Hybrid basis-based damage offshore jacket sparse response reconstruction method

Abstract

The present application relates to offshore structure health monitoring technical field, especially a kind of damage offshore jacket sparse response reconstruction method based on mixed base.It includes: obtaining the free decay acceleration response of source domain structure under local stiffness degradation condition;Based on data processing method, construct fusion space singular spectrum;According to the local coordinates of target jacket damage bar, the fusion space singular spectrum is mapped to damage sensitive area, and local base is formed;Global base representing the global response of jacket is constructed and orthogonally fused with local base, to form enhanced mixed base;According to the structure response collected by sparse sensor, observation equation is established, and generalized coordinate is solved by regularization, to reconstruct acceleration response of damage neighborhood target point or jacket global dynamic response.The method can enhance the representation ability of local damage disturbance for active large marine structure under limited sensor condition, realize virtual sensing and enhanced monitoring for existing damage sensitive area of offshore jacket, and effectively ensure its operation.

Description

Technical Field

[0001] This invention relates to the field of marine structural health monitoring technology, and in particular to a method for reconstructing the sparse response of damaged marine jacket structures based on hybrid bases. Background Technology

[0002] Jacket support structures, with their high overall stiffness, strong load-bearing capacity, and good adaptability to complex marine environments, have become one of the important support structures for offshore equipment in medium and deep water areas. Because jacket structures are continuously subjected to the combined effects of wind, waves, currents, generator operating loads, and marine corrosion during long-term service, their local members, welded joints, and diagonal brace connection areas are prone to fatigue cracks, corrosion thinning, and local stiffness degradation. While some early localized damage may not immediately lead to generator shutdown or overall structural failure, the damaged areas often become sensitive locations for subsequent fatigue propagation and amplified local response, thus requiring continuous monitoring and focused assessment.

[0003] In practical offshore monitoring projects, the number of sensors that can be installed on the jacket structure is usually limited due to factors such as underwater installation conditions, sensor placement space, long-term maintenance costs, and the number of data acquisition channels. On-site monitoring data often only covers the main legs, the vicinity of the platform, or other limited locations where installation is convenient. Damage-sensitive locations such as braces, pipe nodes, and areas with known or suspected damage are often difficult to directly deploy sensors on. Therefore, how to utilize dynamic response data collected from limited measurement points to infer the dynamic response of unmeasured locations, especially target points in the vicinity of damage, and further realize response reconstruction under the damage state of the jacket structure, is a key issue in the health monitoring of offshore jacket structures.

[0004] Existing methods for estimating responses at unmeasured points and reconstructing the full-field response mainly include model-driven methods, data-driven methods, and response extension methods based on global shape functions or basis functions. Model-driven methods typically rely on finite element models, modal extension, Kalman filtering, model correction, or inverse finite element methods to extend the response at finite measured points to the unmeasured region. These methods offer strong physical interpretation, but in actual service environments, jacket structures are affected by factors such as changing boundary conditions, marine organism attachment, erosion, corrosion, node connection flexibility, and model simplification, making it difficult to maintain a high-precision baseline finite element model over the long term. When local damage already exists in the structure, relying solely on global models or constant modal extension methods is insufficient to accurately recover the high-frequency spatial disturbance response caused by local stiffness degradation within the damage neighborhood.

[0005] Therefore, for the problem of reconstructing the response of offshore jacket structures under known or suspected local damage conditions, there is an urgent need for a reconstruction method that can simultaneously characterize the global smooth response and the local damage disturbance response under sparse sensing conditions. Summary of the Invention

[0006] The purpose of this invention is to overcome the aforementioned deficiencies in existing technologies and propose a sparse response reconstruction method for damaged offshore jacket structures based on hybrid bases. This method, even when the number of sensors is limited, it is difficult to directly deploy sensors in damage-sensitive areas, and the target structure's health baseline response is difficult to obtain, transforms the spatial singular perturbation characteristics caused by local stiffness degradation in the source domain structure into transferable physical prior knowledge. This prior knowledge is then orthogonally fused with the global response basis of the target jacket structure, thereby reconstructing the dynamic response of the target point in the damage-sensitive area or the full-field dynamic response of the jacket. This provides technical support for virtual sensing, damage status tracking, and long-term service safety assessment of offshore jacket structures.

[0007] The technical solution of this invention is: A method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases, comprising the following steps: S1. Obtain dynamic response data of the source domain structure under local damage state, and extract source domain damage singular prior knowledge based on the dynamic response data to characterize the spatial singular perturbation features caused by local stiffness degradation. S2. Based on the spatial location of the damage-sensitive region to be reconstructed in the target duct frame structure, the source domain damage singular prior knowledge is mapped to the corresponding rod region of the target duct frame structure to construct a local damage singular basis. S3. Construct a global response basis based on the spatial coordinate information of the target duct structure, and orthogonally fuse the global response basis with the local damage singular basis to obtain an enhanced hybrid basis for characterizing the global response and the local perturbation response; S4. Obtain the measured response data of the target guide frame structure under sparse sensor arrangement conditions, and establish a sparse observation equation based on the enhanced hybrid basis and the measured response data. S5. The sparse observation equation is solved by regularization to obtain the generalized coordinates corresponding to the enhanced hybrid basis, and the dynamic response of a point in the damage-sensitive region of the target jacket structure or the whole field dynamic response is reconstructed based on the enhanced hybrid basis and the generalized coordinates.

[0008] In the preferred step S1, the source domain structure is a tubular component with the same physical properties and similar cross-sectional shape as the rod to be reconstructed in the target jacket structure; By introducing stiffness degradation in a local region of the source domain structure, free attenuation dynamic response data under local damage state is obtained. The dynamic response data includes the acceleration response data of the source domain structure after excitation unloading; Based on the acceleration response data, singular prior knowledge of source domain damage is extracted. This singular prior knowledge of source domain damage is used to characterize the spatial non-smooth perturbation features caused by local stiffness degradation.

[0009] Preferably, in step S1, dynamic response data of the source domain structure under local damage state is obtained, and singular priors of source domain damage are extracted based on the dynamic response data. The implementation process is as follows: S1.1 Establish a source domain structure model. The source domain structure is a tubular component with the same physical properties and similar cross-sectional form as the rod to be reconstructed in the target jacket structure. Stiffness degradation is introduced in a local area of ​​the source domain tubular structure to simulate local damage state. A transient excitation is applied to the source domain tubular structure, and the free decay acceleration response data of the source domain tubular structure is acquired after the excitation is unloaded; Modal separation is performed on the free decay acceleration response data to obtain narrowband acceleration responses corresponding to single or multiple modes; S1.2, regarding the first Narrowband acceleration response at each measurement point Perform Hilbert transform to construct analytic signal The instantaneous amplitude envelope of the analytical signal is extracted to obtain the acceleration signal decay function. Its expression is: ; ; in, Represents the Hilbert transform operator. Represents the imaginary unit. Indicates the first Weighting coefficients for the first mode; For constant terms; S1.3. Calculate the spatial second-order difference of the acceleration signal attenuation function along the local axial coordinates of the source domain structure to obtain the curvature response characteristics. It is used to characterize the spatial abrupt changes caused by local stiffness degradation; S1.4, within the effective time window of free decay Within this range, the curvature-type response characteristics are integrated and averaged to obtain the average curvature-type response characteristics, the expression of which is: ; S1.5. Scale normalization and projection correction are performed on the mean curvature response characteristics to construct a scale-invariant curvature singular vector index. Weighted fusion of the local damage contribution fields corresponding to different modes is then performed to obtain the fused spatial singular spectrum. Its expression is: ; in, Indicates the first Weighting coefficients for the first mode. Indicates the first First mode in local coordinates The dimensionless local damage contribution field at the location, Indicates the modal order involved in the fusion; The fused spatial singular spectrum serves as a singular prior knowledge of source domain damage, used to characterize the high-frequency spatial perturbation features induced by local stiffness degradation.

[0010] Preferably, in step S2, based on the spatial location of the damage-sensitive region to be reconstructed in the target duct frame structure, the source domain damage singular prior is mapped to the corresponding rod region of the target duct frame structure to construct a local damage singular basis. The implementation process is as follows: S2.1 Obtain the coordinates of the two end nodes of the damage-sensitive member to be reconstructed in the target guide frame structure. and And determine the local axial coordinate system of the member based on the coordinates of the two end nodes; S2.2, For any spatial position within the target guide frame structure Projecting this onto the local axial coordinate system yields the local projected coordinates of this spatial position along the axial direction of the damaged member to be reconstructed. ; S2.3, Based on local projection coordinates Spatial interpolation operators are used to fuse the spatial singular spectrum of the source domain. Mapped to the corresponding member region of the target jacket structure; S2.4, Set a spatial window function with tight support characteristics This ensures that the singular prior of source domain damage only works within the damage-sensitive region of the target duct structure. Preferably, a local damage singular basis is constructed based on the mapped fused spatial singular spectrum and spatial window function. Its expression is: ; in, Represents the spatial interpolation operator. Represents a spatial window function; When spatial position When located in a damage-sensitive area, ; When spatial position When located outside the damage-sensitive area, .

[0011] Preferably, in step S3, a global response basis is constructed based on the spatial coordinate information of the target duct structure, and the global response basis is orthogonally fused with the local damage singular basis to obtain an enhanced hybrid basis. The implementation process is as follows: S3.1 Obtain the three-dimensional spatial coordinates of the target guide frame structure. Based on the geometric boundaries of the target guide frame structure, the three-dimensional spatial coordinates are normalized to a dimensionless natural coordinate system to obtain the natural coordinates. Its expression is: ; in, Indicates the center coordinates of the geometrically bounded domain of the target jacket structure. These represent the characteristic half-lengths in the three coordinate directions, respectively. S3.2 Construct a one-dimensional Chebyshev polynomial based on the dimensionless natural coordinates. Its expression is: ; S3.3. Combine the one-dimensional Chebyshev polynomials in the three spatial directions by tensor product to obtain the three-dimensional global response basis functions. Its expression is: ; in, These represent the polynomial truncation orders in the three spatial directions, respectively; S3.4 Substitute the spatial coordinates of the measuring points or points to be reconstructed in the target guide frame structure into the three-dimensional global response basis function to construct the global response basis matrix. ; Preferably, the global response basis matrix is... With local damage singularity Perform column splicing to form an initial mixed base; The projective orthogonalization method is used to remove redundant components in the local damage singular basis that can be linearly represented by the global response baseline, resulting in the orthogonalized local damage singular basis. Its expression is: ; global response basis matrix With orthogonalized local damage singularity base By combining them, an enhanced hybrid base is obtained. Its expression is: ; The enhanced hybrid matrix possesses both global smooth response characterization capability and local damage perturbation response characterization capability.

[0012] Preferably, in step S4, the measured response data of the target guide frame structure under sparse sensor arrangement conditions are obtained, and a sparse observation equation is established based on the enhanced hybrid basis and the measured response data. The implementation process is as follows: A limited number of sensors are placed in locations within the target jacket structure that are easy to install or easy to monitor for a long time, to collect dynamic response data of the target jacket structure under operating conditions, environmental excitation conditions, or artificial excitation conditions. The dynamic response data includes at least one of acceleration response, velocity response, displacement response, or strain response; Based on the location of the sparse sensor, from the enhanced hybrid base Extract the observation rows corresponding to the sensor locations to form a sparse observation basis matrix. ; Based on sparse observation basis matrix Measured response vectors acquired by sparse sensors Establish the sparse observation equation: ; in, This represents the generalized coordinate vector to be solved. This indicates measurement noise.

[0013] Preferably, in step S5, the sparse observation equation is solved using regularization to obtain the generalized coordinates corresponding to the enhanced hybrid basis, and the dynamic response or full-field dynamic response of the damage-sensitive region of the target duct structure is reconstructed based on the enhanced hybrid basis and the generalized coordinates. The implementation process is as follows: To address the underdetermined problem caused by the number of sparse sensors being less than the number of degrees of freedom to be reconstructed, a regularized objective function consisting of a data fidelity term and a solution stability constraint term is constructed. Its expression is: ; in, Represents the regularization parameter. Represents a regularization operator; By solving for the minimum value of the regularization objective function, the estimated value of the generalized coordinate vector is obtained. Its expression is: ; The regularization parameter The L-curve method is used to adaptively determine the regularization parameters, specifically by calculating different regularization parameters. Given the residual norm and solution norm under the given conditions, construct a double logarithmic parameter curve between the residual norm and the solution norm, and select the regularization parameter corresponding to the position of maximum curvature of the double logarithmic parameter curve as the optimal regularization parameter. The generalized coordinate vector obtained by the solution Substitute for enhanced hybrid base The dynamic response of the location to be reconstructed in the target jacket structure is obtained. Its expression is: ; The locations to be reconstructed include target measuring points within the damage-sensitive area, the locations of rods without sensors, and the full-field spatial nodes of the target jacket structure.

[0014] When there are multiple damage-sensitive regions to be reconstructed in the target duct structure, the source domain damage singular prior is mapped to the multiple damage-sensitive regions to be reconstructed, and multiple local damage singular bases are constructed. Multiple local damage singular bases are orthogonalized with the global response base, and then combined with the global response base to form an enhanced hybrid base, so as to realize the dynamic response of the target point or the reconstruction of the dynamic response of the whole field under the condition of multiple damage-sensitive areas.

[0015] The method is used for virtual sensing, continuous monitoring of damage-sensitive areas, and dynamic response completion of unmeasured points in offshore wind power jacket structures under known or suspected local damage conditions. The dynamic response includes at least one of acceleration response, displacement response, velocity response, or strain response.

[0016] The beneficial effects of this invention are: (1) This application constructs a method for extracting singular priors of local damage in source domain tubular structures, and obtains a fused spatial singular spectrum that can characterize the spatial singular perturbation features induced by local damage, providing transferable physical priors for the response reconstruction of the damage-sensitive region of the target duct structure. (2) This application proposes a method for mapping source domain damage singular priors to target duct structure, which transforms the source domain local damage singular features into local damage singular bases in the target duct structure, so that the local damage priors only act on the damage-sensitive region to be reconstructed, avoiding unnecessary interference to the global response topology far from the damage region. (3) This application constructs an enhanced hybrid basis for reconstructing the response of the damage state of the duct stent. The enhanced hybrid basis consists of a Chebyshev global response basis for characterizing the global smooth response of the duct stent and a local damage singular basis for characterizing the local damage perturbation response, which improves the independence and numerical stability of the hybrid basis function space. (4) This application proposes a sparse observation response reconstruction method based on enhanced hybrid basis, establishes a sparse observation equation, and obtains generalized coordinates by combining regularization solution and L curve parameter selection method, so as to achieve stable target point response or full field dynamic response reconstruction under the conditions of limited number of measurement points and the presence of measurement noise. (5) The method proposed in this application can obtain the dynamic response information of unmeasured target points in the damage-sensitive area of ​​the jacket structure based on the structural dynamic response collected from a limited number of measurement points, providing an effective technical means for virtual sensing, enhanced monitoring, damage status tracking and service safety assessment of offshore wind power jacket structures. The method proposed in this application enables continuous response monitoring of known or suspected local damage areas without directly relying on the target jacket structure's health baseline response. It also allows for timely supplementation of missing monitoring data based on the dynamic response of the damaged neighborhood obtained from reconstruction, effectively improving the state awareness and operational safety assurance capabilities of offshore wind turbine jacket structures throughout their entire service life. Attached Figure Description

[0017] Figure 1 This is the overall flowchart of the enhanced hybrid base reconstruction method; Figure 2 This is a schematic diagram of the source domain structure model and the extraction of singular prior damage conditions; Figure 3 The results are the extraction results of the fusion spatial singular spectrum in the source domain structure; (a) is the extraction and smoothing fitting results of the fusion spatial singular spectrum of the damage at the middle (first) point of the source domain tubular structure, and (b) is the extraction and smoothing fitting results of the fusion spatial singular spectrum of the damage at 30% (second) point of the source domain tubular structure. Figure 4 It is a schematic diagram of the target guide frame structure model, external excitation direction, sparse sensor arrangement and damage-sensitive area; Figure 5 These are comparison diagrams of the dynamic response reconstruction results of the target point under single damage conditions; where (a) is a comparison diagram of the acceleration response reconstruction results of the target point of the first damage-sensitive member under single damage conditions, and (b) is a comparison diagram of the acceleration response reconstruction results of the target point of the second damage-sensitive member under single damage conditions. Figure 6 These are comparison diagrams of the dynamic response reconstruction results of the target point under multiple damage conditions; (a) is a comparison diagram of the acceleration response reconstruction results of the target point of the first damage-sensitive member under multiple damage conditions, and (b) is a comparison diagram of the acceleration response reconstruction results of the target point of the second damage-sensitive member under multiple damage conditions. Figure 7 This is a comparison chart of the dynamic response reconstruction results at the experimental target points; Figure 8 yes Figure 4 A magnified view of a portion of point A in the middle. Detailed Implementation

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0019] Specific implementation details are set forth in the following description to provide a full understanding of the invention. However, the invention can be implemented in many ways other than those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0020] The overall process of the hybrid-based damaged offshore jacket reconstruction method described in this invention is as follows: Figure 1 As shown. This method mainly includes the following steps.

[0021] S1, acquire dynamic response data of the source domain structure under local damage state, and extract source domain damage singular prior knowledge based on the dynamic response data to characterize the spatial singular perturbation features caused by local stiffness degradation.

[0022] like Figure 2 As shown in the illustration, in this embodiment, the source domain structure is a tubular structure fixed at both ends. The source domain structure is a component with the same physical properties and similar cross-sectional shape as the reconstructed member in the target jacket structure. Its purpose is not to perform final damage identification on the source domain structure itself, but to extract the spatial singular disturbance characteristics induced by local stiffness degradation from the source domain structure and use them as the physical prior knowledge for the subsequent local response reconstruction of the target jacket structure.

[0023] The extraction process of singular prior knowledge of source domain damage mainly includes the following steps.

[0024] First, a source domain structure model is established, and stiffness degradation is introduced into local regions of the source domain structure to simulate local damage. In this embodiment, the stiffness reduction caused by fatigue cracks, corrosion thinning, or local structural degradation can be equivalently simulated by reducing the elastic modulus of the tubular structural units within the damaged region. Fixed constraints are applied to both ends of the source domain structure to ensure a stable free damped vibration response after the transient excitation is unloaded.

[0025] Second, a transient excitation is applied to the source domain structure, and the free decay acceleration response data of the source domain structure is acquired after the excitation is unloaded. Specifically, several accelerometers are arranged on the source domain structure to collect the acceleration response at each measuring point during the free decay phase. Let the first... The acceleration response at each measuring point is ,in Indicates time, This indicates the measurement point number.

[0026] Third, modal separation is performed on the acquired free decay acceleration response data to obtain narrowband acceleration responses corresponding to single or multiple modes. Modal separation separates the response components of different modal frequency bands in the original acceleration response, thereby reducing the impact of multimodal coupling on the extraction of singular features of local damage.

[0027] Fourth, regarding the first Narrowband acceleration response at each measurement point Perform Hilbert transform to construct analytic signal The instantaneous amplitude envelope of the analytical signal is extracted to obtain the acceleration signal decay function. Its expression is: ; ; in, Represents the Hilbert transform operator. Represents the imaginary unit; Indicates the first The analytical signal corresponding to the narrowband acceleration response at each measurement point. Indicates the first The attenuation function of the acceleration signal at each measuring point.

[0028] The above processing can weaken the influence of high-frequency oscillation carrier in the original acceleration signal and retain the spatial amplitude variation characteristics caused by the degradation of local structural stiffness.

[0029] Fifth, the spatial second-order difference calculation is performed on the attenuation function of the acceleration signal along the local axial coordinates of the source domain structure to obtain the curvature response characteristics. For measuring points arranged at approximately equal intervals along the axial direction of the tubular structure of the source domain, the curvature response characteristics can be expressed as: ; in, Indicates the first First mode in local coordinates Instantaneous curvature response characteristics at the point, Indicates the first First mode in local coordinates The acceleration signal attenuation function at that location, This indicates the axial distance between adjacent measuring points.

[0030] Local stiffness degradation alters the local response propagation path of the source domain structure, causing spatial non-smooth changes in the acceleration signal attenuation function in the damage neighborhood. Therefore, spatial second-order difference can enhance the spatial singular perturbation characteristics caused by local stiffness degradation.

[0031] Sixth, within the effective time window of free decay Within this range, the curvature-type response characteristics are integrated and averaged to obtain the average curvature-type response characteristics, the expression of which is: ; in, and These represent the start and end times of the effective time window for free decay, respectively. By integrating and averaging within the time window, the influence of random noise, transient oscillations, and local anomalies on the extraction of spatial singular features can be suppressed, thereby improving the stability of damaged singular features.

[0032] Seventh, the mean curvature response characteristics are scaled and projected to construct a scale-invariant curvature singular vector index. Specifically, the mean curvature response characteristics corresponding to each mode are dimensionless to reduce the influence of excitation amplitude, modal energy scale, and overall response amplification on local damage characteristics, thereby highlighting the spatial singular perturbations caused by local stiffness degradation.

[0033] Eighth, the local damage contribution fields corresponding to different modes are weighted and fused to obtain the singular spectrum of the fused space. Its expression is: ; in, Representing local coordinates The singular spectral value of the fusion space at that location, Indicates the first Weighting coefficients for the first mode. Indicates the first First mode in local coordinates The dimensionless local damage contribution field at the location, This indicates the modal order involved in the fusion.

[0034] like Figure 3 As shown, by fusing the local damage contribution fields under different modes and excitation conditions, a relatively smooth fused spatial singular spectrum concentrated in the damage neighborhood can be obtained. This fused spatial singular spectrum is not used as the final damage identification result of the source domain structure, but rather as prior knowledge of local damage singularities, used for the subsequent construction of local damage singular bases in the target duct structure.

[0035] S2, based on the spatial location of the damage-sensitive region to be reconstructed in the target duct frame structure, the source domain damage singular prior knowledge is mapped to the corresponding rod region of the target duct frame structure to construct a local damage singular basis.

[0036] like Figure 4As shown in the illustration, the target structure in this embodiment is a jacket structure. The target jacket structure consists of main legs, diagonal bracing members, a platform structure, and a bottom support structure. Sparse sensors are arranged on the main legs, local members, or in locations that facilitate long-term monitoring. Damage-sensitive areas are located in the vicinity of local diagonal bracing members or pipe nodes within the target jacket structure. Figure 4 The figure shows the geometric dimensions of the target guide frame structure, the direction of external excitation, the arrangement of sparse sensors, and the location of the damage-sensitive area.

[0037] It should be noted that the fused spatial singular spectrum obtained in the first step is a one-dimensional spatial singular feature defined in the local coordinates of the source domain structure, and it is not directly equivalent to the response value of the target jacket structure. In order for this prior knowledge of source domain damage singularities to be applied to the target jacket structure, it is necessary to map the source domain fused spatial singular spectrum to the corresponding member region of the target jacket structure according to the spatial location of the damage-sensitive member to be reconstructed in the target jacket, and construct a local damage singular basis.

[0038] The process of mapping singular priors of source domain damage to the target duct structure mainly includes the following steps.

[0039] First, determine the location of the damage-sensitive member to be reconstructed in the target duct frame structure. For any damage-sensitive member to be reconstructed in the target duct frame structure, obtain the spatial coordinates of the two end nodes of the member, denoted as follows: and The damaged sensitive members to be reconstructed can be members with known local damage, or members suspected of damage identified in advance based on inspection, historical monitoring information, or weak points in the structure.

[0040] Second, based on the spatial coordinates of the two end nodes of the damaged member to be reconstructed, a local axial coordinate system for the member is established. Let the axial unit vector of the member be... Then we have: ; in, and These represent the spatial coordinates of the two end nodes of the damage-sensitive member to be reconstructed. Describes the Euclidean norm of a vector. This represents the unit direction vector along the axial direction of the member.

[0041] Third, for any spatial location within the target jacket structure Projecting it onto the local axial coordinate system, the local projected coordinates of this spatial position in the direction of the axis of the damage-sensitive member to be reconstructed are obtained. Its expression is: ; in, Indicates the spatial position within the target jacket structure The projected coordinates of the damaged sensitive member to be reconstructed in the local axial coordinate system. Through this local coordinate projection process, the three-dimensional spatial position of the target jacket structure can be converted into a one-dimensional local coordinate position corresponding to the singular spectrum of the source domain fusion space.

[0042] Fourth, based on the local projected coordinates on the target member. Spatial interpolation operator is used Merge the source domain into the spatial singular spectrum Mapping to the corresponding member region of the target jacket structure. For locations in the source domain fusion spatial singular spectrum that do not strictly correspond to the target member node, the corresponding singular spectrum value can be obtained through linear interpolation, spline interpolation, or other equivalent spatial interpolation methods. This spatial interpolation mapping process can be expressed as: ; in, Indicates the spatial location mapped to the target jacket structure. Singular prior values ​​of local damage at the location Represents the source domain fusion spatial singular spectrum in local projected coordinates The value at that location, This represents the spatial interpolation operator.

[0043] Fifth, to avoid unnecessary interference from singular priors of source domain damage on the global response topology of the target jacket structure far from the damage region, a spatial window function with compact support characteristics is introduced. The spatial window function is used to limit the scope of the singular prior of source domain damage, ensuring that it only operates within the damage-sensitive region of the target duct structure. The spatial window function can be expressed as: ; ; in, This indicates the local effective area centered on the damage-sensitive location. When spatial location... When located in a damage-sensitive area, When spatial position When located outside the damage-sensitive area, .

[0044] Sixth, construct the local damage singular basis based on the mapped fused spatial singular spectrum and spatial window function. Its expression is: ; in, Indicates the spatial location of the target jacket structure Local damage to singular bases, This represents the local damage singular prior value obtained by source domain fusion spatial singular spectrum mapping. Represents the spatial window function.

[0045] Through the above processing, the one-dimensional singular perturbation features induced by local stiffness degradation in the source domain structure are transformed into basis function expressions for the local damage-sensitive regions in the target jacket structure. These local damage singular basis functions have non-zero or significant values ​​only within the local damage-sensitive regions of the target jacket structure, thus supplementing the local non-smooth perturbation features that are difficult to express using traditional global response bases.

[0046] S3. Construct a global response basis based on the spatial coordinate information of the target duct structure, and orthogonally fuse the global response basis with the local damage singular basis to obtain an enhanced hybrid basis for characterizing the global response and the local perturbation response.

[0047] The target jacket structure is a complex space truss structure, and its overall dynamic response typically includes low-frequency, large-scale global smooth response components. Simultaneously, near locally damage-sensitive regions, it may also contain non-smooth perturbation response components caused by local stiffness degradation. To simultaneously characterize these two types of response features, this embodiment constructs an enhanced hybrid basis composed of a global response basis and a local damage singular basis.

[0048] The construction process of enhanced hybrid groups mainly includes the following steps.

[0049] First, obtain the three-dimensional spatial coordinates of each spatial node, measuring point, and location to be reconstructed within the target jacket structure. Let the physical coordinates of any spatial location within the target jacket structure be... Because the jacket structure has significant scale differences in different coordinate directions, directly using physical coordinates to construct polynomial basis functions can easily lead to numerical scale inconsistencies and matrix ill-conditioning. Therefore, it is necessary to normalize the three-dimensional spatial coordinates first.

[0050] Second, based on the geometrically bounded domain of the target duct structure, the three-dimensional physical coordinates are normalized to a dimensionless natural coordinate system. The normalized natural coordinates can be expressed as: ; Represents the normalized natural coordinates. Indicates the center coordinates of the geometrically bounded domain of the target jacket structure. These represent the characteristic half-lengths of the target jacket structure in the x, y, and z directions, respectively. Through this coordinate normalization process, the spatial coordinates of the target jacket structure are mapped to a unified dimensionless coordinate range, thereby improving the numerical stability of subsequent basis function construction.

[0051] Third, a one-dimensional Chebyshev polynomial is constructed based on the dimensionless natural coordinates. The nth-order one-dimensional Chebyshev polynomial can be expressed as: ; in, This represents the nth Chebyshev polynomial. This represents dimensionless natural coordinate variables. Chebyshev polynomials can well characterize continuous and smooth functions within finite intervals and reduce the risk of numerical oscillations at the boundaries of higher-order polynomials.

[0052] Fourth, by combining the one-dimensional Chebyshev polynomials in the three spatial directions through tensor products, the three-dimensional global response basis functions are obtained. Its expression is: ; in, These represent the polynomial truncation orders in the three spatial directions, respectively. By changing... The values ​​of can be used to construct a set of three-dimensional global response basis functions to describe the low-frequency, large-scale global smooth response morphology of the target duct structure.

[0053] Fifth, substitute the natural coordinates of the sensor measurement points, the target points to be reconstructed, or the nodes in the entire field space of the target jacket structure into the three-dimensional global response basis function to construct the global response basis matrix. For a point set containing Np spatial locations, the global response basis matrix can be expressed as: ; Where N represents the total number of global response basis functions selected, and Np represents the number of spatial locations considered.

[0054] Sixth, the locally damaged singular base obtained in the second step... With the global response basis matrix The basis functions are combined to form an initial mixed basis. Since locally damaged singular bases may contain low-frequency smooth components that can be linearly represented by the global response basis, direct column splicing could lead to redundant coupling between basis functions, increasing the ill-conditioning of the sparse observation inverse problem. Therefore, orthogonalization of the locally damaged singular basis is necessary.

[0055] Seventh, the projective orthogonalization method is used to remove redundant components in the local damage singular basis that can be linearly represented by the global response baseline, resulting in the orthogonalized local damage singular basis. Its expression is: ; in, This represents the local damage singular basis before orthogonalization. This represents the local damage singular basis after orthogonalization. This represents the global response basis matrix.

[0056] Eighth, the global response basis matrix With orthogonalized local damage singularity base By performing column combination, an enhanced hybrid base is obtained. Its expression is: ; in, This indicates an enhanced hybrid basis. This enhanced hybrid basis simultaneously includes a global response basis for describing the global smooth response of the target duct structure, and an orthogonalized local damage singular basis for describing the non-smooth perturbation response of locally damage-sensitive regions.

[0057] When multiple damage-sensitive regions to be reconstructed exist in the target duct framework structure, local damage singularities can be constructed for each of the multiple damage-sensitive members, and then orthogonalized to obtain multiple orthogonalized local damage singularities. In this case, the enhanced hybrid basis can be further expressed as: ; in, This indicates the number of damage-sensitive regions to be reconstructed. These represent the orthogonalized local damage singularities corresponding to different damage-sensitive regions.

[0058] Through the above-described process of constructing enhanced hybrid bases, the reconstructed basis function space can simultaneously possess the ability to characterize global responses and enhance local damage perturbations, providing a foundation for response reconstruction under subsequent sparse observation conditions.

[0059] S4. Obtain the measured response data of the target guide frame structure under sparse sensor arrangement conditions, and establish a sparse observation equation based on the enhanced hybrid basis and the measured response data.

[0060] like Figure 4 As shown, in actual offshore jacket structure monitoring, sensors can usually only be deployed near the main outriggers, platform, or other locations that are easy to install and maintain. It is difficult to deploy a sufficient number of sensors in the vicinity of all damage-sensitive members or pipe nodes. Therefore, this embodiment utilizes the limited measurement point responses collected by sparse sensors, combined with the aforementioned enhanced hybrid basis, to establish a sparse observation equation.

[0061] The process of establishing the sparse observation equation mainly includes the following steps.

[0062] First, sparse sensor placement locations are selected within the target ductwork structure. These sensor placement locations can be determined based on structural accessibility, installation convenience, long-term monitoring requirements, proximity of damage-sensitive areas, and coverage of the main force transmission path. In this embodiment, as shown... Figure 4As shown, accelerometers are placed near the main legs and local members of the target jacket structure to obtain the dynamic response of the structure under external excitation.

[0063] Second, dynamic response data of the target jacket structure under operating, environmentally excited, or artificially excited conditions are collected. The dynamic response data includes at least one of acceleration response, velocity response, displacement response, or strain response. In this embodiment, acceleration response is used as the illustrative example, but the invention is not limited to acceleration response data.

[0064] Third, a matching relationship is established between the spatial locations of the sparse sensors and their corresponding spatial locations in the enhanced hybrid matrix. Assume that the target guide frame structure contains... There are 1 sensor, and the set of sensor locations is denoted as . .according to From enhanced hybrid base Extract the observation rows corresponding to the sensor locations to form a sparse observation basis matrix. .

[0065] Fourth, in the enhanced hybrid matrix space, the dynamic response of the target duct structure can be expressed as: ; in, This represents the dynamic response vector of the target jacket structure at the considered spatial location. Indicates enhanced hybrid groups, This represents the generalized coordinate vector to be solved.

[0066] Fifth, since only the response data at the location of the sparse sensor can be obtained in practice, the observation components corresponding to the sparse sensor are extracted from the global response expression to obtain the sparse observation equation: ; in, This represents the measured response vector acquired by the sparse sensor. This represents the sparse observation basis matrix corresponding to the enhanced hybrid basis at the sensor location. This represents the generalized coordinate vector to be solved. This indicates measurement noise or unmodeled error terms.

[0067] Sixth, the sparse observation equation relates the finite measurement point responses to the generalized coordinates in the enhanced hybrid basis space. Since the number of sensors is typically less than the number of degrees of freedom to be reconstructed, the sparse observation equation is generally an underdetermined or ill-conditioned inverse problem, and cannot be directly and stably solved using ordinary least squares. Therefore, a regularized solution method needs to be introduced in step five to obtain stable estimates of the generalized coordinates.

[0068] S5. The sparse observation equation is solved by regularization to obtain the generalized coordinates corresponding to the enhanced hybrid basis, and the dynamic response of a point in the damage-sensitive region of the target jacket structure or the whole field dynamic response is reconstructed based on the enhanced hybrid basis and the generalized coordinates.

[0069] For the sparse observation equation established in the fourth step, this embodiment uses a regularization method to solve the generalized coordinates to suppress ill-conditioned problems caused by insufficient number of sparse measurement points, measurement noise, and basis function correlation. The regularization solution and response reconstruction process mainly includes the following steps.

[0070] First, construct a regularized objective function consisting of a data fidelity term and a solution stability constraint term. Its expression is: ; in, Let the regularization objective function be represented, and the first term be... The first item is the data fidelity item, used to ensure that the reconstructed response at the sensor location is consistent with the measured response; the second item... To solve the stability constraint term, used to suppress the amplification of instability during the generalized coordinate solution process; Represents the regularization parameter; This represents a regularization operator, which can be the identity matrix or other stable constraint operators.

[0071] Second, regarding the regularization objective function By taking the minimum value, we obtain an estimate of the generalized coordinate vector. .when When taking the generalized regularization operator, the generalized coordinate estimate can be expressed as: ; in, This represents the estimated value of the generalized coordinate vector. Using this expression, stable generalized coordinates in the enhanced mixed basis space can be obtained under finite measurement point response constraints.

[0072] Third, determine the regularization parameters. Regularization parameters Used to balance data fidelity terms and solve stability constraints. When When the value is too small, the solution is easily affected by measurement noise and matrix ill-conditioning; when... When the value is too large, the reconstruction result may be over-smoothed, leading to a weakening of the local damage perturbation response. Therefore, this embodiment adopts... Curve method adaptively determines regularization parameters .

[0073] Fourth, based on Curve method for calculating different regularization parameters The residual norm and solution norm under given conditions. Residual norm reconciliation norm It can be represented as: ; ; in, Indicates the regularization parameter The generalized coordinate vector obtained by solving under the given conditions. By changing... By taking the values ​​of , we can obtain a set of points corresponding to the residual norm and the solution norm, and construct a double logarithmic parameter curve.

[0074] Fifth, the regularization parameter corresponding to the position of maximum curvature of the double logarithmic parameter curve is selected as the optimal regularization parameter. The location of maximum curvature typically corresponds to a trade-off between data fidelity and solution stability. Curvature can be expressed as: ; in, They represent and about The first and second derivatives.

[0075] Sixth, the optimal regularization parameter Substituting into the generalized coordinate solution formula, we obtain the final generalized coordinate estimate. Subsequently, By substituting the reinforcing hybrid basis, the dynamic response of the reconfigurable location in the target duct framework structure is obtained: ; in, This represents the reconstructed dynamic response vector. If only the response of the target point in the damage-sensitive region is reconstructed, the row corresponding to the target point can be extracted from the enhancement mixture basis, represented as: ; in, This represents the reconstruction response of the target point in the damage-sensitive region. This represents the row or set of rows corresponding to the target point location of the enhanced hybrid basis.

[0076] Seventh, when it is necessary to reconstruct the full-field dynamic response of the target jacket structure, the coordinates of the full-field spatial nodes in the target jacket structure are substituted into the global response basis and the local damage singular basis to construct a full-field enhanced hybrid basis. The dynamic response across the entire field is obtained from the following formula: ; in, This represents the reconfiguration dynamic response of all spatial nodes of the target jacket structure. This represents the enhanced hybrid basis matrix corresponding to all nodes in the field space.

[0077] To verify the effectiveness of the method described in this invention, this embodiment uses single-damage conditions, multi-damage conditions, and experimental conditions for illustration.

[0078] like Figure 5 As shown, under single-damage conditions, the response of a finite number of measurement points is input into the enhanced hybrid basis reconstruction method to obtain the dynamic response reconstruction result at the target point in the damage-sensitive region. Figure 5 In the study, measured or reference values, global basis prediction results, and enhanced basis prediction results were compared. Compared with the method of reconstruction using global response basis, the enhanced hybrid basis method can better track the amplitude change and decay trend of the dynamic response of the target point, indicating that the local damage singular basis can effectively enhance the expressive ability of the response in the damage neighborhood.

[0079] like Figure 6 As shown, under multi-damage conditions, the target duct framework structure contains multiple damage-sensitive regions that need to be reconstructed. For this type of situation, local damage singularities can be constructed for each of the multiple damage-sensitive regions, and these can be combined with the global response basis to form an enhanced hybrid basis. Figure 6 The comparative results show that the method described in this invention is not only applicable to target point response reconstruction in a single damage-sensitive region, but also to dynamic response reconstruction under conditions of multiple damage-sensitive regions.

[0080] like Figure 7 As shown, under experimental conditions, a limited number of sensors are used to collect the dynamic response of the scaled-down guide frame structure, and the response of the target point in the damage-sensitive area is reconstructed using the method described in this invention. Figure 7 The experimental comparison results show that, under the conditions of limited actual measurement noise and sensor placement, the enhanced hybrid basis method described in this invention can still effectively reconstruct the response of the target point in the damage-sensitive area, indicating that the method has good engineering feasibility.

[0081] As can be seen from the above embodiments, the present invention can transform the spatial singular disturbance characteristics caused by local stiffness degradation in the source domain structure into local damage singular bases in the target jacket structure, and orthogonally fuse them with the global response base, thereby realizing the reconstruction of the dynamic response of the target point in the damage-sensitive area or the dynamic response of the entire field under sparse sensor conditions. This method is applicable to virtual sensing, damage neighborhood enhancement monitoring, and response completion of unmeasured points in offshore jacket structures under known or suspected local damage conditions.

[0082] The above provides a detailed description of the sparse response reconstruction method for damaged offshore jackets based on hybrid bases provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are merely for the purpose of helping to understand the method and core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases, characterized in that, Includes the following steps: S1. Obtain dynamic response data of the source domain structure under local damage state, and extract source domain damage singular prior knowledge based on the dynamic response data to characterize the spatial singular perturbation features caused by local stiffness degradation. S2. Based on the spatial location of the damage-sensitive region to be reconstructed in the target duct frame structure, the source domain damage singular prior knowledge is mapped to the corresponding rod region of the target duct frame structure to construct a local damage singular basis. S3. Construct a global response basis based on the spatial coordinate information of the target duct structure, and orthogonally fuse the global response basis with the local damage singular basis to obtain an enhanced hybrid basis for characterizing the global response and the local perturbation response; S4. Obtain the measured response data of the target guide frame structure under sparse sensor arrangement conditions, and establish a sparse observation equation based on the enhanced hybrid basis and the measured response data. S5. The sparse observation equation is solved by regularization to obtain the generalized coordinates corresponding to the enhanced hybrid basis, and the dynamic response of a point in the damage-sensitive region of the target jacket structure or the whole field dynamic response is reconstructed based on the enhanced hybrid basis and the generalized coordinates.

2. The method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases according to claim 1, characterized in that, In step S1, the source domain structure is a tubular component with the same physical properties and similar cross-sectional shape as the rod to be reconstructed in the target jacket structure; By introducing stiffness degradation in a local region of the source domain structure, free attenuation dynamic response data under local damage state is obtained. The dynamic response data includes the acceleration response data of the source domain structure after excitation unloading; Based on the acceleration response data, singular prior knowledge of source domain damage is extracted. This singular prior knowledge of source domain damage is used to characterize the spatial non-smooth perturbation features caused by local stiffness degradation.

3. The method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases according to claim 2, characterized in that, In step S1, the extraction process of the singular prior knowledge of source domain damage includes the following steps: S1.1 Perform mode separation on the free decay acceleration response of the source domain structure to obtain the narrowband acceleration response corresponding to a single or multiple modes; S1.2 Perform Hilbert transform on the narrowband acceleration response to construct an analytic signal, and extract the instantaneous amplitude envelope of the analytic signal to obtain the acceleration signal decay function; S1.

3. Along the local axial coordinates of the source domain structure, perform spatial second-order difference calculation on the attenuation function of the acceleration signal to obtain curvature response characteristics used to characterize local spatial abrupt changes; S1.

4. Within the effective free decay time window, the curvature response characteristics are integrally averaged to suppress the influence of random noise and instantaneous oscillations on local singular features. S1.

5. The curvature response features after integral averaging are scaled and multi-mode fusion is performed to obtain the fusion spatial singular spectrum, which serves as the source domain damage singular prior knowledge. The construction process of the fused spatial singular spectrum includes: The curvature response characteristics corresponding to each mode are dimensionless to obtain the local damage contribution field of each mode; modal weights are assigned to the local damage contribution fields of each mode, and weighted fusion is performed to obtain the singular spectrum of the fusion space. The fusion space singular spectrum is represented as follows: ； in, Representing local coordinates The singular spectral value of the fusion space at that location, Indicates the first Weighting coefficients for the first mode. Indicates the first First mode in local coordinates The dimensionless local damage contribution field at the location, This indicates the modal order involved in the fusion.

4. The method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases according to claim 1, characterized in that, In step S2, the process of mapping the singular prior of source domain damage to the target duct framework structure includes the following steps: S2.1 Obtain the coordinates of the two end nodes of the damage-sensitive member to be reconstructed in the target guide frame structure, and determine the local axial coordinate system of the member based on the coordinates of the two end nodes; S2.2 Project the coordinates of the spatial nodes in the target guide frame structure onto the local axial coordinate system to obtain the local projected coordinates of the spatial nodes in the axial direction of the damage-sensitive member to be reconstructed; S2.

3. Based on the local projection coordinates, the source domain fusion spatial singular spectrum interpolation is mapped to the corresponding rod region of the target jacket structure; S2.

4. Set a spatial window function with tight support characteristics so that the source domain damage singular prior only acts on the damage-sensitive region of the target duct structure, forming a local damage singular basis.

5. The method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases according to claim 4, characterized in that, The localized damage singularity base is constructed by the following formula: ； in, Indicates the spatial location of the target jacket structure Local damage to singular bases, Represents the spatial interpolation operator. Indicates mapping to local projected coordinates The singular spectrum of the fusion space, Represents a spatial window function; When spatial position When located in a damage-sensitive area, ; When spatial position When located outside the damage-sensitive area, .

6. The method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases according to claim 1, characterized in that, In step S3, the global basis is a Chebyshev polynomial global response basis constructed based on the spatial coordinates of the target duct frame structure. It is obtained by normalizing the three-dimensional spatial coordinates of the target duct frame structure and substituting the normalized dimensionless natural coordinates into the Chebyshev polynomial basis function, and is used to characterize the global response of the target duct frame structure. The process of orthogonally fusing the global response basis with the local damage singular basis includes: The global response basis matrix and the local damage singular basis vectors are column-concatenated to form an initial mixed basis matrix. The projection orthogonalization method is used to remove redundant components in the local damage singular basis that can be linearly represented by the global response basis, while retaining the independent spatial components corresponding to the local damage perturbation. The orthogonalized local damage singular basis is represented as follows: ； The enhanced hybrid group is represented as: ； in, Represents the global response basis matrix. Indicates a singular base of localized damage. This represents the local damage singular basis after orthogonalization. This indicates an enhanced hybrid group.

7. The method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases according to claim 1, characterized in that, In step S4, the measured response data is the dynamic response data of the target duct structure acquired under the condition of sparse sensor arrangement; The sparse sensor arrangement condition refers to the fact that the number of sensors is less than the number of degrees of freedom to be reconstructed, and the sensors are set in a position in the target guide frame structure that is easy to install or easy to monitor for a long time. Based on the location of the sparse sensor, the corresponding observation rows are extracted from the enhanced hybrid basis to form a sparse observation basis matrix, and a sparse observation equation is established: ； in, This represents the measured response vector acquired by the sparse sensor. This represents the sparse observation basis matrix corresponding to the enhanced hybrid basis at the sensor location. This represents the generalized coordinate vector to be solved. This indicates measurement noise.

8. The method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases according to claim 7, characterized in that, Step S5, the process of regularizing the solution of the sparse observation equation, includes: Construct a regularized objective function consisting of a data fidelity term and a solution-stability constraint term: ； in, Describes the regularization objective function. Represents the regularization parameter. Represents a regularization operator; By solving for the minimum value of the regularization objective function, the estimated value of the generalized coordinate vector is obtained: ； For the identity matrix, the regularization parameter The regularization parameter is determined adaptively using the L-curve method; the L-curve method includes: calculating different regularization parameters. Given the residual norm and solution norm under the given conditions, construct a double logarithmic parameter curve between the residual norm and the solution norm, and select the regularization parameter corresponding to the position of maximum curvature of the double logarithmic parameter curve as the optimal regularization parameter.

9. The method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases according to claim 1, characterized in that, In step S5, the process of reconstructing the dynamic response of the target duct structure based on the enhanced hybrid basis and generalized coordinates is as follows: Substituting the generalized coordinates obtained from the solution into the enhanced hybrid basis, the dynamic response of the location to be reconstructed in the target jacket structure is obtained: ； in, This represents the dynamic response obtained from the reconstruction. Indicates enhanced hybrid groups, This represents the generalized coordinate estimate obtained from the solution; The locations to be reconstructed include target measuring points within the damage-sensitive area, the locations of rods without sensors, and the full-field spatial nodes of the target jacket structure.

10. The method for reconstructing the sparse response of damaged offshore jacket structures based on hybrid bases according to claim 1, characterized in that, When there are multiple damage-sensitive regions to be reconstructed in the target duct structure, the source domain damage singular prior is mapped to the multiple damage-sensitive regions to be reconstructed, and multiple local damage singular bases are constructed. Multiple local damage singular bases are orthogonalized with the global response base, and then combined with the global response base to form an enhanced hybrid base, so as to realize the dynamic response of the target point or the reconstruction of the dynamic response of the whole field under the condition of multiple damage-sensitive areas.

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