An elongated marine structure deformation monitoring method based on moving boundary virtual extension

Abstract

The application is an elongated marine structure deformation monitoring method based on a moving boundary virtual extension, and belongs to the technical field of marine engineering structure monitoring based on computer data processing; aiming at the problem of curvature extrapolation instability caused by dynamic disturbance of the structure end, the application constructs a virtual extension boundary at the structure end, establishes a parameterized constraint model with the extension length and the curvature adjustment coefficient as variables, and determines the optimal virtual boundary geometric form with the minimum reconstruction error minimization as the target; the entity and the virtual boundary are spliced into a global analysis domain, and the three-dimensional deformation curve of the central axis is reconstructed based on sparse strain data. The application converts the structure end moving boundary problem into an optimal curvature constraint, effectively suppresses the curvature mutation and error accumulation, and significantly improves the accuracy and stability of the structure deformation reconstruction under the weak constraint condition of the end.

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 for monitoring the deformation of slender marine structures based on the virtual extension of dynamic boundaries. Background Technology

[0002] In recent years, with the rapid 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. As core components for connection, support, or energy conversion, these structures operate for extended periods in harsh marine environments subjected to the combined effects of multiple extreme loads from wind, waves, and currents. Consequently, deformation, vibration, and fatigue damage problems have become increasingly prominent, posing a key factor affecting the safe operation and service life of marine equipment. Therefore, real-time online deformation monitoring and condition assessment of slender marine structures are of significant engineering and strategic value for ensuring the structural safety of deep-sea engineering equipment.

[0003] Slender marine structures endure complex loads from wind, waves, and currents in the marine environment over extended periods. Their ends are typically under dynamic boundary conditions, characterized by time-varying spatial displacement and rotational coupled disturbances. Typical examples include the periodic spatial oscillation at the root of wind turbine blades caused by rotor rotation and pitch control, and the dynamic boundary displacement at the top of deep-sea risers caused by the heave and drift of floating platforms. Due to the complex mechanical connections, corrosion-resistant sealing requirements, and localized high-stress environments at the ends of marine equipment, physical sensors often cannot be directly installed at the structural ends. Therefore, a sensing blind zone lacking strain and displacement information inevitably exists between the actual dynamic boundary of the structure and the effective measuring point at the very end, making it impossible to obtain the initial pose and curvature boundary conditions at the ends through direct measurement.

[0004] Existing deformation reconstruction methods based on discrete surface strain largely rely on ideal static boundary assumptions. When faced with missing dynamic boundary information, traditional techniques typically employ simplification methods such as setting local curvature to zero or linear extrapolation. These methods neglect the physical principle that the curvature of slender, flexible structures exhibits nonlinear axial decay under large deformation conditions and requires a smooth transition, making it difficult to reasonably estimate end boundary conditions within the sensing blind zone. In engineering conditions with sparse sensor deployment, these simplified boundary treatments may amplify minute curvature distortions or abrupt stiffness changes within the end blind zone during subsequent spatial integration or accumulation, resulting in significant deviations in the reconstructed 3D deformation curve at the far end. Geometric nonlinear errors gradually accumulate along the structural axis, affecting the reliability of the monitoring results.

[0005] Therefore, there is an urgent need to develop a technology that can construct virtual boundary constraints to suppress spatial integral divergence without adding physical sensors, so as to achieve accurate reconstruction of the three-dimensional large deformation of slender marine structures under complex working conditions. Summary of the Invention

[0006] To address the spatial integral divergence problem caused by end-sensor blind spots and dynamic boundary conditions, this invention first acquires measured strain within the measured section of the physical structure using sparsely arranged sensors. Through cross-sectional equivalent mapping and physical piecewise interpolation, a locally continuous curvature field covering the sensor deployment area is generated. Based on this, a parameterized virtual dynamic boundary constraint model is introduced. The optimal geometric shape of the virtual extended boundary is determined through systematic parameter space optimization, thereby accurately filling the geometric information blind spots at the ends of the dynamic boundary. Subsequently, the physical structure entity and the virtual extended boundary are concatenated into a global analysis domain to obtain a globally continuous curvature distribution. Based on piecewise constant curvature theory, local geometric features of the physical micro-elements are extracted, a local homogeneous transformation matrix is ​​constructed, and the global pose is recursively derived from the bottom up using the rigid body kinematics chain rule, ultimately reconstructing the three-dimensional large spatial deformation curve of the physical structure.

[0007] This invention overcomes the problems of amplified cumulative errors and spatial morphology distortion caused by the lack of dynamic boundary information by using virtual boundary constraints without increasing the sensing cost of physical sensors. With low sensing cost and high algorithm robustness, it realizes high-fidelity three-dimensional spatial morphology monitoring of slender marine structures under extreme and harsh conditions.

[0008] This invention provides a method for monitoring the deformation of slender marine structures based on the virtual extension of dynamic boundaries, comprising the following processes: S1, for the boundary with dynamic disturbance at the end of the structure, at the physical structural entity dynamic boundary, a virtual extension length is extended outward along the central axis of the structure to form a virtual extension boundary; S2, extract the maximum curvature within the measured section of the structure, multiply it by the curvature adjustment coefficient to obtain the target curvature at the end of the moving boundary; set the curvature of the farthest endpoint of the virtual extension boundary to zero, and interpolate between the zero curvature and the target curvature to establish a parameterized virtual boundary constraint model with the virtual extension length and curvature adjustment coefficient as variables; S3. Based on the distance between measuring points and the curvature extrema within the measured interval, a parameter feasible region consisting of virtual extension length and curvature adjustment coefficient is set. The parameterized virtual boundary constraint model is applied to the global analysis. With the goal of minimizing spatial reconstruction error, the optimal parameters are obtained within the parameter feasible region and substituted back into the virtual boundary constraint model to determine the optimal virtual extension boundary including the optimal virtual extension length and the optimal curvature adjustment coefficient. S4. The structure and the optimal virtual extension boundary are spliced ​​together to form a global analysis domain. Under the condition of unknown initial pose, based on the continuous curvature distribution and the virtual boundary constraint model, the three-dimensional deformation curve of the central axis of the structural entity is reconstructed and output.

[0009] Preferably, in step S1, outside the physical structural entity boundary, a virtual extension length is extended outward along the central axis of the structure to form a virtual extension boundary. The spatial coordinates of the physical entity measurement point closest to the dynamic disturbance boundary are extracted and anchored as the reference extension starting point. Taking the direction of the structural central axis at the reference extension starting point as the extension path, a series of virtual micro-element nodes are generated outward in sequence according to the set spatial discrete step length, until the cumulative span reaches the aforementioned virtual extension length. The discrete topological space jointly defined by the reference extension starting point and the outermost virtual micro-element node constitutes the virtual extension boundary.

[0010] Preferably, in step S2, based on the geometric design data of the slender marine structure, it is divided into multiple physical segments; 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 results in a set of discrete central axial average strain and discrete curvature data in orthogonal directions for the cross section. Furthermore, for any discrete height section within the measured interval... z i The local curvature modulus of the cross section is calculated by synthesizing Euclidean space vectors based on discrete curvature components in orthogonal directions. ; Local curvature modulus of all discrete sections within the measured interval of the physical structure The maximum curvature extremum is extracted, and a curvature adjustment coefficient is introduced as an independent variable. The maximum curvature extremum is multiplied by the curvature adjustment coefficient to define the target constraint curvature at the end of the real moving boundary of the physical structure. The farthest endpoint generated by extrapolating the virtual extension length is used as a virtual anchor node, and the curvature of the farthest endpoint is set to zero. Spatial spline interpolation is performed between the moving boundary end and the farthest endpoint of the virtual extension boundary as spatial nodes to generate a continuous curvature function of the entire virtual extension boundary. A parameterized virtual boundary constraint model with virtual extension length and curvature adjustment coefficient as bivariates is established.

[0011] Preferably, in step S3, based on the physical spacing characteristics between adjacent discrete measurement points in the physical structure and the true curvature extreme value characteristics within the measured interval, a feasible parameter domain consisting of a virtual extension length and a curvature adjustment coefficient is set, and the specific limiting benchmark of its physical constraint boundary is as follows: The virtual extension length to be optimized uses the physical distance between two adjacent discrete strain measurement points in the physical structure as the characteristic scale benchmark, and its value range is limited to 0.5 times to 3.0 times the physical distance to prevent spatial topological distortion caused by virtual extrapolation; the upper limit of the curvature adjustment coefficient to be optimized is limited to 1.0 to ensure that the target constraint curvature calculated by it is not greater than the order of magnitude of the true curvature extreme value in the measured interval.

[0012] Preferably, in step S3, the optimization within the feasible region of parameters aims to minimize the spatial reconstruction error. The specific process is as follows: A discrete parameter grid search strategy is employed, systematically traversing different combinations of spatial extension length and curvature adjustment coefficient within the two-dimensional feasible region according to a preset parameter discrete step size. The three-dimensional spatial reconstructed position vectors of each discrete node on the central axis of the physical structure are extracted, and an evaluation objective function guided by minimizing the root mean square error of the three-dimensional Euclidean displacement is constructed. E ( N , S Its specific mathematical expression is: ; In the formula, N For virtual extension length, S is the curvature adjustment coefficient; K is the total number of extracted discrete nodes; In the current ( N , S The first reconstructed under parameter combination k A column vector of the three-dimensional spatial positions of each node; This is the column vector of the reference positions corresponding to this node; the evaluation objective function is compared under different parameter combinations. E ( N , S The output value of ) is used to determine and extract the optimal virtual extension length and the optimal curvature adjustment coefficient that converge to the minimum value.

[0013] Preferably, the specific process of S4 includes: The target curvature of the physical structure's moving boundary is determined by multiplying the optimal curvature adjustment coefficient obtained from S3 with the maximum curvature of the measured interval. The physical structure entity is then spliced ​​with the optimal virtual extended boundary whose geometric shape is determined in S3 to construct a global analysis domain. Within this global analysis domain, using the curvature of each measuring point in the measured interval, the target curvature, and the virtual far-end zero curvature as interpolation nodes, a continuous curvature distribution function is generated through spline interpolation. The physical structure entity portion within the global analysis domain is then uniformly discretized along its central axis. j Based on a continuous curvature distribution function, the local curvature modulus of each infinitesimal segment on the physical structure entity is extracted. With the main curvature azimuth The actual corrected arc length of each micro-element segment is obtained based on the continuous axial strain function correction. Based on the actual corrected arc length With local equivalent curvature modulus Construct the homogeneous transformation matrix of each infinitesimal segment in the local principal bending plane. Simultaneously, the main bending azimuth angle is 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 initial pose was then set starting from the moving boundary of the slender ocean structure. 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 recursive calculation along the central axis of the structure, the first step on the central axis of the structure can be obtained. k The global pose matrix of each node in the global coordinate system Extract the column vector of the spatial location of the node from it. This allows for the reconstruction and output of the three-dimensional spatial deformation curves of the physical structural entity.

[0014] Preferably, the solution obtains the first [element] on the central axis of the structure. 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. is the initial reference pose matrix at the starting point of the moving boundary; For the first j The complete rigid body transformation matrix of each infinitesimal segment; ∈ Represents a node k The global attitude matrix, column vectors 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.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. High 3D accuracy and high-fidelity reproduction of large spatial deformation: By constructing a virtual extended boundary and setting the curvature of the far end to zero, spline interpolation is performed between the zero curvature and the target curvature of the moving boundary to establish a virtual curvature constraint, which effectively suppresses the divergence of spatial integral accumulation error caused by the lack of initial pose, thereby accurately reproducing the 3D spatial deformation curve of the slender structure under dynamic boundary conditions. 2. Strong applicability and effective solution to the blind spot of sparse measurement points: By dynamically binding the virtual extension length with the distance between measurement points and introducing a parameterized virtual boundary model and a systematic optimization strategy, the optimal extension length and curvature adjustment coefficient are adaptively determined, thereby filling the information blind spot near the moving boundary without increasing the number of physical measurement points, and significantly broadening the engineering applicability of the algorithm to sparsely deployed sensors. 3. Good robustness, ensuring long-term stability under dynamic boundary conditions: By utilizing only the strain information of internal sparse measuring points, without relying on the initial absolute pose or fixed boundary conditions, the three-dimensional deformation curve of the structure's central axis can be reconstructed, thereby effectively coping with complex conditions such as time-varying rotation angles and displacement disturbances at the ends, ensuring the long-term stability and engineering practical value of the monitoring system in harsh environments. Attached Figure Description

[0016] Figure 1 This is the overall flowchart of the monitoring method of the present invention.

[0017] Figure 2 This is a schematic diagram of the extended boundary of an embodiment of the present invention.

[0018] Figure 3 This is a deformation diagram of the load condition of the deep-sea mining riser according to an embodiment of the present invention.

[0019] Figure 4 This is a deformation diagram of the deep-sea mining riser under load conditions according to an embodiment of the present invention.

[0020] Figure 5 This is a comparison diagram of riser configuration reconstruction and error under load conditions applied to deep-sea mining risers according to the present invention; wherein, (a) is a comparison of the riser three-dimensional spatial configuration reconstruction curve and the reference curve, and (b) is the distribution along the path of the relative error of three-dimensional spatial displacement reconstruction at each height section of the riser under conditions with / without virtual extension boundary.

[0021] Figure 6 The diagram shows the comparison of riser configuration reconstruction and error under load condition 2 for the application of the present invention to deep-sea mining risers; (a) is a comparison of the riser three-dimensional spatial configuration reconstruction curve and the reference curve, and (b) is the distribution of the relative error of three-dimensional spatial displacement reconstruction at each height section of the riser under conditions with / without virtual extension boundary. Detailed Implementation

[0022] This invention proposes a method for monitoring the deformation of slender marine structures based on the virtual extension of dynamic boundaries. The overall logic is as follows: Figure 1 As shown, it includes the following steps: S1, for the boundary with dynamic disturbance at the end of the structure, at the physical structural entity dynamic boundary, a virtual extension length is extended outward along the central axis of the structure to form a virtual extension boundary; S2, extract the maximum curvature within the measured section of the structure, multiply it by the curvature adjustment coefficient to obtain the target curvature at the end of the moving boundary; set the curvature of the farthest endpoint of the virtual extension boundary to zero, and interpolate between the zero curvature and the target curvature to establish a parameterized virtual boundary constraint model with the virtual extension length and curvature adjustment coefficient as variables; S3. Based on the distance between measuring points and the curvature extrema within the measured interval, a parameter feasible region consisting of virtual extension length and curvature adjustment coefficient is set. The parameterized virtual boundary constraint model is applied to the global analysis. With the goal of minimizing spatial reconstruction error, the optimal parameters are obtained within the parameter feasible region and substituted back into the virtual boundary constraint model to determine the optimal virtual extension boundary including the optimal virtual extension length and the optimal curvature adjustment coefficient. S4. The structure and the optimal virtual extension boundary are spliced ​​together to form a global analysis domain. Under the condition of unknown initial pose, based on the continuous curvature distribution and the virtual boundary constraint model, the three-dimensional deformation curve of the central axis of the structural entity is reconstructed and output.

[0023] 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.

[0024] This embodiment uses a slender riser in deep-sea mining operations as the monitoring object. During service, the bottom of the deep-sea mining riser is connected to the seabed wellhead or mining vehicle, and the top is connected to a floating platform on the sea surface. Due to the coupling effect of ocean current eddy vibration and platform heave and drift, the top of the riser exhibits a dynamic boundary with strong time-varying spatial displacement and angular disturbance. This embodiment constructs a scaled-down model based on the design parameters of the deep-sea mining riser. The model riser has a total length L = 100m, an outer radius R = 0.057m, a wall thickness of 0.005m, and uses S355 steel with a yield strength of 355MPa, an elastic modulus of 210GPa, a density of 7850kg / m³, and a Poisson's ratio of 0.3. This embodiment simulates the riser being subjected to multi-directional non-uniform ocean current shear force and complex three-dimensional reverse drag force at the bottom, designing two load conditions, such as... Figure 3 and Figure 4As shown: In working condition one, the bottom of the riser bears a spatial lateral load with an x ​​component of -160 N and a y component of -192 N, and a reverse concentrated load with an x ​​component of 50 N and a y component of 60 N. In working condition two, the bottom of the riser bears a more severe lateral load with an x ​​component of -224 N and a y component of -256 N, and a reverse load with an x ​​component of 70 N and a y component of 80 N.

[0025] S1, for boundaries with dynamic disturbances at the ends of the structure, a virtual extension length is extended outward along the central axis of the structure at the moving boundary of the physical structure, forming a virtual extension boundary; such as Figure 2 As shown, the specific implementation process of this embodiment is as follows: For the top of the riser... In the dynamic boundary condition, outside the physical structural entity boundary, extending outward along the central axis of the riser towards the virtual space above sea level, a series of virtual micro-element nodes are generated until a length of [length missing]. N The virtual extended boundary.

[0026] S2, extract the maximum curvature within the measured section of the structure, multiply it by the curvature adjustment coefficient to obtain the target curvature at the end of the moving boundary; set the curvature of the farthest endpoint of the virtual extension boundary to zero, and interpolate between the zero curvature and the target curvature to establish a parameterized virtual boundary constraint model with virtual extension length and curvature adjustment coefficient as variables; the specific implementation process is as follows: based on the geometric design data of the deep-sea mining riser, strain sensors are orthogonally arranged on discrete height sections of the surface. Due to the complex mechanical connections and tensioner structure of the top floating platform, sensors cannot be installed in the underwater 0-10m area. The specific sensor layout along the axial underwater depth coordinates is z = {10, 20, 30,…, 100m}, with a total of 10 discrete measuring point sections, and the physical distance between adjacent measuring points is L. sp = 10 m. Real-time acquisition of azimuth angles of various cross-sections on the surface of deep-sea mining riser. β Discrete strain data at the location By combining the geometric angles between each cross section of the structural surface and the global neutral axis, the measured strain data of each discrete cross section of the riser surface are corrected to a corrected strain parallel to the global neutral axis. Subsequently, based on the Euler-Bernoulli beam theory, the modified strain was... Geometric decoupling results in a set of discrete central axial average strain and discrete curvature data in orthogonal directions for the cross section. Correct 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 heightz i Cross section at x and y The curvature component in the direction, 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.

[0027] Furthermore, for any discrete height section within the measured interval... z i Based on the discrete curvature components in the orthogonal directions, Euclidean space vector synthesis is performed to calculate the local curvature modulus of the cross section. Its specific calculation expression is: ; Based on this, the local curvature modulus of all discrete sections within the tested section of the deep-sea mining riser is traversed, and the maximum curvature extremum is extracted. A curvature adjustment coefficient is introduced as an independent variable, and the maximum curvature extremum is multiplied by the curvature adjustment coefficient to define the target constraint curvature of the actual moving boundary end of the physical structure. The farthest endpoint generated by extrapolating the spatial extension length is used as a virtual anchor node, and the curvature of the farthest endpoint is set to zero. Spatial spline interpolation is performed between the moving boundary end and the farthest endpoint of the virtual extension boundary as spatial nodes to generate a continuous curvature function of the entire virtual extension boundary, and a parameterized virtual boundary constraint model with the spatial extension length and curvature adjustment coefficient as bivariates is established. S3. Based on the distance between measuring points and the curvature extrema within the measured interval, a feasible parameter region consisting of the virtual extension length and the curvature adjustment coefficient is defined. The parameterized virtual boundary constraint model is applied to the global analysis domain, and optimization is performed within the feasible parameter region with the goal of minimizing spatial reconstruction error. The optimal parameters are then substituted back into the model to determine the optimal geometric shape of the virtual extension boundary. The specific implementation process is as follows: Based on the physical spacing characteristics between adjacent discrete measurement points on the physical structure and the true curvature extremum characteristics within the measured interval, a parameter feasible region consisting of the virtual extension length and the curvature adjustment coefficient is defined. The specific limiting benchmarks for its physical constraint boundaries are as follows: the virtual extension length to be optimized uses the physical spacing between two adjacent discrete strain measurement points on the physical structure as the characteristic scale benchmark, and its value range is limited to 0.5 to 3.0 times the physical spacing; the upper limit of the curvature adjustment coefficient to be optimized is limited to 1.2. The aforementioned parameterized virtual boundary constraint model is applied to a global analysis domain containing virtual nodes to construct an evaluation objective function guided by minimizing the three-dimensional spatial reconstruction error of the overall deformation curve of the deep-sea mining riser structure. Within the aforementioned feasible two-dimensional parameter region, a discrete parameter grid search strategy is employed. Following a preset parameter discrete step size, different numerical combinations of the spatial extension length and curvature adjustment coefficient are systematically traversed within the two-dimensional feasible region. The three-dimensional spatial reconstructed position vectors of each discrete node on the central axis of the physical structure are extracted, and an evaluation objective function guided by minimizing the root mean square error of the three-dimensional Euclidean displacement is constructed. E ( N , S Its specific mathematical expression is: ; In the formula, N For virtual extension length, S is the curvature adjustment coefficient; K is the total number of extracted discrete nodes; In the current ( N , S The first reconstructed under parameter combination k A column vector of the three-dimensional spatial positions of each node; This is the column vector representing the baseline reference position for this node. The evaluation objective function is compared under different parameter combinations. E ( N , S The output value of ) is used to determine and extract the optimal virtual extension length and curvature adjustment coefficient that converge to the minimum value.

[0028] S4, based on the optimal curvature adjustment coefficient obtained in S3, multiplies it by the maximum curvature of the measured interval to determine the target curvature of the moving boundary of the deep-sea mining riser physical structure. The deep-sea mining physical structure entity is then spliced ​​with the virtual extended boundary whose geometry was determined in S3 to construct a global analysis domain. Within this global analysis domain, using the curvature of each measuring point in the measured interval, the target curvature, and the virtual far-end zero curvature as interpolation nodes, a continuous curvature distribution function is generated through spline interpolation. This function uniformly discretizes the deep-sea mining riser physical structure entity within the global analysis domain along its central axis. jBased on the continuous curvature distribution function, the local curvature modulus of each micro-segment on the physical structure of the riser is extracted. With the main curvature azimuth The actual corrected arc length of each micro-element segment is obtained based on the continuous axial strain function correction. Based on the actual corrected arc length With local equivalent curvature modulus Construct the homogeneous transformation matrix of each infinitesimal segment in 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: ; ; ; 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.

[0029] The initial pose was then set starting from the moving boundary of the deep-sea mining riser structure. 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 recursive calculation along the central axis of the structure, the first step on the central axis of the structure can be obtained. k The global pose matrix of each node in the global coordinate system Extract the column vector of the spatial location of the node from it. This allows for the reconstruction and output of the three-dimensional spatial deformation curves of the physical structural entity.

[0030] 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. is the initial reference pose matrix at the starting point of the moving boundary; For the first j The complete rigid body transformation matrix of each infinitesimal segment; ∈ Represents a node k The global attitude matrix, column vectors 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.

[0031] Numerical simulation and result analysis: To verify the accuracy and engineering applicability of the extended boundary reconstruction algorithm for large deformation in three-dimensional space of this invention, a scaled-down model of a deep-sea mining riser was established and imported into ANSYS software for numerical simulation analysis. In the ANSYS simulation environment, multi-directional coupled spatial loads were applied to the middle and bottom of the riser to simulate the combined effects of wind and waves under actual sea conditions. Discrete surface strain simulation data were extracted from 10 discrete monitoring sections underwater at 10m, 20m, 30m, 40m, 50m, 60m, 70m, 80m, 90m, and 100m, at four orthogonal circumferential directions (0°, 90°, 180°, 270°), serving as the virtual input signal for the monitoring system of this invention. The discrete strain data was imported into the algorithm, and a rigorous three-dimensional spatial comparison was performed between the three-dimensional continuous deformation curve reconstructed based on the algorithm of this invention and the absolute displacement results of the structural nodes output by the ANSYS finite element method (FEM).

[0032] like Figure 5 and Figure 6 As shown, under both load conditions, the reconstructed three-dimensional spatial configuration of the riser according to this invention agrees well with the finite element simulation results, indicating that the virtual extended boundary method can effectively improve the curvature extrapolation error under weak end constraints. Compared with the method without virtual extended boundaries, this invention exhibits lower overall error and more stable distribution at each height section. Under load condition one, the average relative error decreased from 1.77% to 1.47%, the maximum error decreased from 2.44% to 2.05%, and the comprehensive error decreased from 2.24% to 1.87%, representing reductions of 17.3%, 16.0%, and 16.3%, respectively. Under load condition two, the average relative error decreased from 2.31% to 1.19%, the maximum error decreased from 3.13% to 2.16%, and the comprehensive error decreased from 2.88% to 1.87%. The results show that this invention effectively suppresses abrupt changes in end curvature and error accumulation by transforming uncertain end boundary disturbances into optimizable curvature constraints, significantly improving the accuracy and stability of riser spatial deformation reconstruction.

[0033] 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.

[0034] 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 deformation monitoring of an elongated marine structure based on moving boundary virtual extension, characterized by, Includes the following processes: S1, for the boundary with dynamic disturbance at the end of the structure, at the physical structural entity dynamic boundary, a virtual extension length is extended outward along the central axis of the structure to form a virtual extension boundary; S2, extract the maximum curvature within the measured section of the structure, multiply it by the curvature adjustment coefficient to obtain the target curvature at the end of the moving boundary; set the curvature of the farthest endpoint of the virtual extension boundary to zero, and interpolate between the zero curvature and the target curvature to establish a parameterized virtual boundary constraint model with the virtual extension length and curvature adjustment coefficient as variables; S3. Based on the distance between measuring points and the curvature extrema within the measured interval, a parameter feasible region consisting of virtual extension length and curvature adjustment coefficient is set. The parameterized virtual boundary constraint model is applied to the global analysis. With the goal of minimizing spatial reconstruction error, the optimal parameters are obtained within the parameter feasible region and substituted back into the virtual boundary constraint model to determine the optimal virtual extension boundary including the optimal virtual extension length and the optimal curvature adjustment coefficient. S4. The structure and the optimal virtual extension boundary are spliced ​​together to form a global analysis domain. Under the condition of unknown initial pose, based on the continuous curvature distribution and the virtual boundary constraint model, the three-dimensional deformation curve of the central axis of the structural entity is reconstructed and output.

2. A virtual extension based on moving boundary for deformation monitoring of an elongated marine structure method according to claim 1, characterized in that: In S1, outside the physical structure entity boundary, a virtual extension length is extended outward along the central axis of the structure to form a virtual extension boundary. The spatial coordinates of the physical entity measurement point closest to the dynamic disturbance boundary are extracted and anchored as the reference extension starting point. Using the structural center axis at the starting point of the reference extension as the extension path, according to the set spatial distance step length, push outward in the mathematical space sequence and generate a series of virtual micro-element nodes until the cumulative span reaches the aforementioned virtual extension length. The discrete topological space jointly defined by the reference extension starting point and the outermost virtual micro-element node constitutes the virtual extended boundary.

3. A virtual extension of moving boundary based deformation monitoring method for an elongated marine structure as claimed in claim 1, wherein: In S2, based on the geometric design data of the slender marine structure, it is divided into multiple physical segments; Orthogonal arrangement of strain sensors on discrete height cross sections of the inner surface of the segmented structure, real-time collection of discrete strain data of the inner surface of the segmented structure at each cross section β , combined with the geometric angle between each cross section of the inner surface of the structure and the global neutral axis, the measured strain data of each discrete cross section of the inner surface of the segmented structure is corrected to the corrected strain parallel to the global neutral axis , then, according to the Euler-Bernoulli beam theory, the corrected strain Geometric decoupling into a set of discrete central axis average strain and discrete curvature data in the orthogonal direction of the cross section​ Further, for any discrete height section in the measured interval z i , based on the discrete curvature component in the orthogonal direction, the Euclidean space vector synthesis is performed to calculate the local curvature modulus of the section ; Traversing all discrete cross sections within a physical structure under test interval for local curvature modulus extracting a maximum curvature extreme value therefrom, introducing a curvature adjustment coefficient as an independent variable, multiplying the maximum curvature extreme value by the curvature adjustment coefficient to define a target constraint curvature of a true dynamic boundary end portion of the physical structure The farthest endpoint generated by extrapolating the virtual extension length is used as the virtual anchor node, and the curvature of the farthest endpoint is set to zero. Using the end of the moving boundary and the farthest endpoint of the virtual extended boundary as spatial nodes, spatial spline interpolation is performed between the two nodes to generate a continuous curvature function for the entire virtual extended boundary, thus establishing a parameterized virtual boundary constraint model with virtual extension length and curvature adjustment coefficient as two variables.

4. A virtual extension based on moving boundary for deformation monitoring of an elongated marine structure according to claim 1, characterized in that: In step S3, based on the physical spacing characteristics between adjacent discrete measurement points in the physical structure and the true curvature extreme value characteristics within the measured interval, a feasible parameter domain consisting of the virtual extension length and the curvature adjustment coefficient is set, and the specific limiting benchmark of its physical constraint boundary is as follows: The virtual extension length to be optimized uses the physical distance between two adjacent discrete strain measurement points in the physical structure as the characteristic scale benchmark, and its value range is limited to 0.5 times to 3.0 times the physical distance to prevent spatial topological distortion caused by virtual extrapolation; the upper limit of the curvature adjustment coefficient to be optimized is limited to 1.0 to ensure that the target constraint curvature calculated by it is not greater than the order of magnitude of the true curvature extreme value in the measured interval.

5. A virtual extension based on moving boundary for deformation monitoring of an elongated marine structure according to claim 1, characterized in that: In S3, the optimization within the feasible region of parameters aims to minimize the spatial reconstruction error. The specific process is as follows: The discrete parameter grid search strategy is adopted, preset parameter discrete step length is adopted, and different numerical combinations of the space extension length and the curvature adjustment coefficient in the two-dimensional parameter feasible region are systematically traversed; the three-dimensional space reconstruction position vectors of the discrete nodes on the physical structure center axis are extracted, and an evaluation objective function oriented to the minimization of the three-dimensional space Euclidean displacement relative error mean square root is constructed E ( N , S ), and the specific mathematical expression is: ； In the formula, N is the virtual extension length, S is the curvature adjustment coefficient; K is the total number of discrete nodes extracted; is the three-dimensional space position column vector of the i-th node reconstructed under the current ( N , S ) parameter combination; k is the reference position column vector corresponding to the node; by comparing the output values of the evaluation target function E ( N , S ) under different parameter combinations, the optimal virtual extension length and the optimal curvature adjustment coefficient that make it converge to the minimum value are determined and extracted.​ 6. A virtual extension based on moving boundary for deformation monitoring of an elongated marine structure according to claim 1, characterized in that: The specific process of S4 includes: The target curvature of the physical structure's moving boundary is determined by multiplying the optimal curvature adjustment coefficient obtained from S3 with the maximum curvature of the measured interval. The physical structure entity is then spliced ​​with the optimal virtual extended boundary whose geometric shape is determined in S3 to construct a global analysis domain. Within this global analysis domain, using the curvature of each measuring point in the measured interval, the target curvature, and the virtual far-end zero curvature as interpolation nodes, a continuous curvature distribution function is generated through spline interpolation. The physical structure entity portion within the global analysis domain is then uniformly discretized along its central axis. j Based on a continuous curvature distribution function, the local curvature modulus of each infinitesimal segment on the physical structure entity is extracted. With the main curvature azimuth The actual corrected arc length of each micro-element segment is obtained based on the continuous axial strain function correction. Based on the actual corrected arc length With local equivalent curvature modulus Construct the homogeneous transformation matrix of each infinitesimal segment in the local principal bending plane. Simultaneously, the main bending azimuth angle is 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 initial pose was then set starting from the moving boundary of the slender ocean structure. 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 recursive calculation along the central axis of the structure, the first step on the central axis of the structure can be obtained. k The global pose matrix of each node in the global coordinate system Extract the column vector of the spatial location of the node from it. This allows for the reconstruction and output of the three-dimensional spatial deformation curves of the physical structural entity.

7. The method for monitoring the deformation of slender marine structures based on the virtual extension of dynamic boundaries as described in claim 6, characterized in that: The solution yields the first [item] on the central axis of the structure. k The global pose matrix of each node in the global coordinate system The specific calculation method is as follows: ； wherein, is the global pose matrix of the structure, k is the initial reference pose matrix of the dynamic boundary starting point; is the complete rigid body transformation matrix of the j ∈ represents the global pose matrix of the node k is the three-dimensional space position column vector of the kth node in the global coordinate system; k is the total number of nodes.​​​

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