Deep sea riser spatial configuration inversion method

Abstract

The invention belongs to the technical field of ocean engineering, and provides a deep sea riser spatial configuration inversion method. Dividing the deep sea riser into a plurality of pipe section units by taking the tilt angle sensor as a node; discretizing each pipe section unit into a plurality of infinitesimal sections, and projecting each infinitesimal section in a horizontal coordinate system and a vertical coordinate system to obtain a space curve length equation of each pipe section unit; constructing projection expressions of the space curve of each pipe section in a horizontal coordinate system and a vertical coordinate system in combination with inclination angle information; relative coordinates of the upper end point and the lower end point of each pipe section unit in the pipe section unit local coordinate system where the pipe section unit is located are solved through iteration; and converting the relative coordinates of each pipe section unit in the local coordinate system of each pipe section unit into absolute coordinates under the global coordinate system, and integrating the absolute coordinates of each pipe section unit under the global coordinate system to obtain the deep sea riser spatial configuration. The method realizes spatial configuration reconstruction of the riser in a complex marine environment, and has higher robustness.

Description

Technical Field

[0001] The present invention relates to the field of marine engineering technology, and in particular to a deep-sea riser spatial configuration inversion method. Background Art

[0002] Marine risers, a crucial component of marine oil, gas, and mineral development systems, connect offshore platforms to subsea wellheads. They are essential components for transporting oil, gas, and minerals across all types of platform structures, and are the most complex type of equipment in deep-sea production systems. Throughout the history of deep-sea resource development both domestically and internationally, offshore demonstrations and operations have been repeatedly halted due to unexpected issues like entanglement and kinking in marine risers. Therefore, the development of structural health monitoring technology has significantly promoted vibration monitoring and intelligent control of marine risers, and real-time inversion of the spatial configuration of risers is a key component in health monitoring and intelligent control technologies for deep-sea resource development systems.

[0003] In existing technologies, traditional modal analysis methods reconstruct structural displacements based on strain responses using the principle of modal superposition. This method is unable to achieve coupled solutions for three-dimensional spatial configurations and relies heavily on the accurate expression of structural modal functions. This makes it unsuitable for ultra-slender, flexible structures with complex boundary conditions, such as deep-sea risers. The discrete curvature method transforms the sensor-measured strain into curvature based on the linear relationship between strain and curvature, then integrates and recursively derives the position coordinates of each micro-segment endpoint. However, because it is based on fixed constrained coordinate points and the tangent direction of the starting point is specific, it is also unsuitable for structures such as deep-sea mining risers with top moving boundaries and bottom weakly constrained boundaries. Secondly, in actual kilometer-scale deep-sea riser system engineering, due to the extreme conditions of the deep-sea environment and technical limitations, sensor installation is primarily concentrated within the riser's top, resulting in a monitoring blind spot at the riser's bottom. This wired sensor arrangement poses a greater challenge to the inversion of the riser's spatial configuration, requiring the ability to accurately invert the riser's overall configuration even when sensor information is scarce.

[0004] Therefore, in view of the limitations of traditional modal analysis and discrete curvature methods in dealing with complex boundary conditions and blind spots of actual engineering sensor monitoring, there is an urgent need to develop a new type of riser spatial configuration inversion technology to overcome the shortcomings of existing technologies and solve the key challenges in deep-sea engineering practice. Summary of the Invention

[0005] The purpose of the present invention is to solve the above technical problems and provide a deep-sea riser spatial configuration inversion method.

[0006] In order to achieve the above objectives, some embodiments of the present invention provide the following technical solutions: A deep-sea riser spatial configuration inversion method comprises the following steps: N inclination sensors are installed at intervals on the deep-sea riser. The deep-sea riser is divided into several pipe section units with the inclination sensors as nodes. Each pipe section unit is a pipe section space curve. A global coordinate system is established at the top point of the deep-sea riser, and a local coordinate system of each pipe segment unit is established at the upper end point of each pipe segment unit; Each pipe segment unit is discretized into several infinitesimal segments along its length. Each infinitesimal segment is projected in the horizontal coordinate system and the vertical coordinate system to obtain the projection curve of the infinitesimal segment in the horizontal coordinate system and the vertical coordinate system. The spatial curve length equation of each pipe segment unit is obtained based on the corresponding relationship between the arc length of the infinitesimal segment spatial curve and the projection curve of the infinitesimal segment in the horizontal coordinate system and the vertical coordinate system. Combined with the inclination information collected by the inclination sensors of each pipe segment unit, a projection expression of each pipe segment space curve in the horizontal coordinate system and the vertical coordinate system is constructed; based on the spatial curve length equation of each pipe segment unit and the projection expression, the relative coordinates of the upper and lower endpoints of each pipe segment unit in the local coordinate system of the pipe segment unit where the pipe segment unit is located are iteratively solved; The relative coordinates of each pipe segment unit in the local coordinate system of each pipe segment unit are converted into absolute coordinates in the global coordinate system. The absolute coordinates of each pipe segment unit in the global coordinate system are combined to obtain the spatial configuration of the deep-sea riser.

[0007] In some embodiments of the present application, a method for dividing a deep-sea riser into a plurality of pipe section units using a tilt sensor as a node includes: The pipe section between adjacent inclination sensors is divided into a pipe section unit, or the pipe section between spaced inclination sensors is divided into a pipe section unit.

[0008] In some embodiments of the present application: a method for dividing a deep-sea riser into a plurality of pipe segment units using tilt sensors as nodes includes: dividing the pipe segment between adjacent tilt sensors into one pipe segment unit; Methods for obtaining the spatial curve length equation of each pipe segment unit include: Determine any infinitesimal segment in the pipe unit Q k-1 Q k The initial equation for the length of is:

[0009] Among them, point is the lower endpoint of the infinitesimal segment, and its coordinates in the global coordinate system are ( , , ), Q k is the upper endpoint of the infinitesimal segment, and its coordinates in the global coordinate system are ( , , ), 、 、 They are all intermediate variables and have no practical significance. , , ; According to Lagrange's mean value theorem, we can obtain any infinitesimal segment Q k-1 Q k The length of the first rewrite the equation as:

[0010] in: ; ; 、 、 、 are all polynomial coefficients; For micro-element segment Q k-1 Q k The derivative of the interpolation function in the horizontal coordinate system of the local coordinate system where the infinitesimal segment is located, For micro-element segment Q k-1 Q k The derivative of the interpolation function in the vertical coordinate system of the local coordinate system where the infinitesimal segment is located; Will 、 Substitute into the infinitesimal segment Q k-1 Q k The first rewritten equation is:

[0011] in: 、 、 It is a parameter item, an intermediate variable, and has no practical meaning. ; According to the second rewritten equation, the lengths of all infinitesimal segments of each pipe segment unit are summed up, and the initial equation of the pipe segment unit is obtained as follows:

[0012] in, 、 is a parameter item, is a constant term, ; By integrating the right side of the initial equation of the pipe segment unit, the spatial curve length equation of the pipe segment unit is obtained as follows:

[0013] in, S AB Represents two points on a space curve A and B The length between is a constant term.

[0014] In some embodiments of the present application, a method for constructing a projection expression of each pipe segment space curve in a horizontal coordinate system and a vertical coordinate system by combining the inclination information collected by the inclination sensors of each pipe segment unit includes: Construct the projection expression of each pipe segment space curve in the horizontal coordinate system:

[0015] Construct the projection expression of each pipe segment space curve in the vertical coordinate system:

[0016] in, is the coefficient of the second-order term of the quadratic polynomial of the projection expression of the space curve in the horizontal coordinate system, is the first-order coefficient of the quadratic polynomial of the projection expression of the space curve in the horizontal coordinate system, is the constant term of the quadratic polynomial of the projection expression of the space curve in the horizontal coordinate system, is the coefficient of the second-order term of the quadratic polynomial of the projection expression of the space curve in the vertical coordinate system, is the first-order coefficient of the quadratic polynomial of the projection expression of the space curve in the vertical coordinate system, is the constant term of the quadratic polynomial of the projection expression of the space curve in the vertical coordinate system;

[0017]

[0018]

[0019] in, x A The upper endpoint of the pipe element in the global coordinate system x The coordinates of the axes, x B The lower endpoint of the pipe element in the global coordinate system x The coordinates of the axes, is the mapping angle of the inclination information of the upper end point of the pipe segment unit in the horizontal coordinate system, is the mapping angle of the inclination information of the lower end point of the pipe segment unit in the horizontal coordinate system, is the mapping angle of the inclination information of the upper end point of the pipe segment unit in the vertical coordinate system, It is the mapping angle of the inclination information of the lower end point of the pipe segment unit in the vertical coordinate system; is the two-dimensional projection expression of the pipe unit in the horizontal coordinate system, is the two-dimensional projection expression of the pipe segment unit in the vertical coordinate system.

[0020] In some embodiments of the present application, based on the spatial curve length equation of each pipe segment unit and the projection expression, a method for iteratively solving the relative coordinates of the upper end point and the lower end point of each pipe segment unit in the local coordinate system of the pipe segment unit includes: In each section unit of the deep-sea riser, the coordinate of the upper end point of each section unit in the local coordinate system of the section unit is set to 0, and the coordinate of the lower end point of the section unit in the local coordinate system of the section unit is solved. :

[0021] in: ; The distance between the inclination sensor at the upper end of the pipe section unit and the inclination sensor at the lower end of the pipe section unit; Solution 、 、 、 、 、 , and further solve the coordinates of the lower end point of the pipe segment unit where the top point is located 、 , and obtain the three-dimensional space relative coordinates of the pipe segment unit where the top point is located in its local coordinate system ( ， ， ); Iteratively solve the three-dimensional space relative coordinates of the upper and lower endpoints of each pipe segment unit in their respective local coordinate systems until the relative coordinates of the iteratively solved upper and lower endpoints of each pipe segment unit in the local coordinate system of the pipe segment unit are obtained.

[0022] In some embodiments of the present application, a method for converting the relative coordinates of each pipe segment unit in the local coordinate system of each pipe segment unit into the absolute coordinates in the global coordinate system includes: Assume that the absolute coordinates of the top point of the deep-sea riser in the global coordinate system are , the three-dimensional space relative coordinates of the lower end point B of the pipe segment unit where the top point is located in the local coordinate system are obtained as follows: ; The three-dimensional space relative coordinates of the lower end point of the pipe segment unit where the top point is located in the local coordinate system are superimposed with the three-dimensional space absolute coordinates of the upper end point of the pipe segment unit where the top point is located in the global coordinate system to obtain the three-dimensional space absolute coordinates of the lower end point of the pipe segment unit where the top point is located in the global coordinate system. ; The lower endpoint of the pipe segment unit where the top point is located is used as the upper endpoint of its adjacent pipe segment unit, and the absolute coordinates of the lower endpoint of its adjacent pipe segment unit in three-dimensional space are solved; The absolute coordinates of the upper and lower endpoints of each pipe segment unit in three-dimensional space are solved iteratively until the absolute coordinates of the upper and lower endpoints of each pipe segment unit in three-dimensional space are obtained.

[0023] In some embodiments of the present application, the tilt sensor collects real-time tilt information, updates the projection expression of the spatial curve of each pipe section in the horizontal coordinate system and the vertical coordinate system according to the tilt information at each moment, and updates and solves the relative coordinates and the absolute coordinates to update the spatial configuration of the deep-sea riser.

[0024] Compared with the prior art, the technical solution of this application has the following beneficial effects: The present invention discloses a method for inverting the spatial configuration of a deep-sea riser. The method has high accuracy and reliability when reconstructing the spatial configuration of an unknown position from the inclination information of the known position of the riser, and has excellent versatility for the spatial configuration inversion of different forms of risers. Specifically, the method of the present invention projects the three-dimensional spatial configuration of the riser onto two two-dimensional coordinate planes, divides the riser into multiple pipe segment units with multiple inclination sensors installed on the riser as nodes, uses a high-order interpolation function to describe the projection of each pipe segment unit on the two-dimensional plane, establishes a two-dimensional projection expression based on the inclination information, and combines the spatial curve length equation of the pipe segment unit to obtain the three-dimensional spatial relative coordinates of each pipe segment unit in the corresponding local coordinates. Finally, the three-dimensional spatial relative coordinates of each pipe segment unit in the corresponding local coordinates are converted into three-dimensional spatial absolute coordinates in the global coordinate system, thereby completing the spatial configuration reconstruction of the riser.

[0025] This method overcomes the limitations of traditional modal decomposition methods, which rely heavily on structural vibration mode functions. It achieves spatial configuration reconstruction of risers in complex marine environments with greater robustness and versatility for spatial configuration inversion of different types of risers. By projecting the three-dimensional spatial configuration onto a two-dimensional plane and performing spatial coordinate iteration, the complexity of solving three-dimensional spatial problems is reduced. Iterative inversion using the inclination information at each measuring point at each moment effectively avoids the cumulative effect of inversion errors over time. It can accurately invert the spatial displacement of risers with sparse inclination measurement points, significantly reducing the number of sensors required and the reliance on high-cost, high-density sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0027] Figure 1 This is an overall flow chart of the deep-sea riser spatial configuration inversion method provided in an embodiment of the present application; Figure 2 This is a schematic diagram of the arrangement of a steel catenary riser and sensors for numerical simulation provided in an embodiment of the present application; Figure 3 This is a comparison diagram of the time history curves of the inverted displacement and the true displacement in the xyz direction of the middle part of the steel catenary riser provided in the embodiment of the present application; Figure 4 is a displacement inversion error diagram at various positions of the steel catenary riser provided in an embodiment of the present application; Wherein, the accompanying drawings are marked as follows: 10: riser; 11: pipe section unit; 20: Tilt sensor. DETAILED DESCRIPTION

[0028] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0029] In the embodiments of the present application, prefixes such as "first" and "second" are used only to distinguish different description objects and have no limiting effect on the position, order, priority, quantity or content of the described objects. The use of prefixes such as ordinal numbers to distinguish description objects in the embodiments of the present application does not constitute a restriction on the described objects. For the statement of the described objects, please refer to the description in the context of the claims or embodiments, and the use of such prefixes should not constitute an unnecessary restriction. In addition, in the description of this embodiment, unless otherwise specified, the meaning of "plurality" is two or more.

[0030] The following describes the technical solutions in the embodiments of the present application in conjunction with the accompanying drawings. In the description of the embodiments of the present application, unless otherwise specified, " / " represents "or." For example, A / B can represent A or B. "And / or" in this document is merely a description of the association relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, or B exists alone.

[0031] In the several embodiments provided in the embodiments of the present application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection of some interfaces, devices or units, which can be electrical, mechanical or other forms.

[0032] The present invention provides a method for inverting the spatial configuration of a deep-sea riser. Figure 1 As shown in FIG, it is a flow chart of the inversion method provided by the present invention, which specifically includes the following steps.

[0033] S1: N tilt sensors are installed at intervals on the deep-sea riser. The deep-sea riser is divided into several pipe segment units with the tilt sensors as nodes. Each pipe segment unit is a pipe segment space curve.

[0034] A deepwater riser is a vertical channel device that connects offshore floating platforms (such as FPSOs, TLPs, SPAR platforms, etc.) with seabed equipment (such as underwater wellheads, seabed pipeline terminals, or mining relay stations). It is mainly used to transport resources such as oil, gas, minerals, or drilling fluids from the seabed to the offshore platform. It can also be used for operations such as injection, well repair, and completion.

[0035] Deepwater risers, connected to floating platforms, must adapt to platform motion caused by wind and waves, subjecting them to complex hydrodynamic loads. These hydrodynamic loads can cause positional or angular deviations during operation. Measuring the angle of deepwater risers can reveal these effects.

[0036] refer to Figure 2 As shown in FIG, a plurality of tilt sensors 20 are arranged on the riser 10. The tilt sensors 20 collect tilt information, i.e., the tilt angle, at corresponding positions on the riser. In this embodiment, the deep-sea riser is divided into a plurality of pipe segment units 11, with each tilt sensor placed on the riser as a node.

[0037] In some embodiments of the present application, a method for dividing a deep-sea riser into a plurality of pipe section units using a tilt sensor as a node includes: The pipe section between adjacent inclination sensors is divided into a pipe section unit, or the pipe section between spaced inclination sensors is divided into a pipe section unit.

[0038] Specifically, in actual engineering, each pipe segment unit can be divided into sections between two adjacent inclination sensors, or sections separated by several inclination sensors, depending on factors such as the specific arrangement density of the inclination sensors. Furthermore, in some embodiments, each pipe segment unit can be divided forward from the top of the riser, or backward from the bottom of the riser.

[0039] After the riser is divided into pipe section units, each pipe section unit includes at least two inclination sensors. The inclination data collected by each sensor can reflect the inclination of the pipe section unit.

[0040] For example, if the area between two adjacent inclination sensors forms a pipe segment unit, the data collected by the upper inclination sensor represents the inclination angle at the upper endpoint of the pipe segment unit, while the data collected by the lower inclination sensor represents the inclination angle at the lower endpoint of the pipe segment unit. If multiple inclination sensors form a pipe segment unit, inclination measurement rules can be set to determine which inclination sensor's data is used as the inclination data for each section of the riser.

[0041] S2: A global coordinate system is established at the top point of the deep-sea riser, and a local coordinate system is established at the upper end point of each pipe segment. Each local coordinate system is divided into a horizontal coordinate system and a vertical coordinate system.

[0042] xoy The two-dimensional coordinate plane is the plane where the horizontal coordinate system of the local coordinate system is located. xoz、yoz are two vertical coordinate planes perpendicular to each other in the local coordinate system.

[0043] In the embodiment of the present application, the three-dimensional spatial configuration pipe section unit of the riser is first projected onto two two-dimensional coordinate planes of the local coordinate system. Specifically, in one embodiment, the two two-dimensional coordinate planes are set as xoy Two-dimensional coordinate plane and xoz Two-dimensional coordinate plane, but the present invention is not limited to this, it can also be xoy Two-dimensional coordinate plane and yoz Two-dimensional coordinate plane.

[0044] In the embodiment of the present application, after each pipe section unit is divided, a local coordinate system is established at the upper end point of each pipe section unit, and a global coordinate system is established at the top of the riser. Here, the local coordinate system and the global coordinate system refer to three-dimensional space coordinate systems.

[0045] S3: Discretize each pipe segment into several micro-segments along its length. Project each micro-segment onto the horizontal and vertical coordinate systems to obtain its projection curves. Based on the corresponding relationship between the arc length of the micro-segment's spatial curve and the projection curves of the micro-segment onto the horizontal and vertical coordinate systems, obtain the spatial curve length equation for each pipe segment. The arc length of the micro-segment's spatial curve can be determined based on the actual riser construction conditions.

[0046] In an embodiment of the present application, the spatial curve of each pipe segment unit is discretized in length, and a high-order interpolation function is used to represent the projection of the discretized spatial curve on the two two-dimensional coordinate planes. The relationship between the length of the spatial curve and the projection is established to obtain the length equation of the spatial curve of each pipe segment unit.

[0047] In some embodiments of the present application, a method for dividing a deep-sea riser into a plurality of pipe segment units using tilt sensors as nodes includes dividing the pipe segment between adjacent tilt sensors into one pipe segment unit.

[0048] Specifically, if the distance between two adjacent tilt sensors in actual engineering is S AB The spatial curve length of the pipe unit between the two tilt sensors is simplified to n discrete points n- The length of the spatial straight line composed of one infinitesimal segment approximates the true configuration of the pipe curve.

[0049] Methods for obtaining the spatial curve length equation of each pipe segment unit include: Determine any infinitesimal segment in the pipe unit Q k-1 Q k The initial equation for the length of is: (1) Among them, point is the lower endpoint of the infinitesimal segment, and its coordinates in the global coordinate system are ( , , ), Q k is the upper endpoint of the infinitesimal segment, and its coordinates in the global coordinate system are ( , , ), 、 、 They are all intermediate variables and have no practical significance. , , ; n is the number of discrete points, .

[0050] According to Lagrange's mean value theorem, combined with xoz and xoy The interpolation function of the plane decomposition establishes the relationship between the length of the space curve and the projection of the space curve on the two two-dimensional coordinate planes, and the equation of the length of the infinitesimal segment (1) is further expressed as formula (2), and any infinitesimal segment is obtained. Q k-1 Q k The length of the first rewrite the equation as: (2) in: ; ; 、 、 、 are all polynomial coefficients; For micro-element segment Q k-1 Q k The derivative of the interpolation function in the horizontal coordinate system of the local coordinate system where the infinitesimal segment is located, For micro-element segment Q k-1 Q k The derivative of the interpolation function in the vertical coordinate system of the local coordinate system where the infinitesimal segment is located; the acquisition of the interpolation function belongs to the existing technology and can be obtained based on the projection curve of the infinitesimal segment in the horizontal coordinate system and the vertical coordinate system, which will not be repeated.

[0051] Will 、 Substitute into the infinitesimal segment Q k-1 Q k The first rewritten equation is: (3) in, 、 、 Intermediate variables, no practical meaning, ; According to the second rewritten equation, the lengths of all infinitesimal segments of each pipe segment unit are summed up, and the initial equation of the pipe segment unit is obtained as follows: (4) in, 、 is a parameter item, is a constant term, ; By integrating the right side of the initial equation of the pipe segment unit, the spatial curve length equation of the pipe segment unit is obtained as follows: (5) in, S AB Represents two points on a space curve A and B The length between is a constant term.

[0052] S4: Combined with the inclination information collected by the inclination sensor of each pipe segment unit, a two-dimensional projection expression of the spatial curve of each pipe segment in the horizontal coordinate system and the vertical coordinate system is constructed; based on the spatial curve length equation of each pipe segment unit and the projection expression, the relative coordinates of the upper end point and the lower end point of each pipe segment unit in the local coordinate system of the pipe segment unit where the pipe segment unit is located are iteratively solved to obtain the three-dimensional spatial relative coordinates of each pipe segment unit in the corresponding local coordinate system.

[0053] Based on the given displacement boundary conditions and slope boundary conditions, a quadratic polynomial interpolation function is used to establish the inclination information in xoy Two-dimensional coordinate plane and xoz A two-dimensional projection expression of a two-dimensional coordinate plane, wherein the two-dimensional projection expression is expressed using a quadratic interpolation function. In some embodiments of the present application, a method for constructing a projection expression of each pipe segment space curve in a horizontal coordinate system and a vertical coordinate system in combination with the inclination information collected by the inclination sensors of each pipe segment unit includes: Construct the projection expression of each pipe segment space curve in the horizontal coordinate system: (6-1) Construct the projection expression of each pipe segment space curve in the vertical coordinate system: (6-2) in, is the coefficient of the second-order term of the quadratic polynomial of the projection expression of the space curve in the horizontal coordinate system, is the first-order coefficient of the quadratic polynomial of the projection expression of the space curve in the horizontal coordinate system, is the constant term of the quadratic polynomial of the projection expression of the space curve in the horizontal coordinate system, is the coefficient of the second-order term of the quadratic polynomial of the projection expression of the space curve in the vertical coordinate system, is the first-order coefficient of the quadratic polynomial of the projection expression of the space curve in the vertical coordinate system, is the constant term of the quadratic polynomial of the projection expression of the space curve in the vertical coordinate system; According to the boundary conditions, the coefficient expression is:

[0054] (7)

[0055] in, x A The upper endpoint of the pipe element in the global coordinate system x The coordinates of the axes, x B The lower endpoint of the pipe element in the global coordinate system x The coordinates of the axes, is the mapping angle of the inclination information of the upper end point of the pipe segment unit in the horizontal coordinate system, is the mapping angle of the inclination information of the lower end point of the pipe segment unit in the horizontal coordinate system, is the mapping angle of the inclination information of the upper end point of the pipe segment unit in the vertical coordinate system, It is the mapping angle of the inclination information of the lower end point of the pipe segment unit in the vertical coordinate system; For pipe segment units in the horizontal coordinate system xoy The two-dimensional projection expression of For the pipe unit in the vertical coordinate system xoz The two-dimensional projection expression of .

[0056] Through the above calculation steps, the curve interpolation function and boundary conditions, we can know that the unknowns are coefficients 、 、 、 、 、 And the three-dimensional space relative coordinates of the lower end point of the pipe unit in the local coordinate system ( ， ， The embodiment of the present application adopts an iterative solution method, starting from the pipe section unit at the top of the riser, and gradually solving the coordinates of each pipe section unit.

[0057] In some embodiments of the present application, based on the spatial curve length equation and projection expression of each pipe segment unit, a method for iteratively solving the relative coordinates of the upper and lower endpoints of each pipe segment unit in the local coordinate system of the pipe segment unit includes the following steps.

[0058] Based on the spatial curve length equation of each pipe segment unit and the projection expression, a method for iteratively solving the relative coordinates of the upper end point and the lower end point of each pipe segment unit in the local coordinate system of the pipe segment unit includes: In each section unit of the deep-sea riser, the coordinate of the upper end point of each section unit in the local coordinate system of the section unit is set to 0, and the coordinate of the lower end point of the section unit in the local coordinate system of the section unit is solved. : Solution 、 、 、 、 、 , and further solve the coordinates of the lower end point of the pipe segment unit where the top point is located 、 , and obtain the three-dimensional space relative coordinates of the pipe segment unit where the top point is located in its local coordinate system ( ， ， ); Iteratively solve the three-dimensional space relative coordinates of the upper and lower endpoints of each pipe segment unit in their respective local coordinate systems until the relative coordinates of the iteratively solved upper and lower endpoints of each pipe segment unit in the local coordinate system of the pipe segment unit are obtained.

[0059] For example, the embodiment of the present application iterates and solves the endpoint coordinates of each pipe segment unit step by step from top to bottom. First, the three-dimensional space coordinates of the upper endpoint of the first pipe segment unit can be obtained by the shipboard GPS ( , , ). The three-dimensional space coordinate ( , , ) is relatively zero, and the three-dimensional space coordinates of the upper endpoint ( , , ) changes from (0,0,0). That is, the coordinates of the top point of the deep-sea riser are set to 0, that is, the coordinates of the upper end point of the pipe section unit where the top point is located are also set to 0.

[0060] So formula (7) is simplified to formula (8): (8) Combining the space curve length equation with the two-dimensional projection expression, that is, combining formulas (5)-(8), the three-dimensional space relative coordinates of the lower end point of the first pipe segment unit in the corresponding local coordinate system can be obtained ( ， ， ). Solve the relative coordinates of the lower end point of the pipe segment unit where the top point is located on the X axis Expressed as: (9) in: ; The distance between the inclination sensor at the upper end of the pipe section unit and the inclination sensor at the lower end of the pipe section unit; Solution 、 、 、 、 、 , and further solve the coordinates of the lower end point of the pipe segment unit where the top point is located 、 , and obtain the three-dimensional space relative coordinates of the pipe segment unit where the top point is located in its local coordinate system ( ， ， Specifically, by applying the numerical iteration method, the value in formula (9) is determined within a given error range. X Relative coordinates of the axis The value of , get all the coefficients of the interpolation function ( 、 、 、 、 、 ),pass xoy Two-dimensional coordinate plane and xoz The curve interpolation function of the two-dimensional coordinate plane solves the lower endpoint at Y Relative coordinates of the axis and Z Relative coordinates of the axis , get the three-dimensional space relative coordinates of the lower end point of the pipe unit in the local coordinate system ( ， ， ).

[0061] For each pipe segment unit of the riser, the method for determining the three-dimensional space relative coordinates of the first pipe segment unit in the local coordinate system can be referred to, and the three-dimensional space relative coordinates of the upper end point of each pipe segment unit in the corresponding local coordinate system ( , , ) is relatively zero. Combining the spatial curve length equation with the two-dimensional projection expression, the plane coordinates of the lower endpoint of each pipe segment unit in the two two-dimensional coordinate planes are iteratively solved to obtain the relative three-dimensional coordinates of the lower endpoint in the corresponding local coordinate system. The relative three-dimensional coordinates of each subsequent pipe segment unit in the corresponding local coordinate system are determined in this way, ultimately obtaining the relative three-dimensional coordinates of all pipe segment units on the riser in the corresponding local coordinate system.

[0062] S5: convert the relative coordinates of each pipe segment unit in the local coordinate system of each pipe segment unit into absolute coordinates in the global coordinate system, and combine the absolute coordinates of each pipe segment unit in the global coordinate system to obtain the spatial configuration of the deep-sea riser.

[0063] In some embodiments of the present application, a method for converting the relative coordinates of each pipe segment unit in the local coordinate system of each pipe segment unit into the absolute coordinates in the global coordinate system includes: The top point of the deep-sea riser is located in the first pipe section unit of the riser. For the first pipe section unit, the absolute coordinates of the top point of the deep-sea riser in the global coordinate system are: , the three-dimensional space relative coordinates of the lower end point B of the pipe segment unit where the top point is located in the local coordinate system are obtained as follows: ; The three-dimensional space relative coordinates of the lower end point of the pipe segment unit where the top point is located in the local coordinate system are superimposed with the three-dimensional space absolute coordinates of the upper end point of the pipe segment unit where the top point is located in the global coordinate system to obtain the three-dimensional space absolute coordinates of the lower end point of the pipe segment unit where the top point is located in the global coordinate system. ; The lower endpoint of the pipe segment unit where the top point is located is used as the upper endpoint of its adjacent pipe segment unit, and the absolute coordinates of the lower endpoint of its adjacent pipe segment unit in three-dimensional space are solved; The absolute coordinates of the upper and lower endpoints of each pipe segment unit in three-dimensional space are solved iteratively until the absolute coordinates of the upper and lower endpoints of each pipe segment unit in three-dimensional space are obtained.

[0064] This process is carried out in sequence until the last pipe segment unit, and the absolute coordinates of the lower endpoint N of the last pipe segment unit relative to the global coordinate system are obtained as follows: , , ), and finally obtain the three-dimensional space absolute coordinates of the upper and lower endpoints of all pipe segment units in the global coordinate system: (10) Where, γ x , γ y , γ z They arex 、 y 、 z The deformation coefficient of the riser in different directions can be calibrated by the sensor. 、 、 are the dynamic deformation variables, which are solved by the following formula: (11) Where, q x 、 q y for x and y Direction lateral distribution load, L B is the pipe unit length, E is the elastic modulus of the riser material, I is the moment of inertia of the section, F z for z The axial force in the direction of A is the cross-sectional area of ​​the pipe section.

[0065] Due to the rapidly changing seabed environment, the riser's inclination information can change at any time. This change in inclination can also alter the riser's configuration. To address this issue, some embodiments of the present application further include: a tilt sensor collects real-time inclination information, updates the projection of each pipe segment's spatial curve in the horizontal and vertical coordinate systems based on the inclination information at each moment, and updates the relative and absolute coordinates to update the deep-sea riser's spatial configuration.

[0066] Furthermore, in one embodiment, for any two adjacent pipe segments, the 3D relative coordinates of the current segment in the corresponding local coordinate system are added to the 3D absolute coordinates of the lower endpoint of the previous segment in the global coordinate system to convert the displacement of the current segment in the global coordinate system. This absolute displacement is then combined with a spline interpolation function to reconstruct the 3D absolute coordinates of any position on the riser.

[0067] In one embodiment, a cubic spline interpolation method is used to visualize the absolute coordinates of any position in the three-dimensional space of the riser in an encrypted manner. The coefficients of the spline interpolation function need to be determined by an interpolation condition, a continuity condition, a first-order derivative continuity condition, and a second-order derivative continuity condition.

[0068] Furthermore, in one embodiment, to further improve the accuracy of the configuration inversion, a spatial position sensor is installed at the bottom of the riser to obtain the three-dimensional absolute coordinates of the bottom of the riser in the global coordinate system. The pipe segment units are then reversely partitioned from the bottom of the riser. Based on the three-dimensional absolute coordinates of the bottom of the riser, the spatial curve length equation and the two-dimensional projection expression are combined, and the solution for forward partitioning the pipe segment units from the top of the riser is referred to above. The three-dimensional absolute coordinates of the upper endpoint of the pipe segment unit at the bottom of the riser are calculated, thereby obtaining the three-dimensional absolute coordinates of the upper and lower endpoints of each pipe segment unit in the global coordinate system. The three-dimensional absolute coordinates of the upper and lower endpoints of each pipe segment unit in the global coordinate system obtained from the reverse partitioning are then used to correct the three-dimensional absolute coordinates of the upper and lower endpoints of each pipe segment unit in the global coordinate system obtained from the forward partitioning.

[0069] In some embodiments, the iterative solution of the pipe segment unit coordinates may employ a forward partitioning method and a reverse partitioning method. The forward partitioning method involves iteratively solving the coordinates of the upper and lower endpoints of each pipe segment unit starting from the top of the pipe segment unit, while the reverse partitioning method involves iteratively solving the coordinates of the upper and lower endpoints of each pipe segment unit starting from the bottom of the pipe segment unit.

[0070] In some embodiments, the three-dimensional space absolute coordinates of the upper and lower endpoints of each pipe segment unit in the global coordinate system obtained by reverse division ( , , )、( , , ) and the three-dimensional space absolute coordinates of the upper and lower endpoints of each pipe segment unit in the global coordinate system obtained under the forward division condition ( , , )、( , , ) is fused and solved, and adaptive weighted fusion is introduced. Combined with Kalman filtering, the weights are dynamically adjusted, and the absolute coordinates of the upper and lower endpoints of each pipe segment unit in the global coordinate system are updated to ( , , )、( , , ), and finally the three-dimensional space absolute coordinates of the upper and lower endpoints of all pipe segment units in the global coordinate system are obtained as follows: (11) Where, w* and w ris the weight coefficient of forward deduction and backward deduction, σ is the derived coordinate variance.

[0071] Since the above calculation of the three-dimensional absolute coordinates of each pipe segment unit depends only on the coordinate changes of the upper endpoint of the pipe segment unit and is not affected by time changes, by repeating the above steps for the inclination angle data at each moment, the spatial coordinate information of the riser within a given time domain can be obtained. Thus, in one embodiment, the overall spatial configuration of the riser is further updated based on the inclination angle information collected for each pipe segment unit at different moments, thereby determining the changing trend of the overall spatial configuration of the riser at different moments.

[0072] In order to verify the effect of the deep-sea riser spatial configuration inversion method of the present invention, the following simulation verification is carried out: The steel catenary riser model was established using the commercial software OrcaFlex. The upper float has a total length of 120.0m, a design draft of 7.5m, a gross tonnage of 12625.0t, a total riser length of 1200.0m, an inner diameter of 193.68mm, an outer diameter of 219.08mm, and a unit length mass of 65.56kg / m. Secondly, for the sensor layout, the sensors are evenly arranged, and the pitch sensor spacing is 1 / 4 of the pitch sensor spacing. s =30.0m( s / L =1 / 40) as an example, where s is the distance between adjacent tilt sensors, L is the total length of the riser, such as Figure 2 In this simulation, wave and current loads are applied to the riser system, and the simulation time is 150.0s.

[0073] First, based on the numerical simulation results of the commercial software OrcaFlex, the two-direction inclination data and three-dimensional spatial displacement data of each measuring point of the riser are obtained. The inclination information of the numerical simulation is used as input, and the output spatial displacement data is compared with the displacement data obtained by the numerical simulation. Figure 3 Middle part of steel catenary riser xyz Comparison of the time history curves of directional inversion displacement and true displacement.

[0074] Then, the local coordinate system and the global coordinate system are established. The origin of the global coordinate system is located at the initial moment when the upper floating body contacts the riser ( t =0s). In this global coordinate system, X The axis points to the right as positive. Y The axis points backwards. Z The axis extends vertically upward; the local coordinate system is established with the upper end point of each pipe unit as the origin. x The axis is positive to the right. y The axis is positive when it is backward. z The axis is vertically upward. θ xy Indicates that the three-dimensional riser is xoy The projected tangent line on the plane is x The angle between the axes, xoy When viewed from above the plane, the counterclockwise direction is positive; θ xz Indicates that the three-dimensional riser is xoz The projected tangent line on the plane is x The angle between the axes, xoz The counterclockwise direction when viewed from directly in front of the plane is positive.

[0075] Furthermore, the inclination information obtained at each measuring point is substituted into formula (9), and the spatial coordinates of each pipe segment unit node in the local coordinate system are solved according to the above step S3, thereby obtaining the three-dimensional spatial relative coordinates of all pipe segment units on the riser in the corresponding local coordinate system. At the same time, the coordinates in the local coordinate system are converted to coordinates in the global coordinate system according to step S4.

[0076] Through the above process, the spatial coordinate values ​​of each measuring point of the riser can be obtained. By using the cubic spline interpolation method, the visualization of the spatial coordinate values ​​at any position can be achieved in an encrypted manner.

[0077] By repeating the above steps for the inclination information at each moment, the spatial coordinate information of the riser in a given time domain can be solved and obtained. Figure 4 3 is a displacement inversion error diagram at various positions of the steel catenary riser provided by an embodiment of the present invention.

[0078] From this, it can be seen that the deep-sea riser spatial configuration inversion method proposed in the present invention has high accuracy and reliability when reconstructing the unknown position spatial configuration from the known position inclination information of the riser, and has excellent versatility for spatial configuration inversion of different forms of risers. Specifically, the method of the present invention projects the three-dimensional spatial configuration of the riser onto two two-dimensional coordinate planes, divides the riser into multiple pipe segment units with multiple inclination sensors installed on the riser as nodes, uses high-order interpolation functions to describe the projection of each pipe segment unit on the two-dimensional plane, establishes a two-dimensional projection expression based on the inclination information, combines the spatial curve length equation of the pipe segment unit, obtains the three-dimensional spatial relative coordinates of each pipe segment unit in the corresponding local coordinates, and finally converts the three-dimensional spatial relative coordinates of each pipe segment unit in the corresponding local coordinates into three-dimensional spatial absolute coordinates in the global coordinate system, thereby completing the spatial configuration reconstruction of the riser.

[0079] The deep-sea riser spatial configuration inversion method proposed in this application solves the limitation of the traditional modal decomposition method driven by strain data that is heavily dependent on the structural vibration mode function, realizes the spatial configuration reconstruction of the riser in a complex marine environment under moving boundary conditions, and has higher robustness; and by projecting the three-dimensional spatial configuration onto a two-dimensional plane for spatial coordinate iteration, the complexity of solving three-dimensional space problems is reduced; in addition, the method uses the inclination information at each measuring point at each moment for iterative inversion, effectively avoiding the cumulative effect of inversion error over time; and can accurately invert the spatial displacement of the riser in the case of sparse inclination measuring points, greatly reducing the number of sensors required and reducing the dependence on high-cost, high-density sensors.

[0080] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

[0081] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention by a person skilled in the art should be included within the scope of protection of the present invention. Therefore, the scope of protection of this patent application shall be subject to the scope of protection of the appended claims.

Claims

1. A deep-sea riser spatial configuration inversion method, characterized in that: The following steps are involved: N inclination sensors are installed at intervals on the deep-sea riser. The deep-sea riser is divided into several pipe section units with the inclination sensors as nodes. Each pipe section unit is a pipe section space curve. A global coordinate system is established at the top point of the deep-sea riser, and a local coordinate system of each pipe segment unit is established at the upper end point of each pipe segment unit; Each pipe segment unit is discretized into several infinitesimal segments along its length. Each infinitesimal segment is projected in the horizontal coordinate system and the vertical coordinate system to obtain the projection curve of the infinitesimal segment in the horizontal coordinate system and the vertical coordinate system. The spatial curve length equation of each pipe segment unit is obtained based on the corresponding relationship between the arc length of the infinitesimal segment spatial curve and the projection curve of the infinitesimal segment in the horizontal coordinate system and the vertical coordinate system. Combined with the inclination information collected by the inclination sensors of each pipe segment unit, a projection expression of each pipe segment space curve in the horizontal coordinate system and the vertical coordinate system is constructed; based on the spatial curve length equation of each pipe segment unit and the projection expression, the relative coordinates of the upper and lower endpoints of each pipe segment unit in the local coordinate system of the pipe segment unit where the pipe segment unit is located are iteratively solved; The relative coordinates of each pipe segment unit in the local coordinate system of each pipe segment unit are converted into absolute coordinates in the global coordinate system. The absolute coordinates of each pipe segment unit in the global coordinate system are combined to obtain the spatial configuration of the deep-sea riser.

2. The deep-sea riser spatial configuration inversion method according to claim 1, characterized in that: The method of dividing the deep-sea riser into several pipe section units using the inclination sensor as a node includes: The pipe section between adjacent inclination sensors is divided into a pipe section unit, or the pipe section between spaced inclination sensors is divided into a pipe section unit.

3. The deep-sea riser spatial configuration inversion method according to claim 1 or 2, characterized in that: The method for dividing a deep-sea riser into a plurality of pipe section units with the tilt sensors as nodes includes: dividing the pipe section between adjacent tilt sensors into a pipe section unit; Methods for obtaining the spatial curve length equation of each pipe segment unit include: Determine any infinitesimal segment in the pipe unit Q k-1 Q k The initial equation for the length of is: Among them, point is the lower endpoint of the infinitesimal segment, and its coordinates in the global coordinate system are ( , , ), Q k is the upper endpoint of the infinitesimal segment, and its coordinates in the global coordinate system are ( , , ), 、 、 They are all intermediate variables and have no practical significance. , , ; According to Lagrange's mean value theorem, we can obtain any infinitesimal segment Q k-1 Q k The length of the first rewrite the equation as: in: ; ; 、 、 、 are all polynomial coefficients; For micro-element segment Q k-1 Q k The derivative of the interpolation function in the horizontal coordinate system of the local coordinate system where the infinitesimal segment is located, For micro-element segment Q k-1 Q k The derivative of the interpolation function in the vertical coordinate system of the local coordinate system where the infinitesimal segment is located; Will 、 Substitute into the infinitesimal segment Q k-1 Q k The first rewritten equation is: in, 、 、 It is a parameter item and has no actual meaning. ; According to the second rewritten equation, the lengths of all infinitesimal segments of each pipe segment unit are summed up, and the initial equation of the pipe segment unit is obtained as follows: in, 、 is a parameter item, is a constant term, ; By integrating the right side of the initial equation of the pipe segment unit, the spatial curve length equation of the pipe segment unit is obtained as follows: in, S AB Represents two points on a space curve A and B The length between is a constant term.

4. The deep-sea riser spatial configuration inversion method according to claim 3, characterized in that: Combining the inclination information collected by the inclination sensors of each pipe section unit, a method for constructing a projection expression of the spatial curve of each pipe section in the horizontal coordinate system and the vertical coordinate system includes: Construct the projection expression of each pipe segment space curve in the horizontal coordinate system: Construct the projection expression of each pipe segment space curve in the vertical coordinate system: Among them, is the coefficient of the second-order term of the quadratic polynomial of the projection expression of the space curve in the horizontal coordinate system, is the first-order coefficient of the quadratic polynomial of the projection expression of the space curve in the horizontal coordinate system, is the constant term of the quadratic polynomial of the projection expression of the space curve in the horizontal coordinate system, is the coefficient of the second-order term of the quadratic polynomial of the projection expression of the space curve in the vertical coordinate system, is the first-order coefficient of the quadratic polynomial of the projection expression of the space curve in the vertical coordinate system, is the constant term of the quadratic polynomial of the projection expression of the space curve in the vertical coordinate system; in, x A The upper endpoint of the pipe element in the global coordinate system x The coordinates of the axes, x B The lower endpoint of the pipe element in the global coordinate system x The coordinates of the axes, is the mapping angle of the inclination information of the upper end point of the pipe segment unit in the horizontal coordinate system, is the mapping angle of the inclination information of the lower end point of the pipe segment unit in the horizontal coordinate system, is the mapping angle of the inclination information of the upper end point of the pipe segment unit in the vertical coordinate system, It is the mapping angle of the inclination information of the lower end point of the pipe segment unit in the vertical coordinate system; is the two-dimensional projection expression of the pipe unit in the horizontal coordinate system, is the two-dimensional projection expression of the pipe segment unit in the vertical coordinate system.

5. The deep-sea riser spatial configuration inversion method according to claim 4, characterized in that: Based on the spatial curve length equation of each pipe segment unit and the projection expression, a method for iteratively solving the relative coordinates of the upper end point and the lower end point of each pipe segment unit in the local coordinate system of the pipe segment unit includes: In each section unit of the deep-sea riser, the coordinate of the upper end point of each section unit in the local coordinate system of the section unit is set to 0, and the coordinate of the lower end point of the section unit in the local coordinate system of the section unit is solved. : in: ; The distance between the inclination sensor at the upper end of the pipe section unit and the inclination sensor at the lower end of the pipe section unit; Solution 、 、 、 、 、 , and further solve the coordinates of the lower end point of the pipe segment unit where the top point is located 、 , and obtain the three-dimensional space relative coordinates of the pipe segment unit where the top point is located in its local coordinate system ( ， ， ); Iteratively solve the three-dimensional space relative coordinates of the upper and lower endpoints of each pipe segment unit in their respective local coordinate systems until the relative coordinates of the iteratively solved upper and lower endpoints of each pipe segment unit in the local coordinate system of the pipe segment unit are obtained.

6. The deep-sea riser spatial configuration inversion method according to claim 1, characterized in that: Methods for converting the relative coordinates of each pipe segment unit in the local coordinate system of each pipe segment unit into absolute coordinates in the global coordinate system include: Assume that the absolute coordinates of the top point of the deep-sea riser in the global coordinate system are , the three-dimensional space relative coordinates of the lower end point B of the pipe segment unit where the top point is located in the local coordinate system are obtained as follows: ; The three-dimensional space relative coordinates of the lower end point of the pipe segment unit where the top point is located in the local coordinate system are superimposed with the three-dimensional space absolute coordinates of the upper end point of the pipe segment unit where the top point is located in the global coordinate system to obtain the three-dimensional space absolute coordinates of the lower end point of the pipe segment unit where the top point is located in the global coordinate system. ; The lower endpoint of the pipe segment unit where the top point is located is used as the upper endpoint of its adjacent pipe segment unit, and the absolute coordinates of the lower endpoint of its adjacent pipe segment unit in three-dimensional space are solved; The absolute coordinates of the upper and lower endpoints of each pipe segment unit in three-dimensional space are solved iteratively until the absolute coordinates of the upper and lower endpoints of each pipe segment unit in three-dimensional space are obtained.

7. The deep-sea riser spatial configuration inversion method according to claim 1, characterized in that: Also includes: The inclination sensor collects real-time inclination information, updates the projection expression of each pipe segment space curve in the horizontal coordinate system and the vertical coordinate system according to the inclination information at each moment, and updates the relative coordinates and the absolute coordinates to update the deep-sea riser spatial configuration.

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