A method and system for calculating the time-varying reliability of cable corrosion fatigue in cable-stayed bridges

Abstract

This invention discloses a method and system for calculating the time-varying reliability of cable corrosion fatigue in cable-stayed bridges. The method includes establishing and validating a finite element model of the cable-stayed bridge; simulating the time history of fluctuating wind speeds in the main girder and main tower using the harmonic synthesis method; obtaining the cable stress time history through buffeting analysis; establishing a probability model of equivalent stress amplitude and cycle number using the rainflow counting method and Miner's theory; constructing a probability model of the depth of dangerous pits and corrosion depth of steel wires under different corrosion degrees based on measured data; establishing a multi-stage series formula coupling pit evolution, pit-crack transformation, and crack propagation; constructing a limit state equation with a 2% wire breakage rate as a threshold; calculating the time-varying reliability of the cable under different wind speeds and corrosion degrees using random sampling; and statistically analyzing the mean and standard deviation of corrosion fatigue life. This invention accurately reflects the wind-corrosion coupling and multi-stage failure mechanism, is computationally reliable, and has strong versatility, making it suitable for safety assessment and life prediction of cables in various types of cable-stayed bridges.

Description

Technical Field

[0001] This invention relates to the field of structural engineering technology, and in particular to a method and system for calculating the time-varying reliability of cable corrosion fatigue in cable-stayed bridges. Background Technology

[0002] In cable-stayed bridges (such as suspension bridges, cable-stayed bridges, and arch bridges), the cables are the main load-bearing components. During their service life, they simultaneously bear the fatigue caused by random wind loads and the material degradation caused by environmental corrosion. The coupling of these two factors leads to stress corrosion-fatigue failure, whose failure mechanism includes multiple stages such as pit evolution, pit transformation into cracks, crack propagation, and eventual fracture. It exhibits significant nonlinearity, randomness, and time-varying characteristics.

[0003] In existing technologies, the assessment of cable fatigue life often employs deterministic methods or single stochastic factor analysis. For example, it may only consider the randomness of wind loads while ignoring the time-varying nature of corrosion, or only consider uniform corrosion while ignoring the random distribution of localized pits. A few methods that consider the coupling of these two factors often employ simplified linear cumulative damage theory, failing to accurately reflect the multi-stage physical processes of pit evolution, pit-crack transformation, and crack propagation. Furthermore, they lack the ability to directly output time-varying reliability and life statistical characteristics (mean, standard deviation).

[0004] Therefore, there is an urgent need for a method and system for calculating the time-varying reliability of cable corrosion fatigue that can couple a random wind load probability model with a corrosion surface microstructure probability model and is based on a multi-stage physical failure mechanism. Summary of the Invention

[0005] Based on this, the present invention proposes a method and system for calculating the time-varying reliability of cable corrosion fatigue in cable-stayed bridges. This method can solve the technical problem in the existing technology of calculating the time-varying reliability of cable corrosion fatigue in cable-stayed bridges, which is difficult to simultaneously consider the randomness of load, the time-varying nature of corrosion, and multi-stage physical failure. It can directly calculate the time-varying reliability of cable corrosion fatigue and the mean and standard deviation of fatigue life.

[0006] To achieve the above-mentioned technical objectives, the present invention adopts the following technical solution:

[0007] A method for calculating the time-varying reliability of cable corrosion fatigue in cable-stayed bridges includes the following steps:

[0008] S1: Establish a finite element model of a cable-stayed bridge and verify the dynamic characteristics of the model;

[0009] S2: Based on the finite element model verified in step S1, the wind field simulation method is used to generate the downwind and vertical fluctuating wind speed time histories of the main beam and main tower. Based on the buffeting analysis theory, the above fluctuating wind speed time histories are converted into nodal force time histories and loaded into the finite element model to calculate the stress time history curves of typical cables.

[0010] S3: Extract the stress amplitude and cycle number from the stress time history curve obtained in step S2 using the rainflow counting method, calculate the equivalent stress amplitude based on Miner's linear cumulative damage theory, and establish a probability distribution model of the equivalent stress amplitude and cycle number.

[0011] S4: Based on the measured data of cable steel wires with different degrees of corrosion, establish a probability distribution model of the depth of dangerous corrosion pits and the depth of corrosion on the surface of the steel wire;

[0012] S5: Based on the stress time history curve of step S2 and the probability distribution model of dangerous pit depth and corrosion depth of step S4, establish a multi-stage series formula that couples electrochemical pit evolution, pit-crack transformation critical determination and fracture mechanics crack propagation, and express the fatigue life of the cable as the sum of pit evolution and transformation time and crack propagation to fracture time.

[0013] S6: Using the cable breakage rate reaching a preset threshold as the failure criterion, establish the limit state equation for cable failure based on the multi-stage series formula in step S5.

[0014] S7: Randomly sample the probability distribution model of equivalent stress amplitude and cycle number established in step S3 and the probability distribution model of dangerous pit depth and rust depth on the steel wire surface established in step S4, and substitute the sampling parameters into the multi-stage series formula to calculate the corrosion fatigue failure time of the cable; calculate the corrosion fatigue time-varying reliability of the cable based on the limit state equation of cable failure, and statistically analyze the mean and standard deviation of corrosion fatigue failure time.

[0015] Further, step S1 specifically involves: using T3D2 two-node linear three-dimensional truss elements for the main cable and suspenders, using B31 two-node spatial linear beam elements for the main beam and bridge towers, and using MPC beam simulation for the rigid crossbeams; and completing model verification by calculating the first 10 natural frequencies, mode shapes, and cable forces of the structure and comparing them with engineering health monitoring data and Midas analysis results.

[0016] Furthermore, in step S2, the pulsating wind speed time history is generated using the harmonic synthesis method. The power spectral density of the downwind pulsating wind speed time history is obtained using the Kaimal spectrum, and the power spectral density of the vertical pulsating wind speed time history is obtained using the Panofsky spectrum. These are then used as the target spectrum and verified against the simulated spectrum.

[0017] Furthermore, in step S3, the equivalent stress amplitude is determined according to the Miner linear cumulative damage index D = 1, and a log-normal distribution is used to fit the probability distribution model of the equivalent stress amplitude and the number of cycles.

[0018] Furthermore, in step S5, the multi-stage cascade formula includes the pit evolution equation based on electrochemical corrosion, the critical depth determination condition for pit-crack transformation, and the fracture mechanics crack propagation equation. Thus, the fatigue life of the cable is determined to consist of two parts: the pit evolution and transformation time, and the crack propagation to fracture time, as shown in the following formula:

[0019] ;

[0020] In the formula, For the fatigue life of the cable; This refers to the number of broken wires. This is the threshold value for the stress range at which fatigue cracks occur in the material. denoted as the initial critical pit depth; M is the molecular weight of the material; I0 is the pit current coefficient, which follows a three-parameter Weibull distribution, with α, β, and y being model parameters; θ is the atomic valence; F is the Faraday constant; and ρ is the material density. ξ is the activation energy of the material; ξ is the permeability coefficient; T is the absolute temperature; V is the molar volume of the material. The volume component of the stress vector borne by the material; represents the stress threshold value at which fatigue cracks occur in the material; Y is the shape factor. The stress range; This is the critical depth at which a pit transforms into a crack. For fatigue failure of corroded steel wire, the crack propagation depth is the critical factor. For the fracture toughness of corroded steel wire; The shape factor value is the value of the fatigue fracture of the corroded steel wire; D is the diameter of the cable wire. η represents the maximum stress; η is the stress cycle frequency of the suspension cable under strong wind. , The shape parameters are for the uncorroded steel wire; is the equivalent depth loss rate; κ and γ are reduction coefficients for the shape parameters of steel wire crack propagation after corrosion.

[0021] Furthermore, in step S6, the preset threshold is a wire breakage rate of 2%, and the function of the limit state equation is:

[0022] ;

[0023] In the formula: R represents the structural resistance, i.e. the critical value for determining failure; The service life of the cable under different wire breakage rates; This refers to the service status of the cable.

[0024] Furthermore, in step S7, random sampling is performed using the Monte Carlo method, and the time-varying reliability index, fatigue life mean, and fatigue life standard deviation are finally output.

[0025] This invention further proposes a cable reliability assessment system for cable-stayed bridges, which implements the aforementioned time-varying reliability calculation method for corrosion fatigue of cable-stayed bridges, including:

[0026] The model building and verification module is used to build a finite element analysis model of a cable-stayed bridge and to verify its dynamic characteristics.

[0027] The fluctuating wind speed generation module is used to generate the downwind and vertical fluctuating wind speed time histories at the main beam and main tower using the harmonic synthesis method.

[0028] The stress time history solving module is used to convert the pulsating wind speed time history curve into the nodal force time history and load the bridge finite element model to solve the stress time history curve of a typical cable.

[0029] The load probability modeling module is used to extract the probability distribution model of equivalent stress amplitude and cycle number from the stress time history using the rainflow counting method, and to establish its probability distribution model.

[0030] The rust feature probability modeling module is used to establish a probability distribution model of the depth of dangerous corrosion pits and the depth of rust on steel wires under different degrees of rust based on measured data;

[0031] The multi-stage failure simulation module is used to establish a series formula for the entire stage of pit evolution, crack transformation, and crack propagation based on stress time history, critical pit depth, and corrosion depth. The failure judgment criterion is that the cable breakage rate reaches a preset threshold. The limit state equation for cable failure is established based on the multi-stage series formula.

[0032] The time-varying reliability analysis module is used to randomly sample the load probability model and the corrosion depth and pit depth probability models, substitute the sampling parameters into the multi-stage series formula and limit state equation, calculate the time-varying reliability under different wind speeds and different corrosion degrees, and output the mean lifetime and standard deviation.

[0033] Furthermore, the model building and verification module uses a combination of T3D2 truss elements, B31 beam elements and MPC beams for modeling, and verifies the model by comparing the first 10 natural frequencies, mode shapes, cable forces with measured data and Midas results.

[0034] Furthermore, the pulsating wind speed generation module uses the Kaimal spectrum as the downwind target spectrum and the Panofsky spectrum as the vertical target spectrum to perform wind field simulation and spectrum consistency calibration.

[0035] This invention provides a method and system for calculating the time-varying reliability of cable corrosion fatigue in cable-stayed bridges. Compared with existing reliability calculation methods, it has the following advantages:

[0036] (1) Achieve coupled modeling of wind load randomness and corrosion micro-randomness, significantly improving assessment accuracy: This invention establishes a probability distribution model of equivalent stress amplitude and cycle number under random wind load, and at the same time establishes a probability distribution model of dangerous pit depth and corrosion depth of steel wire under different corrosion degrees. It unifies and couples the random characteristics of wind-induced fatigue with the random distribution of corrosion micro-features, truly reflects the synergistic driving mechanism of wind load and environmental corrosion on cable degradation, and greatly improves the confidence and accuracy of cable corrosion fatigue damage assessment.

[0037] (2) Life prediction is more realistic: This invention constructs a multi-stage series formula that couples electrochemical pit evolution, pit-crack transformation critical determination, and fracture mechanics crack propagation. It clearly divides the cable fatigue life into the pit evolution and transformation stage and the crack propagation to fracture stage, and fully restores the failure mechanism of the cable from corrosion initiation to final fracture. It overcomes the assumption error of the traditional single crack propagation model and significantly improves the reliability of fatigue life prediction.

[0038] (3) Strong engineering applicability: This invention uses the wire breakage rate reaching a preset threshold as the failure criterion, establishes a standard limit state equation, and completes multi-parameter random analysis based on Monte Carlo sampling. It can directly calculate the corrosion fatigue time-varying reliability of the cable under different wind speeds and different degrees of corrosion, and output the mean and standard deviation of fatigue life. It can quantitatively evaluate the safety performance of the cable throughout its entire life cycle and provide direct data support for bridge maintenance, repair and operation decisions.

[0039] (4) The finite element model is accurate and reliable, and the wind field simulation and stress calculation are realistic and credible: The present invention uses a combination of truss elements, beam elements and MPC beams to establish a refined finite element model, and verifies it through dynamic characteristics, cable force and measured data and Midas results to ensure the accuracy of structural response calculation; Kaimal spectrum and Panofsky spectrum are used for wind field simulation and spectrum calibration, and combined with buffeting analysis to obtain the real stress time history, providing high-quality input for subsequent fatigue and reliability calculation.

[0040] (5) The method is highly versatile and has a wide range of applications: This invention uses rainflow counting and Miner's theory to achieve standardized processing of random stress. The probabilistic modeling, multi-stage failure simulation, and time-varying reliability calculation process are clear and reproducible. It does not depend on specific software and unit types and can be applied to the corrosion fatigue time-varying reliability assessment of cables in various cable-stayed bridges such as suspension bridges, cable-stayed bridges, and arch bridges. Attached Figure Description

[0041] Figure 1 It is a finite element analysis model of a cable-stayed bridge;

[0042] Figure 2 These are the time history curves of downwind and vertical pulsating wind speeds;

[0043] Figure 3 It is a comparison between the target spectrum and the simulated power spectrum of the downwind and vertical fluctuating wind speeds;

[0044] Figure 4 It is the time history of the baffle force;

[0045] Figure 5 It is the stress time history curve of the cable under random wind load;

[0046] Figure 6 It is the cable stress amplitude and cycle number extracted by the rainflow counting method;

[0047] Figure 7 It is the probability distribution of the equivalent stress amplitude and cycle number of the cable under random wind load;

[0048] Figure 8 This is the probability distribution of the depth of dangerous corrosion pits on the surface of steel wire under different degrees of corrosion.

[0049] Figure 9 It is the probability distribution of the rust depth of steel wire under different degrees of rust.

[0050] Figure 10 A schematic diagram of a time-varying reliability assessment process for cable corrosion fatigue in cable-stayed bridges provided by this invention;

[0051] Figure 11 These are the calculation results of cable corrosion fatigue life samples;

[0052] Figure 12 It is the probability distribution of cable corrosion fatigue life;

[0053] Figure 13 It is the time-varying reliability of cable corrosion fatigue under different wind speeds and corrosion levels;

[0054] Figure 14 This invention compares the time-varying reliability of cable corrosion fatigue calculation with traditional methods and theoretical calculations. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific implementation examples and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this invention.

[0056] 1. Establish and validate the finite element model of cable-stayed bridges.

[0057] This embodiment uses a long-span suspension bridge as an example, and establishes a finite element model of the cable-stayed bridge using ABAQUS software. The bridge towers, main beams, and cables are simplified using a fishbone design, and the element system consists of truss elements and beam elements.

[0058] Specifically, the main cable and suspenders are simulated using T3D2 two-node linear three-dimensional truss elements, the main beam and bridge towers are simulated using B31 two-node spatial linear beam elements, and the rigid crossbeams are simulated using MPC beams. The established finite element model is as follows: Figure 1 As shown.

[0059] After the model is established, its rationality is verified: the dynamic characteristics of the structure are analyzed and calculated, the first 10 natural frequencies, mode shapes and cable force values ​​are obtained, and compared with the engineering structure health monitoring data and MIDAS analysis results.

[0060] The comparison results show that the established model has good accuracy.

[0061] Table 1. Comparison of bridge natural frequencies and mode shapes with literature and Midas analysis results.

[0062]

[0063] 2. Simulation of fluctuating wind field and time history solution of cable stress:

[0064] like Figure 2 As shown, the wind field at the main girder and bridge towers is simulated using the harmonic synthesis method, generating time histories of fluctuating wind speeds in both the horizontal and vertical directions. The power spectral density function of the fluctuating wind speed in the horizontal direction is represented by the Kaimal spectrum.

[0065] ;

[0066] The power spectral density function of the vertical fluctuating wind speed is expressed using the Panofsky spectrum.

[0067] ;

[0068] In the formula: n is the frequency of wind pulsation; f is the Morning coordinate; The velocity is the airflow friction velocity;

[0069] After the simulation was completed, the Kaimal spectrum was used as the downwind target spectrum and the Panofsky spectrum as the vertical target spectrum for verification. The simulation results showed good agreement with the target spectra. Figure 3 As shown, the simulated wind field has high fidelity.

[0070] See Figure 4As shown, based on Davenport's buffeting analysis theory, the time history of fluctuating wind speed is transformed into the time history of nodal forces acting on the main girder and towers of the bridge. This is then applied to the finite element model, and the stress-time history curves of a typical cable are calculated. Figure 5 .

[0071] 3. Stress amplitude statistics and equivalent stress probability modeling:

[0072] Based on the stress time history curve, the stress amplitude and cycle number of the cable at different locations under different wind speeds were extracted using the rainflow counting method. (See...) Figure 6 As shown. According to Miner's linear cumulative damage theory, when the cumulative damage index D=1, the equivalent stress amplitude is calculated by the following formula:

[0073] ;

[0074] In the formula: S eq S is the equivalent stress amplitude; i n is the stress amplitude of level i; i is the corresponding number of cycles; m is the material fatigue parameter; in this embodiment, m=3.

[0075] The equivalent stress amplitude and cycle number of the cable under different wind speeds were statistically analyzed, and its probability distribution model was fitted using a log-normal distribution. (See...) Figure 7 As shown.

[0076] 4. Modeling the probability distribution of corrosion characteristic parameters:

[0077] See Figure 8 , Figure 9 As shown, samples were taken from the corroded cable, and a 3D scanner was used to test the depth of dangerous pits and the depth of corrosion on the surface of the cable wires. Statistical analysis of the measured data under different corrosion levels shows that both the depth of dangerous pits and the depth of corrosion follow a log-normal distribution.

[0078] 5. Multi-stage corrosion fatigue failure simulation:

[0079] Based on the principles of electrochemical corrosion and considering the stress redistribution of the cable after wire breakage, the fatigue life of the cable consists of two parts: the pitting evolution stage, the pitting-crack transformation stage, and the crack propagation to fracture stage. This can be expressed by the following formula:

[0080] ;

[0081] In the formula, For the fatigue life of the cable; This refers to the number of broken wires. h is the stress threshold value for the material to develop fatigue cracks. pit0ρ represents the initial critical pit depth; M is the molecular weight of the material, taken as 55.85 g / mol; I0 is the pit current coefficient, following a three-parameter Weibull distribution, where α, β, and y are model parameters, taken as 1, 0.25, and 0.25, respectively; θ is the valence, taken as 3; F is the Faraday constant, taken as 96514 C / mol; ρ is the material density, taken as 7.6 × 10⁻⁶. 6 g / m 3 ; ξ is the activation energy of the material, taken as 59.7 kJ / mol; ξ is the aeration coefficient, taken as 8.314 J / (mol·K); T is the absolute temperature, taken as 273+t, where t is the average temperature; V is the molar volume of the material, taken as 7.35 cm³. 3 / mol; ΔK is the volume component of the stress vector borne by the material. th represents the stress threshold value at which fatigue cracks occur in the material; Y is the shape factor. The stress range; Equivalent depth loss rate; The critical depth at which pitting transforms into cracks:

[0082] ;

[0083] In the formula, y is the critical depth at which a pit transforms into a crack; Y is the shape factor. The stress range;

[0084] The crack propagation depth is the factor for fatigue failure of corroded steel wire, expressed as:

[0085] ;

[0086] In the formula, For the fracture toughness of corroded steel wire; This represents the shape factor value when corroded steel wire undergoes fatigue fracture. The maximum stress is D; the diameter of the cable wire is D.

[0087] The expression for the crack propagation depth as a function of time is:

[0088] ;

[0089] In the formula, , For the shape parameters of the uncorroded steel wire, take 4.1 × 10⁻⁶ respectively. -12 3;

[0090] κ and γ are reduction factors for the shape parameters of crack propagation in steel wire after corrosion, and are solved using the following empirical formulas:

[0091] ; ;

[0092] In the formula, The equivalent depth loss rate is given by 'a', where 'a' is the pit depth; the equivalent depth loss rate is given by 'a'. Solve using the following formula:

[0093] ;

[0094] In the formula, The diameter of the uncorroded cable wire; This represents the maximum corrosion depth. The width of the erosion pit;

[0095] η is the stress cycle frequency of the suspension cable under strong wind.

[0096] 6. Failure determination and limit state equation construction:

[0097] Failure is determined when the cable breakage rate reaches a preset threshold. In this embodiment, the threshold is 2% (i.e., 2% of the total number of steel wires break). This value can be adjusted according to the importance level of the bridge. The function of the limit state equation is:

[0098] ;

[0099] In the formula: R represents the structural resistance, i.e. the critical value for determining failure; S(t) is the service life of the cable under different wire breakage rates; For the cable's service status, the reliability index is calculated using the following formula:

[0100] ;

[0101] In the formula, , The values ​​represent the mean and standard deviation of the service life of the cable when the breakage rate reaches 2%.

[0102] , These represent the mean and standard deviation of the time-varying corrosion fatigue life of the cable at time t, respectively.

[0103] 7. Time-varying reliability calculation and lifetime statistics

[0104] according to Figure 10 The process generates 1000 sets of samples based on the probability distribution models in steps S3 and S4. Each set includes random parameters such as equivalent stress amplitude, number of cycles, critical pit depth, corrosion depth, and pit current coefficient. Each set of samples is then substituted into the multi-stage failure formula in step S5 to calculate the cable failure time. Figure 11 .

[0105] For statistical analysis of the sample mean and sample standard deviation, see [link to sample mean and standard deviation]. Figure 12 The service life of the cable body when the wire breakage rate reaches 2% is given based on the limit state equation; the service life of the cable body under different wire breakage rates is calculated, and the time-varying reliability of the cable body due to corrosion fatigue is calculated based on the reliability index. (See...) Figure 13 Repeat the above process to calculate the time-varying reliability and mean and standard deviation of life under different design wind speeds and corrosion levels.

[0106] The present invention's calculation of the time-varying reliability of cable corrosion fatigue, compared with traditional methods and theoretical calculations, shows that traditional methods do not consider the time-varying and random nature of corrosion, thus significantly overestimating the cable's service reliability. The method of the present invention yields results closer to theoretical calculations, ensuring accuracy while improving computational efficiency. Figure 14 .

[0107] To implement the above method, this embodiment also provides a cable reliability assessment system for cable-stayed bridges, as detailed below:

[0108] A time-varying reliability calculation system for cable corrosion fatigue of cable-supported bridges includes: a model establishment and verification module, used to establish a finite element analysis model of the cable-supported bridge and compare it with relevant measured data and the Midas model to ensure the accuracy of the established model;

[0109] The fluctuating wind speed generation module is used for the numerical analysis model of cable-stayed bridges and generates the time histories of downwind and vertical fluctuating wind speeds at the main beam and bridge towers based on the harmonic synthesis method.

[0110] The stress time history solution module is used to convert the fluctuating wind speed time history curve into the nodal force time history based on the buffeting analysis theory and apply it to the bridge finite element model to solve the stress time history curve of a typical cable.

[0111] The load probability modeling module is used to extract the probability distribution model of equivalent stress amplitude and cycle number from the stress time history using the rainflow counting method, and to establish its probability distribution model.

[0112] The rust feature probability modeling module is used to extract and statistically analyze the rust feature parameters of the steel wire surface inside the cable with different degrees of rust, mainly including: dangerous corrosion pits, rust depth, and to establish corresponding probability distribution models.

[0113] A multi-stage failure simulation module is used to establish multi-stage simulation calculation formulas for cable stress corrosion-fatigue failure, including pit evolution, pit-crack transformation, and crack propagation to fracture. A 2% wire breakage rate is considered a critical state for cable life, and the limit state equation for cable failure is given.

[0114] The time-varying reliability analysis module is used to sample based on the probability distribution model of random wind load and corrosion parameters. Using random wind load data and corrosion parameters as random parameter input data, it analyzes the time-varying reliability of cable corrosion fatigue under different wind speeds and corrosion degrees to obtain the output data time-varying reliability index and corresponding mean and standard deviation, and simulates the time-varying corrosion fatigue reliability of cable.

[0115] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calculating the time-varying reliability of a cable of a cable- supported bridge in the presence of corrosion and fatigue, characterized in that, Includes the following steps: S1: Establish a finite element model of a cable-stayed bridge and verify the dynamic characteristics of the model; S2: Based on the finite element model verified in step S1, the wind field simulation method is used to generate the downwind and vertical fluctuating wind speed time histories of the main beam and main tower. Based on the buffeting analysis theory, the above fluctuating wind speed time histories are converted into nodal force time histories and loaded into the finite element model to calculate the stress time history curves of typical cables. S3: Extract the stress amplitude and cycle number from the stress time history curve obtained in step S2 using the rainflow counting method, calculate the equivalent stress amplitude based on Miner's linear cumulative damage theory, and establish a probability distribution model of the equivalent stress amplitude and cycle number. S4: Based on the measured data of cable steel wires with different degrees of corrosion, establish a probability distribution model of the depth of dangerous corrosion pits and the depth of corrosion on the surface of the steel wire; S5: Based on the stress time history curve of step S2 and the probability distribution model of dangerous pit depth and corrosion depth of step S4, establish a multi-stage series formula that couples electrochemical pit evolution, pit-crack transformation critical determination and fracture mechanics crack propagation, and express the fatigue life of the cable as the sum of pit evolution and transformation time and crack propagation to fracture time. S6: Using the cable breakage rate reaching a preset threshold as the failure criterion, establish the limit state equation for cable failure based on the multi-stage series formula in step S5. S7: Randomly sample the probability distribution model of equivalent stress amplitude and number of cycles established in step S3 and the probability distribution model of dangerous pit depth and rust depth on the steel wire surface established in step S4, and substitute the sampling parameters into the multi-stage series formula to calculate the corrosion fatigue failure time of the cable. The corrosion fatigue time-varying reliability of the cable is calculated based on the limit state equation of the cable failure, and the mean and standard deviation of the corrosion fatigue failure time are statistically analyzed. In step S5, the multi-stage cascade formula includes the pit evolution equation based on electrochemical corrosion, the critical depth judgment condition for pit-crack transformation, and the fracture mechanics crack propagation equation. Thus, the fatigue life of the cable is determined to consist of two parts: the pit evolution and transformation time, and the crack propagation to fracture time, as shown in the following formula: ； In the formula, For the fatigue life of the cable; This refers to the number of broken wires. This is the threshold value for the stress range at which fatigue cracks occur in the material. This represents the initial critical pit depth dimension; The molecular weight of the material; The pitting current coefficient follows a three-parameter Weibull distribution, where α, β, and y are model parameters; θ is the atomic valence; F is the Faraday constant; and ρ is the material density. ξ is the activation energy of the material; ξ is the permeability coefficient; T is the absolute temperature; V is the molar volume of the material. Y is the volume component of the stress vector borne by the material; Y is the shape factor. The stress range; This is the critical depth at which a pit transforms into a crack. For fatigue failure of corroded steel wire, the crack propagation depth is the critical factor. For the fracture toughness of corroded steel wire; The shape factor value is the value of the fatigue fracture of the corroded steel wire; D is the diameter of the cable wire. The maximum stress; η is the stress cycle frequency of the suspension cable under strong wind. , These are the shape parameters of the uncorroded steel wire; is the equivalent depth loss rate; κ and γ are reduction coefficients for the shape parameters of steel wire crack propagation after corrosion.

2. The method of claim 1, wherein the method is characterized by: Step S1 specifically involves: using T3D2 two-node linear three-dimensional truss elements for the main cable and suspenders, B31 two-node spatial linear beam elements for the main beam and bridge tower, and MPC beam simulation for the rigid crossbeams; and completing model verification by calculating the first 10 natural frequencies, mode shapes, and cable forces of the structure and comparing them with engineering health monitoring data and Midas analysis results.

3. The method of claim 1, wherein the method is characterized by: In step S2, the pulsating wind speed time history is generated using the harmonic synthesis method. The power spectral density of the downwind pulsating wind speed time history is obtained using the Kaimal spectrum, and the power spectral density of the vertical pulsating wind speed time history is obtained using the Panofsky spectrum. These are then used as the target spectrum and verified against the simulated spectrum.

4. The method of claim 1, wherein the method is characterized by: In step S3, the equivalent stress amplitude is determined according to the Miner linear cumulative damage index D = 1, and a log-normal distribution is used to fit the probability distribution model of the equivalent stress amplitude and the number of cycles.

5. The method for calculating the time-varying reliability of cable corrosion fatigue in cable-stayed bridges as described in claim 1, characterized in that, In step S6, the preset threshold is a wire breakage rate of 2%, and the function of the limit state equation is: ； In the formula, R represents the structural resistance, i.e. the critical value for determining failure; is the service life of the cable body under different wire breakage rates; is the service state of the cable.

6. The method of claim 1, wherein the method is a method of calculating the time- dependent reliability of a cable of a cable-supported bridge subjected to corrosion fatigue, characterized by, In step S7, random sampling is performed using the Monte Carlo method, and the time-varying reliability index, fatigue life mean, and fatigue life standard deviation are finally output.

7. A reliability assessment system for cable-stayed bridges, comprising the time-varying reliability calculation method for corrosion fatigue of cable-stayed bridges as described in any one of claims 1-6, characterized in that, include: The model building and verification module is used to build a finite element analysis model of a cable-stayed bridge and to verify its dynamic characteristics. The fluctuating wind speed generation module is used to generate the downwind and vertical fluctuating wind speed time histories at the main beam and main tower using the harmonic synthesis method. The stress time history solving module is used to convert the pulsating wind speed time history curve into the nodal force time history and load the bridge finite element model to solve the stress time history curve of a typical cable. The load probability modeling module is used to extract the probability distribution model of equivalent stress amplitude and cycle number from the stress time history using the rainflow counting method, and to establish its probability distribution model. The rust feature probability modeling module is used to establish a probability distribution model of the depth of dangerous corrosion pits and the depth of rust on steel wires under different degrees of rust based on measured data; The multi-stage failure simulation module is used to establish a series formula for the entire stage of pit evolution, crack transformation, and crack propagation based on stress time history, critical pit depth, and corrosion depth. The failure judgment criterion is that the cable breakage rate reaches a preset threshold. The limit state equation for cable failure is established based on the multi-stage series formula. The time-varying reliability analysis module is used to randomly sample the load probability model and the corrosion depth and pit depth probability models, substitute the sampling parameters into the multi-stage series formula and limit state equation, calculate the time-varying reliability under different wind speeds and different corrosion degrees, and output the mean lifetime and standard deviation.

8. The cable reliability assessment system of claim 7, wherein, The model building and verification module uses a combination of T3D2 truss elements, B31 beam elements and MPC beams for modeling, and verifies the model by comparing the first 10 natural frequencies, mode shapes, cable forces with measured data and Midas results.

9. The cable reliability assessment system of claim 7, wherein, The pulsating wind speed generation module uses the Kaimal spectrum as the downwind target spectrum and the Panofsky spectrum as the vertical target spectrum to perform wind field simulation and spectrum consistency calibration.

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