Expansion joint vibration reduction detection method and system based on vehicle-bridge-joint coupling vibration analysis

Abstract

This invention relates to the field of structural vibration testing and analysis technology, and discloses a method and system for vibration reduction detection of expansion joints based on vehicle-bridge-joint coupled vibration analysis. The method includes: constructing a cross-sectional coordinate system and obtaining a digitized contour line; performing interferometric analysis based on the load contact envelope to generate a pressure distribution matrix, and obtaining a set of acoustic and vibration characteristic vectors; reconstructing a vibration diagnosis plane and constructing a dynamic performance safety domain; executing a three-layer screening logic to obtain a set of equilibrium calibration parameters; constructing a physical calibration command sequence to drive relevant actuators to perform physical parameter compensation, and obtaining a test compliance verification mark. This invention solves the problem of dynamic distortion caused by the simplification of the cross-section of the beam steel section, realizes multi-index collaborative diagnosis and accurate parameter implementation, eliminates vehicle bounce impact and vibration noise, and improves bridge ride comfort, structural durability, and operational safety.

Description

Technical Field

[0001] This invention relates to the field of structural vibration testing and analysis technology, and more specifically, to a method and system for detecting vibration reduction of expansion joints based on vehicle-bridge-joint coupled vibration analysis. Background Technology

[0002] As large-scale load-bearing engineering structures and their key connecting components evolve towards higher loads and longer spans, the dynamic equilibrium characteristics and vibration response mechanisms of expansion joints, as core components for regulating structural displacement, are receiving increasing attention. However, traditional structural vibration testing and diagnostic methods generally face accuracy bottlenecks, making it difficult to simultaneously improve the detection of dynamic stability and structural fatigue characteristics, and the analysis results are limited by the boundaries of empirical models. Existing technologies mostly focus on verifying the static mechanical properties of expansion joints, or simply use simplified sinusoidal waveforms to simulate the impact of moving loads. They neglect the complex nonlinear interference mechanism between the contact surface of the moving load and the irregular metal cross-section, i.e., the "negative superposition effect of energy" caused by abrupt changes in cross-sectional geometry, which leads to severe distortion in dynamic simulation. This results in the hidden impact energy generated instantaneously across the irregular gap during testing far exceeding the theoretical prediction value; moreover, the high-frequency stress released during excitation induces microscopic geometric distortion in the cross-section, further altering the pressure distribution at the contact interface, causing the vibration monitoring data to fall into a trough of dynamic response imbalance. While traditional structural analysis methods can reveal some vibration patterns, they lack closed-loop test feedback logic that couples with actual physical deviations in real time, making it impossible to guide refined parameter calibration based on test data. Therefore, how to shift from static physical verification to dynamic coupling prediction and high-fidelity testing of the entire system, and transform macroscopic empirical diagnosis into precise analysis and verification of microscopic parameters, thereby overcoming the limitations of dynamic test distortion, is a technical challenge to be solved in this field.

[0003] In the prior art, Chinese patent CN113373802B discloses a vibration-damping expansion joint based on a wire rope damper. This structure includes side longitudinal beams, a middle longitudinal beam, a displacement box, and a wire rope damper. Through the coordinated installation of supporting steel plates, fixed rope clamps, and intermediate rope clamps, a multi-directional displacement damping system is formed, achieving damping, energy dissipation, and vibration reduction functions. It can adapt to earthquake actions and reduce the impact response caused by vehicle loads, while avoiding uneven displacement of the middle longitudinal beam. Through the rigid connection of the mechanical structure and the elastic buffer of the damper, it provides a passive protection technology path for vibration reduction of the expansion joint. Chinese patent CN215518341U discloses a bridge adaptive expansion joint structure. The structure includes a vertical buffer component and a horizontal buffer component. The vertical buffer component uses a support rod, spring, and pulley slide structure to buffer the vertical impact force. The horizontal buffer component adopts a triangular spring and connecting rod design to unload the horizontal impact force. At the same time, the waterproof plate has a built-in groove and spring structure to prevent the components from breaking due to impact, thus combining vibration reduction and protection functions.

[0004] However, while the two existing technologies mentioned above have some value in passive vibration reduction and structural stability improvement of expansion joints, they fail to address the core pain points of dynamic testing distortion, dynamic coupling prediction, and accurate verification of micro-parameters in complex engineering scenarios. Specifically, the patent with authorization announcement number CN113373802B focuses on passive vibration reduction design of mechanically damped structures, without addressing nonlinear interference testing and analysis of moving loads and irregular cross-sections. It lacks a digital characterization and capture mechanism for the "energy negative superposition effect," and cannot avoid the distortion problem of the dynamic simulation model. The patent with authorization announcement number CN215518341U focuses on multi-dimensional vibration reduction of static buffer structures, but it does not establish a dynamic coupling prediction model for the entire vehicle-structure-joint system, making it difficult to quantify and analyze the impact of micro-geometric distortion caused by high-frequency stress. Neither of these technologies sets up closed-loop feedback verification logic based on physical deviations and vibration test results. They cannot break through the boundaries of empirical analysis, nor can they achieve accurate calibration of cross-sectional micro-parameters, failing to meet the refined requirements of large-scale engineering structures for vibration efficiency testing and durability diagnosis of key components. Summary of the Invention

[0005] This invention is applicable to vibration and noise reduction scenarios at expansion joints of urban elevated bridges, such as bridge sections with high-speed traffic and complex steel structures. It can meet the collaborative optimization needs of various vibration damping supports and steel cross-sections. By generating a pressure distribution matrix through virtual envelope interference analysis of cross-sectional coordinate systems, digitized contour lines, and load contact envelopes, it achieves the dual goals of high-fidelity restoration of the excitation source and elimination of dynamic distortion. The vibration diagnosis plane, combined with the dynamic performance safety domain, transforms multi-dimensional discrete features into spatial positioning, accurately identifying potential structural failures and noise exceeding standards, reducing the probability of vehicle bounce and concrete cracking in the anchorage zone. A three-layer screening logic collaboratively balances the calibration parameter set to achieve global parameter optimization. A physical calibration command sequence drives relevant actuators to perform physical parameter compensation, and performance compliance feedback is achieved using test compliance verification marks, shortening the structural calibration cycle and reducing the bridge's life-cycle maintenance costs. This invention comprehensively improves bridge ride comfort, structural durability, and vibration damping adjustment accuracy.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A vibration reduction detection method for expansion joints based on vehicle-bridge-joint coupled vibration analysis includes:

[0008] The initial structural test parameters of the expansion joint of the viaduct are obtained, and a cross-sectional coordinate system is constructed. Based on the cross-sectional coordinate system, feature mapping is performed on the initial structural test parameters to obtain a digitized contour line. The motion parameters of the moving load are obtained to construct the load contact envelope. Based on the load contact envelope and the contour line, virtual envelope interference analysis is performed to generate a pressure distribution matrix. The response analysis is performed on the pressure distribution matrix to obtain a set of acoustic vibration feature vectors.

[0009] Test index reconstruction is performed on the acoustic vibration feature vector set to obtain a vibration diagnosis plane characterizing the performance trade-off state of the expansion joint. A dynamic performance safety domain is constructed based on the vibration diagnosis plane. The inclusion relationship of the dynamic performance safety domain is determined to obtain a parameter diagnosis set. A three-level screening is performed on the parameter diagnosis set to obtain a set of balanced calibration parameters.

[0010] Based on the solution set of the equilibrium calibration parameters, a physical calibration command sequence is constructed to drive the relevant actuators. The physical calibration command sequence is then physically calibrated to obtain a test compliance verification mark that characterizes the vibration reduction performance of the bridge expansion joint vibration reduction structure.

[0011] Furthermore, the method for obtaining the contour line includes:

[0012] Initial structural test parameters include edge curvature radius, slot width spacing, and surface microstructure height;

[0013] The amplitude coordinates of the longitudinal axis of the cross-sectional coordinate system are determined based on the height of the surface microstructure, and the span range of the transverse axis of the cross-sectional coordinate system is determined based on the gap width spacing. At the intersection of the span range of the transverse axis and the amplitude coordinates of the longitudinal axis, geometric envelope constraints are performed using the edge curvature radius. The initial structural test parameters are transformed into a series of coordinate points with unique coordinate values ​​in the cross-sectional coordinate system, which are defined as contour mapping points.

[0014] A series of contour mapping points are fitted to construct a digital contour line of the steel section of the beam steel. An interpolation basis function containing interpolation coefficients is constructed between adjacent contour mapping points. A system of linear equations containing coordinate coincidence constraints, first derivative continuity constraints and second derivative continuity constraints is executed on the interpolation basis function to determine the interpolation coefficients and generate the digital contour line.

[0015] Furthermore, the method for obtaining the load contact envelope includes:

[0016] The vehicle speed is obtained at each sampling moment during the test cycle. The tire radius parameter and static suspension height are obtained through the vehicle's nameplate parameter information. The vehicle speed, tire radius parameter and static suspension height constitute the motion parameters of the moving load.

[0017] At each sampling moment during the test period, the real-time displacement relative to the origin of the cross-sectional coordinate system is calculated based on the vehicle speed. The geometric center of motion of the vehicle tire in the cross-sectional coordinate system is determined based on the real-time displacement and the static suspension height, and is defined as the tire virtual center point.

[0018] Using the virtual center point of the tire as the geometric control center and the tire radius parameter as the radius constraint, a lower semicircular arc function representing the contact profile of the lower part of the vehicle tire is constructed, and at each sampling time, the load contact envelope representing the sinking deformation boundary of the vehicle tire is generated through the lower semicircular arc function.

[0019] Furthermore, the method for obtaining the pressure distribution matrix includes:

[0020] In the cross-sectional coordinate system, the numerical intersection interval of the digitized contour line and the load contact envelope is identified, and the algebraic deviation value of the geometric boundary function and the lower semicircular arc function at each sampling point in the numerical intersection interval is calculated according to the preset spatial step size to obtain the overlap in the vertical direction. The geometric boundary function is the digitized contour line.

[0021] The elastic modulus coefficient is extracted from the tire specification information of the vehicle tires. The elastic modulus coefficient is multiplied by the overlap in the vertical direction to generate the transient contact pressure. The pressure distribution matrix is ​​then generated by arranging the samples according to the index of the preset sampling time.

[0022] Furthermore, the method for obtaining the set of acoustic vibration feature vectors includes:

[0023] Obtain the structural physical properties including material mass and structural stiffness, and construct a set of second-order linear differential equations based on mechanical assembly logic to characterize the overall stress and deformation law of the expansion joint device, which is defined as the structural transfer function;

[0024] The pressure distribution matrix is ​​used as an external input excitation to the structural transmission function. The second-order linear differential equation system is solved using a numerical integration algorithm to obtain the acceleration response characteristics and displacement evolution characteristics of the steel section of the beam at each sampling point.

[0025] The short-time zero-crossing rate is obtained by counting the number of times the acceleration response feature crosses the horizontal axis of the cross-sectional coordinate system within a preset sliding time window, and the centroid frequency and spectral broadening are extracted by performing a fast Fourier transform on the acceleration response feature.

[0026] Normalization was performed on the short-time zero-crossing rate, centroid frequency, and spectral broadening to obtain a set of acoustic-vibration characteristic vectors that characterize the dynamic response of the steel section of the beam steel.

[0027] Furthermore, the method for obtaining the vibration diagnostic plane includes:

[0028] Based on the short-time zero-crossing rate and center of gravity frequency, a positive correlation mapping logic for acoustic subjective annoyance is established. The mean of the normalized short-time zero-crossing rate and the normalized center of gravity frequency is calculated to obtain the driving comfort evaluation quantity.

[0029] The absolute peak value of the displacement evolution characteristics within the test period is extracted using the maximum value retrieval logic to obtain the structural durability evaluation quantity;

[0030] A vibration diagnostic plane is established with the ride comfort evaluation quantity as the horizontal axial coordinate and the structural durability evaluation quantity as the vertical axial coordinate. The ride comfort evaluation quantity and the structural durability evaluation quantity are combined and mapped to a unique coordinate point in the vibration diagnostic plane, which is defined as the performance point.

[0031] Furthermore, the method for obtaining the dynamic performance security domain includes:

[0032] Obtain the environmental sound functional zone category data of the environment where the expansion joint device is located, determine the smoothness constraint threshold based on the environmental sound functional zone category data, obtain the allowable material fatigue stress value of the middle beam steel under cyclic impact load and define it as the durability constraint threshold.

[0033] The thickness of the damping material in the cross section of the central beam steel is obtained, and based on the principle of energy dissipation conservation, a nonlinear envelope curve is established with the independent variable being the ride comfort evaluation quantity and the dependent variable being the structural durability evaluation quantity. This nonlinear envelope curve satisfies the logic of a quadratic parabolic distribution.

[0034] A dynamic performance safety domain is generated within the vibration diagnostic plane by utilizing ride comfort constraint thresholds, durability constraint thresholds, and nonlinear envelope curves. Simultaneously, a multidimensional continuous geometric search space is constructed based on edge curvature radius, slot width spacing, surface microstructure height, and damping material thickness, which is defined as the structural parameter design space.

[0035] Furthermore, the method for obtaining the solution set of the equilibrium calibration parameters includes:

[0036] In the structural parameter design space, multiple initial populations composed of initial parameter individuals are generated. For each initial parameter individual, a corresponding performance point and parameter diagnosis set are generated, which are defined as individual performance point and individual parameter diagnosis set, respectively. The individual parameter diagnosis set includes parameter compliance judgment status and parameter correction instructions.

[0037] If the individual parameter diagnosis set is identified as a parameter correction instruction, it is determined to be an unqualified parameter individual. If it is a parameter compliance judgment state, it is a qualified parameter individual. The qualified parameter individual to be diagnosed is defined as the target judgment individual. The set of qualified parameter individuals other than the target judgment individual is defined as the reference comparison individual set. Only when the ride comfort evaluation quantity and structural durability evaluation quantity corresponding to the individual performance point of the unqualified parameter individual in the reference comparison individual set are both less than the evaluation quantity corresponding to the individual performance point of the target judgment individual, the target judgment individual is determined to be in a non-dominated state.

[0038] Calculate the crowding degree values ​​of qualified parameter individuals in a non-dominated state, sort them in descending order according to the crowding degree values, and obtain the solution set of balance calibration parameters.

[0039] Furthermore, the method for obtaining the test compliance verification identifier includes:

[0040] Obtain the current physical geometry parameters, calculate the difference between the equilibrium calibration parameter solution set and the current physical geometry parameters, and obtain four physical compensation values, namely the first, second, third and fourth physical compensation values. Map the physical compensation values ​​to the device execution control parameters containing displacement control vector, angle control vector and torque control vector. Encapsulate the device execution control parameters to obtain the physical calibration instruction sequence.

[0041] The feedback geometric parameters after physical parameter compensation are obtained according to the physical calibration command sequence, and a second difference operation is performed to obtain the compensation difference set. The compensation difference set is then mapped to generate a second physical calibration command sequence and a second physical parameter compensation is performed to obtain the second feedback geometric parameters.

[0042] Feedback performance points are generated based on the secondary feedback geometric parameters, and the test compliance verification mark is obtained based on the inclusion relationship of the feedback performance points relative to the dynamic performance safety domain.

[0043] A vibration reduction detection system for expansion joints based on vehicle-bridge-joint coupled vibration analysis is provided to implement the aforementioned vibration reduction detection method for expansion joints based on vehicle-bridge-joint coupled vibration analysis. The system includes:

[0044] Acoustic and vibration analysis module: used to obtain the initial structural test parameters of the expansion joint of the viaduct, construct the cross-sectional coordinate system, perform feature mapping on the initial structural test parameters based on the cross-sectional coordinate system to obtain the digitized contour line, obtain the motion parameters of the moving load to construct the load contact envelope, perform virtual envelope interference analysis based on the load contact envelope and the contour line to generate the pressure distribution matrix, perform response analysis on the pressure distribution matrix to obtain the set of acoustic and vibration feature vectors;

[0045] The parameter filtering module is used to reconstruct test indicators from the set of acoustic and vibration feature vectors, obtain a vibration diagnosis plane that characterizes the performance trade-off state of the expansion joint, construct a dynamic performance safety domain based on the vibration diagnosis plane, determine the inclusion relationship of the dynamic performance safety domain, obtain a parameter diagnosis set, perform three-level filtering on the parameter diagnosis set, and obtain a set of balanced calibration parameters.

[0046] Command verification module: It is used to construct the physical calibration command sequence of the driving related actuators based on the solution set of balance calibration parameters, perform physical calibration on the physical calibration command sequence, and obtain the test compliance verification mark characterizing the vibration reduction performance of the bridge expansion joint vibration reduction structure.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] This invention achieves the dual goals of high-fidelity restoration of the excitation source and elimination of dynamic distortion through the analysis of virtual envelope interference of cross-sectional coordinate system, digitized contour lines, and load contact envelope lines. This addresses the pain point of traditional solutions that use simplified loads, resulting in an inability to reflect the true impact effect. The collaborative dynamic performance safety domain of ride comfort evaluation and structural durability evaluation transforms multi-dimensional discrete features into spatial performance point inclusion relationship judgment logic, accurately identifying potential structural failure hazards and noise exceeding standards, and reducing the probability of vehicle bounce impact and concrete cracking in the anchorage zone. The physical calibration command sequence drives relevant actuators to perform physical parameter compensation, and combined with test compliance verification marks, it realizes performance feedback and fine calibration, eliminating manufacturing and installation deviations, ensuring long-term performance compliance, shortening the structural calibration cycle, reducing the maintenance cost of the bridge throughout its entire life cycle, and achieving closed-loop control of expansion joint performance. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a flowchart of a method for detecting vibration reduction in expansion joints based on vehicle-bridge-joint coupled vibration analysis, provided in an embodiment of the present invention.

[0051] Figure 2 This is a schematic cross-sectional view of a vibration reduction structure for an expansion joint of an elevated bridge, provided in an embodiment of the present invention.

[0052] Figure 3 This is a schematic diagram of the contour line generated based on contour mapping point fitting provided in an embodiment of the present invention;

[0053] Figure 4 This is a functional block diagram of an expansion joint vibration reduction detection system based on vehicle-bridge-joint coupling vibration analysis provided in an embodiment of the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] Example 1

[0056] Please see Figure 1 As shown, this embodiment provides a vibration reduction detection method for expansion joints based on vehicle-bridge-joint coupled vibration analysis, including:

[0057] Step S10: Obtain the initial structural test parameters characterizing the expansion joint of the viaduct, and construct a cross-sectional coordinate system. Perform feature mapping on the initial structural test parameters based on the cross-sectional coordinate system to obtain a digitized contour line. Obtain the motion parameters of the moving load to construct the load contact envelope. Perform virtual envelope interference analysis based on the load contact envelope and the contour line to generate a pressure distribution matrix. Perform response analysis on the pressure distribution matrix to obtain a set of acoustic vibration feature vectors.

[0058] Further, step S10 includes:

[0059] Step S11: Obtain the initial structural test parameters of the elevated bridge expansion joint and construct a cross-sectional coordinate system. Perform feature mapping on the initial structural test parameters based on the cross-sectional coordinate system to obtain the digitized contour line.

[0060] During the service of urban viaducts, expansion joints serve as longitudinal expansion compensation devices for the bridge structure. The microscopic geometry of the steel section of the central beam in the expansion joint determines the initial excitation intensity when vehicles pass through it. Since sawtooth or corrugated steel sections exhibit extremely strong nonlinear geometric characteristics at the microscale, traditional techniques typically simplify the central beam steel section to an ideal planar load, neglecting the stress concentration phenomenon that occurs at the edges of the central beam steel section during loading. To eliminate the dynamic distortion caused by model simplification, a reference framework needs to be established that can accurately map the physical structure of the central beam steel section to the digital model—a structured geometric quantification space. The aim is to transform passive, empirical section descriptions into active, high-fidelity digital contours.

[0061] The initial structural test parameters of the steel section of the central beam steel are obtained through a CAD design data parser. The CAD design data parser is a software logic unit capable of identifying and extracting geometric entity attributes through a computer-aided design file interface. Its function is to transform unstructured engineering drawing information into a structured set of numerical values ​​that can be directly accessed. The initial structural test parameters of the central beam steel section include the edge curvature radius R, the gap width spacing W, and the surface microstructure height H. The edge curvature radius refers to the arc parameter of the central beam steel section at the contact point with the vehicle tire, characterizing the smoothness of the edge of the central beam steel section; the gap width spacing refers to the opening width between adjacent central beam steel sections, characterizing the spatial span when the vehicle tire crosses the gap; the surface microstructure height refers to the vertical displacement of the sawtooth or wavy structure relative to the steel section plane, characterizing the degree of microscopic undulation of the central beam steel section. See also... Figure 2 This is a schematic cross-sectional view of a vibration reduction structure for an expansion joint of a viaduct provided in an embodiment of the present invention. Figure 2In the diagram, symmetrically distributed light gray rectangles on both sides simulate the main beam of an elevated bridge in a real-world scenario, providing installation references and spatial boundaries for the expansion joint device. A dark gray irregular structure positioned between the two sets of light gray rectangles simulates the top cross-section of the central beam steel section of the expansion joint under actual working conditions, simulating the physical contact interface where vehicle tires directly pass through and cross the gap. A narrow gray strip spanning below the central beam steel section simulates the supporting beam in a real structure, bearing and transmitting the dynamic impact loads generated by vehicle passage. Two dark blue squares simulate the bearing supports actually installed in the bridge's recesses, providing damping and vibration reduction support for the entire structure. The cross-sectional structure of the central beam steel section uses geometric annotations to illustrate the edge curvature radius R, the gap width spacing W, and the surface microstructure height H. To accurately calculate the trajectory of the vehicle tires as they pass through the cross-section of the central beam steel section, a two-dimensional coordinate system, defined as the cross-sectional coordinate system, is constructed using the transverse centerline of the expansion joint as a reference. Specifically, the geometric center of the cross-section of the central beam steel section is determined as the origin. A straight line parallel to the vehicle's direction of travel is defined as the horizontal axis (X-axis), and a straight line perpendicular to the horizontal axis and passing through the origin is defined as the vertical axis (Y-axis). The cross-sectional coordinate system provides a unified physical reference plane, enabling the initial structural test parameters of different dimensions to be vectorized within the same geometric quantization space.

[0062] The initial structural test parameters are mapped to the cross-sectional coordinate system. Specifically, the amplitude coordinates in the longitudinal direction are determined based on the surface microstructure height, and the span range in the transverse direction is determined based on the seam width spacing. At the intersection of the transverse span range and the amplitude coordinates in the longitudinal direction, geometric envelope constraints are applied using the edge curvature radius. The initial structural test parameters are three-dimensional attribute values ​​describing the physical entity. During the mapping process, the physical profile of the steel section of the central beam is abstracted in the cross-sectional coordinate system as the geometric features of its longitudinal vertical cross-section. Specifically, the seam width spacing characterizes the distribution attribute of the steel section of the central beam in the transverse direction, the surface microstructure height characterizes the geometric response attribute of the steel section of the central beam in the longitudinal direction, and the edge curvature radius characterizes the curvature vector attribute at the local corner of the steel section of the central beam. This achieves a dimensional transformation from physical dimension values ​​to spatial position coordinates, converting the discrete initial structural test parameters into a series of coordinate points with unique coordinate values ​​in the cross-sectional coordinate system, defined as profile mapping points. The contour mapping points are binary numerical pairs consisting of horizontal axis coordinates and vertical axis coordinates. Their function is to transform the physical contour of the steel section of the central beam steel into a discrete feature point cloud that can be processed by computer algorithms, thus realizing the leap from physical entity to digital logical node.

[0063] To ensure the geometric continuity and physical realism of the cross-sectional profile of the central beam steel section, a series of profile mapping points are fitted to construct a digital profile of the central beam steel section. Specifically, a series of profile mapping points in the cross-sectional coordinate system are arranged in ascending order of their horizontal axis coordinates. An interpolation interval is established between every two adjacent profile mapping points, forming a continuous interval chain composed of multiple interpolation intervals. Here, the interpolation interval refers to the horizontal displacement interval defined by two adjacent profile mapping points in the horizontal axis direction in the cross-sectional coordinate system. Within each interpolation interval, a cubic polynomial equation containing four coefficients to be solved is constructed, defined as the interpolation basis function. The four coefficients contained in the interpolation basis function are defined as interpolation coefficients. The interpolation coefficients are used to uniquely determine the geometric curve shape within each interpolation interval. To solve for the interpolation coefficients, a system of linear equations consisting of three layers of geometric constraints is executed. The first layer of geometric constraints is a coordinate coincidence constraint, requiring that the interpolation basis functions of each interpolation interval must completely coincide with the coordinate values ​​of the contour mapping points at the corresponding starting and ending coordinates. Its function is to ensure that the generated contour line strictly adheres to the initial structural test parameters of the steel section of the central beam. The second layer of geometric constraints is a first-order derivative continuity constraint, meaning that at the connection point of two adjacent interpolation intervals, the first derivative of the interpolation basis function of the left interpolation interval is equal to the first derivative of the interpolation basis function of the right interpolation interval. Its function is to ensure that the tangent direction of the contour line remains unique at the connection point, eliminating transient velocity jumps when the vehicle tires pass through the connection point. The third layer of geometric constraints is a second-order derivative continuity constraint, meaning that at the connection point of two adjacent interpolation intervals, the second derivative of the interpolation basis function of the left interpolation interval is equal to the second derivative of the interpolation basis function of the right interpolation interval. Its function is to ensure that the curvature change of the contour line is continuous at the connection point, eliminating transient acceleration abrupt changes when the vehicle tires pass through the connection point. By solving a system of linear equations to determine the interpolation coefficients for all interpolation intervals, and then vector-connecting the interpolation basis functions of all intervals according to the order of their horizontal axis coordinates, the outline of the generated beam section is constructed. This digitized outline is then defined as a geometric boundary function. (See also...) Figure 3 This is a logical schematic diagram of a contour line generated based on contour mapping point fitting provided in an embodiment of the present invention. In the figure, a cross-sectional coordinate system is formed by the mutually perpendicular horizontal axis X and vertical axis Y. The origin of the cross-sectional coordinate system is represented by O. The red dots labeled P1, P2, and P3 represent the corresponding three contour mapping points. The horizontal axis range between P1 and P2 determines the first interpolation interval, and the horizontal axis range between P2 and P3 determines the second interpolation interval. The blue curve in the figure represents the fitted contour line, which continuously passes through P1, P2, and P3, and achieves a smooth transition at P2 through the continuity constraints of the first and second derivatives, which is used to simulate the motion response of a vehicle tire passing through the edge of the central beam steel under actual physical conditions.

[0064] Step S12: Obtain the motion parameters of the moving load to construct the load contact envelope, and perform virtual envelope interference analysis based on the load contact envelope and the contour line to generate the pressure distribution matrix.

[0065] After obtaining the contour line, in order to capture the dynamic response distortion characteristics caused by the negative superposition effect of energy when a vehicle passes through an expansion joint, the negative superposition effect of energy, namely the impact characteristics generated by the geometrical abrupt change of the cross-section of the central beam steel, interferes with the background excitation of the vehicle suspension system in the time domain. Therefore, within the cross-sectional coordinate system, this invention uses the contour line to define a physical interaction logic space for simulating tire dynamic intrusion, in order to solve the problem of hidden impact energy loss caused by the geometric simplification of the contact surface. In simulating the dynamic interaction of a vehicle passing through an overpass expansion joint, the vehicle tire, as an elastic carrier bearing the vehicle load and in direct physical contact with the expansion joint, is subject to strict constraints on the force characteristics of the vehicle tire when crossing irregular gaps at high speed by the nonlinear geometric boundaries in the contour line, which are determined by the edge curvature radius, gap width, and surface microstructure height. Since the contour line provides a high-fidelity geometric reference, a virtual envelope process is established that can map the topological characteristics of the contour line to the transient response of the vehicle tire. The purpose is to transform the single-dimensional ideal planar load in traditional technology into an active, full-contact domain-covering, physically nonlinearly directional dynamic pressure monitoring.

[0066] A dynamic deformation curve of a simulated vehicle tire under a specific downward load is established in the cross-sectional coordinate system, defined as the load contact envelope. The load contact envelope characterizes the geometric edge of the tire's bottom end after elastic compression under contact pressure. Specifically, the vehicle speed V at each sampling moment in the test period T is obtained through a vehicle network information interface. This vehicle network information interface is a data interaction protocol port capable of retrieving real-time vehicle kinematic parameters, used to synchronize dynamic data between the vehicle and the backend. The duration of the test period T is set based on the longitudinal geometric span of the expansion joint and the vibration decay time constant of the bridge structure after excitation, aiming to ensure complete capture of the transient impact response of the vehicle tire crossing the contour line and the subsequent convergence process of structural vibration. Let i represent the index of the sampling moment, ranging from 1 to M, where M represents the total number of sampling moments in the test period, and each sampling moment index corresponds to a vehicle speed. This represents the vehicle speed at the i-th sampling moment in the test cycle. The tire radius parameter and static suspension height Q are obtained from the vehicle's nameplate parameters. These vehicle speed, tire radius parameter, and static suspension height are collectively referred to as the moving load motion parameters. The tire radius parameter quantifies the outer diameter geometric characteristic value of the vehicle tire in a state without elastic deformation. The static suspension height refers to the vertical displacement reference value of the vehicle tire's central axis relative to the horizontal axis of the cross-sectional coordinate system in equilibrium. At each sampling moment, the motion envelope characteristics of the vehicle tire in the cross-sectional coordinate system are calculated using the sampling moment and the corresponding vehicle speed. Specifically, at each sampling moment, the real-time displacement relative to the origin of the cross-sectional coordinate system is calculated based on the vehicle speed. The real-time displacement is used to characterize the absolute distance traveled by the vehicle tire in the horizontal direction. It is obtained by accumulating the product of the vehicle speed from the first sampling time to the Mth sampling time and the sampling interval between two adjacent sampling times. Based on the real-time displacement and the static suspension height, the geometric center of motion of the vehicle tire in the cross-sectional coordinate system is determined and defined as the tire virtual center point. The tire virtual center point characterizes the axial spatial orientation of the vehicle tire in a state without elastic compression. The real-time displacement is used to determine the horizontal axis component of the tire virtual center point in the cross-sectional coordinate system, and the static suspension height is used to determine the vertical axis component of the tire virtual center point in the cross-sectional coordinate system. The horizontal and vertical axis components together determine the spatial coordinate pair of the tire virtual center point at each sampling time. The virtual center point of the tire serves as the geometric reference for the dynamic translation of the load contact envelope within the cross-sectional coordinate system. Using the virtual center point as the geometric control center and the tire radius parameter as the radius constraint, a mathematical equation characterizing the lower contact profile of the vehicle tire is constructed, defined as the lower semicircular arc function. The construction of the lower semicircular arc function is based on the vertical projection offset logic of the standard circle analytical equation in the cross-sectional coordinate system. Specifically, a function mapping relationship is established with the independent variable being the horizontal axis coordinate X and the dependent variable being the vertical axis coordinate Y. The dependent variable y of the lower semicircular arc function is set to be equal to the difference between the static suspension height and a specific arithmetic root value. The specific arithmetic root value is the square root obtained by subtracting the square of the difference between the horizontal axis coordinate X and the real-time displacement from the square of the tire radius parameter. Since the subtraction operation can lock the half-track with the smaller vertical axis coordinate from the complete circular trajectory, at each sampling moment, the geometric curve generated by the lower semicircular arc function represents the load contact envelope characterizing the boundary of the vehicle tire's sinking deformation. This transforms the kinematic properties of the vehicle's motion into a dynamic logical boundary that can be used for interference determination with the contour line.

[0067] Extract the geometric boundary function and simultaneously extract the lower semicircular arc function corresponding to each sampling moment. Identify the numerical intersection interval between the geometric boundary function and the lower semicircular arc function within the horizontal axis range of the cross-sectional coordinate system. This numerical intersection interval refers to the continuous set of horizontal axis coordinates corresponding to when the value of the lower semicircular arc function in the vertical direction is less than or equal to the value of the geometric boundary function in the vertical direction at a specific sampling moment. This represents the horizontal projection range of the physical interference between the vehicle tire and the steel section of the central beam. Calculate the overlap of the geometric boundary function with respect to the lower semicircular arc function in the vertical direction. Specifically, set a spatial step size, which is used to perform small displacement increments for spatial discretization of the numerical intersection interval. The value is set based on the minimum value of the edge curvature radius and the gap width spacing, and is set to no more than one-tenth of the minimum value to ensure that the curvature features of the contour line at the corners can be completely extracted. Along the horizontal axis of the cross-sectional coordinate system, the numerical intersection interval is sampled traversally using the spatial analytical step size to obtain the vertical axis values ​​of the geometric boundary function and the lower semicircular arc function at each sampling point. The algebraic deviation between the vertical axis value of the geometric boundary function and the vertical axis value of the function expression is calculated, and the algebraic deviation value is determined as the overlap in the vertical direction at the sampling point. To accurately quantify the local contact stress generated by the compression of a vehicle tire when passing through irregular gaps, the elastic modulus coefficient is extracted from the tire specification identification information. The tire specification identification information refers to the character sequence or digital feature label marked on the sidewall of the vehicle tire, used to uniquely quantify the tire's structural parameters, material specifications, and load index. Its function is to serve as a performance retrieval index to obtain the physical resistance characteristics of the vehicle tire under specific service conditions. The elastic modulus coefficient is a physical parameter obtained based on the tire model determined by the tire specification identification information, used to characterize the reaction force intensity generated by the tire material under unit compression depth, realizing the dimensional conversion from geometric interference space to stress load space. The elastic modulus coefficient is multiplied by the overlap in the vertical direction corresponding to each sampling point to generate the corresponding transient contact pressure. By traversing all sampling times within the test cycle, the generated series of transient contact pressures are arranged in a matrix according to the index of the sampling time to generate a pressure distribution matrix. The pressure distribution matrix is ​​a multi-dimensional digital feature matrix that integrates time history, spatial coordinates, and pressure amplitude characteristics. The row index corresponds to the index of the sampling time within the test cycle, and the column corresponds to the sampling point within the numerical intersection interval. That is, each matrix element value in the pressure distribution matrix represents the transient contact pressure at a specific sampling time and a specific sampling point location. Its function is to completely reproduce the initial excitation source generated by the vehicle tire when passing through the irregular cross-section determined by the edge curvature radius, the slot width spacing, and the surface microstructure height, providing high-fidelity data input for subsequent determination of the optimization parameters of the vibration reduction structure.

[0068] Step S13: Response analysis is performed based on the pressure distribution matrix to obtain a set of acoustic vibration feature vectors characterizing the dynamic response characteristics of the steel section of the beam steel.

[0069] After generating the pressure distribution matrix, in order to further reveal the physical response law of the expansion joint structure under dynamic excitation and solve the problem that traditional design only focuses on the peak amplitude and ignores the hidden acoustic vibration characteristics induced by the geometric change of the cross section of the central beam steel, the pressure distribution matrix is ​​transformed into a dynamic feature with multi-dimensional evaluation attributes. The purpose is to simulate the dynamic evolution logic of the whole system and provide an objective function input with both acoustic and mechanical orientation for the subsequent process.

[0070] Specifically, the structural physical properties of three components—the central beam steel section, the supporting crossbeam, and the bearing bearing—are obtained. These properties include material mass, structural stiffness, and the mechanical assembly logic of each component. Material mass refers to the product of the volume of each component and its corresponding density constant, obtained through a CAD design data parser; this serves to provide the inertia operator in dynamic simulations. Structural stiffness characterizes the mechanical parameters that allow each component to resist deformation; it provides the conversion coefficient between transient contact pressure and structural deformation. The mechanical assembly logic characterizes the topological connection relationship and displacement constraints between the central beam steel section welded to the top of the supporting crossbeam and the supporting crossbeam elastically supported within the groove of the bridge main beam by the bearing bearing.

[0071] Based on mechanical assembly logic, a structural transmission function characterizing the overall stress and deformation law of the expansion joint device is constructed. This structural transmission function is a mathematical analytical model based on dynamic equilibrium equations, used to transform the pressure distribution matrix into acceleration and displacement response sequences reflecting the forced vibration state of the structure. Specifically, the physical structure of the central beam, supporting beams, and bearing supports is divided into multiple discrete calculation nodes corresponding to sampling points in the cross-sectional coordinate system. For each discrete calculation node, a dynamic equilibrium equation is established according to the mechanical assembly logic. The left side of the dynamic equilibrium equation consists of matrix element values ​​extracted from the pressure distribution matrix corresponding to the sampling time and sampling point position. The right side of the dynamic equilibrium equation consists of two parts: the first part is the inertial term determined by the product of material mass and acceleration response characteristics, and the second part is the elastic term determined by the product of structural stiffness and displacement evolution characteristics. By simultaneously solving the dynamic equilibrium equations of all discrete calculation nodes, a system of second-order linear differential equations characterizing the overall stress and deformation law of the expansion joint device is generated. The acceleration response characteristic refers to the instantaneous acceleration numerical sequence output by the discrete computing node at each sampling moment within the test period. It is a digital physical parameter extracted by performing iterative analysis of the second-order linear differential equations using a numerical integration algorithm, used to quantify the forced vibration intensity of the beam steel after being subjected to transient contact pressure excitation. Logically, it corresponds to the second derivative of the displacement evolution characteristic with respect to the time dimension, used to characterize the rate of motion state switching of the discrete computing node under transient contact pressure. The displacement evolution characteristic refers to the geometric offset of the discrete computing node relative to its initial position in the cross-sectional coordinate system.

[0072] To transform the transient contact pressure contained in the pressure distribution matrix into the acceleration response characteristics and displacement evolution characteristics of the beam steel, thereby establishing a physical logical link between matrix element values ​​and vibration response sequences, specifically, a coordinate correspondence between the pressure distribution matrix and the beam steel is established based on the cross-sectional coordinate system. This coordinate correspondence maps the corresponding sampling points in the pressure distribution matrix to discrete calculation nodes on the horizontal axis of the cross-sectional coordinate system that coincide with the physical coordinates of the top cross-section of the beam steel. Using the time interval between two adjacent sampling moments as the calculation step size, iterative calculations of the second-order linear differential equation system are performed within the test period. For each sampling moment, all matrix element values ​​corresponding to that sampling moment are extracted from the pressure distribution matrix as external input excitation. This external input excitation is input into the structural transfer function, and a numerical integration algorithm is used to solve for the acceleration response characteristics and displacement evolution characteristics of the beam steel at each sampling point. By traversing all sampling moments within the test period, the acceleration response characteristics and displacement evolution characteristics at each sampling point are summarized and combined to generate a vibration response sequence characterizing the dynamic stress response of the beam steel. The vibration response sequence realizes the logical evolution from a discrete pressure distribution matrix to a continuous structural vibration state.

[0073] Acceleration response features are extracted from the vibration response sequence, and a sliding time window is set for local feature capture. The duration of the sliding time window is set based on the ratio of the gap width to the corresponding vehicle speed, ensuring that the sliding time window can fully cover the physical process of the test vehicle tire crossing a single set of gaps. The number of times the acceleration response feature crosses the X-axis of the cross-sectional coordinate system within the sliding time window is counted and defined as the short-time zero-crossing rate. The short-time zero-crossing rate quantifies the density of the vibration frequency of the beam steel and is used to characterize the impact energy activity of the expansion joint device after being excited by the pressure distribution matrix. A fast Fourier transform is performed on the acceleration response features to generate a frequency domain distribution map corresponding to the acceleration response features. The frequency domain distribution map contains a frequency axis composed of multiple discrete frequency points and the energy amplitude corresponding to each discrete frequency point. The value of each discrete frequency point on the frequency axis is multiplied by its corresponding energy amplitude to obtain the partial energy moment; all partial energy moments are summed to obtain the total energy weight sum; the total energy weight sum is divided by the sum of the energy amplitudes corresponding to all discrete frequency points to obtain the center of gravity frequency. The centroid frequency is used to characterize the main excitation frequency distribution region generated by the expansion joint device under the action of the pressure distribution matrix. The energy distribution dispersion of the frequency domain distribution map on the frequency axis is calculated, and the obtained dispersion value is defined as spectral broadening. The spectral broadening is used to quantify the complexity of the signal components in the vibration response sequence of the central beam steel. Specifically, the absolute value of the frequency deviation of each discrete frequency point relative to the centroid frequency in the frequency domain distribution map is obtained. The square of the absolute value of the frequency deviation is multiplied by the energy amplitude corresponding to each discrete frequency point to obtain the discrete characteristic value of each component. The discrete characteristic values ​​of each component are summed to obtain the total discrete energy weighted sum. The total discrete energy weighted sum is divided by the sum of the energy amplitudes corresponding to all discrete frequency points, and the arithmetic square root operation is performed to obtain the spectral broadening. The short-time zero-crossing rate, centroid frequency, and spectral broadening are normalized. The short-time zero-crossing rate, centroid frequency, and spectral broadening are mapped to a dimensionless space between zero and one to obtain a set of acoustic vibration characteristic vectors characterizing the dynamic response characteristics of the steel section of the central beam steel.

[0074] Step S10, by acquiring initial structural test parameters, constructing a cross-sectional coordinate system, contour lines, load contact envelopes, pressure distribution matrices, and a set of acoustic and vibration feature vectors, solves the problem that traditional techniques simplify the cross-section of the central beam steel section to an ideal planar load, resulting in an inability to reflect the high-frequency impact effects and dynamic distortion generated when a vehicle passes over it. This achieves high-fidelity reconstruction of the excitation source and multi-dimensional quantification of the acoustic and vibration response characteristics of the expansion joint device. Specifically, the cross-sectional coordinate system provides a unified vectorized representation space for initial structural test parameters of different dimensions; the digitized contour lines ensure the geometric continuity and physical authenticity of the steel profile; the pressure distribution matrix quantifies the transient compression intensity when the tire crosses the gap using the numerical intersection interval of the load contact envelope and the contour lines, providing a precise initial excitation source; and the set of acoustic and vibration feature vectors uses the structural transfer function to evolve the discrete pressure distribution into a quantitative index characterizing the impact energy activity and signal component complexity.

[0075] Step S20: Perform test index reconstruction on the acoustic vibration feature vector set to obtain a vibration diagnosis plane characterizing the performance trade-off state of the expansion joint. Construct a dynamic performance safety domain based on the vibration diagnosis plane. Determine the inclusion relationship of the dynamic performance safety domain to obtain a parameter diagnosis set. Perform three-level screening on the parameter diagnosis set to obtain a balanced calibration parameter solution set.

[0076] Further, step S20 includes:

[0077] Step S21: Perform test index reconstruction based on the set of acoustic vibration feature vectors to obtain a vibration diagnostic plane characterizing the performance trade-off state of the expansion joint.

[0078] After obtaining the set of acoustic and vibration feature vectors, in order to eliminate the problem of ambiguity in the direction of optimization objectives caused by the dimensional barriers between different performance dimensions, the set of acoustic and vibration feature vectors is reconstructed into a comprehensive evaluation index with physical directionality. The purpose is to construct a digital analytical space that can intuitively quantify the trade-offs between competing performances of multiple objectives, providing a unified spatial coordinate benchmark for subsequent operations.

[0079] Specifically, the normalized short-time zero-crossing rate and normalized center-of-gravity frequency are extracted from the acoustic vibration feature vector set. Based on the physical property of the short-time zero-crossing rate used to quantify the frequency density of the beam steel vibration, and the physical property of the center-of-gravity frequency used to characterize the main excitation frequency distribution area generated by the expansion joint device, a positive correlation mapping logic for acoustic subjective annoyance is established. The physical basis is as follows: the increase in the value of the short-time zero-crossing rate indicates that the excitation frequency of the beam steel after impact has shifted to the high-frequency domain, and the increase in the value of the center-of-gravity frequency indicates that the sound energy center generated by the expansion joint device has shifted to the high-frequency band. Since vibration signals with high-frequency density characteristics and sound energy signals with harshness have stronger penetration and sensory discomfort in the human acoustic perception dimension, the increase in the values ​​of short-time zero-crossing rate and center-of-gravity frequency shows a deterministic positive correlation with the degree of subjective annoyance. The algebraic sum of the normalized short-time zero-crossing rate and the normalized center-of-gravity frequency is calculated, and the algebraic sum is divided by two to mean the result, thus obtaining the driving comfort evaluation quantity. The role of the ride comfort evaluation quantity is to quantify the degree of comprehensive acoustic interference generated when the vehicle tires cross the edge of the central beam steel. Displacement evolution characteristics are extracted from the vibration response sequence. The absolute peak value of the displacement evolution characteristics within the test period is extracted using maximum value retrieval logic, and this absolute peak value is defined as the structural durability evaluation quantity. The role of the structural durability evaluation quantity is to quantify the degree of physical deformation of the central beam steel and supporting crossbeams under the impact of the pressure distribution matrix. Specifically, based on the time-frequency joint response characteristics of the vibration signal, the short-time zero-crossing rate is regarded as a quantitative indicator characterizing the intensity of impact oscillations in the time domain, and the center-of-gravity frequency is regarded as an indicator characterizing the trend of energy concentration towards higher frequencies in the frequency domain. Since the increase in oscillation intensity and the shift towards higher frequencies of energy directly correspond to the instability and aggravation of the structural dynamic response under the condition of rigid impact on the central beam steel, a logical correlation is established between the magnitude of the above two indicators and the degree of system vibration deterioration, thus forming a mapping logic that can quantify the comprehensive impact intensity.

[0080] To establish a spatial logical relationship between the ride comfort evaluation quantity and the structural durability evaluation quantity, a two-dimensional planar coordinate system is constructed, defined as the vibration diagnostic plane. Specifically, the ride comfort evaluation quantity is defined as the horizontal axial coordinate of the vibration diagnostic plane, and the structural durability evaluation quantity is defined as the vertical axial coordinate of the vibration diagnostic plane. The calculated values ​​corresponding to the ride comfort evaluation quantity and the structural durability evaluation quantity are logically combined to map a unique coordinate point within the vibration diagnostic plane, defined as a performance point. The performance point is a pair of real coordinates consisting of horizontal and vertical dimension values. Its function is to transform the comprehensive performance of the expansion joint device under specific vibration reduction structural parameters into a calculable geometric spatial location, achieving logical convergence from multi-dimensional discrete features to a two-dimensional correlated evaluation space.

[0081] Step S22: Construct a dynamic performance safety domain based on the vibration diagnosis plane, and determine the inclusion relationship based on the dynamic performance safety domain to obtain the parameter diagnosis set.

[0082] After obtaining the vibration diagnostic plane, the performance points within it enable precise spatial positioning of the expansion joint device's performance under specific combinations of vibration-damping structural parameters. To achieve automated compliance verification in complex engineering service scenarios and ensure that optimization results improve vehicle quietness without sacrificing structural safety, a dynamic performance safety domain is constructed within the vibration diagnostic plane. This provides a logical comparison benchmark for the performance points based on physical limit constraints.

[0083] Specifically, the environmental sound functional zone category data of the environment where the expansion joint device is located is obtained. This environmental sound functional zone category data refers to characteristic information used to characterize the noise control level of a specific area, as defined by sound environment quality standards. A ride comfort constraint threshold is determined using this data. This ride comfort constraint threshold is a dimensionless physical quantity used to define the maximum permissible numerical boundary of the ride comfort evaluation quantity. It is set by inverse matching between the noise sensitivity represented by the environmental sound functional zone category data and the normalized interval of the ride comfort evaluation quantity. Next, the allowable fatigue stress value of the beam steel under cyclic impact load is obtained. This allowable fatigue stress value refers to the maximum stress amplitude that will not fracture within the service life of the beam steel material, determined based on its stress life. This allowable fatigue stress value is defined as the durability constraint threshold. In the vibration diagnostic plane, the ride comfort constraint threshold is used as the maximum permissible interception point in the horizontal axial direction, and the durability constraint threshold is used as the maximum permissible interception point in the vertical axial direction. Considering that when the central beam steel is subjected to impact from the test vehicle's tires, the increased thickness of the damping material leads to the absorption of noise energy but a delayed structural displacement response, thus inducing greater internal transient stress, a nonlinear envelope curve is established based on the principle of energy dissipation conservation, with ride comfort as the independent variable and structural durability as the dependent variable. The damping material thickness refers to the vertical geometric dimension of the elastic damping medium installed between the support beam and the groove of the bridge main beam, serving to quantify the mechanical filtering capability of the expansion joint device against high-frequency impact energy. This thickness is extracted from the initial structural test parameters of the expansion joint device using a CAD design data parser.

[0084] The nonlinear envelope curve satisfies a quadratic parabolic distribution logic. The analytical expression of the nonlinear envelope curve is as follows: the structural durability evaluation quantity is equal to the difference between the durability constraint threshold and the "specific performance loss term," where the specific performance loss term is equal to the durability constraint threshold multiplied by the square of the ratio of the ride comfort evaluation quantity to the ride comfort constraint threshold. Within the vibration diagnostic plane, the closed geometric region enclosed by the ride comfort constraint threshold, the durability constraint threshold, and the nonlinear envelope curve is defined as the dynamic performance safety domain. Specifically, the derivation logic based on the principle of energy dissipation conservation is as follows: the expansion joint device is considered an energy dissipation system, and the input excitation energy originates from the pressure distribution matrix generated by the moving load, with the total amount considered constant at a specific impact instant. According to the principle of energy dissipation conservation, the total energy is allocated as a kinetic energy dissipation component characterizing high-frequency acoustic radiation and a potential energy dissipation component characterizing structural elastic deformation. Among them, the ride comfort evaluation quantity is constructed based on the short-time zero-crossing rate and center of gravity frequency, which physically quantifies the vibration velocity and frequency intensity of the central beam steel. The corresponding kinetic energy dissipation component and the ratio of the ride comfort evaluation quantity to the ride comfort constraint threshold are proportional to the square, that is, they follow the physical law that vibration energy is proportional to the square of amplitude and frequency. The structural durability evaluation quantity represents the absolute peak value of the displacement evolution characteristics, corresponding to the residual elastic potential energy capacity of the system. Therefore, when the kinetic energy dissipation component occupies the energy share at a square rate due to the increase of the ride comfort evaluation quantity, the residual potential energy capacity used to maintain structural integrity, that is, the structural durability evaluation quantity, must decay in a quadratic parabolic form relative to the durability constraint threshold, thus deriving the logic of the square term included in the specific performance loss term.

[0085] After obtaining the dynamic performance safety domain, the inclusion relationship of performance points relative to the dynamic performance safety domain is determined. The purpose is to use the geometric boundary of the dynamic performance safety domain as a physical screen to identify performance points, thereby outputting a clear parameter compliance determination status. Specifically, the horizontal and vertical dimension values ​​of the real coordinate pairs of the performance points are extracted. The horizontal dimension value is substituted into the nonlinear envelope curve for calculation to obtain the stress critical value. The stress critical value represents the upper limit of the maximum structural stress response that the expansion joint device can allow under the current ride comfort level. The vertical dimension value of the performance point is compared with the stress critical value. If the vertical dimension value is less than or equal to the stress critical value, and the horizontal dimension value is less than the ride comfort constraint threshold, then the performance point is determined to be inside the closed geometric region of the dynamic performance safety domain. A parameter compliance determination status representing compliance with engineering compliance requirements is generated. The parameter compliance determination status is a logical Boolean truth value used to indicate that the vibration reduction structure parameters have passed the dual physical verification of acoustic comfort and structural safety. If the vertical dimension value exceeds the critical stress value or the horizontal dimension value exceeds the ride comfort constraint threshold, the performance point is determined to be outside the closed geometric region of the dynamic performance safety domain. A parameter correction instruction is generated, characterizing the potential for structural failure or excessive noise in the current vibration reduction structure parameters. This parameter correction instruction is a logical Boolean false value used to trigger an elimination or adjustment operation on the current vibration reduction structure parameters. The parameter compliance determination status and the parameter correction instruction are logically encapsulated to obtain a parameter diagnostic set.

[0086] Step S23: Perform a three-layer screening based on the parameter diagnostic set to obtain the solution set of equilibrium calibration parameters.

[0087] After obtaining the parameter diagnostic set, to address the difficulty in balancing the vibration reduction structure parameters caused by the mutual constraints between ride comfort evaluation and structural durability evaluation during actual service of bridge expansion joints, a parameter evolution control mechanism is established to drive the automatic evolution of vibration reduction structure parameters. The aim is to transform the discrete, passive parameter verification process into an active, globally optimal optimization process covering the entire parameter space, outputting a balanced calibration parameter solution set that ensures the vibration reduction performance of bridge expansion joints reaches a globally optimal state.

[0088] Specifically, the edge curvature radius, joint width spacing, surface microstructure height, and damping material thickness are treated as independent design variables for the vibration reduction structure. Each design variable is assigned a numerical variation range that meets the requirements of engineering manufacturing processes. This numerical variation range refers to the continuous closed interval consisting of the minimum and maximum values ​​that can be selected for the vibration reduction structure design variable within the allowable range of the bridge expansion joint vibration reduction structure manufacturing process and under the premise of ensuring the safety of bridge service. For the edge curvature radius, the numerical variation range is determined by the physical contact stability between the tire and the steel section of the central beam, and is set to [5, 50] for example. For the joint width spacing, the numerical variation range is determined based on the annual average temperature difference expansion and contraction displacement requirement of the bridge main beam and the vehicle jump restriction standard, and is set to [20, 120] for example. For the surface microstructure height, the numerical variation range is determined based on the bridge deck drainage efficiency requirement and the anti-slip friction coefficient requirement of the steel surface, and is set to [0, 15] for example. For the damping material thickness, the numerical variation range is determined based on the preset first-order natural frequency suppression range of the expansion joint device and the vertical installation space limitation of the groove of the bridge main beam, and is set to [10, 80] for example. The numerical variation ranges of the edge curvature radius, joint width spacing, surface microstructure height and damping material thickness together construct a multi-dimensional continuous geometric search space, which is defined as the structural parameter design space. Specifically, a four-dimensional Cartesian coordinate system is established, consisting of four mutually orthogonal coordinate axes. The four mutually orthogonal coordinate axes in the four-dimensional Cartesian coordinate system are defined as the edge curvature radius axis, the slot width spacing axis, the surface microstructure height axis, and the damping material thickness axis, respectively. The numerical intervals corresponding to the vibration reduction structure design variables are mapped to the corresponding four mutually orthogonal coordinate axes. Cartesian product operations are performed on the four numerical intervals in the four-dimensional Cartesian coordinate system. A four-dimensional hyperrectangular closed geometry is generated by enclosing and filling the four-dimensional Cartesian coordinate system, which is the structural parameter design space. Each coordinate point in the structural parameter design space is a four-dimensional parameter vector composed of the edge curvature radius, slot width spacing, surface microstructure height, and damping material thickness.

[0089] An initial population is randomly generated within the structural parameter design space. This initial population consists of G initial parameter individuals, each representing a set of four-dimensional parameter vectors randomly selected from the numerical variation range, composed of edge curvature radius, slot width spacing, surface microstructure height, and damping material thickness. The total number G of initial parameter individuals is determined based on the nonlinear complexity of the four-dimensional search dimension of the structural parameter design space, balancing computational resource consumption speed with global search convergence accuracy; for example, it is set to 50. The G initial parameter individuals are then labeled and indexed from 1 to G. Steps S11 to S22 are executed for each initial parameter individual to obtain the performance point corresponding to each individual, defined as the individual performance point, and the corresponding parameter diagnostic set, defined as the individual parameter diagnostic set.

[0090] For each initial parameter individual, a parameter evolution operation consisting of three layers of screening logic is performed: The first layer of screening logic is compliance filtering, which determines whether the initial parameter individual meets the physical constraints of the dynamic performance safety domain based on the individual parameter diagnostic set. If the individual parameter diagnostic set identifies a parameter correction instruction, meaning that the individual performance point of the initial parameter individual does not fall within the dynamic performance safety domain, then the initial parameter individual is determined to be an unqualified parameter individual. If the individual parameter diagnostic set identifies a parameter compliance judgment state, then the initial parameter individual is determined to be a qualified parameter individual and enters the second layer of screening logic. The qualified parameter individual is defined as the initial parameter individual whose individual performance point falls within the dynamic performance safety domain. The second layer of screening logic is dominance relationship judgment, which compares among all qualified parameter individuals, determines the qualified parameter individual to be diagnosed as the target judgment individual, and defines the set of qualified parameter individuals other than the target judgment individual as the reference comparison individual set. Specifically, the coordinate values ​​of the individual performance points of the target individual are compared with the coordinate values ​​of the individual performance points of each qualified parameter individual in the reference comparison set in the vibration diagnostic plane. The target individual is considered to be in a non-dominated state only if the ride comfort evaluation value and structural durability evaluation value corresponding to the individual performance point of any qualified parameter individual in the reference comparison set are both less than the evaluation value corresponding to the individual performance point of the target individual. The non-dominated state means that in the current set of qualified parameter individuals, there is no better performance response scheme than the target individual; that is, the target individual has an irreplaceable advantage in at least one evaluation dimension. The third layer of screening logic is crowding ranking. Crowding values ​​are calculated for qualified parameter individuals in the non-dominated state. The crowding value refers to the Euclidean distance between the individual performance point of the target individual and its two adjacent individual performance points in the vibration diagnostic plane. All qualified parameter individuals in non-dominated states are marked as candidate optimal solutions. After sorting all candidate optimal solutions in descending order using crowding degree values, they are extracted according to a preset solution set size to obtain the optimal solution set. The solution set size is determined based on the mechanical execution accuracy of the bridge expansion joint vibration reduction structure during actual physical adjustment. The edge curvature radius, joint width spacing, surface microstructure height, and damping material thickness corresponding to the optimal solution set are digitally encapsulated to obtain the balance calibration parameter solution set. This balance calibration parameter solution set serves as a physical benchmark to guide the precision manufacturing and structural adjustment of the bridge expansion joint vibration reduction structure, realizing the transformation of expansion joint device design from experience-based design to performance-oriented design.

[0091] Step S20, through the execution of test index reconstruction, vibration diagnostic plane, construction of dynamic performance safety domain, inclusion relationship determination, parameter diagnostic set, and three-layer screening, solves the problem that traditional "trial and error" design struggles to balance the contradiction between ride comfort and structural durability, leading to frequent vehicle bouncing, concrete breakage in the anchorage zone, and severe noise at expansion joints during operation. It achieves collaborative diagnosis of multiple competing performance indicators, automated verification of physical compliance, and global optimization of the optimal parameter combination. Specifically, the vibration diagnostic plane provides an intuitive geometric benchmark for multi-objective trade-offs; the dynamic performance safety domain sets compliance boundaries based on physical limits for performance points; and the three-layer screening logic accurately identifies the equilibrium calibration parameter solution set that simultaneously satisfies physical constraints, achieves optimal performance, and is uniformly distributed.

[0092] Step S30: Construct a physical calibration command sequence for driving the relevant actuators based on the solution set of balance calibration parameters, perform physical calibration on the physical calibration command sequence, and obtain a test compliance verification mark characterizing the vibration reduction performance of the bridge expansion joint vibration reduction structure.

[0093] Further, step S30 includes:

[0094] Step S31: Construct a sequence of physical calibration instructions to drive the relevant actuators based on the solution set of the balance calibration parameters.

[0095] After obtaining the equilibrium calibration parameter set, in order to address the issue of suboptimal vibration reduction performance caused by microscopic geometric deviations in bridge expansion joints during actual manufacturing, installation, or service, an execution system is established that can accurately convert the equilibrium calibration parameter set into a sequence of physical calibration commands. The aim is to eliminate dynamic response distortion induced by abrupt geometric changes in the cross-sectional geometry of the central beam steel sections through physical parameter correction, thereby achieving a synergistic improvement in ride comfort and structural durability.

[0096] Specifically, parameter values ​​consisting of edge curvature radius, joint width spacing, surface microstructure height, and damping material thickness are extracted from the equilibrium calibration parameter solution set, and the current physical geometric parameters of the bridge expansion joint vibration reduction structure are retrieved simultaneously. These current physical geometric parameters refer to the measured physical dimension values ​​of the bridge expansion joint vibration reduction structure at the current moment, used to quantify the current true geometric state of the structure. These include the current edge curvature radius, current joint width spacing, current surface microstructure height, and current damping material thickness. The edge curvature radius, joint width spacing, surface microstructure height, and damping material thickness from the equilibrium calibration parameter solution set are then subjected to a term-by-term difference operation with the current edge curvature radius, current joint width spacing, current surface microstructure height, and current damping material thickness, respectively, to obtain the first physical compensation value, the second physical compensation value, the third physical compensation value, and the fourth physical compensation value. The physical compensation value refers to the geometric displacement correction or material filling increment required to achieve optimal vibration reduction performance of the bridge expansion joint vibration reduction structure.

[0097] The first, second, third, and fourth physical compensation values ​​are mapped to the corresponding equipment execution control parameters of the relevant actuators. The relevant actuators refer to hardware execution devices that integrate a power drive source and servo control logic, capable of responding to digital commands and performing geometric dimension adjustments or mechanical performance compensations on the physical entity of the bridge expansion joint vibration reduction structure. Examples include hydraulic jacks for adjusting the spatial position of the steel section of the central beam, CNC milling devices for performing subtractive processing or surface finishing on the profile of the central beam's steel section, and servo presses for controlling the clamping intensity of damping materials. Specifically, the first physical compensation value is obtained by differentiating the contour line to obtain the tangent slope. The arctangent of the negative reciprocal of the tangent slope is calculated to determine the normal vector angle at the tangent point. The radius difference represented by the first physical compensation value is decomposed along the normal vector angle into a radial component perpendicular to the profile surface of the steel section and a tangential component along the tangent direction of the profile of the steel section. This is then mapped to the displacement control vector and angle control vector of the relevant actuators to adjust the edge curvature radius of the steel section of the middle beam. The second physical compensation value is obtained by directly superimposing the numerical value onto the coordinate value in the horizontal direction of the section coordinate system and performing a linear translation operation. This is mapped to the displacement control vector of the relevant actuators to adjust the gap span between the steel sections of the middle beam. The third physical compensation value is obtained by calculating the vertical height difference between the solution set of the equilibrium calibration parameters and the current physical geometric parameters in the vertical direction under the same horizontal axis coordinate. Simultaneously, the slope change rate is calculated based on the difference of the second derivative of the interpolation basis function. The vertical height difference and slope change rate are the displacement control vector and angle control vector of the relevant actuator, used to adjust the microstructural undulations of the steel section of the central beam. The fourth physical compensation value is obtained by calculating the strain by the ratio of the fourth physical compensation value to the damping material thickness. The strain is then multiplied by the elastic modulus to calculate the stress required to produce the target deformation. This stress is used as the torque control vector of the relevant actuator to adjust the compaction intensity of the damping material inside the bearing support. The displacement control vector, angle control vector, and torque control vector are the equipment execution control parameters. The displacement control vector is a digital command used to control the actuator's linear travel distance within the cross-sectional coordinate system, and the angle control vector is a digital command used to control the operating angle of the relevant actuator relative to the steel section of the central beam of the bridge expansion joint vibration reduction structure. The torque control vector refers to the digital command used to control the working pressure intensity of the relevant actuators when they compress damping materials or widen steel sections. By encapsulating the equipment execution control parameters into a physical calibration command sequence and sending it to the relevant actuators, the actual physical state of the bridge expansion joint vibration reduction structure is kept consistent with the equilibrium calibration parameter solution set, ensuring that the actual profile height of the bridge expansion joint vibration reduction structure matches the digital profile line.Eliminating the dynamic response distortion induced by the geometrical abrupt change in the cross-section of the central beam steel from a physical source, solving the "jumping" impact when vehicle tires cross irregular gaps and the high-frequency vibration noise caused by nonlinear contact, so that the performance of the bridge expansion joint vibration reduction structure meets the constraints of the dynamic performance safety domain.

[0098] Step S32: Perform physical calibration based on the physical calibration command sequence to obtain a test compliance verification mark characterizing the vibration reduction performance of the bridge expansion joint vibration reduction structure.

[0099] After the relevant implementing agencies complete the physical parameter compensation according to the physical calibration instruction sequence, in order to verify whether the actual performance of the bridge expansion joint vibration reduction structure meets expectations and to eliminate residual deviations caused by manufacturing disturbances, a closed-loop verification system capable of performing fine-grained feedback adjustment is established. The physical parameter compensation refers to the process by which the relevant implementing agencies physically correct the bridge expansion joint vibration reduction structure according to the physical calibration instruction sequence.

[0100] Specifically, the feedback geometric parameters of the bridge expansion joint vibration reduction structure after the relevant actuators have completed physical parameter compensation according to the physical calibration command sequence are obtained. These feedback geometric parameters refer to the real-time physical dimension values ​​of the bridge expansion joint vibration reduction structure after physical parameter compensation, including the compensated edge curvature radius, compensated joint width spacing, compensated surface microstructure height, and compensated damping material thickness. Based on the edge curvature radius, joint width spacing, surface microstructure height, and damping material thickness from the equilibrium calibration parameter solution set, a second subtraction operation is performed with the compensated edge curvature radius, compensated joint width spacing, compensated surface microstructure height, and compensated damping material thickness from the feedback geometric parameters, respectively, to obtain a first compensation difference, a second compensation difference, a third compensation difference, and a fourth compensation difference. These first, second, third, and fourth compensation differences are then combined to form a compensation difference set. Following the logic of mapping device execution control parameters in S31, the compensation difference set is mapped again to device execution control parameters, defined as a secondary physical calibration instruction sequence, and the secondary physical calibration instruction sequence is sent to the relevant actuators for secondary physical parameter compensation to obtain secondary feedback geometric parameters.

[0101] The contour line is reconstructed based on the secondary feedback geometric parameters and defined as the feedback contour line. New performance points are generated and defined as feedback performance points. It is then determined whether the feedback performance points fall within the closed geometric region of the dynamic performance safety domain. If the feedback performance points fall within the closed geometric region of the dynamic performance safety domain, the physical state of the bridge expansion joint vibration reduction structure is determined to fully meet the design requirements, resulting in a test compliance verification mark. This test compliance verification mark indicates that the bridge expansion joint vibration reduction structure has successfully eliminated the dynamic response distortion induced by the abrupt geometric changes in the cross-sectional geometry of the central beam steel, and that the ride comfort and structural durability of the bridge expansion joint vibration reduction structure have both met the standards. Through the test compliance verification mark, closed-loop control of the physical root causes of "jumping" impacts and high-frequency vibration noise is achieved, ensuring the performance stability of the bridge expansion joint vibration reduction structure throughout its entire life cycle.

[0102] Step S30, through a physical calibration command sequence and test compliance verification markers, solves the problem that the actual vibration reduction performance of expansion joints falls short of expectations due to microscopic geometric deviations during manufacturing and installation, and that precise feedback adjustments cannot be made for residual deviations. This achieves a closed-loop guarantee, ensuring that vibration reduction parameters are accurately implemented from theoretical optimization to physical implementation and that performance meets standards. Specifically, the physical calibration command sequence transforms digitized feature vectors into executable digital control logic flows, driving relevant actuators to perform microscopic adjustments to the actual contour and material distribution of the bridge expansion joint vibration reduction structure. The test compliance verification markers utilize quadratic interpolation calculations and feedback performance point determination to ensure that the physically corrected bridge expansion joint vibration reduction structure remains within a safe service range throughout its entire lifecycle.

[0103] Example 2

[0104] This embodiment, based on Embodiment 1, provides an expansion joint vibration reduction detection system based on vehicle-bridge-joint coupled vibration analysis, such as... Figure 4 As shown, it includes:

[0105] Acoustic and vibration analysis module: used to obtain the initial structural test parameters of the expansion joint of the viaduct, construct the cross-sectional coordinate system, perform feature mapping on the initial structural test parameters based on the cross-sectional coordinate system to obtain the digitized contour line, obtain the motion parameters of the moving load to construct the load contact envelope, perform virtual envelope interference analysis based on the load contact envelope and the contour line to generate the pressure distribution matrix, perform response analysis on the pressure distribution matrix to obtain the set of acoustic and vibration feature vectors;

[0106] The parameter filtering module is used to reconstruct test indicators from the set of acoustic and vibration feature vectors, obtain a vibration diagnosis plane that characterizes the performance trade-off state of the expansion joint, construct a dynamic performance safety domain based on the vibration diagnosis plane, determine the inclusion relationship of the dynamic performance safety domain, obtain a parameter diagnosis set, perform three-level filtering on the parameter diagnosis set, and obtain a set of balanced calibration parameters.

[0107] Command verification module: It is used to construct the physical calibration command sequence of the driving related actuators based on the solution set of balance calibration parameters, perform physical calibration on the physical calibration command sequence, and obtain the test compliance verification mark characterizing the vibration reduction performance of the bridge expansion joint vibration reduction structure.

[0108] In the acoustic vibration analysis module, the initial structural test parameters characterizing the expansion joints of the viaduct are obtained, and a cross-sectional coordinate system is constructed. Feature mapping is performed on the initial structural test parameters based on the cross-sectional coordinate system to obtain a digitized contour line. Moving load motion parameters are obtained to construct a load contact envelope. Virtual envelope interference analysis is performed between the load contact envelope and the contour line to generate a pressure distribution matrix. Response analysis is then performed on the pressure distribution matrix to obtain a set of acoustic vibration feature vectors, including:

[0109] Step S11: Obtain the initial structural test parameters of the elevated bridge expansion joint, construct a cross-sectional coordinate system, and perform feature mapping on the initial structural test parameters based on the cross-sectional coordinate system to obtain the digitized contour line.

[0110] Step S12: Obtain the motion parameters of the moving load to construct the load contact envelope, and perform virtual envelope interference analysis based on the load contact envelope and the contour line to generate a pressure distribution matrix;

[0111] Step S13: Perform response analysis based on the pressure distribution matrix to obtain a set of acoustic vibration feature vectors characterizing the dynamic response properties of the steel section.

[0112] In the parameter filtering module, the test index reconstruction is performed on the acoustic vibration feature vector set to obtain a vibration diagnosis plane characterizing the performance trade-off state of the expansion joint. A dynamic performance safety domain is constructed based on the vibration diagnosis plane. The inclusion relationship of the dynamic performance safety domain is determined to obtain a parameter diagnosis set. A three-layer filtering is performed on the parameter diagnosis set to obtain a balanced calibration parameter solution set, including:

[0113] Step S21: Perform test index reconstruction based on the acoustic vibration feature vector set to obtain a vibration diagnostic plane characterizing the performance trade-off state of the expansion joint;

[0114] Step S22: Construct a dynamic performance safety domain based on the vibration diagnosis plane, and determine the inclusion relationship based on the dynamic performance safety domain to obtain the parameter diagnosis set;

[0115] Step S23: Perform a three-layer screening based on the parameter diagnostic set to obtain the solution set of equilibrium calibration parameters.

[0116] In the instruction verification module, the physical calibration instruction sequence for driving the relevant actuators is constructed based on the solution set of the balance calibration parameters. Physical calibration is then performed on the physical calibration instruction sequence to obtain a test compliance verification identifier characterizing the vibration reduction performance of the bridge expansion joint vibration reduction structure. This identifier includes:

[0117] Step S31: Construct a sequence of physical calibration instructions to drive the relevant actuators based on the solution set of balance calibration parameters;

[0118] Step S32: Perform physical calibration based on the physical calibration command sequence to obtain a test compliance verification mark characterizing the vibration reduction performance of the bridge expansion joint vibration reduction structure.

[0119] In addition, the parts of the technical solutions provided in the embodiments of this application that are consistent with the implementation principles of the corresponding technical solutions in the prior art have not been described in detail, so as to avoid excessive elaboration.

[0120] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A vibration reduction detection method for expansion joints based on vehicle-bridge-joint coupled vibration analysis, characterized in that, The method includes: The initial structural test parameters of the expansion joint of the viaduct are obtained, and a cross-sectional coordinate system is constructed. Based on the cross-sectional coordinate system, feature mapping is performed on the initial structural test parameters to obtain a digitized contour line. The motion parameters of the moving load are obtained to construct the load contact envelope. Based on the load contact envelope and the contour line, virtual envelope interference analysis is performed to generate a pressure distribution matrix. The response analysis is performed on the pressure distribution matrix to obtain a set of acoustic vibration feature vectors. Test index reconstruction is performed on the acoustic vibration feature vector set to obtain a vibration diagnosis plane characterizing the performance trade-off state of the expansion joint. A dynamic performance safety domain is constructed based on the vibration diagnosis plane. The inclusion relationship of the dynamic performance safety domain is determined to obtain a parameter diagnosis set. A three-level screening is performed on the parameter diagnosis set to obtain a set of balanced calibration parameters. The three-layer screening refers to performing a parameter evolution operation consisting of three layers of screening logic for each preset initial parameter individual, including a first-layer screening logic, a second-layer screening logic, and a third-layer screening logic. The first-layer screening logic is compliance filtering, which determines whether the initial parameter individual meets the physical constraints of the dynamic performance safety domain based on the individual parameter diagnosis set. The second-layer screening logic is dominance relationship determination, which compares among all qualified parameter individuals, determines the qualified parameter individual to be diagnosed as the target judgment individual, and defines the set of qualified parameter individuals other than the target judgment individual as the reference comparison individual set. The third-layer screening logic is crowding degree sorting, which calculates the crowding degree value for qualified parameter individuals in a non-dominated state. The crowding degree value refers to the Euclidean distance between the individual performance point of the target judgment individual and its two adjacent individual performance points in the vibration diagnosis plane. Based on the solution set of the equilibrium calibration parameters, a physical calibration command sequence is constructed to drive the relevant actuators. The physical calibration command sequence is then physically calibrated to obtain a test compliance verification mark that characterizes the vibration reduction performance of the bridge expansion joint vibration reduction structure.

2. The expansion joint vibration reduction detection method based on vehicle-bridge-joint coupled vibration analysis according to claim 1, characterized in that, The method for obtaining the contour line includes: Initial structural test parameters include edge curvature radius, slot width spacing, and surface microstructure height; The amplitude coordinates of the longitudinal axis of the cross-sectional coordinate system are determined based on the height of the surface microstructure, and the span range of the transverse axis of the cross-sectional coordinate system is determined based on the gap width spacing. At the intersection of the span range of the transverse axis and the amplitude coordinates of the longitudinal axis, geometric envelope constraints are performed using the edge curvature radius. The initial structural test parameters are transformed into a series of coordinate points with unique coordinate values ​​in the cross-sectional coordinate system, which are defined as contour mapping points. A series of contour mapping points are fitted to construct a digital contour line of the steel section of the beam steel. An interpolation basis function containing interpolation coefficients is constructed between adjacent contour mapping points. A system of linear equations containing coordinate coincidence constraints, first derivative continuity constraints and second derivative continuity constraints is executed on the interpolation basis function to determine the interpolation coefficients and generate the digital contour line.

3. The expansion joint vibration reduction detection method based on vehicle-bridge-joint coupled vibration analysis according to claim 2, characterized in that, The method for obtaining the load contact envelope includes: The vehicle speed is obtained at each sampling moment during the test cycle. The tire radius parameter and static suspension height are obtained through the vehicle's nameplate parameter information. The vehicle speed, tire radius parameter and static suspension height constitute the motion parameters of the moving load. At each sampling moment during the test period, the real-time displacement relative to the origin of the cross-sectional coordinate system is calculated based on the vehicle speed. The geometric center of motion of the vehicle tire in the cross-sectional coordinate system is determined based on the real-time displacement and the static suspension height, and is defined as the tire virtual center point. Using the virtual center point of the tire as the geometric control center and the tire radius parameter as the radius constraint, a lower semicircular arc function representing the contact profile of the lower part of the vehicle tire is constructed, and at each sampling time, the load contact envelope representing the sinking deformation boundary of the vehicle tire is generated through the lower semicircular arc function.

4. The expansion joint vibration reduction detection method based on vehicle-bridge-joint coupled vibration analysis according to claim 3, characterized in that, The method for obtaining the pressure distribution matrix includes: In the cross-sectional coordinate system, the numerical intersection interval of the digitized contour line and the load contact envelope is identified, and the algebraic deviation value of the geometric boundary function and the lower semicircular arc function at each sampling point in the numerical intersection interval is calculated according to the preset spatial step size to obtain the overlap in the vertical direction. The geometric boundary function is the digitized contour line. The elastic modulus coefficient is extracted from the tire specification information of the vehicle tires. The elastic modulus coefficient is multiplied by the overlap in the vertical direction to generate the transient contact pressure. The pressure distribution matrix is ​​then generated by arranging the samples according to the index of the preset sampling time.

5. The expansion joint vibration reduction detection method based on vehicle-bridge-joint coupled vibration analysis according to claim 4, characterized in that, The method for obtaining the acoustic vibration feature vector set includes: Obtain the structural physical properties including material mass and structural stiffness, and construct a set of second-order linear differential equations based on mechanical assembly logic to characterize the overall stress and deformation law of the expansion joint device, which is defined as the structural transfer function; The pressure distribution matrix is ​​used as an external input excitation to the structural transmission function. The second-order linear differential equation system is solved using a numerical integration algorithm to obtain the acceleration response characteristics and displacement evolution characteristics of the steel section of the beam at each sampling point. The short-time zero-crossing rate is obtained by counting the number of times the acceleration response feature crosses the horizontal axis of the cross-sectional coordinate system within a preset sliding time window, and the centroid frequency and spectral broadening are extracted by performing a fast Fourier transform on the acceleration response feature. Normalization was performed on the short-time zero-crossing rate, centroid frequency, and spectral broadening to obtain a set of acoustic-vibration characteristic vectors that characterize the dynamic response of the steel section of the beam steel.

6. The expansion joint vibration reduction detection method based on vehicle-bridge-joint coupled vibration analysis according to claim 5, characterized in that, The method for obtaining the vibration diagnostic plane includes: Based on the short-time zero-crossing rate and center of gravity frequency, a positive correlation mapping logic for acoustic subjective annoyance is established. The mean of the normalized short-time zero-crossing rate and the normalized center of gravity frequency is calculated to obtain the driving comfort evaluation quantity. The absolute peak value of the displacement evolution characteristics within the test period is extracted using the maximum value retrieval logic to obtain the structural durability evaluation quantity; A vibration diagnostic plane is established with the ride comfort evaluation quantity as the horizontal axial coordinate and the structural durability evaluation quantity as the vertical axial coordinate. The ride comfort evaluation quantity and the structural durability evaluation quantity are combined and mapped to a unique coordinate point in the vibration diagnostic plane, which is defined as the performance point.

7. The expansion joint vibration reduction detection method based on vehicle-bridge-joint coupled vibration analysis according to claim 6, characterized in that, The method for obtaining the dynamic performance security domain includes: Obtain the environmental sound functional zone category data of the environment where the expansion joint device is located, determine the smoothness constraint threshold based on the environmental sound functional zone category data, obtain the allowable material fatigue stress value of the middle beam steel under cyclic impact load and define it as the durability constraint threshold. The thickness of the damping material in the cross section of the central beam steel is obtained, and based on the principle of energy dissipation conservation, a nonlinear envelope curve is established with the independent variable being the ride comfort evaluation quantity and the dependent variable being the structural durability evaluation quantity. This nonlinear envelope curve satisfies the logic of a quadratic parabolic distribution. A dynamic performance safety domain is generated within the vibration diagnostic plane by utilizing ride comfort constraint thresholds, durability constraint thresholds, and nonlinear envelope curves. Simultaneously, a multidimensional continuous geometric search space is constructed based on edge curvature radius, slot width spacing, surface microstructure height, and damping material thickness, which is defined as the structural parameter design space.

8. The expansion joint vibration reduction detection method based on vehicle-bridge-joint coupled vibration analysis according to claim 7, characterized in that, The method for obtaining the solution set of the equilibrium calibration parameters includes: In the structural parameter design space, multiple initial populations composed of initial parameter individuals are generated. For each initial parameter individual, a corresponding performance point and parameter diagnosis set are generated, which are defined as individual performance point and individual parameter diagnosis set, respectively. The individual parameter diagnosis set includes parameter compliance judgment status and parameter correction instructions. If the individual parameter diagnosis set is identified as a parameter correction instruction, it is determined to be an unqualified parameter individual. If it is a parameter compliance judgment state, it is a qualified parameter individual. The qualified parameter individual to be diagnosed is defined as the target judgment individual. The set of qualified parameter individuals other than the target judgment individual is defined as the reference comparison individual set. Only when the ride comfort evaluation quantity and structural durability evaluation quantity corresponding to the individual performance point of the unqualified parameter individual in the reference comparison individual set are both less than the evaluation quantity corresponding to the individual performance point of the target judgment individual, the target judgment individual is determined to be in a non-dominated state. Calculate the crowding degree values ​​of qualified parameter individuals in a non-dominated state, sort them in descending order according to the crowding degree values, and obtain the solution set of balance calibration parameters.

9. The expansion joint vibration reduction detection method based on vehicle-bridge-joint coupled vibration analysis according to claim 8, characterized in that, The method for obtaining the test compliance verification mark includes: Obtain the current physical geometry parameters, calculate the difference between the equilibrium calibration parameter solution set and the current physical geometry parameters, and obtain four physical compensation values, namely the first, second, third and fourth physical compensation values. Map the physical compensation values ​​to the device execution control parameters containing displacement control vector, angle control vector and torque control vector. Encapsulate the device execution control parameters to obtain the physical calibration instruction sequence. The feedback geometric parameters after physical parameter compensation are obtained according to the physical calibration command sequence, and a second difference operation is performed to obtain the compensation difference set. The compensation difference set is then mapped to generate a second physical calibration command sequence and a second physical parameter compensation is performed to obtain the second feedback geometric parameters. Feedback performance points are generated based on the secondary feedback geometric parameters, and the test compliance verification mark is obtained based on the inclusion relationship of the feedback performance points relative to the dynamic performance safety domain.

10. A vibration reduction detection system for expansion joints based on vehicle-bridge-joint coupled vibration analysis, used to implement the vibration reduction detection method for expansion joints based on vehicle-bridge-joint coupled vibration analysis as described in any one of claims 1-9, characterized in that, The system includes: Acoustic and vibration analysis module: used to obtain the initial structural test parameters of the expansion joint of the viaduct, construct the cross-sectional coordinate system, perform feature mapping on the initial structural test parameters based on the cross-sectional coordinate system to obtain the digitized contour line, obtain the motion parameters of the moving load to construct the load contact envelope, perform virtual envelope interference analysis based on the load contact envelope and the contour line to generate the pressure distribution matrix, perform response analysis on the pressure distribution matrix to obtain the set of acoustic and vibration feature vectors; The parameter filtering module is used to reconstruct test indicators from the set of acoustic and vibration feature vectors, obtain a vibration diagnosis plane that characterizes the performance trade-off state of the expansion joint, construct a dynamic performance safety domain based on the vibration diagnosis plane, determine the inclusion relationship of the dynamic performance safety domain, obtain a parameter diagnosis set, perform three-level filtering on the parameter diagnosis set, and obtain a set of equilibrium calibration parameters. Command verification module: It is used to construct the physical calibration command sequence of the driving related actuators based on the solution set of balance calibration parameters, perform physical calibration on the physical calibration command sequence, and obtain the test compliance verification mark characterizing the vibration reduction performance of the bridge expansion joint vibration reduction structure.

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