A method and system for monitoring the deformation of slender marine structures
By sparsely arranging sensors and reconstructing large deformation curves in three-dimensional space using the theory of piecewise constant curvature, the accuracy problem of three-dimensional deformation monitoring of slender marine structures was solved, achieving high-fidelity monitoring results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- OCEAN UNIV OF CHINA
- Filing Date
- 2026-05-12
- Publication Date
- 2026-07-17
AI Technical Summary
Existing monitoring methods are insufficient to accurately capture the three-dimensional overall deformation of complex and slender marine structures, especially in cases of segmented discontinuities, variable cross sections, and easy bending-torsional coupling deformation. Traditional methods cannot achieve high-fidelity monitoring.
The measured strain is obtained by sparsely arranging sensors. The three-dimensional large deformation curve is reconstructed by combining the piecewise constant curvature theory and the three-dimensional special Euclidean group SE(3) spatial rigid body transformation matrix. The data is processed by fiber optic strain sensor array and signal demodulation unit to construct a local homogeneous transformation matrix and realize high-precision three-dimensional deformation monitoring.
It achieves high-fidelity three-dimensional spatial deformation monitoring of slender marine structures, overcomes the geometric nonlinearity cumulative error of traditional methods, adapts to discontinuous variable cross-section structures, and has high robustness and engineering applicability.
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Figure CN122174582B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of marine engineering structure monitoring technology based on computer data processing, and particularly relates to a method and system for monitoring the deformation of slender marine structures. Background Technology
[0002] In recent years, with the vigorous development of marine engineering and deep-sea resource development technologies, complex and slender marine structures, such as offshore wind turbine towers, blades, deep-sea mining risers, and umbilical cables, have been increasingly widely used in marine equipment. These structures, as core components for connection, support, or energy conversion, operate for extended periods in harsh marine environments, enduring the coupled effects of multiple sources of extreme and complex loads, including wind, waves, and currents. Under these service conditions, structural deformation, vibration, and fatigue damage have become increasingly prominent issues, directly impacting the safe and stable operation and service life of the entire marine equipment. Therefore, real-time, online deformation monitoring and condition assessment of slender marine structures are of paramount engineering significance for ensuring the structural safety of deep-sea engineering equipment.
[0003] Slender marine structures typically exhibit physical characteristics such as high flexibility, large span, and low natural frequency. To meet diverse mechanical and functional requirements, these structures often display significant spatial heterogeneous distribution characteristics and cross-sectional discontinuities. For example, wind turbine blades not only have complex airfoil cross-sections and torsion angle distributions but are also highly susceptible to large deformations caused by bending-torsional coupling; wind turbine towers often employ segmented flange combinations, exhibiting significant variable cross-section characteristics and stiffness jumps; while deep-sea mining risers, suspended over long distances, are highly susceptible to vortex-induced vibrations and large spatial nonlinear deflections due to ocean currents. This multi-source heterogeneous shape and position characteristics and stiffness discontinuities result in highly three-dimensional spatial nonlinearity and local abrupt changes in the actual deformation of the structure, posing a severe challenge to the spatial resolution and monitoring accuracy of the monitoring system.
[0004] Currently, methods for monitoring the deformation of slender marine structures still have significant limitations. Traditional point-based measurements, such as inclinometers, GPS, and acoustic positioning, struggle to capture the continuous deformation profile across the entire structural height, and suffer from installation limitations and signal attenuation issues in deep-sea or dynamic service conditions. In recent years, surface strain monitoring methods have gained traction, but they encounter significant algorithmic bottlenecks when dealing with variable cross-section structures exhibiting segmented discontinuities and three-dimensional spatial coupling characteristics. Existing classical deformation reconstruction algorithms are often based on the assumption of continuous uniform beams or simple two-dimensional plane fitting, which not only fails to accurately characterize stiffness jumps and local nonlinear deformations at connections such as flanges and joints, but also struggles to rigorously decouple the spatially irregular distribution characteristics exhibited by slender structures under complex conditions. Traditional planar accumulation algorithms are prone to spatial mapping distortion, causing monitoring errors to accumulate divergently along the structural axis, making high-fidelity three-dimensional deformation monitoring impossible.
[0005] In summary, there is currently no mature algorithm specifically designed for complex, slender marine structures that are segmented, discontinuous, have variable cross-sections, and are prone to bending-torsional coupling deformation, and that can accurately monitor their three-dimensional overall deformation curves based on a limited number of surface measuring points. Summary of the Invention
[0006] To address the aforementioned issues, this invention acquires measured strain using sparsely arranged sensors, generates a continuous curvature vector field that allows for stiffness step changes through cross-sectional equivalent mapping and physical piecewise interpolation; subsequently, based on the piecewise constant curvature theory, the structure is discretized, local geometric features of the micro-element are extracted, and a local homogeneous transformation matrix is constructed in the three-dimensional special Euclidean group SE(3) space; finally, the global pose is recursively derived using the chain rule to reconstruct the large deformation curve in three-dimensional space. This invention avoids cumbersome modal parameter identification, rigorously decouples spatial bending deformation, eliminates the geometric nonlinearity accumulation error caused by plane integration from the bottom layer, and overcomes the limitations of high-fidelity monitoring of complex spatial morphologies such as variable cross-section towers and irregular blades with extremely low sensing costs.
[0007] The first aspect of this invention provides a method for monitoring the deformation of slender marine structures, comprising the following steps:
[0008] S1, acquire surface strain data of multiple discrete sections of a slender marine structure, and decouple them into a discrete curvature data set and a central axial average strain;
[0009] S2, physical segmentation is performed with the cross section of abrupt structural property change as the boundary, and the discrete curvature data set and the discrete central axial average strain are interpolated within each segment to generate a continuous curvature vector field and a continuous axial strain function, and the curvature is allowed to step at the boundary.
[0010] S3, the continuous structure is discretized into several micro-segments along the axial direction; the initial discrete arc length of each micro-segment is corrected using the continuous axial strain function, the actual corrected arc length of each micro-segment is obtained, and the local curvature modulus and principal bending azimuth of each micro-segment are extracted based on the continuous curvature vector field.
[0011] S4, based on the actual corrected arc length and the local curvature modulus, construct the homogeneous transformation matrix of each micro-segment in the local principal curvature plane, introduce the principal curvature azimuth angle for spatial rotation alignment, and generate the three-dimensional special Euclidean group of each micro-segment. SE (3) The transformation matrix of a complete rigid body in space;
[0012] S5, based on the chain rule of rigid body kinematics, multiplies the complete rigid body transformation matrix of each infinitesimal segment step by step to calculate the three-dimensional position and orientation of the nodes on the central axis of the structure, and then obtains the relative displacement and rotation angle to determine the global three-dimensional spatial deformation curve of the structure.
[0013] Preferably, in step S1, based on the geometric design data of the slender marine structure, it is divided into multiple physical segments; fiber optic strain sensors are orthogonally arranged on discrete height sections of the inner surface of the segmented structure to collect the azimuth angles of each section of the inner surface of the segmented structure in real time. β Discrete strain data at the location By combining the geometric angles between each section of the inner surface of the structure and the global neutral axis, the measured strain data of each discrete section of the inner surface of the segmented structure are corrected to the corrected strain parallel to the global neutral axis. Subsequently, based on the Euler-Bernoulli beam theory, the modified strain was... Geometric decoupling is defined as the discrete central axial average strain and the discrete curvature data set in the orthogonal directions of the cross section.
[0014] Preferably, the correction strain Geometric decoupling involves the discrete central axial average strain and the discrete curvature data set in orthogonal directions of the cross section. The specific calculation method is as follows:
[0015] ;
[0016] In the formula, , They are respectively height z i Cross section at x and y The curvature component in the direction, ( z i (for height) z i The central axial average strain at the cross-sectional measuring point. d ( z i (for height) z i The inner diameter of the tower section. For height z i Azimuth of the cross section β Corrective strain at the location; z i These are the height coordinates of the discrete cross-section.
[0017] Preferably, the specific process of S2 includes:
[0018] Based on the discrete curvature data set obtained in S1, the structure is segmented with the structural wall thickness or abrupt material change sections as natural boundaries. Within each segment, the discrete curvature data set is interpolated using a segmented cubic spline interpolation method. x and yInterpolation is performed in two orthogonal directions. At the connection nodes of the segmented structure, curvature continuity is no longer forced, allowing the curvature function to undergo a step while maintaining the continuity of displacement and rotation, thus generating a continuous curvature vector field across the entire height of the inner surface of the slender marine structure. With continuous axial strain function (z).
[0019] Preferably, the specific process of S3 includes:
[0020] Based on the piecewise constant curvature theory, the structure is uniformly discretized along its entire axial length into... j Each micro-element segment is divided into several micro-segments; and based on the continuous axial strain function obtained from S2, the initial discrete arc length of each micro-element segment is corrected by axial scaling to obtain the actual corrected arc length of each micro-element segment. Then, based on the continuous curvature vector field of the entire height obtained in S2, Calculate the local curvature modulus at the geometric center of each infinitesimal segment. With the main curvature azimuth The actual corrected arc length is mentioned. Local curvature modulus With the main curvature azimuth The specific calculation method is as follows:
[0021] ;
[0022] ;
[0023] ;
[0024] In the formula, For the first j The actual corrected arc length of each infinitesimal segment; For the first j Local curvature modulus of each infinitesimal segment; For the first j The principal bending azimuth angle of each infinitesimal segment; ds is the initial discrete length of the infinitesimal segment; ( z j ) represents the axial strain value at the center of the micro-element segment; and The center of each micro-element segment is located at x and y Curvature components in the direction; j Let be the sequence number of the infinitesimal segment, and j =1, 2,… , N .
[0025] Preferably, the specific process of S4 includes:
[0026] Actual corrected arc length of the micro-segment obtained based on S3 Local curvature modulus With the main curvature azimuth A local spatial geometric recursive model of the infinitesimal segments is established, mapping each infinitesimal segment to its corresponding local principal bending plane and equivalent to a circular arc infinitesimal element. The actual corrected arc length is then used. With local equivalent curvature modulus Analyze the relative bending angle and displacement components of the end of the infinitesimal segment in the local coordinate system, and construct a homogeneous transformation matrix representing the local principal bending plane. The main bending azimuth angle is further introduced. Construct the rotation transformation matrix about the local tangential axis Finally, the rotation transformation matrix is used to... Spatial pose correction is performed to generate a three-dimensional special Euclidean group for each infinitesimal element. SE (3) Complete rigid body transformation matrix in space The homogeneous transformation matrix and complete rigid body transformation matrix The specific calculation method is as follows:
[0027] ;
[0028] ;
[0029] ;
[0030] In the formula, For the first j The complete rigid body transformation matrix of each infinitesimal segment; This is the homogeneous transformation matrix within the local principal bending plane; Let be the rotation transformation matrix about the local tangential axis.
[0031] Preferably, the specific process of S5 includes:
[0032] Based on the infinitesimal segments derived from S4, in the three-dimensional special Euclidean group SE (3) Complete rigid body transformation matrix in space The initial pose is set with the fixed end of the slender marine structure as the origin of the global coordinate system. T 0, Based on the chain rule of rigid body kinematics, the complete rigid body transformation matrix of each infinitesimal segment is... By performing a cumulative multiplication recursive calculation from bottom to top along the structural axis, the global pose matrix of the k-th node on the structural central axis in the global coordinate system can be obtained. Extract the spatial position column vector and attitude matrix of the node from it;
[0033] The first on the central axis kThe global pose matrix of each node in the global coordinate system The specific calculation method is as follows:
[0034] ;
[0035] In the formula, For the structure of the first k The global pose matrix of each node Let be the initial pose matrix of the fixed segment, and ; For the first j The complete rigid body transformation matrix of each infinitesimal segment; ∈ Represents a node k The global attitude matrix, column vectors r k = [ x k , y k , z k ] T This is the column vector of the three-dimensional spatial position of the k-th node in the global coordinate system; k This represents the total number of nodes. Furthermore, based on the physical quantities extracted from the above calculations, the three-dimensional spatial coordinates of each node are... r k By comparing it with its initial design coordinates, the spatial relative displacement at any height on the central axis of the structure can be accurately obtained; at the same time, the global attitude matrix can be... By performing inverse Euler angle analysis, the bending and rotation angles of the nodes in three-dimensional space can be obtained. By integrating the position and attitude data of all micro-segment nodes across the entire height range, the spatial deformation curve of the central axis of the slender marine structure can be fitted, thereby achieving high-fidelity monitoring of the global three-dimensional spatial deformation of the slender marine structure.
[0036] The second aspect of this invention provides a deformation monitoring system for slender marine structures, which uses a deformation monitoring method for slender marine structures as described in the first aspect as the core deformation reconstruction solution unit to obtain relative displacement and rotation angle, thereby determining the global three-dimensional spatial deformation curve of the structure; it also includes:
[0037] Sparse strain sensing unit: used to acquire discrete strain light signals of multiple cross sections of the structure under load in real time through an array of fiber optic strain sensors deployed on the inner surface of a slender marine structure.
[0038] Signal demodulation and transmission unit: It is communicatively connected to the sparse strain sensing unit, and is used to receive the discrete strain optical signal, and to analyze and convert it into high-precision digital discrete strain data through an optical fiber demodulator, which is then applied to the core deformation reconstruction calculation unit.
[0039] Visualization and Status Assessment Unit: This unit receives the three-dimensional spatial deformation monitoring curve and displays it dynamically in a three-dimensional graphical format on a computer terminal interface. Simultaneously, based on the deformation curve information and structural material property information, it compares the preset safety threshold with the finite element simulation deformation analysis software to assess the real-time safety status of the structure under test and triggers an early warning mechanism when the limit is exceeded.
[0040] Compared with the prior art, the present invention has the following beneficial effects:
[0041] 1. High three-dimensional accuracy and high-fidelity reproduction of large spatial deformation: By introducing the piecewise constant curvature theory and the SE(3) group spatial rigid body transformation matrix, the geometric mapping relationship of "strain-curvature-spatial pose" is rigorously derived, overcoming the geometric nonlinearity accumulation error of classical plane integral under large deflection, thus accurately reproducing the real three-dimensional spatial bending mode of slender structure;
[0042] 2. Strong applicability and effective solution to the problem of discontinuous variable cross section: Through the physics-based piecewise interpolation and micro-element geometric decoupling strategy, it perfectly adapts to the geometric step and stiffness change at the flange connection, overcomes the industry pain point that traditional continuous beam theory cannot accurately handle discontinuous complex structures, and thus greatly expands the engineering application boundary of the monitoring algorithm.
[0043] 3. Robustness and reliability throughout the system's lifecycle: The sensing strategy of sparse cross-section distribution on the inner surface physically isolates the sensitive sensors in the enclosed space inside the structure, effectively avoiding direct erosion from harsh marine environments such as high salt spray, typhoons, and wave impacts. This ensures the long-term stability of the underlying data acquisition from the source and has outstanding engineering practical value. Attached Figure Description
[0044] Figure 1 This is the overall flowchart of the monitoring method of the present invention.
[0045] Figure 2 This is a model diagram of a slender offshore wind turbine tower with variable cross-section according to an embodiment of the present invention; wherein, (a) is a diagram defining the global geometric parameters and coordinate system of the tower, and (b) is a diagram showing the orthogonal arrangement of the variable cross-section features and FBG sensors, with the yellow part being the FBG sensors.
[0046] Figure 3 This is a load-condition deformation diagram of a multi-segment variable cross-section slender offshore wind turbine tower according to an embodiment of the present invention.
[0047] Figure 4 This is a comparison chart of the overall deformation curve of the tower obtained by monitoring the tower structure of the slender offshore wind turbine using the variable cross-section method of this invention, and the overall deformation curve of the tower extracted by Ansys.
[0048] Figure 5This is a framework diagram of the monitoring system of the present invention. Detailed Implementation
[0049] This invention proposes a method for monitoring the deformation of slender marine structures, the overall logic of which is as follows: Figure 1 As shown, it includes the following steps:
[0050] S1. Select several discrete monitoring sections along the entire length of the slender marine structure and collect discrete surface strain data of the inner surface of each section in real time. Combine the geometric parameters of each section to determine the position of the neutral axis of the section about the centroidal principal axis, and decouple the discrete strain into a set of discrete curvature data relative to the neutral axis and the average strain along the central axis.
[0051] S2, using the cross-section of abrupt changes in structural geometry or physical properties as the natural boundary, performs physical segmentation. Within each segment, the discrete curvature data set and the discrete central axial average strain are processed using a cubic spline interpolation method based on physical segmentation to generate a continuous curvature vector field and a continuous axial strain function covering the entire height of the structure, and allowing the curvature to step at the boundary of the physical segment.
[0052] S3, based on the piecewise constant curvature reconstruction theory, the continuous structure is discretized into several micro-segments along the axial direction; the initial discrete arc length of each micro-segment is corrected using the continuous axial strain function, the actual corrected arc length of each micro-segment is obtained, and the local curvature modulus and principal bending azimuth of each micro-segment are extracted according to the continuous curvature vector field.
[0053] S4. Based on the actual corrected arc length and the local equivalent curvature modulus, calculate the bending deformation of each micro-segment in the local principal bending plane and construct the local homogeneous transformation matrix. Further introduce the principal bending azimuth angle for spatial rotation alignment to generate the complete rigid body transformation matrix of each micro-segment in the three-dimensional special Euclidean group SE(3) space.
[0054] S5, based on the chain rule of rigid body kinematics, the complete rigid body transformation matrix of each micro-element segment is multiplied step by step from the bottom fixed end to calculate the three-dimensional position and orientation of the nodes on the central axis of the structure, and then the relative displacement and rotation angle are obtained to determine the global three-dimensional spatial deformation curve of the structure.
[0055] The present invention will be further described below with reference to embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0056] This example models a 10MW offshore wind turbine tower based on a DUT (Device Under Test). The tower base is fixed, with a height of 115.63m, a bottom outer diameter of 8.3m, and a top outer diameter of 5.5m. Figure 2 As shown in (a), the tower is divided into 10 segmented structures, as follows: Figure 2 As shown in (b), the tower is made of S355 steel, with a yield strength of 355 MPa, a material elastic modulus of 210 GPa, and a density of 7850 kg / m³. 3 The Poisson's ratio is 0.3. However, in reality, the mass of secondary structures such as ladders, cables, and paint will also be considered, so the overall density of the tower is 8500 kg / m³. 3 The tower's self-weight is applied by defining gravitational acceleration. The tower is modeled using second-order solid elements, comprising 2,336,638 elements and 4,663,968 finite element analysis (FEM) nodes. The strain data used in the algorithm comes from ANSYS numerical simulations. Two orthogonal horizontal forces F are simultaneously applied at the top of the tower. x =4000kN and F y =5000kN, and the maximum bending moment of the tower base caused by this three-dimensional coupled load is also strictly controlled within the elastic yield limit of the material. The deformation diagram of the tower under load conditions is shown below. Figure 3 As shown.
[0057] S1. Obtain surface strain data from multiple discrete sections of a slender marine structure and decouple them into a discrete curvature data set and a discrete central axial average strain. The specific implementation process is as follows: Taking the 10MW offshore wind turbine tower of the DUT as the slender marine structure to be tested, according to its structural design and installation data, due to flange connection and manufacturing process, the wall thickness of the tower exhibits a segmented step change, that is, the wall thickness remains constant within the same physical segment, but decreases stepwise from bottom to top. Based on this physical step characteristic, the tower is divided into 10 segments. In order to capture the three-dimensional spatial bending and axial expansion and contraction of the structure under complex wind and wave loads, this embodiment takes the bottom of the tower as the zero point of calculation and selects 10 discrete monitoring sections along the axial height, with elevations set as 2m, 14m, 26m, 38m, 50m, 62m, 74m, 86m, 98m and 110m respectively. Figure 3 As shown. In each of the above discrete monitoring sections (uniformly denoted as height)... z i , where the serial number i On the inner surface of the cross section (=1, 2, …, 10), a strict circumferential orthogonal sparse distribution strategy is adopted: that is, FBG fiber optic strain sensors are physically attached at four orthogonal azimuth angles of 0°, 90°, 180° and 270° at each cross section, and the azimuth angles of each cross section are collected in real time by a fiber optic demodulator. β Discrete measured surface strain data Considering the variable cross-section geometry of the tower's outer surface as a smooth conical surface, the discrete measured surface strain data are corrected to obtain discrete corrected strain values. ε ( z i , β ):
[0058] ;
[0059] In the formula, H , D B , D T These are the total height of the tower, the bottom diameter, and the top diameter, respectively.
[0060] Subsequently, based on the Euler-Bernoulli beam theory formula and the inner surface diameter d of the measuring point section, z i Discrete corrected strain data ε ( z i , β Geometric decoupling is performed to obtain the structure. x direction and y Discrete curvature data set of directions and discrete center axial mean strain ( z i ),
[0061] ;
[0062] In the formula, , They are respectively height z i Cross section at x and y The curvature component in the direction, ( z i (for height) z i The central axial average strain at the cross-sectional measuring point. d ( z i (for height) z i The inner diameter of the tower section. For height z i Azimuth of the cross section β Corrective strain at the location; z i These are the height coordinates of the discrete cross-section.
[0063] S2, using the abrupt change in structural properties as the boundary, performs physical segmentation. Within each segment, interpolates the discrete curvature data set and the discrete central axial average strain to generate a continuous curvature vector field and a continuous axial strain function, allowing curvature steps at the boundaries. The specific implementation process is as follows: using the abrupt change in tower wall thickness as the natural boundary, combined with the discrete monitoring sections in S1, the tower is discretized into... m ( m =1,…,10) independent continuous beam segments. Within each independent beam segment, the obtained discrete curvature data set is processed using a piecewise cubic spline interpolation method, within each pair of adjacent measuring point intervals [z... i , z i+1 On the above, construct independent cubic spline functions respectively. S m,i (z) is used to describe the continuous curvature distribution in the x or y direction:
[0064] ;
[0065] In the formula: z is the height coordinate along the axial direction of the tower; S m,i (z) is the first i A continuous curvature function with interpolation intervals; a i , b i , c i , d i The coefficients to be determined are determined by the following boundary conditions and continuity conditions:
[0066] ;
[0067] In the formula, K i , K i+1 For the calculated first z i and the z i+1 Discrete curvature values of the cross section; S' and S'' represent the function with respect to height coordinates, respectively. z The first and second derivatives.
[0068] Boundary condition constraints are introduced at the bottom and top of the tower. Considering the mechanical characteristics of the tower structure, the curvature distribution in the local regions at the bottom and top of the tower is approximately linear. Based on this physical prior, this study adopts natural boundary conditions at the beginning and end of the global spline interpolation, i.e., the second derivative of the curvature function is zero at the two endpoints.
[0069] ;
[0070] In the formula, This represents the second derivative of curvature of the first interpolation interval at the bottom of the tower. This represents the second derivative of curvature of the last interpolation interval at the top layer of the tower.
[0071] By combining the continuity condition within the segment with the natural boundary conditions at both ends mentioned above, the solution can be obtained. a i , b i , c i , d i All undetermined coefficients. At the global piecewise nodes of the structure with abrupt changes in wall thickness, maintaining continuity of displacement and rotation while allowing for a step in curvature, through... x and y By performing the above interpolation calculations in two orthogonal directions respectively, the continuous curvature vector field across the entire height range of the tower can be finally obtained. Similarly, taking the section with abrupt changes in wall thickness as the boundary, the axial average strain at the discrete center is... (zi) is constructed as a globally continuous axial strain function ε(z).
[0072] S3, based on the piecewise constant curvature reconstruction theory, the tower structure is discretized into several micro-segments along the axial direction; the initial discrete arc length of each micro-segment is corrected using the continuous axial strain function, and the local equivalent curvature modulus and principal bending azimuth angle of each micro-segment are extracted based on the continuous curvature vector field; the specific implementation process is as follows: the continuous tower is discretized along the entire axial length... H Uniformly discretized j (j=1,…, N ) infinitesimal segments, where N M, step size of infinitesimal segment ds = H / N Ignoring the curvature gradient of the infinitesimal segment and treating it as a circular arc segment with constant curvature, for the axial expansion and contraction effect of the tower, the initial discrete arc length of the infinitesimal segment is corrected based on the global continuous axial strain function ε(z) obtained from S2, to obtain the first... j The actual corrected arc length of each infinitesimal segment :
[0073] ;
[0074] In the formula, For the first j The actual corrected arc length of each infinitesimal segment after being affected by axial strain; ds is the initial infinitesimal segment step size; ε( z j ) is the geometric center of the j-th infinitesimal segment. zj Axial strain at the location.
[0075] Subsequently, the global continuous curvature vector field obtained based on S2 was... Calculate any height z of the tower j Local curvature modulus at [0, H] k ( z j ) and principal curvature azimuth ( z j The geometric decoupling process is as follows:
[0076] ;
[0077] ;
[0078] In the formula, For the first j Local curvature modulus of each infinitesimal segment; For the first j The principal curvature azimuth of each micro-element segment; and The first j The curvature components of each infinitesimal element in the x and y directions; j Let j be the index of the infinitesimal segment, and j = 1, 2, ..., N .
[0079] S4, based on the actual corrected arc length and local curvature modulus obtained in S3, constructs the local homogeneous transformation matrix for each micro-element segment, introduces the principal bending azimuth angle for spatial rotation alignment, and generates the three-dimensional special Euclidean group of each micro-element segment. SE (3) Complete rigid body transformation matrix in space; the specific implementation process is as follows: based on the actual corrected arc length of the infinitesimal segment obtained by S3. Local curvature modulus With the main curvature azimuth A local spatial geometric recursive model of the infinitesimal segments is established, mapping each infinitesimal segment to its corresponding local principal bending plane and equivalent to a circular arc infinitesimal element. The actual corrected arc length is then used. With local curvature modulus Analyze the relative bending angle and displacement components of the end of the infinitesimal segment in the local coordinate system, and construct a homogeneous transformation matrix representing the local principal bending plane. The main bending azimuth angle is further introduced. Construct the rotation transformation matrix about the local tangential axis Finally, the rotation transformation matrix is used to... Spatial pose correction is performed to generate a three-dimensional special Euclidean group for each infinitesimal element. SE(3) Complete rigid body transformation matrix in space The homogeneous transformation matrix and complete rigid body transformation matrix The specific calculation method is as follows:
[0080] First, based on the actual corrected arc length With local curvature modulus Construct a homogeneous transformation matrix to characterize the bending deformation of the infinitesimal segment in the local principal bending plane. :
[0081] ;
[0082] Furthermore, the principal bending azimuth angle calculated in S3 is introduced. j Construct the spatial rotation transformation matrix of the infinitesimal segment about the local tangential axis. R z ( j ) ∈ SE (3) is used to align the local master bending plane to the global three-dimensional space:
[0083] ;
[0084] Finally, the rotation transformation matrix is used to... Perform spatial pose correction to generate the infinitesimal segment in a three-dimensional special Euclidean group. SE (3) Complete rigid body transformation matrix in space :
[0085] .
[0086] S5, based on the chain rule of rigid body kinematics, progressively multiplies the complete rigid body transformation matrix of each infinitesimal segment to solve for the three-dimensional position vector and attitude matrix of the structural nodes in the global coordinate system, thereby realizing three-dimensional spatial deformation reconstruction; the specific implementation process is as follows: based on the three-dimensional special Euclidean group of each infinitesimal segment derived in S4 SE (3) Complete rigid body transformation matrix in space The initial pose matrix is set with the bottom fixed end of the offshore wind turbine tower as the origin of the global coordinate system. T 0. Based on the chain rule of rigid body kinematics, the complete rigid body transformation matrix of each infinitesimal segment is... By performing a cumulative multiplication recursive calculation from bottom to top along the structural axis, the global pose matrix of the k-th node on the structural central axis in the global coordinate system can be obtained. The specific method for calculating the cumulative multiplication is as follows:
[0087] ;
[0088] In the formula, For the structure of the first k The global pose matrix of each node Let be the initial pose matrix of the fixed segment, and ; For the first j The complete rigid body transformation matrix of each infinitesimal segment ∈ Represents a node k The global attitude matrix, column vectors r k = [ x k , y k , z k ] T This is the column vector of the three-dimensional spatial position of the k-th node in the global coordinate system; k This represents the total number of nodes. Furthermore, based on the physical quantities extracted from the above calculations, the three-dimensional spatial coordinates of each node are... r k By comparing it with its initial design coordinates, the spatial relative displacement at any height on the central axis of the structure can be accurately obtained; at the same time, the global attitude matrix can be... By performing inverse Euler angle analysis, the bending angle of the node in three-dimensional space can be obtained. By integrating the position and attitude data of all micro-segment nodes across the entire height range, the spatial deformation curve of the central axis of the offshore wind turbine tower structure can be fitted, thereby achieving high-fidelity monitoring of the global three-dimensional spatial deformation of the slender offshore wind turbine structure.
[0089] Based on the above method, this embodiment provides a deformation monitoring system for slender marine structures, such as... Figure 5 As shown, it includes:
[0090] (1) Sparse strain sensing unit: used to collect multi-section discrete strain optical signals of the structure under load in real time. Taking a 10MW variable cross-section tower as an example, it is divided into 10 segments along its height. On the inner surface of each segment, four fiber Bragg grating (FBG) strain sensors are sparsely arranged in a circumferential orthogonal pattern on several discrete cross-sections. This specific orthogonal layout can maximize the decoupling of spatial curvature, while the inner surface layout effectively isolates it from the erosion of the harsh marine environment;
[0091] (2) Signal demodulation and transmission unit: This unit is communicatively connected to the sparse strain sensing unit and is used to receive discrete strain optical signals. Each sensor is cascaded to the fiber optic demodulator via an optical fiber network. This unit analyzes and converts the received discrete strain optical signals into high-precision digital discrete strain data, which is then transmitted to the downstream processing terminal via an industrial communication network.
[0092] (3) Core Deformation Reconstruction Solving Unit: Contains a processor and memory, and is the computational core of this system. Its running storage contains computer programs of the above methods to execute the following algorithm flow: Receive the above discrete strain data, combine the geometric distance from the measuring point to the neutral axis to equivalently map to discrete curvature; use the physical piecewise cubic spline interpolation method to generate the continuous inner surface curvature function of the tower at the full height that allows for stiffness step at the flange, and derive it to the overall curvature of the outer surface according to the wall thickness; then strictly extract the geometric features of each micro-element based on the piecewise constant curvature theory, and in the three-dimensional special Euclidean group SE( 3) Construct a local homogeneous transformation matrix in space, and recursively derive the global pose matrix through the rigid body kinematics chain rule, and finally calculate the three-dimensional spatial large deformation curve of the structure with high fidelity.
[0093] (4) Visualization and Status Assessment Unit: Receives the calculated three-dimensional spatial large deformation curve and displays it dynamically in a three-dimensional graphical format on the computer terminal interface. Simultaneously, based on the deformation curve and tower material information, it compares the tower's real-time safety status with preset safety thresholds and triggers an early warning when the limit is exceeded.
[0094] Numerical simulation and result analysis:
[0095] To verify the accuracy and engineering applicability of the three-dimensional spatial large deformation reconstruction algorithm of this invention, a three-dimensional finite element model of a 10MW segmented variable wall thickness offshore wind turbine tower was established and imported into ANSYS software for numerical simulation analysis. Based on the actual structural design data of the offshore wind turbine tower, it was divided into 10 physical segments with variable wall thickness along its height. In the ANSYS simulation environment, a spatial multi-directional coupled load (simulating the combined action of wind and waves under actual sea conditions, causing spatial distortion and three-dimensional bending of the structure) was applied to the top of the tower. Discrete surface strain simulation data at four orthogonal circumferential directions (0°, 90°, 180°, 270°) at 10 discrete monitoring sections with elevations of 2m, 14m, 26m, 38m, 50m, 62m, 74m, 86m, 98m, and 110m were extracted and used as the virtual input signal for the monitoring system of this invention. The discrete strain data mentioned above is imported into the core calculation unit of this system. According to the method provided by this invention: first, the data is mechanically decoupled to obtain the orthogonal discrete curvature and axial strain of each section; then, piecewise cubic spline interpolation that allows curvature steps at physical boundaries is performed to generate a global continuous curvature vector field; finally, based on the piecewise constant curvature theory, the infinitesimal segments are discretized, and a homogeneous transformation matrix is constructed in the three-dimensional special Euclidean group SE(3) space. The three-dimensional spatial position column vector of the tower's full height is calculated using the kinematic chain recursion rule. The three-dimensional continuous deformation curve reconstructed based on the algorithm of this invention is rigorously compared with the absolute displacement results of the structural nodes output by ANSYS finite element method (FEM) in three-dimensional space. Figure 4 As shown, the three-dimensional spatial morphology and displacement values of the reconstructed curve and the FEM simulation curve exhibit a high degree of consistency. Further, combining the quantitative comparison data at different relative normalized heights (z / H) in Table 1 (comparison error analysis table of the overall deformation curve of the tower obtained by monitoring the tower structure of a slender offshore wind turbine using variable cross-section and the overall deformation curve extracted by Ansys), it can be seen that at the free end where the deformation is most severe (z / H=1.0), the absolute error of the deformation curve monitored by this invention is only 0.0364 m, and the maximum relative error of the main displacement component is controlled within 1.5%. This comparison result strongly verifies the effectiveness and extremely high accuracy of the proposed algorithm that integrates sparse strain sensing and SE(3) spatial rigid body pose recursion. This indicates that the method fundamentally overcomes the nonlinear cumulative error of traditional plane integrals when dealing with piecewise variable cross-sections, and can accurately reconstruct the real three-dimensional spatial large deformation response of large, discontinuous, complex, and slender marine structures under multi-directional coupled loads.
[0096] Table 1. Error Analysis Table for Deformation Curve Comparison
[0097]
[0098] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.
[0099] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.
Claims
1. A method for monitoring the deformation of slender marine structures, characterized in that, Includes the following processes: S1, acquire surface strain data of multiple discrete sections of a slender marine structure, and decouple them into a discrete curvature data set and a central axial average strain; S2, physical segmentation is performed with the cross section of abrupt structural property change as the boundary, and the discrete curvature data set and the discrete central axial average strain are interpolated within each segment to generate a continuous curvature vector field and a continuous axial strain function, and the curvature is allowed to step at the boundary. S3, the continuous structure is discretized into several micro-segments along the axial direction; the initial discrete arc length of each micro-segment is corrected using the continuous axial strain function, the actual corrected arc length of each micro-segment is obtained, and the local curvature modulus and principal bending azimuth of each micro-segment are extracted based on the continuous curvature vector field. S4, based on the actual corrected arc length and the local curvature modulus, construct the homogeneous transformation matrix of each micro-segment in the local principal curvature plane, introduce the principal curvature azimuth angle for spatial rotation alignment, and generate the three-dimensional special Euclidean group of each micro-segment. SE (3) The transformation matrix of a complete rigid body in space; S5, based on the chain rule of rigid body kinematics, multiplies the complete rigid body transformation matrix of each infinitesimal segment step by step to calculate the three-dimensional position and orientation of the nodes on the central axis of the structure, and then obtains the relative displacement and rotation angle to determine the global three-dimensional spatial deformation curve of the structure.
2. The method for monitoring the deformation of slender marine structures as described in claim 1, characterized in that: In S1, based on the geometric design data of the slender marine structure, it is divided into multiple physical segments; Fiber grating strain sensors are orthogonally arranged on discrete height sections of the inner surface of the segmented structure to collect the azimuth angles of each section of the inner surface of the segmented structure in real time. β Discrete strain data at the location By combining the geometric angles between each section of the inner surface of the structure and the global neutral axis, the measured strain data of each discrete section of the inner surface of the segmented structure are corrected to the corrected strain parallel to the global neutral axis. Subsequently, based on the Euler-Bernoulli beam theory, the modified strain was... Geometric decoupling is defined as the discrete central axial average strain and the discrete curvature data set in the orthogonal directions of the cross section.
3. The method for monitoring the deformation of slender marine structures as described in claim 2, characterized in that: The correction strain Geometric decoupling involves the discrete central axial average strain and the discrete curvature data set in orthogonal directions of the cross section. The specific calculation method is as follows: ； In the formula, , They are respectively height z i Cross section at x and y The curvature component in the direction, ( z i (for height) z i The central axial average strain at the cross-sectional measuring point. d ( z i (for height) z i The inner diameter of the tower section; For height z i Azimuth of the cross section β Corrective strain at the location; z i These are the height coordinates of the discrete cross-section.
4. The method for monitoring the deformation of slender marine structures as described in claim 1, characterized in that: The specific process of S2 includes: Based on the discrete curvature data set obtained in S1, the structure is segmented with the structural wall thickness or abrupt material change sections as natural boundaries. Within each segment, the discrete curvature data set is interpolated using a segmented cubic spline interpolation method. x and y Interpolation is performed in two orthogonal directions. At the connection nodes of the segmented structure, curvature continuity is no longer forced, allowing the curvature function to undergo a step while maintaining the continuity of displacement and rotation, thus generating a continuous curvature vector field across the entire height of the inner surface of the slender marine structure. With continuous axial strain function (z).
5. The method for monitoring the deformation of a slender marine structure as described in claim 1, characterized in that: The specific process of S3 includes: based on the piecewise constant curvature theory, uniformly discretizing the structure along the entire axial length into... j Each micro-element segment is divided into several micro-segments; and based on the continuous axial strain function obtained from S2, the initial discrete arc length of each micro-element segment is corrected by axial scaling to obtain the actual corrected arc length of each micro-element segment. Then, based on S2, the continuous curvature vector field is obtained. Calculate the local curvature modulus at the geometric center of each infinitesimal segment. With the main curvature azimuth The actual corrected arc length Local curvature modulus With the main curvature azimuth The specific calculation method is as follows: ； ； ； In the formula, For the first j The actual corrected arc length of each infinitesimal segment; For the first j Local curvature modulus of each infinitesimal segment; For the first j The principal bending azimuth angle of each infinitesimal segment; ds is the initial discrete length of the infinitesimal segment; ( z j ) represents the axial strain value at the center of the micro-element segment; and The center of each micro-element segment is located at x and y Curvature components in the direction; j Let be the sequence number of the infinitesimal segment, and j =1, 2,… , N .
6. The method for monitoring the deformation of a slender marine structure as described in claim 5, characterized in that: The specific process of S4 includes: Actual corrected arc length of the micro-segment obtained based on S3 Local curvature modulus With the main curvature azimuth A local spatial geometric recursive model of the infinitesimal segments is established, mapping each infinitesimal segment to its corresponding local principal bending plane and equivalent to a circular arc infinitesimal element. The actual corrected arc length is then used. With local equivalent curvature modulus Analyze the relative bending angle and displacement components of the end of the infinitesimal segment in the local coordinate system, and construct a homogeneous transformation matrix representing the local principal bending plane. The main bending azimuth angle is further introduced. Construct the rotation transformation matrix about the local tangential axis Finally, the rotation transformation matrix is used to... Spatial pose correction is performed to generate a three-dimensional special Euclidean group for each infinitesimal element. SE (3) Complete rigid body transformation matrix in space .
7. The method for monitoring the deformation of a slender marine structure as described in claim 6, characterized in that: The specific process of S5 includes: Based on the infinitesimal segments derived from S4, in the three-dimensional special Euclidean group SE (3) Complete rigid body transformation matrix in space The initial pose is set with the fixed end of the slender marine structure as the origin of the global coordinate system. T 0, Based on the chain rule of rigid body kinematics, the complete rigid body transformation matrix of each infinitesimal segment is... By performing a cumulative multiplication recursive calculation from bottom to top along the structural axis, the global pose matrix of the k-th node on the structural central axis in the global coordinate system can be obtained. Extract the spatial position column vector and attitude matrix of the node from it; The first on the central axis k The global pose matrix of each node in the global coordinate system The specific calculation method is as follows: ； In the formula, For the structure of the first k The global pose matrix of each node. Let be the initial pose matrix of the fixed segment, and ; For the first j The complete rigid body transformation matrix of each infinitesimal segment; ∈ Represents a node k The global attitude matrix, column vectors r k = [ x k , y k , z k ] T This is the column vector of the three-dimensional spatial position of the k-th node in the global coordinate system; k The total number of nodes; the three-dimensional spatial coordinates of each node. r k By comparing the coordinates with the initial design coordinates, the spatial relative displacement at any height on the central axis of the structure is obtained; simultaneously, the global attitude matrix is... Perform inverse Euler angles to obtain the bending angle of the node in three-dimensional space.
8. A deformation monitoring system for slender marine structures, characterized in that: The deformation monitoring method for slender marine structures as described in any one of claims 1 to 7 is used as the core deformation reconstruction solution unit to obtain relative displacement and rotation angle, and to determine the three-dimensional spatial deformation monitoring curve of the structure. Also includes: Sparse strain sensing unit: used to acquire discrete strain light signals of multiple cross sections of the structure under load in real time through an array of fiber optic strain sensors deployed on the inner surface of a slender marine structure. Signal demodulation and transmission unit: It is communicatively connected to the sparse strain sensing unit, and is used to receive the discrete strain optical signal, and to analyze and convert it into high-precision digital discrete strain data through an optical fiber demodulator, which is then applied to the core deformation reconstruction calculation unit. Visualization and Status Assessment Unit: This unit receives the three-dimensional spatial deformation monitoring curve and displays it dynamically in a three-dimensional graphical format on a computer terminal interface. Simultaneously, based on the deformation curve information and structural material property information, it compares the preset safety threshold with the finite element simulation deformation analysis software to assess the real-time safety status of the structure under test and triggers an early warning mechanism when the limit is exceeded.