CN114740010A - Intelligent monitoring method for pavement diseases - Google Patents

Intelligent monitoring method for pavement diseases Download PDF

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CN114740010A
CN114740010A CN202210387506.7A CN202210387506A CN114740010A CN 114740010 A CN114740010 A CN 114740010A CN 202210387506 A CN202210387506 A CN 202210387506A CN 114740010 A CN114740010 A CN 114740010A
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control module
central control
distance
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CN114740010B (en
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刘玉庆
乔君磊
李建威
查杰
张亚峰
王树林
张昕
田宇
孙晓剑
石云飞
何亚楼
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/84Systems specially adapted for particular applications
    • G01N21/88Investigating the presence of flaws or contamination
    • G01N21/8851Scan or image signal processing specially adapted therefor, e.g. for scan signal adjustment, for detecting different kinds of defects, for compensating for structures, markings, edges
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/30Measuring arrangements characterised by the use of optical techniques for measuring roughness or irregularity of surfaces
    • G01B11/303Measuring arrangements characterised by the use of optical techniques for measuring roughness or irregularity of surfaces using photoelectric detection means
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S17/00Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
    • G01S17/02Systems using the reflection of electromagnetic waves other than radio waves
    • G01S17/06Systems determining position data of a target
    • G01S17/08Systems determining position data of a target for measuring distance only
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/01Arrangements or apparatus for facilitating the optical investigation
    • G01N2021/0106General arrangement of respective parts
    • G01N2021/0112Apparatus in one mechanical, optical or electronic block

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Abstract

The invention relates to an intelligent monitoring method for pavement diseases, which relates to the technical field of pavement disease monitoring and comprises the following steps: step S1, performing laser beam distribution ranging on the road section to be detected to generate a distance displacement curve; step S2, establishing a standard reference function according to the distance displacement curve, and judging whether cracks, bulges and subsidence appear on the road surface; step S3, carrying out image analysis on the distance displacement curve and a standard reference function, and judging the crack direction; in step S4, when it is determined that no crack, protrusion, or depression has occurred, the flatness and roughness of the road surface to be detected are determined. The movable laser ranging device is arranged to carry out laser scanning on the road surface, so that laser rays can be irradiated into tiny cracks, the distance displacement curve is generated and analyzed by the central control module, tiny cracks on the surface of the road surface can be rapidly detected, pavement diseases such as protrusion and sinking are not obvious, real-time monitoring on the road is realized, and the safety of the road is guaranteed.

Description

Intelligent monitoring method for pavement diseases
Technical Field
The invention relates to the technical field of pavement disease monitoring, in particular to an intelligent pavement disease monitoring method.
Background
Whether the cement pavement or the asphalt pavement is used for a period of time after the vehicle is opened, the cement pavement or the asphalt pavement can be damaged, deformed or have other defects, the defects are called as pavement diseases, the defects existing on the pavement are timely maintained and treated, the pavement is ensured to be smooth so as to ensure the stable and safe running of vehicles, and therefore, the pavement diseases are timely found, and the intelligent automatic monitoring of the pavement diseases of the highway has extremely important significance.
However, in the existing intelligent road surface monitoring method, image acquisition and analysis are mostly adopted, and prediction and analysis are carried out in a deep self-learning mode, so that tiny cracks of the road surface, unobvious road surface protrusions and road surface subsidence cannot be detected, and the intelligent road surface monitoring cannot meet the actual monitoring requirement and the safety guarantee effect.
Disclosure of Invention
Therefore, the invention provides an intelligent monitoring method for road surface diseases, which is used for overcoming the problems that fine cracks and unobvious road surface protrusions and road surface depressions of a road surface cannot be detected in the prior art.
In order to achieve the above object, the present invention provides an intelligent monitoring method for road surface diseases, comprising:
step S1, placing special road detection equipment in the transverse direction of a road section to be detected, performing laser distribution ranging on the road section to be detected at an initial detection angle through a laser ranging device arranged in the special road detection equipment, wherein the laser ranging device can move in the special road detection equipment, performing continuous ranging on the transverse direction of the road section to be detected through moving the laser ranging device, and a central control module is arranged in the special road detection equipment and generates a distance displacement curve of the initial detection angle according to the laser detection distance and the transverse displacement of the laser ranging device;
step S2, the central control module generates a linear function according to two end points of the distance displacement curve and establishes the linear function as a standard reference function of the distance displacement curve, the central control module compares the distance displacement curve with the standard reference function and calculates a real-time detection distance difference, and the central control module compares the real-time detection distance difference with an internally set standard distance difference so as to judge whether cracks, bulges and subsides appear in the transverse direction of the road surface;
step S3, when the central control module judges that the real-time detection distance difference exceeds the standard distance difference, the central control module obtains two image relations of a distance displacement curve and a standard reference function, obtains the real-time out-of-tolerance displacement of a continuous part of which the real-time detection distance difference exceeds the standard distance difference, compares the real-time out-of-tolerance displacement with the standard crack displacement, judges that the ground to be detected has longitudinal cracks, transverse cracks or subsidence, and carries out longitudinal continuous distance measurement on the transverse displacement position corresponding to the middle point of the real-time out-of-tolerance displacement by adjusting the initial detection angle of the laser distance measuring device so as to distinguish the subsidence and the transverse cracks of the ground to be detected;
and step S4, when the central control module judges that the real-time detection distance difference does not exceed the standard distance difference, the central control module analyzes the distance displacement curve image, and judges that the road surface to be detected is a flat road surface, a rough road surface or an uneven road surface according to the adjacent extreme value displacement between the quantity of the extreme value part and the two extreme values in the distance displacement curve.
Furthermore, an initial detection angle Kc is arranged in the central control module, the laser ranging device continuously ranges the distance in the transverse direction of the road section to be detected by using the initial detection angle Kc, the central control module generates a distance displacement curve f (X) ═ L, X ∈ [0, W ] of the initial detection angle according to the laser detection distance L and the transverse displacement X of the laser ranging device, wherein W is the width of the road surface to be detected, the central control module obtains the laser detection distance La at X ═ 0 and the laser detection distance Lz at X ═ W from the curve f (X) ═ L, and generates a linear function f (M) according to the laser detection distances La and Lz, wherein M ∈ [0, W ], the linear function f (M) passes through two points (0, La) and (W, Lz), and the central control module establishes the linear function f (M) as a standard reference function.
Furthermore, the central control module is provided with a standard distance difference Δ Lb, the central control module compares the distance displacement curve f (x) ═ L of the initial detection angle Kc with a standard reference function f (m) by an image, calculates the real-time detection distance difference Δ Lc on any lateral displacement according to the image and the distance displacement curve f (x) ═ L with the standard reference function f (m), compares the real-time detection distance difference Δ Lc with the standard distance difference Δ Lb,
when the delta Lc is less than or equal to the delta Lb, the central control module judges that the real-time detection distance difference does not exceed the standard distance difference, the central control module judges that cracks, bulges and subsidence do not occur in the transverse direction of the road surface detected by the initial detection angle Kc, and the central control module judges the flatness of the road section to be detected according to the distance displacement curve f (X) which is L;
when the distance Δ Lc is larger than the distance Δ Lb, the central control module determines that the real-time detection distance difference exceeds the standard distance difference, and the central control module determines what kind of diseases exist on the road surface to be detected according to the relationship between the distance displacement curve f (x) L and the standard reference function f (m).
Further, when the central control module determines that the real-time detection distance difference exceeds the standard distance difference, the central control module obtains a two-image relationship between the distance displacement curve f (x) ═ L and the standard reference function f (m) at the real-time detection distance difference Δ Lc,
when the distance displacement curve f (X) is higher than the standard reference function f (M), the central control module judges that the detection distance of the road surface to be detected at the position with the real-time detection distance difference of delta Lc is increased and exceeds the standard distance difference range, and the central control module judges that the road surface to be detected sinks or cracks appear according to the continuous transverse displacement exceeding the standard distance difference range;
when the distance displacement curve f (x) ═ L is lower than the standard reference function f (m), the central control module determines that the detected distance of the road surface to be detected at the position with the real-time detection distance difference Δ Lc is reduced and exceeds the standard distance difference range, and the central control module determines that the position with the real-time detection distance difference Δ Lc is a protruded road surface.
Furthermore, a standard crack displacement Xb is arranged in the central control module, when the central control module judges that the detection distance of the road surface to be detected with the real-time detection distance difference of delta Lc is increased and exceeds the standard distance difference range, the central control module obtains continuous real-time out-of-tolerance displacement Xs with the real-time detection distance difference exceeding the standard distance difference from a distance displacement curve f (X) L image, the central control module compares the real-time out-of-tolerance displacement Xs with the standard crack displacement Xb,
when Xs is less than or equal to Xb, the central control module judges that the real-time out-of-tolerance displacement does not exceed the standard crack displacement, and the central control module judges that the pavement to be detected has cracks in the real-time out-of-tolerance displacement Xs and judges that the pavement to be detected has longitudinal cracks;
and when Xs is larger than Xb, the central control module judges that the real-time out-of-tolerance displacement exceeds the standard crack displacement, and the central control module controls the laser ranging device to longitudinally and continuously range the real-time out-of-tolerance displacement Xs so as to judge that sinking or transverse cracks occur at the real-time out-of-tolerance displacement Xs.
Further, when the central control module judges that the real-time out-of-tolerance displacement exceeds the standard crack displacement, the central control module carries out longitudinal continuous distance measurement on the transverse displacement position corresponding to the midpoint of the real-time out-of-tolerance displacement Xs by adjusting the initial detection angle of the laser distance measuring device, a longitudinal distance displacement curve is generated according to the longitudinal displacement of the laser distance measurement detection point on the road surface and the laser detection distance, the central control module repeats the operation of establishing a standard reference function and comparing the standard distance difference, and determines the longitudinal real-time out-of-tolerance displacement Ys, the central control module compares the longitudinal real-time out-of-tolerance displacement Ys with the standard crack displacement Xb,
when Ys is less than or equal to Xb, the central control module judges that the longitudinal real-time out-of-tolerance displacement does not exceed the standard crack displacement, and the central control module judges that a transverse crack appears at the real-time out-of-tolerance displacement Xs;
and when Ys is larger than Xb, the central control module judges that the longitudinal real-time out-of-tolerance displacement exceeds the standard crack displacement, and the central control module judges that the road surface subsides appear at the real-time out-of-tolerance displacement Xs.
Furthermore, a standard flat extreme number Tb is arranged in the central control module, when the central control module determines that the real-time detection distance difference in the distance displacement curve f (X) L does not exceed the standard distance difference, the central control module detects the real-time extreme number Ts in the distance displacement curve f (X) L image, the central control module compares the real-time extreme number Ts with the standard flat extreme number Tb,
when Ts is less than or equal to Tb, the central control module judges that the real-time extreme number does not exceed the standard leveling extreme number, and the central control module judges that the road surface detected by the initial detection angle Kc is a leveling road surface transversely;
and when Ts is larger than Tb, the central control module judges that the real-time extreme value number exceeds the standard leveling extreme value number, and the central control module performs leveling judgment on the road section to be detected according to the displacement between the two extreme values in the distance displacement curve f (X) and L.
Furthermore, a rough extreme value standard displacement Xp and a rough extreme value standard displacement difference Δ Xp are arranged in the central control module, when the central control module determines that the real-time extreme value number exceeds the standard flat extreme value number, the central control module obtains an adjacent extreme value displacement Xj between any two adjacent extreme values in a distance displacement curve f (x) ═ L, the central control module calculates an adjacent extreme value displacement difference Δ Xj according to the adjacent extreme value displacement Xj and the rough extreme value standard displacement Xp, the Δ Xj ═ Xp-Xj |, the central control module compares the adjacent extreme value displacement difference Δ Xj with the rough extreme value standard displacement difference Δ Xp,
when the delta Xj is less than or equal to the delta Xp, the central control module judges that the displacement difference of the adjacent extreme values is within the standard displacement difference range of the rough extreme values, and the central control module judges that the position of the displacement Xj of the adjacent extreme values of the road surface to be detected is the rough road surface;
and when the delta Xj is larger than the delta Xp, the central control module judges that the adjacent extreme value displacement difference is not in the range of the rough extreme value standard displacement difference, and the central control module judges the road state according to the adjacent extreme value displacement and the rough extreme value standard displacement.
Further, when the central control module determines that the adjacent extreme value displacement difference is not within the range of the rough extreme value standard displacement difference, the central control module compares the adjacent extreme value displacement Xj with the rough extreme value standard displacement Xp,
when Xj is larger than Xp, the central control module judges that the displacement of the adjacent extreme value is higher than the standard displacement of the rough extreme value, and the central control module judges that the position of the displacement Xj of the adjacent extreme value of the road surface to be detected is an uneven road surface;
and when Xj is less than Xp, the central control module judges that the displacement of the adjacent extreme value is lower than the standard displacement of the rough extreme value, and the central control module judges that the position of the displacement Xj of the adjacent extreme value of the road surface to be detected is a flat road surface.
Furthermore, when the laser ranging device carries out longitudinal continuous ranging, the central control module can set unit ranging displacement Xo, continuously measuring the distance at the transverse displacement position corresponding to the real-time out-of-tolerance displacement Xs for R times by transversely moving the laser distance measuring device Xo displacement every time to generate R groups of longitudinal distance displacement curves, wherein, R is Xs/Xo, the central control module repeats the operations of establishing the standard reference function and comparing the standard distance difference and determining the longitudinal real-time out-of-tolerance displacement, and for the R groups of longitudinal distance displacement curves, respectively calculating corresponding longitudinal real-time out-of-tolerance displacements Y1, Y2 and Y3 … YR, and calculating the area Sy of the pavement crack or subsidence by the central control module according to the longitudinal real-time out-of-tolerance displacement and the unit distance measurement displacement Xo of the R groups of longitudinal distance displacement curves, wherein the Sy is (Y1 Xo) + (Y2 XO) + (Y3 Xo) … (YR XO).
Compared with the prior art, the invention has the advantages that by arranging the special road detection equipment and arranging the movable laser ranging device in the special road detection equipment, the laser scanning is carried out on the road surface to be detected by utilizing the laser ranging device, the laser rays can be easily irradiated into tiny cracks on the surface of the road surface, the laser irradiation distance is analyzed by arranging the central control module, the tiny cracks on the surface of the road surface can be detected, the depth of the cracks can be directly obtained, the crack area can be calculated by the central control module, simultaneously, the distance of the laser scanning of the road surface to be detected by utilizing the central control module and the laser ranging device generates a distance displacement curve, the distance displacement curve is analyzed, the road surface diseases such as the protrusion and the sinking of the surface of the road surface can be rapidly judged, and the more fine analysis and judgment can be carried out on the distance displacement curve, the method comprises the steps of determining the flatness and roughness of the surface of a road to be detected, realizing timely detection of tiny cracks and unobvious road surface protrusions and road surface depressions of the road surface, and meanwhile, realizing real-time monitoring of road diseases by the aid of special road detection equipment arranged above the road surface, such as a traffic control post or a red road lamp, and guaranteeing real-time safety of the road.
Furthermore, the standard reference function can be quickly established on different distance displacement curves by acquiring the distance values of two end points of the road section to be detected in the transverse direction and establishing the standard reference function according to the distance values of the two end points, the reference is more accurate when the distance displacement curves are compared and judged, meanwhile, the standard reference function in the form of the straight line function is established at the two ends of the road surface to be detected, errors caused by detection of road surface diseases by specific inclined road surfaces can be effectively avoided, and normal detection of the road surface diseases is guaranteed.
Especially, through being equipped with the standard distance difference in the central control module, calculate the real-time detection distance difference of distance displacement curve and standard reference function on arbitrary lateral displacement, compare standard distance difference and real-time detection distance difference, judge the disease condition on the road surface of waiting to detect, real-time detection distance difference can be more meticulous demonstrate unsmooth state, can also reduce or increase through standard distance difference simultaneously, judge the crackle of the different degree of depth, realize road surface disease intelligent monitoring's adjustable.
Further, when the central control module judges that the real-time detection distance difference exceeds the standard distance difference, the relationship between the distance displacement curve and the standard reference function is judged, when the distance displacement curve is higher than the standard reference function, the fact that the detection distance is increased and the ground is sunk or cracked is shown, when the distance displacement curve is lower than the standard reference function, the fact that the detection distance is reduced and the detection ground surface is raised is shown, and initial judgment of the road surface damage is rapidly achieved.
Furthermore, when the central control module judges that the detection distance of the road surface to be detected is increased and exceeds the standard distance difference range, the central control module judges that the road surface has sinking or cracks, because one transverse direction of the road surface is detected in the detection, the difference between the transverse cracks and the sinking cannot be judged, and through setting the standard crack displacement, the longitudinal cracks are quickly judged on the basis of the width of the cracks, so that the efficiency of detecting and judging the road surface diseases is improved.
Furthermore, when the central control module judges that the real-time out-of-tolerance displacement exceeds the standard crack displacement, the central control module cannot judge whether the position is a transverse crack or a ground sinking, longitudinal distance measurement is carried out on a road surface to be detected at the same displacement by controlling the detection angle of the laser distance measuring device, a longitudinal distance displacement curve is generated, the real-time road surface damage condition is judged, the sinking, the protrusion and the crack of the road surface are judged, the crack direction can be determined, the analysis and the judgment on the tiny crack can be realized, and the intelligent monitoring precision of the road surface damage is improved.
Further, when the central control module determines that the real-time detection distance difference in the distance displacement curve does not exceed the standard distance difference, the fact that the road surface has no crack, protrusion or sinking defect in the detection of the transverse position is indicated, the central control module obtains a curve extreme value in the distance displacement curve, wherein the curve extreme value represents the fine concave-convex condition of the road surface, and whether the road surface is a flat road surface is determined according to the number of the determined curve extreme values, so that intelligent disease monitoring of the road surface is achieved.
Particularly, the displacement between any two extreme values in the distance displacement curve is judged, the displacement between the two extreme values can show the roughness of the road surface, whether the road surface to be detected is the rough road surface at the position of the adjacent extreme value displacement is judged by setting the standard displacement difference of the rough extreme values and comparing the calculated adjacent extreme value displacement difference with the calculated adjacent extreme value displacement difference, and when the central control module judges that the adjacent extreme value displacement difference is not in the range of the standard displacement difference of the rough extreme values, the central control module judges the adjacent extreme value displacement and the standard displacement of the rough extreme values so as to ensure the normal monitoring of the intelligent diseases of the road surface.
Furthermore, when the central control module judges that the displacement difference of the adjacent extreme values is not within the standard displacement difference range of the rough extreme values, the displacement of the adjacent extreme values is compared with the standard displacement of the rough extreme values, the displacement of the adjacent extreme values is higher than the standard displacement of the rough extreme values, and the distance between the two extreme values in the curve is far, because the number of the extreme values in the curve is large, the central control module judges that the monitored position is an uneven road surface, the displacement of the adjacent extreme values is lower than the standard displacement of the rough extreme values, and the distance between the two extreme values in the curve is close, and the monitored position is a smooth road surface.
Particularly, when the laser ranging device carries out longitudinal continuous ranging, unit ranging displacement is arranged in the central control module, longitudinal continuous ranging is carried out once when the laser ranging device moves the unit ranging displacement, a plurality of longitudinal distance displacement curves are generated, longitudinal real-time out-of-tolerance displacement of each curve is determined according to a crack characteristic determination method, the area of a pavement crack or subsidence is calculated according to the longitudinal real-time out-of-tolerance displacement and the unit ranging displacement, the depth determination of pavement diseases is realized, the real-time monitoring of the pavement diseases is realized, and the real-time safety of the pavement is guaranteed.
Drawings
Fig. 1 is a flowchart of an intelligent monitoring method for a road surface disease according to this embodiment.
Detailed Description
In order that the objects and advantages of the invention will be more clearly understood, the invention is further described below with reference to examples; it should be understood that the specific embodiments described herein are merely illustrative of the invention and do not delimit the invention.
Preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only for explaining the technical principle of the present invention, and do not limit the scope of the present invention.
It should be noted that in the description of the present invention, the terms of direction or positional relationship indicated by the terms "upper", "lower", "left", "right", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, which are only for convenience of description, and do not indicate or imply that the device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention.
Furthermore, it should be noted that, in the description of the present invention, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
Referring to fig. 1, which is a flowchart illustrating an intelligent monitoring method for a road surface defect according to the present embodiment, the present embodiment discloses an intelligent monitoring method for a road surface defect, including:
step S1, placing special road detection equipment in the transverse direction of a road section to be detected, performing laser distribution ranging on the road section to be detected at an initial detection angle through a laser ranging device arranged in the special road detection equipment, wherein the laser ranging device can move in the special road detection equipment, performing continuous ranging on the transverse direction of the road section to be detected through moving the laser ranging device, and a central control module is arranged in the special road detection equipment and generates a distance displacement curve of the initial detection angle according to the laser detection distance and the transverse displacement of the laser ranging device;
step S2, the central control module generates a straight line function according to two end points of the distance displacement curve and establishes the straight line function as a standard reference function of the distance displacement curve, the central control module performs image comparison on the distance displacement curve and the standard reference function and calculates a real-time detection distance difference, and the central control module compares the real-time detection distance difference with an internally set standard distance difference so as to judge whether cracks, bulges and subsidence appear in the transverse direction of the road surface;
step S3, when the central control module judges that the real-time detection distance difference exceeds the standard distance difference, the central control module obtains two image relations of a distance displacement curve and a standard reference function, obtains the real-time out-of-tolerance displacement of a continuous part of which the real-time detection distance difference exceeds the standard distance difference, compares the real-time out-of-tolerance displacement with the standard crack displacement, judges that the ground to be detected has longitudinal cracks, transverse cracks or subsidence, and carries out longitudinal continuous distance measurement on the transverse displacement position corresponding to the middle point of the real-time out-of-tolerance displacement by adjusting the initial detection angle of the laser distance measuring device so as to distinguish the subsidence and the transverse cracks of the ground to be detected;
and step S4, when the central control module judges that the real-time detection distance difference does not exceed the standard distance difference, the central control module analyzes the distance displacement curve image, and judges that the road surface to be detected is a flat road surface, a rough road surface or an uneven road surface according to the adjacent extreme value displacement between the quantity of the extreme value part and the two extreme values in the distance displacement curve.
By arranging the special road detection equipment and arranging the movable laser ranging device in the special road detection equipment, the laser ranging device is utilized to carry out laser scanning on the road surface to be detected, laser rays can be easily irradiated into tiny cracks on the surface of the road surface, the laser irradiation distance is analyzed by arranging the central control module, the tiny cracks on the surface of the road surface can be detected, the depth of the cracks can be directly obtained, the crack area can be calculated by the central control module, simultaneously, the distance of the laser scanning on the road surface to be detected by the central control module and the laser ranging device is utilized to generate a distance displacement curve, the distance displacement curve is analyzed, the road surface diseases such as the protrusion and the sinking of the surface of the road surface can be rapidly judged, and the more subtle analysis and judgment can be carried out on the distance displacement curve to determine the leveling condition and the roughness condition of the surface of the road surface to be detected, the realization is protruding and the in time detection of road surface subsides to the tiny crack and the obscure road surface of highway road surface, and simultaneously, special way check equipment also can be through setting up in road surface top for example restricted driving pole or red street lamp position, realizes the real-time supervision to the road disease, ensures the real-time security of road.
Specifically, an initial detection angle Kc is arranged in the central control module, the laser ranging device continuously ranges the distance in the transverse direction of the road to be detected by the initial detection angle Kc, the central control module generates a distance displacement curve f (X) ═ L, X ∈ [0, W ], of the initial detection angle according to the laser detection distance L and the transverse displacement X of the laser ranging device, wherein W is the width of the road to be detected, the central control module acquires the laser detection distance La at X ═ 0 and the laser detection distance Lz at X ═ W from the curve f (X) ═ L, and generates a straight line function f (M), M ∈ [0, W ], according to the laser detection distances La and Lz, the central control module passes through two points (0, La) and (W, Lz), and the central control module establishes the straight line function f (M) as a standard reference function.
The distance values of two end points of the road section to be detected in the transverse direction are obtained, the standard reference function is established according to the distance values of the two end points, the standard reference function can be quickly established on different distance displacement curves, the reference is more accurate when the distance displacement curves are contrasted and judged, meanwhile, the standard reference function in the form of a linear function is established at the two ends of the road surface to be detected, errors caused by detection of road surface diseases by specific inclined road surfaces can be effectively avoided, and normal detection of the road surface diseases is guaranteed.
Specifically, the central control module is provided with a standard distance difference Δ Lb, the central control module compares a distance displacement curve f (x) L of an initial detection angle Kc with a standard reference function f (m) by an image, calculates a real-time detection distance difference Δ Lc between the distance displacement curve f (x) L and the standard reference function f (m) on any horizontal displacement according to the image, compares the real-time detection distance difference Δ Lc with the standard distance difference Δ Lb,
when the delta Lc is less than or equal to the delta Lb, the central control module judges that the real-time detection distance difference does not exceed the standard distance difference, the central control module judges that cracks, bulges and subsidence do not occur in the transverse direction of the road surface detected by the initial detection angle Kc, and the central control module judges the flatness of the road section to be detected according to the distance displacement curve f (X) which is equal to L;
when the distance Δ Lc is larger than the distance Δ Lb, the central control module determines that the real-time detection distance difference exceeds the standard distance difference, and the central control module determines what kind of diseases exist on the road surface to be detected according to the relationship between the distance displacement curve f (x) L and the standard reference function f (m).
Through being equipped with standard distance difference in well accuse module, calculate the real-time detection distance difference of distance displacement curve and standard reference function on arbitrary lateral displacement, compare standard distance difference and real-time detection distance difference, judge the disease condition on wait to detect the road surface, real-time detection distance difference can be more meticulous demonstrate unsmooth state, can also reduce or increase through being poor to standard distance simultaneously, judge the crackle of the different degree of depth, realize road surface disease intelligent monitoring's adjustable.
Specifically, when the central control module determines that the real-time detection distance difference exceeds the standard distance difference, the central control module obtains a two-image relationship between the distance displacement curve f (x) ═ L and the standard reference function f (m) at the real-time detection distance difference Δ Lc,
when the distance displacement curve f (X) is higher than the standard reference function f (M), the central control module judges that the detection distance of the road surface to be detected at the position with the real-time detection distance difference of delta Lc is increased and exceeds the standard distance difference range, and the central control module judges that the road surface to be detected sinks or cracks according to continuous transverse displacement exceeding the standard distance difference range;
when the distance displacement curve f (x) ═ L is lower than the standard reference function f (m), the central control module determines that the detected distance of the road surface to be detected at the position with the real-time detection distance difference of Δ Lc is reduced and exceeds the standard distance difference range, and the central control module determines that the position with the real-time detection distance difference of Δ Lc is a protruded road surface.
When the central control module judges that the real-time detection distance difference exceeds the standard distance difference, the relationship between the distance displacement curve and the standard reference function is judged, when the distance displacement curve is higher than the standard reference function, the fact that the detection distance is increased and the ground is sunk or cracked is indicated, when the distance displacement curve is lower than the standard reference function, the fact that the detection distance is reduced and the detection ground surface is raised is indicated, and the initial judgment of the road surface damage is rapidly achieved.
Specifically, a standard crack displacement Xb is arranged in the central control module, when the central control module determines that the detection distance of the road surface to be detected at the position with the real-time detection distance difference of delta Lc is increased and exceeds the standard distance difference range, the central control module acquires continuous real-time out-of-tolerance displacement Xs of the part with the real-time detection distance difference exceeding the standard distance difference from a distance displacement curve f (X) L, and compares the real-time out-of-tolerance displacement Xs with the standard crack displacement Xb,
when Xs is less than or equal to Xb, the central control module judges that the real-time out-of-tolerance displacement does not exceed the standard crack displacement, and the central control module judges that the pavement to be detected has cracks in the real-time out-of-tolerance displacement Xs and judges that the pavement to be detected has longitudinal cracks;
and when Xs is larger than Xb, the central control module judges that the real-time out-of-tolerance displacement exceeds the standard crack displacement, and the central control module controls the laser ranging device to longitudinally and continuously range the real-time out-of-tolerance displacement Xs so as to judge that sinking or transverse cracks occur at the real-time out-of-tolerance displacement Xs.
When the central control module judges that the detection distance of the pavement to be detected is increased and exceeds the standard distance difference range, the central control module judges that the pavement is sunken or cracked, because the detection is carried out on one transverse direction of the pavement, the difference between the transverse crack and the sunken pavement can not be judged, through setting the standard crack displacement and taking the width of the crack as the basis, the longitudinal crack is quickly judged, and the efficiency of detecting and judging the pavement diseases is increased.
Specifically, when the central control module judges that the real-time out-of-tolerance displacement exceeds the standard crack displacement, the central control module carries out longitudinal continuous distance measurement on a transverse displacement position corresponding to the midpoint of the real-time out-of-tolerance displacement Xs by adjusting the initial detection angle of the laser distance measuring device, a longitudinal distance displacement curve is generated according to the longitudinal displacement of a laser distance measurement detection point on the road surface and the laser detection distance, the central control module repeats the operation of establishing a standard reference function and comparing the standard reference function with the standard distance difference and determines the longitudinal real-time out-of-tolerance displacement Ys, the central control module compares the longitudinal real-time out-of-tolerance displacement Ys with the standard crack displacement Xb,
when Ys is less than or equal to Xb, the central control module judges that the longitudinal real-time out-of-tolerance displacement does not exceed the standard crack displacement, and the central control module judges that a transverse crack appears at the real-time out-of-tolerance displacement Xs;
and when Ys is larger than Xb, the central control module judges that the longitudinal real-time out-of-tolerance displacement exceeds the standard crack displacement, and the central control module judges that the road surface subsides appear at the real-time out-of-tolerance displacement Xs.
When the central control module judges that the real-time out-of-tolerance displacement exceeds the standard crack displacement, the central control module cannot judge whether the position is a transverse crack or a ground sinking, longitudinal distance measurement is carried out on a road surface to be detected at the same displacement by controlling the detection angle of the laser distance measuring device, a longitudinal distance displacement curve is generated, the real-time road surface damage condition is judged, the sinking, the protrusion and the crack of the road surface are judged, the crack direction can be determined, the analysis and the judgment on the tiny crack can be realized, and the intelligent monitoring precision of the road surface damage is improved.
Specifically, a standard flat extreme number Tb is set in the central control module, when the central control module determines that the real-time detection distance difference in the distance displacement curve f (x) L does not exceed the standard distance difference, the central control module detects the real-time extreme number Ts in the distance displacement curve f (x) L image, the central control module compares the real-time extreme number Ts with the standard flat extreme number Tb,
when Ts is less than or equal to Tb, the central control module judges that the real-time extreme number does not exceed the standard leveling extreme number, and the central control module judges that the pavement detected by the initial detection angle Kc is a leveled pavement transversely;
when Ts is larger than Tb, the central control module judges that the real-time extreme value number exceeds the standard flat extreme value number, and the central control module carries out flat judgment on the road section to be detected according to the displacement between two extreme values in the distance displacement curve f (X) L.
When the central control module determines that the real-time detection distance difference in the distance displacement curve does not exceed the standard distance difference, the defect that cracks, bulges and depressions do not occur in the detection of the transverse position of the road surface is indicated, the central control module acquires a curve extreme value in the distance displacement curve, wherein the curve extreme value represents the fine concave-convex condition of the road surface, and whether the road surface is a smooth road surface is determined according to the number of the determined curve extreme values, so that the intelligent disease monitoring of the road surface is realized.
Specifically, the central control module is provided with a rough extreme value standard displacement Xp and a rough extreme value standard displacement difference Δ Xp, when the central control module determines that the real-time extreme value number exceeds the standard flat extreme value number, the central control module obtains an adjacent extreme value displacement Xj between any two adjacent extreme values in a distance displacement curve f (x) ═ L, the central control module calculates an adjacent extreme value displacement difference Δ Xj according to the adjacent extreme value displacement Xj and the rough extreme value standard displacement Xp, the Δ Xj ═ Xp-Xj |, the central control module compares the adjacent extreme value displacement difference Δ Xj with the rough extreme value standard displacement difference Δ Xp,
when the delta Xj is less than or equal to the delta Xp, the central control module judges that the displacement difference of the adjacent extreme values is within the standard displacement difference range of the rough extreme values, and the central control module judges that the position of the displacement Xj of the adjacent extreme values of the road surface to be detected is the rough road surface;
when the delta Xj is larger than the delta Xp, the central control module judges that the adjacent extreme value displacement difference is not in the range of the rough extreme value standard displacement difference, and the central control module judges the road state according to the adjacent extreme value displacement and the rough extreme value standard displacement.
Through judging the displacement between two arbitrary extremums in the distance displacement curve, the displacement between two extremums can show the roughness on road surface, through setting up the standard displacement difference of rough extremum, and compare the adjacent extremum displacement difference that calculates with it, judge whether the road surface of waiting to detect is rough road surface in adjacent extremum displacement department, when well accuse module judges that adjacent extremum displacement difference is not in the standard displacement difference range of rough extremum, well accuse module will judge adjacent extremum displacement and the standard displacement of rough extremum, in order to ensure the normal clear of road surface intelligent disease monitoring.
Specifically, when the central control module determines that the adjacent extreme value displacement difference is not within the rough extreme value standard displacement difference range, the central control module compares the adjacent extreme value displacement Xj with the rough extreme value standard displacement Xp,
when Xj is larger than Xp, the central control module judges that the displacement of the adjacent extreme value is higher than the standard displacement of the rough extreme value, and the central control module judges that the position of the displacement Xj of the adjacent extreme value of the road surface to be detected is an uneven road surface;
and when Xj is less than Xp, the central control module judges that the displacement of the adjacent extreme value is lower than the standard displacement of the rough extreme value, and the central control module judges that the position of the displacement Xj of the adjacent extreme value of the road surface to be detected is a flat road surface.
When the central control module judges that the displacement difference of the adjacent extreme values is not within the standard displacement difference range of the rough extreme values, the displacement of the adjacent extreme values is compared with the standard displacement of the rough extreme values, the displacement of the adjacent extreme values is higher than the standard displacement of the rough extreme values, the fact that the position distance of the two extreme values in the curve is far is shown, the number of the extreme values in the curve is large, the central control module judges that the monitored part is an uneven road surface, the displacement of the adjacent extreme values is lower than the standard displacement of the rough extreme values, the fact that the position distance of the two extreme values in the curve is near is shown, the monitored part is a smooth road surface is judged, more accurate judgment of the road surface smoothness condition is completed through analysis of curve characteristics, and the comprehensiveness of road disease monitoring is guaranteed.
Specifically, when the laser ranging device carries out longitudinal continuous ranging, the central control module can set a unit ranging displacement Xo, continuously measuring the distance at the transverse displacement position corresponding to the real-time out-of-tolerance displacement Xs for R times by transversely moving the laser distance measuring device Xo displacement every time to generate R groups of longitudinal distance displacement curves, wherein, R is Xs/Xo, the central control module repeats the operations of establishing the standard reference function and comparing the standard distance difference and determining the longitudinal real-time out-of-tolerance displacement, and for the R groups of longitudinal distance displacement curves, respectively calculating corresponding longitudinal real-time out-of-tolerance displacements Y1, Y2 and Y3 … YR, and calculating the area Sy of the pavement crack or subsidence by the central control module according to the longitudinal real-time out-of-tolerance displacement and the unit distance measurement displacement Xo of the R groups of longitudinal distance displacement curves, wherein the Sy is (Y1 Xo) + (Y2 XO) + (Y3 Xo) … (YR XO).
When the laser ranging device carries out longitudinal continuous ranging, unit ranging displacement is arranged in the central control module, longitudinal continuous ranging is carried out once when the laser ranging device moves the unit ranging displacement, a plurality of longitudinal distance displacement curves are generated, longitudinal real-time out-of-tolerance displacement of each curve is determined according to a crack characteristic determination method, the area of a pavement crack or subsidence is calculated according to the longitudinal real-time out-of-tolerance displacement and the unit ranging displacement, the depth determination of pavement diseases is realized, the real-time monitoring of the pavement diseases is realized, and the real-time safety of the pavement is guaranteed.
So far, the technical solutions of the present invention have been described in connection with the preferred embodiments shown in the drawings, but it is easily understood by those skilled in the art that the scope of the present invention is obviously not limited to these specific embodiments. Equivalent changes or substitutions of related technical features can be made by those skilled in the art without departing from the principle of the invention, and the technical scheme after the changes or substitutions can be within the protection scope of the invention.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention; various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. An intelligent monitoring method for pavement diseases is characterized by comprising the following steps:
step S1, placing special road detection equipment in the transverse direction of a road section to be detected, performing laser distribution ranging on the road section to be detected at an initial detection angle through a laser ranging device arranged in the special road detection equipment, wherein the laser ranging device can move in the special road detection equipment, performing continuous ranging on the transverse direction of the road section to be detected through moving the laser ranging device, and a central control module is arranged in the special road detection equipment and generates a distance displacement curve of the initial detection angle according to the laser detection distance and the transverse displacement of the laser ranging device;
step S2, the central control module generates a straight line function according to two end points of the distance displacement curve and establishes the straight line function as a standard reference function of the distance displacement curve, the central control module performs image comparison on the distance displacement curve and the standard reference function and calculates a real-time detection distance difference, and the central control module compares the real-time detection distance difference with an internally set standard distance difference so as to judge whether cracks, bulges and subsidence appear in the transverse direction of the road surface;
step S3, when the central control module judges that the real-time detection distance difference exceeds the standard distance difference, the central control module obtains two image relations of a distance displacement curve and a standard reference function, obtains the real-time out-of-tolerance displacement of a continuous part of which the real-time detection distance difference exceeds the standard distance difference, compares the real-time out-of-tolerance displacement with the standard crack displacement, judges that the ground to be detected has longitudinal cracks, transverse cracks or subsidence, and carries out longitudinal continuous distance measurement on the transverse displacement position corresponding to the middle point of the real-time out-of-tolerance displacement by adjusting the initial detection angle of the laser distance measuring device so as to distinguish the subsidence and the transverse cracks of the ground to be detected;
and step S4, when the central control module judges that the real-time detection distance difference does not exceed the standard distance difference, the central control module analyzes the distance displacement curve image, and judges that the road surface to be detected is a flat road surface, a rough road surface or an uneven road surface according to the adjacent extreme value displacement between the quantity of the extreme value part and the two extreme values in the distance displacement curve.
2. The intelligent monitoring method for road surface diseases according to claim 1, characterized in that an initial detection angle Kc is set in the central control module, the laser ranging device carries out continuous ranging on the transverse direction of a road section to be detected by using an initial detection angle Kc, the central control module generates a distance displacement curve f (X) L of the initial detection angle according to the laser detection distance L and the transverse displacement X of the laser ranging device, wherein X belongs to [0, W ], the central control module obtains a laser detection distance La at the position where X is 0 and a laser detection distance Lz at the position where X is W from a curve f (X) (L), generates a straight line function f (M) according to the laser detection distances La and Lz, wherein M belongs to [0, W ], the straight line function f (M) passes through two points of (0, La) and (W, Lz), and establishes the straight line function f (M) as a standard reference function.
3. The intelligent pavement damage monitoring method according to claim 2, wherein a standard distance difference Δ Lb is set in the central control module, the central control module compares the distance displacement curve f (x) ═ L of the initial detection angle Kc with a standard reference function f (m) by an image, calculates a real-time detection distance difference Δ Lc between the distance displacement curve f (x) ═ L and the standard reference function f (m) at any lateral displacement according to the image, compares the real-time detection distance difference Δ Lc with the standard distance difference Δ Lb,
when the delta Lc is less than or equal to the delta Lb, the central control module judges that the real-time detection distance difference does not exceed the standard distance difference, the central control module judges that cracks, bulges and subsidence do not occur in the transverse direction of the road surface detected by the initial detection angle Kc, and the central control module judges the flatness of the road section to be detected according to the distance displacement curve f (X) which is L;
when the distance Δ Lc is larger than the distance Δ Lb, the central control module determines that the real-time detection distance difference exceeds the standard distance difference, and the central control module determines what kind of diseases exist on the road surface to be detected according to the relationship between the distance displacement curve f (x) L and the standard reference function f (m).
4. The intelligent monitoring method for road surface diseases according to claim 3, characterized in that when the central control module determines that the real-time detection distance difference exceeds the standard distance difference, the central control module obtains the relationship between the distance displacement curve f (X) and the standard reference function f (M) at the position where the real-time detection distance difference is Δ Lc,
when the distance displacement curve f (X) is higher than the standard reference function f (M), the central control module judges that the detection distance of the road surface to be detected at the position with the real-time detection distance difference of delta Lc is increased and exceeds the standard distance difference range, and the central control module judges that the road surface to be detected sinks or cracks appear according to the continuous transverse displacement exceeding the standard distance difference range;
when the distance displacement curve f (x) ═ L is lower than the standard reference function f (m), the central control module determines that the detected distance of the road surface to be detected at the position with the real-time detection distance difference Δ Lc is reduced and exceeds the standard distance difference range, and the central control module determines that the position with the real-time detection distance difference Δ Lc is a protruded road surface.
5. The intelligent monitoring method for the pavement diseases according to claim 4, characterized in that a standard crack displacement Xb is set in the central control module, when the central control module determines that the detected distance of the pavement to be detected at the real-time detection distance difference Δ Lc increases and exceeds the standard distance difference range, the central control module obtains a continuous real-time out-of-tolerance displacement Xs of the portion where the real-time detection distance difference exceeds the standard distance difference in the distance displacement curve f (X) L image, the central control module compares the real-time out-of-tolerance displacement Xs with the standard crack displacement Xb,
when Xs is less than or equal to Xb, the central control module judges that the real-time out-of-tolerance displacement does not exceed the standard crack displacement, and the central control module judges that the pavement to be detected has cracks in the real-time out-of-tolerance displacement Xs and judges that the pavement to be detected has longitudinal cracks;
and when Xs is larger than Xb, the central control module judges that the real-time out-of-tolerance displacement exceeds the standard crack displacement, and the central control module controls the laser ranging device to longitudinally and continuously range the real-time out-of-tolerance displacement Xs so as to judge that sinking or transverse cracks occur at the real-time out-of-tolerance displacement Xs.
6. The intelligent pavement damage monitoring method according to claim 5, wherein when the central control module determines that the real-time out-of-tolerance displacement exceeds the standard crack displacement, the central control module performs continuous longitudinal distance measurement at the lateral displacement corresponding to the midpoint of the real-time out-of-tolerance displacement Xs by adjusting an initial detection angle of the laser distance measuring device, generates a longitudinal distance displacement curve according to the longitudinal displacement of the laser distance measurement detection point on the pavement and the laser detection distance, repeats the operation of establishing the standard reference function and comparing the standard distance difference, and determines the real-time longitudinal out-of-tolerance displacement Ys, and compares the real-time longitudinal out-of-tolerance displacement Ys with the standard crack displacement Xb,
when Ys is less than or equal to Xb, the central control module judges that the longitudinal real-time out-of-tolerance displacement does not exceed the standard crack displacement, and the central control module judges that a transverse crack appears at the real-time out-of-tolerance displacement Xs;
and when Ys is larger than Xb, the central control module judges that the longitudinal real-time out-of-tolerance displacement exceeds the standard crack displacement, and the central control module judges that the road surface subsides appear at the real-time out-of-tolerance displacement Xs.
7. The intelligent monitoring method for road surface diseases according to claim 3, characterized in that a standard flattening extreme number Tb is provided in the central control module, when the central control module determines that the real-time detection distance difference in the distance displacement curve f (X) L does not exceed the standard distance difference, the central control module detects the real-time extreme number Ts in the distance displacement curve f (X) L image, the central control module compares the real-time extreme number Ts with the standard flattening extreme number Tb,
when Ts is less than or equal to Tb, the central control module judges that the real-time extreme number does not exceed the standard leveling extreme number, and the central control module judges that the pavement detected by the initial detection angle Kc is a leveled pavement transversely;
when Ts is larger than Tb, the central control module judges that the real-time extreme value number exceeds the standard flat extreme value number, and the central control module carries out flat judgment on the road section to be detected according to the displacement between two extreme values in the distance displacement curve f (X) L.
8. The method according to claim 7, wherein the central control module has a rough extreme value standard displacement Xp and a rough extreme value standard displacement difference Δ Xp, and when the central control module determines that the real-time extreme value number exceeds the standard flat extreme value number, the central control module obtains an adjacent extreme value displacement Xj between any two adjacent extreme values in a deviation curve f (x) ═ L, the central control module calculates an adjacent extreme value displacement difference Δ Xj according to the adjacent extreme value displacement Xj and the rough extreme value standard displacement Xp, and the central control module compares the adjacent extreme value displacement difference Δ Xj with the rough extreme value standard displacement difference Δ Xp,
when the delta Xj is less than or equal to the delta Xp, the central control module judges that the displacement difference of the adjacent extreme values is within the standard displacement difference range of the rough extreme values, and the central control module judges that the position of the displacement Xj of the adjacent extreme values of the road surface to be detected is the rough road surface;
when the delta Xj is larger than the delta Xp, the central control module judges that the adjacent extreme value displacement difference is not in the range of the rough extreme value standard displacement difference, and the central control module judges the road state according to the adjacent extreme value displacement and the rough extreme value standard displacement.
9. The intelligent pavement damage monitoring method according to claim 8, wherein when the central control module determines that the adjacent extreme value displacement difference is not within the rough extreme value standard displacement difference range, the central control module compares the adjacent extreme value displacement Xj with the rough extreme value standard displacement Xp,
when Xj is larger than Xp, the central control module judges that the displacement of the adjacent extreme value is higher than the standard displacement of the rough extreme value, and the central control module judges that the position of the displacement Xj of the adjacent extreme value of the road surface to be detected is an uneven road surface;
and when Xj is less than Xp, the central control module judges that the displacement of the adjacent extreme value is lower than the standard displacement of the rough extreme value, and the central control module judges that the position of the displacement Xj of the adjacent extreme value of the road surface to be detected is a flat road surface.
10. The intelligent monitoring method for pavement diseases according to claim 6, when the laser ranging device carries out longitudinal continuous ranging, the central control module can set unit ranging displacement Xo, continuously measuring the distance at the transverse displacement position corresponding to the real-time out-of-tolerance displacement Xs for R times by transversely moving the laser distance measuring device Xo displacement every time to generate R groups of longitudinal distance displacement curves, wherein, R is Xs/Xo, the central control module repeats the operations of establishing the standard reference function and comparing the standard distance difference and determining the longitudinal real-time out-of-tolerance displacement, and for the R groups of longitudinal distance displacement curves, respectively calculating corresponding longitudinal real-time out-of-tolerance displacements Y1, Y2 and Y3 … YR, and calculating the area Sy of the pavement crack or subsidence by the central control module according to the longitudinal real-time out-of-tolerance displacement and the unit distance measurement displacement Xo of the R groups of longitudinal distance displacement curves, wherein the Sy is (Y1 Xo) + (Y2 XO) + (Y3 Xo) … (YR XO).
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