CN111709131B - Tunnel axis determination method and device - Google Patents
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Abstract
The application discloses a tunnel axis determining method and device, wherein the method comprises the following steps: determining an initial unit direction vector; the tunnel segment dividing unit is used for constructing a projection plane in the center of each unit; constructing a local coordinate system; determining projection points projected to a projection plane within a specified range as effective points; converting the geodetic coordinates of the effective points into local coordinates under a local coordinate system; fitting a circle on the projection plane by using the effective points of each unit, and determining the local coordinates of the circle center of the fitted circle; performing space straight line fitting on the circular center geodetic coordinates of all units of each segment to obtain a first axis; determining a first unit direction vector according to the first axis; determining a second axis and a second unit direction vector from the first unit direction vector; determining the deviation of the first and second unit direction vectors; and if the deviation is less than or equal to the deviation threshold value, determining the second axis as the tunnel axis of the section. The present application makes it possible to obtain a precise axis of the tunnel section.
Description
Technical Field
The application relates to the technical field of tunnel detection, in particular to a tunnel axis determining method and device.
Background
This section is intended to provide a background or context to the embodiments of the invention that are recited in the claims. The description herein is not admitted to be prior art by inclusion in this section.
The geometric information of the section of the tunnel structure is acquired, the state evaluation of the stress of the tunnel structure and the stability of the tunnel in the operation period is carried out regularly, and the service life and the safety of the tunnel structure can be improved. The tunnel axis is the basis for extracting the tunnel section and analyzing the deformation. Extracting point cloud data of the tunnel section and carrying out deformation analysis, wherein the intercepted tunnel section is required to be orthogonal to the trend of the tunnel section; on the other hand, the tunnel axis represents the whole trend and the space posture of the tunnel, and reflects the deformation condition of the tunnel structure to a certain extent. The existing methods for extracting the tunnel axis comprise a projection method, a minimum bounding box method, a fitting cylindrical surface method, a slice point cloud method and the like. The background of the research methods is mostly a tunnel in a construction stage, the purpose is to monitor the whole deformation of the tunnel in the construction stage and the tunneling direction of a shield machine, and the axis precision obtained by the method is not suitable for deformation analysis in the tunnel operation period.
Disclosure of Invention
The embodiment of the application provides a tunnel axis determining method, which is used for obtaining the accurate axis of a tunnel section and providing a basis for the local deformation analysis of a tunnel, and comprises the following steps:
acquiring geodetic coordinates of each point on each section of the tunnel to be detected under a geodetic coordinate system; aiming at each segment, selecting a target point at each of two ends of the vault of the segment, and determining an initial unit direction vector according to geodetic coordinates of the two target points; dividing each segment into a plurality of units with equal length along the direction of the initial unit direction vector, and constructing a plane perpendicular to the initial unit direction vector at the center of each unit to be used as a projection plane; constructing a local coordinate system by taking the intersection point of the projection plane and the initial unit direction vector as an origin; projecting each point on each unit to a projection plane, and determining the projection point projected to a specified range as an effective point; converting the geodetic coordinates of the effective points into local coordinates under a local coordinate system; fitting a circle on the projection plane by using the effective points of each unit, and determining the local coordinates of the circle center of the fitted circle; converting the local coordinates of the circle center into the geodetic coordinates of the circle center; performing space straight line fitting on the circular center geodetic coordinates of all units of each segment to obtain a first axis; determining a first unit direction vector from the first axis; determining a second axis and a second unit direction vector for each segment from the first unit direction vector using a method of determining the first axis and the first unit direction vector from the initial unit direction vector; determining a deviation of the first unit direction vector from the second unit direction vector; and if the deviation is less than or equal to the deviation threshold value, determining the second axis as the tunnel axis of the section of tunnel.
The embodiment of the present application further provides a tunnel axis determining apparatus, which is used to obtain the precise axis of the tunnel segment, and provide a basis for the local deformation analysis of the tunnel, and the apparatus includes:
the acquisition module is used for acquiring the geodetic coordinates of each point on each segment of the tunnel to be detected under the geodetic coordinate system; the determining module is used for selecting a target point at each of two ends of the vault of each segment and determining an initial unit direction vector according to geodetic coordinates of the two target points acquired by the acquiring module; the coordinate system construction module is used for dividing each section into a plurality of units with equal length along the direction of the initial unit direction vector determined by the determination module, and constructing a plane perpendicular to the initial unit direction vector at the center of each unit to be used as a projection plane; constructing a local coordinate system by taking the intersection point of the projection plane and the initial unit direction vector as an origin; the coordinate conversion module is used for projecting each point on each unit to the projection plane determined by the coordinate system construction module and determining the projection point projected to the specified range as an effective point; converting the geodetic coordinates of the effective points into local coordinates under a local coordinate system; the fitting module is used for fitting a circle on the projection plane by using the effective points of each unit determined by the coordinate conversion module and determining the local coordinates of the circle center of the fitted circle; converting the local coordinates of the circle center into the geodetic coordinates of the circle center; the fitting module is also used for performing spatial straight line fitting on the circular center geodetic coordinates of all units of each section to obtain a first axis; determining a first unit direction vector according to the first axis; an optimization module for determining a second axis and a second unit direction vector for each segment from the first unit direction vector using a method of determining a first axis and a first unit direction vector from an initial unit direction vector; the determining module is further used for determining the deviation of the first unit direction vector and the second unit direction vector determined by the fitting module; and the determining module is further used for determining the second axis as the tunnel axis of the section of the tunnel when the deviation is less than or equal to the deviation threshold value.
In the embodiment of the application, the units are divided for each section of the tunnel, the points on each unit are projected onto the projection plane, the projection points in the designated range are reserved as effective points, the circle centers of the units are determined by circle fitting of the effective points, the axes are determined by fitting the circle centers of the divided units, the axes of the sections of the tunnel are determined by iterative updating, the accurate axes of the sections of the tunnel can be obtained, the obtained axes are high in precision, the method is suitable for deformation analysis in the tunnel operation period, and a basis is provided for local deformation analysis of the tunnel.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative efforts. In the drawings:
fig. 1 is a flowchart of a tunnel axis determination method in an embodiment of the present application;
FIG. 2 is a schematic diagram of a mobile tunnel scanning according to an embodiment of the present application;
FIG. 3 is a schematic view of a plane cut at a seam in an embodiment of the present application;
FIG. 4 is a schematic diagram of a tunnel axis determination method according to an embodiment of the present application;
FIG. 5 is a schematic diagram illustrating a principle of determining a valid point in an embodiment of the present application;
FIG. 6 shows a V in the embodiment of the present application (t0) And V t Schematic diagram of deviation of direction;
FIG. 7 is a schematic illustration of an updated segment axis in an embodiment of the present application;
FIG. 8 is an axis diagram illustrating the axis deviation of the segment calculated twice before and after in the embodiment of the present application within the deviation threshold range;
FIG. 9 is another flow chart of a tunnel axis determination method in an embodiment of the present application;
fig. 10 is a schematic structural view of a tunnel axis determination device in an embodiment of the present application.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present application more apparent, the embodiments of the present application are further described in detail below with reference to the accompanying drawings. The exemplary embodiments and descriptions of the present application are provided to explain the present application and should not be interpreted as limiting the present application.
The embodiment of the application provides a tunnel axis determining method, as shown in fig. 1, the method includes steps 101 to 109:
101, acquiring the geodetic coordinates of each point on each segment of the tunnel to be detected in the geodetic coordinate system.
Specifically, the geodetic coordinates of each point on each segment of the tunnel to be measured can be acquired by using a three-dimensional laser scanning technology. The three-dimensional laser scanning technology has the advantages of high measurement precision, non-contact and the like, is widely applied to tunnel geometric information acquisition in a construction period or an operation period, is mainly divided into two types of station-by-station combined measurement and mobile type according to different measurement modes, is mainly applied to the tunnel construction period, has the advantages of high measurement efficiency, small traffic interference and the like, is mainly applied to the operation period, and is shown in fig. 2 as a schematic diagram of the principle of mobile type scanning.
During three-dimensional laser scanning, a geodetic coordinate system is generally established by taking the initial position of the instrument as an origin and following a right-hand rule. In the established geodetic coordinate system, XOY is a horizontal plane, a Z axis indicates a vertical elevation, and a Y axis is consistent with the trend of the tunnel line. The three-dimensional laser scanner automatically converts the acquired position information of each point on the tunnel to be measured into geodetic coordinates on a geodetic coordinate system.
The tunnel is made up of a plurality of segments, with seams at the junctions of different segments, in the present embodiment, the tunnel axis of one segment is determined on a segment-by-segment basis. Correspondingly, the tunnel point coordinate data acquired by the three-dimensional laser scanner is segmented according to the segment to which the tunnel point coordinate data belongs, and geodetic coordinates of all points of the segment to be analyzed are obtained. Illustratively, fig. 2 and 3 each show a schematic representation of the joining seam between different segments, and the cutting plane at the seam.
And 102, selecting a target point at each of two ends of the vault of each segment, and determining an initial unit direction vector according to geodetic coordinates of the two target points.
The point at which the Z value is maximum at each port of the vault is selected as the target point. The two selected target points are respectively P s (x s ，y s ，z s )、P e (x e ，y e ，z e ) Calculating an initial unit direction vector V according to the following formula t ：
V t ＝(x t ，y t ，z t )＝(x e -x s ，y e -y s ，z e -z s )/S
Wherein S is P s To P e The modulus of the vector is such that,
and 103, dividing each segment into a plurality of units with equal length along the direction of the initial unit direction vector, constructing a plane perpendicular to the initial unit direction vector at the center of each unit as a projection plane, and constructing a local coordinate system by taking the intersection point of the projection plane and the initial unit direction vector as an origin.
In the embodiment of the present application, taking the mobile scanning data as an example, the length of each unit covers 2 to 5 spiral scanning lines, and when dividing according to the length, the segment can be divided into an integer number of units. The length of each unit can be determined by a user according to actual conditions, and the lengths of different segment units can also be different, and the length of each unit is not limited herein. Illustratively, one cell j in one segment is indicated by Δ L in fig. 4.
Let the total number of segmented units be M, and the number of each unit be j, j =1, 2. Referring to FIG. 4, a vector V corresponding to the initial unit direction is constructed at the center of the cell j t Perpendicular plane
V t And plane surface
Has a cross point of P se-j Point of intersection P se-j The coordinates are expressed as (x) in the geodetic coordinate system se-j ，y se-j ，z se-j ) The calculation formula is as follows:
(x se-j ，y se-j ，z se-j )＝(j-0.5)SV t /M+(x s ，y s ，z s )
projection plane
The equation is calculated as:
x t (x-x se-j )+y t (y-y se-j )+z t (z-z se-j )＝0
to facilitate the use of least squares on the projection plane
Constructing a fitting circle, constructing a local coordinate system on the projection plane, wherein the local coordinate system follows a right-hand spiral rule, and the origin is arranged at the intersection point P of the projection plane and the initial unit direction vector se-j Here, the X-axis direction in the geodetic coordinate system is taken as the y-axis direction of the local coordinate system, the opposite direction of the projection plane of the Z-axis in the geodetic coordinate system toward the vertical elevation is taken as the X-axis direction of the local coordinate system, the direction of the initial unit direction vector is taken as the Z-axis direction of the local coordinate system, and the local coordinate system layout is as shown in fig. 4.
104, projecting each point on each unit to a projection plane, and determining the projection point projected to a specified range as an effective point; and converting the geodetic coordinates of the effective points into local coordinates in a local coordinate system.
Referring to fig. 5, fig. 5 is a schematic diagram of a projection plane after each point on a cell is projected onto the projection plane. The x-axis direction and the y-axis direction of the local coordinate system are shown in fig. 5.
In the embodiment of the application, two points with the largest distance are selected as longitudinal axis outer edge points in all projection points along the y-axis direction, one point of the tunnel vault is selected as a transverse axis outer edge point along the x-axis direction, and an outer boundary circle is determined by utilizing the two longitudinal axis outer edge points and the transverse axis outer edge point to obtain the circle center and the radius of the outer boundary circle; determining a circle which is concentric with the outer boundary circle and has a radius smaller than the radius of the outer boundary circle by a preset offset as an inner boundary circle; a circular ring formed by the inner boundary circle and the outer boundary circle is determined as a specified range. As shown in fig. 5, the projected points falling within the inner and outer boundary rings are regarded as valid points, and the remaining points are regarded as invalid points. The instability of the tunnel wall electrification hanging column, ventilation duct, traffic indication, lighting, communication, ornament and other accessory facilities and measuring systems is a main factor causing invalid points.
The preset offset delta d is determined by the distance measurement precision of a measuring system for measuring geodetic coordinates such as a tunnel longitudinal slope and a three-dimensional laser scanner, and the specific calculation mode is as follows:
Δd＝α(ΔL|z t |+2δ)
wherein alpha represents an empirical coefficient and is used for linearly and comprehensively adjusting the tunnel longitudinal slope and measuring the precision influence of the system; Δ L represents the length of the cell; | z t | represents the absolute value of the subentry of the vector in the initial unit direction; and delta represents the ranging precision of the tunnel geodetic coordinate measuring system, namely the ranging precision of measuring systems such as a three-dimensional laser scanner and the like. In general, a measurement system such as a three-dimensional laser scanner measures parameters such as a distance and an angle to obtain geodetic coordinates by conversion, and since the measurement system provides distance measurement accuracy, δ used here can be directly acquired from a geodetic coordinate measurement system such as a three-dimensional laser scanner.
Geodetic coordinates P on each cell i After each space point of (2) is projected to the projection plane, the geodetic coordinates of the projection point in the geodetic coordinate system
The calculation is performed according to the following method:
wherein T represents a matrix transposition operation; z is a radical of formula se-j Indicates the point of intersection P se-j Represents a dot product.
Placing the unit j in a plane
The calculation method for converting the coordinates (X, Y, Z) of any point in the geodetic coordinate system into the coordinates (X, Y, Z) in the local coordinate system comprises the following steps:
(x，y，z) T ＝R{(X，Y，Z) T +Q}
wherein, x, y and z respectively represent coordinate values of an x axis, a y axis and a z axis in a local coordinate system; x, Y and Z respectively represent coordinate values of an X axis, a Y axis and a Z axis in a geodetic coordinate system; r represents a rotation matrix transformed from a geodetic coordinate system to a local coordinate system; q represents a translation vector transformed from the geodetic coordinate system to the local coordinate system;
specifically, R and Q are calculated according to the following methods, respectively:
Q＝[-x se-j -y se-j -z se-j ] T
in the above formula, u x ＝(u xi ，u xj ，u xk )，u z ＝(u yi ，u yj ，u yk )，u y ＝(u zi ，u zj ，u zk )，u x 、u y 、u z The unit coordinate vectors of the x axis, the y axis and the z axis of the local coordinate system in the geodetic coordinate system are respectively.
Due to u x In projection plane with the Z axis of the geodetic coordinate system
The upward projection is consistent in the opposite direction and has a coordinate of P i Projection plane from any point in space
Projected coordinates of
Calculation method of calculating projection plane
The unit coordinate vector of the x-axis of the inner local coordinate system in the geodetic coordinate system. In particular, u x 、u z 、u y According to the following formulaThe following method is used for calculation:
u z ＝V t ＝(x t ，y t ，z t )
u y ＝u z ×u x
u is obtained by calculation x 、u z 、u y The rotation matrix R can then be determined.
And 105, fitting a circle on the projection plane by using the effective points of each unit, determining the local coordinates of the circle center of the fitted circle, and converting the local coordinates of the circle center into the geodetic coordinates of the circle center.
It should be noted that fitting a circle by using coordinates of points and a least square method and determining a center coordinate of the fitted circle are common technical means in the art, and details of the specific process are not described herein.
The calculation method for converting the local coordinates of the circle center into the geodetic coordinates of the circle center under the geodetic coordinate system comprises the following steps:
(X，Y，Z) T ＝R -1 (x，y，z) T -Q
106, performing space straight line fitting on the circular center geodetic coordinates of all units of each segment to obtain a first axis; a first unit direction vector is determined from the first axis.
The center-to-earth coordinates of each unit in the segment can be determined according to the methods in step 103 and step 105, and the first axis can be obtained by performing a spatial line fitting on the center-to-earth coordinates of all the units, illustratively, as shown in fig. 4, ax (t0) I.e. from the center of the circle
Fitting the resulting first axis.
Any M spatial coordinate points are fitted with a spatial straight-line projective equation, that is, the parametric equation of the first axis is:
in the above equation, a matrix to be solved constructed by equation coefficients is constructed:
A＝[a 1 a 2 ] T ＝(Z 1 Z 1 T ) -1 Z 1 X 1
B＝[b 1 b 2 ] T ＝(Z 1 Z 1 T ) -1 Z 1 Y 1
wherein, X 1 、Y 1 、Z 1 As M point coordinates (x) 1 ，y 1 ，z 1 )、...、(x M ，y M ，z M ) The constructed computing element is constructed by the following method:
X 1 ＝[x 1 x 2 … x M ] T ，Y 1 ＝[y 1 y 2 … y M ] T ，
a can be determined according to the above formula 1 And b 1 I.e. the direction vector (a) of the first axis can be determined 1 ，b 1 ，1)。
The first unit direction vector V (t0) Geodetic coordinate (x) t0 ，y t0 ，z t0 ) Comprises the following steps:
Target point P picked up by vault at two ends of segment s 、P e The section is artificially selected, the section possibly deviates from the direction of the tunnel axis, and the section is fitted with a first unit squareVector V (t0) And V t The directions are deviated as shown in fig. 6.
This step consists in updating the segment axis calculation. To obtain V (t0) Rear, along V (t0) The units are divided again, and each unit constructs a new projection plane
To the axis Ax (t0) Perpendicular to and passing through the axis Ax (t0) Division point P Ax0-j Projecting the point group in the unit j to
The point-to-plane projection calculation method is shown in step 104. At P Ax0-j Constructing a local coordinate system (x-y-z) at the point, wherein the local coordinate system follows a right-handed spiral rule, and the origin is arranged at P Ax0-j Here, the local coordinate system setting is consistent with the step 103 method. Converting the coordinates of the point groups from a geodetic coordinate system to a local coordinate system, and grouping the points in each unit
Fitting the circle with the projection point according to least square method to obtain the coordinate of the circle center in the local coordinate system, converting the coordinate in the local coordinate system to the geodetic coordinate system to obtain the coordinate of the circle center
The calculation method for converting the coordinates of the point group from the geodetic coordinate system to the local coordinate system is shown in step 104, and the calculation method for converting the coordinates of the point from the local coordinate system to the geodetic coordinate system is shown in step 105. Center coordinates of the circle in the geodetic coordinate system calculated by M units
Performing space straight line fitting to obtain an axis Ax (t1) And a unit vector V (t1) Is provided with V (t1) ＝(x t1 ，y t1 ，z t1 ) The method for fitting the spatial straight line and calculating the unit vector thereof is shown in step 106. The updated segment axis is shown in fig. 7.
And step 108, determining the deviation of the first unit direction vector and the second unit direction vector.
In particular, according to C =1-V (t0) ·V (t1) ＝1-x t0 x t1 -y t0 y t1 -z t0 z t1 Determining a first unit direction vector V (t0) And a second unit direction vector V (t1) Deviation C of (a).
And step 109, if the deviation is less than or equal to the deviation threshold value, determining the second axis as the tunnel axis of the section of tunnel.
Step 108 and step 109 are to determine the degree of coincidence (or referred to as parallelism) between the updated segment axis and the initially calculated segment axis, and if the deviation between the two is within the deviation threshold, the two calculated segment axes are considered to be parallel to each other, and the second axis is determined as the tunnel axis of the segment tunnel. The axis deviation of the two segments before and after is within the limit value, and the state is shown in fig. 8.
If a deviation exceeding a deviation threshold exists between the first unit direction vector and the second unit direction vector, referring to fig. 9, the second unit direction vector updated this time is taken as a new first unit direction vector, a new second unit direction vector and a second axis are calculated according to the new first unit direction vector until the deviation between the first unit direction vector and the second unit direction vector obtained extremely is smaller than or equal to the deviation threshold, and the second axis obtained by the last calculation is determined as the tunnel axis of the segment of tunnel.
Each segment of the tunnel is calculated according to the method in steps 102 to 109, and the tunnel axes of all the segments of the tunnel can be obtained.
In the embodiment of the application, the units are divided for each section of the tunnel, the points on each unit are projected onto the projection plane, the projection points in the designated range are reserved as effective points, the circle centers of the units are determined by circle fitting of the effective points, the axes are determined by fitting the circle centers of the divided units, the axes of the sections of the tunnel are determined by iterative updating, the accurate axes of the sections of the tunnel can be obtained, the obtained axes are high in precision, the method is suitable for deformation analysis in the tunnel operation period, and a basis is provided for local deformation analysis of the tunnel.
The embodiment of the present application further provides a tunnel axis determining apparatus, as shown in fig. 10, the apparatus 1000 includes an obtaining module 1001, a determining module 1002, a coordinate system constructing module 1003, a coordinate converting module 1004, a fitting module 1005, and an optimizing module 1006.
The obtaining module 1001 is configured to obtain geodetic coordinates of each point on each segment of the tunnel to be measured in the geodetic coordinate system.
A determining module 1002, configured to select a target point at each of two ends of the dome of the segment, and determine an initial unit direction vector according to the geodetic coordinates of the two target points acquired by the acquiring module 1001.
A coordinate system constructing module 1003, configured to divide each segment into a plurality of units with equal length along the direction of the initial unit direction vector determined by the determining module 1002, and construct a plane perpendicular to the initial unit direction vector at the center of each unit as a projection plane; and constructing a local coordinate system by taking the intersection point of the projection plane and the initial unit direction vector as an origin.
A coordinate conversion module 1004, configured to project each point on each unit onto the projection plane determined by the coordinate system construction module 1003, and determine a projection point projected into a specified range as a valid point; and converting the geodetic coordinates of the effective points into local coordinates in a local coordinate system.
A fitting module 1005, configured to fit a circle on the projection plane using the effective points of each unit determined by the coordinate conversion module 1004, and determine local coordinates of a center of the fitted circle; and converting the local coordinates of the circle center into the geodetic coordinates of the circle center.
The fitting module 1005 is further configured to perform spatial straight line fitting on the circle center geodetic coordinates of all the units of each segment to obtain a first axis; a first unit direction vector is determined from the first axis.
An optimization module 1006 for determining the second axis and the second unit direction vector of each segment from the first unit direction vector using a method of determining the first axis and the first unit direction vector from the initial unit direction vector.
The determining module 1002 is further configured to determine a deviation of the first unit direction vector and the second unit direction vector determined by the fitting module 1005.
The determining module 1002 is further configured to determine the second axis as a tunnel axis of the segment of the tunnel when the deviation is less than or equal to the deviation threshold.
In an implementation manner of the embodiment of the present application, two target points are P respectively s (x s ，y s ，z s )、P e (x e ，y e ，z e ) A determining module 1002 configured to:
according to V t ＝(x t ，y t ，z t )＝(x e -x s ，y e -y s ，z e -z s ) Calculating initial unit direction vector V by using/S t ；
Wherein S is P s To P e The modulus of the vector is such that,
in an implementation manner of the embodiment of the present application, the coordinate system building module 1003 is configured to:
and constructing the local coordinate system by taking the intersection point of the projection plane and the initial unit direction vector as the origin of the local coordinate system, taking the X-axis direction in the geodetic coordinate system as the y-axis direction of the local coordinate system, taking the opposite direction of the projection of the Z-axis which points to the vertical elevation on the projection plane in the geodetic coordinate system as the X-axis direction of the local coordinate system, and taking the direction of the initial unit direction vector as the Z-axis direction of the local coordinate system.
In an implementation manner of the embodiment of the present application, the coordinate transformation module 1004 is further configured to transform the coordinate into a coordinate frame
Selecting two points with the largest distance from all the projection points along the y-axis direction as outer edge points of a longitudinal axis, selecting one point of the vault of the tunnel along the x-axis direction as an outer edge point of a transverse axis, and determining an outer boundary circle by using the two outer edge points of the longitudinal axis and the outer edge point of the transverse axis to obtain the circle center and the radius of the outer boundary circle;
according to Δ d = α (Δ L | z) t | +2 δ) is confirmedSetting a preset offset delta d; wherein α represents an empirical coefficient; Δ L represents the length of the cell; | z t I represents the absolute value of the subentry of the vector in the initial unit direction; δ represents the range accuracy of the tunnel geodetic surveying system.
Determining a circle which is concentric with the outer boundary circle and has a radius smaller than the radius of the outer boundary circle by a preset offset as an inner boundary circle;
and determining a circular ring consisting of the inner boundary circle and the outer boundary circle as a specified range.
In an implementation manner of the embodiment of the present application, the coordinate conversion module 1004 is further configured to:
according to (x) se-j ，y se-j ，z se-j )＝(j-0.5)SV t /M+(x s ，y s ，z s ) Determining the intersection point P se-j Coordinate (x) of se-j ，y se-j ，z se-j )；
Where j denotes the jth cell of the division, j =1, 2.
A coordinate conversion module 1004 for:
according to
Determining geodetic coordinates of an active point
Using (x, y, z) T ＝R{(X，Y，Z) T + Q, converting the earth coordinates of the effective points into local coordinates;
wherein, P i Representing geodetic coordinates of the spatial points on the unit corresponding to the ith valid point; v t Represents an initial unit direction vector; t represents a matrix transposition operation; z is a radical of se-j Indicates the point of intersection P se-j Z-axis coordinates of (a); x, y and z respectively represent coordinate values of an x axis, a y axis and a z axis in a local coordinate system; x, Y and Z respectively represent coordinate values of an X axis, a Y axis and a Z axis in a geodetic coordinate system; r represents a rotation matrix transformed from a geodetic coordinate system to a local coordinate system; q represents transformation from the geodetic coordinate systemTranslation vectors to the local coordinate system,. Representing point multiplications;
wherein the content of the first and second substances,
Q＝[-x se-j -y se-j -z se-j ] T ，
u z ＝(u yi ，u yj ，u yk )＝V t ＝(x t ，y t ，z t )，u y ＝(u zi ，u zj ，u zk )＝u z ×u x ，u x 、u y 、u z the unit coordinate vectors of the x axis, the y axis and the z axis of the local coordinate system in the geodetic coordinate system are respectively.
In an implementation manner of the embodiment of the present application, the fitting module 1005 is configured to:
constructing a parametric equation for a first axis
Wherein a is 1 、a 2 、b 1 、b 2 Is a parameter to be solved of the parameter equation;
according to [ a ] 1 a 2 ] T ＝(Z 1 Z 1 T ) -1 Z 1 X 1 ，[b 1 b 2 ] T ＝(Z 1 Z 1 T ) -1 Z 1 Y 1 Determining a parameter a to be solved of a parametric equation 1 、a 2 、b 1 、b 2 (ii) a Wherein, X 1 ＝[x 1 x 2 … x M ] T ，Y 1 ＝[y 1 y 2 … y M ] T ，
(x 1 ，y 1 ，z 1 )、...、(x M ，y M ，z M ) Circle center geodetic coordinates of a first unit to an Mth unit which are divided for the segments respectively;
according to
Angle-determining first unit direction vector V (t0) Geodetic coordinate (x) t0 ，y t0 ，z t0 )。
In an implementation manner of the embodiment of the present application, the determining module 1002 is configured to:
according to C =1-V (t0) ·V (t1) ＝1-x t0 x t1 -y t0 y t1 -z t0 z t1 Determining a first unit direction vector V (t0) And a second unit direction vector V (t1) Wherein (x) t1 ，y t1 ，z t1 ) Is a second unit direction vector V (t1) The geodetic coordinates of (a).
In an implementation manner of the embodiment of the present application, the determining module 1002 is further configured to:
and if the deviation is greater than the deviation threshold value, taking the second unit direction vector as a new first unit direction vector, calculating a new second unit direction vector and a second axis according to the new first unit direction vector until the deviation of the calculated first unit direction vector and the second unit direction vector is less than or equal to the deviation threshold value, and determining the second axis obtained by the last calculation as the tunnel axis of the section of tunnel.
In the embodiment of the application, the units are divided for each section of the tunnel, the points on each unit are projected onto the projection plane, the projection points in the designated range are reserved as effective points, the circle fitting is carried out on the effective points to determine the center of the unit, the centers of the divided units are fitted to determine the axes, the axes of the tunnel sections are determined through iterative updating, the accurate axes of the tunnel sections can be obtained, the obtained axes are high in precision, the method is suitable for tunnel operation period deformation analysis, and a basis is provided for local deformation analysis of the tunnel.
The embodiment of the present application further provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the processor executes the computer program, any one of the methods described in step 101 to step 109 and various implementations thereof is implemented.
An embodiment of the present application further provides a computer-readable storage medium, where a computer program for executing any one of the methods described in step 101 to step 109 and various implementation manners thereof is stored in the computer-readable storage medium.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above-mentioned embodiments are further described in detail for the purpose of illustrating the invention, and it should be understood that the above-mentioned embodiments are only illustrative of the present invention and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (11)
1. A tunnel axis determination method, the method comprising:
acquiring geodetic coordinates of each point on each section of the tunnel to be detected under a geodetic coordinate system;
aiming at each segment, selecting a target point at each of two ends of the vault of the segment, and determining an initial unit direction vector according to geodetic coordinates of the two target points;
dividing each segment into a plurality of units with equal length along the direction of the initial unit direction vector, and constructing a plane perpendicular to the initial unit direction vector at the center of each unit to be used as a projection plane; constructing a local coordinate system by taking the intersection point of the projection plane and the initial unit direction vector as an origin;
projecting each point on each unit to a projection plane, and determining the projection point projected to a specified range as an effective point; converting the geodetic coordinates of the effective points into local coordinates under a local coordinate system;
fitting a circle on the projection plane by using the effective points of each unit, and determining the local coordinates of the circle center of the fitted circle; converting the local coordinates of the circle center into the geodetic coordinates of the circle center;
performing space straight line fitting on the circular center geodetic coordinates of all units of each segment to obtain a first axis; determining a first unit direction vector according to the first axis;
determining a second axis and a second unit direction vector for each segment from the first unit direction vector using a method of determining a first axis and a first unit direction vector from an initial unit direction vector;
determining a deviation of the first unit direction vector from the second unit direction vector;
and if the deviation is less than or equal to the deviation threshold value, determining the second axis as the tunnel axis of the section of the tunnel.
2. The method of claim 1, wherein the two targets are each P s (x s ，y s ，z s )、P e (x e ，y e ，z e ) Determining an initial unit direction vector according to geodetic coordinates of two target points, comprising:
according to V t ＝(x t ，y t ，z t )＝(x e -x s ，y e -y s ，z e -z s ) Calculating initial unit direction vector V by using/S t ；
Wherein S is P s To P e The modulus of the vector is such that,
3. the method of claim 1, wherein constructing a local coordinate system using an intersection of the projection plane and the initial unit direction vector as an origin comprises:
and constructing the local coordinate system by taking the intersection point of the projection plane and the initial unit direction vector as the origin of the local coordinate system, taking the X-axis direction in the geodetic coordinate system as the y-axis direction of the local coordinate system, taking the opposite direction of the projection of the Z-axis which points to the vertical elevation on the projection plane in the geodetic coordinate system as the X-axis direction of the local coordinate system, and taking the direction of the initial unit direction vector as the Z-axis direction of the local coordinate system.
4. The method according to claim 3, wherein before determining the projected points projected into the specified range as the valid points, the method further comprises:
selecting two points with the largest distance from all the projection points along the y-axis direction as outer edge points of a longitudinal axis, selecting one point of the vault of the tunnel along the x-axis direction as an outer edge point of a transverse axis, and determining an outer boundary circle by using the two outer edge points of the longitudinal axis and the outer edge point of the transverse axis to obtain the circle center and the radius of the outer boundary circle;
according to Δ d = α (Δ L | z) t | +2 δ) determining a preset offset Δ d; wherein α represents an empirical coefficient; Δ L represents the length of the cell; | z t I represents the absolute value of the subentry of the vector in the initial unit direction; delta represents the distance measurement precision of the tunnel geodetic coordinate measurement system;
determining a circle which is concentric with the outer boundary circle and has a radius smaller than the radius of the outer boundary circle by a preset offset as an inner boundary circle;
and determining a circular ring consisting of the inner boundary circle and the outer boundary circle as a specified range.
5. The method of claim 1, wherein prior to converting the geodetic coordinates of the effective point to local coordinates in a local coordinate system, the method further comprises:
according to (x) se-j ，y se-j ，z se-j )＝(j-0.5)SV t /M+(x s ，y s ，z s ) Determining the intersection point P of the projection plane and the initial unit direction vector se-j Coordinate (x) of se-j ，y se-j ，z se-j ) (ii) a Where j represents the jth cell of the division, j =1, 2.., M represents the total number of cells of the segment division;
the converting the geodetic coordinates of the effective points into local coordinates in a local coordinate system includes:
according to
Determining geodetic coordinates P of the active point i (P) ；
Using (x, y, z) T ＝R{(X，Y，Z) T + Q, converting the earth coordinates of the effective points into local coordinates;
wherein, P i Representing geodetic coordinates of the spatial points on the unit corresponding to the ith valid point; v t Represents an initial unit direction vector; t represents a matrix transposition operation; z is a radical of formula se-j Indicates the point of intersection P se-j Z-axis coordinates of (a); x, y and z respectively represent coordinate values of an x axis, a y axis and a z axis in a local coordinate system; x, Y and Z respectively represent coordinate values of an X axis, a Y axis and a Z axis in a geodetic coordinate system; r represents a rotation matrix transformed from a geodetic coordinate system to a local coordinate system; q represents a translation vector transformed from the geodetic coordinate system to the local coordinate system,. Represents a point product;
wherein the content of the first and second substances,
Q＝[-x se-j -y se-j -z se-j ] T ，
u z ＝(u yi ，u yj ，u yk )＝V t ＝(x t ，y t ，z t )，u y ＝(u zi ，u zj ，u zk )＝u z ×u x ，u x 、u y 、u z the unit coordinate vectors of the x axis, the y axis and the z axis of the local coordinate system in the geodetic coordinate system are respectively.
6. The method according to claim 1, characterized in that the circle center coordinates of all units of each segment are subjected to spatial straight line fitting to obtain a first axis; determining a first unit direction vector from the first axis, comprising:
constructing a parametric equation for a first axis
Wherein a is 1 、a 2 、b 1 、b 2 Is a parameter to be solved of a parameter equation;
according to [ a ] 1 a 2 ] T ＝(Z 1 Z 1 T ) -1 Z 1 X 1 ，[b 1 b 2 ] T ＝(Z 1 Z 1 T ) -1 Z 1 Y 1 Determining a parameter a to be solved of a parametric equation 1 、a 2 、b 1 、b 2 (ii) a Wherein, X 1 ＝[x 1 x 2 …x M ] T ，Y 1 ＝[y 1 y 2 …y M ] T ，
(x 1 ，y 1 ，z 1 )、...、(x M ，y M ，z M ) Circle center geodetic coordinates of the first unit to the Mth unit which are divided into the segments respectively;
according to
Determining a first unit direction vector V (t0) Geodetic coordinate (x) t0 ，y t0 ，z t0 )。
7. The method of claim 6, wherein determining the deviation of the first unit direction vector from the second unit direction vector comprises:
according to C =1-V (t0) .V (t1) ＝1-x t0 x t1 -y t0 y t1 -z t0 z t1 Determining a first unit direction vector V (t0) And a second unit direction vector V (t1) Wherein (x) t1 ，y t1 ，z t1 ) Is a second unit direction vector V (t1) The geodetic coordinates of (a).
8. The method of claim 1 or 7, wherein after determining the deviation of the first unit direction vector from the second unit direction vector, the method further comprises:
and if the deviation is greater than the deviation threshold value, taking the second unit direction vector as a new first unit direction vector, calculating a new second unit direction vector and a second axis according to the new first unit direction vector until the deviation of the calculated first unit direction vector and the second unit direction vector is less than or equal to the deviation threshold value, and determining the second axis obtained by the last calculation as the tunnel axis of the section of tunnel.
9. A tunnel axis determination apparatus, the apparatus comprising:
the acquisition module is used for acquiring the geodetic coordinates of each point on each segment of the tunnel to be detected under the geodetic coordinate system;
the determining module is used for selecting a target point at each of two ends of the vault of each segment, and determining an initial unit direction vector according to geodetic coordinates of the two target points acquired by the acquiring module;
the coordinate system construction module is used for dividing each section into a plurality of units with equal length along the direction of the initial unit direction vector determined by the determination module, and constructing a plane perpendicular to the initial unit direction vector at the center of each unit to be used as a projection plane; constructing a local coordinate system by taking the intersection point of the projection plane and the initial unit direction vector as an origin;
the coordinate conversion module is used for projecting each point on each unit to the projection plane determined by the coordinate system construction module and determining the projection point projected to the specified range as an effective point; converting the geodetic coordinates of the effective points into local coordinates under a local coordinate system;
the fitting module is used for fitting a circle on the projection plane by using the effective points of each unit determined by the coordinate conversion module and determining the local coordinates of the circle center of the fitted circle; converting the local coordinates of the circle center into the geodetic coordinates of the circle center;
the fitting module is also used for performing spatial straight line fitting on the circular center geodetic coordinates of all units of each section to obtain a first axis; determining a first unit direction vector from the first axis;
an optimization module for determining a second axis and a second unit direction vector for each segment from the first unit direction vector using a method of determining the first axis and the first unit direction vector from the initial unit direction vector;
the determining module is further used for determining the deviation of the first unit direction vector and the second unit direction vector determined by the fitting module;
the determining module is further used for determining the second axis as the tunnel axis of the section of tunnel when the deviation is smaller than or equal to the deviation threshold value.
10. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the method of any one of claims 1 to 8 when executing the computer program.
11. A computer-readable storage medium, characterized in that the computer-readable storage medium stores a computer program for executing the method of any one of claims 1 to 8.
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