Floating foundation structure dynamic response real-time analysis system and method

Abstract

The invention relates to the technical field of computer-aided analysis, in particular to a floating foundation structure dynamic response real-time analysis system and method.The system comprises a residual vector calculation module for generating a residual force vector based on a full-order external excitation force vector, an increment base generation module for calculating a modal amplitude and constructing an increment base vector, and an increment base generation module for generating an increment base vector; the reduced-order matrix updating module constructs an enhanced reduced-order model by using the updated projection matrix, and the transient response solving module solves and obtains a corrected generalized coordinate value based on the enhanced reduced-order model and maps the corrected generalized coordinate value into a dynamic displacement field. According to the method, a residual vector is generated by calculating a difference value between full-order external excitation and internal force, residual force is mapped into static deformation distribution by using a stiffness matrix inverse operator, an incremental base is constructed through orthogonalization processing, adaptive updating of a projection space of a reduced-order model is realized, the system dimension is reduced, and the precision is guaranteed. And the calculation efficiency and the real-time performance of dynamic response analysis of the floating structure are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer-aided analysis, in particular to a floating foundation structure dynamic response real-time analysis system and method. BACKGROUND

[0002] The technical field of computer-aided analysis refers to the technology of using computer software and hardware systems to numerically model physical objects and predict their physical performance and behavior characteristics under different working conditions through calculation simulation. Among them, the traditional floating foundation structure dynamic response real-time analysis system refers to welding strain gauges at key nodes of the floating platform and arranging accelerometers, connecting the sensors to a multi-channel data acquisition instrument through a shielded cable, converting the analog voltage signal to a digital signal by the data acquisition instrument and transmitting it to the shore-based server, the server running the general finite element analysis software to establish a three-dimensional grid model of the structure, and performing matrix operations according to the input wave load parameters to obtain the vibration response data of the structure.

[0003] The prior art relies on the shore-based server to run the general finite element software to establish a three-dimensional grid model and perform full-matrix operations. In the face of complex floating foundation structure with massive degrees of freedom, the size of the overall stiffness matrix and mass matrix is large, resulting in huge consumption of computing resources and memory space in the numerical calculation process. Under the continuous action of dynamic wave load, repeated execution of high-dimensional matrix inversion and iterative solution process will produce significant time lag, making it difficult to meet the timeliness requirements of real-time monitoring and rapid early warning of structural dynamic response, and seriously restricting the realization of high-fidelity physical field evolution in the condition of limited computing power. SUMMARY

[0004] The purpose of the present application is to solve the shortcomings in the prior art and propose a floating foundation structure dynamic response real-time analysis system and method.

[0005] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions, a floating foundation structure dynamic response real-time analysis system comprises: A residual vector calculation module is configured to construct a full-order external excitation force vector by a wave pressure distribution value, estimate generalized coordinate displacement and velocity values using an initial reduced-order model, calculate the difference between the full-order external excitation force vector and internal inertia force and elastic restoring force inverted based on the generalized coordinate displacement and velocity values, and generate a residual force vector; An increment base generation module is configured to calculate the modal amplitude of the residual force vector, and if the modal amplitude exceeds an error tolerance threshold, call a structure stiffness matrix inverse operator to calculate the static deformation distribution shape corresponding to the residual force vector, perform Schmidt orthogonalization processing on the static deformation distribution shape, and construct an increment base vector; An order reduction matrix updating module is configured to append the incremental basis vector to a projection matrix, perform a local projection transformation operation on a full-order system matrix by using the updated projection matrix, calculate a cross term of the incremental basis vector, and construct an enhanced order reduction model; A transient response solving module is configured to solve a structure dynamics response equation by using the Newmark-Beta method based on the enhanced order reduction model, obtain a corrected generalized coordinate value, and map the corrected generalized coordinate value to a dynamic displacement field.

[0006] As a further scheme of the present application, the residual vector calculating module is specifically implemented as: An excitation constructing submodule is configured to obtain discrete wave pressure data acting on a surface of a floating foundation structure, perform spatial integration processing on the discrete wave pressure data based on preset structure finite element grid node information, and generate a full-order external excitation force vector; A state estimating submodule is configured to solve a low-dimensional dynamics equation corresponding to an initial order reduction model based on a system state at a previous time step, obtain an estimated generalized coordinate at a current time step, and derive generalized coordinate displacement and velocity values according to a time integration scheme; A difference calculating submodule is configured to call a full-order mass matrix and a full-order stiffness matrix, map the generalized coordinate displacement and velocity values back to a physical space by using a basis function matrix of the initial order reduction model, calculate a sum of an inertial force term and an elastic force term, subtract the sum from the full-order external excitation force vector, and generate a residual force vector.

[0007] As a further scheme of the present application, the incremental basis generating module is specifically implemented as: An amplitude determining submodule is configured to calculate a Euclidean norm of the residual force vector as a modal amplitude, compare the modal amplitude with a preset error tolerance threshold, and trigger a basis vector correction process if the comparison result exceeds the threshold; A static correction submodule is configured to obtain a sparse decomposition form of the full-order stiffness matrix as a structure stiffness matrix inverse operator, input the residual force vector as a static load, perform a linear equation set solving operation, and generate a static deformation distribution shape; An orthogonal processing submodule is configured to traverse an existing projection basis space, calculate projection components of the static deformation distribution shape in directions of a plurality of basis vectors, eliminate all the projection components from the static deformation distribution shape, and perform normalization processing to generate an incremental basis vector.

[0008] As a further scheme of the present application, the order reduction matrix updating module is specifically implemented as: A space expanding submodule is configured to append the incremental basis vector as a current column vector to a right side of an original projection matrix, and establish an extended projection basis matrix; The matrix projection sub-module performs local matrix multiplication operation on the newly added row and column area of the incremental basis vector in the full-order system matrix by using the extended projection basis matrix, to generate newly added block data; The model reconstruction sub-module assembles the newly added block data into the original reduced-order system matrix, updates the reduced-order mass matrix, the reduced-order damping matrix and the reduced-order stiffness matrix, to construct an enhanced reduced-order model.

[0009] As a further scheme of the present application, the specific function of the transient response solving module is implemented as: The parameter initialization sub-module constructs an equivalent dynamic stiffness matrix and an equivalent load vector at the current time according to the time integration constant of the Newmark-Beta method and the updated system matrix in the enhanced reduced-order model; The integral solving sub-module performs linear solving operation on the equivalent load vector by using the equivalent dynamic stiffness matrix, to obtain the modified generalized coordinate value at the next time in the reduced-order space; The result mapping sub-module performs matrix-vector multiplication operation on the modified generalized coordinate value and the updated projection matrix, to reconstruct the generalized solution in the low-dimensional space into the node displacement data in the full-order physical space, to generate a dynamic displacement field.

[0010] As a further scheme of the present application, the process of calculating the residual force vector in the difference calculation sub-module is specifically performed according to the following formula: ; Wherein, represents the residual force vector generated at the current time step, represents the full-order external excitation force vector, represents the full-order mass matrix, represents the full-order damping matrix, represents the full-order stiffness matrix, represents the basis vector matrix of the initial reduced-order model, 、 、 respectively represent the generalized displacement, the generalized velocity and the generalized acceleration included in the generalized coordinate displacement and velocity values.

[0011] As a further scheme of the present application, the Schmidt orthogonalization processing performed by the orthogonal processing sub-module includes: All basis vectors included in the current projection matrix are obtained, the inner product value of the static deformation distribution shape and each included basis vector is calculated, to generate an inner product value; constructing a projection vector on a subspace spanned by the included basis vectors based on the inner product value, generating a projection vector, calculating an orthogonal residual vector after the static deformation distribution shape is subtracted by the projection vector, generating an orthogonal residual vector; calculating a module length of the orthogonal residual vector, dividing the orthogonal residual vector by the module length to complete unitization, and generating the incremental basis vector.

[0012] As a further scheme of the present application, the process of the matrix projection sub-module calculating the cross terms of the incremental basis vector includes: extracting the full-order mass matrix, calculating the product of the transposed vector of the incremental basis vector and the full-order mass matrix, and performing right multiplication operation on the product result with the original projection matrix and the incremental basis vector itself respectively, to generate a mass matrix cross term block; extracting the full-order stiffness matrix, calculating the product of the transposed vector of the incremental basis vector and the full-order stiffness matrix, and performing right multiplication operation on the product result with the original projection matrix and the incremental basis vector itself respectively, to generate a stiffness matrix cross term block; filling the mass matrix cross term block and the stiffness matrix cross term block to the right side columns and the bottom rows of the reduced-order system matrix respectively, completing the expansion and update of the reduced-order model system matrix, and generating an updated reduced-order system matrix.

[0013] As a further scheme of the present application, the process of the integral solution sub-module acquiring the modified generalized coordinate value includes: calculating the unbalanced force vector of the system based on the estimated value of the modified generalized coordinate value, generating an unbalanced force vector, and judging whether the convergence norm of the unbalanced force vector is less than a preset iteration termination threshold; If the convergence norm does not meet the requirement, calculating the inverse matrix of the tangent stiffness matrix, multiplying the inverse matrix with the unbalanced force vector to obtain a generalized coordinate increment, generating a generalized coordinate increment, and modifying the modified generalized coordinate value using the generalized coordinate increment; repeating the above unbalanced force calculation and coordinate modification steps until the convergence norm meets the iteration termination threshold, and outputting the converged modified generalized coordinate value.

[0014] A floating foundation structure dynamic response real-time analysis method based on the floating foundation structure dynamic response real-time analysis system described above, including the following steps: S1: Construct a full-order external excitation force vector based on the wave pressure distribution value, estimate the generalized coordinate displacement and velocity value by using the initial reduced-order model, calculate the difference between the full-order external excitation force vector and the internal inertia force and elastic restoring force inverted based on the generalized coordinate displacement and velocity value, and generate a residual force vector; S2: Calculate the modal amplitude of the residual force vector, and if the modal amplitude exceeds the error tolerance threshold, calculate the static deformation distribution shape corresponding to the residual force vector by using the structural stiffness matrix inverse operator, perform Schmidt orthogonalization processing on the static deformation distribution shape, and construct an incremental basis vector; S3: Append the incremental basis vector to the projection matrix, perform local projection transformation operation on the full-order system matrix by using the updated projection matrix, calculate the cross term of the incremental basis vector, and construct an enhanced reduced-order model; S4: Based on the enhanced reduced-order model, call the Newmark-Beta method to integrate and solve the structure dynamics response equation, obtain the corrected generalized coordinate value, and map the corrected generalized coordinate value to a dynamic displacement field.

[0015] Compared with the prior art, the advantages and positive effects of the present application are that: In the present application, the residual vector is generated by calculating the difference between the full-order external excitation and the internal force inverted based on the reduced-order model, the dynamic characteristics that cannot be characterized by the current projection subspace are accurately captured, the residual force exceeding the error tolerance threshold is mapped to the static deformation distribution by using the stiffness matrix inverse operator, and the incremental basis is appended to the projection matrix after orthogonalization processing to construct the incremental basis, thereby realizing adaptive local updating and expansion of the reduced-order model projection space, greatly reducing the system degree of freedom dimension while ensuring the model accuracy, and significantly improving the calculation efficiency and real-time performance of the dynamic response analysis of the floating structure under complex wave conditions. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 A main flowchart of a floating foundation structure dynamic response real-time analysis system of the present application; Figure 2 A detailed operation flowchart of a residual vector calculation module of the present application; Figure 3 A detailed operation flowchart of an incremental basis generation module of the present application; Figure 4 A detailed operation flowchart of a reduced-order matrix updating module of the present application; Figure 5 A detailed operation flowchart of a transient response solving module of the present application. DETAILED DESCRIPTION

[0017] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions realized based on software are described in detail below in combination with system architecture diagrams and embodiments. It should be understood that the specific embodiments described herein are only used to explain the technical solutions of the present application and do not constitute a limitation on the protection scope.

[0018] In the description of the present application, the system architecture relationship or data processing flow indicated by the terms "hierarchy", "module", "interface", "data flow", "client", "server" and the like are defined based on the corresponding architecture diagrams or flowcharts of the embodiments. This description method is only used to clearly explain the logical relationship of each element in the technical solution, and does not limit the physical deployment form. The "multiple" includes two or more technical units, including but not limited to multiple data nodes, processing threads, service instances or functional components, and other scalable elements. The specific number is determined according to the actual business scenario.

[0019] Please refer to Figure 1 and Figure 2 , the present application provides a kind of technical scheme: a floating foundation structure dynamic response real-time analysis system includes: Residual vector calculation module, for the numerical operation function of computer program, by wave pressure distribution numerical construction full order external excitation force vector, utilize the initial reduced order model stored in computer memory to estimate generalized coordinate displacement and velocity value, and the difference between the full order external excitation force vector and the internal inertia force and elastic restoring force based on generalized coordinate displacement and velocity value is calculated by the logic operation unit of processor, to generate residual force vector; The specific function of residual vector calculation module is realized as: Excitation construction submodule, obtains the discrete wave pressure data acting on the surface of floating foundation structure, combines the preset structure finite element grid node information, and the discrete wave pressure data is subjected to spatial integration processing, to generate full order external excitation force vector; State estimation submodule, based on the system state of last time step, solve the low-dimensional dynamic equation corresponding to the initial reduced order model, obtain the estimated generalized coordinate of current time step, and derive the generalized coordinate displacement and velocity value according to time integration scheme; Difference calculation submodule, call full order mass matrix and full order stiffness matrix, utilize the basis function matrix of initial reduced order model to map generalized coordinate displacement and velocity value back to physical space, calculate the sum of inertia force term and elastic force term, and subtract the sum value from full order external excitation force vector to generate residual force vector; The process of calculating residual force vector in difference calculation submodule is executed according to the following formula: ; Wherein, Residual force vector generated at current time step, represent the full-order external excitation force vector, represent the full-order mass matrix, represent the full-order damping matrix, represent the full-order stiffness matrix, represent the basis vector matrix of the initial reduced-order model, , , represent the generalized displacement, velocity and acceleration included in the generalized coordinate displacement and velocity values, respectively.

[0020] For a three-column semi-submersible floating wind turbine foundation structure with a working water depth of 200 meters, the system first performs the construction process of the full-order external excitation force vector. The system collects discrete wave pressure data through the water dynamic pressure sensor array deployed on the wet surface of the floating foundation. The total number of nodes of the structure finite element model is set to 2,400, of which the number of wet surface nodes directly affected by waves is 2,400. At the current time step , the system reads the discrete wave pressure data. In order to ensure the availability and accuracy of the data, the pressure values and corresponding node control areas of some key monitoring nodes are selected, as shown in Table 1.

[0021] Table 1 Wave pressure monitoring data table of key nodes on the wet surface of the floating foundation

[0022] The system performs spatial integration processing on the above discrete data according to the finite element grid topological relationship. For each force node , the node force vector acted on it is calculated, where is the outer normal unit vector of the node surface. For the Node_1024 node, the component force in the axis direction is calculated as . The system traverses all the force nodes and assembles the calculated node forces into the full-order external excitation force vector , which has a dimension of .

[0023] Subsequently, the system performs state estimation. Based on the converged state at the last time step (i.e. 10.48s, time step ), the generalized coordinates at the current time are predicted using the time explicit integration format. The current initial reduced-order model contains basis vectors, i.e. the initial projection matrix has a dimension of . The generalized coordinates at the last time are known, and the generalized coordinate displacement at the current time is calculated and predicted as​ , generalized velocity , and generalized acceleration . The generalized coordinate component value corresponding to the 5th order mode is set as: , , .

[0024] Next, the system calls the full-order system matrix in the computer database to perform internal force inversion and residual calculation. The full-order mass matrix , the full-order damping matrix , and the full-order stiffness matrix are pre-stored in the sparse matrix library. The calculation process is performed according to the following formula: ; wherein represents the residual force vector generated at the current time step , with the unit of Newton (N), and the vector has the physical meaning of the part of the external excitation that cannot be balanced out by the current reduced-order model; represents the full-order external excitation force vector, which is obtained by pressure integration, with the dimension of ; represents the full-order mass matrix, with the dimension of , containing the structural mass and the additional water mass, with the unit of kilogram (kg); represents the full-order damping matrix, with the dimension of , with the unit of Newton second per meter (N·s / m); represents the full-order stiffness matrix, with the dimension of , containing the hydrostatic restoring stiffness and the linearized stiffness of the mooring system, with the unit of Newton per meter (N / m); represents the basis vector matrix of the initial reduced-order model, with the dimension of , and each column represents a modal shape; , , respectively represent the generalized displacement, generalized velocity, and generalized acceleration vectors with the dimension of .

[0025] The directional degree of freedom (i.e., the 3070th degree of freedom) corresponding to Node_1024 in the full-order vector is selected for verification calculation. The external excitation force component corresponding to this degree of freedom is known.

[0026] After matrix-vector operation, the internal force component results corresponding to this degree of freedom are as follows: inertial force term ; damping force term ; elastic force term .

[0027] Substitute the above values ​​into the formula to calculate the residual components: .

[0028] This result indicates that in Node_1024 In terms of direction, the current reduced-order model has an unbalanced force of 2.679 kN, which will serve as the source term for subsequent incremental basis generation.

[0029] Please see Figure 1 and Figure 3 The incremental basis generation module is used to calculate the modal amplitude of the residual force vector. If the modal amplitude exceeds the error tolerance threshold, the inverse operator of the structural stiffness matrix is ​​called to calculate the static deformation distribution shape corresponding to the residual force vector. The static deformation distribution shape is subjected to Schmitt orthogonalization to construct the incremental basis vector. The specific functional implementation of the incremental base generation module is as follows: The amplitude determination submodule calculates the Euclidean norm of the residual force vector as the modal amplitude, compares the modal amplitude with the preset error tolerance threshold, and if the determination result exceeds the threshold, the basis vector correction process is triggered. The static correction submodule obtains the sparse decomposition form of the full-order stiffness matrix as the inverse operator of the structural stiffness matrix, takes the residual force vector as the static load input, and generates the static deformation distribution shape by solving the linear equation system. The orthogonal processing submodule traverses the existing projection basis space, calculates the projection components of the static deformation distribution shape in multiple basis vector directions, removes all projection components from the static deformation distribution shape and performs normalization processing to generate incremental basis vectors. The Schmitt orthogonalization process performed by the orthogonal processing submodule includes: Obtain all basis vectors included in the current projection matrix, calculate the inner product value between the static deformation distribution shape and each included basis vector, and generate the inner product value; Based on the inner product value, construct the projection vector of the static deformation distribution shape on the subspace spanned by the included basis vectors, generate the projection vector, calculate the orthogonal residual vector after subtracting the projection vector from the static deformation distribution shape, and generate the orthogonal residual vector. Calculate the magnitude of the orthogonal residual vector, divide the orthogonal residual vector by the magnitude to normalize it, and generate the incremental basis vector.

[0030] Obtaining the residual force vector Then, the modal amplitude determination process is executed first. The system calculates... Euclidean norm ( The norm is used as an indicator of modal amplitude. The calculation formula is as follows: In the aforementioned steps, the calculation has been performed. The residual distribution of other DOF in the full-order system is squared and summed to obtain the overall modal amplitude .

[0031] Set the error tolerance threshold . The threshold is determined by the maximum design load of the floating foundation structure in extreme sea conditions , which is 0.5% of . For the floating wind turbine foundation in this example, the design maximum wave shear force is , so the threshold is set to . The system compares the calculated modal amplitude with the threshold: . If the result is "above threshold", it indicates that the current reduced-order basis space is insufficient to accurately describe the current dynamic response, and the basis vector modification process is triggered immediately.

[0032] Subsequently, the structure stiffness matrix inverse operator is called to calculate the static deformation distribution shape . This step is essentially solving a linear system of equations . Since the full-order stiffness matrix has a dimension of and has a sparse strip-like characteristic, the system uses the pre-computed Cholesky decomposition factor (satisfying ) to solve it by forward substitution and back substitution. Let a local stiffness , the corresponding local residual , then the calculated local static deformation component . The system obtains the full-field static deformation distribution vector through this process, which has a dimension of .

[0033] The Cholesky decomposition factor mentioned above refers to the decomposition of a symmetric positive definite matrix into the product of a lower triangular matrix and its transpose matrix, which is used to accelerate the numerical solution process of linear systems of equations.

[0034] Finally, perform Schmidt orthogonalization on to construct the incremental basis vector . This operation aims to eliminate the known modal components contained in , ensuring that the new basis vector is linearly independent of the original projection space .

[0035] The orthogonalization process follows the following steps: 1. The computer program obtains the current projection matrix .

[0036] 2. Calculate the inner product value: for each , calculate the projection coefficient The projection coefficient of the first modal is calculated The projection coefficient of the second modal is calculated The rest of the coefficients are calculated in turn.

[0037] 3. The projection vector is constructed and the elimination is performed: Suppose the length of the projection vector is After subtracting each projection component, the length of the remaining orthogonal residual vector is reduced to .

[0038] 4. Unitization processing: Divide by its length to generate the unitized incremental basis vector . This vector is the 16th modal basis that is about to be expanded to the reduced-order space.

[0039] The Schmidt orthogonalization processing described above refers to a mathematical algorithm for converting a set of linearly independent vectors into a set of orthogonal vectors to eliminate the correlation between vectors and ensure that the newly generated basis vectors are independent in the spatial direction.

[0040] Please refer to Figure 1 and Figure 4 , the reduced-order matrix updating module is used to append the incremental basis vector to the projection matrix using the memory management mechanism of the computer, and to perform local projection transformation operation on the full-order system matrix using the updated projection matrix, to calculate the cross terms of the incremental basis vector, and to construct an enhanced reduced-order model; The specific function implementation of the reduced-order matrix updating module is: The space expansion submodule appends the incremental basis vector as the current column vector to the right side of the original projection matrix to establish an extended projection basis matrix; The matrix projection submodule performs local matrix multiplication operation on the newly added row and column area of the incremental basis vector in the full-order system matrix using the extended projection basis matrix to generate new block data; The model reconstruction submodule assembles the new block data into the original reduced-order system matrix to update the reduced-order mass matrix, the reduced-order damping matrix, and the reduced-order stiffness matrix, thereby constructing an enhanced reduced-order model; The process of calculating the cross terms of the incremental basis vector by the matrix projection submodule includes: Extract the full-order mass matrix, calculate the product of the transpose vector of the incremental basis vector and the full-order mass matrix, and perform right multiplication operation on the product result with the original projection matrix and the incremental basis vector itself respectively to generate the mass matrix cross term block; ​The transpose vector of the increment basis vector is multiplied with the full-order stiffness matrix, and the multiplication result is right-multiplied with the original projection matrix and the increment basis vector itself respectively to generate the stiffness matrix cross-term block; The mass matrix cross-term block and the stiffness matrix cross-term block are filled into the right side column and the bottom row of the reduced-order system matrix respectively to complete the expansion and update of the reduced-order model system matrix, and the updated reduced-order system matrix is generated.

[0041] After generating the increment basis vector (the dimension is ), the system performs the update operation of the reduced-order matrix. First, the spatial expansion submodule appends as the 16th column vector to the right side of the original projection matrix (the dimension is ) to form the extended projection basis matrix (the dimension is ). That is .

[0042] Subsequently, the system performs local projection transformation on the full-order system matrix using . In order to avoid full recalculation of the reduced-order matrix of the entire , the system only calculates the cross-term corresponding to the increment basis vector, i.e. the newly added 16th row and 16th column elements.

[0043] Taking the update of the mass matrix as an example, the specific calculation process is as follows: 1. Calculate the intermediate vector . This operation involves the multiplication of the sparse matrix and the vector . Suppose that the non-zero elements of a certain row in are , and the corresponding position elements are , then the corresponding elements of are .

[0044] 2. Calculate the column cross-term: . This is a vector representing the mass coupling term between the original 15 modes and the new mode. The dot product of the first column of and is , which is the element at position in the reduced-order mass matrix .

[0045] 3. Calculate the diagonal term: . The calculation result is .

[0046] For stiffness matrix and damping matrix Perform the exact same local projection operation. Calculate the stiffness cross term. The first element is Stiffness diagonal term .

[0047] The model reconstruction submodule assembles the block data obtained from the above calculations into the original reduced-order system matrix. (Original reduced-order stiffness matrix) (dimension is) (It remains unchanged and is located in the top left corner.) Fill the first 15 rows up to column 16. Fill the first 15 columns up to row 16. Fill to the 1st The position of the main diagonal. This leads to the construction of the updated reduced-order stiffness matrix. (dimension is) Similarly, update... and At this point, the enhanced reduced-order model is complete, possessing the ability to describe the high-frequency or local nonlinear response at the current moment.

[0048] Please see Figure 1 and Figure 5 The transient response solution module is used to solve the structural dynamic response equation by calling the Newmark-Beta method through an enhanced reduced-order model, obtain the corrected generalized coordinate values, and map the corrected generalized coordinate values ​​into a dynamic displacement field. The specific functions of the transient response solving module are as follows: The parameter initialization submodule constructs the equivalent dynamic stiffness matrix and the equivalent load vector at the current moment based on the time integration constant of the Newmark-Beta method and the updated system matrix in the enhanced reduced-order model. The integral solution submodule uses the equivalent dynamic stiffness matrix to perform linear solution operations on the equivalent load vector to obtain the corrected generalized coordinate values ​​in the reduced-order space at the next moment. The result mapping submodule performs matrix-vector multiplication on the corrected generalized coordinate values ​​and the updated projection matrix, reconstructing the generalized solution in the low-dimensional space into nodal displacement data in the full-order physical space, and generating a dynamic displacement field. The process of obtaining the corrected generalized coordinate values ​​in the integral solving submodule includes: Based on the estimated value of the corrected generalized coordinate values, the unbalanced force vector of the system is calculated, the unbalanced force vector is generated, and it is determined whether the convergence norm of the unbalanced force vector is less than the preset iteration termination threshold. If the convergence norm does not meet the requirements, calculate the inverse matrix of the tangent stiffness matrix, multiply the inverse matrix by the unbalanced force vector to obtain the generalized coordinate increment, generate the generalized coordinate increment, and use the generalized coordinate increment to correct the generalized coordinate value. Repeat the above steps of unbalanced force calculation and coordinate correction until the convergence norm meets the iteration termination threshold, and output the converged corrected generalized coordinate values.

[0049] Using the enhanced order reduction model built in S3 (including Vie The system adopts Newmark-Beta (Newmark- The explicit time integration method is used. First, parameter initialization is performed. The integration constant is set. , Time step Based on the Newmark algorithm, an equivalent dynamic stiffness matrix is ​​constructed. The calculation process is performed according to the following formula:

[0050] in, Represents the equivalent dynamic stiffness matrix, with dimension . ; Represents the reduced-order stiffness matrix; Represents the reduced-order quality matrix; Represents the reduced-order damping matrix; and This represents the Newmark time integration constant, used to control the stability and accuracy of the algorithm; Represents the time step.

[0051] The Newmark-Beta method mentioned above is a numerical integration method widely used in structural dynamics. It is used to solve time-varying second-order differential equations through computer iterative calculations to calculate the displacement, velocity, and acceleration of the structure at different times.

[0052] Substitute specific values ​​to calculate the coefficients: , .

[0053] Main diagonal elements of the reduced stiffness matrix The main diagonal elements of the quality matrix Damping matrix main diagonal element .

[0054] The equivalent stiffness matrix is ​​calculated using the main diagonal elements as follows: .

[0055] The system calculates and assembles the complete .

[0056] At the same time, the equivalent load vector at the current time is calculated . This vector contains the projected external excitation force and the inertia and damping terms determined by the motion state at the previous time. Then, the integral solution and iterative correction process are entered. Since the floating foundation involves mooring nonlinearity, the system uses Newton-Raphson iteration to solve the nonlinear algebraic equation. In the first iterative step, the unbalanced force vector is calculated. The iterative termination threshold is set to . If the unbalanced force convergence norm , the incremental equation is solved, and the generalized coordinates are updated. After 3 iterations, the unbalanced force norm decreases from to , meeting the convergence requirement. At this time, the corrected generalized coordinate value is output, which has a dimension of . The 16th component of the calculation result is .

[0057] Finally, the result mapping submodule performs matrix vector multiplication operation: . is the node displacement vector in the full-order physical space, with a dimension of . The system multiplies the update projection matrix of with the corrected generalized coordinate vector of . Taking the Node_1024 direction displacement as an example, its value is the linear superposition of the mode shape values of all 16 modes at this point multiplied by the corresponding generalized coordinates. The calculation result shows that the final dynamic displacement of Node_1024 is . This data constitutes part of the dynamic displacement field, which is used for subsequent stress analysis and safety evaluation.

[0058] A floating foundation structure dynamic response real-time analysis method based on the above floating foundation structure dynamic response real-time analysis system is executed, comprising the following steps: S1: based on the wave pressure distribution value, construct the full-order external excitation force vector, use the initial reduced-order model to estimate the generalized coordinate displacement and velocity value, calculate the difference between the full-order external excitation force vector and the internal inertia force and elastic restoring force inverted based on the generalized coordinate displacement and velocity value, generate the residual force vector; S2: calculate the modal amplitude of the residual force vector, if the modal amplitude exceeds the error tolerance threshold, call the structure stiffness matrix inverse operator to calculate the static deformation distribution shape corresponding to the residual force vector, perform Schmidt orthogonalization processing on the static deformation distribution shape, and construct the incremental basis vector; S3: Append the incremental basis vector to the projection matrix, perform a local projection transformation operation on the full-order system matrix using the updated projection matrix, calculate the cross term of the incremental basis vector, and construct an enhanced reduced-order model; S4: Based on the enhanced reduced-order model, call the Newmark-beta method to integrate and solve the structural dynamics response equation, obtain the corrected generalized coordinate value, and map the corrected generalized coordinate value to a dynamic displacement field.

[0059] The above embodiments demonstrate the preferred embodiments of the present application, and any equivalent adjustment of the technical scheme based on software engineering methods is within the protection scope, including but not limited to: implementing algorithm logic in different programming languages, service reconstruction of functional modules, adjustment of data interaction protocol, optimization of resource scheduling strategy and other technical improvements. Any implementation scheme derived by reasonable modification of the data processing flow, service calling link or system architecture level without deviating from the technical core of the present application shall be considered within the protection scope of the present application.

Claims

1. A real-time system for dynamic response analysis of floating foundation structures, characterized by, The system comprises: a residual vector calculation module, configured to construct a full-order external excitation force vector by wave pressure distribution values, to predict generalized coordinate displacement and velocity values by using an initial reduced-order model, to calculate a difference between the full-order external excitation force vector and internal inertia force and elastic restoring force values inverted based on the generalized coordinate displacement and velocity values, and to generate a residual force vector; an incremental basis generation module, configured to calculate modal amplitudes of the residual force vector, to call a structural stiffness matrix inverse operator to calculate a static deformation distribution shape corresponding to the residual force vector if the modal amplitudes exceed an error tolerance threshold, to perform Schmidt orthogonalization processing on the static deformation distribution shape, and to construct an incremental basis vector; a reduced-order matrix updating module, configured to append the incremental basis vector to a projection matrix, to perform local projection transformation operation on a full-order system matrix by using the updated projection matrix, to calculate cross terms of the incremental basis vector, and to construct an enhanced reduced-order model; a transient response solving module, configured to call Newmark-Beta method to integrate and solve a structure dynamics response equation by using the enhanced reduced-order model, to obtain corrected generalized coordinate values, and to map the corrected generalized coordinate values into a dynamic displacement field.

2. The real-time analysis system for dynamic response of floating foundation structures according to claim 1, characterized in that, The residual vector calculation module is specifically implemented as: an excitation construction submodule, configured to obtain discrete wave pressure data acting on a surface of a floating foundation structure, to perform spatial integration processing on the discrete wave pressure data in combination with preset structure finite element grid node information, and to generate a full-order external excitation force vector; a state prediction submodule, configured to solve a low-dimensional dynamics equation corresponding to an initial reduced-order model based on a system state of a previous time step, to obtain predicted generalized coordinates of a current time step, and to derive generalized coordinate displacement and velocity values according to a time integration scheme; a difference calculation submodule, configured to call a full-order mass matrix and a full-order stiffness matrix, to map the generalized coordinate displacement and velocity values back to a physical space by using a basis function matrix of the initial reduced-order model, to calculate a sum of inertia force items and elastic force items, and to subtract the sum from the full-order external excitation force vector to generate a residual force vector.

3. The real-time analysis system for dynamic response of floating foundation structures according to claim 2, characterized in that, The incremental basis generation module is specifically implemented as: an amplitude determination submodule, configured to calculate a Euclidean norm of the residual force vector as a modal amplitude, to compare the modal amplitude with a preset error tolerance threshold, and to trigger a basis vector correction process if the determination result exceeds the threshold; a static correction submodule, configured to obtain a sparse decomposition form of the full-order stiffness matrix as a structural stiffness matrix inverse operator, to input the residual force vector as a static load, to perform linear equation set solving operation, and to generate a static deformation distribution shape; an orthogonal processing submodule, configured to traverse an existing projection basis space, to calculate projection components of the static deformation distribution shape in multiple basis vector directions, to eliminate all the projection components from the static deformation distribution shape and to perform normalization processing, and to generate an incremental basis vector.

4. The real-time analysis system for dynamic response of a floating foundation structure of claim 3, wherein, The reduced-order matrix updating module is specifically implemented as: a space expansion submodule, configured to append the incremental basis vector as a current column vector to a right side of an original projection matrix to establish an extended projection basis matrix. The matrix projection submodule performs local matrix multiplication operation on the newly added row and column area of the incremental basis vector in the full-order system matrix by using the extended projection basis matrix, to generate new block data; The model reconstruction submodule assembles the new block data into the original reduced-order system matrix, updates the reduced-order mass matrix, the reduced-order damping matrix and the reduced-order stiffness matrix, thereby constructing an enhanced reduced-order model.

5. The real-time analysis system for dynamic response of floating foundation structures according to claim 4, characterized in that, The specific function of the transient response solving module is: The parameter initialization submodule constructs an equivalent dynamic stiffness matrix and an equivalent load vector at the current time based on the time integration constant of the Newmark-beta method and the updated system matrix in the enhanced reduced-order model; The integral solving submodule performs linear solving operation on the equivalent load vector by using the equivalent dynamic stiffness matrix, to obtain the modified generalized coordinate value at the next time in the reduced-order space; The result mapping submodule performs matrix-vector multiplication operation on the modified generalized coordinate value and the updated projection matrix, reconstructs the generalized solution in the low-dimensional space into the node displacement data in the full-order physical space, to generate a dynamic displacement field.

6. The real-time analysis system for dynamic response of floating foundation structures according to claim 2, characterized in that, The process of calculating the residual force vector in the difference calculation submodule is specifically performed according to the following formula: ； wherein, represents the residual force vector generated at the current time step, represents the full order external excitation force vector, represents the full order mass matrix, represents full order damping matrix, represents the full order stiffness matrix, represents the basis vector matrix of the initial reduced order model, , , respectively represent the generalized displacement, generalized velocity and generalized acceleration included in the generalized coordinate displacement and velocity values.

7. The real-time analysis system for dynamic response of floating foundation structures according to claim 3, characterized in that, The Schmidt orthogonalization processing performed by the orthogonal processing submodule includes: All basis vectors included in the current projection matrix are obtained, the inner product value of the static deformation distribution shape and each included basis vector is calculated, to generate an inner product value; A projection vector of the static deformation distribution shape on the subspace spanned by the included basis vectors is constructed based on the inner product value, to generate a projection vector, and an orthogonal residual vector after the static deformation distribution shape is subtracted from the projection vector is calculated, to generate an orthogonal residual vector; The module length of the orthogonal residual vector is calculated, and the orthogonal residual vector is divided by the module length to complete unitization, to generate the incremental basis vector.

8. The real-time analysis system for dynamic response of floating foundation structures according to claim 4, characterized in that, The process of calculating the cross term of the incremental basis vector by the matrix projection submodule includes: The full-order mass matrix is extracted, the product of the transpose vector of the incremental basis vector and the full-order mass matrix is calculated, and the product result is right-multiplied by the original projection matrix and the incremental basis vector itself respectively, to generate a mass matrix cross term block; The full-order stiffness matrix is extracted, the product of the transpose vector of the incremental basis vector and the full-order stiffness matrix is calculated, and the product result is right-multiplied by the original projection matrix and the incremental basis vector itself respectively, to generate a stiffness matrix cross term block; The mass matrix cross term block and the stiffness matrix cross term block are filled into the right side column and the bottom row of the reduced-order system matrix respectively, to complete the expansion and update of the reduced-order model system matrix, and to generate an updated reduced-order system matrix.

9. The real-time analysis system for dynamic response of floating foundation structures according to claim 5, characterized in that, The process of obtaining the modified generalized coordinate value by the integral solving submodule includes: Based on the estimated value of the modified generalized coordinate value, the unbalanced force vector of the system is calculated, to generate an unbalanced force vector, and it is judged whether the convergence norm of the unbalanced force vector is less than a preset iteration termination threshold value; If the convergence norm does not meet the requirement, the inverse matrix of the tangent stiffness matrix is calculated, the inverse matrix is multiplied by the unbalanced force vector to obtain a generalized coordinate increment, a generalized coordinate increment is generated, and the modified generalized coordinate value is modified using the generalized coordinate increment; The above unbalanced force calculation and coordinate correction steps are repeatedly performed until the convergence norm meets the iteration termination threshold, and the converged modified generalized coordinate value is output.

10. A method of real-time analysis of dynamic response of a floating foundation structure, characterized by, The method is used to realize the floating foundation structure dynamic response real-time analysis system of any one of claims 1-9, comprising the following steps: S1: based on the wave pressure distribution numerical construction full order external excitation force vector, using the initial order model to estimate the generalized coordinate displacement and velocity value, calculate the difference between the full order external excitation force vector and the internal inertia force and elastic restoring force based on the generalized coordinate displacement and velocity value, generate residual force vector; S2: calculate the modal amplitude of the residual force vector, if the modal amplitude exceeds the error tolerance threshold, call the structure stiffness matrix inverse operator to calculate the static deformation distribution shape corresponding to the residual force vector, perform Schmidt orthogonalization processing on the static deformation distribution shape, and construct an incremental basis vector; S3: append the incremental basis vector to the projection matrix, and perform local projection transformation operation on the full order system matrix using the updated projection matrix, calculate the cross term of the incremental basis vector, and construct an enhanced reduced order model; S4: based on the enhanced reduced order model, call the Newmark-Beta method to integrate and solve the structure dynamics response equation, obtain the modified generalized coordinate value, and map the modified generalized coordinate value to the dynamic displacement field.

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