CN109297426A - A kind of large-scale precision industrial equipment deflection and servo angle detecting method - Google Patents
A kind of large-scale precision industrial equipment deflection and servo angle detecting method Download PDFInfo
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- CN109297426A CN109297426A CN201811031030.3A CN201811031030A CN109297426A CN 109297426 A CN109297426 A CN 109297426A CN 201811031030 A CN201811031030 A CN 201811031030A CN 109297426 A CN109297426 A CN 109297426A
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- coordinate system
- photogrammetric
- laser tracker
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
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- General Physics & Mathematics (AREA)
- Length Measuring Devices By Optical Means (AREA)
- Length Measuring Devices With Unspecified Measuring Means (AREA)
Abstract
The invention discloses a kind of large-scale precision industrial equipment deflections and servo angle detecting method, belong to the technical field that commercial measurement intersects with geodesic survey.Present invention uses the technologies that industrial photogrammetry system, laser tracker are combined with high precision total station, BROAD SUMMARY has: 1. on the basis of station meter, also it regard the both threads segment length that laser tracker measures as photogrammetric length standard, can also mutually be checked while improving photogrammetric space scale precision;2. self-control shooting auxiliary telescopic bar, allows measurement camera to be capable of any position of photographic subjects at any angle, solves the observation problem of large scale equipment;3. the local gravity horizontal coordinates established by laser tracker are as transition, the high-precision for realizing photogrammetric coordinate system to earth coordinates is converted.
Description
Technical field
The invention belongs to the technical fields that commercial measurement intersects with geodesic survey, specifically, being about a kind of large-scale essence
Close industrial equipment deflection and servo angle detecting method.
Background technique
Existing measurement method there are the problem of:Achievement is independent photogrammetric coordinate system, is lacked and country's the earth
The high-precision conversion method of coordinate system;It is limited by factors such as the commercial measurement camera depth of field, photography sign back angles, to big
Type equipment is easy to produce blind area when shooting;The lenth ratio of large scale equipment and station meter is excessive, is unfavorable for global space ruler
Spend precision controlling.The deflection and servo angle detection project of Xinjiang large-scale precision industrial equipment have been accepted by our unit, are gram
Prior art deficiency is taken, technology disclosed in this invention is had developed.
Summary of the invention
The present invention is solves the problems, such as to refer in background technique, has studied a kind of industrial photogrammetry system, laser tracks
The method that instrument, high precision total station combine, to detect the gravity and temperature deformation amount of large-scale precision industrial equipment, and big
Ground, which measures, detects servo angle under coordinate system.It is verified by project, this method is big with observation area, acquisition speed is fast, achievement
The advantages such as precision is high, coordinate is convertible effectively increase the efficiency of large-scale precision industrial equipment deflection and the detection of servo angle
With precision, and the earth coordinates that achievement is included in unification of the motherland can be will test, to the manufacture and assembly of large-scale precision industrial equipment
It is of great significance.
To realize the above-mentioned technical purpose, the technical scheme adopted by the invention is as follows:
A kind of large-scale precision industrial equipment deflection and servo angle detecting method, it is characterized in that: the following steps are included:
Step 1: reconnaissance trip: to the geomery of industrial equipment, external environment, peripheral control point point bit distribution and intervisibility item
Part carries out reconnaissance trip, determines that the measurement mark layout scheme of industrial equipment, laser tracker set up point, industrial photogrammetry
Set up an office position and total station of system tray sets up point, and magnetic base is installed at determining measurement mark;
Step 2: establishing laser tracker coordinate system and determining laser tracker coordinate system common point mark: being tracked using laser
The measurement horizontal plane function of instrument obtains local gravity horizontal plane, and using laser tracker center as origin, horizontal plane normal direction is Z
Axis, the north establish independent right hand rectangular coordinate system in space, laser tracker coordinate system are named as, in magnetic base to for X-axis
Middle placement laser tracker reflection sphere reflects ball position with laser tracker measurement laser tracker, each magnetic base is made to exist
There is coordinate, wherein there are at least four magnetic bases to be defined as laser tracker coordinate system public in laser tracker coordinate system
Point mark;
Step 3: establishing photogrammetric coordinate system and determining photogrammetric coordinate system common point mark: being with photogrammetric center
Origin establishes photogrammetric coordinate system, and a foundation object staff is fixed at magnetic base, and photography mark target is placed in magnetic base
Ball, photography mark the target ball centre of sphere and the laser tracker reflection sphere centre of sphere overlapping, with industrial Digital Photogrammetric System to industrial equipment into
Row photography, obtains photogrammetric data;By measurement, the actual length of at least two benchmark line segments is obtained, benchmark line segment is magnetic
Property pedestal sphere centre coordinate between line, bring benchmark line segment length into photogrammetric data, to photogrammetric data carry out
Adjustment resolves, and magnetic base is made to have coordinate in photogrammetric coordinate system, while it is flat to obtain station meter in photogrammetric data
The length that station meter adjustment in photogrammetric data resolves is compared the length that difference resolves with the actual length of station meter,
To verify the photogrammetric space scale precision for resolving achievement;It will be defined as the magnetic of laser tracker coordinate system common point mark
Property pedestal is defined as photogrammetric coordinate system common point mark;
Step 4: determining earth coordinates common point mark: laying total station on the inside of the building locating for industrial equipment on metope
Reflector plate, reflector plate position for internal observation pier and laser tracker website will intervisibility it is good, observation angle is suitable, reflection
Piece is uniformly distributed in solid space;Using the total station oriented in national earth coordinates, all reflector plate centers are measured
Three-dimensional coordinate of the point in earth coordinates;Laser tracker is held into gauge head and withstands reflector plate center, measures all reflector plates
Three-dimensional coordinate of the center in laser tracker coordinate system;
Step 5: association photogrammetric coordinate system and earth coordinates: due to laser tracker coordinate system common point mark with take the photograph
Shadow measurement coordinate system common point mark position is identical, and as common point pair, computational photogrammetry coordinate system and laser are tracked
The conversion parameter of instrument coordinate system;Using reflector plate central point as common point pair, laser tracker coordinate system and geodetic coordinates are calculated
The conversion parameter of system;To obtain the conversion parameter of photogrammetric coordinate system and earth coordinates, photogrammetric coordinate system is realized
With being associated with for earth coordinates;
Step 6: gravity is detected from temperature deformation: deformation can be generated under the different gravity and state of temperature of industrial equipment, measured
Personnel carry measurement camera, to industrial equipment multi-angle take pictures measurement and extract measurement mark in photogrammetric coordinate system three
Coordinate is tieed up, obtains three of industrial equipment in earth coordinates using the conversion parameter of photogrammetric coordinate system and earth coordinates
Coordinate is tieed up, and utilizes the deflection of these coordinate analysis industrial equipments;
Step 7: servo angle detects: the measurement marker coordinates that will be extracted in step 6 utilize photogrammetric coordinate system and the earth
The conversion parameter of coordinate system obtains three-dimensional coordinate of the industrial equipment in earth coordinates, and it is flat to calculate main rule on industrial equipment
The method direction in face, by compared with, detecting the precision of servo angle with the earth north.
To optimize above-mentioned technical proposal, the concrete measure taken further include:
In above-mentioned step three, the selection mode of benchmark line segment are as follows: in the magnetic as laser tracker coordinate system common point mark
Property pedestal in choose four, as far as possible close to rectangle, benchmark line segment is that the sphere centre coordinate of four magnetic bases is diagonally connected for distribution
The two lines section that line obtains.
Coding maker is arranged in above-mentioned bottom and back in industrial equipment, at the high elevation angle by equipment itself with set
Standby pedestal associates.
In above-mentioned step six, survey crew's carrying measurement camera is more by lifting device and shooting auxiliary telescopic bar progress
Angle is taken pictures measurement, and the lifting device is elevator, and the shooting auxiliary telescopic bar is three-section type telescopic rod, overall length 6
Rice, is fixed on elevator.
Above-mentioned each measurement mark will be captured by the industrial photogrammetry system of four or more different locations.
The length of above-mentioned benchmark line segment is longer than station meter length.
To realize the above-mentioned technical purpose, the summary of the invention of this method mainly has:
Summary of the invention one, on the basis of station meter, by laser tracker measure both threads segment length be also used as it is photogrammetric
The length standard of resolving.The reason is that the ratio of large-scale precision industrial equipment size and station meter length is excessive, benchmark is used alone
Ruler can not effectively control the dimensional accuracy of the photogrammetric middle overall situation, and be considerably longer than the benchmark line segment of station meter by length to make
For length standard, the overall situation can be preferably held, improves measurement accuracy.
Summary of the invention two, the high-precision conversion method of photogrammetric coordinate system to earth coordinates.By establish laser with
Track instrument coordinate system and photogrammetric coordinate system, and several magnetic bases as common point are set on industrial equipment, in work
The means of setting reflection patch around industry equipment, so that photogrammetric coordinate system, laser tracker coordinate system and earth coordinates
It can mutually convert, the high-precision for finally realizing photogrammetric coordinate system to earth coordinates is converted.
Summary of the invention three, the coverage and shooting angle for expanding commercial measurement camera using homemade shooting auxiliary telescopic bar
Degree.When large industry equipment is in high elevation angle state, photogrammetric personnel and equipment can not be sent to specified shooting by elevator
Position needs to shoot auxiliary telescopic bar and assists photogrammetric equipment shooting.Shoot auxiliary telescopic bar by aluminum profile rod piece (3, often
2 meters of root), the accessories composition such as camera carriage.6 are connected by a word connector with aluminum profile rod piece by 3 in shooting process
Rice is long to be fixed on elevator basket arm rest, pulls camera carriage that camera is enable to reach aluminum profile rod piece by wirerope
Upper any position.
Specific embodiment
The embodiment of the present invention is described in further detail below.
A kind of large-scale precision industrial equipment deflection and servo angle detecting method of the invention, comprising the following steps:
Step 1: reconnaissance trip: fully understanding industrial equipment geomery and external environment, peripheral control point point bit distribution and lead to
Depending on condition, in conjunction with measurement demand of the large-scale precision industrial equipment under each posture state and required precision, mark cloth is primarily determined
If scheme, measuring device set up point, workflow design etc..Particular content has:
1) understand the information such as shape, the size of large-scale precision industrial equipment, provide foundation for the selection of lifting equipment, and determine magnetic
The installation position of property pedestal and station meter.
2) understand the information such as color, the material of large-scale precision industrial equipment, the selection for target of photographing provides foundation.
3) servo-system for understanding large-scale precision industrial equipment rotates section, determines the azimuth in the detection of gravity deformation amount
With the combination of pitch angle.
4) understand the air-conditioning system of large-scale precision industrial equipment, ambient temperature value combination in the detection of temperature deflection.
5) understand control point (earth coordinates) the point bit distribution and sighting condition outside large-scale precision industrial equipment, really
Determine the erection point of total station and laser tracker.
6) understand ground and the metope situation around large-scale precision industrial equipment, determine the installation position of reflector plate.
Step 2: laying measurement mark: measurement mark is broadly divided into photography mark, laser tracker coordinate system mark by purposes
Will, earth coordinates mark and coding maker.
1) it lays photogrammetric mark: 1. establishing length standard.In plant bottom case side while fixed reference ruler, with swash
Optical tracker system measures two detection length along path and is also used as length standard, and the two can check mutually.2. laying measurement mark.According to
Constant spacing lays measurement mark matched with Digital Photogrammetric System on industrial equipment surface.3. increasing coding maker.In industry
The bottom and back of equipment increase coding maker, to associate device and plant bottom case at the high elevation angle.
The laying principle of photography mark: 1. guarantee every photo at least four coding maker;2. guaranteeing on every photo at least
12 measurement marks being evenly distributed;3. guaranteeing that each measurement mark is at least imaged on the photo of 3 different locations;4. maximum
Limit maintains the status of large industry equipment and reduces the workload in surface mount photography mark.
2) it lays the common point mark of photogrammetric coordinate system and laser tracker coordinate system: considering measure field space
The convenience that limitation, the depth of field of photogrammetric camera, laser tracker and photogrammetric coordinate system are converted, at industrial equipment bottom
Seat 5 general magnetic pedestals of side arrangement turn for disposing photography hemisphere mark and laser tracker reflection sphere as coordinate system
Change common point.
3) the common point mark of laser tracker and earth coordinates is laid: in order in laser tracker coordinate system and whole station
It is converted between instrument coordinate system, needs to lay the reflector plate of total station on the inside metope of the building locating for equipment.Reflector plate
Position for internal observation pier and laser tracker website will intervisibility it is good, and observation angle is suitable, and reflector plate is three-dimensional empty
Between be uniformly distributed.
Step 3: establishing coordinate system using laser tracker: obtaining office using the measurement horizontal plane function of laser tracker
Portion's gravity level, using laser tracker center as origin, horizontal plane normal (upward) direction is Z axis, and the north is built to for X-axis
Independent right hand rectangular coordinate system in space is found, laser tracker coordinate system is named as.
Step 4: calculating the conversion parameter of laser tracker coordinate system and photogrammetric coordinate system.Detailed step is as follows.
1) several (at least three) tracker reflection sphere magnetic bases, ball seat position are chosen in the base side of industrial equipment
It is evenly distributed, guarantees not point-blank in solid space.
2) 1.5 inches of diameter (38.1mm) of tracker reflection sphere is placed in magnetic base, and uses laser tracker
Measure the three-dimensional coordinate of the centre of sphere.
3) the mark target ball (hemisphere, 1.5 inches of diameter) that Digital Photogrammetric System is placed in magnetic base, is surveyed using photography
It measures system photographs and resolves and obtain target ball sphere centre coordinate.
4) after being placed into magnetic base, the spatial position of two centre ofs sphere is for tracker reflection sphere and photography mark target ball
It is overlapped, can be used as common point pair, the conversion parameter of computational photogrammetry coordinate system and laser tracker coordinate system.
Step 5: calculating the conversion parameter of laser tracker coordinate system and national earth coordinates.Detailed step is as follows.
1) ground and metope choose several (at least three) total station reflector plates near industrial equipment, and guarantee reflector plate
It is evenly distributed, guarantees not point-blank in solid space.
2) geodetic coordinates of building interior observation pier locating for industrial equipment is measured.
(a) by measure field periphery known to GPS control point coordinates longitude and latitude (B, L) principle throwing is just being calculated according to gauss projection
Shadow to Gaussian plane obtain plane coordinates (x, y), and use independent elevation system.
(b) total station is set up using the outer control point of building locating for industrial plants as survey station, is seen with other any control point orientations
Measurement equipment is locating to build interior control point coordinates, will be in the incoming building of exterior coordinate system.
(c) other control points in addition to orientation point are utilized to redirect, measuring device is locating to build interior control point coordinates conduct
It checks.
3) total station is set up in building interior observation pier, and is oriented with external control point, under national earth coordinates,
Measure the three-dimensional coordinate of all reflector plate central points.
4) laser tracker is held into gauge head (placement 0.1mm probe) and withstands reflector plate center, in laser tracker coordinate
Under system, the three-dimensional coordinate at all reflector plate centers is measured.
5) using reflector plate central point as common point pair, the conversion for calculating laser tracker coordinate system and earth coordinates is joined
Number.
Step 6: gravity is detected from temperature deformation amount: keeping the different pitch angles and state of temperature of industrial equipment, measure people
Member carries measurement camera, carries out multi-angle by lifting device and self-control shooting auxiliary telescopic bar and take pictures measurement and to extract index point
Three-dimensional coordinate (photogrammetric coordinate system), and utilize these coordinate analysis deflections.
The design of photogrammetric middle net type: camera camera site and the orientation of target object constitute the shape of measurement net,
The various factors for influencing precision will be taken into account by taking the photograph station location not only, also take into account the property of available space, the camera itself of working environment
It can (such as field angle, the depth of field) and the limitation factor indicated to incidence angle of photographing.The planning and designing of measurement net form follow following original
Then:
(a) make each index point taking the photograph captured by station by four or more different locations as far as possible.From multiple and different positions to mark
Point carries out intersection measurement, can not only improve precision, and increase excess observation, the reliability of measurement result can be improved.
(b) make the intersection angle of each index point between 60 ° ~ 120 ° as far as possible.
(c) as far as possible to the photography incidence angle of each index point less than 45 °, maximum is no more than 60 °.
(d) make each station of taking the photograph that can shoot all marks as far as possible, that is, keep having 100% overlapping between all photos;If
It can only photograph to partial target, make that there is more overlapping and common point between adjacent shots as far as possible.
(e) station is at least taken the photograph at one, and camera is rotated by 90 ° shooting once.
For planar structure measured object, forming completely overlapped measurement net is best situation.But if object is too big or surveys
It, can only be using the photography that partly overlaps in the limited situation of quantity space.When measured object, which is, polyhedral structure, first to each surface
Net model location is carried out by preceding method, then takes the photograph station in the increase of face junction and photographs, the connection on surface each so is just established
Get up.
Step 7: servo angle detects: the index point coordinate that will be extracted in step 6 is first converted by photogrammetric coordinate system
Earth coordinates are transformed into laser tracker coordinate system, then by laser tracker coordinate system.It calculates and is mainly advised on industrial equipment
Then the precision of servo angle is detected to the angle of, horizontal plane in the method direction of plane and the earth north.
The main regular planar of industrial equipment refers to some larger and fixed with the position of equipment entirety plane of area.It is main
Want the normal direction calculation method of regular planar :(a) extract the photography index point coordinate for belonging to the plane;(b) least square is used
Plane fitting algorithm obtains the math equation of the plane;(c) normal equation of the plane is calculated.
The above is only the preferred embodiment of the present invention, protection scope of the present invention is not limited merely to above-described embodiment,
All technical solutions belonged under thinking of the present invention all belong to the scope of protection of the present invention.It should be pointed out that for the art
For those of ordinary skill, several improvements and modifications without departing from the principles of the present invention should be regarded as protection of the invention
Range.
Claims (6)
1. a kind of large-scale precision industrial equipment deflection and servo angle detecting method, it is characterized in that: the following steps are included:
Step 1: reconnaissance trip: to the geomery of industrial equipment, external environment, peripheral control point point bit distribution and intervisibility item
Part carries out reconnaissance trip, determines that the measurement mark layout scheme of industrial equipment, laser tracker set up point, industrial photogrammetry
Set up an office position and total station of system tray sets up point, and magnetic base is installed at determining measurement mark;
Step 2: establishing laser tracker coordinate system and determining laser tracker coordinate system common point mark: being tracked using laser
The measurement horizontal plane function of instrument obtains local gravity horizontal plane, and using laser tracker center as origin, horizontal plane normal direction is Z
Axis, the north establish independent right hand rectangular coordinate system in space, laser tracker coordinate system are named as, in magnetic base to for X-axis
Middle placement laser tracker reflection sphere reflects ball position with laser tracker measurement laser tracker, each magnetic base is made to exist
There is coordinate, wherein there are at least four magnetic bases to be defined as laser tracker coordinate system public in laser tracker coordinate system
Point mark;
Step 3: establishing photogrammetric coordinate system and determining photogrammetric coordinate system common point mark: being with photogrammetric center
Origin establishes photogrammetric coordinate system, and a foundation object staff is fixed at magnetic base, and photography mark target is placed in magnetic base
Ball, photography mark the target ball centre of sphere and the laser tracker reflection sphere centre of sphere overlapping, with industrial Digital Photogrammetric System to industrial equipment into
Row photography, obtains photogrammetric data;By measurement, the actual length of at least two benchmark line segments is obtained, benchmark line segment is magnetic
Property pedestal sphere centre coordinate between line, bring benchmark line segment length into photogrammetric data, to photogrammetric data carry out
Adjustment resolves, and magnetic base is made to have coordinate in photogrammetric coordinate system, while it is flat to obtain station meter in photogrammetric data
The length that station meter adjustment in photogrammetric data resolves is compared the length that difference resolves with the actual length of station meter,
To verify the photogrammetric space scale precision for resolving achievement;It will be defined as the magnetic of laser tracker coordinate system common point mark
Property pedestal is defined as photogrammetric coordinate system common point mark;
Step 4: determining earth coordinates common point mark: laying total station on the inside of the building locating for industrial equipment on metope
Reflector plate, reflector plate position for internal observation pier and laser tracker website will intervisibility it is good, observation angle is suitable, reflection
Piece is uniformly distributed in solid space;Using the total station oriented in national earth coordinates, all reflector plate centers are measured
Three-dimensional coordinate of the point in earth coordinates;Laser tracker is held into gauge head and withstands reflector plate center, measures all reflector plates
Three-dimensional coordinate of the center in laser tracker coordinate system;
Step 5: association photogrammetric coordinate system and earth coordinates: due to laser tracker coordinate system common point mark with take the photograph
Shadow measurement coordinate system common point mark position is identical, and as common point pair, computational photogrammetry coordinate system and laser are tracked
The conversion parameter of instrument coordinate system;Using reflector plate central point as common point pair, laser tracker coordinate system and geodetic coordinates are calculated
The conversion parameter of system;To obtain the conversion parameter of photogrammetric coordinate system and earth coordinates, photogrammetric coordinate system is realized
With being associated with for earth coordinates;
Step 6: gravity is detected from temperature deformation: deformation can be generated under the different gravity and state of temperature of industrial equipment, measured
Personnel carry measurement camera, to industrial equipment multi-angle take pictures measurement and extract measurement mark in photogrammetric coordinate system three
Coordinate is tieed up, obtains three of industrial equipment in earth coordinates using the conversion parameter of photogrammetric coordinate system and earth coordinates
Coordinate is tieed up, and utilizes the deflection of these coordinate analysis industrial equipments;
Step 7: servo angle detects: the measurement marker coordinates that will be extracted in step 6 utilize photogrammetric coordinate system and the earth
The conversion parameter of coordinate system obtains three-dimensional coordinate of the industrial equipment in earth coordinates, and it is flat to calculate main rule on industrial equipment
The method direction in face, by compared with, detecting the precision of servo angle with the earth north.
2. a kind of large-scale precision industrial equipment deflection according to claim 1 and servo angle detecting method, feature
It is: in step 3, the selection mode of benchmark line segment are as follows: in the magnetic base as laser tracker coordinate system common point mark
Four are chosen, as far as possible close to rectangle, benchmark line segment is that the sphere centre coordinate of four magnetic bases carries out what diagonal line obtained for distribution
Two lines section.
3. a kind of large-scale precision industrial equipment deflection according to claim 1 and servo angle detecting method, feature
It is: coding maker is set in the bottom of industrial equipment and back, for being associated with equipment itself with plant bottom case at the high elevation angle
Get up.
4. a kind of large-scale precision industrial equipment deflection according to claim 1 and servo angle detecting method, feature
Be: in step 6, survey crew, which carries measurement camera and carries out multi-angle by lifting device and shooting auxiliary telescopic bar, to take pictures survey
Amount, the lifting device are elevator, and the shooting auxiliary telescopic bar is three-section type telescopic rod, 6 meters of overall length, are fixed on liter
On drop machine.
5. a kind of large-scale precision industrial equipment deflection according to claim 1 and servo angle detecting method, feature
Be: each measurement mark will be captured by the industrial photogrammetry system of four or more different locations.
6. a kind of large-scale precision industrial equipment deflection according to claim 1 and servo angle detecting method, feature
Be: the length of the benchmark line segment is longer than station meter length.
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CN113686254A (en) * | 2021-08-13 | 2021-11-23 | 中铁第四勘察设计院集团有限公司 | Method and device for measuring surface stretching deformation of shield tunnel segment |
CN113686254B (en) * | 2021-08-13 | 2023-12-01 | 中铁第四勘察设计院集团有限公司 | Method and device for measuring surface expansion deformation of shield tunnel segment |
CN114877870A (en) * | 2022-05-18 | 2022-08-09 | 大连理工大学 | Large-size photogrammetry precision improving method based on virtual reference scale |
CN115265366A (en) * | 2022-07-29 | 2022-11-01 | 华能澜沧江水电股份有限公司 | Object deformation detection method and device, terminal equipment and storage medium |
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