CN113091630B - Method and system for analyzing deformation of inner wall of closed rectangular water delivery structure - Google Patents
Method and system for analyzing deformation of inner wall of closed rectangular water delivery structure Download PDFInfo
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Abstract
The invention relates to a deformation analysis method and a system for an inner wall of a closed rectangular water delivery structure, which are characterized by comprising the following steps: 1) under the state that the water delivery structure is emptied, carrying out three-dimensional laser scanning on the inner wall of the water delivery structure at a certain fixed position in the water delivery structure by a laser scanning device, and determining the rectangular coordinates of each scanning point on a right section which is perpendicular to the water flow direction and corresponds to the fixed position; 2) performing curve fitting on the determined rectangular coordinates of the scanning points on the normal section, and the pre-assumed flexural deformation equations and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure to determine the flexural deformation equations of the axes of all sides of the normal section; 3) changing the position of the laser scanning device along the water flow direction, and entering the step 1), determining the flexural deformation equation of each side axis of each right section of the inner wall of the water delivery structure along the water flow direction, and further determining the deformation form of the water delivery structure.
Description
Technical Field
The invention relates to a deformation analysis method and a deformation analysis system for an inner wall of a closed rectangular water delivery structure, and belongs to the technical field of structural engineering.
Background
At present, in engineering practice, the shape of the inner wall of a closed rectangular water delivery structure such as a water delivery structure, an inverted siphon, a hidden culvert and the like after being emptied can be generally obtained by adopting a three-dimensional laser scanning method, so that the deformation state of the water delivery structure can be deduced, and data support is provided for safety evaluation of the water delivery structure. However, after the actual water conveying structure is emptied, silts, mactra and other sediments with different thicknesses are attached to the inner wall of the water conveying structure, so that a large error is brought to laser ranging, and the accuracy of safety assessment of the water conveying structure is affected.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a method and a system for analyzing the deformation of an inner wall of a closed rectangular water delivery structure, which can determine the deformation accurately.
In order to achieve the purpose, the invention adopts the following technical scheme: a deformation analysis method for an inner wall of a closed rectangular water delivery structure comprises the following steps:
1) under the state that the water delivery structure is emptied, carrying out three-dimensional laser scanning on the inner wall of the water delivery structure at a certain fixed position in the water delivery structure by a laser scanning device, and determining the rectangular coordinates of each scanning point on a right section which is perpendicular to the water flow direction and corresponds to the fixed position;
2) performing curve fitting on the rectangular coordinates of the scanning points on the determined normal section, and the pre-assumed flexural deformation equations and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure by adopting a nonlinear optimization method based on a least square method, determining undetermined coefficients in the flexural deformation equations, and further determining the flexural deformation equations of the side axes of the normal section;
3) changing the position of the laser scanning device along the water flow direction, and entering the step 1), determining the flexural deformation equation of each side axis of each right section of the inner wall of the water delivery structure along the water flow direction, and further determining the deformation form of the water delivery structure.
Further, the specific process of the step 1) is as follows:
1.1) carrying out three-dimensional laser scanning on the inner wall of the water conveying structure at a certain fixed position in the water conveying structure by a laser scanning device under the emptying state of the water conveying structure, and determining the space coordinates (r, theta, psi) of each scanning point on the inner wall of the water conveying structure under a spherical coordinate system taking the rotation center of the laser scanning device as the origin, wherein the positive section psi vertical to the water flow directionx∈[ψmin,ψmax]，ψminFor controlling the minimum horizontal azimuth angle psi during three-dimensional laser scanningmaxThe maximum horizontal azimuth angle controlled during three-dimensional laser scanning is obtained;
1.2) extracting scanning points of θ ═ 0 and π from the three-dimensional laser scanning results to obtain (r)11,0,ψ1)、(r21,0,ψ2)、(r31,0,ψ3)、……、(r12,π,ψ1)、(r22,π,ψ2)、(r32,π,ψ3) … …; let parameter d1＝r11+r12，d2＝r21+r22，d3＝r31+r32，……，di＝ri1+ri2… …, and obtaining dminCorresponding toPositive section psixWherein ψ1、ψ2、ψ3… … is the horizontal azimuth; r is11、r21、r31……ri1The horizontal distance from the rotation center to the inner wall of the water conveying structure when the rotation angle of the vertical surface of the laser scanning device is 0 radian; r is12、r22、r32……ri2The horizontal distance from the rotating center to the inner wall when the rotating angle of the vertical surface of the laser scanning device is pi radian; dminIs a parameter d1、d2、d3… …, i is the number of scanning points;
1.3) let rix＝ri1cos(ψx-ψ1) To obtain each scanning point (r) on the normal section1x,θ1,ψx)、(r2x,θ2,ψx)、(r3x,θ3,ψx) … …, and converting the coordinates of each scanning point on the right section into rectangular coordinates, wherein rixDenotes r1x、r2x、r3x… …, x is a right cross section, theta1、θ2、θ3… … is r1x、r2x、r3xThe corresponding laser scanning device rotates at the vertical surface.
Further, the specific process of step 2) is as follows:
2.1) assuming a flexural deformation equation and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure;
and 2.2) performing curve fitting by using a nonlinear optimization method based on a least square method according to rectangular coordinates of each scanning point on the normal section and by combining the assumed flexural deformation equations and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure, determining undetermined coefficients in the assumed flexural deformation equations, and further determining the flexural deformation equations of the axes of all sides of a certain normal section of the inner wall of the water delivery structure.
Further, the specific process of step 2.1) is as follows:
2.1.1) deflection of the axes of the left and right side walls of the inner wall of the water transport structure in a rectangular coordinate system parallel to the axesThe shape equation is a fourth order polynomial, therefore, assume the left wall deflection equation f1(y) is:
f1(y)＝A1y4+B1y3+C1y2+D1y+E1
wherein A is1、B1、C1、D1And E1Are all undetermined coefficients;
deflection equation f for right side wall2(y) is:
f2(y)＝A2y4+B2y3+C2y2+D2y+E2
wherein A is2、B2、C2、D2And E2Are all undetermined coefficients;
2.1.2) deflection equation of the bottom and top plate axes of the inner wall of the water transport structure in a rectangular coordinate system parallel to the axes is a sixth order polynomial, therefore, the deflection equation g of the bottom plate is assumed1(x) Comprises the following steps:
g1(x)＝A3x6+B3x5+C3x4+D3x3+E3x2+F3x+G3
wherein A is3、B3、C3、D3、E3、F3And G3Are all undetermined coefficients;
the flexural deformation equation for the top plate is:
g2(x)＝A4x6+B4x5+C4x4+D4x3+E4x2+F4x+G4
wherein A is4、B4、C4、D4、E4、F4And G4Are all undetermined coefficients;
2.1.3) the above-assumed respective flexural deformation equations should satisfy the constraint curve f1(y)⊥g1(x)、f1(y)⊥g2(x)、f2(y)⊥g1(x) And f2(y)⊥g2(x)。
Further, in the step 2), when wedge-shaped chamfers exist between the left and right side walls of the inner wall of the water delivery structure and the bottom plate, the rotation angles of the axes of the left and right side walls are determined:
firstly, determining rectangular coordinates of each scanning point on a wedge-shaped chamfer on the inner wall of a water delivery structure through three-dimensional laser scanning of a laser scanning device, and determining the slope k of the bevel edge of the wedge-shaped chamfer under the rectangular coordinate system1；
According to determined slope k1And the slope k of the bevel edge of the wedge chamfer in the design drawing2And obtaining a corner alpha of the wedge-shaped chamfer angle of the inner wall of the water delivery structure, taking the corner alpha as the corners of the axes of the left and right walls of the inner wall of the water delivery structure, and further assuming that the flexural deformation equation of the left and right walls of the inner wall of the water delivery structure with the wedge-shaped chamfer angle exists according to the corners of the axes of the left and right walls of the inner wall of the water delivery structure.
Further, in the step 2.2), the following method is adopted to simplify the simultaneous equations:
a) move rectangular coordinate system to the intersection point position of the left side wall axis of water delivery structure and bottom plate axis to rotate to and be parallel with left side wall axis, then the flexural deformation equation of the left side wall axis of water delivery structure is:
f1(y)＝A1y4+B1y3+C1y2
b) the rectangular coordinate system is moved to the intersection point position of the right side wall axis and the bottom plate axis of the water conveying structure, and is rotated to be parallel to the left side wall axis, and then the flexural deformation equation of the right side wall axis of the water conveying structure is as follows:
f2(y)＝A2y4+B2y3+C2y2
c) the rectangular coordinate system is moved to the intersection point position of the left side wall axis and the bottom plate axis of the water conveying structure, and is rotated to be parallel to the bottom plate axis, and then the flexural deformation equation of the bottom plate of the water conveying structure is as follows:
g1(x)＝A3x6+B3x5+C3x4+D3x3+E3x2
d) the rectangular coordinate system is moved to the intersection point position of the left side wall axis and the top plate axis of the water conveying structure, and is rotated to be parallel to the top plate axis, and then the flexural deformation equation of the top plate of the water conveying structure is as follows:
g2(x)＝A4x6+B4x5+C4x4+D4x3+E4x2。
further, in the step 2.2), the following method is adopted to simplify the simultaneous equations:
A) move rectangular coordinate system to the intersection point position of the left side wall inner wall of water delivery structure and bottom plate inner wall to rotate to and be parallel with left side wall axis, then the flexural deformation equation of the left side wall inner wall of water delivery structure is:
f1(y)＝A1y4+B1y3+C1y2+0.5H1
wherein H1Is the thickness of the left side wall;
B) move the right side wall inner wall of rectangular coordinate system to water delivery structure and the intersect position of bottom plate inner wall to rotate to and be parallel with left side wall axis, then the flexural deformation equation of the right side wall inner wall of water delivery structure is:
f2(y)＝A2y4+B2y3+C2y2-0.5H2
wherein H2Is the thickness of the left side wall;
C) the rectangular coordinate system is moved to the intersection point position of the inner wall of the side wall of the water conveying structure and the inner wall of the bottom plate, and is rotated to be parallel to the axis of the bottom plate, and then the flexural deformation equation of the bottom plate of the water conveying structure is as follows:
g1(x)＝A3x6+B3x5+C3x4+D3x3+E3x2+0.5H3
wherein H3Is the thickness of the bottom plate;
D) the rectangular coordinate system is moved to the intersection point position of the inner wall of the side wall of the water conveying structure and the inner wall of the top plate, and is rotated to be parallel to the axis of the top plate, and then the flexural deformation equation of the top plate of the water conveying structure is as follows:
g2(x)＝A4x6+B4x5+C4x4+D4x3+E4x2-0.5H4
wherein H4Is the thickness of the base plate.
Further, for a water delivery structure with double or multiple parallel tanks, one tank is emptied, the flexural deformation equation of the empty tank under the water filling operation condition of the other tanks is determined, and the flexural deformation equation of the empty tank under different water level conditions is obtained by changing the operation water level.
Furthermore, the laser scanning device adopts a movable laser scanning device to perform three-dimensional laser scanning on the inner wall of the water delivery structure at a certain speed in a moving state.
An enclosed rectangular water delivery structure inner wall deformation analysis system, comprising:
the rectangular coordinate determination module is used for carrying out three-dimensional laser scanning on the inner wall of the water delivery structure at a certain fixed position in the water delivery structure through the laser scanning device under the emptying state of the water delivery structure and determining the rectangular coordinate of each scanning point on a right section which is corresponding to the fixed position and is vertical to the water flow direction;
the nonlinear optimization module is used for performing curve fitting on the rectangular coordinates of the scanning points on the determined normal section, and the pre-assumed flexural deformation equations and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure by adopting a nonlinear optimization method based on a least square method, determining undetermined coefficients in the flexural deformation equations and further determining the flexural deformation equations of the axes of the sides of the normal section;
and the deformation form determining module is used for determining the deformation form of the water delivery structure according to the flexural deformation equation of each side axis of each regular section of the inner wall of the water delivery structure along the water flow direction.
Due to the adoption of the technical scheme, the invention has the following advantages: the invention is based on the point cloud data of three-dimensional laser scanning, and according to the theory of structural mechanics, a nonlinear optimization method based on a least square method is adopted to fit and obtain the flexural deformation equation of the left and right side walls, the bottom plate, the top plate and other members of the inner wall of the water delivery structure, so that the deformation form of the water delivery structure can be determined, and the deformation of the inner wall of the water delivery structure can be analyzed.
Drawings
FIG. 1 is a schematic diagram of a laser scanning result and a fitted deflection curve of an inner wall of a cross section of a closed rectangular water delivery structure according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of an established spherical coordinate system according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a deformed shape of a cross section of a closed rectangular water delivery structure according to an embodiment of the present invention, in which fig. 3(a) is a schematic diagram of a deformed shape of a left side wall of a cross section of a water delivery structure, fig. 3(b) is a schematic diagram of a deformed shape of a right side wall of a cross section of a water delivery structure, fig. 3(c) is a schematic diagram of a deformed shape of a bottom plate of a cross section of a water delivery structure, and fig. 3(d) is a schematic diagram of a deformed shape of a top plate of a cross section of a water delivery structure;
fig. 4 is a schematic diagram of a deformed shape of a cross section of a closed rectangular water delivery structure according to another embodiment of the present invention, in which fig. 4(a) is a schematic diagram of a deformed shape of a left side wall of a cross section of a water delivery structure, fig. 4(b) is a schematic diagram of a deformed shape of a right side wall of a cross section of a water delivery structure, fig. 4(c) is a schematic diagram of a deformed shape of a bottom plate of a cross section of a water delivery structure, and fig. 4(d) is a schematic diagram of a deformed shape of a top plate of a cross section of a water delivery structure;
fig. 5 is a schematic cross-sectional view of a closed rectangular water delivery structure according to an embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It is to be understood that the terminology used herein is for the purpose of describing particular example embodiments only, and is not intended to be limiting. As used herein, the singular forms "a", "an" and "the" may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms "comprises," "comprising," "including," and "having" are inclusive and therefore specify the presence of stated features, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and/or groups thereof. The method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order described or illustrated, unless specifically identified as an order of performance. It should also be understood that additional or alternative steps may be used.
Although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms may be only used to distinguish one element, component, region, layer or section from another region, layer or section. Terms such as "first," "second," and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the example embodiments.
For convenience of description, spatially relative terms, such as "inner", "outer", "lower", "upper", and the like, may be used herein to describe one element or feature's relationship to another element or feature as illustrated in the figures. Such spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures.
As shown in fig. 1, which is a schematic diagram of deformation of an inner wall of a water delivery structure, the method and the system for analyzing deformation of an inner wall of a closed rectangular water delivery structure provided by the embodiment of the present invention analyze deformation forms of the inner wall of the water delivery structure by controlling curves of a side wall and a bottom plate to be continuous at an intersection point position and determining a flexural deformation equation of the side wall and the bottom plate by a nonlinear optimization method based on a least square method based on a conventional detection result and according to a basic principle of material mechanics.
Example 1
The embodiment provides a deformation analysis method for an inner wall of a closed rectangular water delivery structure, which comprises the following steps:
1) under the state that the water conveying structure is empty, the laser scanning device carries out three-dimensional laser scanning on the inner wall of the water conveying structure at a certain fixed position in the water conveying structure, and the space coordinates (r, theta, psi) of each scanning point on the inner wall of the water conveying structure under a spherical coordinate system taking the rotation center of the laser scanning device as an origin are determined, as shown in figure 2, wherein the normal section perpendicular to the water flow direction is within the scanning range, namely the normal section psix∈[ψmin,ψmax]，ψminFor controlling the minimum horizontal azimuth angle psi during three-dimensional laser scanningmaxThe maximum horizontal azimuth angle controlled during three-dimensional laser scanning.
2) (r) can be obtained by extracting a scanning point where θ is 0 and pi from the three-dimensional laser scanning result11,0,ψ1)、(r21,0,ψ2)、(r31,0,ψ3)、……、(r12,π,ψ1)、(r22,π,ψ2)、(r32,π,ψ3) … …. Let parameter d1＝r11+r12，d2＝r21+r22，d3＝r31+r32，……，di＝ri1+ri2… …, and obtaining dminCorresponding normal section psixWherein ψ1、ψ2、ψ3… … is the horizontal azimuth; r is11、r21、r31……ri1The horizontal distance from the rotation center to the inner wall of the water conveying structure when the rotation angle of the vertical surface of the laser scanning device is 0 radian; r is12、r22、r32……ri2The horizontal distance from the rotating center to the inner wall when the rotating angle of the vertical surface of the laser scanning device is pi radian; dminIs a parameter d1、d2、d3……diI is the number of scanning points.
3) Let r beix＝ri1cos(ψx-ψ1) Each scanning point (r) on the normal section can be obtained1x,θ1,ψx)、(r2x,θ2,ψx)、(r3x,θ3,ψx) … …, and converting the coordinates of each scanning point on the right section into rectangular coordinates, wherein rixDenotes r1x、r2x、r3x… …, x is a right cross section, theta1、θ2、θ3… … is r1x、r2x、r3xThe corresponding laser scanning device rotates at the vertical surface.
4) Performing curve fitting on the rectangular coordinates of the scanning points on the normal section obtained in the step 3) and the pre-assumed flexural deformation equations and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure by using a nonlinear optimization method based on a least square method, determining undetermined coefficients in the flexural deformation equations, and further determining the flexural deformation equations of the side axes of the normal section, wherein the method specifically comprises the following steps:
4.1) assuming the flexural deformation equation and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water conveying structure:
4.1.1) the flexural deformation equation of the left and right sidewall axes of the inner wall of the water transport structure in a rectangular coordinate system parallel to the axes is a fourth order polynomial, therefore, assume the flexural deformation equation f of the left sidewall1(y) is:
f1(y)＝A1y4+B1y3+C1y2+D1y+E1 (1)
wherein A is1、B1、C1、D1And E1Are all undetermined coefficients.
Deflection equation f for right side wall2(y) is:
f2(y)＝A2y4+B2y3+C2y2+D2y+E2 (2)
wherein A is2、B2、C2、D2And E2Are all undetermined coefficients.
4.1.2) deflection equation of the bottom and top plate axes of the inner wall of the water transport structure in a rectangular coordinate system parallel to the axes is a sixth order polynomial, therefore, the deflection equation g of the bottom plate is assumed1(x) Comprises the following steps:
g1(x)＝A3x6+B3x5+C3x4+D3x3+E3x2+F3x+G3 (3)
wherein A is3、B3、C3、D3、E3、F3And G3Are all undetermined coefficients.
The flexural deformation equation for the top plate is:
g2(x)＝A4x6+B4x5+C4x4+D4x3+E4x2+F4x+G4 (4)
wherein A is4、B4、C4、D4、E4、F4And G4Are all undetermined coefficients.
4.1.3) the above assumed respective flexural deformation equations should satisfy the constraint curve f1(y)⊥g1(x)、f1(y)⊥g2(x)、f2(y)⊥g1(x) And f2(y)⊥g2(x)。
4.2) adopting a nonlinear optimization method based on a least square method, carrying out curve fitting according to the rectangular coordinates of each scanning point on the normal section obtained in the step 3) and the flexural deformation equations and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure assumed in the step 4.1), determining undetermined coefficients in each assumed flexural deformation equation, and further determining the flexural deformation equations of the side axes of a certain normal section of the inner wall of the water delivery structure.
5) Changing the position of the laser scanning device along the water flow direction, and entering the step 1), and determining the flexural deformation equation of each side axis of each right section of the inner wall of the water delivery structure along the water flow direction.
6) And determining the deformation form of the water delivery structure according to the flexural deformation equation of the axis of each side of each positive section of the inner wall of the water delivery structure along the water flow direction, and further analyzing the deformation of the inner wall of the water delivery structure.
For example: as shown in fig. 3(a) to 3(d), the deformation forms of the left and right side walls of the water delivery structure are basically symmetrical, and the top of the side wall has an obvious recurved tendency, which indicates that the top plate tie rod has good performance and the relative deformation difference between the bottom and the top of the left and right side walls is not large.
As shown in fig. 4(a) to 4(d), the deformation of the left side wall of the cross section of the water delivery structure is obvious, which illustrates that the pull rod of the top plate of the cross section basically has no limit effect on the deformation of the left side wall, i.e. the connection performance between the pull rod and the side wall is poor; the right side wall of the section of the water conveying structure is not deformed, and the difference of the relative deformation of the top and the bottom of the left side wall and the right side wall is large. Meanwhile, the top plate of the water delivery structure has a tendency of obviously inclining towards the right.
In a preferred embodiment, in step 4), as shown in fig. 5, when there is a wedge-shaped chamfer between the left and right side walls of the inner wall of the water delivery structure and the bottom plate, the rotation angle of the axis of the left and right side walls can be obtained according to the following method:
firstly, determining rectangular coordinates of each scanning point on a wedge-shaped chamfer on the inner wall of a water delivery structure through three-dimensional laser scanning of a laser scanning device, and determining the slope k of the bevel edge of the wedge-shaped chamfer under the rectangular coordinate system1，
According to determined slope k1And the slope k of the bevel edge of the wedge chamfer in the design drawing2To obtain a wedge-shaped chamfer on the inner wall of the water delivery structureAnd the rotation angle alpha is used as the rotation angle of the axes of the left and right walls of the inner wall of the water delivery structure, and the deflection deformation equation of the left and right walls of the inner wall of the water delivery structure with the wedge-shaped chamfer angle can be assumed according to the rotation angle of the axes of the left and right walls of the inner wall of the water delivery structure.
In a preferred embodiment, in step 4.2) above, the simultaneous equations can be simplified in the following way:
a) move rectangular coordinate system to the intersection point position of the left side wall axis of water delivery structure and bottom plate axis to rotate to and be parallel with left side wall axis, then the flexural deformation equation of the left side wall axis of water delivery structure can simplify as:
f1(y)＝A1y4+B1y3+C1y2 (5)
b) move the right side wall axis of rectangular coordinate system to the water delivery structure and the intersect position of bottom plate axis to rotate to and be parallel with the left side wall axis, then the flexural deformation equation of the right side wall axis of water delivery structure can simplify as:
f2(y)＝A2y4+B2y3+C2y2 (6)
c) move rectangular coordinate system to the intersection point position of the left side wall axis of water delivery structure and bottom plate axis to rotate to and be parallel with the bottom plate axis, then the flexural deformation equation of the bottom plate of water delivery structure can simplify to:
g1(x)＝A3x6+B3x5+C3x4+D3x3+E3x2 (7)
d) move rectangular coordinate system to the intersection point position of the left side wall axis of water delivery structure and roof axis to rotate to and be parallel with the roof axis, then the flexural deformation equation of the roof of water delivery structure can simplify to:
g2(x)＝A4x6+B4x5+C4x4+D4x3+E4x2 (8)
in a preferred embodiment, in step 4.2) above, the simultaneous equations can be simplified in the following way:
A) move rectangular coordinate system to the intersection point position of the left side wall inner wall of water delivery structure and bottom plate inner wall to rotate to and be parallel with left side wall axis, then the flexural deformation equation of the left side wall inner wall of water delivery structure can simplify to:
f1(y)＝A1y4+B1y3+C1y2+0.5H1 (9)
wherein H1Is the thickness of the left side wall.
B) Move the right side wall inner wall of rectangular coordinate system to water delivery structure and the intersect position of bottom plate inner wall to rotate to and be parallel with left side wall axis, then the flexural deformation equation of the right side wall inner wall of water delivery structure can simplify to:
f2(y)＝A2y4+B2y3+C2y2-0.5H2 (10)
wherein H2Is the thickness of the left side wall.
C) Move the right angle coordinate system to the position of the intersection point of the inner wall of the side wall of the water conveying structure and the inner wall of the bottom plate, and rotate to be parallel to the axis of the bottom plate, then the flexural deformation equation of the bottom plate of the water conveying structure can be simplified as:
g1(x)＝A3x6+B3x5+C3x4+D3x3+E3x2+0.5H3 (11)
wherein H3Is the thickness of the base plate.
D) Move the right angle coordinate system to the side wall inner wall of water delivery structure and the intersect position of roof inner wall to rotate to parallel with the roof axis, then the flexural deformation equation of the roof of water delivery structure can simplify to:
g2(x)＝A4x6+B4x5+C4x4+D4x3+E4x2-0.5H4 (12)
wherein H4Is the thickness of the base plate.
In a preferred embodiment, the deformation of the inner wall of the water conveying structure can be analyzed by adopting the method of the invention at different times, and the time-lapse change of the flexural deformation equation of each side axis of each right section of the inner wall of the water conveying structure along the water flow direction can be obtained.
In a preferred embodiment, for a double or multiple parallel-tank water delivery structure, one of the tanks is emptied, the flexural deformation equation of the emptied tank is determined under the water-filled operating condition of the remaining tanks, and the flexural deformation equation of the emptied tank under different water level conditions can be obtained by changing the operating water level.
In a preferred embodiment, the laser scanning device can be a mobile laser scanning device, and the three-dimensional laser scanning is carried out on the inner wall of the water conveying structure at a certain speed in a moving state.
Example 2
The embodiment provides a closed rectangle water delivery structure inner wall deformation analysis system, includes:
and the rectangular coordinate determination module is used for carrying out three-dimensional laser scanning on the inner wall of the water delivery structure at a certain fixed position in the water delivery structure through the laser scanning device under the emptying state of the water delivery structure and determining the rectangular coordinate of each scanning point on a right section which is corresponding to the fixed position and is vertical to the water flow direction.
And the nonlinear optimization module is used for performing curve fitting on the rectangular coordinates of the scanning points on the determined normal section, and the pre-assumed flexural deformation equations and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water conveying structure by adopting a nonlinear optimization method based on a least square method, determining undetermined coefficients in the flexural deformation equations, and further determining the flexural deformation equations of the axes of the sides of the normal section.
And the deformation form determining module is used for determining the deformation form of the water delivery structure according to the flexural deformation equation of each side axis of each regular section of the inner wall of the water delivery structure along the water flow direction.
The above embodiments are only used for illustrating the present invention, and the structure, connection mode, manufacturing process, etc. of the components may be changed, and all equivalent changes and modifications performed on the basis of the technical solution of the present invention should not be excluded from the protection scope of the present invention.
Claims (10)
1. A deformation analysis method for an inner wall of a closed rectangular water delivery structure is characterized by comprising the following steps:
1) under the state that the water delivery structure is emptied, carrying out three-dimensional laser scanning on the inner wall of the water delivery structure at a certain fixed position in the water delivery structure by a laser scanning device, and determining the rectangular coordinates of each scanning point on a right section which is perpendicular to the water flow direction and corresponds to the fixed position;
2) performing curve fitting on the rectangular coordinates of the scanning points on the determined normal section, and the pre-assumed flexural deformation equations and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure by adopting a nonlinear optimization method based on a least square method, determining undetermined coefficients in the flexural deformation equations, and further determining the flexural deformation equations of the side axes of the normal section;
3) changing the position of the laser scanning device along the water flow direction, and entering the step 1), determining the flexural deformation equation of each side axis of each right section of the inner wall of the water delivery structure along the water flow direction, and further determining the deformation form of the water delivery structure.
2. The method for analyzing the deformation of the inner wall of the closed rectangular water conveying structure according to claim 1, wherein the specific process of the step 1) is as follows:
1.1) carrying out three-dimensional laser scanning on the inner wall of the water conveying structure at a certain fixed position in the water conveying structure by a laser scanning device under the emptying state of the water conveying structure, and determining the space coordinates (r, theta, psi) of each scanning point on the inner wall of the water conveying structure under a spherical coordinate system taking the rotation center of the laser scanning device as the origin, wherein the positive section psi vertical to the water flow directionx∈[ψmin,ψmax]，ψminFor controlling the minimum horizontal azimuth angle psi during three-dimensional laser scanningmaxThe maximum horizontal azimuth angle controlled during three-dimensional laser scanning is obtained;
1.2) extracting theta from three-dimensional laser scanning results(r) is obtained as a scanning point of 0 and pi11,0,ψ1)、(r21,0,ψ2)、(r31,0,ψ3)、……、(r12,π,ψ1)、(r22,π,ψ2)、(r32,π,ψ3) … …; let parameter d1＝r11+r12，d2＝r21+r22，d3＝r31+r32，……，di＝ri1+ri2… …, and obtaining dminCorresponding normal section psixWherein ψ1、ψ2、ψ3… … is the horizontal azimuth; r is11、r21、r31……ri1The horizontal distance from the rotation center to the inner wall of the water conveying structure when the rotation angle of the vertical surface of the laser scanning device is 0 radian; r is12、r22、r32……ri2The horizontal distance from the rotating center to the inner wall when the rotating angle of the vertical surface of the laser scanning device is pi radian; dminIs a parameter d1、d2、d3… …, i is the number of scanning points;
1.3) let rix＝ri1cos(ψx-ψ1) To obtain each scanning point (r) on the normal section1x,θ1,ψx)、(r2x,θ2,ψx)、(r3x,θ3,ψx) … …, and converting the coordinates of each scanning point on the right section into rectangular coordinates, wherein rixDenotes r1x、r2x、r3x… …, x is a right cross section, theta1、θ2、θ3… … is r1x、r2x、r3xThe corresponding laser scanning device rotates at the vertical surface.
3. The method for analyzing the deformation of the inner wall of the closed rectangular water conveying structure according to claim 1, wherein the specific process of the step 2) is as follows:
2.1) assuming a flexural deformation equation and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure;
and 2.2) performing curve fitting by using a nonlinear optimization method based on a least square method according to rectangular coordinates of each scanning point on the normal section and by combining the assumed flexural deformation equations and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure, determining undetermined coefficients in the assumed flexural deformation equations, and further determining the flexural deformation equations of the axes of all sides of a certain normal section of the inner wall of the water delivery structure.
4. The method for analyzing the deformation of the inner wall of the closed rectangular water conveying structure according to claim 3, wherein the specific process of the step 2.1) is as follows:
2.1.1) the flexural deformation equation of the left and right sidewall axes of the inner wall of the water transport structure in a rectangular coordinate system parallel to the axes is a fourth order polynomial, thus, the flexural deformation equation f of the left sidewall is assumed1(y) is:
f1(y)＝A1y4+B1y3+C1y2+D1y+E1
wherein A is1、B1、C1、D1And E1Are all undetermined coefficients;
deflection equation f for right side wall2(y) is:
f2(y)＝A2y4+B2y3+C2y2+D2y+E2
wherein A is2、B2、C2、D2And E2Are all undetermined coefficients;
2.1.2) deflection equation of the bottom and top plate axes of the inner wall of the water transport structure in a rectangular coordinate system parallel to the axes is a sixth order polynomial, therefore, the deflection equation g of the bottom plate is assumed1(x) Comprises the following steps:
g1(x)＝A3x6+B3x5+C3x4+D3x3+E3x2+F3x+G3
wherein A is3、B3、C3、D3、E3、F3And G3Are all undetermined coefficients;
the flexural deformation equation for the top plate is:
g2(x)＝A4x6+B4x5+C4x4+D4x3+E4x2+F4x+G4
wherein A is4、B4、C4、D4、E4、F4And G4Are all undetermined coefficients;
2.1.3) the above-assumed respective flexural deformation equations should satisfy the constraint curve f1(y)⊥g1(x)、f1(y)⊥g2(x)、f2(y)⊥g1(x) And f2(y)⊥g2(x)。
5. The method for analyzing the deformation of the inner wall of the closed rectangular water conveying structure according to claim 3, wherein in the step 2), when the wedge-shaped chamfers exist between the left side wall, the right side wall and the bottom plate of the inner wall of the water conveying structure, the rotation angles of the axes of the left side wall and the right side wall are determined:
firstly, determining rectangular coordinates of each scanning point on a wedge-shaped chamfer on the inner wall of a water delivery structure through three-dimensional laser scanning of a laser scanning device, and determining the slope k of the bevel edge of the wedge-shaped chamfer under the rectangular coordinate system1；
According to determined slope k1And the slope k of the bevel edge of the wedge chamfer in the design drawing2And obtaining a corner alpha of the wedge-shaped chamfer angle of the inner wall of the water delivery structure, taking the corner alpha as the corners of the axes of the left and right walls of the inner wall of the water delivery structure, and further assuming that the flexural deformation equation of the left and right walls of the inner wall of the water delivery structure with the wedge-shaped chamfer angle exists according to the corners of the axes of the left and right walls of the inner wall of the water delivery structure.
6. The method for analyzing the deformation of the inner wall of the closed rectangular water conveying structure according to claim 5, wherein in the step 2.2), the simultaneous equations are simplified in the following way:
a) move rectangular coordinate system to the intersection point position of the left side wall axis of water delivery structure and bottom plate axis to rotate to and be parallel with left side wall axis, then the flexural deformation equation of the left side wall axis of water delivery structure is:
f1(y)＝A1y4+B1y3+C1y2
b) the rectangular coordinate system is moved to the intersection point position of the right side wall axis and the bottom plate axis of the water conveying structure, and is rotated to be parallel to the left side wall axis, and then the flexural deformation equation of the right side wall axis of the water conveying structure is as follows:
f2(y)＝A2y4+B2y3+C2y2
c) the rectangular coordinate system is moved to the intersection point position of the left side wall axis and the bottom plate axis of the water conveying structure, and is rotated to be parallel to the bottom plate axis, and then the flexural deformation equation of the bottom plate of the water conveying structure is as follows:
g1(x)＝A3x6+B3x5+C3x4+D3x3+E3x2
d) the rectangular coordinate system is moved to the intersection point position of the left side wall axis and the top plate axis of the water conveying structure, and is rotated to be parallel to the top plate axis, and then the flexural deformation equation of the top plate of the water conveying structure is as follows:
g2(x)＝A4x6+B4x5+C4x4+D4x3+E4x2。
7. the method for analyzing the deformation of the inner wall of the closed rectangular water conveying structure according to claim 5, wherein in the step 2.2), the simultaneous equations are simplified in the following way:
A) move rectangular coordinate system to the intersection point position of the left side wall inner wall of water delivery structure and bottom plate inner wall to rotate to and be parallel with left side wall axis, then the flexural deformation equation of the left side wall inner wall of water delivery structure is:
f1(y)＝A1y4+B1y3+C1y2+0.5H1
wherein H1Is the thickness of the left side wall;
B) move the right side wall inner wall of rectangular coordinate system to water delivery structure and the intersect position of bottom plate inner wall to rotate to and be parallel with left side wall axis, then the flexural deformation equation of the right side wall inner wall of water delivery structure is:
f2(y)＝A2y4+B2y3+C2y2-0.5H2
wherein H2Is the thickness of the left side wall;
C) the rectangular coordinate system is moved to the intersection point position of the inner wall of the side wall of the water conveying structure and the inner wall of the bottom plate, and is rotated to be parallel to the axis of the bottom plate, and then the flexural deformation equation of the bottom plate of the water conveying structure is as follows:
g1(x)＝A3x6+B3x5+C3x4+D3x3+E3x2+0.5H3
wherein H3Is the thickness of the bottom plate;
D) the rectangular coordinate system is moved to the intersection point position of the inner wall of the side wall of the water conveying structure and the inner wall of the top plate, and is rotated to be parallel to the axis of the top plate, and then the flexural deformation equation of the top plate of the water conveying structure is as follows:
g2(x)＝A4x6+B4x5+C4x4+D4x3+E4x2-0.5H4
wherein H4Is the thickness of the base plate.
8. The method for analyzing the deformation of the inner wall of the closed rectangular water conveying structure according to any one of claims 1 to 7, wherein for a water conveying structure with double tanks or multiple tanks connected in parallel, one tank is emptied, the flexural deformation equation of the emptied tank under the water-filled operation condition of the rest tanks is determined, and the flexural deformation equation of the emptied tank under the different water level conditions is obtained by changing the operation water level.
9. The method for analyzing the deformation of the inner wall of the closed rectangular water conveying structure according to any one of claims 1 to 7, wherein the laser scanning device adopts a movable laser scanning device to perform three-dimensional laser scanning on the inner wall of the water conveying structure at a certain speed in a moving state.
10. A closed type rectangular water conveying structure inner wall deformation analysis system is characterized by comprising:
the rectangular coordinate determination module is used for carrying out three-dimensional laser scanning on the inner wall of the water delivery structure at a certain fixed position in the water delivery structure through the laser scanning device under the emptying state of the water delivery structure and determining the rectangular coordinate of each scanning point on a right section which is corresponding to the fixed position and is vertical to the water flow direction;
the nonlinear optimization module is used for performing curve fitting on the rectangular coordinates of the scanning points on the determined normal section, and the pre-assumed flexural deformation equations and constraint conditions of the left and right side walls, the bottom plate and the top plate of the inner wall of the water delivery structure by adopting a nonlinear optimization method based on a least square method, determining undetermined coefficients in the flexural deformation equations and further determining the flexural deformation equations of the axes of the sides of the normal section;
and the deformation form determining module is used for determining the deformation form of the water delivery structure according to the flexural deformation equation of each side axis of each regular section of the inner wall of the water delivery structure along the water flow direction.
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