and L0 is taken as the X axis. Meanwhile, another route is selected at the damaged position and is marked as L1, and under the condition that the road section is not damaged, the situation of the motion trail of the R point of the epicycloid model shown in the figure 1 exists. That is, for the horizontal road surface path L0 that is not broken, the only contact point with the ground when the circle O does not roll is defined as the initial position of the point R, i.e., the origin; the position of the origin in the rectangular coordinate system is (0, 0).
When the circle O runs on the L1 selected on the damaged road surface, the trajectory is as shown in fig. 4. At this time, the trajectory of the operation exit point R on the damaged route L1 is A1, and the rule of A1 also conforms to the formula (1) and the formula (2). The present invention recognizes that there is a road surface damage at di by comparing the difference between the A1 and A0 tracks, that is, the calculation method of the initial origin distance coordinates di of the damaged point bi and the point R in the damaged road surface marked in fig. 4, as shown in the following formula (3):
di＝ti×r (3)
wherein di is a distance coordinate between the damaged point bi and the initial origin of the point R; ti is a rotation angle value of the circle O corresponding to the damaged position, expressed in radian, and i is a positive integer.
For the road surface in fig. 2, a first route L0 is selected at the undamaged part of the road section to be detected, and the first route L0 is taken as an X axis; selecting a circular object O with the radius of 50cm as a measuring tool, rolling the circular object O on a route L0, and then carrying out the following steps through a formula (1)Calculating rows, wherein r is the radius of the circular real object O, and r =50cm in the embodiment; t is the rolling angle of the circular real object O, the interval of t is 0.1 radian in the embodiment, and the elevation data y of the track data A0 of the 45 groups A0 is calculated by the formula (1) A0 (ii) a Specifically, the results are shown in Table 1.
Selecting a route from the possible damaged road sections, recording the route as L1, performing measurement and calculation, selecting a circular object O with the radius of 50cm as a measuring tool, enabling the circular object O to roll on the route L1, recording the track data of A1 every 5cm, namely every 5.72 degrees of rotation, and recording 45 groups of data in the embodiment; the data includes a roll angle ti and A1 elevation data y for the circle O A1 Specifically, the examples are shown in Table 1.
After comparing the trajectory data of A0 and A1, it is found that there are 16 different data of trajectory A0 and trajectory A1 in 45 sets of data, and the angle value ti corresponding to the 16 data is recorded.
As shown in fig. 5, 16 groups of abnormal data existing in 45 recording points acquired on the route L1 are calculated by using the formula (3) through the found 16 groups of abnormal data, that is, the 16 groups of data ti angles t1 to t16 corresponding to b1 to b 16; indicating that the damage exists on the road surface with the distance d 1-d 16 from the initial origin of the R on the road section of 2.2 m; these data are labeled on L1.
As shown in fig. 6, a new route except L1 is selected again on the damaged road surface, which is marked as L2, L3, L4, L5 \8230, wherein if there is no damage on the route, the motion trajectory of the point R of the circle O thereon will be identical to that in the standard epicycloid model, i.e. to the A0 data on L0; on the other hand, if there is a damage on each of the routes, there is a damage on the road surface at a distance d1 to d16 from the origin of the distance R as in L1.
Points with damages on each route are marked on the corresponding route Li, and the elevation data of A0 is compared with the elevation data of A1, as shown in Table 1.
TABLE 1 summary of AO and A1 elevation data
The A0 elevation refers to the altitude of each point on the track A0 moved by the point R on the L0 to the horizontal ground; the elevation of A1 refers to the height of the poster of each point on a track A0 moved by a point R on L1 relative to the horizontal ground, and the elevation difference of a damaged position is obtained by subtracting the elevation of A0 on L0 from the elevation of A1 on each route:
Δ y = damaged road surface elevation-undamaged road surface elevation = y A1 -y A0 (4)
At the moment, if the delta y is a negative value, the damaged road surface elevation is lower than the undamaged road surface elevation; and when the delta y is a positive value, the damaged road surface elevation is higher than the undamaged road surface elevation. The calculation method of A1 elevation and A0 elevation is that y is calculated in the above formula (1) A0 The parts of (a), namely:
y A0 ＝r(1-cost) (5)
and calculating the distance data of the positions of the damaged singular points, namely bi, on the damaged route L1 and the corresponding height difference with the A0 motion track on the undamaged standard road surface. The data are summarized in table 2:
TABLE 2 summary of elevation difference data for A1 and A0
As is clear from table 2, taking L1 as an example, there are 16 road surface damages in a section of 60cm to 135cm from the origin of R.
Claims (4)
1. A road surface damage detection method based on an epicycloid model is characterized by comprising the following steps:
(1) Constructing an epicycloid model: setting a circle O, wherein r is the radius of the circle O, and t is the angle swept by the radius when the circle O moves; r is a point on the circle, and when the circle O rolls towards the fixed direction along the straight line L0 for the distance of the circumference, the point R on the circle O moves out of a section of track A0 in the process, which is called as an arch; the position relation between the circle O and the point R on the circle O is a standard epicycloid model;
establishing a plane rectangular coordinate system by taking the initial position of the point R as an origin and the L0 as an X axis, and regarding the mathematical expression of the track A0 drawn by the plane rectangular coordinate system, namely the coordinate (X) of each point on the A0 A0 ，y A0 ) The way in which the parametric equations are used is expressed as:
wherein x is A0 y A0 Rolling a circle O by a perimeter, wherein in the process of rotating the angle from 0 to 2 pi, a point R on the circle moves to the spatial position of one arch; r is the radius of the circle O, t is the angle of rotation of the circle O, t ranges from [0:2 pi]To (c) to (d);
(2) The route of the circle O in the standard epicycloid model for completing one arch is L0, and the motion trail of a point R on the circle is A0;
(3) For the road section to be detected with damage, the movement route of the circle O is marked as L1, and the epicycloid track of R on the L1 is A1;
(4) At the same angle ti, compare the spatial positions of the R points in A1 and A0 (x) A1 ，y A1 ) And (x) A0 ，y A0 ) The difference in data is denoted as a breakage point bi; recording the rotation angle ti of the circle O at the moment, wherein i is a positive integer;
(5) Calculating the distance positions between all the damaged points bi and the original point, and marking the distance positions on L1; comparing the elevation data of A0 with the elevation data of A1;
(6) And (5) re-selecting a route on the residual damaged road surface, marking the route as L2, and repeating the steps (3) to (5) until all the road surface areas are measured.
2. The epicycloidal-model-based road surface damage detection method according to claim 1, wherein the coordinate x of the point on A0 in step (2) is A0 ，y A0 The relationship between them is:
coordinates (x) of point R A0 ，y A0 ) Is dependent only on the radius of the circle O and on the angle t over which the circle turns, and not on other factors.
3. The epicycloidal-model-based road surface damage detection method according to claim 1, wherein the distance di between the damage point bi and the origin in step (5) is:
di＝ti×r(3)
wherein di is the distance between the damaged point bi and the origin, ti is the rotation angle of the circle O corresponding to the damaged point, and i is a positive integer.
4. The epicycloid model-based road surface damage detection method according to claim 1, wherein the comparing of the elevation data of A0 with the elevation data of A1 in step (5) is performed as follows:
subtracting the A1 elevation from the A0 elevation to obtain the elevation difference of the damaged part:
Δ y = damaged road surface elevation-undamaged road surface elevation = y A1 -y A0 ；
Wherein, when the value of the delta y is a negative value, the elevation of the damaged road surface is lower than that of the undamaged road surface; if the delta y is a positive value, the elevation of the damaged road surface is higher than that of the undamaged road surface; the A0 elevation refers to the altitude of each point on the track A0 moved by the point R on the L0 to the horizontal ground; the elevation of A1 refers to the poster height of each point on the track A0 moved by the point R on L1 to the horizontal ground.
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