Method and system for dynamic response analysis of double-layer sea-crossing beam bridge under combined action of wind and wave

Abstract

The application provides a method and system for analyzing dynamic response of a double-layer sea-crossing beam bridge under combined action of wind and wave, which first acquires environmental parameters of a target sea area, constructs a three-dimensional correlation probability model based on a C-Vine Copula function, and determines a design combination value under a specified joint return period through Monte Carlo simulation; then a refined finite element model of the double-layer sea-crossing continuous beam bridge is established and dynamic characteristics are verified, wherein a hanger rod is simulated by a tensile rod element only; time histories of fluctuating wind load of the main beam and wave load of the lower structure are simulated based on the design combination value, and are applied to the model for transient dynamics analysis to obtain dynamic responses of the upper and lower main beams and the lower structure; finally, the responses are compared with the limit values in the specification, and design optimization conclusions are output. The application can accurately quantify the coupling effect of wind and wave, solve the problem that the response characteristics of the double-layer bridge under combined action are not clear, and effectively guide the structural design optimization.

Description

Technical Field

[0001] This invention relates to the technical field of bridge structural design, and in particular to a method and system for analyzing the dynamic response of a double-deck sea-crossing beam bridge under the combined action of wind and waves. Background Technology

[0002] Cross-sea bridges serve as crucial transportation hubs connecting the mainland with islands or peninsulas. In certain coastal areas, due to restrictions on surrounding airspace clearance and the need for tiered traffic functions, double-deck continuous beam bridges have become a highly representative cross-sea transportation infrastructure solution due to their significant advantages such as high space utilization and structural stiffness. However, these bridges operate in complex environments, constantly facing the combined effects of random pulsating wind loads and nonlinear wave loads, resulting in highly complex structural dynamic responses.

[0003] Existing bridge wind and wave resistance design codes typically treat wind and wave loads as independent random events, and habitually use the extreme values ​​under their independent return periods for linear superposition calculations. This design method fails to effectively capture the inherent physical correlation between environmental parameters such as wind speed, wave height, and wave period, often leading to significant deviations between the calculated dynamic response of the structure and actual service conditions. This results in engineering bottlenecks such as excessive redundancy in material usage or insufficient safety redundancy under extreme weather conditions.

[0004] Although existing patents, such as CN109657409A, have proposed a method for evaluating the joint wind and wave distribution based on Copula functions, the probabilistic models they establish are mostly limited to the two-dimensional statistical characteristics of wind speed and wave height, neglecting the crucial influence of wave period on the structural natural vibration response and fatigue characteristics. Furthermore, they do not provide refined modeling for the unique "main beam-suspender-secondary beam" spatial coupling system of double-deck beam bridges. Another patent, CN109635509A, while involving load combination calculations, primarily focuses on long-span flexible cable-stayed bridges. Their stress mechanisms differ fundamentally from those of stiffer double-deck continuous beam bridges, and they lack the precise description of asymmetric correlations among multiple variables, as seen in Vine Copula structures. Therefore, for double-deck continuous beam bridges across the sea in scenarios with limited flight clearance, there is an urgent need to develop a systematic technical solution that can integrate a three-dimensional joint probabilistic model of wind, wave, and period, and deeply reveal the dynamic interference laws and design optimization principles of double-deck structures under suspender connections. Summary of the Invention

[0005] To address the aforementioned technical problems, this application provides a method and system for analyzing the dynamic response of a double-deck sea-crossing beam bridge under the combined action of wind and waves. This method can accurately quantify the nonlinear correlation of wind and wave environmental parameters and synergistically consider the aerodynamic disturbances of the double-deck main girder and the hydrodynamic effects of the substructure, thereby providing a scientific and economical decision-making basis for the safety assessment and performance optimization of sea-crossing bridges.

[0006] In a first aspect, this invention proposes a dynamic response analysis method for double-deck sea-crossing beam bridges under combined wind and wave action, the method comprising:

[0007] S1. Obtain environmental parameters such as wind speed, wave height, and wave period of the target sea area. Construct a three-dimensional correlation probability model of the environmental parameters based on the C-Vine Copula function. Determine the design combination value of environmental parameters under a specified joint return period through Monte Carlo simulation. S2. A finite element model of a double-layer continuous beam bridge across the sea is established. The coupling relationship of the suspenders is simulated by elements with nonlinear stress characteristics, and the dynamic characteristics of the finite element model are verified. S3, based on the design combination values ​​of environmental parameters, simulates the time histories of pulsating wind loads acting on the main beam of the bridge and wave loads acting on the substructure of the bridge, respectively. S4. Simulated pulsating wind load and wave load are applied to the finite element model to perform transient dynamic analysis and obtain the dynamic response of the upper and lower main beams and the substructure of the bridge under the combined action of wind and waves. S5 compares the dynamic response with the specification limits and outputs conclusions based on the response characteristics to guide the optimization of bridge structural design.

[0008] The above technical solution, by constructing a complete process system from probabilistic modeling of multidimensional environmental parameters to analysis of nonlinear dynamic response of structures, achieves high-fidelity simulation of the stress characteristics of double-deck sea-crossing beam bridges under complex wind and wave coupling conditions, providing a scientific quantitative basis for structural safety assessment and design optimization under extreme conditions.

[0009] Furthermore, the three-dimensional joint probability density function of the three-dimensional correlation probability model Decomposed into:

[0010] In the formula, These are wind speed, significant wave height, and wave period, respectively. For wind speed and significant wave height variables, use a two-dimensional Copula density function. Given the effective wave height variable, the conditional two-dimensional Copula density function is given the wind speed and wave period. , , These are the marginal distribution functions of wind speed, significant wave height, and wave period variables, respectively. , These are the conditional distribution function values ​​of wind speed and wave period variables, respectively, given a significant wave height.

[0011] The above technical solution utilizes the chain decomposition characteristics of the C-Vine Copula structure to transform the complex dependencies between high-dimensional variables into multiple nested two-dimensional correlation functions, effectively overcoming the limitations of traditional multivariate probability models in describing the asymmetry, tail correlation, and multimodal distribution of environmental parameters. This method can accurately capture the nonlinear coupling mechanism among wind, waves, and cycles, providing a high-fidelity joint probability density foundation for subsequent calculations of the joint return period.

[0012] Furthermore, the joint return period is determined based on a three-dimensional correlation probability model, satisfying the following formula:

[0013] In the formula, To specify the joint return period; , respectively, are the marginal cumulative distribution functions of wind speed, significant wave height, and wave period; C is the three-dimensional joint Copula distribution function constructed through the C-Vine structure.

[0014] The aforementioned technical solution achieves a leap from the traditional "single-variable independent return period" to the "multi-factor coupled return period" by constructing a failure probability calculation model based on a three-dimensional joint distribution function. This technique can quantify the true probability of extreme events occurring simultaneously with different environmental factors, significantly reducing the risk of structural failure of cross-sea bridges due to insufficient load estimation during their design lifespan. It also avoids overly conservative engineering investment caused by simply linearly superimposing environmental parameters.

[0015] Furthermore, step S1 includes: S11, acquire measured time history data of wind speed, significant wave height and wave period for a long sequence in the target sea area; S12, based on the goodness-of-fit evaluation criteria, the marginal distribution of wind speed, significant wave height and wave period variables is optimized; among them, the wind speed variable adopts a non-parametric probability density estimation model, and the significant wave height and wave period variables adopt a parametric probability distribution model for fitting. S13, construct a three-dimensional correlation probability model with wind speed variable as the root node; wherein, the first correlation function with upper tail dependence is selected to describe the correlation between wind speed and significant wave height, and the second correlation function with lower tail dependence is selected to describe the correlation between wind speed and wave period. S14, determine the parameters of the first correlation function and the second correlation function, and use the Monte Carlo random sampling method to extract the environmental parameter design combination values ​​with a specified joint return period in the multidimensional probability space.

[0016] The above technical solution fully leverages the advantages of different statistical models by implementing a differentiated marginal distribution fitting strategy. For wind speed variables with drastic fluctuations and complex distribution patterns, non-parametric estimation preserves the true distribution characteristics of the original data; for wave variables with extreme value tendencies, parametric distribution ensures statistical stability when extrapolated to long return periods. This ensures high accuracy and robustness of the model at the basic data processing level.

[0017] Furthermore, in step S12, the non-parametric probability density estimation model adopts a kernel density estimation model; the parametric probability distribution model adopts a generalized extreme value distribution model, whose probability density function... The expression for is:

[0018] In the formula, Variables for effective wave height or wave period; The base of the natural logarithm The exponential function; For position parameters; For scale parameters; For shape parameters.

[0019] In the aforementioned technical solution, a generalized extreme value distribution model is introduced to characterize the significant wave height and wave period. This model can accurately fit the heavy-tailed distribution characteristics of wave elements through the synergistic optimization of shape, scale, and position parameters. In particular, this model enhances the predictive ability of "extreme value intervals," providing more statistically significant boundary value references for the safety design of cross-sea bridges under extreme sea conditions.

[0020] Furthermore, in step S13, the first correlation function is the Gumbel Copula function, which is expressed as:

[0021] In the formula, , which are the edge distribution function values ​​of wind speed and wave height, respectively; The Gumbel Copula parameter describes the correlation between wind speed and wave height; These are the marginal distribution functions for wind speed and significant wave height, respectively; The second correlation function is the Clayton Copula function, which is expressed as follows:

[0022] In the formula, , which are the conditional distribution function values ​​of wind speed and wave period under given effective wave height; The Clayton Copula parameter describes the correlation between wind speed and wave period variables under this condition; These are the marginal distribution functions for wind speed, significant wave height, and wave period, respectively.

[0023] In the above technical solution, a differentiated modeling scheme (combining non-parametric kernel density estimation and parametric extreme value distribution) is implemented for the statistical characteristics of different environmental elements. This fully considers the upper and lower tail dependence characteristics of wind speed and waves in the large value range, and significantly improves the physical rationality and calculation accuracy of the environmental parameter design combination values ​​under extreme recurrence periods.

[0024] Furthermore, step S2 specifically includes: S21 uses variable cross-section beam elements to simulate the upper concrete main beam and constant cross-section beam elements to simulate the lower fish-belly steel box girder; by adjusting the material density, the mass ratio of the lower fish-belly steel box girder to the upper concrete main beam is controlled between 0.6 and 0.8. S22 uses LINK10 bar elements under tension only to simulate the hangers connecting the upper and lower main beams; the initial strain of the LINK10 elements is set according to the hanger preload to characterize the nonlinear relaxation characteristics of the hangers under the combined action of wind and waves; S23 uses node coupling or elastic connection units to simulate the anchorage constraint of cable clamps on the upper and lower main beams; beam units are used to simulate the lower piers and pile foundations, and spring units are used to simulate the pile-soil interaction. S24. Perform modal analysis on the assembled finite element model to extract the first-order natural frequencies and mode shapes. Compare the extracted natural frequencies with environmental excitation test data or empirical formulas for similar structures. If the frequency error is within a preset threshold, the model is determined to be accurate.

[0025] In the above technical solution, by constraining the mass distribution of the heterogeneous structure (concrete and steel box girder) of the double-layer bridge and accurately characterizing the nonlinear characteristics of the unidirectional tension of the hangers, the finite element model is able to accurately capture the displacement incoordination phenomenon and dynamic stiffness change under the alternating excitation of wind and waves, thereby improving the model's simulation realism of complex vibration behavior.

[0026] Furthermore, in step S3, the simulation process of pulsating wind load includes: S31, based on the environmental parameter design combination value, the time history of the pulsating wind acting on the upper and lower beam nodes is generated by the harmonic synthesis method. S32, through computational fluid dynamics numerical simulation, the aerodynamic drag coefficients of the main beam sections of the upper and lower layers were obtained respectively. Lift coefficient Torque coefficient and its first derivative ; S33, the time history of the buffeting force acting on the main beam is calculated based on the quasi-steady buffeting force model. The formula for calculating the buffeting force per unit length of the main beam is as follows: Aerodynamic drag Lift Torque In the formula, air density, The average wind speed, The characteristic width of the main beam This represents the time history of vertical pulsating wind speed.

[0027] In the above technical solution, by combining the aerodynamic three-component force coefficients and their derivatives calibrated by computational fluid dynamics, the complex aerodynamic interference effects between the double-layer main beams can be taken into account. The quasi-steady flutter force model realizes the simulation of the refined wind load time history of large-span flexible structures, thereby improving the credibility of wind-induced dynamic response analysis.

[0028] Furthermore, in step S3, the simulation of wave load specifically involves: calculating the effective wave height and wave period based on the design combination values ​​of environmental parameters, using linear wave theory and the Morison equation to calculate the wave force on the pile foundation; and calculating the wave force acting on a unit length of the circular pile foundation. Calculate according to the following formula:

[0029] in, The density of seawater; and These are the wave resistance coefficient and the inertial force coefficient, respectively. The diameter of the circular pile foundation; The horizontal velocity of the water particles; The symbol is for partial differentials; This represents the time history of the horizontal acceleration of water particles.

[0030] Furthermore, the simulation of wave loads also includes introducing a pile group disturbance coefficient when calculating the total wave force on a pile group foundation. Correction for wave force on single piles; interference coefficient for pile groups. The value was calibrated through a three-dimensional numerical wave flume test, and its range was 0.7-0.9.

[0031] In the above technical solution, by introducing the group pile interference coefficient calibrated by numerical flume into the Morison equation, the effect of fluid mutual interference between pile foundation groups on the reduction or enhancement of wave force is quantified, overcoming the calculation deviation caused by the simple superposition of single pile forces in the traditional method, and ensuring the safety of the stress analysis of deep-water bridge pier foundation.

[0032] Furthermore, step S4 includes: S41, based on d'Alembert's principle, applies a vector of fluctuating wind load. and wave load vector Transient dynamic analysis was performed using a finite element model; S42, via Newmark- The following dynamic equations can be solved using the following method:

[0033] In the formula, These are the mass matrix, damping matrix, and stiffness matrix of the structure, respectively. These are the acceleration vector, velocity vector, and displacement vector of the node, respectively. S43, obtain the time history response of the upper and lower main beams and the substructure of the bridge under the combined action of wind and waves. The response includes displacement, velocity, acceleration and internal forces of key components.

[0034] In the above technical solution, by establishing the dynamic equilibrium equation of the entire bridge that includes structural mass, damping and stiffness characteristics, the simultaneous solution of the spatial vibration of the double-layer main beam and the fluid-structure interaction effect of the substructure is realized. This method can fully reveal the energy transfer mechanism of the entire structure under the joint excitation of wind and waves, and provide high-fidelity numerical basis for evaluating the coordinated stress performance and seismic / disaster resistance of key parts of the double-layer cross-sea bridge.

[0035] Secondly, this invention proposes a dynamic response analysis system for a double-deck sea-crossing beam bridge under the combined action of wind and waves: The wind and wave joint probability analysis module is configured to acquire environmental parameters such as wind speed, wave height, and wave period of the target sea area, construct a three-dimensional correlation probability model of environmental parameters based on the C-Vine Copula function, and determine the design combination value of environmental parameters under a specified joint return period through Monte Carlo simulation. The finite element modeling and verification module is configured to establish a finite element model of a double-layer continuous beam bridge spanning the sea. It simulates the coupling relationship of the hangers using elements with nonlinear stress characteristics and verifies the dynamic characteristics of the finite element model. The wind and wave load simulation module is configured to simulate the time histories of pulsating wind loads acting on the main girder of the bridge and wave loads acting on the substructure of the bridge, based on the design combination values ​​of environmental parameters. The dynamic response solution module is configured to apply simulated pulsating wind loads and wave loads to the finite element model, perform transient dynamic analysis, and obtain the dynamic response of the upper and lower main beams and the substructure of the bridge under the combined action of wind and waves. The design optimization and feedback module is configured to compare the dynamic response with the specification limits and output conclusions based on the response characteristics to guide the optimization of bridge structural design.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention constructs a three-dimensional probabilistic model for disaster assessment of double-deck sea-crossing beam bridges. By introducing a C-Vine Copula structure for the first time, a three-dimensional joint probabilistic model of wind speed, significant wave height, and wave period, driven by wind speed variables, was successfully established. Compared with traditional two-dimensional models or simple linear superposition methods, this model can more realistically quantify the asymmetric and nonlinear correlations between marine environmental parameters. The design combination values ​​of environmental parameters determined based on the three-dimensional correlation probabilistic model are more scientific than the design values ​​of simple superposition of independent return periods, effectively avoiding excessive conservatism in engineering design and significantly saving engineering costs while ensuring structural safety.

[0037] 2. This invention enables refined simulation and verification of the complex dynamic characteristics of a double-layer continuous beam bridge spanning the sea. By establishing a refined finite element model, particularly utilizing the LINK10 element with nonlinear stress characteristics to simulate the coupling relationship of the suspenders, and strictly controlling the mass ratio of the lower steel box girder to the upper main girder between 0.6 and 0.8, this invention can accurately characterize the inertial distribution and stiffness abrupt change behavior of the double-layer heterogeneous structure under wind and wave excitation. Through modal analysis and extraction and verification of natural vibration characteristics, the analysis process ensures its direct guiding significance for the wind and wave resistant design of this special bridge type.

[0038] 3. This invention deeply reveals the unique structural response mechanism and load transfer law of double-deck bridges. It systematically clarifies that for a double-deck coupled system, pulsating wind load is the dominant factor causing significant vertical vibration in the lower main girder, while wave load mainly affects the lateral response of the piers and pile foundations, with negligible influence on the torsional and vertical displacement of the main girder. Simultaneously, by quantitatively comparing the calculation results of "combined wind and wave action" and "simple superposition of individual load responses," it reveals the coupling weakening effect between the two, proving that the actual response value is generally smaller than the linear superposition value of the individual load effects. This quantitative finding can be directly used to correct conservative design assumptions, providing theoretical support for the optimization of load combination coefficients.

[0039] 4. This invention establishes an integrated and portable standardized analysis and design optimization system. It integrates complex environmental probability analysis, nonlinear load simulation, transient dynamic finite element calculation, and specification limit assessment into a unified technical framework, with a clear process and strong operability. Quantitative analysis results show that the structural response under a 100-year joint return period can increase by up to 56% to 75% compared to a 50-year period, providing precise limits for safety design under extreme conditions. This standardized process is not only applicable to double-deck sea-crossing beam bridges but can also be extended to offshore platforms, wind turbine foundations, and other marine structures with similar fluid-structure interaction systems. Attached Figure Description

[0040] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments and, together with the description, serve to explain the principles of the invention. Many anticipated advantages of the embodiments and other embodiments of the invention will be readily recognized as they become better understood through reference to the following detailed description. Elements in the drawings are not necessarily to scale. The same reference numerals refer to corresponding similar parts.

[0041] Figure 1 This is a flowchart of a dynamic response analysis method for a double-deck sea-crossing beam bridge under the combined action of wind and waves according to an embodiment of the present invention; Figure 2 This is a framework diagram of a dynamic response analysis system for a double-deck sea-crossing beam bridge under the combined action of wind and waves according to an embodiment of the present invention. Figure 3a This is a spatial layout of the three-dimensional spatial topology, span distribution, and suspender coupling system of a double-layer continuous beam bridge across the sea according to an embodiment of the present invention. Figure 3b According to an embodiment of the present invention, the interaction details between the pile foundation structure and the surrounding soil environment are demonstrated through boundary constraint simulation. Figure 4a This is the time history of the transverse displacement of node 31 of the upper beam under single wind action according to an embodiment of the present invention; Figure 4b This is the time history of the vertical displacement of node 31 of the upper beam under single wind action according to an embodiment of the present invention; Figure 4c This is the torsional displacement time history of node 31 of the upper beam under single wind action according to an embodiment of the present invention; Figure 4d This is the time history of the transverse bridge displacement of node 153 of the lower beam under single wind action according to an embodiment of the present invention; Figure 4e This is the time history of the vertical displacement of node 153 of the lower beam under single wind action according to an embodiment of the present invention; Figure 4f This is the torsional displacement time history of node 153 of the lower beam under single wind action according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of a computer system used to implement the electronic device of the present application. Detailed Implementation

[0042] In the following detailed description, reference is made to the accompanying drawings, which form part of the detailed description and are illustrated by specific illustrative embodiments in which the invention may be practiced. In this regard, directional terms such as “top,” “bottom,” “left,” “right,” “up,” “down,” etc., are used with reference to the orientation of the described figures. Because components of the embodiments can be positioned in several different orientations, directional terms are used for illustrative purposes and are by no means limiting. It should be understood that other embodiments may be utilized or logical changes may be made without departing from the scope of the invention. Therefore, the following detailed description should not be taken in a limiting sense, and the scope of the invention is defined by the appended claims.

[0043] This invention proposes a method for analyzing the dynamic response of a double-deck sea-crossing beam bridge under the combined action of wind and waves. For example... Figure 1 As shown, the method includes: S1. Obtain environmental parameters such as wind speed, wave height, and wave period of the target sea area. Construct a three-dimensional correlation probability model of the environmental parameters based on the C-Vine Copula function. Determine the design combination value of environmental parameters under a specified joint return period through Monte Carlo simulation. In some specific embodiments, step S1 includes: S11, acquire measured time history data of wind speed, significant wave height and wave period for a long sequence in the target sea area; S12, based on the goodness-of-fit evaluation criteria, the marginal distribution of wind speed, significant wave height and wave period variables is optimized; among them, the wind speed variable adopts a non-parametric probability density estimation model, and the significant wave height and wave period variables adopt a parametric probability distribution model for fitting. Specifically, the non-parametric probability density estimation model uses a kernel density estimation model; the parametric probability distribution model uses a generalized extreme value distribution model, whose probability density function... The expression for is:

[0044] In the formula, Variables for effective wave height or wave period; The base of the natural logarithm The exponential function is used to construct a continuous curve of the probability distribution; This refers to the position parameter, i.e., the limit range of the effective wave height or wave period data; For scale parameters; For shape parameters.

[0045] S13, construct a three-dimensional correlation probability model with wind speed variable as the root node; wherein, the first correlation function with upper tail dependence is selected to describe the correlation between wind speed and significant wave height, and the second correlation function with lower tail dependence is selected to describe the correlation between wind speed and wave period. Specifically, the first association function is the Gumbel Copula function, which is expressed as:

[0046] In the formula, , which are the edge distribution function values ​​of wind speed and wave height, respectively; The Gumbel Copula parameter describes the correlation between wind speed and wave height; These are the marginal distribution functions for wind speed and significant wave height, respectively; The second correlation function is the Clayton Copula function, which is expressed as follows:

[0047] In the formula, , which are the conditional distribution function values ​​of wind speed and wave period under given effective wave height; The Clayton Copula parameter describes the correlation between wind speed and wave period variables under this condition; Wind speed variables Significant wave height variable Wave period variables The marginal cumulative distribution function.

[0048] S14, determine the parameters of the first correlation function and the second correlation function, and use the Monte Carlo random sampling method to extract the design combination values ​​of environmental parameters under the specified joint return period in the multidimensional probability space.

[0049] Specifically, marginal distribution fitting was performed on wind speed, wave height, and wave period data, and the optimal marginal distribution model for each parameter was determined based on the goodness-of-fit evaluation. A three-dimensional correlation probability model of the environmental parameter design combination values ​​was constructed using a C-Vine Copula structure with wind speed as the root node, wherein the joint return period was specified. Determined based on mathematical relationships, that is In the formula, To specify the joint return period, in years; Wind speed variables Significant wave height variable Wave period variables The marginal cumulative distribution function; C is the three-dimensional joint Copula distribution function constructed through the C-Vine structure.

[0050] S2. A finite element model of a double-layer continuous beam bridge across the sea is established. The coupling relationship of the suspenders is simulated by elements with nonlinear stress characteristics, and the dynamic characteristics of the finite element model are verified. In some specific embodiments, step S2 specifically includes: S21 uses variable cross-section beam elements to simulate the upper concrete main beam and constant cross-section beam elements to simulate the lower fish-belly steel box girder; by adjusting the material density, the mass ratio of the lower fish-belly steel box girder to the upper concrete main beam is controlled between 0.6 and 0.8. S22 uses LINK10 rod elements that are only under tension to simulate the suspenders connecting the upper and lower main beams; the initial strain of the LINK10 element is set according to the preload of the suspender to characterize the nonlinear relaxation characteristics of the suspender under the combined action of wind and waves, that is, the element can only withstand tension, and its stiffness is automatically set to zero when it is under compression. S23 uses node coupling or elastic connection units to simulate the anchorage constraint of cable clamps on the upper and lower main beams; beam units are used to simulate the lower piers and pile foundations, and spring units are used to simulate the pile-soil interaction. S24. Perform modal analysis on the assembled finite element model to extract the first-order natural frequencies and mode shapes. Compare the extracted natural frequencies with environmental excitation test data or empirical formulas for similar structures. If the frequency error is within a preset threshold, the model is determined to be accurate.

[0051] S3, based on the design combination values ​​of environmental parameters, simulates the time histories of pulsating wind loads acting on the main beam of the bridge and wave loads acting on the substructure of the bridge, respectively.

[0052] In some specific embodiments, the simulation process of pulsating wind load includes: S31, based on the environmental parameter design combination value, the time history of the pulsating wind acting on the upper and lower beam nodes is generated by the harmonic synthesis method. S32, through computational fluid dynamics numerical simulation, the aerodynamic drag coefficients of the main beam sections of the upper and lower layers were obtained respectively. Lift coefficient Torque coefficient and its first derivative ; S33, the time history of the buffeting force acting on the main beam is calculated based on the quasi-steady buffeting force model. The formula for calculating the buffeting force per unit length of the main beam is as follows: Aerodynamic drag Lift Torque In the formula, The density of air is generally taken as 1.225 kg / m³. 3 , To calculate the average wind speed at the cross-section, The characteristic width of the main girder is usually taken as the width of the upper deck for double-deck bridges. This represents the time history of vertical pulsating wind speed.

[0053] The simulation of wave load specifically involves: calculating the effective wave height and wave period based on the design combination of environmental parameters, using linear wave theory and the Morison equation to calculate the wave force on the pile foundation; and calculating the wave force acting per unit length on the circular pile foundation. Calculate according to the following formula:

[0054] in, For the height of the circular pile foundation Wave force time history per unit length at a given location The density of seawater is generally taken as 1025 kg / m³. 3 , and These are the wave drag coefficient and the inertial force coefficient, respectively. The diameter of the circular pile foundation is... The horizontal velocity of the water particles is calculated based on linear wave theory. The symbol is for partial differentials. This represents the time history of the horizontal acceleration of water particles.

[0055] Furthermore, the simulation of wave loads also includes introducing a pile group disturbance coefficient when calculating the total wave force of the pile group foundation. Correction for wave force on single piles; interference coefficient for pile groups. The value was calibrated through a three-dimensional numerical wave flume test, and its range was 0.7-0.9.

[0056] S4 applies simulated pulsating wind and wave loads to the finite element model to perform transient dynamic analysis and obtain the dynamic response of the upper and lower main beams and the substructure of the bridge under the combined action of wind and waves.

[0057] In some specific embodiments, the dynamic response includes the root mean square values ​​of the displacement responses of key nodes in the upper and lower beams. The calculation formula is as follows:

[0058] in, This represents the total number of time steps. For the first The displacement value at each time step.

[0059] S5 compares the dynamic response with the specification limits and outputs conclusions based on the response characteristics to guide the optimization of bridge structural design.

[0060] In some specific embodiments, based on the coupling reduction effect that the dynamic response under the combined action of wind and waves is less than the linear superposition of the responses under individual actions, suggestions for correcting the load combination coefficients for the combined load condition are proposed. Furthermore, based on the response characteristics of pulsating wind load as the dominant factor in vertical vibration of the lower main beam, the adjustment range of design parameters for strengthening the lower main beam section or hanger components is determined. Through in-depth exploration of the nonlinear coupling effect under the combined action of wind and waves, the problem of overly conservative or dangerous structural designs caused by the simple linear superposition of loads in traditional specifications is overcome. Simultaneously, by identifying the unique vibration-dominant excitation source of double-deck bridges, precise parameter decision support is provided for the dimensional optimization and wind-resistant vibration reduction design of key components in complex systems.

[0061] Continue to refer to Figure 2 As an implementation of the above method, in a second aspect, this application provides an embodiment of a framework diagram for a dynamic response analysis system of a double-deck sea-crossing beam bridge under combined wind and wave action. This system embodiment is similar to... Figure 1 Corresponding to the illustrated method embodiment, this system can be specifically applied to various electronic devices. The system 200 includes a wind and wave joint probability analysis module 201, a finite element modeling and verification module 202, a wind and wave load simulation module 203, a dynamic response solution module 204, and a design optimization and feedback module 205, all interconnected. The wind and wave joint probability analysis module 201 is configured to acquire environmental parameters such as wind speed, wave height and wave period of the target sea area, construct a three-dimensional correlation probability model of environmental parameters based on the C-Vine Copula function, and determine the design combination value of environmental parameters under a specified joint return period through Monte Carlo simulation. The finite element modeling and verification module 202 is configured to establish a finite element model of a double-layer continuous beam bridge spanning the sea. In this module, the coupling relationship of the suspenders is simulated by elements with nonlinear stress characteristics, and the dynamic characteristics of the finite element model are verified. The wind and wave load simulation module 203 is configured to simulate the time history of pulsating wind load acting on the main beam of the bridge and wave load acting on the substructure of the bridge based on the design combination value of environmental parameters. The dynamic response solution module 204 is configured to apply simulated pulsating wind loads and wave loads to the finite element model, perform transient dynamic analysis, and obtain the dynamic response of the upper and lower main beams and the substructure of the bridge under the combined action of wind and waves. The design optimization and feedback module 205 is configured to compare the dynamic response with the specification limits and output conclusions based on the response characteristics to guide the optimization of bridge structure design.

[0062] Example 1 Based on a real-world engineering project, this study focuses on a unique double-deck continuous beam bridge spanning the sea. The proposed double-deck, four-span continuous beam bridge (span arrangement 42.5 + 2 × 60 + 42.5 meters) utilizes a variable-section concrete continuous beam for the upper vehicular bridge to optimize load-bearing performance, while the lower pedestrian bridge employs a fish-belly-shaped, uniform-height continuous steel box girder to reduce wind resistance. The lower structure provides vertical support through H-shaped piers and is supplemented by a span-mounted suspender system to form a collaborative load-bearing unit with the upper main beam. Specifically, two pairs of suspenders are installed in the 42.5m side span, and three pairs are installed in the 60m middle span, maintaining a longitudinal spacing of 14m between the suspenders. High-strength cable clamps at both ends of the suspenders achieve a rigid connection between the upper and lower beams. The upper anchor clamp is precisely anchored within the pre-embedded nodes of the upper concrete box girder, thereby achieving vibration transmission and suppression under wind and wave loads through the dynamic coupling effect of the suspenders.

[0063] Historical measured data from marine observation stations near the target bridge site were collected through the data acquisition unit of the wind and wave joint probability analysis module 201, covering hourly observation sequences of wind speed, significant wave height, and wave period over many years. Within the wind and wave joint probability analysis module 201, the marginal distribution fitting unit was invoked to statistically model the wind speed, wave height, and wave period sequences. The goodness-of-fit was tested using the root mean square error (RMSE) evaluation index to determine the optimal marginal distributions for each variable: the wind speed sequence was represented using kernel density estimation (KDE) to capture its complex probability density characteristics; the wave height and wave period sequences were characterized using the generalized extreme value distribution (GEV), whose probability density function... The expression for is:

[0064] In the formula, The effective wave height or wave period; The base of the natural logarithm The exponential function is used to construct a continuous curve of the probability distribution; This refers to the position parameter, i.e., the limit range of the effective wave height or wave period data; For scale parameters; For shape parameters, using the Copula function library, two-dimensional joint distributions of wind speed-wave height (optimally Gumbel Copula) and wind speed-wave period (optimally Clayton Copula) are established respectively. A three-dimensional joint distribution model of C-Vine Copula is constructed: considering that wind speed is the main meteorological factor driving wave generation, this invention chooses wind speed as the root node of the C-Vine Copula structure. Under a given wind speed, there is a conditional correlation between wave height and wave period. Therefore, the three-dimensional joint probability density function... It can be decomposed into: In the formula, in the formula, For wind speed and significant wave height variables, use a two-dimensional Copula density function. Given the effective wave height variable, the conditional two-dimensional Copula density function is given the wind speed and wave period. , , These are the marginal distribution functions of wind speed, significant wave height, and wave period variables, respectively. , These are the conditional distribution function values ​​of wind speed and wave period variables, respectively, given a significant wave height.

[0065] Furthermore, in the C-Vine Copula structure, the two-dimensional joint distribution of wind speed and wave height is represented by the Gumbel Copula function, the expression of which is: In the formula, , which are the edge distribution function values ​​of wind speed and wave height, respectively; The Gumbel Copula parameters describe the correlation between wind speed and wave height. The two-dimensional joint distribution of wind speed and wave period, conditioned on wind speed, is expressed using the Clayton Copula function, which is: In the formula, , which are the conditional distribution function values ​​of wind speed and wave period under given wave height conditions; The Clayton Copula parameter describes the correlation between wind speed and wave period under this condition.

[0066] In the finite element model module 202, using ANSYS finite element analysis software, a refined finite element model as shown in Figure 3 is constructed based on the bridge design drawings and parameters. Figure 3 shows a schematic diagram of the finite element model of a double-layer continuous beam bridge across the sea according to an embodiment of the present invention; wherein... Figure 3a The three-dimensional spatial topology, span distribution, and spatial layout of the suspender coupling system of the double-layer continuous beam bridge across the sea according to the present invention are shown. Figure 3bThis paper illustrates the interaction details between the pile foundation structure and the surrounding soil environment through boundary constraint simulation according to the present invention. As shown in the figure, multi-mode analysis of the finite element model is performed by calling the model verification unit to extract the first 10 natural frequencies and mode shape characteristics. If the extracted frequency error is within the preset threshold range and the mode shape evolution law is consistent, the finite element model is judged to have physical accuracy. In terms of element selection, BEAM4 spatial beam elements are used to simulate the upper concrete main beam, the lower fish-belly steel box girder, piers and pile foundation structure. LINK10 tension-only rod elements with bilinear stiffness characteristics are used to simulate the suspension coupling system connecting the upper and lower main beams. MASS21 structural mass elements are used to simulate the additional mass distribution of bridge deck ancillary facilities. During the parameter calibration process, the material density properties of the upper and lower structures are finely adjusted to strictly control the mass ratio of the lower fish-belly steel box girder to the upper concrete main beam between 0.6 and 0.8, so as to accurately characterize the inertial distribution characteristics and dynamic response characteristics of the double-layer heterogeneous structure.

[0067] In the wind and wave load simulation module 203, the wind load element is used to generate the pulsating wind time history acting on the upper and lower beam nodes based on the 50-year / 100-year return period design wind speed collected by the data acquisition unit, using the harmonic synthesis method. The three-component force coefficients of the upper and lower beam sections, pre-calculated using Fluent, are then called. , , and its first derivative Based on the quasi-steady buffeting force model formula, the time history of the buffeting force acting on the main beam was calculated. The formula for calculating the buffeting force per unit length of the main beam is as follows: Aerodynamic drag Lift Torque In the formula, air density, The average wind speed, The characteristic width of the main beam The time history of vertical fluctuating wind speed is given. Using the effective wave height and wave period collected by the data acquisition unit in the wave load element, and based on linear wave theory and the Morison equation, the time histories of the force and moment exerted by the waves on each pier pile foundation are calculated. The wave force acting per unit length on the circular pile foundation is calculated by the following formula.

[0068] in, The density of seawater, and These are the wave resistance and inertia coefficients, respectively. For the pile diameter, and These represent the horizontal velocity and acceleration of the water particles, respectively. For pile foundations, the pile effect needs to be considered; the wave force calculated above should be multiplied by the pile disturbance coefficient. , In the formula, This represents the center-to-center distance between adjacent piles. The time history of the buffeting force is applied to the corresponding nodes of the main beam, and the time history of the wave force is applied to the corresponding nodes of the pile foundation, using the load application unit.

[0069] In the dynamic response solution module 204, transient dynamic analysis is performed on the finite element model under applied load, and the following dynamic equations are solved: In the formula, These are the mass matrix, damping matrix, and stiffness matrix of the structure, respectively. These are the acceleration, velocity, and displacement vectors of the node, respectively. and These are the wind load and wave load vectors, respectively. Selected as follows... Figure 3a The displacement response time history of the key feature extraction points shown By analyzing the time history curves shown in Figure 4, the root mean square (RMS) and peak value of the displacement response can be calculated. The specific feature extraction points include: the first node (model number 31) located at the mid-span of the upper concrete main beam, and the second node (model number 153) located at the corresponding mid-span of the lower fish-belly steel box girder. The dynamic response characteristics of the double-layer main beam are analyzed by extracting the displacement time history data of these nodes. The formula for calculating the root mean square is: In the formula, This represents the total number of time steps. For the first The displacement values ​​at each time step. Referring to Figure 4, Figure 4 shows an example diagram of the displacement response time history curves of the upper and lower beams under the combined action of wind and waves according to an embodiment of the present invention; wherein, Figure 4a , Figure 4b and Figure 4c The time histories of transverse displacement, vertical displacement, and torsional angular displacement of node 31 of the upper concrete main beam under the combined excitation condition are shown respectively. Figure 4d , Figure 4e and Figure 4f The time histories of transverse displacement, vertical displacement, and torsional angular displacement of node 153 of the lower-level fish-belly steel box girder under corresponding working conditions are presented respectively; through analysis of... Figures 4a to 4f Statistical analysis of the time history curves for each degree of freedom shown can accurately extract the root mean square (RMS) value and peak value of the displacement response of the double-layer bridge structure under extreme wind and wave conditions, thereby providing data support for quantitatively assessing the degree of dynamic interference between the upper and lower structures and the risk of slack in the hangers.

[0070] In the design optimization and feedback module 205, the displacement response (such as the RMS value and peak value of lateral displacement) obtained from the dynamic response solution module 204 is compared with the limits in the bridge design code. By comparing the response under single wind, single wave, and combined wind and wave action, analysis conclusions are output, such as "the wave load on this bridge type has an impact on lateral vibration but a negligible impact on vertical and torsional vibration. The wind-resistant design should focus on the effect of pulsating wind, and the vertical vibration of the lower beam is significant," providing specific guidance for the design.

[0071] This invention constructs a three-dimensional joint probability distribution model of environmental parameters based on Copula function correlation theory, quantifying the correlation between wind speed, significant wave height, and wave period variables. This allows for the derivation of design combination values ​​for environmental parameters under 50-year and 100-year joint return periods, enabling bridge design to adopt more realistic and economical load combinations. Based on this, a refined finite element model of a double-deck continuous beam bridge across the sea is established for dynamic characteristic analysis. Computational fluid dynamics numerical simulation is used to extract the aerodynamic force coefficients of the upper and lower main beams. The static wind stability of the structure is verified through static wind displacement calculations under different wind speeds. Subsequently, based on the design combination values ​​of environmental parameters, the time histories of pulsating wind load and wave load are calculated and used as external excitation inputs. A dynamic equilibrium equation for the combined wind and wave action of the entire bridge is established for dynamic response analysis and comparison with code limits.

[0072] This invention reveals the dynamic response characteristics of a double-deck continuous beam bridge under wind and wave action, clarifying that pulsating wind load is the dominant factor causing significant vertical vibration of the lower main beam, and confirming that wave load mainly affects lateral vibration with negligible effects on vertical and torsional vibration. Simultaneously, it quantifies the coupling effect, revealing that the combined wind and wave response is less than the linear superposition of individual responses, rather than a simple worst-case scenario superposition. Comparison shows that the response increase under a 100-year combined return period is 56%–75% higher than that under a 50-year return period, enhancing design safety. Furthermore, comprehensive numerical simulations confirm that the multidimensional displacement (lateral, vertical, and torsional) responses of this double-deck bridge type under 100-year return period extreme wind and wave conditions are all far below the standard limits. This provides a solid theoretical basis and data support for promoting a double-deck bridge system with both transportation and aesthetic functions in coastal areas with limited flight clearance, and establishes a standardized technical system that can be extended to offshore platforms, wind turbines, and other water-related structures.

[0073] The following is for reference. Figure 5 It shows a schematic diagram of the structure of a computer system suitable for implementing the electronic device of the present application. Figure 5 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0074] like Figure 5As shown, the computer system includes a CPU 501, which can perform various appropriate actions and processes based on a program stored in ROM 502 or a program loaded into RAM 503 from storage section 508. RAM 503 also stores various programs and data required for system operation. The CPU 501, ROM 502, and RAM 503 are interconnected via bus 504. Input / output (I / O) interface 505 is also connected to bus 504.

[0075] The following components are connected to I / O interface 505: an input section 506 including a keyboard, mouse, etc.; an output section 507 including a liquid crystal display (LCD) and speakers, etc.; a storage section 508 including a hard disk, etc.; and a communication section 509 including a network interface card such as a LAN card and a modem, etc. The communication section 509 performs communication processing via a network such as the Internet. A drive 510 is also connected to I / O interface 505 as needed. A removable medium 511, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 510 as needed so that computer programs read from it can be installed into storage section 508 as needed.

[0076] Specifically, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable storage medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 509, and / or installed from removable medium 511. When the computer program is executed by central processing unit (CPU) 501, it performs the functions defined in the methods of this application. It should be noted that the computer-readable storage medium of this application can be a computer-readable signal medium or a computer-readable storage medium, or any combination of the two. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable storage medium other than a computer-readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. Program code contained on a computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0077] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—as well as conventional procedural programming languages—such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0078] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0079] The modules described in the embodiments of this application can be implemented in software or in hardware.

[0080] In another aspect, this application also provides a computer-readable storage medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The aforementioned computer-readable storage medium carries one or more programs. When the aforementioned one or more programs are executed by the electronic device, the electronic device causes the following: to acquire environmental parameters of wind speed, wave height, and wave period of the target sea area; to construct a three-dimensional correlation probability model of the environmental parameters based on the C-Vine Copula function; and to determine the design combination value of the environmental parameters under a specified joint return period through Monte Carlo simulation; to establish a finite element model of the upper and lower double-layer continuous beam bridge across the sea, wherein the coupling relationship of the suspenders is simulated by elements with nonlinear stress characteristics, and the dynamic characteristics of the finite element model are verified; based on the design combination value of the environmental parameters, to simulate the time histories of pulsating wind loads acting on the main beam of the bridge and wave loads acting on the substructure of the bridge; to apply the simulated pulsating wind loads and wave loads to the finite element model, to perform transient dynamic analysis, and to obtain the dynamic response of the upper and lower main beams and the substructure of the bridge under the combined action of wind and waves; to compare the dynamic response with the standard limits, and to output conclusions to guide the optimization of bridge structural design based on the response characteristics.

[0081] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for analyzing the dynamic response of a double-deck sea-crossing beam bridge under combined wind and wave action, characterized in that, The method includes: S1. Obtain environmental parameters such as wind speed, wave height, and wave period of the target sea area, construct a three-dimensional correlation probability model of the environmental parameters based on the C-Vine Copula function, and determine the design combination value of environmental parameters under a specified joint return period through Monte Carlo simulation. S2. Establish a finite element model of a double-layer continuous beam bridge across the sea. The coupling relationship of the suspenders is simulated by elements with nonlinear stress characteristics, and the dynamic characteristics of the finite element model are verified. S3, based on the environmental parameters, design combination values ​​to simulate the time histories of pulsating wind load acting on the main beam of the bridge and wave load acting on the substructure of the bridge, respectively. S4. The simulated pulsating wind load and wave load are applied to the finite element model to perform transient dynamic analysis and obtain the dynamic response of the upper and lower main beams and the substructure of the bridge under the combined action of wind and waves. S5. The dynamic response is compared with the standard limit, and conclusions are output based on the response characteristics to guide the optimization of bridge structure design.

2. The dynamic response analysis method for a double-deck sea-crossing beam bridge under combined wind and wave action as described in claim 1, characterized in that, The three-dimensional joint probability density function of the three-dimensional correlation probability model Decomposed into: In the formula, These are wind speed, significant wave height, and wave period, respectively. For wind speed and significant wave height variables, use a two-dimensional Copula density function. Given the effective wave height variable, the conditional two-dimensional Copula density function is given the wind speed and wave period. , , These are the marginal distribution functions of wind speed, significant wave height, and wave period variables, respectively. , These are the conditional distribution function values ​​of wind speed and wave period variables, respectively, given a significant wave height.

3. The dynamic response analysis method for a double-deck sea-crossing beam bridge under combined wind and wave action as described in claim 1, characterized in that, The specified joint return period is determined based on the three-dimensional correlation probability model and satisfies the following formula: In the formula, To specify the joint return period; , respectively, are the marginal cumulative distribution functions of wind speed, significant wave height, and wave period; C is the three-dimensional joint Copula distribution function constructed through the C-Vine structure.

4. The dynamic response analysis method for a double-deck sea-crossing beam bridge under combined wind and wave action as described in claim 1, characterized in that, Step S1 includes: S11, Obtain measured time history data of wind speed, significant wave height and wave period for a long sequence in the target sea area; S12, Based on the goodness-of-fit evaluation criterion, the marginal distribution of wind speed, significant wave height and wave period variables is optimized; among them, the wind speed variable adopts a non-parametric probability density estimation model, and the significant wave height and the wave period variable are fitted using a parametric probability distribution model. S13, construct a three-dimensional correlation probability model with the wind speed variable as the root node; wherein, a first correlation function with upper tail dependence is selected to describe the correlation between the wind speed and the effective wave height, and a second correlation function with lower tail dependence is selected to describe the correlation between the wind speed and the wave period. S14, determine the parameters of the first correlation function and the second correlation function, and use the Monte Carlo random sampling method to extract the environmental parameter design combination value under the specified joint return period in the multidimensional probability space.

5. The dynamic response analysis method for a double-deck sea-crossing beam bridge under combined wind and wave action as described in claim 4, characterized in that, In step S12, the non-parametric probability density estimation model adopts a kernel density estimation model; the parameterized probability distribution model adopts a generalized extreme value distribution model, whose probability density function... The expression for is: In the formula, Variables for effective wave height or wave period; The base of the natural logarithm The exponential function; For position parameters; For scale parameters; For shape parameters.

6. The dynamic response analysis method for a double-deck sea-crossing beam bridge under combined wind and wave action as described in claim 4, characterized in that, In step S13, the first association function is the Gumbel Copula function, which is expressed as follows: In the formula, , which are the edge distribution function values ​​of wind speed and wave height, respectively; The Gumbel Copula parameter describes the correlation between wind speed and wave height; These are the marginal distribution functions for wind speed and significant wave height, respectively; The second correlation function is the Clayton Copula function, which is expressed as follows: In the formula, , which are the conditional distribution function values ​​of wind speed and wave period under given effective wave height; The Clayton Copula parameter describes the correlation between wind speed and wave period variables under this condition; These are the marginal distribution functions for wind speed, significant wave height, and wave period, respectively.

7. The dynamic response analysis method for a double-deck sea-crossing beam bridge under combined wind and wave action as described in claim 1, characterized in that, The S2 step specifically includes: S21, variable cross-section beam elements are used to simulate the upper concrete main beam, and constant cross-section beam elements are used to simulate the lower fish-belly steel box girder; by adjusting the material density, the mass ratio of the lower fish-belly steel box girder to the upper concrete main beam is controlled between 0.6 and 0.

8. S22, the LINK10 rod element, which is only under tension, is used to simulate the hanger connecting the upper and lower main beams; the initial strain of the LINK10 element is set according to the preload of the hanger to characterize the nonlinear relaxation characteristics of the hanger under the combined action of wind and waves; S23 uses node coupling or elastic connection units to simulate the anchorage constraint of cable clamps on the upper and lower main beams; beam units are used to simulate the lower piers and pile foundations, and spring units are used to simulate the pile-soil interaction. S24. Perform modal analysis on the assembled finite element model to extract the first-order natural frequencies and mode shapes; compare the extracted natural frequencies with environmental excitation test data or empirical formulas for similar structures; if the frequency error is within a preset threshold, the model is determined to be accurate.

8. The dynamic response analysis method for a double-deck sea-crossing beam bridge under combined wind and wave action as described in claim 1, characterized in that, In step S3, the simulation process of the pulsating wind load includes: S31, Based on the environmental parameters, the combined values ​​are designed and the harmonic synthesis method is used to generate the time history of the pulsating wind acting on the upper and lower beam nodes; S32, through computational fluid dynamics numerical simulation, the aerodynamic drag coefficients of the main beam sections of the upper and lower layers were obtained respectively. Lift coefficient Torque coefficient and its first derivative ; S33, the time history of the buffeting force acting on the main beam is calculated based on the quasi-steady buffeting force model. The formula for calculating the buffeting force per unit length of the main beam is as follows: Aerodynamic drag Lift Torque In the formula, air density, The average wind speed, The characteristic width of the main beam This represents the time history of vertical pulsating wind speed.

9. The method for analyzing the dynamic response of a double-deck sea-crossing beam bridge under the combined action of wind and waves according to claim 1, characterized in that, In step S3, the simulation of wave load specifically involves: based on the effective wave height and wave period of the environmental parameter design combination values, calculating the wave force on the pile foundation using linear wave theory and the Morison equation; and calculating the wave force acting on a unit length of the circular pile foundation. Calculate according to the following formula: in, The density of seawater; and These are the wave resistance coefficient and the inertial force coefficient, respectively. The diameter of the circular pile foundation; The horizontal velocity of the water particles; The symbol is for partial differentials; The time history of horizontal acceleration of water particles; The simulation of wave loads also includes introducing a pile group interference coefficient when calculating the total wave force on the pile group foundation. Correction is applied to the wave force of a single pile; the interference coefficient of the pile group is also considered. The value was calibrated through a three-dimensional numerical wave flume test, and its range was 0.7-0.

9.

10. The method for analyzing the dynamic response of a double-deck sea-crossing beam bridge under the combined action of wind and waves according to claim 1, characterized in that, The S4 step includes: S41, based on d'Alembert's principle, applies a vector of fluctuating wind load. and wave load vector Transient dynamic analysis was performed using a finite element model; S42, via Newmark- The following dynamic equations can be solved using the following method: In the formula, These are the mass matrix, damping matrix, and stiffness matrix of the structure, respectively. These are the acceleration vector, velocity vector, and displacement vector of the node, respectively. S43, Obtain the time history response of the upper and lower main beams and the substructure of the bridge under the combined action of wind and waves, the response including displacement, velocity, acceleration and internal forces of key components.

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