CN114152245B - Multi-dimensional motion pose measurement system and calculation method for underwater suspension tunnel test - Google Patents
Multi-dimensional motion pose measurement system and calculation method for underwater suspension tunnel test Download PDFInfo
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- CN114152245B CN114152245B CN202210125047.5A CN202210125047A CN114152245B CN 114152245 B CN114152245 B CN 114152245B CN 202210125047 A CN202210125047 A CN 202210125047A CN 114152245 B CN114152245 B CN 114152245B
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Abstract
The invention relates to the technical field of ocean engineering, in particular to a multidimensional movement pose measuring system and a calculating method for an underwater suspension tunnel test, and solves the problem of measuring multidimensional and multimodal flexible movement deformation of an underwater suspension tunnel. The measurement and calculation method and the system can measure the bending, torsion or combined dynamic deformation of the suspension tunnel, obtain the displacement or posture of any section of the tunnel pipe body and realize the multi-dimensional and multi-mode flexible motion response measurement of the full-span structure of the suspension tunnel; the measuring method and the system provided by the invention have the advantages of clear principle, simple system composition, simple and convenient algorithm, high operation efficiency and convenience for installation and use, can be used for the research of the suspension tunnel technology, can also be used for the test measurement of other underwater long-span suspension and floating structures, and have wide application prospect.
Description
Technical Field
The invention relates to the technical field of ocean engineering, in particular to a multi-dimensional motion pose measuring system and a calculating method for an underwater suspension tunnel test.
Background
The floating tunnel is a large-scale cross-sea tunnel structure constructed in water and is a strategic and subversive technology for solving the crossing of deep water fjords in the future, but at present, the floating tunnel is not constructed in the world and is still in the research stage. Due to the large structural span and complex composition, the hydrodynamic response mechanism of the suspended tunnel structure system is very complex under the transient and variable marine power environment, and the problem to be broken through by researchers in various countries at present is urgently solved. The method directly simulates the effect of complex wave water flow load on the suspension tunnel in a test pool, obtains data such as the motion displacement and the attitude of the structure, and is the most direct means for researching hydrodynamic response of the suspension tunnel. The motion form of the long-span suspension tunnel structure is very complex, combined flexible motion deformation such as bending and torsion can be presented on the same tunnel section, more complex multi-dimensional and multi-modal flexible motion deformation can be presented on the whole span, and the measurement difficulty in a model test is greatly increased.
The existing non-contact floating body structure measuring system can only obtain six-dimensional motion data of a single target point, cannot measure multi-dimensional flexible motion of a full-span structure of a suspension tunnel, and cannot obtain displacement or posture of any section of a tunnel pipe body. Meanwhile, because the tunnel model is submerged underwater, the traditional contact-type measuring instrument can generate large interference on a wave water flow dynamic field, and the precision of test measurement is further influenced. In addition, the existing water measurement method needs to erect a higher and heavier instrument mounting bracket on the test model, and the additional mass and the vibration of the bracket caused by the instrument mounting bracket also have great influence on the measurement result.
Disclosure of Invention
Aiming at the problems, the invention aims to overcome the defects of the prior art, provides a multi-dimensional motion pose measurement system and a calculation method for an underwater suspension tunnel test, and solves the problem of multi-dimensional and multi-modal flexible motion deformation measurement of the underwater suspension tunnel. The invention adopts the underwater measurement method, thereby effectively avoiding the influence of the additional mass caused by the instrument mounting bracket and the self vibration of the bracket on the measurement result in the existing water measurement method; compared with the traditional single-target point six-dimensional floating body measurement system, the measurement method and the system provided by the invention can measure the bending, torsion or combined dynamic deformation of the suspended tunnel, obtain the displacement or posture of any section of the tunnel pipe body and realize the multi-dimensional and multi-modal flexible motion response measurement of the full-span structure of the suspended tunnel; compared with the traditional contact type measuring method, the measuring method and the system provided by the invention do not require the contact of the measuring instrument and the measured object, and the interference of the instrument on the wave water flow dynamic field is reduced to the maximum extent. Meanwhile, the measuring method and the system provided by the invention have the advantages of clear principle, simple system composition, simple algorithm, high operation efficiency and convenience in installation and use, can be used for research of the suspension tunnel technology, can also be used for test measurement of other underwater long-span suspension and floating structures, and have wide application prospects.
The technical scheme adopted by the invention for solving the technical problems is as follows: experimental multidimension degree motion position appearance measurement system of suspension tunnel under water, including suspension tunnel body, it is submarine, suspension tunnel surface is equipped with multiunit reflex reflector, reflex reflector is fixed connection with the suspension tunnel, the reflex reflector lower extreme is equipped with the displacement sensor device, displacement sensor device and submarine fixed connection, the displacement sensor device is connected with pencil C electricity, be equipped with turbidity appearance on the pencil C, turbidity appearance and pencil C electricity are connected, pencil C one end is equipped with multichannel data acquisition transceiver, multichannel data acquisition transceiver one end is equipped with the host computer, the host computer is connected with multichannel data acquisition transceiver electricity, the multichannel data acquisition transceiver other end is connected with turbidity appearance and pencil C electricity.
Further, the displacement sensor device comprises a laser sensor A, a laser sensor B, a laser sensor C and a wiring harness A, wherein the laser sensor A, the laser sensor B and the laser sensor C are electrically connected with each other, the laser sensor A, the laser sensor B and the laser sensor C are fixedly connected with the water bottom, and the laser sensor A, the laser sensor B and the laser sensor C are electrically connected with the wiring harness C through the wiring harness A.
The calculation method of the multi-dimensional motion pose measurement system for the underwater suspension tunnel test comprises the following steps:
s1: firstly, establishing a full-span coordinate system of an underwater suspension tunnel model;
s2: the coordinates y of each set of displacement sensor devices are then determinediX-direction distance DiAnd the radius R of the suspension tunnel;
s3: then obtaining the displacement value measured by each group of displacement sensor devices at the initial moment and the displacement value of the laser sensor ADisplacement value of laser sensor BDisplacement value of laser sensor C;
S4: then obtaining the displacement value measured by each group of displacement sensor devices at any other time and the displacement value of the laser sensor ADisplacement value of laser sensor BDisplacement value of laser sensor C;
S5: then calculating tube body at section position of suspension tunnel measured by each group of displacement sensor devices at any momentxTo the relative displacement valueB, andzrelative displacement value of;
S6: and finally, calculating to obtain the displacement and attitude value of any section of the underwater suspended tunnel.
Further, the origin of coordinates of the full-span coordinate system of the suspended tunnel model in S1 is located at the center of one end of the tunnel, the y-axis of the coordinate system is located in the horizontal plane and points to the axial direction of the tunnel, the x-axis of the coordinate system is located in the horizontal plane and points to the downstream direction of the wave water flow perpendicular to the axial direction of the tunnel, and the z-axis of the coordinate system is vertically upward.
Further, y in S2iIs a projection point of the coordinate origin on the water bottom to the secondiDistance of the lines of the group displacement sensor devices, DiAnd R is the radius of the suspended tunnel pipe body and is the minimum value of the distance between every two adjacent laser sensors.
Further, among the S3 and S4Anddefined as the displacement value measured by the laser sensor a,anddefined as the displacement value measured by the laser sensor C,andthe displacement value measured by the laser sensor B is defined, the 0 time is indicated by the superscript "0", and the other arbitrary time is indicated by the superscript "n".
Further, in said S5, The calculation method of (2) is as follows: the vertical upward and horizontal downstream movement of the tube body is defined as positive.
in the formula (I), the compound is shown in the specification,D i ,R,, , ,, , all the measured quantities are known quantities, and the displacement value of the pipe body at each measured cross section at any n moments is calculated by simultaneous equation sets and utilizing the Newton iteration method and the least square method principle,。
Further, the calculation method in S6 is that, after obtaining the displacements at several known cross sections, the displacement and attitude data at any cross section along the tunnel at any time can be obtained by interpolation,
in the formula (I), the compound is shown in the specification,andrespectively the x-direction and z-direction relative displacement values at the y-coordinate position along the tunnel at any moment,α k andβ k respectively at any time along the tunnely k The rotation angle of the tube body around the z-axis and the x-axis is at the coordinate.
The invention has the advantages that: the invention provides a multi-dimensional motion pose measuring system and a calculating method for an underwater suspended tunnel test, and the underwater measurement method is adopted, so that the influence of additional mass caused by an instrument mounting bracket and the vibration of the bracket on a measuring result in the existing water measurement method is effectively avoided; compared with the traditional single-target point six-dimensional floating body measurement system, the measurement method and the system provided by the invention can measure the bending, torsion or combined dynamic deformation of the suspended tunnel, obtain the displacement or posture of any section of the tunnel pipe body and realize the multi-dimensional and multi-modal flexible motion response measurement of the full-span structure of the suspended tunnel; compared with the traditional contact type measuring method, the measuring method and the system provided by the invention do not require the contact of the measuring instrument and the measured object, and the interference of the instrument on the wave water flow dynamic field is reduced to the maximum extent. Meanwhile, the measuring method and the system provided by the invention have the advantages of clear principle, simple system composition, simple algorithm, high operation efficiency and convenience in installation and use, can be used for research of the suspension tunnel technology, can also be used for test measurement of other underwater long-span suspension and floating structures, and have wide application prospects.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic perspective view of the present invention;
FIG. 2 is a schematic plan view, partially in section, of the present invention;
FIG. 3 is a schematic diagram of the coordinates of a laser sensor according to the present invention;
FIG. 4 is a schematic plan view of a partial cross-sectional coordinate system of the present invention;
FIG. 5 is a schematic diagram of the displacement coordinates of the suspension conduit of the present invention;
FIG. 6 shows the measurement using the laser sensor A of the present invention,Reference is made to the figure;
FIG. 7 shows the measurement using the laser sensor B of the present invention,Reference is made to the figure;
FIG. 8 shows the measurement using the laser sensor C of the present invention,Reference is made to the figure;
FIG. 9 is a schematic diagram of the present invention for full span displacement interpolation using displacement at a known cross-section.
Wherein:
1. a suspension tunnel; 2. a light reflecting means; 3. a displacement sensor device; 31. a laser sensor A; 32. a laser sensor B; 33. a laser sensor C; 34. a wire harness A; 4. a wire harness C; 5. a turbidity meter; 6. an upper computer; 7. a multi-channel data acquisition transceiver; 8. the surface of the water.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that unless otherwise explicitly specified or limited, the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplicity of description, and do not indicate or imply that the referred 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, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance, and 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 in specific cases to those skilled in the art.
Example 1:
fig. 1 is a schematic view of a three-dimensional structure of the invention, fig. 2 is a schematic view of a plane partial section of the invention, a plurality of groups of light reflecting devices 2 are arranged on the outer surface of a suspension tunnel 1, the light reflecting devices 2 are fixedly connected with the suspension tunnel 1, a displacement sensor device 3 is arranged at the lower end of the light reflecting devices 2, the displacement sensor device 3 is fixedly connected with the water bottom, the displacement sensor device 3 is electrically connected with a wiring harness C4, a turbidity meter 5 is arranged on the wiring harness C4, the turbidity meter 5 is electrically connected with the wiring harness C4, a multi-channel data acquisition transceiver 7 is arranged at one end of the wiring harness C4, an upper computer 6 is arranged at one end of the multi-channel data acquisition transceiver 7, the upper computer 6 is electrically connected with the multi-channel data acquisition transceiver 7, and the other end of the multi-channel data acquisition transceiver 7 is electrically connected with the turbidity meter 5 and the wiring harness C4. The displacement sensor device 3 comprises a laser sensor A31, a laser sensor B32, a laser sensor C33 and a wiring harness A34, wherein the laser sensor A31, the laser sensor B32 and the laser sensor C33 are all sensors of L4-40 types, the laser sensor A31, the laser sensor B32 and the laser sensor C33 are electrically connected with each other, the laser sensor A31, the laser sensor B32 and the laser sensor C33 are fixedly connected with the water bottom, and the laser sensor A31, the laser sensor B32 and the laser sensor C33 are electrically connected with the wiring harness C4 through the wiring harness A34. The underwater displacement sensor device comprises a plurality of groups of underwater displacement sensor devices 3 arranged along the axis direction of a tunnel, at least 3 sensors in each group are arranged under a tube body side by side at equal intervals, the connecting line of the sensors is vertical to the axis direction of the suspended tunnel, one of the sensors is arranged on the axis of the tube body passing through the center of a circle, and the other two sensors are arranged on two sides of the tube body at equal intervals. The reflecting device 2 can be designed into a flexible white material with a rough surface, is attached to the lower surface of the suspension tunnel 1 test model, can form diffuse reflection on laser, and the area of the reflecting device 2 is enough to cover the irradiation range of a laser spot. Laser emitted by the laser sensor is reflected back by the reflecting device below the test model of the suspension tunnel 1 and then returns back to the laser sensor again, so that distance data between the laser sensor and the corresponding reflecting point is obtained. The turbidity meter 5 is arranged near any one group of displacement sensor devices 3 under water and is used for measuring the turbidity of water in real time so as to correct and compensate the distance measurement value of the underwater displacement sensor and ensure the measurement accuracy. The multichannel data acquisition transceiver 7 is connected with all the underwater displacement sensor devices 3 and the turbidity meter 5, can synchronously acquire distance data and underwater turbidity data of the underwater laser sensor, and converts the distance data and the underwater turbidity data into digital signals through an internal data conversion module to be transmitted to an operating system of the upper computer 6. The upper computer 6 operating system further integrates and analyzes the collected digital signals through a matched software analysis system, so that the multi-dimensional and multi-modal motion displacement and attitude data of the whole underwater suspension tunnel 1 are calculated.
Example 2:
the calculation method is as follows
FIG. 3 is a schematic diagram of the coordinates of a laser sensor according to the present invention, and FIG. 4 is a schematic diagram of the coordinates of a planar partial cross-section according to the present invention; fig. 5 is a schematic diagram of displacement coordinates of a suspension pipeline, and the calculation method of the underwater suspension tunnel test multi-dimensional motion pose measurement system shown in fig. 3 includes the following steps:
s1: firstly, establishing a full-span coordinate system of an underwater suspension tunnel 1 model;
s2: the coordinates y of each set of displacement sensor devices 3 are then determinediX-direction distance DiAnd the radius R of the suspension tunnel 1;
s3: then, the displacement value measured by each set of displacement sensor device 3 at the initial time, the displacement value of the laser sensor a31 is obtainedDisplacement value of laser sensor B32Displacement value of the laser sensor C33;
S4: then obtaining the displacement value measured by each group of displacement sensor devices at any other time and the displacement value of the laser sensor ADisplacement value of laser sensor BDisplacement value of laser sensor C;
S5: then calculating the relative displacement value of the pipe body at the section of the suspension tunnel 1 measured by each group of displacement sensor devices 3 at any moment,;
S6: and finally, calculating to obtain the displacement and attitude value of any section of the underwater suspended tunnel 1.
The origin of coordinates of the full-span coordinate system of the S1 suspension tunnel 1 model is arranged at the center of one end of the tunnel, the y axis of the coordinate system is arranged in the horizontal plane and points to the axial direction of the tunnel, the x axis of the coordinate system is arranged in the horizontal plane and is perpendicular to the axial direction of the tunnel and points to the downstream direction of the wave water flow, and the z axis of the coordinate system is vertically upward.
Y in S2iIs the distance from the projected point of the origin of coordinates on the water bottom to the connecting line of the i-th group of displacement sensor devices 3, DiFor the minimum of every group adjacent two laser sensor distance between, because for tunnel length, the bending deformation volume in tunnel is very little, so this application is looked displacement sensor device 3 and is measured the cross-section and be the circle cross-section, and R is the radius of suspension tunnel 1 body.
In S3 and S4Anddefined as the displacement value measured by the laser sensor a31,anddefined as the displacement value measured by the laser sensor C33,andthe displacement value measured by the laser sensor B32 is defined as the time 0 is indicated by the superscript "0", and the other arbitrary time is indicated by the superscript "n".
In S5, The calculation method of (2) is as follows: the vertical upward movement and the horizontal downstream movement of the pipe body are defined as positive respectively,
in the formula (I), the compound is shown in the specification,D i ,R,,,,, , all the measured quantities are known quantities, and the displacement value of the pipe body at each measured cross section at any n moments is calculated by simultaneous equation sets and utilizing the Newton iteration method and the least square method principle, 。
The calculation method in S6 is as follows, and after obtaining displacements at a plurality of known cross sections, displacement and attitude data at any cross section along the tunnel at any time can be obtained by using a polynomial interpolation method. In this embodiment, the data interpolation is performed by using the conventional commonly used lagrangian interpolation formula (Lagrange interpolation format).
As shown in FIG. 9, the number of the known cross sections of the suspension tunnel 1 is set asMThen is aty0xAt any n time in the planeMRelative displacement coordinates of the cross section of each suspension tunnel: (y 1, )、(y 2, )…(y i , )…(y M, ) (ii) a In the same way, it isy0zAnd M relative displacement coordinates of the cross sections of the suspension tunnels exist at any n moments in the plane: (y 1, )、(y 2, )…(y i , )…(y M,)。
Directly applying Lagrange interpolation formula (Lagrange interpolation formula) to obtain the line of the suspended tunnel at any n momentyAt coordinatesxTo andzthe relative displacement value is as follows:
then, by utilizing the relation between the slope of the curve and the derivative of the function and the principle of solving the angle by the inverse trigonometric function, the line of the suspended tunnel at any moment can be solvedy k Rotation angle of tube body around z axis at coordinateα k And angle of rotation about the x-axisβ k 。
The displacement and attitude data of any section along the tunnel at any time are brought intoα k Andβ k the formula of the inverse trigonometric function is obtained:
in the formula (I), the compound is shown in the specification,andrespectively the x-direction and z-direction relative displacement values at the y-coordinate position along the tunnel at any moment,α k andβ k respectively at any time along the tunnely k The rotation angle of the tube body around the z-axis and the x-axis is at the coordinate.
The measuring method and the system provided by the invention have the advantages of clear principle, simple system composition, simple and convenient algorithm, high operation efficiency and convenience for installation and use, can be used for the research of the suspension tunnel technology, can also be used for the test measurement of other underwater long-span suspension and floating structures, and have wide application prospect.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (7)
1. Experimental multidimension degree motion position appearance measurement system of suspension tunnel under water, including suspension tunnel (1) body, its characterized in that: the outer surface of the suspension tunnel (1) is provided with a plurality of groups of light reflecting devices (2), the light reflecting devices (2) are fixedly connected with the suspension tunnel (1), the lower end of each light reflecting device (2) is provided with a displacement sensor device (3), the displacement sensor device (3) is fixedly connected with the bottom of the water, the displacement sensor device (3) is electrically connected with a wiring harness C (4), a turbidity meter (5) is arranged on the wiring harness C (4), the turbidity meter (5) is electrically connected with the wiring harness C (4), one end of the wiring harness C (4) is provided with a multi-channel data acquisition transceiver (7), one end of the multi-channel data acquisition transceiver (7) is provided with an upper computer (6), the upper computer (6) is electrically connected with the multi-channel data acquisition transceiver (7), and the other end of the multi-channel data acquisition transceiver (7) is electrically connected with the turbidity meter (5) and the wiring harness C (4); the calculation method of the multi-dimensional motion pose measurement system for the underwater suspension tunnel test comprises the following steps:
s1: firstly, establishing a full-span coordinate system of an underwater suspension tunnel (1) model;
s2: then determining the coordinates y of each set of displacement sensor devices (3)iX-direction distance DiAnd the radius R of the suspension tunnel (1);
s3: then, the displacement value measured by each group of displacement sensor devices (3) at the initial moment and the displacement value of the laser sensor A (31) are obtainedAnd the displacement value of the laser sensor B (32)And the displacement value of the laser sensor C (33);
S4: then, the displacement value measured by each group of displacement sensor devices at any other time and the displacement value of the laser sensor A (31) are obtainedAnd the displacement value of the laser sensor B (32)And the displacement value of the laser sensor C (33);
S5: then theCalculating the x-direction relative displacement value of the pipe body at the section of the suspension tunnel (1) measured by each group of displacement sensor devices (3) at any momentAnd z-direction relative displacement value;
S6: and finally, calculating to obtain the displacement and attitude values of any section of the underwater suspended tunnel (1).
2. The underwater suspended tunnel test multi-dimensional motion pose measurement system according to claim 1, characterized in that: the displacement sensor device (3) comprises a laser sensor A (31), a laser sensor B (32), a laser sensor C (33) and a wiring harness A (34), the laser sensor A (31), the laser sensor B (32) and the laser sensor C (33) are electrically connected with each other, the laser sensor A (31), the laser sensor B (32) and the laser sensor C (33) are fixedly connected with the water bottom, and the laser sensor A (31), the laser sensor B (32) and the laser sensor C (33) are electrically connected with the wiring harness C (4) through the wiring harness A (34).
3. The calculation method of the underwater suspended tunnel test multi-dimensional motion pose measurement system according to claim 1, characterized in that: the origin of coordinates of a full-span coordinate system of the suspended tunnel (1) model in the S1 is arranged at the center of one end of the tunnel, the y axis of the coordinate system is arranged in the horizontal plane and points to the axial direction of the tunnel, the x axis of the coordinate system is arranged in the horizontal plane and points to the downstream direction of the wave water flow perpendicular to the axial direction of the tunnel, and the z axis of the coordinate system is vertically upward.
4. The calculation method of the underwater suspended tunnel test multi-dimensional motion pose measurement system according to claim 1, characterized in that: y in S2iIs the distance from the projection point of the coordinate origin point on the water bottom to the connecting line of the ith group of displacement sensor devices (3),Diand R is the radius of the pipe body of the suspension tunnel (1) and is the minimum value of the distance between every two adjacent laser sensors.
5. The calculation method of the underwater suspended tunnel test multi-dimensional motion pose measurement system according to claim 1, characterized in that: of the S3 and S4Anddefined as the displacement value measured by the laser sensor A (31),anddefined as the displacement value measured by the laser sensor C (33),andthe displacement value measured by the laser sensor B (32) is defined, and the time 0 is indicated by a superscript "0", and the other arbitrary time is indicated by a superscript "n".
6. The calculation method of the underwater suspended tunnel test multi-dimensional motion pose measurement system according to claim 1, characterized in that: in said S5, The calculation method of (2) is as follows: defining the wave water of the pipe body respectively vertically upwards and horizontallyThe movement of the downstream is positive,
in the formula, Di,R,,,,,,All the measured values are known quantities, and the x-direction relative displacement value of the pipe body at each measured cross section at any n moments is calculated and obtained by simultaneous equation sets and the Newton iteration method and the least square method principleAnd z-direction relative displacement value。
7. The calculation method of the underwater suspended tunnel test multi-dimensional motion pose measurement system according to claim 1, characterized in that: the calculation method in S6 is as follows, when the displacement at several known cross sections is obtained, the displacement and attitude data at any cross section along the tunnel at any time can be obtained by interpolation method,
in the formula (I), the compound is shown in the specification,andrespectively is the x-direction and z-direction relative displacement value alpha of the y coordinate position along the tunnel at any timekAnd betakRespectively at any time along the tunnelkThe rotation angle of the tube body around the z-axis and the x-axis is at the coordinate.
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CN103969068A (en) * | 2014-04-11 | 2014-08-06 | 中国科学院力学研究所 | Method and device for simulating axial interaction between undersea pipe system structure and seabed soil body |
CN105091858A (en) * | 2015-08-02 | 2015-11-25 | 上海砺晟光电技术有限公司 | Two-dimension inclination angle non-contact measurement method and system based on absolute distance measurement |
CN109297427A (en) * | 2018-10-17 | 2019-02-01 | 北京市政建设集团有限责任公司 | A kind of portable laser monitoring instrument applied to tunnel convergence Deformation control |
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