POD reduced order fast calculation method of transmission tower based on static and dynamic load separation modeling

Abstract

The application provides a power transmission tower POD reduced-order fast calculation method based on static and dynamic load separation modeling, comprising the following steps: respectively constructing snapshot matrices corresponding to permanent load and variable load; extracting principal components of the snapshot matrices, and respectively constructing corresponding reduced bases; projecting high-dimensional finite element control equations of the tower on a subspace formed by the reduced bases to respectively obtain a static reduced-order model and a dynamic reduced-order model; solving the static reduced-order model for a new permanent load working condition to obtain a static working condition generalized coordinate, and reconstructing the static working condition generalized coordinate by using the corresponding reduced base to obtain a static displacement state of the tower; and solving the dynamic reduced-order model based on the obtained static displacement state for a new variable load working condition to obtain a dynamic working condition generalized coordinate, and reconstructing the dynamic working condition generalized coordinate by using the corresponding reduced base to obtain a dynamic displacement and stress response of the tower. The application converts solving high-dimensional finite element equation sets into solving reduced-order models with extremely low dimensions, and fundamentally bypasses a calculation bottleneck of a traditional method.

Description

Technical Field

[0001] This invention belongs to the field of structural analysis and calculation technology of transmission towers, specifically involving a rapid calculation method for reduced order of POD of transmission towers based on static and dynamic load separation modeling. Background Technology

[0002] Transmission tower systems are crucial power energy infrastructure and have long been a primary research focus in power systems both domestically and internationally. Establishing mechanical models for transmission tower systems is of great significance for monitoring, evaluating, and mitigating disasters in power transmission systems. Transmission towers, as an important component of transmission lines, primarily support conductors and ground wires, ensuring electrical insulation and providing the necessary conditions for the safe operation of the lines.

[0003] However, existing methods for analyzing tower structures have significant computational bottlenecks, especially when performing dynamic analysis or parametric simulation. Faced with the complex structure and variable load conditions of towers, traditional high-fidelity numerical simulation methods (such as the finite element method) often involve huge computational loads and excessive time consumption. This makes it difficult for such methods to meet the efficiency requirements of structural optimization design, real-time condition assessment, and disaster prevention and mitigation decision-making. Therefore, a more efficient computational method is urgently needed. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a rapid calculation method for reduced-order POD of transmission towers based on static and dynamic load separation modeling.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A rapid calculation method for reduced-order dynamic displacement (POD) of transmission towers based on static and dynamic load separation modeling includes: obtaining the structural displacement responses of the tower under typical working conditions for permanent and variable loads, and constructing corresponding snapshot matrices; extracting the principal components of the snapshot matrices and constructing corresponding reduced-order bases according to the energy criterion; projecting the high-dimensional finite element control equations of the tower onto the subspace formed by the reduced-order bases to obtain static and dynamic reduced-order models respectively; solving the static reduced-order model for a new permanent load condition to obtain the generalized coordinates of the static condition, and reconstructing the static displacement state of the tower using the corresponding reduced-order bases; solving the dynamic reduced-order model based on the obtained static displacement state for a new variable load condition to obtain the generalized coordinates of the dynamic condition, and reconstructing the dynamic displacement and stress response of the tower using the corresponding reduced-order bases.

[0006] Furthermore, the method for extracting the principal components of the snapshot matrix and constructing corresponding reduced bases according to the energy criterion includes: using the intrinsic orthogonal decomposition method to calculate the correlation matrix of the snapshot matrix; calculating the eigenvalues ​​and eigenvectors of the correlation matrix; arranging the eigenvalues ​​in descending order; and selecting the eigenvectors corresponding to the first r eigenvalues ​​according to the energy criterion to form the reduced bases.

[0007] Furthermore, the energy criterion is expressed as: , r is the order, and m is the number of eigenvector elements. Let argmin be the i-th eigenvalue, and let argmin represent taking the eigenvalue that satisfies The minimum r value, ε represents the maximum percentage threshold of energy that can be cut off from the total energy.

[0008] Furthermore, methods for projecting the high-dimensional finite element governing equations of the tower onto a subspace composed of reduced bases to obtain a statically reduced-order model include: Substituting the original statics equations, we obtain the first equation. ;in It is a static reduction base. For permanent load vectors, , Let be the full-order displacement vector and the reduced-order displacement vector of the permanent load, respectively, and K be the full-order stiffness matrix; multiply both sides of the first equation by on the left. By projecting the first equation onto an r-dimensional reduced-order space, a static reduced-order model is obtained. .

[0009] Furthermore, methods for projecting the high-dimensional finite element governing equations of the tower onto a subspace composed of reduced bases to obtain a reduced-order dynamic model include: , and Substituting into the second-order ordinary differential equations of dynamics, we obtain the second equation. ; For dynamic shrinkage base, , , , , , Let M, C, and K be the full-order displacement vector, full-order velocity vector, full-order acceleration vector, reduced-order displacement vector, reduced-order velocity vector, and reduced-order acceleration vector of the wind load, respectively; and M, C, and K be the full-order mass matrix, full-order damping matrix, and full-order stiffness matrix, respectively. Multiply both sides of the second equation to the left by... By projecting the second equation onto an r-dimensional reduced-order space, we obtain a dynamical reduced-order model. .

[0010] Furthermore, for new variable load conditions, methods for obtaining the generalized coordinates of the dynamic condition by solving the reduced-order dynamic model based on the obtained static displacement state include: using the reduced-order mass matrix of the reduced-order dynamic model. Reduced-order damping matrix and reduced stiffness matrix Calculate the reduced-order effective stiffness matrix Set initial speed Set the initial displacement based on the static displacement state. Using the equation of motion at t=0, solve for the initial acceleration. ; Calculate all constants based on the selected integration parameters and time step Δt. ~ Iterative solution is performed step-by-step, iteratively utilizing the time-mapping data at each time step. This forms a generalized coordinate system for dynamic operating conditions.

[0011] Furthermore, when iterating step-by-step, the calculation method for each time step includes: utilizing the known state at time t and the reduced-order wind load vector at time t+Δt. Calculate the reduced-order effective wind load vector The known states include displacements. ,speed acceleration Solving for the reduced-order displacement at time t+Δt yields the solution. Update the acceleration and velocity at time t+Δt; update the known state and proceed to the next time step calculation.

[0012] Furthermore, methods for obtaining the structural displacement responses of towers under permanent and variable loads under typical working conditions and constructing corresponding snapshot matrices include: Calculate the permanent load on the tower; after applying the permanent load to the tower, obtain the static displacement vector of the corresponding node through static analysis of multiple load steps; combine the static displacement vectors in the order of load steps to obtain the static snapshot matrix representing the permanent load; The standard value for determining wind load is ,in As the reference wind pressure, This is the wind pressure height variation coefficient. This is the body size coefficient. For wind vibration coefficient, This is the factor that amplifies the wind load on tower components due to icing. The projected area of ​​the windward component is given; a representative parameter combination is selected to perform dynamic analysis of the wind load on the tower, and the dynamic displacement vector at each moment under each working condition is obtained; the dynamic displacement vectors are combined in the order of time steps to obtain a dynamic snapshot matrix representing the variable load.

[0013] Furthermore, the permanent loads include the structure's self-weight, the weight of auxiliary equipment, and the static load of the conductor; the variable loads include wind loads.

[0014] Furthermore, the calculated permanent load is g is the acceleration due to gravity, m is the mass per unit length of the conductor, L is the length of the conductor, λ is the load factor, and c is the total mass of the auxiliary equipment. , and These are the spans on both sides of the tower. and These represent the height difference between the hanging points on both sides of the tower.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention innovatively employs a decoupling strategy, constructing independent static and dynamic reduction bases to address the differences in physical characteristics between permanent and variable loads. This strategy allows static and dynamic analyses to utilize their respective optimized reduction bases for calculation. The static reduction base focuses on capturing structural deformation modes under permanent loads, while the dynamic reduction base focuses on capturing structural deformation modes under wind load excitation. This avoids the problem of reduced expressive power caused by a single reduction base needing to consider both load characteristics, thus ensuring both computational efficiency and high accuracy.

[0016] This invention projects the original high-dimensional finite element governing equations onto a low-dimensional subspace composed of reduced bases, transforming a full-order system of dimension n×n into a system of dimension r×r. The reduced-order model, whether for static or dynamic analysis, completes the solution process in the reduced-order space, fundamentally bypassing the computational bottleneck of traditional high-fidelity numerical simulation methods (such as the finite element method) for solving large-scale equation systems. In dynamic analysis, the effective stiffness matrix of the reduced-order model only needs to undergo one numerical decomposition and can be reused throughout all time steps, further reducing computation time. Verification through calculations on multiple tower examples shows that computational efficiency can be improved by approximately 3 times, and the computational speedup remains stable with changes in the reduced basis dimension, demonstrating predictable performance. Attached Figure Description

[0017] The present invention will now be described in further detail with reference to the accompanying drawings.

[0018] Figure 1 : A schematic diagram of the process of this invention; Figure 2 : Schematic diagram for calculating the conductor length of this invention; Figure 3 : A schematic diagram of the wind load snapshot matrix constructed in this invention; Figure 4 : A schematic diagram of extracting principal components of the snapshot matrix when constructing the reduced basis in this invention; Figure 5 : A schematic diagram of the energy criterion for constructing the reduced basis in this invention; Figure 6 Data tables (a) and (b) of this invention; Figure 7 Data tables (c) and (d) of this invention; Figure 8 Performance comparison results of full-order model and reduced-order model with different dimensions under static conditions. Detailed Implementation

[0019] To better understand the present invention, the content of the invention is further clearly illustrated below with reference to embodiments and accompanying drawings. However, the scope of protection of the present invention is not limited to the embodiments described below. Numerous specific details are set forth in the following description to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the present invention can be practiced without one or more of these details.

[0020] Example 1: See Figures 1-8 The purpose of this embodiment is to provide a rapid calculation method for reduced-order POD of transmission towers based on static and dynamic load separation modeling, including: S1. Obtain the structural displacement response of the tower under permanent and variable loads under typical working conditions, and construct the corresponding snapshot matrices respectively.

[0021] The snapshot matrix constructed in this step includes the static snapshot matrix. Wind load snapshot matrix .

[0022] The permanent loads of a tower include its structural self-weight (the gravity of all structural components such as the tower body, crossarms, and foundation), the weight of auxiliary equipment (the gravity of various insulator strings such as suspension strings, tension strings, and V-strings, hardware, and other accessories), and the static load of the conductor and ground wire. The static load of the conductor and ground wire is a constant load exerted on the tower by the conductor and ground wire due to its own weight and pre-set tension. The specific components of this load (longitudinal, transverse, and vertical) are precisely calculated based on the tower type (e.g., straight-line tower, angle tower) and the method of wire placement. For example, the length of the conductor and ground wire is calculated based on the span and height difference between the two sides of the tower. ,like Figure 2 As shown, and These are the spans on both sides of the tower. and The elevation difference between the two suspension points on either side of the tower is taken as the basis; then, the permanent load is calculated based on the unit length mass of the conductor and the weight of the auxiliary equipment. Where g is the gravitational acceleration, m is the mass per unit length of the conductor, L is the length of the conductor, λ is the load factor (a correction factor considering factors such as sag), and c is the total mass of the auxiliary equipment.

[0023] After applying a permanent load to the tower, the displacement vectors of the corresponding nodes are obtained through static analysis of multiple load steps. Combining these displacement vectors generated by different static conditions in the order of load steps constitutes a static snapshot matrix representing the permanent load. , n is the structural degrees of freedom, and k is the load step number. This represents the nodal displacement vector corresponding to the initial load step. Let f be the nodal displacement vector corresponding to the k-th load step, and ∆f be the load step interval.

[0024] The variable loads on the tower include wind loads, and the standard value of wind load is... , is the body shape coefficient, a preset constant that does not change with operating conditions. Calculated value of the projected area of ​​the windward component , Let i be the surface area of ​​a single component i, and N be the number of components on the windward side. Let i be the wind direction angle (the angle between the vertical axis and the wind direction). It varies with the wind direction angle θ.

[0025] Body type coefficient η is the wind load reduction factor on the leeward side of the tower. The wind load reduction factor η on the leeward side of the tower is based on... Figure 6 - The data in (a) was obtained using linear interpolation. In the table, P is the outline area of ​​the tower, a is the width of the windward side of the tower, and b is the distance between the windward and leeward sides of the tower.

[0026] The factor representing the increase in wind load due to icing on tower components is 1.1 for all cases designed with icing, 1.2 for 5mm icing areas, 1.2 for 10mm icing areas, and 1.0 for no-ice cases.

[0027] Wind pressure height variation coefficient The coefficients in this invention are determined according to the ground roughness category and altitude. The wind pressure height variation coefficient is determined based on the ground roughness category corresponding to a fixed altitude of 60m: A (nearshore sea surface, islands, coast, lake shore, and desert areas), B (fields, villages, jungles, hills, and sparsely populated towns and suburbs), C (urban areas with dense building clusters), and D (urban areas with dense building clusters and tall buildings). The values ​​are 1.97, 1.71, 1.20, and 0.77, respectively.

[0028] Wind vibration coefficient ξ is the pulsation amplification coefficient. This represents the influence coefficient of wind pressure pulsation and wind pressure height variation. To account for the influence of mode shapes and structural shape, the pulsation amplification factor ξ is calculated based on... Figure 6 The data table in (b) was obtained using linear interpolation. Reference wind pressure (unit) T is the fundamental natural period of the structure (in seconds). The influence coefficients of wind pressure pulsation and wind pressure height variation are also considered. according to Figure 7 -(c) The data table was obtained using linear interpolation, but approximate indices can also be used (e.g., if the tower height is 91m, it can be selected based on a height of 100m). The influence coefficients of mode shape and structural shape should be considered. Based on the actual dimensions of the tower to be analyzed, its structural width ratio is calculated, and the relative height of different parts of the tower is also calculated. Then, based on these two parameters... Figure 7 The data table for -(d) was obtained using linear interpolation.

[0029] Reference wind pressure Its wind speed In this invention, the variable parameter for wind load is wind speed. The range of variation is set between 20m / s and 35m / s.

[0030] In summary, for wind loads on power poles, ground roughness α and wind speed can be set. Wind direction angle θ and icing wind load amplification factor It is a variable parameter. Therefore, as... Figure 3 As shown, representative parameter combinations can be selected for different working conditions to perform dynamic analysis of wind loads on the tower. Then, the displacement vectors at each moment under each working condition are collected into a matrix to form a wind load snapshot matrix. , n is the structural degrees of freedom, and m is the time step. Let be the nodal displacement vector at the initial moment. Let m∆t be the nodal displacement vector at time m∆t, where ∆t is the time step.

[0031] S2. Extract the principal components of the snapshot matrix and construct the corresponding reduced basis according to the energy criterion.

[0032] This step uses the POD (Proper Orthogonal Decomposition) technique to extract the principal components (including eigenvalues ​​and eigenvectors) of the static snapshot matrix and the wind load snapshot matrix, and then constructs the corresponding static reduction basis. and dynamic shrinkage base .

[0033] Let matrix A represent the static snapshot matrix. Or wind load snapshot matrix Assuming matrix A has n degrees of freedom and m snapshots, then:

[0034] Calculate the correlation matrix D of matrix A. The ultimate goal is to extract different snapshot matrices to construct a reduction base.

[0035] Calculate the eigenvalues ​​of the correlation matrix D and eigenvectors , , The eigenvalues ​​are all greater than 0. Then the eigenvalues ​​( ~ Arrange in descending order, such as Figure 4 As shown.

[0036] Based on the energy criterion, the eigenvectors corresponding to the eigenvalues ​​of the first r orders are selected to form the reduced basis, such as... Figure 5 As shown. The energy criterion is... , argmin means taking the values ​​that satisfy the condition. The minimum r value, ε represents the energy cutoff tolerance (the maximum percentage of total energy that can be cut off).

[0037] After determining the value of r, calculate and assemble the reduced basis corresponding to matrix A: , .

[0038] S3. Project the high-dimensional finite element control equations of the tower onto the subspace composed of reduced basis to obtain the static reduced-order model and the dynamic reduced-order model respectively.

[0039] This step projects the high-dimensional finite element governing equations of the tower, namely the static equations and the dynamic equations, onto the subspaces composed of static and dynamic reduction bases, respectively, to obtain the static order reduction model and the dynamic order reduction model.

[0040] Perform static analysis, Substitute into the original static equations (where q is the full-order displacement vector, K is the full-order stiffness matrix, and F is the load vector), thus obtaining ,in The reduced displacement vector (generalized coordinates) for permanent loads. This is the permanent load vector. Due to the approximate displacement field... and It is an approximate relationship, and the above formula usually cannot be satisfied exactly, resulting in a residual vector. In order to find the optimal solution Using the classic Galerkin projection method, the residual vector is made... With the selected base Orthogonal means multiplying both sides of the equation to the left simultaneously. This projects the original equation from the n-dimensional physical space to a reduced-order r-dimensional space, i.e. Ultimately, we obtain a result regarding the unknown quantity. A static reduced-order model of dimension r×r: The reduced-order displacement vector is obtained by solving. Then, approximation relationships can be used. We then reconstruct it back into a high-dimensional physical space to obtain the approximate displacement field of the full-order model.

[0041] Perform dynamic analysis, and respectively , and Substituting into the second-order ordinary differential equations of dynamics (q, , Let M, C, and K be the full-order displacement vector, full-order velocity vector, and full-order acceleration vector, respectively; M, C, and K be the full-order mass matrix, full-order damping matrix, and full-order stiffness matrix, respectively; and F be the load vector. ,in , , These represent the reduced-order displacement vector (generalized coordinates), reduced-order velocity vector (generalized velocity), and reduced-order acceleration vector (generalized acceleration) of the wind load, respectively. Let be the wind load vector. Similar to static analysis, Galerkin projection is used, multiplying both sides of the above equation by . This projects the original equation from the n-dimensional physical space to a reduced-order r-dimensional space: Through processing, a dynamical reduced-order model with dimension r×r is finally obtained: .

[0042] S4. Solve the static reduced-order model for the new permanent load condition to obtain the generalized coordinates of the static condition, and reconstruct the static displacement state of the tower using the corresponding reduced basis.

[0043] For the new permanent load conditions After solving the static reduced-order model, the corresponding generalized coordinates of the static working condition are obtained. , By reconstructing the model using static reduced bases, an approximate displacement field for the full-order model is obtained. The static displacement state of the tower is obtained.

[0044] A specific static load case was selected to verify the effectiveness and computational performance of this static analysis step. The configuration of the conductor and ground wire and the insulator string were consistent with the training load case used to construct the static reduced-order base. In the calculations, static reduced-order models with dimension 1 (r=1) and dimension 3 (r=3) were used respectively, and their calculation results were compared with the full-order model (benchmark). Detailed performance comparison results are as follows... Figure 8 As shown, the peak displacement, relative error, and computational speedup of key components are included. In the static analysis step, the POD reduction method exhibits significant characteristics: First, the accuracy is extremely sensitive to the dimension of the reduced basis. The error drops sharply from approximately 3% to 0.02% simply by increasing the dimension from 1st to 3rd order, indicating that the energy convergence speed of the static reduced basis is very fast. The computation time difference between 1st and 3rd order is only 9ms (6%), suggesting that increasing the dimension of the reduced basis has little marginal impact on computation time. Second, the computational speedup remains stable at around 3 times, showing no sensitivity to increases in the number of basis vectors.

[0045] S5. For the new variable load conditions, solve the dynamic reduced-order model based on the obtained static displacement state to obtain the generalized coordinates of the dynamic conditions, and then reconstruct the dynamic displacement and stress response of the tower using the corresponding reduced basis.

[0046] For new wind load conditions Newmark-β solution for the generalized dynamic coordinates of the reduced-order dynamic model. : 1.1 Assembling the Reduced-Order Effective Stiffness Matrix: This involves assembling the reduced-order mass matrix from the dynamic reduction model. Reduced-order damping matrix and reduced stiffness matrix Calculate the reduced-order effective stiffness matrix And perform a numerical decomposition on it beforehand: ; 1.2 Setting initial conditions: Setting the initial velocity The initial displacement is set according to the static displacement state in step S4. , This is the approximate displacement field for the full-order model; 1.3 Calculate the initial acceleration: Solve for the initial acceleration using the equation of motion at t=0. ; 1.4 Calculation of constants: Calculate all integration constants based on the selected integration parameters (Newmark parameters) and time step Δt. ~ (The Newmark parameter β is set to 0.25 during the calculation).

[0047] During the time step iteration phase, for each time step, perform the following operations in a loop: 2.1 Calculate the reduced-order effective load vector: using the known state (displacement) at time t ,speed acceleration The reduced-order wind load vector at time t+Δt. Calculate the reduced-order effective wind load vector :

[0048] 2.2 Solving for the reduced-order displacement: Solving for the reduced-order displacement at time t+Δt. ; 2.3 Update velocity and acceleration: using formulas Calculate the acceleration at time t+Δt using the formula Calculate the velocity at time t+Δt, where γ is the Newmark parameter, preferably 0.5.

[0049] 2.4 Update the state and proceed to the next time step: Take the currently calculated state as the "known state" for the next time step, that is, let... , , Then return to step 2.1 and repeat the entire process to calculate the next time step until the total analysis time is reached.

[0050] After solving with Newmark-β, the reduced-order displacement sequence at each time step is obtained. That is, the corresponding dynamic generalized coordinates Subsequently, the reduced-order displacements at each time step are reconstructed using a dynamic reduction basis to obtain the approximate displacement field of the full-order model. Finally, the stress response of each element of the tower is recovered by calculating element by element using the conventional stress-displacement relationship in the finite element method, and the global displacement and stress response of the tower under wind load are finally obtained.

[0051] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Any other modifications or equivalent substitutions made by those skilled in the art to the technical solutions of the present invention, as long as they do not depart from the spirit and scope of the technical solutions of the present invention, should be covered within the scope of the claims of the present invention.

Claims

1. A method for rapid calculation of the reduced order of power transmission tower POD based on static and dynamic load separation modeling, characterized in that, include: Obtain the structural displacement response of the tower under typical working conditions with permanent and variable loads, and construct the corresponding snapshot matrices respectively; Extract the principal components of the snapshot matrix and construct the corresponding reduced basis according to the energy criterion; By projecting the high-dimensional finite element control equations of the tower onto a subspace composed of reduced bases, static reduced-order models and dynamic reduced-order models are obtained respectively. For the new permanent load condition, the static reduced-order model is solved to obtain the generalized coordinates of the static condition, and the static displacement state of the tower is obtained after reconstruction using the corresponding reduced basis. For the new variable load conditions, the dynamic reduced-order model is solved based on the obtained static displacement state to obtain the generalized coordinates of the dynamic conditions. After reconstruction using the corresponding reduced basis, the dynamic displacement and stress response of the tower are obtained.

2. The method for rapid calculation of transmission tower POD order reduction based on static and dynamic load separation modeling according to claim 1, characterized in that, Methods for extracting the principal components of the snapshot matrix and constructing corresponding reduced bases based on the energy criterion include: The correlation matrix of the snapshot matrix is ​​calculated using the eigenorthogonal decomposition method. Calculate the eigenvalues ​​and eigenvectors of the correlation matrix; Sort the eigenvalues ​​in descending order; Based on the energy criterion, the eigenvectors corresponding to the eigenvalues ​​of the first r orders are selected to form the reduced basis.

3. The method for rapid calculation of transmission tower POD order reduction based on static and dynamic load separation modeling according to claim 2, characterized in that, The energy criterion is expressed as: , r is the order, and m is the number of eigenvector elements. Let argmin be the i-th eigenvalue, and let argmin represent taking the eigenvalue that satisfies The minimum r value, ε represents the maximum percentage threshold of energy that can be cut off from the total energy.

4. The method for rapid calculation of transmission tower POD order reduction based on static and dynamic load separation modeling according to claim 1, characterized in that, Methods for projecting the high-dimensional finite element governing equations of the tower onto a subspace composed of reduced bases to obtain a statically reduced-order model include: Will Substituting the original statics equations, we obtain the first equation. ;in It is a static reduction base. For permanent load vectors, , These are the full-order displacement vector and the reduced-order displacement vector of the permanent load, respectively, and K is the full-order stiffness matrix; Multiply both sides of the first equation to the left by... By projecting the first equation onto an r-dimensional reduced-order space, a static reduced-order model is obtained. .

5. The method for rapid calculation of transmission tower POD order reduction based on static and dynamic load separation modeling according to claim 1, characterized in that, Methods for obtaining a reduced-order dynamic model by projecting the high-dimensional finite element governing equations of the tower onto a subspace composed of reduced bases include: Will , and Substituting into the second-order ordinary differential equations of dynamics, we obtain the second equation. ; For dynamic shrinkage base, , , , , , Let M, C, and K be the full-order displacement vector, full-order velocity vector, full-order acceleration vector, reduced-order displacement vector, reduced-order velocity vector, and reduced-order acceleration vector of the wind load, respectively; and let M, C, and K be the full-order mass matrix, full-order damping matrix, and full-order stiffness matrix, respectively. Multiply both sides of the second equation to the left by... By projecting the second equation onto an r-dimensional reduced-order space, we obtain a dynamical reduced-order model. .

6. The method for rapid calculation of transmission tower POD order reduction based on static and dynamic load separation modeling according to claim 1, characterized in that, For new variable load conditions, methods for obtaining generalized coordinates of the dynamic load condition by solving the reduced-order dynamic model based on the obtained static displacement state include: Reduced mass matrix through dynamic reduction model Reduced-order damping matrix and reduced stiffness matrix Calculate the reduced-order effective stiffness matrix ; Set initial speed Set the initial displacement based on the static displacement state. ; Solve for the initial acceleration using the equation of motion at t=0. ; Calculate all constants based on the selected integration parameters and time step Δt. ~ ; Iterative solution is performed step by step, iteratively utilizing the time-step data. This forms a generalized coordinate system for dynamic operating conditions.

7. The method for rapid calculation of transmission tower POD order reduction based on static and dynamic load separation modeling according to claim 6, characterized in that, When iterating step-by-step, the calculation method for each time step includes: Using the known state at time t and the reduced-order wind load vector at time t+Δt Calculate the reduced-order effective wind load vector The known states include displacements. ,speed acceleration ; Solving for the reduced displacement at time t+Δt ; Update the acceleration and velocity at time t+Δt; Update the known state and proceed to the next time step for calculation.

8. The method for rapid calculation of transmission tower POD order reduction based on static and dynamic load separation modeling according to claim 1, characterized in that, Methods for obtaining the structural displacement response of towers under typical working conditions with permanent and variable loads, and constructing corresponding snapshot matrices, include: Calculate the permanent load on the tower; after applying the permanent load to the tower, obtain the static displacement vector of the corresponding node through static analysis of multiple load steps; combine the static displacement vectors in the order of load steps to obtain the static snapshot matrix representing the permanent load; The standard value for determining wind load is ,in As the reference wind pressure, This is the wind pressure height variation coefficient. This is the body size coefficient. For wind vibration coefficient, This is the factor that amplifies the wind load on tower components due to icing. The projected area of ​​the windward component is given; a representative parameter combination is selected to perform dynamic analysis of the wind load on the tower, and the dynamic displacement vector at each moment under each working condition is obtained; the dynamic displacement vectors are combined in the order of time steps to obtain a dynamic snapshot matrix representing the variable load.

9. The method for rapid calculation of transmission tower POD order reduction based on static and dynamic load separation modeling according to claim 1, characterized in that, The permanent loads include the structure's self-weight, the weight of auxiliary equipment, and the static load of the conductor; the variable loads include wind loads.

10. The method for rapid calculation of transmission tower POD order reduction based on static and dynamic load separation modeling according to claim 8, characterized in that, The calculated permanent load is g is the acceleration due to gravity, m is the mass per unit length of the conductor, L is the length of the conductor, λ is the load factor, and c is the total mass of the auxiliary equipment. , and These are the spans on both sides of the tower. and These represent the height difference between the hanging points on both sides of the tower.

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