A method and system for solving parameters of a transverse shock absorption system of a large-span bridge in a mountainous area

Abstract

The present application relates to a kind of mountainous large-span bridge transverse damping system parameter solving method and system, method includes: obtaining bridge structure, establish spatial finite element model, obtain target design displacement, set the initial damping parameter of each position damper of bridge;Actual displacement is calculated based on the damping parameter at this time, and the adjusted vector of damper is obtained according to the difference between target design displacement and actual displacement, combined with adjusted vector and influence matrix, calculate the application vector, the adjusted damping parameter is calculated based on application vector, it is judged whether the adjusted damping parameter satisfies design requirement, if satisfy, then the adjusted damping parameter is regarded as final damping parameter, otherwise, repeat this step.Compared with prior art, the basic principle of influence matrix is used, the multi-tower / pier coupling effect in transverse damping system and the strong nonlinear behavior of damping measure are considered, and the reasonable design parameters of damping system at each tower / pier position can be determined by the iterative calculation of fast and stable convergence.

Description

Technical Field

[0001] This invention relates to the field of vibration reduction technology for bridge engineering structures, and in particular to an efficient solution method and system for determining the design parameters of the vibration reduction system at each tower / pier location on a long-span bridge in mountainous areas. Background Technology

[0002] A new peak in bridge construction has emerged. Due to mountainous and hilly terrain, and numerous deeply eroded river valleys, there is a high demand for long-span bridges with single spans ranging from 100m to 400m. Commonly used bridge types include long-span continuous beam bridges, arch bridges, and single-tower cable-stayed bridges. However, frequent strong earthquakes and the significant risk of seismic disasters pose serious challenges to the design and construction of these bridges. Compared to medium and small-span bridges, long-span bridges have higher beam heights, larger superstructure mass, and greater inertial force response under seismic loading. More importantly, due to the influence of mountainous, hilly, and valley terrain, the pier heights of the substructure of these long-span bridges often vary greatly. Since the lateral stiffness of a pier is inversely proportional to the cube of its height, the lateral restraint stiffness at each tower / pier location often differs by orders of magnitude. This difference leads to a highly irregular distribution of the overall lateral stiffness of the structure, resulting in a very unfavorable response state under seismic dynamic loading.

[0003] Numerous studies have shown that in high-intensity seismic zones, attempting to resist seismic forces by increasing pier size and reinforcement is neither economical nor feasible. Appropriate seismic isolation and damping measures are needed to establish a seismic isolation and damping mechanism. However, unlike longitudinal seismic loading where the seismic response of the main girder at each tower / pier location is generally consistent, lateral seismic loading results in different amplitudes and potentially significant differences in frequency characteristics at each tower / pier location. This is particularly true for bridges located in mountainous areas with significant differences in tower / pier height. Consequently, the response of seismic isolation and damping measures varies considerably. Therefore, a reasonable seismic isolation and damping system should employ different design parameters at each tower / pier location to adapt to and balance the impact of these pier height differences.

[0004] Because the main beams at each tower and pier location require lateral restraint under normal operating loads, displacement-dependent dampers are commonly used for lateral vibration reduction in bridges. Niu et al. proposed a design method using displacement response as the design control objective for a transverse vibration reduction system using steel dampers in cable-stayed bridges. Camara et al. determined the maximum damping force of viscous dampers and the yield force of steel dampers by measuring the critical cracking force of concrete at the base of the main tower of a cable-stayed bridge, and proposed an approximate design method based on an equivalent single degree of freedom. However, for bridges with significant differences in pier height in mountainous areas, their seismic response cannot be equivalent to a single degree of freedom. Wen et al. explored the reasonable damper parameter setting range for a lateral vibration reduction system using triangular steel dampers in long-span cable-stayed bridges based on component damage probability analysis. In actual long-span bridge projects, such as the Lanzhou Xigu Yellow River Bridge, Yongning Yellow River Bridge, Ningbo Chunxiao Bridge, Yinchuan Binhe Yellow River Bridge, Zhangshu Ganjiang Second Bridge, Lanzhou Chaijiaxia Yellow River Bridge, Shanghai Kunyang Road River-Crossing Bridge, and Guangxi Xiangsi Island Bridge, the approximate optimal values ​​of damping parameters were calculated using a parameter sensitivity analysis method based on preset multi-condition scenarios. Shen et al. further focused on the vibration reduction and energy dissipation device of triangular steel plate dampers, combining numerical software programming with a fully exhaustive method to calculate the reasonable design parameters of the damper.

[0005] It should be noted that due to the influence of the lateral flexibility of the main girder, there is a significant coupling effect in the seismic response at each tower / pier location in the transverse seismic resistance system of the bridge. In other words, the design parameters of the damping measures at each tower / pier location are not independent variables. In addition, the damping measures exhibit strong nonlinear behavior under strong earthquakes. The parameter sensitivity analysis method based on the exhaustive method can better consider these coupling effects and strong nonlinear behaviors. However, since the reasonable design parameters of the damping measures at each tower / pier location are not uniform, and the damping measures themselves often have multiple design parameters and a large range of parameter values, this method requires a large number of parameter case combination calculations. Furthermore, the so-called optimal solution can only be selected from all the preset parameter case combinations. Therefore, it can only be an approximate solution of reasonable design parameters and cannot directly obtain the optimal solution.

[0006] It is evident that the differences in pier heights caused by the terrain of long-span bridges in mountainous areas objectively require the corresponding seismic isolation system to select different seismic isolation design parameters at each tower / pier location. However, the current equivalent single-degree-of-freedom algorithm based on bridges with equal pier heights is not applicable, while the parameter sensitivity analysis method based on the exhaustive method principle is inefficient and can only obtain approximate solutions. Therefore, there is an urgent need for an efficient algorithm that can obtain the optimal solution. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a method and system for solving the parameters of the transverse damping system of long-span bridges in mountainous areas. This method avoids the problems of low computational efficiency and only being able to obtain approximate solutions caused by the multi-tower / pier coupling effect in the transverse damping system and the strong nonlinear behavior of damping measures in traditional parameter analysis methods.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] According to a first aspect of the present invention, a method for solving the parameters of a lateral damping system for a long-span bridge in mountainous areas is provided, comprising:

[0010] Obtain the bridge structure, establish a spatial finite element model, obtain the target design displacement, and set the initial damping parameters of the dampers at various locations on the bridge.

[0011] Based on the damping parameters at this time, the actual displacement is calculated using a spatial finite element model. The damper's adjustment vector is obtained based on the difference between the target design displacement and the actual displacement. The adjustment vector is then calculated by combining the adjustment vector with the influence matrix of the damping parameters at this time. The adjusted damping parameters are then calculated based on the adjustment vector. It is then determined whether the adjusted damping parameters meet the design requirements. If they do, the adjusted damping parameters are used as the final damping parameters. Otherwise, this step is repeated.

[0012] Furthermore, determining whether the adjusted damping parameters meet the design requirements involves the following steps:

[0013] The adjusted damping parameters are used to calculate the adjusted actual displacement using a spatial finite element model. The relative error between the target design displacement and the adjusted actual displacement is calculated. If the relative error is not greater than a preset threshold, the adjusted damping parameters meet the design requirements.

[0014] Furthermore, the preset threshold is 1%.

[0015] Furthermore, the influence matrix is ​​as follows: The influence vector of the damper at each location { δ j The matrix formed by}

[0016]

[0017]

[0018] in, The number of locations where dampers are installed on a bridge affects the vector { δ j} is the first j Caused by a unit change in the damper parameters at a given location m The change in damper displacement at each location.

[0019] Furthermore, the modulated vector { }for The target design displacement of the damper at each location { } and its actual displacement { The difference between}

[0020]

[0021] in, =0, 1, 2, ... This is used to represent the actual displacement corresponding to the initial damping parameters of the dampers at various locations on the bridge, as well as the actual displacement corresponding to the adjusted damping parameters.

[0022] Furthermore, the modulation vector { }for The damping parameters of the damper at each location are adjusted relative to the initial damping parameters:

[0023]

[0024] in, For the influence matrix, It is the modulated vector.

[0025] Furthermore, the adjusted damping parameters are as follows:

[0026]

[0027] in, Used to indicate the initial and adjusted damping parameters of the dampers at various locations on the bridge.

[0028] Furthermore, the damping parameter of the damper is the yield force, and the initial damping parameters of the dampers at various locations on the bridge are specifically set as follows:

[0029] The initial yield force of each damper { Q 0} is set to 10%{ V},in,{ V} represents the seismic shear force vector at each tower / pier location in the laterally fixed system.

[0030] Furthermore, when solving the influence matrix, a certain range of amplitude is used at the corresponding yield force. Q n , Q n + ΔQ The secant compliance within the matrix is ​​used instead of the tangent compliance to obtain a relatively stable influence matrix, where ΔQ Take 3% { V}

[0031] A system for solving the parameters of a lateral damping system for long-span bridges in mountainous areas, based on the method for solving the parameters of a lateral damping system for long-span bridges in mountainous areas as described in the first aspect of this invention, includes:

[0032] Initialize the module, obtain the bridge structure, establish a spatial finite element model, obtain the target design displacement, and set the initial damping parameters of the dampers at various locations on the bridge.

[0033] The solution module calculates the actual displacement using a spatial finite element model based on the damping parameters at this time. It obtains the damper's adjustment vector based on the difference between the target design displacement and the actual displacement. Combining the adjustment vector and the influence matrix of the damping parameters at this time, it calculates the applied adjustment vector. Based on the applied adjustment vector, it calculates the adjusted damping parameters and determines whether the adjusted damping parameters meet the design requirements. If they do, the adjusted damping parameters are used as the final damping parameters; otherwise, this step is repeated.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] 1) Based on the fundamental principle of the influence matrix, considering the multi-tower / pier coupling effect in the transverse damping system and the strong nonlinear behavior of damping measures, the reasonable design parameters of the damping system at each tower / pier location are determined through iterative calculations with fast, stable convergence.

[0036] 2) Select initial damper design parameters that have the same distribution law as reasonable damper design parameters to reduce the number of iterative calculations, and select appropriate yield force secant amplitude to achieve stable convergence. Attached Figure Description

[0037] Figure 1 It is a typical long-span single-tower cable-stayed bridge in mountainous areas;

[0038] Figure 2 This is a diagram showing the mass distribution of the main girder and the stiffness distribution of the system.

[0039] Figure 3 A flowchart for the calculation of the influence matrix;

[0040] Figure 4 A comparison diagram of the yield force of the reasonable dampers at each tower / pier location of the bridge and the shear force of the fixed system support.

[0041] Figure 5 This is a diagram illustrating the iterative process of secant amplitudes for different yield forces. Detailed Implementation

[0042] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are implemented based on the technical solutions of the present invention, providing detailed implementation methods and specific operating procedures. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them, and the scope of protection of the present invention is not limited to the following embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0043] The term "an embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the invention. In the description of the invention, it should be understood that the terms "first," "second," and "third," etc., in the specification, claims, and accompanying drawings are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0044] This specification provides method operation steps as shown in the embodiments or flowcharts, but based on conventional or non-inventive labor, more or fewer operation steps may be included. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only execution order. In actual system or server products, the method can be executed in the order shown in the embodiments or drawings, or in parallel (e.g., in a parallel processor or multi-threaded processing environment), or the execution order of steps without timing constraints can be adjusted.

[0045] This invention provides a method for solving the parameters of a transverse damping system for long-span bridges in mountainous areas, including:

[0046] Obtain the bridge structure, establish a spatial finite element model, obtain the target design displacement, and set the initial damping parameters of the dampers at each location on the bridge. Based on the damping parameters at this time, calculate the actual displacement through the spatial finite element model. Obtain the damper's adjustment vector according to the difference between the target design displacement and the actual displacement. Calculate the applied adjustment vector by combining the adjusted vector and the influence matrix of the damping parameters at this time. Calculate the adjusted damping parameters based on the applied adjustment vector. Determine whether the adjusted damping parameters meet the design requirements. If they do, use the adjusted damping parameters as the final damping parameters; otherwise, repeat this step.

[0047] Figure 1The image shows a typical long-span single-tower cable-stayed bridge in a mountainous area, with the main bridge spans arranged as 340m + 72m + 48m + 32m. Figure 2 The figure shows the distribution of the main beam mass and system stiffness. Table 1 shows the displacement, acceleration, and support shear force of the main beam at each pier / tower location under a laterally fixed system. It can be seen that the distribution of structural mass, stiffness, and various response quantities is significantly non-uniform.

[0048] Table 1 Structural Lateral Seismic Response

[0049]

[0050] In this embodiment, the flowchart of the solution method is as follows: Figure 3 As shown.

[0051] (1) Obtain the structure of long-span bridges in mountainous areas and establish a spatial finite element model;

[0052] (2) Obtain the target design displacement. The target design displacement is the displacement requirement that needs to be achieved according to the engineering requirements. It can be set as needed.

[0053] (3) Set the initial damping parameters of the dampers at each location on the bridge;

[0054] The damping parameter of the damper is the yield force.

[0055] (4) Calculate the initial damping parameters of the damper { Q The initial actual displacement corresponding to 0} };

[0056] The initial damping parameters { Q Substituting 0} into the established spatial finite element model, the corresponding initial actual displacement { is obtained through simulation. };

[0057] (5) Obtain the damper's tuning vector based on the difference between the target design displacement and the actual displacement;

[0058] The modulated vector { }for The target design displacement of the damper at each location { } and its actual displacement { The difference between}

[0059]

[0060] in, =0, 1, 2, ... This is used to represent the actual displacement corresponding to the initial damping parameters of the dampers at various locations on the bridge, as well as the actual displacement corresponding to the adjusted damping parameters.

[0061] (6) Calculate the applied adjustment vector by combining the adjusted vector and the influence matrix of the damping parameters at this time;

[0062] The application vector { }for The damping parameters of the damper at each location are adjusted relative to the initial damping parameters:

[0063]

[0064] in, For the influence matrix, It is the modulated vector.

[0065] The influence matrix is The influence vector of the damper at each location { δ j A matrix formed by arranging the elements in sequence:

[0066]

[0067]

[0068] in, The number of locations where dampers are installed on a bridge affects the vector { δ j} is the first j Caused by a unit change in the damper parameters at a given location m The change in damper displacement at each location.

[0069] (7) The adjusted damping parameters are calculated based on the applied adjustment vector;

[0070] The adjusted damping parameters are:

[0071]

[0072] in, Used to indicate the initial and adjusted damping parameters of the dampers at various locations on the bridge.

[0073] (8) Determine whether the adjusted damping parameters meet the design requirements. If they do, use the adjusted damping parameters as the final damping parameters. Otherwise, repeat step (5).

[0074] Specifically, determining whether the adjusted damping parameters meet the design requirements involves:

[0075] Based on the adjusted damping parameters, the adjusted actual displacement is calculated using a spatial finite element model. The relative error between the target design displacement and the adjusted actual displacement is calculated. If the relative error is not greater than a preset threshold, the adjusted damping parameters meet the design requirements. In this embodiment, based on experience, the preset threshold is 1%. In specific implementations, the threshold can be set according to experience, or other conditions can be used to determine whether the adjusted damping parameters meet the design requirements. Of course, in other implementations, a maximum number of iterations can be set. If the maximum number of iterations is reached or the damping parameters have remained essentially unchanged in the most recent K iterations, the iteration stops, and the damping parameters at this point are output as the final damping parameters.

[0076] Since the seismic response of a real structural damping system is a complex nonlinear process, and the influence matrix is ​​not a constant matrix, multiple iterations are required until the actual displacement meets the target displacement requirements.

[0077] To achieve rapid and stable convergence of the above iterative process, the initial yield force and influence matrix of the damper are solved according to the following requirements:

[0078] 1) Initial yield force of the damper { Q There are several ways to choose {0}. Since the actual displacement-yield force curve is not an ideally smooth curve, it exhibits strong fluctuations at the yield force of {0}, thus potentially yielding a negative yield force {0}. Q 1}, but the actual displacement-yield force curves of the dampers at various locations are basically only within 0~10%. V Significant fluctuations occurred within the specified section; therefore, the initial yield force of each damper was adjusted. Q 0} is set to 10%{ V} can significantly enhance the stability of damper yield force calculation, where, { V} represents the seismic shear force vector at each tower / pier location in the laterally fixed system. In this embodiment, the initial yield force of each damper is taken as { Q 0} is 10%{ V},in{ V}={11238.4, 54701.4, 2003.9, 4712.2, 31051.6} (kN).

[0079] 2) The influence matrix of damper yield force at each location { δ Theoretically, the yield force can be taken as {} for solving the problem. Q n The tangent compliance at the yield force is not stable due to the nonlinearity of the structure and the randomness of seismic action, which is not conducive to the fast convergence of the algorithm. Therefore, a certain range of amplitude at the corresponding yield force is adopted. Q n ,Q n + ΔQ The secant flexibility within the matrix is ​​used instead of the tangent flexibility to obtain a relatively stable influence matrix. In this embodiment, ΔQ Take 3% { V},in{ V}={11238.4, 54701.4,2003.9, 4712.2, 31051.6} (kN).

[0080] After the above calculations, the reasonable design parameters of the steel damper that are consistent with the calculated displacement and the target displacement can be obtained, as shown in Table 2.

[0081] Table 2. Rational Design Parameters for Steel Dampers

[0082]

[0083] Figure 4 The figure shows the final reasonable yield force and initial yield force of the steel dampers at each tower / pier location, i.e., the support shear force of the 10% transversely fixed system. It can be seen that the overall distribution pattern of the two is consistent and the difference is small, which shows that the initial yield force adopted in this invention is very reasonable.

[0084] Figure 5 The figure shows the secant amplitude. ΔQ Take 1% respectively V 2% V 3% V 4% V 5% V A comparative analysis of the stability and convergence speed of iterative calculations under various working conditions is presented. The figure shows that when the secant amplitude... ΔQ Take 1% V At that time, the iterative process produces a divergence phenomenon; when the secant amplitude... ΔQ Take 2% ～ 4% V At that time, the iterative process was stable and converged rapidly, with 3% of the time being... V The corresponding number of iterations is the fewest; while when the secant amplitude is... ΔQ Increase to 5% V Although convergence is possible, the error is larger than that of the target displacement, which shows that the secant amplitude used in this invention has the characteristics of stable and fast convergence.

[0085] It is understandable that although this invention was proposed to solve the problem of solving the design parameters of the vibration reduction system for long-span bridges in mountainous areas, similarly, this invention is also applicable to bridges on non-flat terrain that require lateral vibration reduction and isolation design. Applicable bridge types include long-span continuous beam bridges, cable-stayed bridges, and multi-span arch bridges, and applicable damper types include all displacement-dependent, velocity-dependent, acceleration-dependent, and related combinations.

[0086] The beneficial effects of this invention are as follows:

[0087] 1) For continuous multi-span, multi-tower / pier long-span bridges, the computational workload can be significantly reduced compared to traditional parameter sensitivity analysis methods;

[0088] 2) It can fully consider the coupling effect between multiple towers / piers in the transverse damping system of long-span bridges in mountainous areas and the strong nonlinear behavior of damping measures to obtain the optimal solution;

[0089] 3) By adopting the suggested initial yield force value and the yield force secant amplitude of the influence matrix, stable and fast convergence can be obtained.

[0090] This invention also provides a system for solving the parameters of the lateral damping system of long-span bridges in mountainous areas, based on the above-mentioned method for solving the parameters of the lateral damping system of long-span bridges in mountainous areas, including:

[0091] The initialization module acquires the structure of a long-span bridge in a mountainous area, establishes a spatial finite element model, obtains the target design displacement, and sets the initial damping parameters of the dampers at various locations on the bridge.

[0092] The solution module calculates the actual displacement using a spatial finite element model based on the damping parameters at this time. It obtains the damper's adjustment vector based on the difference between the target design displacement and the actual displacement. Combining the adjustment vector and the influence matrix of the damping parameters at this time, it calculates the applied adjustment vector. Based on the applied adjustment vector, it calculates the adjusted damping parameters and determines whether the adjusted damping parameters meet the design requirements. If they do, the adjusted damping parameters are used as the final damping parameters; otherwise, this step is repeated.

[0093] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the described module can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0094] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for solving the parameters of a transverse damping system for a long-span bridge in mountainous areas, characterized in that, include: Obtain the bridge structure, establish a spatial finite element model, obtain the target design displacement, and set the initial damping parameters of the dampers at various locations on the bridge. Based on the damping parameters at this time, the actual displacement is calculated using a spatial finite element model. The damper's adjustment vector is obtained based on the difference between the target design displacement and the actual displacement. The adjustment vector is then calculated by combining the adjustment vector and the influence matrix of the damping parameters at this time. The adjusted damping parameters are then calculated based on the adjustment vector. It is then determined whether the adjusted damping parameters meet the design requirements. If they do, the adjusted damping parameters are used as the final damping parameters. Otherwise, this step is repeated. The influence matrix is ​​as follows: The influence vector of the damper at each location { δ j The matrix formed by} in, The number of locations where dampers are installed on a bridge affects the vector { δ j } is the first j Caused by a unit change in the damper parameters at a given location m The change in damper displacement at each location; The modulated vector { }for The target design displacement of the damper at each location { } and its actual displacement { The difference between} in, =0, 1, 2, ... Used to represent the actual displacement corresponding to the initial damping parameters of the dampers at various locations on the bridge, and the actual displacement corresponding to the adjusted damping parameters. The application vector { }for The damping parameters of the damper at each location are adjusted relative to the initial damping parameters: in, For the influence matrix, It is the modulated vector.

2. The method for solving the parameters of a transverse damping system for a long-span bridge in mountainous areas according to claim 1, characterized in that, To determine whether the adjusted damping parameters meet the design requirements, the following steps are taken: The adjusted damping parameters are used to calculate the adjusted actual displacement using a spatial finite element model. The relative error between the target design displacement and the adjusted actual displacement is calculated. If the relative error is not greater than a preset threshold, the adjusted damping parameters meet the design requirements.

3. The method for solving the parameters of a transverse damping system for a long-span bridge in mountainous areas according to claim 2, characterized in that, The preset threshold is 1%.

4. The method for solving the parameters of a transverse damping system for a long-span bridge in mountainous areas according to claim 1, characterized in that, The adjusted damping parameters are: in, Used to indicate the initial and adjusted damping parameters of the dampers at various locations on the bridge.

5. The method for solving the parameters of a transverse damping system for a long-span bridge in mountainous areas according to claim 1, characterized in that, The damping parameter of the damper is the yield force. The initial damping parameters of the dampers at various locations on the bridge are set as follows: The initial yield force of each damper { Q 0} is set to 10%{ V },in,{ V } represents the seismic shear force vector at each tower / pier location in the laterally fixed system.

6. The method for solving the parameters of a transverse damping system for a long-span bridge in mountainous areas according to claim 5, characterized in that, When solving the influence matrix, a certain range of amplitude is used at the corresponding yield force. Q n , Q n + ΔQ The secant compliance within the matrix is ​​used instead of the tangent compliance to obtain a relatively stable influence matrix, where ΔQ Take 3% { V } 7. A parameter solution system for a transverse damping system of a long-span bridge in mountainous areas, characterized in that, The method for solving the parameters of the transverse damping system for long-span bridges in mountainous areas, as described in any one of claims 1-6, includes: Initialize the module, obtain the bridge structure, establish a spatial finite element model, obtain the target design displacement, and set the initial damping parameters of the dampers at various locations on the bridge. The solution module calculates the actual displacement using a spatial finite element model based on the damping parameters at this time. It obtains the damper's adjustment vector based on the difference between the target design displacement and the actual displacement. Combining the adjustment vector and the influence matrix of the damping parameters at this time, it calculates the applied adjustment vector. Based on the applied adjustment vector, it calculates the adjusted damping parameters and determines whether the adjusted damping parameters meet the design requirements. If they do, the adjusted damping parameters are used as the final damping parameters; otherwise, this step is repeated.

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