Bridge anti-fatigue performance analysis and optimization method and system based on finite element analysis

Abstract

The invention discloses a bridge anti-fatigue performance analysis and optimization method and system based on finite element analysis. The method comprises the following steps: constructing a bridge finite element basic model and a random fleet time-varying load spectrum, and executing damage-rigidity dynamic coupling iterative calculation; a fatigue sensitive area is automatically identified through the strain energy density gradient, a high-precision sub-model is generated, a basic model stiffness matrix is updated in real time through a sub-model calculation result, and a fatigue evolution cloud picture containing a stiffness degradation track is generated; and finally, identifying a damage hotspot based on the cloud picture, and generating an optimization strategy containing a traffic current limiting threshold and a structure reinforcement opportunity by using a genetic algorithm. According to the method, the problem of prediction deviation of traditional static analysis is solved by simulating the reverse influence of damage on rigidity and internal force redistribution, and accurate evaluation and scientific decision-making of the whole life cycle of the bridge are achieved.

Description

Technical Field

[0001] This invention relates to the fields of bridge engineering and computational mechanics, and in particular to a method and system for analyzing and optimizing the fatigue performance of bridges based on finite element analysis. Background Technology

[0002] Long-span bridges, as vital components of modern transportation networks, endure repeated impacts from vehicle loads and environmental erosion during their long service life. Fatigue damage has become a core threat to their structural safety and durability. To assess the health status of bridges, the engineering community widely employs fatigue performance analysis techniques based on the finite element method. However, most existing analysis methods are based on the idealized assumption of "constant structural stiffness," assuming that the material remains in a linear elastic state throughout its service life, neglecting the negative weakening effect of cumulative fatigue damage on the stiffness of the components.

[0003] During the service life of actual engineering structures, as microcracks initiate and propagate, the effective cross-sectional area of ​​components inevitably decreases, leading to local stiffness degradation. This change in the stiffness field directly triggers the redistribution of internal forces within the structural system, causing loads to automatically transfer to intact components with higher stiffness. Current technologies lack this dynamic coupling mechanism of "damage-stiffness," making it impossible to simulate this crucial mechanical behavior of internal force redistribution. Consequently, predictions of the remaining life of structures are often based solely on linear extrapolation from the initial state, easily leading to significant deviations and even overlooking the risk of chain reactions caused by local failures.

[0004] Furthermore, existing technologies face irreconcilable contradictions in simulation modeling and application decision-making. On the one hand, capturing stress concentrations in minute areas such as weld toes requires extremely high-density meshes, which contradicts the computational efficiency requirements of macroscopic analysis of the entire bridge, making it difficult to achieve refined simulations in engineering. On the other hand, existing load inputs mostly use simplified standard traffic flows, which cannot reflect the complex conditions of mixed vehicle types, heavy vehicle queuing, and environmental thermal coupling in actual traffic. More importantly, current analysis methods mostly stop at passive assessment of the current situation, lacking a closed-loop mechanism to transform analysis results into specific operation and maintenance decisions. They cannot provide targeted traffic restriction standards or optimal reinforcement timing, making it difficult to meet the urgent needs of proactive maintenance throughout the entire life cycle of bridges. Summary of the Invention

[0005] One of the objectives of this invention is to provide a method and system for analyzing and optimizing the fatigue performance of bridges based on finite element analysis, so as to solve the problems pointed out in the background art.

[0006] In a first aspect, the bridge fatigue performance analysis and optimization method based on finite element analysis provided in the embodiments of the present invention includes the following steps: Obtain geometric topology data, material physical property data, and historical traffic flow monitoring data of the bridge to be analyzed; Based on the geometric topology data and the material physical property data, a finite element basic model of the bridge reflecting the initial physical state of the bridge to be analyzed is constructed. A time-varying traffic load spectrum containing random vehicle sequences is constructed using the historical traffic flow monitoring data; The time-varying traffic load spectrum is used as a dynamic excitation input to the bridge finite element foundation model, and damage-stiffness dynamic coupling iterative calculation is performed. The iterative calculation calculates the global strain energy density distribution in each simulation time step, automatically identifies fatigue-sensitive areas based on the strain energy density gradient and generates a high-precision sub-model, and uses the calculation results of the high-precision sub-model to update the stiffness matrix of the corresponding element in the bridge finite element foundation model in real time, generating a bridge fatigue evolution cloud map containing the stiffness degradation trajectory throughout the entire life cycle. Based on the fatigue evolution cloud map of the bridge, fatigue damage hotspots are identified, and with the goal of extending the remaining fatigue life of the fatigue damage hotspots, a bridge fatigue resistance optimization strategy including traffic restriction thresholds and structural reinforcement timing is generated.

[0007] Optionally, the steps for constructing the bridge finite element basic model specifically include: Parametric modeling technology is used to discretize the main beam, piers and cable tower components of the bridge to be analyzed into several solid elements; A nonlinear spring damping unit is installed at the connection between the main beam and the pier to simulate the boundary constraint effect of the support; The solid element and the nonlinear spring-damped element are coupled together to generate the finite element foundation model of the bridge.

[0008] Optionally, the step of constructing a time-varying traffic load spectrum containing random vehicle sequences using the historical traffic flow monitoring data specifically includes: The historical traffic flow monitoring data is fitted with a probability distribution to obtain the vehicle type ratio distribution function, vehicle weight distribution function, and vehicle headway distribution function. A Monte Carlo random sampling algorithm is used to generate a virtual vehicle queue based on the vehicle type distribution function, the vehicle weight distribution function, and the vehicle headway distribution function; Based on the axle load parameters and wheelbase parameters of the virtual vehicle queue, the time-varying traffic load spectrum is constructed, which dynamically changes with time and spatial location.

[0009] Optionally, the step of generating the bridge fatigue resistance optimization strategy specifically includes: Different combinations of traffic flow restriction thresholds and the timing of structural reinforcement interventions are set as decision variables; Construct a multi-objective optimization function, which covers the sub-objectives of maximizing remaining fatigue life and minimizing maintenance economic cost; The decision variables are optimized using a genetic algorithm to obtain a Pareto optimal solution set, which is then transformed into the bridge fatigue resistance optimization strategy.

[0010] Optionally, the step of performing the damage-stiffness dynamic coupling iterative calculation specifically includes: Within the current time step, the transient dynamic response of the bridge finite element foundation model is calculated using the Newmark-β method, and the displacement of each node and the strain energy of each element are extracted. Calculate the strain energy density gradient modulus between adjacent units, and mark the region where the strain energy density gradient modulus exceeds a preset singular threshold as the fatigue-sensitive region; Based on the geometric boundary of the fatigue-sensitive region, an adaptive mesh refinement algorithm is used to generate the high-precision sub-model, the mesh density of which is higher than that of the bridge finite element foundation model.

[0011] Optionally, the step of performing the damage-stiffness dynamic coupling iterative calculation further includes: Extract the nodal displacement response of the bridge finite element foundation model at the boundary of the fatigue-sensitive region; The nodal displacement response is mapped to the dynamic displacement boundary conditions of the high-precision sub-model using shape function interpolation. Driven by the dynamic displacement boundary conditions, the high-precision sub-model is subjected to elastoplastic damage calculation, and the local cumulative damage index is output.

[0012] Optionally, the real-time updating of the stiffness matrix of the corresponding element in the bridge finite element foundation model specifically includes: Based on the theory of damage mechanics of continuum, a negative correlation mapping function between the local cumulative damage index and the elastic modulus of the material is established. Substitute the local cumulative damage index into the negative correlation mapping function to calculate the equivalent residual elastic modulus at the current moment; Calculate the ratio of the equivalent residual elastic modulus to the initial elastic modulus, and use it as the stiffness reduction factor; The stiffness reduction factor is used to correct the element stiffness matrix located in the fatigue-sensitive region of the bridge finite element foundation model for simulation calculation at the next time step.

[0013] Optionally, a thermo-mechanical coupling correction mechanism is also introduced in the step of performing the damage-stiffness dynamic coupling iterative calculation: Collect the environmental temperature time history data of the area where the bridge to be analyzed is located, and calculate the non-uniform temperature field distribution of the finite element foundation model of the bridge at each time step. The thermal strain components of each unit are calculated based on the non-uniform temperature field distribution, and the thermal strain components are superimposed on the calculation process of the transient dynamic response. Based on the influence of temperature on the fatigue performance of materials, the SN fatigue curve of the material is dynamically corrected using real-time temperature values.

[0014] Optionally, after the step of generating a bridge fatigue evolution cloud map containing the stiffness degradation trajectory throughout its entire life cycle, the method further includes: Topological clustering analysis was performed on the fatigue evolution cloud map of the bridge to identify multiple damage region clusters with synchronized stiffness degradation rates; Calculate the geometric centroid and damage weighted average of each damage region cluster, and mark the region cluster with the highest damage weighted average as the fatigue damage hot spot region.

[0015] Secondly, the bridge fatigue performance analysis and optimization system based on finite element analysis provided in the embodiments of the present invention includes: The data acquisition module is used to acquire the geometric topology data, material physical property data, and historical traffic flow monitoring data of the bridge to be analyzed. The model building module is used to construct a basic finite element model of the bridge based on the geometric topology data and the material physical property data. The load spectrum generation module is used to construct a time-varying traffic load spectrum containing random vehicle sequences using the historical traffic flow monitoring data; The coupled iterative calculation module is used to input the time-varying traffic load spectrum into the bridge finite element foundation model, perform damage-stiffness dynamic coupled iterative calculation, automatically identify fatigue-sensitive areas by calculating the strain energy density gradient and call the high-precision sub-model, update the element stiffness matrix in real time and generate a bridge fatigue evolution cloud map. The strategy generation module is used to identify fatigue damage hotspots based on the bridge fatigue evolution cloud map and generate a bridge fatigue resistance optimization strategy that includes traffic restriction thresholds and structural reinforcement timing.

[0016] The present invention has achieved the following beneficial effects: This invention constructs a damage-stiffness dynamic coupling iterative computation mechanism. By establishing a negative correlation mapping function between the local cumulative damage index and the material's elastic modulus based on continuum damage mechanics, the stiffness matrix of the damaged element can be updated in real time under the drive of a time-varying load spectrum. This dynamic evolution analysis method realistically reproduces the structural internal force redistribution process caused by local damage, reveals the load transfer path after stiffness degradation, thereby improving the physical reality and accuracy of full-life-cycle fatigue life prediction and avoiding misjudgments of safety due to neglecting stiffness degradation.

[0017] Meanwhile, this invention resolves the scale contradiction between macroscopic analysis of large structures and microscopic stress capture. Utilizing automatic identification technology based on strain energy density gradients, the system can intelligently locate stress singular regions across the entire bridge and dynamically generate high-precision sub-models using an adaptive mesh refinement algorithm. Through shape function interpolation mapping of displacement boundary conditions, this invention retains the high computational efficiency of the full-bridge foundation model while achieving precise capture of stress concentrations in key structural details, thus improving the accuracy of local stress analysis while ensuring the timeliness of engineering calculations.

[0018] Furthermore, this invention constructs a scientific decision-making system that closely resembles a realistic stochastic dynamic loading environment and a closed loop. By integrating Monte Carlo stochastic traffic flow simulation with a thermo-coupled correction mechanism, the robustness of the model under complex service environments such as heavy vehicle queuing and extreme temperature differences is significantly enhanced. Building upon this, the invention further transforms fatigue evolution cloud maps into quantitative decision-making criteria, utilizing a multi-objective genetic algorithm to find the Pareto optimal solution between remaining lifespan and economic cost, automatically generating optimization strategies that include specific flow-limiting thresholds and reinforcement timing, providing strong technical support for the scientific health management of bridges.

[0019] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description and the accompanying drawings.

[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0021] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a schematic diagram of the bridge fatigue performance analysis and optimization method based on finite element analysis in an embodiment of the present invention; Figure 2This is a schematic diagram of a bridge fatigue performance analysis and optimization system based on finite element analysis in an embodiment of the present invention. Detailed Implementation

[0022] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0023] Example 1: This invention provides a method for analyzing and optimizing the fatigue performance of bridges based on finite element analysis. In the current field of transportation infrastructure maintenance, bridges, as vital transportation arteries, are of paramount importance for their safety performance. Traditional bridge fatigue analysis often relies on static, idealized models, which fail to accurately reflect the randomness of vehicle loads and the stiffness degradation caused by cumulative damage to bridge materials over time. Addressing the shortcomings of existing technologies, such as low computational efficiency, insufficient accuracy, and a lack of dynamic optimization strategies, this embodiment proposes a full-process, dynamically coupled analysis scheme. This method aims to overcome the deficiency in existing technologies that ignore the inverse impact of structural damage on dynamic characteristics, achieving accurate simulation throughout the entire life cycle by introducing a stiffness degradation mechanism.

[0024] like Figure 1 As shown, the method mainly includes the following processing flow: Step S1: Obtain the geometric topology data, material physical property data, and historical traffic flow monitoring data of the bridge to be analyzed.

[0025] In practical engineering implementation, data acquisition is the foundation for building high-fidelity simulation models and a prerequisite for ensuring that subsequent analysis results have practical engineering significance. This step is not simply data reading, but a deep perception and digital reconstruction of the physical world.

[0026] This embodiment does not limit itself to traditional two-dimensional drawing reading for acquiring geometric topology data. Although design drawings provide the theoretical dimensions of the bridge, errors inevitably occur during the construction of actual bridges, and permanent deformations (such as concrete creep and uneven foundation settlement) will occur during long-term service. Therefore, to ensure the consistency between the model and the actual structure, this embodiment preferably adopts a combination of ground-based three-dimensional laser scanning technology (LiDAR) and UAV oblique photogrammetry technology. Through high-precision point cloud data acquisition, the actual geometric shape of the bridge structure after long-term service is captured, including the actual alignment of the main beam, the inclination of the piers, and the spatial position of the cables. After noise reduction, registration, and meshing, this point cloud data can generate a three-dimensional geometric model reflecting the current state of the bridge. In addition, the geometric topology data should also include detailed connection relationships of various bridge components, such as the bevel form of welded joints, the arrangement of bolt groups, and the spacing of stiffening ribs. These geometric features are often the source of fatigue cracks and need to be accurately recorded during the data acquisition stage.

[0027] For material physical property data, in addition to obtaining standard parameters (such as elastic modulus, Poisson's ratio, and density) from design drawings, this embodiment also performs experimental corrections to the material properties of existing structures. Specifically, the actual compressive strength, tensile strength, and carbonation depth of concrete are obtained through rebound testing, ultrasonic testing, or micro-destructive core sampling; the actual yield strength, ultimate strength, and fatigue crack propagation threshold of steel are obtained through corrosion rate testing, magnetic particle testing, and metallographic analysis of steel structures. Particularly, for the fatigue characteristics of materials, this embodiment not only uses the SN curve but also corrects it by considering the actual service life of the material and environmental corrosion conditions, or uses material fatigue crack propagation rate parameters based on fracture mechanics. These experimental data are used to correct the constitutive model of the material, ensuring that the material parameters in the finite element model accurately reflect the current service condition.

[0028] Historical traffic flow monitoring data primarily originates from dynamic weighing systems and video traffic monitoring systems installed at key bridge sections (such as bridgeheads and mid-span). The system continuously collects vehicle passage records over a period of time (e.g., one year or longer). The collected data includes the timestamp, speed, lane affiliation, vehicle type (e.g., sedan, bus, single-axle truck, semi-trailer tractor), number of axles, wheelbase, axle load, and total vehicle weight for each vehicle crossing the bridge. This massive amount of data forms the statistical basis for subsequently constructing the random traffic flow load spectrum. To ensure data quality, the raw data also needs to be preprocessed to remove abnormal data caused by sensor malfunctions, signal interference, or vehicle violations (e.g., driving over lane lines, driving against traffic), and to interpolate and complete data missing due to system maintenance or other reasons.

[0029] Step S2: Based on the geometric topology data and the material physical property data, construct a finite element foundation model of the bridge that reflects the initial physical state of the bridge to be analyzed.

[0030] This step is the core foundation of the entire analysis. Considering the massive size and numerous components of large bridge structures, if the entire bridge were modeled using extremely fine solid elements, the computational load would increase exponentially, making it impractical in engineering. Therefore, this embodiment employs a strategy that combines parametric modeling techniques with multi-scale modeling concepts.

[0031] Specifically, parametric modeling technology is employed, utilizing a scripting language to drive the preprocessing kernel of the finite element software. The main girder, piers, and pylon components of the bridge under analysis are discretized into several solid or shell elements. For the main girder, if it is a steel box girder, shell elements are typically used to simulate the top plate, bottom plate, web, and diaphragms to accurately reflect the local buckling and shear hysteresis effects of the thin-walled structure; if it is a concrete box girder, solid elements are preferred to simulate its volumetric effects. For the piers and pylons, beam elements or solid elements can be selected based on their slenderness ratio.

[0032] In constructing a finite element model of a bridge, the handling of boundary conditions is crucial. This embodiment uses nonlinear spring-damped elements at the connection between the main beam and the pier to simulate the boundary constraint effect of the bearings. Traditional methods often simplify bearings to rigid constraints, hinges, or linear springs, neglecting the nonlinear hysteresis characteristics and frictional slip behavior of the bearings under large displacements. For example, pot bearings exhibit significant frictional slip characteristics under horizontal forces and may show nonlinear hardening as displacement increases; lead-core rubber bearings exhibit significant hysteretic energy dissipation characteristics. By setting nonlinear spring-damped elements and defining their force-displacement constitutive relations based on experimental or measured data from the bearing manufacturer, the interaction forces between the superstructure and substructure can be more realistically transmitted, thereby accurately calculating the stress concentration near the bearings.

[0033] Finally, the various element types (solid elements, shell elements, beam elements, and nonlinear spring-damped elements) are assembled through nodal degree-of-freedom coupling, multi-point constraint equations, or contact pairs. After assembly, a mesh quality check must be performed to ensure that the Jacobian determinant, aspect ratio, warpage, and other parameters of all elements meet the requirements of finite element calculation, thus avoiding shear locking or volumetric locking phenomena in numerical calculations. The generated finite element foundation model of the bridge represents the physical state of the bridge at the current moment (the starting point of the analysis).

[0034] Step S3: Construct a time-varying traffic load spectrum containing random vehicle sequences using the historical traffic flow monitoring data.

[0035] Real traffic flow is highly random, and a single vehicle load or a fixed platoon load cannot reflect actual fatigue conditions. This embodiment uses a combination of mathematical statistics and Monte Carlo simulation to reconstruct random traffic flow.

[0036] First, statistical analysis is performed on the cleaned historical traffic flow monitoring data. Using maximum likelihood estimation or nonparametric kernel density estimation, probability distribution functions for vehicle type ratio, vehicle weight, and headway are fitted, respectively. These distribution functions constitute the statistical characteristic parameter set of random traffic flow.

[0037] Next, a Monte Carlo random sampling algorithm is employed. The computer performs extensive random sampling based on the aforementioned probability distribution function. First, the vehicle type is determined by sampling based on the vehicle model proportion distribution; then, the total vehicle weight is determined by sampling based on the vehicle weight distribution function for that model, and the axle weight is calculated according to the typical axle load distribution coefficient for that model; next, the wheelbase is determined based on the wheelbase statistics for that model; finally, the distance between the vehicle and the vehicle in front is determined based on the headway distribution function. In this way, a series of virtual vehicles are generated and linked together to form a virtual vehicle queue that can last for hours, days, or even years.

[0038] To transform these vehicle platoons into load inputs recognizable by finite element software, the axle loads of the vehicles need to be converted into dynamic moving force sequences or moving surface forces that vary with time and spatial location, i.e., a real-time traffic load spectrum, based on the virtual vehicles' speed and lane positions. This load spectrum not only includes information on the magnitude of the loads but also the movement of the load's position over time, as well as the merging and platooning effects of multiple vehicles simultaneously appearing on the bridge. This allows for a realistic recreation of the complex dynamic excitations faced by the bridge during its service life.

[0039] Step S4: Input the time-varying traffic load spectrum as a dynamic excitation into the bridge finite element foundation model and perform damage-stiffness dynamic coupling iterative calculation.

[0040] This is one of the core innovations of this invention. Traditional fatigue analysis often assumes damage accumulation but constant stiffness, meaning that fatigue damage to the material will not affect the dynamic response of the structure. However, in reality, as microcracks initiate and propagate, the effective cross-sectional area of ​​the component decreases, and the effective stiffness gradually decreases, thereby altering the redistribution of internal forces and the dynamic characteristics of the structure. This embodiment corrects this bias through dynamic coupling iterative calculation of damage and stiffness.

[0041] The specific process of this iterative calculation is as follows: Iterative calculations are performed using a macro-micro dual-timescale decoupling algorithm. The specific steps are as follows: Define the time scale: Set the macroscopic fatigue renewal cycle. (e.g., in units of 6 months) and microdynamic integral step size (e.g., 0.01 seconds).

[0042] Microscopic dynamic response calculation: In the current macroeconomic cycle Within this model, it is assumed that the stiffness matrix of the bridge's finite element foundation remains temporarily constant. Using Newmark- Newmark- With micro step size Transient dynamic response analysis was performed on the structure to extract the stress-strain time history during representative time periods.

[0043] Damage rate extrapolation: Based on the statistical strain energy density of the micro-response and rainflow circulation, the current damage evolution rate is calculated. It is assumed that this rate is... The internal stability is maintained, and the cumulative damage index at the end of the macroeconomic cycle is calculated by linear extrapolation.

[0044] Stiffness Update and Restart: Based on the updated cumulative damage index, the new elastic modulus of each element is calculated using the following stiffness mapping function. The model stiffness matrix is ​​updated as the next macroscopic cycle by calling the finite element solver's Restart function or a user-defined field variable subroutine (such as USDFLD). The initial state is calculated again. This process is repeated until the preset lifespan is reached, generating a bridge fatigue evolution cloud map that includes the stiffness degradation trajectory throughout the entire lifespan.

[0045] To address the timescale difference between transient dynamic response (milliseconds) and fatigue damage accumulation (years), this embodiment employs a micro-macro dual-timescale decoupling algorithm. Specifically, the entire lifespan is divided into several macroscopic time steps. In each Within this model, maintaining a constant overall stiffness matrix, dynamic calculations are performed using a representative time-varying load spectrum. Based on the microscopic dynamic response, the damage rate is calculated using the Chaboche nonlinear continuous damage mechanics model. The damage increment per stress cycle is also calculated. Defined as: in, This is the equivalent stress amplitude. is a material constant.

[0046] Furthermore, a local cumulative damage index was established. The negative correlation mapping function between the material's elastic modulus and the material's elastic modulus: in For residual stiffness, The initial elastic modulus of the material in an undamaged state. The shape factor is taken into account for crack closure effect (0.2 for compression and 1.0 for tension).

[0047] Step S5: Identify fatigue damage hotspots based on the bridge fatigue evolution cloud map, and generate a bridge fatigue resistance optimization strategy that includes traffic restriction thresholds and structural reinforcement timing, with the goal of extending the remaining fatigue life of the fatigue damage hotspots.

[0048] By performing topological clustering analysis on the evolution cloud map, the regions with the most severe stiffness degradation and the most concentrated damage were identified, namely the fatigue damage hotspot regions.

[0049] Generating fatigue-resistant optimization strategies for these areas is a multi-objective decision-making process. This embodiment sets two-dimensional decision variables: one is the traffic flow restriction threshold, including limiting the maximum axle load of heavy vehicles, limiting traffic flow density, or closing some lanes during specific periods; the other is the timing of structural reinforcement intervention.

[0050] To find the optimal solution, a multi-objective optimization function is constructed. This function contains two conflicting sub-objectives: maximizing the remaining fatigue life and minimizing the maintenance economic cost. A genetic algorithm is used to optimize the decision variables, obtaining a Pareto optimal solution set, which is then transformed into the bridge fatigue resistance optimization strategy.

[0051] Example 2: This embodiment focuses on the in-depth technical implementation of the thermo-coupling correction mechanism in the damage-stiffness dynamic coupling iterative calculation step. In actual bridge engineering, changes in ambient temperature are a significant source of load. Especially for long-span steel bridges, the non-uniform temperature field caused by solar radiation leads to significant thermal stress. This stress is often cyclical and can itself cause thermal fatigue. Furthermore, it is superimposed on the mechanical stress generated by vehicle loads, accelerating the accumulation of fatigue damage. In addition, the mechanical properties of materials (such as elastic modulus, yield strength, and fatigue limit) are also functions of temperature. Therefore, fatigue analysis that ignores temperature effects is inaccurate.

[0052] The thermo-coupling correction mechanism proposed in this embodiment includes two levels: macroscopic thermo-structure coupling calculation and microscopic dynamic correction of material properties.

[0053] In macroscopic thermal-structural coupling calculations, the first step is to establish a thermal conduction analysis model for the bridge. This can typically utilize the same finite element mesh as the structural analysis, but the element type needs to be converted to heat transfer elements. The system input consists of time-varying environmental meteorological parameters, including atmospheric temperature, solar radiation intensity, and wind speed. For solar radiation, the bridge's geographical location, orientation, date, and time need to be considered to accurately calculate the solar incidence angle, and a shading algorithm is used to determine the actual amount of radiation received on the surfaces of each component. For the interior of the box girder, convective heat transfer within the enclosed cavity also needs to be considered. By solving the transient heat conduction equations, the three-dimensional temperature field distribution of the entire bridge structure at each time step can be obtained.

[0054] After obtaining the temperature field, it is applied as a volume load to the structural analysis model. Thermal strain is calculated based on the material's coefficient of thermal expansion. This thermal strain is then incorporated into the constitutive equations. By solving the equilibrium equations, the temperature stress caused by temperature changes can be obtained. This temperature stress is vector-superimposed with the stress caused by vehicle loads, thus altering the average stress level and amplitude of the stress cycle. For example, during the high temperatures of summer, the bridge deck experiences compressive stress due to thermal expansion, which may offset some of the tensile stress generated by vehicle loads. However, during nighttime cooling, the tensile stress generated by contraction will superimpose with the vehicle loads, exacerbating fatigue.

[0055] Regarding the dynamic correction of microscopic material properties, this embodiment establishes a material parameter database that includes a temperature dimension. For steel and concrete, the parameters of their SN curves (curves describing the relationship between stress amplitude and fatigue life) change with temperature. Generally, as the temperature decreases, the strength of steel increases but its toughness decreases, and its brittleness increases, potentially making the SN curve steeper; conversely, as the temperature increases, the material softens, fatigue strength decreases, and the SN curve shifts downward. When performing fatigue damage calculations, the system reads the real-time temperature value of the current element, obtains the corresponding SN curve parameters from the database using an interpolation algorithm, and then calculates the damage degree by combining it with the current stress amplitude. Similarly, the elastic modulus of the material is also corrected according to the real-time temperature. Through this bidirectional, real-time correction, this method can accurately simulate the impact of low-temperature brittleness or high-temperature softening on the fatigue life of bridges.

[0056] Example 3: This embodiment details the specific implementation method of the nonlinear spring damping unit in the process of constructing the finite element foundation model of a bridge.

[0057] In bridge structures, bearings are crucial components connecting the superstructure (main beam) and the substructure (piers / cap beams). Traditional finite element analysis often simplifies this by modeling bearings as ideal rigid connections, hinged joints, or linear spring elements. While this simplification may be manageable in static analysis, in dynamic fatigue analysis, especially when vehicle impacts, braking, and environmental vibrations are involved, the nonlinear behavior of the bearings has a decisive impact on the structure's dynamic response.

[0058] In this embodiment, the nonlinear spring-damped unit is implemented by defining complex force-displacement skeleton curves and hysteresis rules. This unit typically contains six degrees of freedom (three translational and three rotational), and the mechanical behavior in each direction can be defined independently.

[0059] Taking a common pot bearing as an example, it is typically designed as a movable bearing in the longitudinal direction of a bridge, allowing for displacement. However, this movement is not without resistance. In fact, friction exists within the bearing. This embodiment uses a Coulomb friction model combined with a bilinear spring to simulate this behavior. The specific settings are as follows: When the displacement is small, the support exhibits a large initial stiffness; when the external force exceeds the friction threshold, the support begins to slide, and the stiffness drops sharply to the sliding stiffness. This nonlinear behavior causes the support to exhibit a significant hysteresis loop during vehicle braking or starting, consuming energy and changing the instantaneous stiffness of the structure.

[0060] Vertically, the support primarily bears compressive stress. However, considering the possibility of support slippage, this embodiment defines a model with asymmetrical compressive and tensile stiffness. Under compression, the stiffness is extremely high, simulating the compressive stiffness of rubber and steel basins; under tension, the stiffness is close to zero, simulating support slippage.

[0061] Furthermore, to simulate the viscoelastic damping of rubber materials, this embodiment also incorporates a velocity-dependent damper in parallel with the spring unit. This nonlinear damping more realistically reflects the energy dissipation mechanism of the structure under high-frequency impact loads.

[0062] In the modeling process, connection points are first created between the bottom nodes of the main beam and the top nodes of the pier. To avoid stress concentration, a set of nodes in the bottom support region of the main beam is typically rigidly coupled to one end of the connection point, and a set of nodes in the top support region of the pier is rigidly coupled to the other end of the connection point. Then, the nonlinear properties defined above are assigned to this connection point. In this way, the huge impact force and horizontal braking force generated when a vehicle passes can be transmitted to the pier through this realistic virtual support, while the deformation and slippage of the support will in turn affect the vibration characteristics of the main beam.

[0063] Example 4: This embodiment provides a detailed explanation of the step of constructing a time-varying traffic load spectrum containing random vehicle sequences using the historical traffic flow monitoring data, particularly regarding the specific application logic of the Monte Carlo random sampling algorithm.

[0064] Traffic load is the fundamental external factor causing bridge fatigue. To generate a high-fidelity time-varying load spectrum, it is necessary to accurately simulate the microscopic behavior of traffic flow. The Monte Carlo method used in this embodiment is not simply random sampling, but a stratified sampling strategy based on traffic flow conditions.

[0065] First, the system performs cluster analysis on historical WIM data to identify different traffic flow states, such as free-flow, synchronous flow, and congested flow. The statistical characteristics of vehicles differ under each state.

[0066] When generating random vehicle sequences, the system first generates a macroscopic state sequence, which simulates the switching of traffic flow states over a 24-hour period.

[0067] Then, for each time period, the corresponding probability model is invoked to generate micro-vehicles: Sampling is based on the vehicle type proportion matrix under this condition. For example, in nighttime free-flow conditions, the proportion of heavy-duty trucks may be significantly higher than during the day.

[0068] Sampling is performed based on the vehicle weight distribution function of this vehicle type under this condition. It is worth noting that this embodiment introduces a Copula function to describe the correlation between vehicle weight and vehicle queuing. Actual observations show that heavy vehicles often travel in platoons. Therefore, if the preceding vehicle is a heavy vehicle, the probability of the next vehicle being a heavy vehicle will increase accordingly using the Copula function. This approach can simulate the heavy vehicle queuing condition, which is extremely detrimental to bridge fatigue. This embodiment uses a binary t-Copula function to construct a joint distribution model of the total weight of adjacent vehicles. Its probability density function expression is: in The correlation coefficient (value > 0.6) For degrees of freedom, These are the marginal cumulative distribution probability values ​​of the weights of two adjacent vehicles. For degrees of freedom Standard student The inverse function. In the formula... For the loop variable in the multiplication operation, take respectively and , Degrees of freedom Standard student Distribution on independent variable The derivative of the probability density function (i.e., the value of the probability density function). Sampling using this function can significantly increase the probability of generating a vehicle that is immediately followed by another vehicle.

[0069] Sampling was conducted based on the headway distribution under this condition. In congested flow conditions, the headway is extremely short, with vehicles almost touching end to end, posing a severe challenge to the overall stress on long-span bridges.

[0070] Based on traffic flow theory models (such as car-following models), the instantaneous speed and position of each vehicle are determined. Vehicles do not pass at a constant speed, but accelerate or decelerate according to the state of the vehicle in front.

[0071] Finally, the generated virtual traffic flow, containing information on vehicle type, axle load, wheelbase, position, and speed, is converted into a load step file recognizable by the finite element software. In this file, each time step defines several moving concentrated forces, the magnitude of which is equal to the axle load, and the position coordinates are updated over time. For two-way multi-lane bridges, the system generates multiple traffic flows simultaneously, considering the lateral load movement caused by lane changes. The resulting load spectrum exhibits extremely high realism in both the time and spatial domains.

[0072] Example 5: This embodiment details the specific implementation process of fatigue-sensitive area identification and high-precision sub-model technology, which is a key technology for resolving the contradiction between the overall bridge scale and the local detail scale.

[0073] In finite element analysis, stress concentration points are often the initiation points of fatigue cracks. However, to control the computational scale, full-bridge models typically use large mesh sizes, making it impossible to capture stress concentrations at the millimeter level at the weld toe. This embodiment employs a coarse-to-fine, dynamically focused strategy.

[0074] In the initial calculation phase, the system runs the basic model. Although the stress values ​​in the basic model are locally inaccurate, its energy distribution is relatively reasonable. The system calculates the strain energy density (SED) for each element. SED is a scalar representing the elastic potential energy per unit volume. Compared to vector stress, SED has rotational invariance and is more sensitive to stress concentration.

[0075] The system iterates through the full-bridge model, calculating the gradient of the SED between adjacent elements. Specifically, the calculation employs the element center difference method: for any target element, it searches all its neighboring elements sharing a node, calculates the ratio of the difference in strain energy density between the target element and its neighboring elements to the distance between their geometric centers, and takes the maximum value as the gradient modulus of that element. A preset singularity threshold is set to three times the average gradient modulus of all elements in the initial state of the full-bridge. The system sets a threshold based on statistical principles. When the gradient modulus of an element exceeds this threshold, that element and its neighborhood are marked as regions of interest.

[0076] The system will perform geometric connectivity analysis on these regions of interest, merging spatially connected units of interest into a single fatigue-sensitive region. Then, the sub-model generation process will be automatically initiated.

[0077] The sub-model is a cut-off section of the fatigue-sensitive region in the base model. The system reads the original geometry and topology of this region (including detailed chamfers and weld contours) and meshes it with an extremely fine mesh. The boundary of the sub-model should be selected in a region with a relatively gentle stress gradient to satisfy Saint-Venant's principle.

[0078] To drive the sub-model, boundary condition mapping is necessary. The system extracts the nodal displacements of the base model on the sub-model's cutting boundary. Since the mesh nodes of the base model and the sub-model do not coincide, the system uses shape function interpolation to interpolate the nodal displacements of the base model onto the boundary nodes of the sub-model. This process is performed at every time step, therefore the boundary conditions of the sub-model change dynamically over time.

[0079] Within the sub-model, high-precision stress analysis is performed. At this point, more complex material constitutive models can be introduced. The calculated local stress-strain histories are directly used for fatigue damage calculations. This method achieves a balance between computational efficiency and accuracy by utilizing both the accurate overall deformation mode obtained from the basic model and the true local stress levels captured by the sub-model.

[0080] Example 6: This embodiment focuses on the stiffness update algorithm and loop control logic in the dynamic coupling iterative calculation of damage and stiffness. This is the core algorithm for realizing the simulation of performance evolution throughout the entire life cycle.

[0081] The algorithm is encapsulated in a main control program that cyclically executes the process of dynamic analysis, damage assessment, and stiffness correction.

[0082] Dynamic analysis: Within the time interval, the dynamic equations are solved using the finite element solver. The stiffness matrix is ​​a function of the damage variables.

[0083] Damage assessment: Extract stress / strain time histories of key points in the sub-model. Extract the cyclic load spectrum using the rainflow counting method. Calculate the damage increment within this time period based on the cumulative damage model.

[0084] Stiffness Correction: According to continuum damage mechanics, damage leads to material stiffness degradation. This embodiment goes a step further by considering the anisotropy of damage. For example, for concrete, tensile damage primarily causes a decrease in tensile stiffness, while compressive stiffness may remain unchanged. The system reconstructs the constitutive matrix of the element based on the updated damage variables.

[0085] Model Update: The finite element model is updated using the modified material properties. For severely damaged elements, the system can reduce their stiffness to a minimum, simulating material failure or crack initiation, so that they no longer bear tensile forces.

[0086] Cyclic progression: Time advances to the next interval, and the dynamic equations are solved again using the updated stiffness matrix.

[0087] Through this segment-by-segment coupling method, the redistribution effect of internal forces caused by structural damage is naturally captured. For example, when the stiffness of a hanger decreases due to fatigue damage, the tensile force it bears will automatically transfer to adjacent hangers, leading to an increase in the stress amplitude of adjacent hangers and accelerating damage. This chain reaction cannot be predicted by static analysis or uncoupled analysis, and it is the key to the accurate prediction of the remaining life of the structure by this invention.

[0088] Example 7: This embodiment details the application of a multi-objective optimization algorithm in generating a bridge fatigue resistance optimization strategy that includes traffic flow restriction thresholds and structural reinforcement timing.

[0089] Having obtained the fatigue evolution cloud map of the bridge, the future damage evolution path of each component is known. The task now is to develop intervention strategies to alter this path and guide it in a favorable direction.

[0090] Decision variables include traffic restriction strategies and reinforcement timing and schemes. Traffic restriction strategies are coded as a set of parameters, such as maximum permissible axle load, minimum headway, and whether nighttime traffic restrictions apply. Reinforcement timing and schemes represent the year of reinforcement implementation, reinforcement methods (such as steel plate bonding, external prestressing, and component replacement), and reinforcement locations (targeting specific hotspot areas).

[0091] The objective function includes a lifespan target and a cost target. The lifespan target is the remaining lifespan of the bridge predicted by a finite element model after the strategy is implemented. The cost target includes the social costs to users caused by traffic restrictions (detour fees, time losses) and the direct costs of reinforcement works.

[0092] The mathematical model for the multi-objective optimization function is as follows: Objective function 1 (maximizing remaining lifetime): In the formula, This refers to the numbering of critical bridge components or fatigue hotspots. This is the set of all fatigue hotspots to be evaluated. In decision variables Under the action, the first Predicted remaining fatigue life for hotspot areas.

[0093] Objective function 2 (minimize total lifecycle cost): in, For decision variables (current limiting threshold and reinforcement time). For direct engineering costs, For losses caused by traffic delays due to traffic restrictions, To determine the specific timing of intervention for structural reinforcement, The calculation period for the whole life cycle cost analysis is the length of the time frame. This represents the social cost weighting coefficient.

[0094] Specifically, the social transportation delay losses Quantitative calculations were performed using an improved BPR (Bureau of Public Roads) road resistance function model: In the formula, For a moment Traffic flow; The social cost coefficient per unit time; For free-flow time; Design the bridge to accommodate traffic flow. The traffic flow restriction threshold (i.e., the decision variable, with a value ranging from 0 to 1) is defined in the formula; 0.15 and 4 are the classic shape parameters of the BPR road resistance function. This model constructs the traffic flow restriction threshold. The non-linear mathematical relationship between the genetic algorithm and the cost of delay allows the genetic algorithm to accurately assess fitness.

[0095] The algorithm uses a genetic algorithm, and the specific execution steps are as follows: Initialization: Randomly generate multiple policy combinations as the initial population; Evaluation: Calculate the objective function value for each individual; Sort: The population is stratified using a non-dominated sorting method. Individuals located on the Pareto front are currently the best. Crowding calculation: In order to maintain the diversity of solutions, the crowding distance of individuals in the target space is calculated, and individuals in sparse regions are retained first. Selection, crossover, and mutation: mimicking biological evolution, preserving superior genes, and generating a new generation of populations; Iteration: Repeat the above steps until the preset number of algebras is reached.

[0096] The final output is a Pareto optimal solution set. Decision-makers can select a solution from the solution set that is cost-effective and significantly extends the lifespan, based on the fiscal budget for the year.

[0097] Example 8: This embodiment describes the visualization and interactive design of the bridge fatigue evolution cloud map in this invention, which is an important interface for presenting the analysis results to the user.

[0098] The fatigue evolution cloud map of a bridge is not a static image, but a dynamic data field in four dimensions (three-dimensional space + one-dimensional time).

[0099] The user interface features a timeline slider; dragging the slider displays a color cloud map on the bridge model that changes over time. A warm / cool color mapping is typically used, with blue representing no damage and red representing severe damage. Through animation, users can clearly see how damage initiates at the weld and then spreads along the stress flow path.

[0100] Since much fatigue damage occurs inside the component and is not visible from the outside, the system provides a sectioning tool that allows users to slice the model at any location and observe the damage distribution within the cross-section.

[0101] The fatigue damage hotspots automatically identified by the system will be marked with flashing circles on the model. When the mouse hovers over a hotspot, a pop-up window will appear displaying detailed information about that point: current damage level, predicted remaining life, main types of traffic causing the damage, and suggested repair methods.

[0102] When a user selects any key node, the system can display a curve showing how the node's stiffness changes over time in the sidebar. This curve visually reflects the rate of structural performance degradation, and the inflection points often correspond to the critical moments of accelerated damage, serving as an important reference for developing maintenance plans.

[0103] Example 9: This embodiment provides a bridge fatigue performance analysis and optimization system based on finite element analysis. This system is the hardware carrier and software implementation of the above method.

[0104] like Figure 2 As shown, the system architecture is divided into a data layer, a computing layer, and an application layer.

[0105] Data Layer: This layer includes a sensor network (fiber optic gratings, accelerometers, WIM, weather stations) deployed at the bridge site and data acquisition servers. It is responsible for real-time data acquisition, preprocessing, transmission, and storage. A distributed time-series database is used to store massive amounts of monitoring data.

[0106] Computational Layer: Deployed in a high-performance computing center or cloud platform. It includes a model building module, a load spectrum generation module, a coupled iterative calculation module (integrating a finite element solver, damage calculation engine, and stiffness update engine), and an optimization algorithm module. Parallel computing technology is used to accelerate large-scale matrix solutions.

[0107] Application Layer: A user-facing visualization terminal. It provides a 3D digital twin interface to display real-time fatigue evolution cloud maps of the bridge. An interactive operation panel is also provided, allowing users to set analysis parameters and view optimization strategy reports.

[0108] The system also has a self-learning function. By comparing simulation results with measured responses (such as measured strain and measured deflection), it automatically corrects the physical parameters of the model (such as support stiffness and boundary conditions) using inverse analysis algorithms. As time goes on, the system's prediction accuracy becomes higher and higher, truly realizing intelligent management and maintenance of bridges.

[0109] Example 10: This embodiment uses a specific engineering case (a double-tower, double-cable-stayed steel box girder bridge with a main span of 420 meters) to illustrate the entire application process of the present invention.

[0110] Background: This bridge is located on a heavy-duty traffic artery. After 10 years of service, multiple fatigue cracks appeared at the U-rib fillet welds on the top plate of the steel box girder. The method and system of this invention were used for analysis.

[0111] Step 1: Data Acquisition. A 3D laser scanner was used to scan the entire bridge, revealing deflection in the mid-span region of the main girder. Combined with core sampling, the elastic modulus parameters of the concrete bridge towers were corrected. WIM data was retrieved, revealing frequent passage of severely overloaded vehicles at night.

[0112] Step 2: Modeling. Based on the scanned and corrected geometric data, a hybrid model of the entire bridge deck shell and solid was established. Nonlinear model elements were used to simulate the damper locations where the main girder connects to the bridge tower.

[0113] Step 3: Load Spectrum. Using the Monte Carlo method, a random traffic flow load spectrum for the next 50 years, reflecting the characteristics of heavily loaded vehicles at night, was generated.

[0114] Step 4: Coupled Calculation. Input the load spectrum into the model. Simulation shows that in the next 5 years, the damage index at the weld connecting the U-shaped rib and the top plate in the mid-span region will increase sharply, the stiffness will decrease significantly, and the stress will begin to transfer to adjacent ribs.

[0115] Step 5: Thermo-coupling. The extreme high-temperature conditions of the local summer were superimposed. Analysis revealed that high temperatures softened the asphalt pavement, increasing the local stress amplitude at the weld joints and further accelerating the damage.

[0116] Step 6: Optimization Strategy. The system identified the U-shaped rib welds within a certain range of the mid-span as fatigue hotspots. After optimization using a genetic algorithm, the optimal strategy proposed by the system is: immediately implement ultra-high toughness concrete pavement layer reconstruction in the mid-span area and strictly limit vehicles with axle loads exceeding a certain tonnage to cross the bridge. Predictions show that after implementing this strategy, the stress amplitude of critical welds will be significantly reduced, the remaining lifespan of the bridge can be greatly extended, and the overall life-cycle cost will be the lowest.

[0117] Example 11: This embodiment is a further detailed explanation of the negative correlation mapping function between the local cumulative damage index and the material elastic modulus based on the theory of continuous medium damage mechanics. This is a key mathematical model in actual programming implementation.

[0118] In traditional linear cumulative damage theory, damage is defined as the ratio of the number of cycles to the fatigue life. However, this damage is merely a counter and lacks a clear physical meaning to guide stiffness degradation. This embodiment introduces a damage definition based on energy dissipation.

[0119] The damage variable is defined as the ratio of the area of ​​microvoids and microcracks in a representative volume element of the material to the total cross-sectional area. According to the concept of effective stress, effective stress equals nominal stress divided by (1 - damage variable). Assuming the principle of strain equivalence holds, that is, the strain of damaged material under nominal stress equals the strain of undamaged material under effective stress, it can be deduced that the damage modulus equals the initial modulus multiplied by (1 - damage variable).

[0120] However, damage evolution is typically nonlinear. This embodiment employs a nonlinear continuous damage model. The damage evolution rate depends not only on the current stress amplitude but also on the current cumulative damage state. In the subroutine of the finite element software, the system maintains a state variable at each integration point. At the end of each load cycle, this variable is updated according to the nonlinear evolution law, and then the stiffness matrix is ​​updated. This nonlinear mapping function can simulate the characteristics of slow early-stage fatigue damage development followed by a sudden acceleration. Through this underlying mechanical constitutive model, the system achieves true physics-driven simulation.

[0121] Example 12: This embodiment describes a special mesh transition technique used in the generation of high-precision sub-models to ensure the smoothness and accuracy of the calculation results.

[0122] When transferring displacement boundary conditions from the base model to the sub-model, if the mesh size span is too large, spurious stress wave reflections or numerical oscillations may occur at the boundaries. Therefore, this embodiment introduces a transition buffer during the sub-model construction.

[0123] The sub-model is geometrically divided into three regions: Core Area of ​​Concern: This area contains fatigue welds or notches and employs an extremely fine, high-quality hexahedral mesh with fully integrated elements to capture precise stress peaks.

[0124] Transition buffer zone: Enclosing the core region, the mesh size gradually transitions from fine to coarser. In this region, tetrahedral meshes or pyramidal elements can be used for a rapid transition. The calculation results in this region are not used for fatigue assessment, but only for smoothing load transfer.

[0125] Boundary-driven region: Located at the outermost layer of the sub-model, its mesh nodes correspond one-to-one with the interpolation points of the base model.

[0126] During interpolation, the system not only interpolates displacements but also uses the derivatives of shape functions to interpolate rotation angles, ensuring consistent deformation at the boundaries.

[0127] To address the challenge of data interaction between high-precision sub-models (fine mesh) and the base model (coarse mesh), this embodiment employs a volume weighted homogenization method based on strain energy equivalence to feed back the damage of the sub-model to the base model.

[0128] Let the volume of a coarse element in the basic model be... Its spatial range includes the sub-models Each fine unit (volume is) The calculated damage is The strain energy density is The equivalent damage scalar is then fed back to the corresponding unit of the basic model. The calculation formula is: The system utilizes this equivalent damage scalar The stiffness matrix of the basic model is modified. This method ensures that the increase in compliance caused by local microcracks is accurately reflected in the calculation of the redistribution of internal forces in the entire bridge.

[0129] Example 13: This embodiment illustrates the processing logic for special vehicles in load spectrum generation.

[0130] In actual traffic flow, although special vehicles account for a small percentage, the damage they cause to bridges in a single instance can be equivalent to that of thousands of ordinary cars. Relying solely on probability sampling may miss these low-probability but high-risk events.

[0131] To address this, this embodiment introduces an importance sampling technique in the Monte Carlo simulation. The system artificially amplifies the probability of special vehicles appearing, generating a reinforced load spectrum that includes a large number of special vehicles. Then, when calculating damage, the results are restored through weighting.

[0132] The purpose of this is to ensure that the combined operating conditions of special vehicles can be fully traversed and simulated within a limited simulation time. This is crucial for evaluating the ultimate fatigue resistance of bridges. For example, this method might reveal that the simultaneous braking of two special vehicles at mid-span is a fatal condition that leads to the instantaneous fracture of a critical weld, thus allowing the optimization strategy to incorporate traffic control measures specifically for special vehicles.

[0133] Example 14: This embodiment describes the implementation of the method of the present invention on a computer storage medium.

[0134] The method steps of this invention can be programmed into computer-executable instruction code and stored in one or more non-volatile computer-readable storage media. These media include, but are not limited to, hard disk drives, solid-state drives, optical disks, USB flash drives, magnetic tapes, and cloud storage servers.

[0135] When these instructions are read and executed by one or more processors of the computer, the computer will sequentially perform all steps such as data acquisition, model building, load generation, coupled calculation, result analysis, and strategy generation according to a predetermined timing and logic.

[0136] Specifically, to protect intellectual property rights, the core algorithm modules in the storage medium can be encrypted or obfuscated. During use, authentication via a hardware dongle or cloud-based authorization server is required before decryption and execution. Furthermore, the generated project files are stored using a proprietary compression format to save storage space and prevent unauthorized third-party software from reading the data.

[0137] In summary, the bridge fatigue performance analysis and optimization method and system based on finite element analysis provided by this invention constructs a closed-loop, high-fidelity bridge life-cycle health management solution through refined full-parameter modeling, realistic random traffic flow simulation, in-depth damage-stiffness-thermal coupling calculation, and intelligent multi-objective decision optimization.

[0138] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for analyzing and optimizing the fatigue performance of bridges based on finite element analysis, characterized in that, Includes the following steps: Obtain geometric topology data, material physical property data, and historical traffic flow monitoring data of the bridge to be analyzed; Based on the geometric topology data and the material physical property data, a finite element basic model of the bridge reflecting the initial physical state of the bridge to be analyzed is constructed. A time-varying traffic load spectrum containing random vehicle sequences is constructed using the historical traffic flow monitoring data; The time-varying traffic load spectrum is used as a dynamic excitation input to the bridge finite element foundation model, and damage-stiffness dynamic coupling iterative calculation is performed. The iterative calculation calculates the global strain energy density distribution within each simulation time step, automatically identifies fatigue-sensitive areas based on the strain energy density gradient, and generates a high-precision sub-model. The stiffness matrix of the corresponding element in the bridge finite element foundation model is updated in real time using the calculation results of the high-precision sub-model, and a bridge fatigue evolution cloud map containing the stiffness degradation trajectory throughout the entire life cycle is generated. Based on the fatigue evolution cloud map of the bridge, fatigue damage hotspots are identified, and with the goal of extending the remaining fatigue life of the fatigue damage hotspots, a bridge fatigue resistance optimization strategy including traffic restriction thresholds and structural reinforcement timing is generated.

2. The method for analyzing and optimizing the fatigue performance of bridges based on finite element analysis according to claim 1, characterized in that, The specific steps for constructing the finite element model of the bridge include: Parametric modeling technology is used to discretize the main beam, piers and cable tower components of the bridge to be analyzed into several solid elements; A nonlinear spring damping unit is installed at the connection between the main beam and the pier to simulate the boundary constraint effect of the support; The solid element and the nonlinear spring-damped element are coupled together to generate the finite element foundation model of the bridge.

3. The method for analyzing and optimizing the fatigue performance of bridges based on finite element analysis according to claim 1, characterized in that, The step of constructing a time-varying traffic load spectrum containing random vehicle sequences using the historical traffic flow monitoring data specifically includes: The historical traffic flow monitoring data is fitted with a probability distribution to obtain the vehicle type ratio distribution function, vehicle weight distribution function, and vehicle headway distribution function. A Monte Carlo random sampling algorithm is used to generate a virtual vehicle queue based on the vehicle type distribution function, the vehicle weight distribution function, and the vehicle headway distribution function; Based on the axle load parameters and wheelbase parameters of the virtual vehicle queue, the time-varying traffic load spectrum is constructed, which dynamically changes with time and spatial location.

4. The method for analyzing and optimizing the fatigue performance of bridges based on finite element analysis according to claim 1, characterized in that, The steps for generating the bridge fatigue resistance optimization strategy specifically include: Different combinations of traffic flow restriction thresholds and the timing of structural reinforcement interventions are set as decision variables; Construct a multi-objective optimization function, which covers the sub-objectives of maximizing remaining fatigue life and minimizing maintenance economic cost; The decision variables are optimized using a genetic algorithm to obtain a Pareto optimal solution set, which is then transformed into the bridge fatigue resistance optimization strategy.

5. The method for analyzing and optimizing the fatigue performance of bridges based on finite element analysis according to claim 1, characterized in that, The specific steps for performing the damage-stiffness dynamic coupling iterative calculation include: Within the current time step, the transient dynamic response of the bridge finite element foundation model is calculated using the Newmark-β method, and the displacement of each node and the strain energy of each element are extracted. Calculate the strain energy density gradient modulus between adjacent units, and mark the region where the strain energy density gradient modulus exceeds a preset singular threshold as the fatigue-sensitive region; Based on the geometric boundary of the fatigue-sensitive region, an adaptive mesh refinement algorithm is used to generate the high-precision sub-model, the mesh density of which is higher than that of the bridge finite element foundation model.

6. The method for analyzing and optimizing the fatigue performance of bridges based on finite element analysis according to claim 5, characterized in that, The step of performing dynamic coupling iterative calculation of damage and stiffness also includes: Extract the nodal displacement response of the bridge finite element foundation model at the boundary of the fatigue-sensitive region; The nodal displacement response is mapped to the dynamic displacement boundary conditions of the high-precision sub-model using shape function interpolation. Driven by the dynamic displacement boundary conditions, the high-precision sub-model is subjected to elastoplastic damage calculation, and the local cumulative damage index is output.

7. The method for analyzing and optimizing the fatigue performance of bridges based on finite element analysis according to claim 6, characterized in that, The real-time updating of the stiffness matrix of the corresponding element in the bridge finite element foundation model specifically includes: Based on the theory of damage mechanics of continuum, a negative correlation mapping function between the local cumulative damage index and the elastic modulus of the material is established. Substitute the local cumulative damage index into the negative correlation mapping function to calculate the equivalent residual elastic modulus at the current moment; Calculate the ratio of the equivalent residual elastic modulus to the initial elastic modulus, and use it as the stiffness reduction factor; The stiffness reduction factor is used to correct the element stiffness matrix located in the fatigue-sensitive region of the bridge finite element foundation model for simulation calculation at the next time step.

8. The method for analyzing and optimizing the fatigue performance of bridges based on finite element analysis according to claim 1, characterized in that, In the step of performing dynamic coupling iterative calculation of damage and stiffness, a thermo-coupling correction mechanism is also introduced: Collect the environmental temperature time history data of the area where the bridge to be analyzed is located, and calculate the non-uniform temperature field distribution of the finite element foundation model of the bridge at each time step. The thermal strain components of each unit are calculated based on the non-uniform temperature field distribution, and the thermal strain components are superimposed on the calculation process of the transient dynamic response. Based on the influence of temperature on the fatigue performance of materials, the SN fatigue curve of the material is dynamically corrected using real-time temperature values.

9. The method for analyzing and optimizing the fatigue performance of bridges based on finite element analysis according to claim 1, characterized in that, After the step of generating a bridge fatigue evolution cloud map containing the stiffness degradation trajectory throughout the entire life cycle, the method further includes: Topological clustering analysis was performed on the fatigue evolution cloud map of the bridge to identify multiple damage region clusters with synchronized stiffness degradation rates; Calculate the geometric centroid and damage weighted average of each damage region cluster, and mark the region cluster with the highest damage weighted average as the fatigue damage hot spot region.

10. A bridge fatigue performance analysis and optimization system based on finite element analysis, characterized in that, include: The data acquisition module is used to acquire the geometric topology data, material physical property data, and historical traffic flow monitoring data of the bridge to be analyzed. The model building module is used to construct a basic finite element model of the bridge based on the geometric topology data and the material physical property data. The load spectrum generation module is used to construct a time-varying traffic load spectrum containing random vehicle sequences using the historical traffic flow monitoring data; The coupled iterative calculation module is used to input the time-varying traffic load spectrum into the bridge finite element foundation model, perform damage-stiffness dynamic coupled iterative calculation, automatically identify fatigue-sensitive areas by calculating the strain energy density gradient and call the high-precision sub-model, update the element stiffness matrix in real time and generate a bridge fatigue evolution cloud map. The strategy generation module is used to identify fatigue damage hotspots based on the bridge fatigue evolution cloud map and generate a bridge fatigue resistance optimization strategy that includes traffic restriction thresholds and structural reinforcement timing.

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