An optimization modal stress reconstruction method incorporating unit load superposition method

Abstract

The application discloses an optimization modal stress reconstruction method based on unit load superposition method, and relates to the technical field of structure health monitoring. The application discloses an optimization modal stress reconstruction method based on unit load superposition method, and relates to the technical field of structure health monitoring. The application discloses an optimization modal stress reconstruction method based on unit load superposition method, and relates to the technical field of structure health monitoring. The application discloses an optimization modal stress reconstruction method based on unit load superposition method, and relates to the technical field of structure health monitoring. The application discloses an optimization modal stress reconstruction method based on unit load superposition method, and relates to the technical field of structure health monitoring. The application discloses an optimization modal stress reconstruction method based on unit load superposition method, and relates to the technical field of structure health monitoring. The application discloses an optimization modal stress reconstruction method based on unit load superposition method, and relates to the technical field of structure health monitoring. The application discloses an optimization modal stress reconstruction method based on unit load superposition method, and relates to the technical field of structure health monitoring. The application discloses an optimization modal stress reconstruction method based on unit load superposition method, and relates to the technical field of structure health monitor

Description

Technical Field

[0001] This invention relates to the field of structural health monitoring technology, and in particular to an optimized modal stress reconstruction method incorporating the unit load superposition method. Background Technology

[0002] With the development of larger, more intelligent ships and structural health monitoring technologies, ship structural safety assessment is shifting from periodic inspections to real-time monitoring and intelligent operation and maintenance. Large ore carriers operate in complex sea conditions for extended periods, with their hulls simultaneously subjected to multiple sources of stress, including wave loads, cargo loads, inertial loads, and local structural constraints. Due to the large open decks, high-density cargo, abrupt changes in compartment stiffness, and long-term cyclic loads, areas such as cargo hold areas, hatch edges, angled bottom plate corners, longitudinal bulkheads, and inner bottom plates are prone to high stresses, making them key areas for structural health monitoring and fatigue assessment.

[0003] In actual monitoring, due to limitations in sensor deployment space, installation and maintenance costs, wiring difficulty, and the number of data acquisition channels, ships typically only have a limited number of measurement points, making it difficult to directly obtain the complete stress field of the entire ship or key compartments. The stress reconstruction method based on modal superposition can represent the structural response as a linear combination of several basic modal responses and use measurement point data to invert the modal participation coefficients, thereby reconstructing the stress response at unmeasured locations. This method has advantages such as clear physical meaning and high computational efficiency. However, traditional modal superposition methods mainly rely on low-order modes of the entire ship, suitable for describing the overall response of hull beam bending and torsion, but difficult to characterize the stress concentration and time history details of local structures in cargo holds under multi-source loads. If only direct reconstruction of the entire ship's modes is used, it can easily lead to underestimation of hot spot stress amplitude, weakening of peaks and valleys, phase drift, and increased errors in directly loaded areas.

[0004] Reconstruction methods based on unit load or influence coefficients can compensate for local load response characteristics, but if used independently of the overall ship response, they are difficult to reflect the global boundary transmission effect caused by wave loads. How to integrate the overall response representation capability of modal superposition with the local load characterization capability of unit load superposition under limited measurement points, and establish an optimized modal stress reconstruction method that takes into account global wave-induced response, local multi-source loads, and hotspot stress distribution, is a key problem that urgently needs to be solved in ship structural health monitoring.

[0005] Therefore, those skilled in the art are dedicated to developing an optimized modal stress reconstruction method that incorporates the unit load superposition method. Summary of the Invention

[0006] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is that the existing ship structural health monitoring system is unable to directly obtain the complete time-domain stress field of local key areas, and is insufficient for ship structural health monitoring and fatigue assessment.

[0007] To achieve the above objectives, this invention provides an optimized modal stress reconstruction method incorporating the unit load superposition method, the method comprising the following steps: S101: Establishing the basis for global modal reconstruction of the entire ship structure: Equivalently treat the ship structure as a linear damped multi-degree-of-freedom system, establish the motion equations in physical coordinates, project the physical displacement response onto the modal space, and calculate the global stress response; S103: Constructing the global monitoring points and modal stress matrix: Based on the global longitudinal stress monitoring points, the measured stress at the same moment is assembled into a sensor response vector, and the global modal stress contribution is extracted at the monitoring location to form a global modal stress matrix for solving the modal participation coefficient; S105: Identify global modal coordinates and obtain global reconstruction results: Solve for modal coordinates based on the sensor response vector and the global modal stress matrix, multiply the global modal stress vector at the target position with the modal coordinates, and obtain the global stress reconstruction results for the entire ship or local boundary positions; S107: Establish the fractional unit load response basis of the local sub-model: For the target cargo hold or local hot spot area, construct the wave boundary transfer unit load case and the cargo inertia unit load case respectively, extract the corresponding unit load response field, and form the local wave response basis and cargo inertia response basis. S109: Construct wave component response matrices based on local response identification points, and reconstruct local wave-induced stress response and cargo inertial load stress response; S111: The local wave-induced response and the cargo inertial load response are superimposed to obtain the final time-domain stress response of the target area or verification point under multi-source load and output it.

[0008] Further, in step S101, the equation of motion is:

[0009] The global stress response is:

[0010] in,

[0011] In the formula, Let be the displacement vector, velocity vector, and acceleration vector at time t, respectively. For external excitation vectors, For position Place Global modal reconstruction stress at time t, The r-th order global mode at position The corresponding modal stress components at that location, For modal coordinate vectors, For the first First modal coordinates, The first The first and second time derivatives of the modal coordinates. For the first Generalized modal forces, The modal shape matrix consists of the preserved modes. Let r be the mode shape vector. The mass matrix of the ship's hull structure. The damping matrix of the hull structure. Here is the stiffness matrix of the hull structure. The damping ratio of the r-th mode is... The natural angular frequency of order r is... For time variables, subscript Represents the global modal reconstruction quantity. The modal order is... This is the modal order number.

[0012] Furthermore, in step S101, when solving the global stress response, the physical displacement response is projected onto the modal space through the equation of motion, and the decoupled modal equation is obtained under classical damping and mass normalization conditions. The target position is described by the superposition of global modal stress components, and the global stress response is obtained.

[0013] Further, in step S103, the measured stress vector of the global monitoring points is constructed as follows:

[0014] in, for One global monitoring point at The measured stress vector composed of time intervals, This represents the modal stress matrix at the global monitoring points. Let be the modal coordinate vector to be identified. For the first The global mode of order 1 in the first order is... Stress contribution at each global monitoring point This represents the total number of global stress monitoring points. Number the monitoring point.

[0015] Furthermore, in step S105, when solving for the modal coordinates, the Moore-Penrose pseudo-inverse or least squares method is used, and the global stress reconstruction result is:

[0016] in, For target location Place The global stress reconstruction result at time t. Let be the global modal stress row vector at the target location. This is the modal coordinate estimation vector obtained from measured stress identification. for Moore-Penrose pseudo-inverse matrix, The measured stress vector at the global monitoring points. The target point or target area location is indicated by the symbol "^".

[0017] Further, in step S107, under the conditions of small deformation, linear elasticity, and unchanged structural configuration, the unit load response field is extracted to form wave-induced local stress components and cargo inertial local stress components, wherein: The wave-induced local stress components are:

[0018] The local inertial stress components of the cargo are:

[0019] In the formula, For position Place Wave-induced local stress components at any given time. For the first The wave unit load response base at position Stress response at the point, The wave response participation factor. For position The wave response basis vector or matrix at the location, This represents the wave response participation coefficient vector. The number of wave unit load response bases; For position Place Local stress components of cargo inertia at time. For the first The inertial unit load response of a cargo is based on its position. Stress response at the point, This represents the corresponding inertial response participation factor for the cargo. For position The basis vector or matrix of the inertial response of the goods at that location. Let be the vector of inertial response participation coefficients for the cargo. The number of basic load responses per unit load of cargo inertia, subscript Indicates wave-induced components, subscript Indicates the inertial component of the cargo.

[0020] Further, in step S109, based on the multi-condition trial calculation results, multiple virtual monitoring input points are selected from locations with high global modal reconstruction accuracy and stable local response propagation relationships. The wave-induced or reconstructed responses at the identification points are assembled into local wave response vectors, and the responses of each wave unit load response basis at the identification points form a local wave unit load response matrix. The local wave response vector is:

[0021] In the formula, For the first Wave-induced response vector at each local response identification point for 3D wave unit load response matrix, For the first The wave unit load response basis at the th wave unit load basis in the th wave Stress response at a local identification point This represents the wave response participation coefficient vector. For the first Location of a local response identification point Here, s represents the local identification point number, and s represents the number of local response identification points. For the number of wave response bases, The wave response base number is used.

[0022] Further, in step S109, based on the local wave response vector and the wave unit load response matrix, the participation coefficients of the wave load response basis are solved using the least squares method, and the local wave-induced stress response under boundary transfer is reconstructed using the wave unit load response matrix at the target location.

[0023] in, For target location Wave-induced local stress reconstruction results at the location, The wave unit load response matrix at the target location. This is the wave response participation coefficient estimation vector. This is the wave response participation coefficient estimation vector. for Moore-Penrose pseudo-inverse matrix, This represents the wave-induced response vector at the local identification point. The target location.

[0024] Further, in step S109, the equivalent inertial load generated by the cargo on the local cargo hold structure is taken as an independent load source. The participation coefficient of the cargo inertial response basis is determined by combining the ship motion monitoring data, and the cargo inertial load stress response under the action of cargo inertia is reconstructed using the cargo inertial unit load response matrix at the target location.

[0025] in, For target location The results of the reconstruction of local inertial stress of the cargo at the location, The inertial unit load response matrix of the cargo at the target location is given. This is the estimated vector of the cargo inertial response participation coefficient determined based on ship motion monitoring data.

[0026] Further, in step S111, the local wave-induced stress response and the cargo inertial load stress response are superimposed on the same time coordinate to obtain the final time-domain stress response of the target area or verification point under multi-source loads:

[0027] in, Target location The final optimized reconstruction of the longitudinal normal stress along the ship's length direction, This is the result of reconstructing the local wave-induced stress response. The results are the reconstructed stress response of the cargo under inertial loads. This is the participation coefficient estimation vector for the wave components. This is the participation coefficient estimation vector for the inertial components of the cargo. Let be the wave response basis matrix at the target location. Let be the basis matrix of the inertial response of the cargo at the target location.

[0028] In a preferred embodiment of the present invention, compared with the prior art, the present invention has the following beneficial technical effects: 1. This invention combines whole-ship modal reconstruction with local sub-model analysis to form an optimized reconstruction framework that progressively transfers stress response from the overall ship response to local key areas. This allows local sub-models to participate in stress reconstruction even in the absence of direct boundary measurements. In this way, local sub-models no longer rely on pre-known real boundary loads, but instead use the whole-ship reconstruction results to provide boundary transfer conditions. This allows the wave-induced bending, torsion, and overall structural deformation effects of the whole ship to be naturally transferred to local areas, achieving continuous reconstruction from the overall response to the local stress field.

[0029] 2. This invention achieves temporal stress reconstruction in key local areas without measuring points without significantly increasing the number of sensors, solving the problem of traditional local sub-models struggling to obtain boundary conditions. Compared with the simple modal superposition method, this method maintains the advantages of high computational efficiency and clear physical meaning in whole-ship modal reconstruction, while utilizing local sub-models to improve the structural detail representation of areas such as cargo holds, bulkheads, and inner floor plates. It can improve problems such as underestimated hotspot stress amplitude, phase shift, and local response time history distortion, thereby enhancing the usability of ship structural health monitoring and fatigue assessment.

[0030] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0031] Figure 1 This is an implementation step of the optimized modal stress reconstruction method of a preferred embodiment of the present invention; Figure 2 This is a schematic diagram of the full finite element model and a partial cargo hold section finite element model of a large ore carrier according to a preferred embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the application method of boundary load and cargo inertial load in a partial cargo hold section according to a preferred embodiment of the present invention; Figure 4 This is a schematic diagram of the arrangement of longitudinal stress monitoring points throughout the ship according to a preferred embodiment of the present invention; Figure 5 This is a schematic diagram of the arrangement of stress monitoring points in a local cargo hold area according to a preferred embodiment of the present invention; Figure 6 This is a schematic diagram of the target area and verification point layout according to a preferred embodiment of the present invention; Figure 7 This is the stress reconstruction result under a typical asymmetric working condition in a preferred embodiment of the present invention. Detailed Implementation

[0032] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0033] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0034] like Figure 1 As shown, existing ship structural health monitoring systems are limited by sensor deployment space, installation and maintenance costs, the number of data acquisition channels, and the ship's service environment, making it difficult to directly obtain the complete temporal stress field of key local areas such as cargo holds, bulkheads, inner floor plates, and angled bottom plate bends. This invention provides an optimized modal stress reconstruction method incorporating the unit load superposition method. This method includes the following steps: S101: Establish the basis for global modal reconstruction of the entire ship structure.

[0035] The ship's hull structure is equivalent to a linearly damped multi-degree-of-freedom system. The equations of motion in physical coordinates are established, the physical displacement response is projected onto the modal space, and the global stress response is calculated.

[0036] The established equations of motion are:

[0037] The method for calculating the global stress response is as follows:

[0038] in,

[0039] In the formula, Let be the displacement vector, velocity vector, and acceleration vector at time t, respectively. For external excitation vectors, For position Place Global modal reconstruction stress at time t, The r-th order global mode at position The corresponding modal stress components at that location, For modal coordinate vectors, For the first First modal coordinates, The first The first and second time derivatives of the modal coordinates. For the first Generalized modal forces, The modal shape matrix consists of the preserved modes. Let r be the mode shape vector. The mass matrix of the ship's hull structure. The damping matrix of the hull structure. Here is the stiffness matrix of the hull structure. The damping ratio of the r-th mode is... The natural angular frequency of order r is... For time variables, subscript Represents the global modal reconstruction quantity. The modal order is... This is the modal order number.

[0040] In this embodiment, when solving the global stress response, the physical displacement response is projected onto the modal space through the equation of motion. Under the conditions of classical damping and mass normalization, the decoupled modal equation is obtained, and the target position is described by the superposition of global modal stress components to obtain the global stress response.

[0041] S103: Construct global monitoring points and modal stress matrix.

[0042] Based on the global longitudinal stress monitoring points, the measured stress at the same moment is assembled into a sensor response vector, and the global modal stress contribution is extracted at the monitoring location to form a global modal stress matrix for solving the modal participation coefficient.

[0043] In this embodiment, the measured stress vector of the constructed global monitoring points is:

[0044] in, for One global monitoring point at The measured stress vector composed of time intervals, This represents the modal stress matrix at the global monitoring points. Let be the modal coordinate vector to be identified. For the first The global mode of order 1 in the first order is... Stress contribution at each global monitoring point This represents the total number of global stress monitoring points. Number the monitoring point.

[0045] S105: Identify global modal coordinates and obtain global reconstruction results.

[0046] Modal coordinates are obtained by solving the sensor response vector and global modal stress matrix. The global modal stress vector at the target location is multiplied by the modal coordinates to obtain the global stress reconstruction result at the whole ship or local boundary location.

[0047] In this embodiment, the Moore-Penrose pseudo-inverse or least squares method is used to solve for the modal coordinates, and the global stress reconstruction result is as follows:

[0048] in, For target location Place The global stress reconstruction result at time t. Let be the global modal stress row vector at the target location. This is the modal coordinate estimation vector obtained from measured stress identification. for Moore-Penrose pseudo-inverse matrix, The measured stress vector at the global monitoring points. The target point or target area location is indicated by the symbol "^".

[0049] S107: Establish the fractional unit load response basis for the local sub-model.

[0050] For the target cargo hold or local hotspot area, wave boundary transfer unit load case and cargo inertia unit load case are constructed respectively, and the corresponding unit load response field is extracted to form local wave response basis and cargo inertia response basis.

[0051] In this embodiment, under conditions of small deformation, linear elasticity, and unchanged structural configuration, the unit load response field is extracted to form wave-induced local stress components and cargo inertial local stress components, wherein: The wave-induced local stress components are:

[0052] The local inertial stress components of the cargo are:

[0053] In the formula, For position Place Wave-induced local stress components at any given time. For the first The wave unit load response base at position Stress response at the point, The wave response participation factor. For position The wave response basis vector or matrix at the location, This represents the wave response participation coefficient vector. The number of wave unit load response bases; For position Place Local stress components of cargo inertia at time. For the first The inertial unit load response of a cargo is based on its position. Stress response at the point, This represents the corresponding inertial response participation factor for the cargo. For position The basis vector or matrix of the inertial response of the goods at that location. Let be the vector of inertial response participation coefficients for the cargo. The number of basic load responses per unit load of cargo inertia, subscript Indicates wave-induced components, subscript Indicates the inertial component of the cargo.

[0054] S109: Construct wave component response matrices based on local response identification points, and reconstruct local wave-induced stress response and cargo inertial load stress response.

[0055] In this embodiment, based on the results of multi-condition trial calculations, multiple virtual monitoring input points are selected from locations with high global modal reconstruction accuracy and stable local response propagation relationships. The wave-induced or reconstructed responses at the identification points are assembled into local wave response vectors, and the responses of each wave unit load response basis at the identification points form a local wave unit load response matrix. The local wave response vector is:

[0056] In the formula, For the first Wave-induced response vector at each local response identification point for 3D wave unit load response matrix, For the first The wave unit load response basis at the th wave unit load basis in the th wave Stress response at a local identification point This represents the wave response participation coefficient vector. For the first Location of a local response identification point Here, s represents the local identification point number, and s represents the number of local response identification points. For the number of wave response bases, The wave response base number is used.

[0057] When reconstructing the local wave-induced stress response, the participation coefficients of the wave load response basis are solved using the least squares method based on the local wave response vector and the wave unit load response matrix. Then, the local wave-induced stress response under boundary transfer is reconstructed using the wave unit load response matrix at the target location.

[0058] in, For target location Wave-induced local stress reconstruction results at the location, The wave unit load response matrix at the target location. This is the wave response participation coefficient estimation vector. This is the wave response participation coefficient estimation vector. for Moore-Penrose pseudo-inverse matrix, This represents the wave-induced response vector at the local identification point. The target location.

[0059] To reconstruct the cargo inertial load stress response under cargo inertia, the equivalent inertial load generated by the cargo on the local cargo hold structure is taken as an independent load source. The participation coefficient of the cargo inertial response basis is determined by combining ship motion monitoring data, and the cargo inertial load stress response under cargo inertia is reconstructed using the cargo inertial unit load response matrix at the target location.

[0060] in, For target location The results of the reconstruction of local inertial stress of the cargo at the location, The inertial unit load response matrix of the cargo at the target location is given. This is the estimated vector of the cargo inertial response participation coefficient determined based on ship motion monitoring data.

[0061] S111: Superimpose the local wave-induced response and the cargo inertial load response to obtain and output the final time-domain stress response of the target area or verification point under multi-source load.

[0062] In this embodiment, the local wave-induced stress response and the cargo inertial load stress response are superimposed on the same time coordinate to obtain the final time-domain stress response of the target area or verification point under multi-source loads:

[0063] in, Target location The final optimized reconstruction of the longitudinal normal stress along the ship's length direction, This is the result of reconstructing the local wave-induced stress response. The results are the reconstructed stress response of the cargo under inertial loads. This is the participation coefficient estimation vector for the wave components. This is the participation coefficient estimation vector for the inertial components of the cargo. Let be the wave response basis matrix at the target location. Let be the basis matrix of the inertial response of the cargo at the target location.

[0064] Compared with existing technologies, the optimized modal stress reconstruction method incorporating the unit load superposition method provided in this invention has the following beneficial effects: 1. Existing ship structural health monitoring systems are limited by sensor deployment space, installation and maintenance costs, the number of data acquisition channels, and the ship's service environment. They typically only obtain responses from a limited number of measurement points, making it difficult to directly acquire the complete temporal stress field of key local areas such as cargo holds, bulkheads, inner floor plates, and angled bottom plate bends. Traditional modal superposition stress reconstruction methods mainly rely on low-order modes of the entire ship, suitable for describing overall responses such as beam bending and torsion, but insufficient for characterizing local structural details, boundary transfer effects, and hotspot stress concentrations. While local sub-model analysis can preserve structural details, it usually requires known boundary conditions, making it difficult to directly apply to local stress inversion under sparse monitoring conditions on actual ships. This invention proposes an optimized modal stress reconstruction method for sparse monitoring conditions, combining whole-ship modal reconstruction with local sub-model analysis to form an optimized reconstruction framework that progressively transfers stress responses from the overall ship response to key local areas. This invention does not simply extrapolate local stress directly using low-order modes. Instead, based on the modal reconstruction results of the entire ship, it extracts the boundary response of the target section or local structure and transforms it into the equivalent boundary input of the local sub-model, thereby enabling the local sub-model to participate in stress reconstruction in the absence of direct boundary measurements.

[0065] This invention first inverts the participation coefficients of the structural basic modes based on the responses of a limited number of monitoring points throughout the ship, obtaining the overall time-domain response across the entire ship. Then, it extracts displacement, stress, or equivalent response information obtained from the full-ship modal reconstruction at the boundary of a target local region and applies it to the boundary of a local sub-model. In this way, the local sub-model no longer relies on pre-known true boundary loads, but instead uses the boundary transfer conditions provided by the full-ship reconstruction results. This allows wave-induced bending, torsion, and overall structural deformation effects to be naturally transferred to the local region, achieving continuous reconstruction from the overall response to the local stress field. This invention can achieve time-domain stress reconstruction in key local regions without significantly increasing the number of sensors, solving the problem of traditional local sub-models struggling to obtain boundary conditions. Compared to simple modal superposition methods, this method retains the advantages of high computational efficiency and clear physical meaning of full-ship modal reconstruction, while utilizing local sub-models to improve the structural detail representation of areas such as cargo holds, bulkheads, and inner floor plates. It can improve problems such as underestimated hotspot stress amplitude, phase shift, and local response time history distortion, enhancing the usability of ship structural health monitoring and fatigue assessment.

[0066] 2. The local structural response of large ore carriers is not only affected by the wave-induced bending moment and torque of the entire ship, but also by the combined effects of multiple load sources, including cargo inertia, bulkhead pressure, inboard pressure, local component constraints, and abrupt stiffness changes. Traditional modal superposition methods typically incorporate local responses into the overall ship modal framework, making it difficult to distinguish the contributions of different load sources to local stresses. This can easily lead to weakening of peak values ​​in directly loaded areas, deviation of low-frequency envelopes, and aliasing of response components. While using unit load or influence coefficient methods alone can characterize the effects of local loads, they fail to reflect the overall boundary transfer effect caused by wave loads if separated from the overall ship response. This invention incorporates the unit load superposition method into the optimized modal stress reconstruction framework, constructing a unified technical route of "overall ship modal reconstruction—local boundary transfer—unit load component compensation". This innovation uses the unit load superposition method as a local response correction step, rather than replacing the whole ship modal reconstruction. By considering the global wave-induced response and the local multi-source load response separately, the reconstruction process can inherit the overall deformation characteristics of the whole ship modal response, and supplement the stress components caused by local loads such as cargo inertia, bulkhead pressure, and inboard pressure.

[0067] This invention pre-establishes stress response libraries or influence coefficient libraries under different unit loads in local sub-models, such as constructing unit response components under bulkhead pressure, inboard pressure, and cargo inertial loads. During online reconstruction, the local basic response is first obtained from whole-ship modal reconstruction and boundary transfer. Then, the contribution coefficients of different unit loads are inverted based on the response errors after local measurement points or boundary transfer. Finally, the whole-ship boundary transfer response is superimposed with the various unit load response components to obtain the total stress time history of the target area under the combined action of multiple loads. This invention can effectively compensate for the problem of insufficient characterization of local multi-source load responses by single-modal reconstruction, enabling more accurate recovery of stress amplitude, peak-valley variations, and time history characteristics in local hot spots, directly loaded areas, and areas with abrupt stiffness changes. Compared with the method of superimposing individual unit loads, this technique retains the overall wave-induced response and boundary transfer effect of the whole ship, avoiding the loss of overall response caused by isolated solutions of local models. This can improve the accuracy, stability, and engineering applicability of local stress reconstruction under complex working conditions, providing a more reliable data foundation for ship fatigue damage assessment, condition awareness, and life management.

[0068] The present invention will now be described in detail with reference to preferred embodiments.

[0069] The purpose of this invention is to establish an optimized modal stress reconstruction method incorporating the unit load superposition method. This method utilizes a small number of ship-wide and local stress monitoring points to achieve time-domain stress reconstruction in key compartments and critical structural areas of large ships. This method is particularly suitable for cargo hold areas of large ore carriers, enabling stress estimation of critical areas such as hatch edges, decks, longitudinal bulkhead sloped bottom plate angles, and inner bottom plates, providing a basis for hull structural health monitoring, fatigue assessment, and operational safety assessment.

[0070] This embodiment uses a 325K DWT large ore carrier as an example. The ship is approximately 339.9 m long, 30.0 m deep, and 62.0 m wide. The hatch openings are approximately 28.0 m long and 19.8 m wide. Figure 2 As shown, a full-ship finite element model and two partial cargo hold finite element models were established based on the ship's structural design data. In the full-ship model, the plate structure was simulated using shell elements, and stiffeners and other components were simulated using beam elements, with a mesh size of 400 mm × 400 mm. The partial models were used to describe the detailed response of the cargo hold internal structure, inclined bottom plate, longitudinal bulkheads, transverse bulkheads, inner bottom plate, and their connection areas.

[0071] The loads in this embodiment mainly include the longitudinal bending, transverse bending, and torsional responses of the entire ship caused by waves, as well as the local inertial loads caused by cargo movement. For the local cargo hold model, equivalent boundary loads such as vertical bending moment, transverse bending moment, and torque are applied at the end boundaries through multi-point constraints; cargo inertial loads are applied in the transverse bulkheads, longitudinal bulkheads, and inner floor areas of the cargo hold. By calculating the structural response under each individual load, a unit load response database is established.

[0072] The optimized modal stress reconstruction method incorporating the unit load superposition method proposed in this invention can be simply referred to as the optimized modal-unit load superposition reconstruction method, while the traditional direct modal superposition stress reconstruction method can be simply referred to as the MS method.

[0073] In this embodiment, the stress monitoring points throughout the ship are as follows: Figure 4 As shown, the monitoring points are arranged near 1 / 4L, 1 / 2L, and 3 / 4L along the ship's length, as well as on the midship deck and near the waterline, to obtain the overall longitudinal stress response of the hull. Local stress monitoring points are shown below. Figure 5 As shown, these are arranged at locations such as the angled bottom plate bends, longitudinal bulkhead bends, and inner bottom plate of the cargo hold, and are used to invert the local unit load contribution coefficients. For example... Figure 6 As shown, representative target points V1-V4 were selected at areas such as the hatch edge, deck, longitudinal bulkhead sloping bottom plate angle, and inner bottom plate to verify the stress reconstruction results. The unit load basis is as follows: Figure 3 As shown, it includes end vertical bending moment, end lateral bending moment, end torque, inertial load of cargo in the transverse bulkhead, inertial load of cargo in the longitudinal bulkhead, and inertial load of cargo in the inner bottom plate.

[0074] The optimized modal stress reconstruction method incorporating the unit load superposition method provided in this embodiment specifically includes the following steps: Step 1: Establish the global modal reconstruction basis for the entire ship structure.

[0075] The ship's hull structure is equivalent to a linearly damped multi-degree-of-freedom system, and the equations of motion in physical coordinates are established. The physical displacement response is projected onto the modal space, and the decoupled modal equations are obtained under classical damping and mass normalization conditions. The global stress response at the target position is described by the superposition of global modal stress components. Here, the subscript g represents the global modal reconstruction quantity.

[0076]

[0077] In the formula, M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the hull structure, respectively; , , Let f(t) be the displacement vector, velocity vector, and acceleration vector at time t, respectively; f(t) be the external excitation vector; and t be the time variable.

[0078]

[0079] In the formula, The modal shape matrix consists of the preserved modes; The modal coordinate vector; Let r be the mode shape vector; is the coordinate of the r-th mode; n is the reserved global mode order; r is the mode order number.

[0080]

[0081] In the formula, , These are the first and second time derivatives of the r-th modal coordinates, respectively; The damping ratio of the r-th mode; The r-th natural angular frequency; is the r-th order generalized modal force; n is the total number of retained modes.

[0082]

[0083] In the formula, Let g be the global modal reconstruction stress at position x at time t; the subscript g indicates the global modal reconstruction amount. Let x be the modal stress component corresponding to the r-th global mode at position x; is the participation coefficient or modal coordinate of the r-th mode; n is the order of the modes involved in the superposition.

[0084] Step 2: Construct the global monitoring points and modal stress matrix.

[0085] Based on m sparse global longitudinal stress monitoring points, the measured stress at the same moment is assembled into a sensor response vector, and the nth-order global modal stress contribution is extracted at the monitoring location to form a global modal stress matrix for solving the modal participation coefficient.

[0086]

[0087] In the formula, Let be the measured stress vector composed of m global monitoring points at time t; This represents the modal stress matrix at the global monitoring points; is the modal coordinate vector to be identified; m is the number of global stress monitoring points.

[0088]

[0089] In the formula, The global modal stress matrix is ​​m×n dimensional. The stress contribution of the r-th global mode at the k-th global monitoring point is given by , where k = 1, 2, ..., m are the monitoring point numbers, r = 1, 2, ..., n are the modal order numbers, m is the number of global monitoring points, and n is the retained modal order.

[0090] Step 3: Identify global modal coordinates and obtain global reconstruction results.

[0091] Based on the sensor response vector and the global modal stress matrix, the modal coordinates are solved using the Moore-Penrose pseudo-inverse or least squares method. Then, the global modal stress vector at the target location is multiplied by the modal coordinates to obtain the global longitudinal stress reconstruction result at the entire ship or local boundary location. This result serves as the boundary transfer information of the local sub-model and the source of virtual monitoring input.

[0092]

[0093] In the formula, This is the modal coordinate estimation vector obtained from measured stress identification; for Moore-Penrose pseudo-inverse matrix; The measured stress vector at the global monitoring points; the symbol "^" represents the estimated value.

[0094]

[0095] In the formula, For target location X T The global stress reconstruction result at time t; This represents the global modal stress row vector at the target location; The modal coordinate estimation vector obtained from identification; X T Indicates the location of the target point or target area.

[0096] Step 4: Establish the fractional unit load response basis of the local sub-model.

[0097] For the target cargo hold or local hotspot areas, wave boundary-transferred unit load cases and cargo inertial unit load cases are constructed respectively. Under the conditions of small deformation, linear elasticity, and unchanged structural configuration, the corresponding unit load response fields are extracted to form local wave response bases and cargo inertial response bases, respectively. Here, the subscript w represents the wave-induced component, and the subscript c represents the cargo inertial component.

[0098]

[0099] In the formula, The wave-induced local stress component at position x and time t; the subscript w indicates the wave-induced component; The stress response of the j-th wave unit load response basis at position x; This represents the corresponding wave response participation factor; Let x be the basis vector or matrix of the wave response at position x; The wave response participation coefficient vector; The number of wave unit load response bases.

[0100]

[0101] In the formula, Let x be the local inertial stress component of the cargo at time t; the subscript c indicates the inertial component of the cargo. Let x be the stress response of the j-th cargo inertial unit load response basis at position x; This is the corresponding inertial response participation factor for the cargo; Let x be the basis vector or matrix of the inertial response of the cargo at position x; For the inertial response participation coefficient vector of the cargo; This represents the number of basic load responses per unit load of the cargo inertia.

[0102] Step 5: Select local response identification points and assemble wave component response matrices.

[0103] Based on the multi-condition trial calculation results, s virtual monitoring input points are selected from the locations with high global modal reconstruction accuracy and stable relationship with local response transmission. The known or reconstructed wave-induced responses at the identification points are assembled into local wave response vectors, and the responses of each wave unit load response basis at the identification points are used to form a local wave unit load response matrix.

[0104]

[0105] In the formula, Let x1, x2, ..., x3 be the wave-induced response vectors at s local response identification points; x1, x2, ..., x3 s For identifying the location of local response points; The wave unit load response matrix is ​​obtained by assembling at the local identification point; is the wave response participation coefficient vector; s is the number of local response identification points.

[0106]

[0107] In the formula, For s×p w 3D wave unit load response matrix; Let be the stress response of the j-th wave unit load response basis at the k-th local identification point; k=1,2,…,s are the local identification point numbers; j=1,2,…,p ws represents the wave response basis number; s represents the number of identification points; The number of wave response bases.

[0108] Step 6: Identify the local wave-induced response components.

[0109] Using the local wave response vector and wave unit load response matrix obtained in step 5 as input, the participation coefficients of the wave load response basis are solved in the least squares form, and the local wave-induced stress response under boundary transfer is reconstructed using the wave unit load response vector or matrix at the target location.

[0110]

[0111] In the formula, To identify the obtained wave response participation coefficient estimation vector; for Moore-Penrose pseudo-inverse matrix; This is the wave-induced response vector at the local identification point; the subscript w is used to distinguish it from the cargo inertial component.

[0112]

[0113] In the formula, For target location X T Wave-induced local stress reconstruction results at the location; This is the wave unit load response vector or matrix at the target location; X is the wave response participation coefficient estimation vector; T Indicates the location of the target point or target area.

[0114] Step 7: Identify the inertial load response components of the cargo.

[0115] The equivalent inertial load generated by the cargo on the local cargo hold structure is used as an independent load source. The participation coefficient of the cargo inertial response basis is determined by combining the ship motion monitoring data. The local stress response under the cargo inertial action is reconstructed by using the cargo inertial unit load response vector or matrix at the target location. All parameters in this step are indicated by the subscript c to distinguish them from the wave-induced components in step S6.

[0116]

[0117] In the formula, For target location X T The results of local inertial stress reconstruction of the cargo at the location; This is the inertial unit load response vector or matrix of the cargo at the target location; X is the estimated vector of the cargo inertial response participation coefficient determined based on ship motion monitoring data; TIndicates the location of the target point or target area.

[0118] Step 8: Superimpose the multi-source response and output the time-domain stress of the target region.

[0119] The local wave-induced stress response and the cargo inertial stress response are superimposed on the same time coordinate to obtain the final time-domain stress response of the target area or verification point under multi-source loads; the output is preferably the longitudinal normal stress σ along the ship's length. x This allows for characterization of the hull beam bending and key stress responses in local cargo hold structures. In online applications, only pre-established global modal stress databases, local unit load response databases, and real-time monitoring data are accessed; recalculation of the finite element method is unnecessary.

[0120]

[0121] In the formula, For target location X T The final optimized reconstruction of the longitudinal normal stress along the ship's length direction; the subscript x indicates the longitudinal normal stress component, and the subscript ML indicates the optimized reconstruction result; The results are for wave-induced local stress reconstruction. This is the result of reconstructing the local inertial stress of the cargo; , These are the wave response basis matrix and the cargo inertial response basis matrix at the target location, respectively. , These are the participation coefficient estimation vectors for the wave component and the cargo inertia component, respectively.

[0122] To evaluate the reconstruction effect of this invention, typical target areas such as the deck, hatch edges, longitudinal bulkhead sloping bottom plate angles, and inner bottom plate can be selected as verification points. The reconstruction results of this invention are then compared with finite element calculation results or measured results. Evaluation indicators may include the coefficient of determination R², Pearson correlation coefficient r, normalized root mean square error NRMSE, and maximum cross-correlation coefficient Rho. R² is used to evaluate the explanatory power of the reconstruction results for the fluctuations in the actual response amplitude; r is used to evaluate the consistency of curve shape and trend; NRMSE is used to evaluate the magnitude of numerical error; and Rho is used to evaluate phase consistency under small time lag conditions. The closer R², r, and Rho are to 1, and the smaller the NRMSE, the more reliable the stress reconstruction results. Taking a typical asymmetric working condition as an example, the stress reconstruction time history results are as follows: Figure 7 As shown in Table 1, the corresponding evaluation parameters are as follows.

[0123] Table 1. Stress reconstruction evaluation parameters under typical asymmetric conditions

[0124] according to Figure 7As shown in Table 1, under typical asymmetric operating conditions, the method of this invention outperforms the direct modal superposition method at all four representative target points. For indirect load-bearing areas such as hatch edges V1 and decks V2, both methods can capture the main response trends, but this invention further reduces NRMSE and improves R², r, and Rho; specifically, the NRMSE of V2 decreases from 20.7011% to 17.7141%. For areas directly affected by cargo loads and with significant local stiffness changes, such as longitudinal bulkhead sloping bottom plate angles V3 and inner bottom plates V4, the improvement effect is even more pronounced: the R² of V3 increases from 0.1677 to 0.9283, and the NRMSE decreases from 91.2288% to 26.7843%; the R² of V4 increases from 0.5383 to 0.9605, and the NRMSE decreases from 67.9519% to 19.8644%.

[0125] Depend on Figure 7 As can be seen, at each target point from V1 to V4, the optimized mode-unit load superposition reconstruction result can more stably follow the low-frequency envelope, local peaks and valleys, and phase changes of the actual response curve. Especially at V3 and V4, the traditional MS method exhibits significant amplitude attenuation, low-frequency baseline deviation, and phase drift, while the method of this invention, by compensating for the local multi-source load response through unit load superposition, enables the stress reconstruction result in the target region to be closer to the true response in terms of amplitude, trend, numerical magnitude, and phase.

[0126] Test results show that the optimized modal stress reconstruction method incorporating the unit load superposition method proposed in this invention achieves key improvements over the traditional modal superposition method: it obtains the overall wave-induced response through full-ship modal superposition, compensates for cargo loads and local structural responses through local unit load superposition, and obtains the complete stress time history of the target region through global-local coupling. Under typical asymmetric multi-source load conditions, this method can improve the stress reconstruction accuracy of local hotspot regions under limited measurement point input conditions, and improve the problems of amplitude underestimation, low-frequency envelope deviation, and phase drift in local loaded regions caused by the direct modal superposition method, while maintaining high computational efficiency and physical interpretability.

[0127] Therefore, this invention can provide a high-precision, low-cost, and deployable technical solution for large ship structural health monitoring, real-time stress simulation in key areas, fatigue damage assessment, and operation and maintenance decision-making.

[0128] Compared with existing technologies, this invention has significant advantages over traditional stress monitoring and single-mode superposition stress reconstruction methods. The stress reconstruction process of this invention only requires a limited number of stress or strain sensors to be deployed at the overall response location and key local structural locations throughout the ship. It eliminates the need to deploy monitoring equipment at all hotspots, and can deduce the stress response in areas without measurement points. This helps reduce the hardware cost, wiring complexity, and maintenance difficulty of the monitoring system.

[0129] This invention employs a combination of offline databases and online rapid solution. The finite element modal database, global-local boundary response database, and unit load basis response database can all be pre-established during the ship design, sea trials, or structural health monitoring system deployment phases. During actual shipboard operation, only the strain or stress data collected in real-time by sensors needs to be input. The stress response of the target region can be obtained through matrix inversion and linear superposition, eliminating the need for online access to large-scale finite element calculation software. This results in lower computational resource requirements and makes it suitable for embedding into existing ship structural health monitoring systems.

[0130] This invention can improve the reconstruction reliability of local hotspot areas. For indirectly loaded areas such as decks and hatch edges, this method can further improve the consistency of response amplitude and trend based on the traditional modal superposition results. For areas directly affected by cargo loads, such as longitudinal bulkhead sloping bottom plate corners and inner bottom plates, this method can effectively compensate for the problem of insufficient expression of local load response by the whole-ship modal method, and improve amplitude underestimation, envelope bias and phase drift.

[0131] Furthermore, this invention exhibits good interpretability. The modal superposition component corresponds to the overall vibration and wave-induced response of the hull, while the unit load superposition component corresponds to the contributions of different local loads. The final reconstruction result is composed of both the global wave-induced response and the local multi-source load response. This process can clearly explain the influence of different load sources on the stress in the target area, providing a reliable basis for structural condition assessment, fatigue damage calculation, abnormal response identification, and operation and maintenance decisions.

[0132] In summary, this invention can achieve high-precision, near-real-time stress reconstruction of a large-scale ship structure and key local areas under limited monitoring data conditions. It is applicable to health monitoring scenarios of large ore carriers, bulk carriers, container ships, and other large ships with obvious global-local coupling characteristics, and has good prospects for engineering application and industrialization.

[0133] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. An optimized modal stress reconstruction method incorporating the unit load superposition method, characterized in that, The method includes the following steps: S101: Establishing the basis for global modal reconstruction of the entire ship structure: Equivalently treat the ship structure as a linear damped multi-degree-of-freedom system, establish the motion equations in physical coordinates, project the physical displacement response onto the modal space, and calculate the global stress response; S103: Constructing the global monitoring points and modal stress matrix: Based on the global longitudinal stress monitoring points, the measured stress at the same moment is assembled into a sensor response vector, and the global modal stress contribution is extracted at the monitoring location to form a global modal stress matrix for solving the modal participation coefficient; S105: Identify global modal coordinates and obtain global reconstruction results: Solve for modal coordinates based on the sensor response vector and the global modal stress matrix, multiply the global modal stress vector at the target position with the modal coordinates, and obtain the global stress reconstruction results for the entire ship or local boundary positions; S107: Establish the fractional unit load response basis of the local sub-model: For the target cargo hold or local hot spot area, construct the wave boundary transfer unit load case and the cargo inertia unit load case respectively, extract the corresponding unit load response field, and form the local wave response basis and cargo inertia response basis. S109: Construct wave component response matrices based on local response identification points, and reconstruct local wave-induced stress response and cargo inertial load stress response; S111: The local wave-induced response and the cargo inertial load response are superimposed to obtain the final time-domain stress response of the target area or verification point under multi-source load and output it.

2. The method as described in claim 1, wherein in step S101, the equation of motion is: The global stress response is: in, In the formula, Let be the displacement vector, velocity vector, and acceleration vector at time t, respectively. For external excitation vectors, For position Place Global modal reconstruction stress at time t, The r-th order global mode at position The corresponding modal stress components at that location, For modal coordinate vectors, For the first First modal coordinates, The first The first and second time derivatives of the modal coordinates. For the first Generalized modal forces, The modal shape matrix consists of the preserved modes. Let r be the mode shape vector. The mass matrix of the ship's hull structure. The damping matrix of the hull structure. Here is the stiffness matrix of the hull structure. The damping ratio of the r-th mode is... The natural angular frequency of order r is... For time variables, subscript Represents the global modal reconstruction quantity. The modal order is... This is the modal order number.

3. The method as described in claim 2, in step S101, when solving the global stress response, the physical displacement response is projected onto the modal space through the motion equation, and the decoupled modal equation is obtained under classical damping and mass normalization conditions. The target position is described by the superposition of global modal stress components, and the global stress response is obtained.

4. The method as described in claim 3, wherein in step S103, the measured stress vector of the constructed global monitoring point is: in, for One global monitoring point at The measured stress vector composed of time intervals, This represents the modal stress matrix at the global monitoring points. Let be the modal coordinate vector to be identified. For the first The global mode of order 1 in the first order is... Stress contribution at each global monitoring point This represents the total number of global stress monitoring points. Number the monitoring point.

5. The method as described in claim 4, wherein in step S105, when solving for the modal coordinates, the Moore-Penrose pseudo-inverse or least squares method is used, and the global stress reconstruction result is: in, For target location Place The global stress reconstruction result at time t. Let be the global modal stress row vector at the target location. This is the modal coordinate estimation vector obtained from measured stress identification. for Moore-Penrose pseudo-inverse matrix, The measured stress vector at the global monitoring points. The target point or target area location is indicated by the symbol "^".

6. The method as described in claim 5, wherein in step S107, the unit load response field is extracted under the conditions of small deformation, linear elasticity, and unchanged structural configuration to form wave-induced local stress components and cargo inertial local stress components, wherein: The wave-induced local stress components are: The local inertial stress components of the cargo are: In the formula, For position Place Wave-induced local stress components at any given time. For the first The wave unit load response base at position Stress response at the point, The wave response participation factor. For position The wave response basis vector or matrix at the location, This represents the wave response participation coefficient vector. The number of wave unit load response bases; For position Place Local stress components of cargo inertia at time. For the first The inertial unit load response of a cargo is based on its position. Stress response at the point, This represents the corresponding inertial response participation factor for the cargo. For position The basis vector or matrix of the inertial response of the goods at that location. Let be the vector of inertial response participation coefficients for the cargo. The number of basic load responses per unit load of cargo inertia, subscript Indicates wave-induced components, subscript Indicates the inertial component of the cargo.

7. The method as described in claim 6, wherein in step S109, based on the multi-condition trial calculation results, multiple virtual monitoring input points are selected from positions with high global modal reconstruction accuracy and stable local response transmission relationship; the wave-induced or reconstructed responses at the identification points are assembled into local wave response vectors; and the responses of each wave unit load response basis at the identification points form a local wave unit load response matrix, wherein the local wave response vector is: In the formula, For the first Wave-induced response vector at each local response identification point for 3D wave unit load response matrix, For the first The wave unit load response basis at the th wave unit load basis in the th wave Stress response at a local identification point This represents the wave response participation coefficient vector. For the first Location of a local response identification point Here, s represents the local identification point number, and s represents the number of local response identification points. For the number of wave response bases, The wave response base number is used.

8. The method as described in claim 7, wherein in step S109, based on the local wave response vector and the wave unit load response matrix, the participation coefficients of the wave load response basis are solved using a least-squares method, and the local wave-induced stress response under boundary transfer is reconstructed using the wave unit load response matrix at the target location: in, For target location Wave-induced local stress reconstruction results at the location, The wave unit load response matrix at the target location. This is the wave response participation coefficient estimation vector. This is the wave response participation coefficient estimation vector. for Moore-Penrose pseudo-inverse matrix, This represents the wave-induced response vector at the local identification point. The target location.

9. The method as described in claim 8, wherein in step S109, the equivalent inertial load generated by the cargo on the local cargo hold structure is taken as an independent load source, the participation coefficient of the cargo inertial response basis is determined in conjunction with ship motion monitoring data, and the cargo inertial load stress response under cargo inertial action is reconstructed using the cargo inertial unit load response matrix at the target location: in, For target location The results of the reconstruction of local inertial stress of the cargo at the location, The inertial unit load response matrix of the cargo at the target location is given. This is the estimated vector of the cargo inertial response participation coefficient determined based on ship motion monitoring data.

10. The method as described in claim 9, wherein in step S111, the local wave-induced stress response and the cargo inertial load stress response are superimposed on the same time coordinate to obtain the final time-domain stress response of the target area or verification point under multi-source loads: in, Target location The final optimized reconstruction of the longitudinal normal stress along the ship's length direction, This is the result of reconstructing the local wave-induced stress response. The results are the reconstructed stress response of the cargo under inertial loads. This is the participation coefficient estimation vector for the wave components. This is the participation coefficient estimation vector for the inertial components of the cargo. Let be the wave response basis matrix at the target location. Let be the basis matrix of the inertial response of the cargo at the target location.

Images