Parameter optimization method of inerter damper for double-layer three-span subway station vibration reduction

Abstract

This invention discloses a parameter optimization method for inertial capacitive dampers used for vibration reduction in double-layer, three-span subway stations, belonging to the field of vibration control technology. By establishing a refined soil-structure-TID coupled finite element model, defining a multi-objective optimization function, selecting and inputting ground motion records as input for optimization analysis, applying a genetic algorithm for multi-objective parameter optimization, nested system dynamic time history analysis, and engineering decision-making based on Pareto fronts, the method comprehensively verifies and analyzes the vibration reduction and isolation performance. The complete technical process, from refined modeling, multi-objective function definition, ground motion set input, intelligent algorithm optimization to comprehensive verification and analysis, guides seismic energy towards self-dissipation, effectively protecting the main structure of the station. It fills the gap in refined optimization methods for TID parameters of complex underground structures. The optimization objectives directly correspond to the inter-story drift angle and floor acceleration, which are of most concern in engineering, and provide visual decision support through Pareto fronts, making the optimization results easily adoptable in engineering practice.

Description

Technical Field

[0001] This invention relates to a method for optimizing the parameters of an inertial capacitive damper, and more particularly to a method for optimizing the parameters of an inertial capacitive damper suitable for vibration reduction in double-layer, three-span subway stations in urban rail transit networks, belonging to the field of vibration control technology. Background Technology

[0002] With the rapid development of urban rail transit networks, double-layer, three-span subway stations have become a common station structure in urban underground transportation systems. These stations typically consist of a top slab, middle slab, bottom slab, side walls, and central columns, characterized by large spans, complex spatial divisions, concentrated stress on vertical components, and high density of personnel and equipment. When seismic forces caused by subway entry and exit are transmitted to the underground structure, double-layer, three-span subway stations not only bear the overall dynamic forces caused by the deformation of the surrounding soil, but also experience significant inter-story relative deformation and localized internal force concentration in the connection areas of the central columns, floor slabs, and side walls. In particular, significant damage to the connection nodes between the central columns and floor slabs can easily affect the overall stability of the station's main structure and its post-earthquake operational functionality.

[0003] Existing seismic designs for double-layer, three-span subway stations largely rely on the strength of the main structure, the ductility of components, and conventional structural measures to resist earthquakes. However, under strong earthquakes or complex site conditions, relying solely on the structure's own energy dissipation can easily lead to problems such as excessive deformation of the central column, significant floor slab acceleration response, difficulty in repairing damaged components, and interruption of station function. This makes it difficult to meet the engineering requirements for rapid recovery and continuous operation of subway stations after an earthquake. Therefore, for the specific underground frame structure of double-layer, three-span subway stations, there is an urgent need for a seismic mitigation parameter design method that can reduce inter-story deformation, decrease floor slab dynamic response, and take into account the feasibility of structural installations.

[0004] A tuned inertial-capacitive damper is a vibration reduction device composed of a spring, a damper, and an inertial container. It combines tuned vibration reduction with inertial enhancement, transferring the vibration energy of the main structure to the damping device for dissipation through parameter matching, thereby reducing the seismic response of the structure. However, when tuned inertial-capacitive dampers are used in double-layer, three-span subway stations, empirical parameters from above-ground structures or simplified single-degree-of-freedom structures cannot be directly applied. This is because the double-layer, three-span subway station and the surrounding soil form a soil-structure dynamic interaction system. Soil constraints, station burial conditions, the arrangement of the two-layer, three-span frame, and the stress characteristics of the column-floor connection nodes all affect the dominant vibration characteristics of the structure.

[0005] Specifically, the damping performance of a tuned inertial-capacitive damper is highly dependent on its stiffness. Damping coefficient Inertia Precise matching of the three core parameters is crucial. If the parameter values ​​are too small, it will be difficult to effectively absorb the vibration energy of the main structure of a double-layer, three-span subway station. If the parameter values ​​are too large, it may lead to excessive output at the TID connection nodes, increasing the risk of local stress in the connection areas of the central column, floor slab, or side wall. If the tuning parameters do not match the dominant frequency of the station after soil-structure coupling, it may weaken the damping effect or even cause amplification of local dynamic response. At the same time, the damping design of a double-layer, three-span subway station not only needs to control the maximum inter-story drift angle, but also needs to control the absolute acceleration of the top slab, middle slab, and bottom slab, and limit the output of the TID itself. This makes the TID parameter design a multi-objective constrained optimization problem.

[0006] Furthermore, the input of ground motion has significant uncertainties. Differences in the spectral characteristics, peak acceleration, and duration of different ground motion records can lead to different dynamic responses in a two-level, three-span subway station. It is difficult to guarantee the stability and robustness of the optimization results in actual engineering if the TID parameters are determined based on a single ground motion or a single control index. Summary of the Invention

[0007] Technical Problem: The purpose of this invention is to overcome the shortcomings of existing technologies and provide a parameter optimization method for inertial capacitive dampers used for vibration reduction in double-layer, three-span subway stations. This method utilizes a soil-structure-TID coupled finite element model, considering indicators such as maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output, to achieve TID stiffness. Damping coefficient Inertia The synergistic optimization of the system can improve the structural safety, equipment operation stability, and post-earthquake functional recovery capability of double-layer, three-span subway stations under seismic loads.

[0008] Technical solution: The present invention provides a method for optimizing the parameters of an inertial capacitive damper for vibration reduction in a double-layer, three-span subway station, comprising the following steps:

[0009] S1. Establish a refined soil-structure-TID coupled finite element model.

[0010] Based on the construction design drawings and geotechnical investigation report of the double-layer, three-span subway station, modeling data was extracted. From the construction design drawings, the axial position, total width, total height, top slab thickness, middle slab thickness, bottom slab thickness, side wall thickness, central column cross-sectional dimensions, central column spacing, left span clear span dimensions, middle span clear span dimensions, right span clear span dimensions, concrete material parameters of each component, and TID installation node locations of the station's main structure were extracted. From the geotechnical investigation report, the soil layer thickness, density, elastic modulus, Poisson's ratio, cohesion, internal friction angle, and damping ratio of the soil surrounding the station were extracted. Using ABAQUS finite element software, a model of the main structure of the double-layer, three-span subway station, a model of the soil surrounding the station, and a TID connection unit model were established to form an overall TID model. Simultaneously, ABAQUS finite element software was used to establish the double-layer, three-span subway station main structure model, the model of the soil surrounding the station, and the TID connection unit model. A TID (Transient Inertial Device) model is formed by combining the main structure model of the subway station and the surrounding soil model. The main structure of the double-layer, three-span subway station is an underground two-layer, three-span frame structure composed of a top slab, middle slab, bottom slab, two side walls, and a central column. The two ends of the TID are connected between nodes of adjacent structural members on the same floor. One end is connected to the intersection node of the central column and the floor slab, and the other end is connected to the intersection node of the side wall and the floor slab on the same floor or the intersection node of the adjacent central column and the floor slab. The TID is arranged along the lateral force direction of the station. A series of spring-damped-inertial container combined units are used to simulate the TID. The spring-damped-inertial container combined units are used to simulate the interaction of the TID between the nodes of the main structure of the double-layer, three-span subway station. The input parameters of the spring-damped-inertial container combined units include the TID stiffness k. tid TID damping coefficient c tid and TID inertial mass m tid Where the TID stiffness k tid The TID damping coefficient c is used to control the restoring force generated by the relative displacement between the two ends of the TID connection unit. tid The energy dissipation capability used to control the relative velocity between the two nodes of the TID connection unit, TID inertial mass m tid The inertial enhancement effect generated by the relative acceleration between the two nodes of the TID connection unit is used to control the dynamic response of the soil, the dynamic response of the station main structure and the TID vibration reduction response. This results in a refined soil-structure-TID coupled finite element model that simultaneously calculates the dynamic response of the soil, the dynamic response of the station main structure and the TID vibration reduction response.

[0011] S2. Define the multi-objective optimization function.

[0012] Using the refined soil-structure-TID coupled finite element model established in step S1 as the analysis object, a set of TID parameter combinations is used as the input variables for a first optimization calculation. The TID parameter combination includes the TID stiffness k. tid TID damping coefficient c tid and TID inertial mass m tidAfter assigning the set of TID parameters to the spring-damped-inertial container combined unit in step S1, the seismic dynamic response is calculated. From the calculation results, three target values ​​are extracted: maximum inter-story drift angle, maximum story absolute acceleration, and maximum TID output force. The following multi-objective optimization function is established:

[0013] ;

[0014] Where X represents the TID parameter vector, f1(X) represents the objective function of the maximum inter-story drift angle, f2(X) represents the objective function of the maximum floor absolute acceleration, and f3(X) represents the objective function of the maximum TID output. The maximum inter-story drift angle is obtained by dividing the relative inter-story displacements of the first and second floors of the double-layer three-span subway station under seismic action by the corresponding floor heights and taking the maximum value. It is used to characterize the deformation control effect of the double-layer three-span subway station main frame. The maximum floor absolute acceleration is obtained by taking the maximum value of the absolute acceleration time histories of the top slab, middle slab, and bottom slab representative nodes. It is used to characterize the strength of the dynamic response of the station floor slab, station equipment, and personnel environment. The maximum TID output is obtained by taking the maximum value of the output time histories of the TID connection units. It is used to characterize the engineering stress level of the TID device and its connection nodes.

[0015] The multi-objective optimization function is defined by simultaneously minimizing the three objectives of maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output. This transforms structural deformation control, floor acceleration control, and TID device force control into three optimization objectives that can be evaluated and compared by a genetic algorithm.

[0016] S3. Select and input ground motion records as input for optimization analysis.

[0017] The selection criteria for seismic ground motions are determined based on the seismic fortification intensity, site category, and design response spectrum of the location of the double-layer, three-span subway station. Seismic ground motion records with different spectral characteristics are selected from engineering seismic design data, publicly available strong ground motion record databases, or artificial ground motion files generated according to the design response spectrum. Acceleration time history, peak ground acceleration, time interval, and duration information are extracted for each ground motion record. After amplitude adjustment of each ground motion record, a seismic ground motion input set is constructed. This seismic ground motion input set is represented as follows:

[0018] ;

[0019] Where G represents the seismic motion input set, ag1(t), ag2(t), and agn(t) represent the 1st, 2nd, and nth seismic motion acceleration time histories, respectively, t represents time, and n represents the number of seismic motion records. n is set to 6 so that the three optimization objectives are calculated under the same seismic motion input set. Different seismic motion input sets have different spectral characteristics, so as to avoid the optimization results being applicable only to a single seismic motion record.

[0020] S4. Applying genetic algorithms for multi-objective parameter optimization

[0021] Based on a refined soil-structure-TID coupled finite element model, three optimization objectives, and a set of seismic motion inputs, the three parameters of TID stiffness, damping coefficient, and inertia are encoded as chromosomes in a genetic algorithm. The TID stiffness (ktid), TID damping coefficient (ctid), and TID inertia (mtid) are used as parameters to be optimized. A set of TID stiffness, TID damping coefficient, and TID inertia is used as an individual in the genetic algorithm. Each individual corresponds to a computable soil-structure-TID coupled finite element model in step S1. The TID parameter vector is represented as follows:

[0022] ;

[0023] Wherein, ktid represents TID stiffness, ctid represents TID damping coefficient, and mtid represents TID inertia. The parameter value range is determined by the dynamic characteristic analysis results of the station model without TID control in step S1, the allowable range of TID device construction, and the bearing capacity of TID connection nodes. After generating the initial population within this parameter value range, each individual in the initial population is evaluated according to the three optimization objectives. New TID parameter combinations are generated through selection, crossover, and mutation operations, so that the initial population can successively select parameter combinations that have better comprehensive performance in the three objectives of maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output.

[0024] S5. Perform nested system dynamic time history analysis

[0025] In each iteration of the genetic algorithm, the TID stiffness ktid, TID damping coefficient ctid, and TID inertial mass mtid corresponding to the current individual are assigned to the spring-damped-inertial container combined unit established in step S1. Each ground motion record in the ground motion input set formed in step S3 is then input sequentially. Dynamic time history analysis is performed on the updated refined soil-structure-TID coupled finite element model. After the calculation is completed, the inter-story displacement time history of the first and second floors, the absolute acceleration time history of the top plate node, the absolute acceleration time history of the middle plate node, the absolute acceleration time history of the bottom plate node, and the output time history of the TID connection unit are extracted from the ABAQUS output results. Then, according to the definition of the three optimization objectives, the maximum inter-story displacement angle, the maximum floor absolute acceleration, and the maximum TID output are calculated for each ground motion. The average value or envelope value of the three objectives under all ground motion records is returned to the genetic algorithm as the final evaluation result of the TID parameter combination.

[0026] S6. Engineering Decision-Making Based on Pareto Fronts

[0027] Once the genetic algorithm reaches the preset number of iterations or meets the convergence condition, it obtains a non-dominated solution set composed of multiple TID parameter combinations. The non-dominated solution set is compared according to three objectives: maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output. The performance differences of each TID parameter combination are displayed in a three-dimensional target space or a two-dimensional projection plane. Based on the requirements for main structure deformation control, floor acceleration control, and TID connection node output control in the engineering design of a double-layer, three-span subway station, a TID parameter combination that takes into account the three optimization objectives is selected from the non-dominated solution set as the recommended parameter combination for the project.

[0028] S7. Conduct comprehensive verification and mechanism analysis of seismic isolation and vibration reduction performance.

[0029] Ground motion records that did not participate in the multi-objective parameter optimization using the genetic algorithm in step S4 and have different spectral characteristics from the ground motion input set in step S3 were selected as verification ground motion input data. Using ABAQUS software, under the same soil parameters, structural parameters, boundary conditions, ground motion input, and calculation conditions, soil-structure finite element models without TID control, soil-structure-TID coupled finite element models with initial empirical parameter TID, and soil-structure-TID coupled finite element models with the engineering recommended parameter combination TID in step S6 were established and calculated respectively. The maximum inter-story drift angle, maximum absolute floor acceleration, TID output, and structural energy response of the three types of models were compared to verify the seismic isolation effect of the TID parameter combination obtained in step S6 relative to the model without TID control and the initial empirical parameter TID model. The mechanism by which TID transfers and dissipates the vibration energy of the main structure of the double-layer three-span subway station through inertial enhancement, tuned energy absorption, and damping energy dissipation was analyzed.

[0030] In step S1, the underground two-story three-span frame structure includes the lower space between the bottom slab and the middle slab and the upper space between the middle slab and the top slab. The floor numbers are i=1 and i=2, where i=1 represents the lower floor and i=2 represents the upper floor. The maximum subsequent floor is the second floor. The three spans include the left span, the middle span, and the right span formed by the left side wall, the middle column, and the right side wall.

[0031] The TID installation node locations are divided into the intersection nodes of the top of the upper middle column and the top plate, the intersection nodes of the bottom of the upper middle column and the middle plate, the intersection nodes of the top of the lower middle column and the middle plate, and the intersection nodes of the bottom of the lower middle column and the bottom plate; the intersection nodes of the top of the upper middle column and the top plate and the intersection nodes of the top of the lower middle column and the middle plate are preferred as the initial TID layout nodes;

[0032] The expression for the inertial force generated by the inertial container is as follows:

[0033] ;

[0034] in, and The acceleration of the connection nodes at both ends of the TID along the TID layout direction is given. The connection nodes at both ends are determined by the intersection of the central column and the floor slab, the intersection of the side wall and the floor slab on the same floor, or the intersection of the adjacent central column and the floor slab.

[0035] In step S2, the multi-objective optimization function takes the refined soil-structure-TID coupled finite element model established in step S1 as the analysis object, and the top slab, middle slab, bottom slab, and TID connection units in the two-story, three-span underground frame structure as the response extraction objects. After assigning the same set of TID stiffness, damping coefficient, and inertial mass to the spring-damped-inertial container combined unit in step S1 and completing the dynamic time history analysis, the vibration reduction performance of this set of TID parameters is evaluated according to the following three objective functions:

[0036] The objective function is to minimize the maximum inter-story drift angle, as shown in the formula: ,in ;

[0037] in, For floor displacement, For floor height, It is the floor number, and The value is consistent with the floor numbering of the double-layer, three-span subway station. This indicates the lower space between the bottom plate and the middle plate. The upper space between the middle slab and the top slab is represented. Therefore, the maximum inter-story drift angle refers to the response value with the largest absolute value among all inter-story drift angle time histories of the 1st and 2nd floors. The minimization refers to the genetic algorithm prioritizing the parameter combination that makes the maximum inter-story drift angle smaller among different TID parameter combinations, so as to reduce the risk of inter-story deformation damage in the connection area of ​​the middle column, side wall and floor slab.

[0038] Objective function two is to minimize the maximum floor absolute acceleration, formula: The floor absolute acceleration is obtained by extracting the acceleration time histories of the top, middle and bottom representative nodes of the refined soil-structure-TID coupled finite element model in step S1. The maximum floor absolute acceleration refers to the response value that is the largest among all the absolute acceleration time histories of the top, middle and bottom representative nodes. Minimization refers to the genetic algorithm prioritizing the parameter combination that makes the maximum floor absolute acceleration smaller among different TID parameter combinations, so as to reduce the impact of dynamic response on the station floor, station equipment and personnel environment.

[0039] Objective function three is to minimize the maximum damper output, as shown in the formula: The damper output is obtained by extracting the output time history of the TID connection unit in step S1 under the action of seismic input. The maximum damper output refers to the output value with the largest absolute value among all TID connection units and their full-time output response. Minimization means that the genetic algorithm prioritizes the parameter combination that makes the maximum damper output smaller and meets the vibration reduction requirements among different TID parameter combinations, so as to avoid excessive local stress in the TID device and its column-to-floor connection nodes, sidewall-to-floor connection nodes or adjacent component connection nodes. Thus, the three objectives of maximum inter-story drift angle, maximum floor absolute acceleration and maximum damper output correspond to the deformation control of the station main structure, the dynamic response control of the floor and the stress control of the TID project, respectively.

[0040] In step S3, the establishment of the seismic motion input set is based on the double-layer, three-span subway station project site in step S1, and corresponds to the three optimization objectives in step S2: maximum inter-story drift angle, maximum absolute floor acceleration, and maximum TID output. First, the selection criteria for seismic motion records are determined according to the seismic fortification intensity, site category, and design response spectrum of the station location. Then, 5-8 seismic motion records are selected as optimization inputs from the seismic design data of the project, the publicly available strong ground motion record database, or the artificial wave file generated according to the design response spectrum. For each seismic motion record, the acceleration time history, peak acceleration, time interval, and duration should be extracted. The data should be provided, and the source of the data should be noted. The selected ground motion records should cover different spectral characteristics with more obvious low-frequency components, more obvious mid-frequency components, and more obvious high-frequency components. Before inputting the refined soil-structure-TID coupled finite element model established in step S1, the amplitude should be adjusted so that the maximum inter-story drift angle, maximum absolute floor acceleration, and maximum TID output of each set of TID parameters are calculated under the same ground motion input set. This ensures that the optimized TID parameter results are not local results for a single ground motion record, but rather robust solutions with stable damping performance for a two-story, three-span subway station under different ground motion input conditions.

[0041] In step S4, each chromosome contains at least and at most the three TID parameters mentioned above. Each chromosome corresponds to a set of TID parameter combinations that can be assigned to the spring-damped-inertial container unit, and a conflict objective function is constructed based on the structural critical response.

[0042] ;

[0043] In the formula, F(m) tid ,k tid ,c tid () represents a multi-objective evaluation function vector determined by a set of TID parameters, which is also the set of objective functions used by the genetic algorithm to evaluate the combination of TID parameters corresponding to a chromosome. tidThe inertial mass parameter of the TID (Transient Inertial Container) is the equivalent inertial parameter of the container, used to characterize the inertial enhancement effect caused by the relative acceleration of the connecting nodes at both ends of the TID. k tid Indicates the stiffness of the TID, used to characterize the restoring force generated by the relative displacement of the connecting nodes at both ends of the TID, c tid f1(u) represents the TID damping coefficient, used to characterize the damping energy dissipation capacity generated by the relative velocity of the connecting nodes at both ends of the TID. max The first objective function (u) evaluates the maximum inter-story drift angle between the first and second floors of a double-layer, three-span subway station under seismic loading. This function characterizes the effectiveness of the inter-story deformation control of the main structure. max This represents the maximum value of the inter-story drift angle in the time history between the 1st and 2nd floors. Specifically, it is obtained by removing the relative displacement between adjacent floors and taking the maximum absolute value after deducting the corresponding floor height. f2(a max () represents the second objective function, which evaluates the maximum absolute floor acceleration of the nodes represented by the top, middle, and bottom slabs. This acceleration characterizes the strength of the dynamic response experienced by the station floors, station equipment, and personnel environment. max This represents the maximum absolute acceleration values ​​in the time histories of the top, middle, and bottom plate nodes, f3(F TID,max ) represents the third objective function, which evaluates the maximum output force of the TID connection unit and is used to characterize the engineering stress level of the TID device and its connection nodes;

[0044] During the initialization of the population within the range of TID parameter values, the TID stiffness, damping coefficient, and inertia of each individual must not be less than the lower limit of the corresponding parameter and must not be greater than the upper limit of the corresponding parameter. The lower limit and upper limit of the parameter are jointly determined by the dynamic characteristic analysis results of the double-layer three-span subway station without TID control model in step S1, the allowable range of TID device construction, and the bearing capacity of TID connection nodes.

[0045] For each individual in the initial population, dynamic time history analysis was performed using ABAQUS finite element software with all ground motion records input. The fitness evaluation results of the individual were then calculated based on three target values: maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output. Individuals with better comprehensive evaluation were selected through tournament selection. Then, TID parameter information was exchanged between two parent individuals through simulated binary crossover. Finally, new candidate parameter combinations were generated within the parameter value range through polynomial mutation. Non-dominated sorting was used to distinguish the superiority and inferiority levels of different individuals on the three optimization objectives. Crowding distance was used to maintain the uniformity of the distribution of the solution set within the same level, so that the population evolved towards the Pareto front generation by generation.

[0046] Based on the Pareto front and the engineering requirements of a double-layer, three-span subway station, a robust solution is selected. These requirements include reducing the maximum inter-story drift angle of the first and second floors in the double-layer, three-span structure, reducing the maximum absolute floor acceleration of the top, middle, and bottom slabs, and limiting the maximum output of the TID connection unit. This ensures that the TID can still work with the main structure to achieve the vibration reduction target under parameter fluctuations. ,in The weighting factor is used to represent the relative importance of the three objectives—maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output—in the engineering decision-making stage, and the use of the weighting factor does not change the definition of the three optimization objectives in step S2.

[0047] In step S5, when evaluating any TID parameter combination X, the genetic algorithm first considers the TID stiffness k in the TID parameter combination X. tid TID damping coefficient c tid and TID inertial mass m tid The values ​​are assigned to the spring-damped-inertial container combined unit described in step S1, and then each ground motion record in the ground motion input set G formed in step S3 is input sequentially. After completing the dynamic time history analysis under the action of each ground motion record, the inter-story displacement time history of the first and second layers, the absolute acceleration time history of the top plate node, the absolute acceleration time history of the middle plate node, the absolute acceleration time history of the bottom plate node, and the output time history of the TID connection unit, which were determined in step S2, are extracted from the ABAQUS output results. Then, according to the calculation formulas corresponding to objective function one, objective function two, and objective function three in claim 3, the maximum value under the action of the ground motion is calculated respectively. The objective function values ​​are f1(X) for inter-story drift angle, f2(X) for maximum absolute floor acceleration, and f3(X) for maximum TID output. If the average evaluation criterion is adopted, the arithmetic mean of f1(X), f2(X), and f3(X) of all ground motion records in the ground motion input set G in step S3 is taken. If the safety envelope evaluation criterion is adopted, the maximum value of f1(X), f2(X), and f3(X) of all ground motion records in the ground motion input set G in step S3 is taken. The arithmetic mean or the maximum envelope value is returned to the genetic algorithm as the final performance index of the TID parameter combination X.

[0048] In step S6, the Pareto front-based engineering decision-making includes: visualizing and comparing a set of non-dominated solutions obtained by multi-objective parameter optimization using a genetic algorithm in a three-dimensional target space or a two-dimensional projection plane; in step S1, the maximum inter-story drift angle, maximum absolute floor acceleration, and maximum TID output calculated by the refined soil-structure-TID coupled finite element model under seismic input constitute the structure; wherein, the maximum inter-story drift angle is used to characterize the deformation control effect of the main structure of the double-layer three-span subway station, the maximum absolute floor acceleration is used to characterize the dynamic response control effect of the station structure and auxiliary equipment, and the maximum TID output is used to characterize the stress level and engineering feasibility of the tuned inertial capacitive damper; according to the distribution relationship of the non-dominated solution set in the three-dimensional target space, a combination of TID parameters that takes into account structural deformation control, acceleration control, and damper output constraints is selected as the recommended engineering solution.

[0049] In step S7, the comprehensive verification and mechanism analysis of seismic isolation and vibration reduction performance includes: based on the seismic fortification intensity, site category and design response spectrum of the location of the double-layer three-span subway station, selecting at least one actual strong earthquake record or artificially synthesized earthquake record that did not participate in the optimization calculation in step S3 and has different spectral characteristics from the optimized input earthquake ground motion record as the verification earthquake ground motion input.

[0050] In step S1, the TID is arranged between the central column and the floor slab, between the side wall and the floor slab, and at key connection nodes in the station structure that require seismic response control in a double-layer, three-span subway station. The two ends of the TID are connected to adjacent component nodes in the main station structure, and it consists of spring units, damping units, and inertial capacitance units. The parameters of the spring units, damping units, and inertial capacitance units are the optimized stiffness parameters of the TID. Damping coefficient and inertia The TID, together with the main structure of the station, forms a soil-structure-TID coupled finite element model, which is used for seismic isolation and reduction analysis of a two-story, three-span subway station under seismic input.

[0051] In step S1, the optimized TID parameters are used to control and analyze the dynamic response of a double-layer, three-span subway station structure under seismic input. During the dynamic response analysis of the main station structure, the time histories of absolute acceleration of the floor slabs, inter-story displacement, TID output, and structural energy response data are extracted. The absolute acceleration time histories of the floor slabs include the absolute acceleration responses of the corresponding nodes of the top, middle, and bottom slabs. The structural energy response data include seismic input energy, structural strain energy, structural damping energy dissipation, and TID energy dissipation. By comparing the response data of the model without TID control, the model with initial empirical TID parameters, and the model with optimized TID parameters under the same seismic input, the applicability of the optimized TID parameters in a double-layer, three-span subway station is verified.

[0052] Beneficial effects: By adopting the above technical solution, this invention achieves TID stiffness. Damping coefficient Inertia The synergistic optimization improves the structural safety, equipment operational stability, and post-earthquake functional recovery capability of double-layer, three-span subway stations under seismic loading, and has the following advantages compared with existing technologies:

[0053] This invention utilizes a soil-structure-TID coupled finite element model, considering indicators such as maximum inter-story drift angle, maximum absolute floor acceleration, and maximum TID output. It provides a complete technical process from refined modeling, multi-objective function definition, seismic motion set input, intelligent algorithm optimization to comprehensive verification analysis, filling the gap in refined optimization methods for TID parameters of complex underground structures. The optimization objectives directly correspond to the inter-story drift angle and floor acceleration that are of most concern in engineering, and provide visual decision support through Pareto fronts, making the optimization results easy to adopt in engineering practice.

[0054] This invention, by considering soil-structure coupling effects and seismic uncertainties, optimizes the TID parameter (Xopt) to ensure optimal synergy between the device and the main structure in complex real-world environments, maximizing its vibration reduction potential and ensuring stable and reliable performance. This makes the TID a precisely designable and predictably performable "structural fuse." The TID optimized and applied using this method can guide seismic energy towards its own dissipation, effectively protecting the station's main structure, significantly reducing post-earthquake damage and repair costs, ensuring rapid restoration of subway system functionality, and embodying the resilient design philosophy of modern engineering. It has significant socio-economic benefits and broad applicability within this technical field. Attached Figure Description

[0055] Figure 1This is a flowchart of the inertial capacitive damper parameter optimization method for vibration reduction in double-layer, three-span subway stations according to the present invention.

[0056] Figure 2 This is a block diagram of the soil-structure-TID coupled dynamic response analysis system for the application of the inertial capacitive damper parameter optimization method of the present invention in the seismic isolation of double-layer three-span subway stations. Detailed Implementation

[0057] The present invention provides a method for optimizing the parameters of an inertial capacitive damper for vibration reduction in a double-layer, three-span subway station, comprising the following steps:

[0058] S1. Establish a refined soil-structure-TID coupled finite element model.

[0059] Based on the construction design drawings and geotechnical investigation report of the double-layer, three-span subway station, modeling data was extracted. From the construction design drawings, the axial position, total width, total height, top slab thickness, middle slab thickness, bottom slab thickness, side wall thickness, central column cross-sectional dimensions, central column spacing, left span clear span dimensions, middle span clear span dimensions, right span clear span dimensions, concrete material parameters of each component, and TID installation node locations of the station's main structure were extracted. From the geotechnical investigation report, the soil layer thickness, density, elastic modulus, Poisson's ratio, cohesion, internal friction angle, and damping ratio of the soil surrounding the station were extracted. Using ABAQUS finite element software, a model of the main structure of the double-layer, three-span subway station, a model of the soil surrounding the station, and a TID connection unit model were established to form an overall TID model. Simultaneously, ABAQUS finite element software was used to establish the double-layer, three-span subway station main structure model, the model of the soil surrounding the station, and the TID connection unit model. A TID (Transient Inertial Device) model is formed by combining the main structure model of the subway station and the surrounding soil model. The main structure of the double-layer, three-span subway station is an underground two-layer, three-span frame structure composed of a top slab, middle slab, bottom slab, two side walls, and a central column. The two ends of the TID are connected between nodes of adjacent structural members on the same floor. One end is connected to the intersection node of the central column and the floor slab, and the other end is connected to the intersection node of the side wall and the floor slab on the same floor or the intersection node of the adjacent central column and the floor slab. The TID is arranged along the lateral force direction of the station. A series of spring-damped-inertial container combined units are used to simulate the TID. The spring-damped-inertial container combined units are used to simulate the interaction of the TID between the nodes of the main structure of the double-layer, three-span subway station. The input parameters of the spring-damped-inertial container combined units include the TID stiffness k. tid TID damping coefficient c tid and TID inertial mass m tid Where the TID stiffness k tid The TID damping coefficient c is used to control the restoring force generated by the relative displacement between the two ends of the TID connection unit. tid The energy dissipation capability used to control the relative velocity between the two nodes of the TID connection unit, TID inertial mass m tidThe inertial enhancement effect generated by the relative acceleration between the two nodes of the TID connection unit is used to control the dynamic response of the soil, the dynamic response of the station main structure and the TID vibration reduction response. This results in a refined soil-structure-TID coupled finite element model that simultaneously calculates the dynamic response of the soil, the dynamic response of the station main structure and the TID vibration reduction response.

[0060] In step S1, the underground two-story three-span frame structure includes the lower space between the bottom slab and the middle slab and the upper space between the middle slab and the top slab. The floor numbers are i=1 and i=2, where i=1 represents the lower floor and i=2 represents the upper floor. The maximum subsequent floor is the second floor. The three spans include the left span, the middle span, and the right span formed by the left side wall, the middle column, and the right side wall.

[0061] The TID installation node locations are divided into the intersection nodes of the top of the upper middle column and the top plate, the intersection nodes of the bottom of the upper middle column and the middle plate, the intersection nodes of the top of the lower middle column and the middle plate, and the intersection nodes of the bottom of the lower middle column and the bottom plate; the intersection nodes of the top of the upper middle column and the top plate and the intersection nodes of the top of the lower middle column and the middle plate are preferred as the initial TID layout nodes;

[0062] The expression for the inertial force generated by the inertial container is as follows:

[0063] ;

[0064] in, and The acceleration of the connection nodes at both ends of the TID along the TID layout direction is given. The connection nodes at both ends are determined by the intersection of the central column and the floor slab, the intersection of the side wall and the floor slab on the same floor, or the intersection of the adjacent central column and the floor slab.

[0065] In step S1, the TID is arranged between the central column and the floor slab, between the side wall and the floor slab, and at key connection nodes in the station structure that require seismic response control in a double-layer, three-span subway station. The two ends of the TID are connected to adjacent component nodes in the main station structure, and it consists of spring units, damping units, and inertial capacitance units. The parameters of the spring units, damping units, and inertial capacitance units are the optimized stiffness parameters of the TID. Damping coefficient and inertia The TID, together with the main structure of the station, forms a soil-structure-TID coupled finite element model, which is used for seismic isolation and reduction analysis of a two-story, three-span subway station under seismic input.

[0066] In step S1, the optimized TID parameters are used to control and analyze the dynamic response of a double-layer, three-span subway station structure under seismic input. During the dynamic response analysis of the main station structure, the time histories of absolute acceleration of the floor slabs, inter-story displacement, TID output, and structural energy response data are extracted. The absolute acceleration time histories of the floor slabs include the absolute acceleration responses of the corresponding nodes of the top, middle, and bottom slabs. The structural energy response data include seismic input energy, structural strain energy, structural damping energy dissipation, and TID energy dissipation. By comparing the response data of the model without TID control, the model with initial empirical TID parameters, and the model with optimized TID parameters under the same seismic input, the applicability of the optimized TID parameters in a double-layer, three-span subway station is verified.

[0067] S2. Define the multi-objective optimization function.

[0068] Using the refined soil-structure-TID coupled finite element model established in step S1 as the analysis object, a set of TID parameter combinations is used as the input variables for a first optimization calculation. The TID parameter combination includes the TID stiffness k. tid TID damping coefficient c tid and TID inertial mass m tid After assigning the set of TID parameters to the spring-damped-inertial container combined unit in step S1, the seismic dynamic response is calculated. From the calculation results, three target values ​​are extracted: maximum inter-story drift angle, maximum story absolute acceleration, and maximum TID output force. The following multi-objective optimization function is established:

[0069] ;

[0070] Where X represents the TID parameter vector, f1(X) represents the objective function of the maximum inter-story drift angle, f2(X) represents the objective function of the maximum floor absolute acceleration, and f3(X) represents the objective function of the maximum TID output. The maximum inter-story drift angle is obtained by dividing the relative inter-story displacements of the first and second floors of the double-layer three-span subway station under seismic action by the corresponding floor heights and taking the maximum value. It is used to characterize the deformation control effect of the double-layer three-span subway station main frame. The maximum floor absolute acceleration is obtained by taking the maximum value of the absolute acceleration time histories of the top slab, middle slab, and bottom slab representative nodes. It is used to characterize the strength of the dynamic response of the station floor slab, station equipment, and personnel environment. The maximum TID output is obtained by taking the maximum value of the output time histories of the TID connection units. It is used to characterize the engineering stress level of the TID device and its connection nodes.

[0071] The multi-objective optimization function is defined by simultaneously minimizing the three objectives of maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output. This transforms structural deformation control, floor acceleration control, and TID device force control into three optimization objectives that can be evaluated and compared by a genetic algorithm.

[0072] In step S2, the multi-objective optimization function takes the refined soil-structure-TID coupled finite element model established in step S1 as the analysis object, and the top slab, middle slab, bottom slab, and TID connection units in the two-story, three-span underground frame structure as the response extraction objects. After assigning the same set of TID stiffness, damping coefficient, and inertial mass to the spring-damped-inertial container combined unit in step S1 and completing the dynamic time history analysis, the vibration reduction performance of this set of TID parameters is evaluated according to the following three objective functions:

[0073] The objective function is to minimize the maximum inter-story drift angle, as shown in the formula: ,in ;

[0074] in, For floor displacement, For floor height, It is the floor number, and The value is consistent with the floor numbering of the double-layer, three-span subway station. This indicates the lower space between the bottom plate and the middle plate. The upper space between the middle slab and the top slab is represented. Therefore, the maximum inter-story drift angle refers to the response value with the largest absolute value among all inter-story drift angle time histories of the 1st and 2nd floors. The minimization refers to the genetic algorithm prioritizing the parameter combination that makes the maximum inter-story drift angle smaller among different TID parameter combinations, so as to reduce the risk of inter-story deformation damage in the connection area of ​​the middle column, side wall and floor slab.

[0075] Objective function two is to minimize the maximum floor absolute acceleration, formula: The floor absolute acceleration is obtained by extracting the acceleration time histories of the top, middle and bottom representative nodes of the refined soil-structure-TID coupled finite element model in step S1. The maximum floor absolute acceleration refers to the response value that is the largest among all the absolute acceleration time histories of the top, middle and bottom representative nodes. Minimization refers to the genetic algorithm prioritizing the parameter combination that makes the maximum floor absolute acceleration smaller among different TID parameter combinations, so as to reduce the impact of dynamic response on the station floor, station equipment and personnel environment.

[0076] Objective function three is to minimize the maximum damper output, as shown in the formula: The damper output is obtained by extracting the output time history of the TID connection unit in step S1 under the action of seismic input. The maximum damper output refers to the output value with the largest absolute value among all TID connection units and their full-time output response. Minimization means that the genetic algorithm prioritizes the parameter combination that makes the maximum damper output smaller and meets the vibration reduction requirements among different TID parameter combinations, so as to avoid excessive local stress in the TID device and its column-to-floor connection nodes, sidewall-to-floor connection nodes or adjacent component connection nodes. Thus, the three objectives of maximum inter-story drift angle, maximum floor absolute acceleration and maximum damper output correspond to the deformation control of the station main structure, the dynamic response control of the floor and the stress control of the TID project, respectively.

[0077] S3. Select and input ground motion records as input for optimization analysis.

[0078] The selection criteria for seismic ground motions are determined based on the seismic fortification intensity, site category, and design response spectrum of the location of the double-layer, three-span subway station. Seismic ground motion records with different spectral characteristics are selected from engineering seismic design data, publicly available strong ground motion record databases, or artificial ground motion files generated according to the design response spectrum. Acceleration time history, peak ground acceleration, time interval, and duration information are extracted for each ground motion record. After amplitude adjustment of each ground motion record, a seismic ground motion input set is constructed. This seismic ground motion input set is represented as follows:

[0079] ;

[0080] Where G represents the seismic motion input set, ag1(t), ag2(t), and agn(t) represent the 1st, 2nd, and nth seismic motion acceleration time histories, respectively, t represents time, and n represents the number of seismic motion records. n is set to 6 so that the three optimization objectives are calculated under the same seismic motion input set. Different seismic motion input sets have different spectral characteristics, so as to avoid the optimization results being applicable only to a single seismic motion record.

[0081] In step S3, the establishment of the seismic motion input set is based on the double-layer, three-span subway station project site in step S1, and corresponds to the three optimization objectives in step S2: maximum inter-story drift angle, maximum absolute floor acceleration, and maximum TID output. First, the selection criteria for seismic motion records are determined according to the seismic fortification intensity, site category, and design response spectrum of the station location. Then, 5-8 seismic motion records are selected as optimization inputs from the seismic design data of the project, the publicly available strong ground motion record database, or the artificial wave file generated according to the design response spectrum. For each seismic motion record, the acceleration time history, peak acceleration, time interval, and duration should be extracted. The data should be provided, and the source of the data should be noted. The selected ground motion records should cover different spectral characteristics with more obvious low-frequency components, more obvious mid-frequency components, and more obvious high-frequency components. Before inputting the refined soil-structure-TID coupled finite element model established in step S1, the amplitude should be adjusted so that the maximum inter-story drift angle, maximum absolute floor acceleration, and maximum TID output of each set of TID parameters are calculated under the same ground motion input set. This ensures that the optimized TID parameter results are not local results for a single ground motion record, but rather robust solutions with stable damping performance for a two-story, three-span subway station under different ground motion input conditions.

[0082] S4. Applying genetic algorithms for multi-objective parameter optimization

[0083] Based on a refined soil-structure-TID coupled finite element model, three optimization objectives, and a set of seismic motion inputs, the three parameters of TID stiffness, damping coefficient, and inertia are encoded as chromosomes in a genetic algorithm. The TID stiffness (ktid), TID damping coefficient (ctid), and TID inertia (mtid) are used as parameters to be optimized. A set of TID stiffness, TID damping coefficient, and TID inertia is used as an individual in the genetic algorithm. Each individual corresponds to a computable soil-structure-TID coupled finite element model in step S1. The TID parameter vector is represented as follows:

[0084] ;

[0085] Wherein, ktid represents TID stiffness, ctid represents TID damping coefficient, and mtid represents TID inertia. The parameter value range is determined by the dynamic characteristic analysis results of the station model without TID control in step S1, the allowable range of TID device construction, and the bearing capacity of TID connection nodes. After generating the initial population within this parameter value range, each individual in the initial population is evaluated according to the three optimization objectives. New TID parameter combinations are generated through selection, crossover, and mutation operations, so that the initial population can successively select parameter combinations that have better comprehensive performance in the three objectives of maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output.

[0086] In step S4, each chromosome contains at least and at most the three TID parameters mentioned above. Each chromosome corresponds to a set of TID parameter combinations that can be assigned to the spring-damped-inertial container unit, and a conflict objective function is constructed based on the structural critical response.

[0087] ;

[0088] In the formula, F(m) tid ,k tid ,c tid () represents a multi-objective evaluation function vector determined by a set of TID parameters, which is also the set of objective functions used by the genetic algorithm to evaluate the combination of TID parameters corresponding to a chromosome. tid The inertial mass parameter of the TID (Transient Inertial Container) is the equivalent inertial parameter of the container, used to characterize the inertial enhancement effect caused by the relative acceleration of the connecting nodes at both ends of the TID. k tid Indicates the stiffness of the TID, used to characterize the restoring force generated by the relative displacement of the connecting nodes at both ends of the TID, c tid f1(u) represents the TID damping coefficient, used to characterize the damping energy dissipation capacity generated by the relative velocity of the connecting nodes at both ends of the TID. max The first objective function (u) evaluates the maximum inter-story drift angle between the first and second floors of a double-layer, three-span subway station under seismic loading. This function characterizes the effectiveness of the inter-story deformation control of the main structure. max This represents the maximum value of the inter-story drift angle in the time history between the 1st and 2nd floors. Specifically, it is obtained by removing the relative displacement between adjacent floors and taking the maximum absolute value after deducting the corresponding floor height. f2(a max () represents the second objective function, which evaluates the maximum absolute floor acceleration of the nodes represented by the top, middle, and bottom slabs. This acceleration characterizes the strength of the dynamic response experienced by the station floors, station equipment, and personnel environment. max This represents the maximum absolute acceleration values ​​in the time histories of the top, middle, and bottom plate nodes, f3(F TID,max ) represents the third objective function, which evaluates the maximum output force of the TID connection unit and is used to characterize the engineering stress level of the TID device and its connection nodes;

[0089] During the initialization of the population within the range of TID parameter values, the TID stiffness, damping coefficient, and inertia of each individual must not be less than the lower limit of the corresponding parameter and must not be greater than the upper limit of the corresponding parameter. The lower limit and upper limit of the parameter are jointly determined by the dynamic characteristic analysis results of the double-layer three-span subway station without TID control model in step S1, the allowable range of TID device construction, and the bearing capacity of TID connection nodes.

[0090] For each individual in the initial population, dynamic time history analysis was performed using ABAQUS finite element software with all ground motion records input. Then, the TID stiffness k was calculated based on three target values: maximum inter-story drift angle, maximum story absolute acceleration, and maximum TID output. tid TID damping coefficient c tid and TID inertial mass m tid The fitness evaluation results of individuals are composed of a set of candidate TID parameter combinations that can be assigned to the spring-damped-inertial container combined unit in step S1; individuals with better comprehensive evaluation are retained through tournament selection, and TID parameter information is exchanged between two parent individuals through simulated binary crossover. Finally, new candidate parameter combinations are generated within the parameter value range through polynomial mutation, and the superiority and inferiority levels of different individuals on the three optimization objectives are distinguished by non-dominated sorting. The uniformity of the distribution of solution sets within the same level is maintained by crowding distance, so that the population evolves towards the Pareto front generation by generation.

[0091] Based on the Pareto front and the engineering requirements of a double-layer, three-span subway station, a robust solution is selected. These requirements include reducing the maximum inter-story drift angle of the first and second floors in the double-layer, three-span structure, reducing the maximum absolute floor acceleration of the top, middle, and bottom slabs, and limiting the maximum output of the TID connection unit. This ensures that the TID can still work with the main structure to achieve the vibration reduction target under parameter fluctuations. ,in The weighting factor is used to represent the relative importance of the three objectives—maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output—in the engineering decision-making stage, and the use of the weighting factor does not change the definition of the three optimization objectives in step S2.

[0092] S5. Perform nested system dynamic time history analysis

[0093] In each iteration of the genetic algorithm, the TID stiffness ktid, TID damping coefficient ctid, and TID inertial mass mtid corresponding to the current individual are assigned to the spring-damped-inertial container combined unit established in step S1. Each ground motion record in the ground motion input set formed in step S3 is then input sequentially. Dynamic time history analysis is performed on the updated refined soil-structure-TID coupled finite element model. After the calculation is completed, the inter-story displacement time history of the first and second floors, the absolute acceleration time history of the top plate node, the absolute acceleration time history of the middle plate node, the absolute acceleration time history of the bottom plate node, and the output time history of the TID connection unit are extracted from the ABAQUS output results. Then, according to the definition of the three optimization objectives, the maximum inter-story displacement angle, the maximum floor absolute acceleration, and the maximum TID output are calculated for each ground motion. The average value or envelope value of the three objectives under all ground motion records is returned to the genetic algorithm as the final evaluation result of the TID parameter combination.

[0094] In step S5, when evaluating any TID parameter combination X, the genetic algorithm first considers the TID stiffness k in the TID parameter combination X. tid TID damping coefficient c tid and TID inertial mass m tid The values ​​are assigned to the spring-damped-inertial container combined unit described in step S1, and then each ground motion record in the ground motion input set G formed in step S3 is input sequentially. After completing the dynamic time history analysis under the action of each ground motion record, the inter-story displacement time history of the first and second layers, the absolute acceleration time history of the top plate node, the absolute acceleration time history of the middle plate node, the absolute acceleration time history of the bottom plate node, and the output time history of the TID connection unit, which were determined in step S2, are extracted from the ABAQUS output results. Then, according to the calculation formulas corresponding to objective function one, objective function two, and objective function three in claim 3, the maximum value under the action of the ground motion is calculated respectively. The objective function values ​​are f1(X) for inter-story drift angle, f2(X) for maximum absolute floor acceleration, and f3(X) for maximum TID output. If the average evaluation criterion is adopted, the arithmetic mean of f1(X), f2(X), and f3(X) of all ground motion records in the ground motion input set G in step S3 is taken. If the safety envelope evaluation criterion is adopted, the maximum value of f1(X), f2(X), and f3(X) of all ground motion records in the ground motion input set G in step S3 is taken. The arithmetic mean or the maximum envelope value is returned to the genetic algorithm as the final performance index of the TID parameter combination X.

[0095] S6. Engineering Decision-Making Based on Pareto Fronts

[0096] Once the genetic algorithm reaches the preset number of iterations or meets the convergence condition, it obtains a non-dominated solution set composed of multiple TID parameter combinations. The non-dominated solution set is compared according to three objectives: maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output. The performance differences of each TID parameter combination are displayed in a three-dimensional target space or a two-dimensional projection plane. Based on the requirements for main structure deformation control, floor acceleration control, and TID connection node output control in the engineering design of a double-layer, three-span subway station, a TID parameter combination that takes into account the three optimization objectives is selected from the non-dominated solution set as the recommended parameter combination for the project.

[0097] In step S6, the Pareto front-based engineering decision-making includes: visualizing and comparing a set of non-dominated solutions obtained by multi-objective parameter optimization using a genetic algorithm in a three-dimensional target space or a two-dimensional projection plane; in step S1, the maximum inter-story drift angle, maximum absolute floor acceleration, and maximum TID output calculated by the refined soil-structure-TID coupled finite element model under seismic input constitute the structure; wherein, the maximum inter-story drift angle is used to characterize the deformation control effect of the main structure of the double-layer three-span subway station, the maximum absolute floor acceleration is used to characterize the dynamic response control effect of the station structure and auxiliary equipment, and the maximum TID output is used to characterize the stress level and engineering feasibility of the tuned inertial capacitive damper; according to the distribution relationship of the non-dominated solution set in the three-dimensional target space, a combination of TID parameters that takes into account structural deformation control, acceleration control, and damper output constraints is selected as the recommended engineering solution.

[0098] S7. Conduct comprehensive verification and mechanism analysis of seismic isolation and vibration reduction performance.

[0099] Ground motion records that did not participate in the multi-objective parameter optimization using the genetic algorithm in step S4 and have different spectral characteristics from the ground motion input set in step S3 were selected as verification ground motion input data. Using ABAQUS software, under the same soil parameters, structural parameters, boundary conditions, ground motion input, and calculation conditions, soil-structure finite element models without TID control, soil-structure-TID coupled finite element models with initial empirical parameter TID, and soil-structure-TID coupled finite element models with the engineering recommended parameter combination TID in step S6 were established and calculated respectively. The maximum inter-story drift angle, maximum absolute floor acceleration, TID output, and structural energy response of the three types of models were compared to verify the seismic isolation effect of the TID parameter combination obtained in step S6 relative to the model without TID control and the initial empirical parameter TID model. The mechanism by which TID transfers and dissipates the vibration energy of the main structure of the double-layer three-span subway station through inertial enhancement, tuned energy absorption, and damping energy dissipation was analyzed.

[0100] In step S7, the comprehensive verification and mechanism analysis of seismic isolation and vibration reduction performance includes: based on the seismic fortification intensity, site category and design response spectrum of the location of the double-layer three-span subway station, selecting at least one actual strong earthquake record or artificially synthesized earthquake record that did not participate in the optimization calculation in step S3 and has different spectral characteristics from the optimized input earthquake ground motion record as the verification earthquake ground motion input.

[0101] The invention will now be further described with reference to the embodiments shown in the accompanying drawings:

[0102] Example 1

[0103] like Figure 1 Figure 2As shown, a method for optimizing the parameters of an inertial capacitive damper used for vibration reduction in a double-layer, three-span subway station includes the following steps:

[0104] S1. First, a refined soil-structure-TID coupled finite element model is established. Based on the station design drawings, a refined model of a double-layer three-span frame is established using finite element software. At the predetermined installation position, a series of spring-damping-inertial container combination units are used to simulate TID.

[0105] S2. Define a multi-objective optimization function, with the maximum inter-story drift angle, story acceleration and damper output as the core multi-objective function, to transform the comprehensive requirements of seismic isolation and vibration reduction in engineering into quantifiable and optimizable mathematical objectives, providing a clear optimization direction for the algorithm;

[0106] S3. Select and input ground motion records as input for optimization analysis to ensure the robustness of optimization results;

[0107] S4. Apply genetic algorithms to optimize multi-objective parameters, including stiffness. Damping coefficient Inertia Multi-objective optimization using three main parameters;

[0108] S5. Nested system dynamic time history analysis: Assign the TID parameters represented by the current individual to the TID elements in the finite element model, and perform nonlinear dynamic time history analysis on the updated soil-structure-TID coupled model.

[0109] S6. Based on Pareto front engineering decisions, the solution set is displayed on a three-dimensional target space or a two-dimensional projection plane.

[0110] S7. Comprehensive verification and mechanism analysis of seismic isolation and damping performance: Using new ground motion records not involved in optimization, comparative analysis was conducted on uncontrolled structures, structures with pre-optimized TID, and structures with optimized TID. The dynamic response of the structure was studied to fully verify the superiority and generalization ability of the optimized scheme.

[0111] In step S1, the spring-damped-inertial container assembly receives three core parameter inputs: stiffness. Damping coefficient Inertia Inertial force generated by the inertial container ,in and Given the acceleration difference at the connection points, the optimization function in step S2 consists of three objective functions. Objective function one: Minimize the maximum inter-story drift angle.

[0112] formula: ,in , For floor displacement, For floor height, Floor number;

[0113] Objective function 2: Minimize the maximum floor absolute acceleration: Formula: ;

[0114] Objective function 3: Minimize the maximum damper output:

[0115] formula: In step S3, based on the seismic fortification intensity, site category, and design spectrum of the station site, multiple actual strong earthquake records or artificial waves with different spectral characteristics are selected to form a seismic motion input set. The optimization process will be performed on all records in this set to obtain robustness that performs well under different seismic characteristics. In step S4, the parameters are encoded into chromosomes, and a conflict objective function is constructed based on the structural critical responses.

[0116] Next, the population is initialized, and offspring are generated through tournament selection, simulated binary crossover, and polynomial mutation. Individuals are then selected using non-dominated sorting and crowding distance to allow the population to evolve toward the Pareto front. Finally, robust solutions are selected from the front based on engineering requirements to ensure that the TID can still work in conjunction with the main structure to achieve the seismic isolation and reduction target even under parameter fluctuations. ,in As a weighting factor, step S5 extracts the inter-story displacement, story acceleration, and TID output time histories for each time history. The three objective function values ​​for each seismic motion are calculated according to the formula in step 2. Finally, the average or envelope value of the objective function values ​​for all seismic motions is taken as the final performance index of the set of TID parameters and returned to the genetic algorithm. Step 6, the Pareto front-based engineering decision-making, specifically involves visualizing a set of non-dominated solutions obtained by the genetic algorithm in a three-dimensional target space or a two-dimensional projection plane. The three-dimensional target consists of the maximum inter-story displacement angle, story acceleration, and damper output. Step 7, the comprehensive verification and mechanism analysis of seismic isolation and damping performance, specifically involves selecting a seismic motion record that is different from the optimized input record's spectral characteristics and not involved in optimization, establishing and calculating an uncontrolled structural model, a structural model with initial empirical TID parameters, and a structural model with optimized TID parameters.

[0117] By using a set of ground motion inputs for optimization and verifying the results with new ground motions, the optimized TID parameters (Xopt) are ensured to have good adaptability to ground motion uncertainties, thereby improving the reliability of the damping device in actual earthquakes.

[0118] Example 2

[0119] like Figure 1As shown, Example 2 further elaborates on Example 1, utilizing a tuned inertial-capacitive damper (TID) for seismic isolation in a two-story, three-span subway station. Its core lies in precise optimization, enabling the device to work collaboratively with the complex underground soil-structure system. In practice, the optimized TID is typically placed at key connection points between the station's central column and the floor slab or side wall. When an earthquake occurs, the TID is tuned to the dominant frequency after the structure couples with the surrounding soil. Through inertial enhancement and resonance energy absorption mechanisms, it efficiently transfers and dissipates the vibrational energy of the main structure. This directly affects the station's most vulnerable points: significantly reducing the inter-story drift angle of the central column, effectively preventing column damage or joint cracking due to excessive deformation, and ensuring the overall stability and continuity of the structure. This method achieves the goal of "seismic isolation." The TID (Transient Isolation Device) also directly reduces the acceleration response of each floor slab through energy dissipation, which is crucial for the internal environment of the station. On the one hand, it protects the normal operation and safety of automatic ticket vending machines, signaling systems, ventilation equipment, and precision instruments. On the other hand, it significantly improves the comfort and sense of security of waiting passengers and staff in the station, achieving the effect of "shock reduction." Throughout the process, the energy input by the earthquake is preferentially directed to the TID, a designable and replaceable device, so that the damage to the main structure of the station can be controlled and its functions can be quickly restored after the earthquake. This reflects the modern resilient earthquake-resistant design concept. The TID parameters optimized by this method can show stable shock reduction performance under various seismic inputs, proving its robustness in dealing with earthquake uncertainties.

[0120] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the parameters of an inertial capacitive damper used for vibration reduction in a double-layer, three-span subway station, characterized in that, Includes the following steps: S1. Establish a refined soil-structure-TID coupled finite element model. Based on the construction design drawings and geotechnical investigation report of the double-layer, three-span subway station, modeling data was extracted. From the construction design drawings, the axial position, total width, total height, top slab thickness, middle slab thickness, bottom slab thickness, side wall thickness, central column cross-sectional dimensions, central column spacing, left span clear span dimensions, middle span clear span dimensions, right span clear span dimensions, concrete material parameters of each component, and TID installation node locations of the station's main structure were extracted. From the geotechnical investigation report, the soil layer thickness, density, elastic modulus, Poisson's ratio, cohesion, internal friction angle, and damping ratio of the soil surrounding the station were extracted. Using ABAQUS finite element software, a model of the main structure of the double-layer, three-span subway station, a model of the soil surrounding the station, and a TID connection unit model were established to form an overall TID model. Simultaneously, ABAQUS finite element software was used to establish the double-layer, three-span subway station main structure model, the model of the soil surrounding the station, and the TID connection unit model. A TID (Transient Inertial Device) model is formed by combining the main structure model of the subway station and the surrounding soil model. The main structure of the double-layer, three-span subway station is an underground two-layer, three-span frame structure composed of a top slab, middle slab, bottom slab, two side walls, and a central column. The two ends of the TID are connected between nodes of adjacent structural members on the same floor. One end is connected to the intersection node of the central column and the floor slab, and the other end is connected to the intersection node of the side wall and the floor slab on the same floor or the intersection node of the adjacent central column and the floor slab. The TID is arranged along the lateral force direction of the station. A series of spring-damped-inertial container combined units are used to simulate the TID. The spring-damped-inertial container combined units are used to simulate the interaction of the TID between the nodes of the main structure of the double-layer, three-span subway station. The input parameters of the spring-damped-inertial container combined units include the TID stiffness k. tid TID damping coefficient c tid and TID inertial mass m tid Where the TID stiffness k tid The TID damping coefficient c is used to control the restoring force generated by the relative displacement between the two ends of the TID connection unit. tid The energy dissipation capability used to control the relative velocity between the two nodes of the TID connection unit, TID inertial mass m tid The inertial enhancement effect generated by the relative acceleration between the two nodes of the TID connection unit is used to control the dynamic response of the soil, the dynamic response of the station main structure and the TID vibration reduction response. This results in a refined soil-structure-TID coupled finite element model that simultaneously calculates the dynamic response of the soil, the dynamic response of the station main structure and the TID vibration reduction response. S2. Define the multi-objective optimization function. Using the refined soil-structure-TID coupled finite element model established in step S1 as the analysis object, a set of TID parameter combinations is used as the input variables for a first optimization calculation. The TID parameter combination includes the TID stiffness k. tid TID damping coefficient c tid and TID inertial mass m tid After assigning the set of TID parameters to the spring-damped-inertial container combined unit in step S1, the seismic dynamic response is calculated. From the calculation results, three target values ​​are extracted: maximum inter-story drift angle, maximum story absolute acceleration, and maximum TID output force. The following multi-objective optimization function is established: ； Where X represents the TID parameter vector, f1(X) represents the objective function of the maximum inter-story drift angle, f2(X) represents the objective function of the maximum floor absolute acceleration, and f3(X) represents the objective function of the maximum TID output. The maximum inter-story drift angle is obtained by dividing the relative inter-story displacements of the first and second floors of the double-layer three-span subway station under seismic action by the corresponding floor heights and taking the maximum value. It is used to characterize the deformation control effect of the double-layer three-span subway station main frame. The maximum floor absolute acceleration is obtained by taking the maximum value of the absolute acceleration time histories of the top slab, middle slab, and bottom slab representative nodes. It is used to characterize the strength of the dynamic response of the station floor slab, station equipment, and personnel environment. The maximum TID output is obtained by taking the maximum value of the output time histories of the TID connection units. It is used to characterize the engineering stress level of the TID device and its connection nodes. The multi-objective optimization function is defined by simultaneously minimizing the three objectives of maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output. This transforms structural deformation control, floor acceleration control, and TID device force control into three optimization objectives that can be evaluated and compared by a genetic algorithm. S3. Select and input ground motion records as input for optimization analysis. The selection criteria for seismic ground motions are determined based on the seismic fortification intensity, site category, and design response spectrum of the location of the double-layer, three-span subway station. Seismic ground motion records with different spectral characteristics are selected from engineering seismic design data, publicly available strong ground motion record databases, or artificial ground motion files generated according to the design response spectrum. Acceleration time history, peak ground acceleration, time interval, and duration information are extracted for each ground motion record. After amplitude adjustment of each ground motion record, a seismic ground motion input set is constructed. This seismic ground motion input set is represented as follows: ； Where G represents the seismic motion input set, ag1(t), ag2(t), and agn(t) represent the 1st, 2nd, and nth seismic motion acceleration time histories, respectively, t represents time, and n represents the number of seismic motion records. n is set to 6 so that the three optimization objectives are calculated under the same seismic motion input set. Different seismic motion input sets have different spectral characteristics, so as to avoid the optimization results being applicable only to a single seismic motion record. S4. Applying genetic algorithms for multi-objective parameter optimization Based on a refined soil-structure-TID coupled finite element model, three optimization objectives, and a set of seismic motion inputs, the three parameters of TID stiffness, damping coefficient, and inertia are encoded as chromosomes in a genetic algorithm. The TID stiffness (ktid), TID damping coefficient (ctid), and TID inertia (mtid) are used as parameters to be optimized. A set of TID stiffness, TID damping coefficient, and TID inertia is used as an individual in the genetic algorithm. Each individual corresponds to a computable soil-structure-TID coupled finite element model in step S1. The TID parameter vector is represented as follows: ； Wherein, ktid represents TID stiffness, ctid represents TID damping coefficient, and mtid represents TID inertia. The parameter value range is determined by the dynamic characteristic analysis results of the station model without TID control in step S1, the allowable range of TID device construction, and the bearing capacity of TID connection nodes. After generating the initial population within this parameter value range, each individual in the initial population is evaluated according to the three optimization objectives. New TID parameter combinations are generated through selection, crossover, and mutation operations, so that the initial population can successively select parameter combinations that have better comprehensive performance in the three objectives of maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output. S5. Perform nested system dynamic time history analysis In each iteration of the genetic algorithm, the TID stiffness ktid, TID damping coefficient ctid, and TID inertial mass mtid corresponding to the current individual are assigned to the spring-damped-inertial container combined unit established in step S1. Each ground motion record in the ground motion input set formed in step S3 is then input sequentially. Dynamic time history analysis is performed on the updated refined soil-structure-TID coupled finite element model. After the calculation is completed, the inter-story displacement time history of the first and second floors, the absolute acceleration time history of the top plate node, the absolute acceleration time history of the middle plate node, the absolute acceleration time history of the bottom plate node, and the output time history of the TID connection unit are extracted from the ABAQUS output results. Then, according to the definition of the three optimization objectives, the maximum inter-story displacement angle, the maximum floor absolute acceleration, and the maximum TID output are calculated for each ground motion. The average value or envelope value of the three objectives under all ground motion records is returned to the genetic algorithm as the final evaluation result of the TID parameter combination. S6. Engineering Decision-Making Based on Pareto Fronts Once the genetic algorithm reaches the preset number of iterations or meets the convergence condition, it obtains a non-dominated solution set composed of multiple TID parameter combinations. The non-dominated solution set is compared according to three objectives: maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output. The performance differences of each TID parameter combination are displayed in a three-dimensional target space or a two-dimensional projection plane. Based on the requirements for main structure deformation control, floor acceleration control, and TID connection node output control in the engineering design of a double-layer, three-span subway station, a TID parameter combination that takes into account the three optimization objectives is selected from the non-dominated solution set as the recommended parameter combination for the project. S7. Conduct comprehensive verification and mechanism analysis of seismic isolation and vibration reduction performance. Ground motion records that did not participate in the multi-objective parameter optimization using the genetic algorithm in step S4 and have different spectral characteristics from the ground motion input set in step S3 were selected as verification ground motion input data. Using ABAQUS software, under the same soil parameters, structural parameters, boundary conditions, ground motion input, and calculation conditions, soil-structure finite element models without TID control, soil-structure-TID coupled finite element models with initial empirical parameter TID, and soil-structure-TID coupled finite element models with the engineering recommended parameter combination TID in step S6 were established and calculated respectively. The maximum inter-story drift angle, maximum absolute floor acceleration, TID output, and structural energy response of the three types of models were compared to verify the seismic isolation effect of the TID parameter combination obtained in step S6 relative to the model without TID control and the initial empirical parameter TID model. The mechanism by which TID transfers and dissipates the vibration energy of the main structure of the double-layer three-span subway station through inertial enhancement, tuned energy absorption, and damping energy dissipation was analyzed.

2. The TID parameter optimization method for vibration reduction of double-layer three-span subway stations according to claim 1, characterized in that: In step S1, the underground two-story three-span frame structure includes the lower space between the bottom slab and the middle slab and the upper space between the middle slab and the top slab. The floor numbers are i=1 and i=2, where i=1 represents the lower floor and i=2 represents the upper floor. The maximum subsequent floor is the second floor. The three spans include the left span, the middle span, and the right span formed by the left side wall, the middle column, and the right side wall. The TID installation node locations are divided into the intersection nodes of the top of the upper middle column and the top plate, the intersection nodes of the bottom of the upper middle column and the middle plate, the intersection nodes of the top of the lower middle column and the middle plate, and the intersection nodes of the bottom of the lower middle column and the bottom plate; the intersection nodes of the top of the upper middle column and the top plate and the intersection nodes of the top of the lower middle column and the middle plate are preferred as the initial TID layout nodes; The expression for the inertial force generated by the inertial container is as follows: ； in, and The acceleration of the connection nodes at both ends of the TID along the TID layout direction is given. The connection nodes at both ends are determined by the intersection of the central column and the floor slab, the intersection of the side wall and the floor slab on the same floor, or the intersection of the adjacent central column and the floor slab.

3. The method for optimizing the parameters of an inertial capacitive damper for vibration reduction in a double-layer, three-span subway station according to claim 1, characterized in that, In step S2, the multi-objective optimization function takes the refined soil-structure-TID coupled finite element model established in step S1 as the analysis object, and the top slab, middle slab, bottom slab, and TID connection units in the two-story, three-span underground frame structure as the response extraction objects. After assigning the same set of TID stiffness, damping coefficient, and inertial mass to the spring-damped-inertial container combined unit in step S1 and completing the dynamic time history analysis, the vibration reduction performance of this set of TID parameters is evaluated according to the following three objective functions: The objective function is to minimize the maximum inter-story drift angle, as shown in the formula: ,in ; in, For floor displacement, For floor height, It is the floor number, and The value is consistent with the floor numbering of the double-layer, three-span subway station. This indicates the lower space between the bottom plate and the middle plate. The upper space between the middle slab and the top slab is represented. Therefore, the maximum inter-story drift angle refers to the response value with the largest absolute value among all inter-story drift angle time histories of the 1st and 2nd floors. The minimization refers to the genetic algorithm prioritizing the parameter combination that makes the maximum inter-story drift angle smaller among different TID parameter combinations, so as to reduce the risk of inter-story deformation damage in the connection area of ​​the middle column, side wall and floor slab. Objective function two is to minimize the maximum floor absolute acceleration, formula: The floor absolute acceleration is obtained by extracting the acceleration time histories of the top, middle and bottom representative nodes of the refined soil-structure-TID coupled finite element model in step S1. The maximum floor absolute acceleration refers to the response value that is the largest among all the absolute acceleration time histories of the top, middle and bottom representative nodes. Minimization refers to the genetic algorithm prioritizing the parameter combination that makes the maximum floor absolute acceleration smaller among different TID parameter combinations, so as to reduce the impact of dynamic response on the station floor, station equipment and personnel environment. Objective function three is to minimize the maximum damper output, as shown in the formula: The damper output is obtained by extracting the output time history of the TID connection unit in step S1 under the action of seismic input. The maximum damper output refers to the output value with the largest absolute value among all TID connection units and their full-time output response. Minimization means that the genetic algorithm prioritizes the parameter combination that makes the maximum damper output smaller and meets the vibration reduction requirements among different TID parameter combinations, so as to avoid excessive local stress in the TID device and its column-to-floor connection nodes, sidewall-to-floor connection nodes or adjacent component connection nodes. Thus, the three objectives of maximum inter-story drift angle, maximum floor absolute acceleration and maximum damper output correspond to the deformation control of the station main structure, the dynamic response control of the floor and the stress control of the TID project, respectively.

4. The method for optimizing the parameters of an inertial capacitive damper for vibration reduction in a double-layer, three-span subway station according to claim 1, characterized in that: In step S3, the establishment of the seismic motion input set is based on the double-layer, three-span subway station project site in step S1, and corresponds to the three optimization objectives in step S2: maximum inter-story drift angle, maximum absolute floor acceleration, and maximum TID output. First, the selection criteria for seismic motion records are determined according to the seismic fortification intensity, site category, and design response spectrum of the station location. Then, 5-8 seismic motion records are selected as optimization inputs from the seismic design data of the project, the publicly available strong ground motion record database, or the artificial wave file generated according to the design response spectrum. For each seismic motion record, the acceleration time history, peak acceleration, time interval, and duration should be extracted. The data should be provided, and the source of the data should be noted. The selected ground motion records should cover different spectral characteristics with more obvious low-frequency components, more obvious mid-frequency components, and more obvious high-frequency components. Before inputting the refined soil-structure-TID coupled finite element model established in step S1, the amplitude should be adjusted so that the maximum inter-story drift angle, maximum absolute floor acceleration, and maximum TID output of each set of TID parameters are calculated under the same ground motion input set. This ensures that the optimized TID parameter results are not local results for a single ground motion record, but rather robust solutions with stable damping performance for a two-story, three-span subway station under different ground motion input conditions.

5. The method for optimizing the parameters of an inertial capacitive damper for vibration reduction in a double-layer, three-span subway station according to claim 1, characterized in that: In step S4, each chromosome contains at least and at most the three TID parameters mentioned above. Each chromosome corresponds to a set of TID parameter combinations that can be assigned to the spring-damped-inertial container unit, and a conflict objective function is constructed based on the structural critical response. ； In the formula, F(m) tid ,k tid ,c tid () represents a multi-objective evaluation function vector determined by a set of TID parameters, which is also the set of objective functions used by the genetic algorithm to evaluate the combination of TID parameters corresponding to a chromosome. tid The inertial mass parameter of the TID (Transient Inertial Container) is the equivalent inertial parameter of the container, used to characterize the inertial enhancement effect caused by the relative acceleration of the connecting nodes at both ends of the TID. k tid Indicates the stiffness of the TID, used to characterize the restoring force generated by the relative displacement of the connecting nodes at both ends of the TID, c tid f1(u) represents the TID damping coefficient, used to characterize the damping energy dissipation capacity generated by the relative velocity of the connecting nodes at both ends of the TID. max The first objective function (u) evaluates the maximum inter-story drift angle between the first and second floors of a double-layer, three-span subway station under seismic loading. This function characterizes the effectiveness of the inter-story deformation control of the main structure. max This represents the maximum value of the inter-story drift angle in the time history between the 1st and 2nd floors. Specifically, it is obtained by removing the relative displacement between adjacent floors and taking the maximum absolute value after deducting the corresponding floor height. f2(a max () represents the second objective function, which evaluates the maximum absolute floor acceleration of the nodes represented by the top, middle, and bottom slabs. This acceleration characterizes the strength of the dynamic response experienced by the station floors, station equipment, and personnel environment. max This represents the maximum absolute acceleration values ​​in the time histories of the top, middle, and bottom plate nodes, f3(F TID,max ) represents the third objective function, which evaluates the maximum output force of the TID connection unit and is used to characterize the engineering stress level of the TID device and its connection nodes; During the initialization of the population within the range of TID parameter values, the TID stiffness, damping coefficient, and inertia of each individual must not be less than the lower limit of the corresponding parameter and must not be greater than the upper limit of the corresponding parameter. The lower limit and upper limit of the parameter are jointly determined by the dynamic characteristic analysis results of the double-layer three-span subway station without TID control model in step S1, the allowable range of TID device construction, and the bearing capacity of TID connection nodes. For each individual in the initial population, dynamic time history analysis was performed using ABAQUS finite element software with all ground motion records input. The fitness evaluation results of the individual were then calculated based on three target values: maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output. Individuals with better comprehensive evaluation were selected through tournament selection. Then, TID parameter information was exchanged between two parent individuals through simulated binary crossover. Finally, new candidate parameter combinations were generated within the parameter value range through polynomial mutation. Non-dominated sorting was used to distinguish the superiority and inferiority levels of different individuals on the three optimization objectives. Crowding distance was used to maintain the uniformity of the distribution of the solution set within the same level, so that the population evolved towards the Pareto front generation by generation. Based on the Pareto front and the engineering requirements of a double-layer, three-span subway station, a robust solution is selected. These requirements include reducing the maximum inter-story drift angle of the first and second floors in the double-layer, three-span structure, reducing the maximum absolute floor acceleration of the top, middle, and bottom slabs, and limiting the maximum output of the TID connection unit. This ensures that the TID can still work with the main structure to achieve the vibration reduction target under parameter fluctuations. ,in The weighting factor is used to represent the relative importance of the three objectives—maximum inter-story drift angle, maximum floor absolute acceleration, and maximum TID output—in the engineering decision-making stage, and the use of the weighting factor does not change the definition of the three optimization objectives in step S2.

6. The method for optimizing the parameters of an inertial capacitive damper for vibration reduction in a double-layer, three-span subway station according to claim 1, characterized in that: In step S5, when evaluating any TID parameter combination X, the genetic algorithm first considers the TID stiffness k in the TID parameter combination X. tid TID damping coefficient c tid and TID inertial mass m tid The values ​​are assigned to the spring-damped-inertial container combined unit described in step S1, and then each ground motion record in the ground motion input set G formed in step S3 is input sequentially. After completing the dynamic time history analysis under the action of each ground motion record, the inter-story displacement time history of the first and second layers, the absolute acceleration time history of the top plate node, the absolute acceleration time history of the middle plate node, the absolute acceleration time history of the bottom plate node, and the output time history of the TID connection unit, which were determined in step S2, are extracted from the ABAQUS output results. Then, according to the calculation formulas corresponding to objective function one, objective function two, and objective function three in claim 3, the maximum value under the action of the ground motion is calculated respectively. The objective function values ​​are f1(X) for inter-story drift angle, f2(X) for maximum absolute floor acceleration, and f3(X) for maximum TID output. If the average evaluation criterion is adopted, the arithmetic mean of f1(X), f2(X), and f3(X) of all ground motion records in the ground motion input set G in step S3 is taken. If the safety envelope evaluation criterion is adopted, the maximum value of f1(X), f2(X), and f3(X) of all ground motion records in the ground motion input set G in step S3 is taken. The arithmetic mean or the maximum envelope value is returned to the genetic algorithm as the final performance index of the TID parameter combination X.

7. The method for optimizing the parameters of an inertial capacitive damper for vibration reduction in a double-layer, three-span subway station according to claim 1, characterized in that: In step S6, the Pareto front-based engineering decision-making includes: visualizing and comparing a set of non-dominated solutions obtained by multi-objective parameter optimization using a genetic algorithm in a three-dimensional target space or a two-dimensional projection plane; in step S1, the maximum inter-story drift angle, maximum absolute floor acceleration, and maximum TID output calculated by the refined soil-structure-TID coupled finite element model under seismic input constitute the structure; wherein, the maximum inter-story drift angle is used to characterize the deformation control effect of the main structure of the double-layer three-span subway station, the maximum absolute floor acceleration is used to characterize the dynamic response control effect of the station structure and auxiliary equipment, and the maximum TID output is used to characterize the stress level and engineering feasibility of the tuned inertial capacitive damper; according to the distribution relationship of the non-dominated solution set in the three-dimensional target space, a combination of TID parameters that takes into account structural deformation control, acceleration control, and damper output constraints is selected as the recommended engineering solution.

8. The method for optimizing the parameters of an inertial capacitive damper for vibration reduction in a double-layer, three-span subway station according to claim 1, characterized in that: In step S7, the comprehensive verification and mechanism analysis of seismic isolation and vibration reduction performance includes: based on the seismic fortification intensity, site category and design response spectrum of the location of the double-layer three-span subway station, selecting at least one actual strong earthquake record or artificially synthesized earthquake record that did not participate in the optimization calculation in step S3 and has different spectral characteristics from the optimized input earthquake ground motion record as the verification earthquake ground motion input.

9. The method for optimizing the parameters of an inertial capacitive damper for vibration reduction in a double-layer, three-span subway station according to claim 1, characterized in that: In step S1, the TID is arranged between the central column and the floor slab, between the side wall and the floor slab, and at key connection nodes in the station structure that require seismic response control in a double-layer, three-span subway station. The two ends of the TID are connected to adjacent component nodes in the main station structure, and it consists of spring units, damping units, and inertial capacitance units. The parameters of the spring units, damping units, and inertial capacitance units are the optimized stiffness parameters of the TID. Damping coefficient and inertia The TID, together with the main structure of the station, forms a soil-structure-TID coupled finite element model, which is used for seismic isolation and reduction analysis of a two-story, three-span subway station under seismic input.

10. The method for optimizing the parameters of an inertial capacitive damper for vibration reduction in a double-layer, three-span subway station according to claim 1, characterized in that: In step S1, the optimized TID parameters are used to control and analyze the dynamic response of a double-layer, three-span subway station structure under seismic input. During the dynamic response analysis of the main station structure, the time histories of absolute acceleration of the floor slabs, inter-story displacement, TID output, and structural energy response data are extracted. The absolute acceleration time histories of the floor slabs include the absolute acceleration responses of the corresponding nodes of the top, middle, and bottom slabs. The structural energy response data include seismic input energy, structural strain energy, structural damping energy dissipation, and TID energy dissipation. By comparing the response data of the model without TID control, the model with initial empirical TID parameters, and the model with optimized TID parameters under the same seismic input, the applicability of the optimized TID parameters in a double-layer, three-span subway station is verified.

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