Method for evaluating corrosion fatigue damage of steel bridge based on multi-source information fusion

Abstract

The application discloses a kind of multi-source information fusion's steel bridge corrosion fatigue damage evaluation method, comprising: the establishment includes corrosion steel bridge welding fatigue crack propagation model of undetermined parameter;Through corrosion fatigue crack propagation test, the measured data of undetermined parameter is obtained, and the prior distribution of the parameter is established;Establish corrosion fatigue crack propagation bayesian network model to characterize the uncertainty relationship of variable, undetermined parameter and observation data;Fusion parameter matrix, interval and observation point information such as multi-source information, realize the posterior calibration of the parameter by maximum entropy criterion;Based on the calibrated parameter, realize steel bridge welding detail corrosion fatigue damage evaluation and structure residual life prediction.The application fuses limited indirect observation information with multi-source information in the service process of steel bridge, reduces the influence of cognitive uncertainty in the process of steel bridge damage evaluation.The method is reasonable, the prediction accuracy is higher, the calculation efficiency is high, and is suitable for bridge structure safety evaluation and intelligent operation.

Description

Technical Field

[0001] This invention relates to the field of safety assessment of bridges in service, and particularly to a method for assessing corrosion fatigue damage of steel bridges using multi-source information fusion. Background Technology

[0002] With the continuous increase in vehicle axle load and traffic volume, fatigue damage is becoming one of the key issues affecting the service safety of steel bridges. Welded details are weak points in steel bridge structures, constantly subjected to repeated vehicle loads during service. Simultaneously, due to welding quality issues, materials may contain defects such as oxidation, impurities, and inhomogeneity. Stress concentrations often occur at these defects, easily inducing crack initiation under fatigue loading. Furthermore, long-term environmental corrosion during service further accelerates the fatigue fracture process of welded details, significantly reducing the remaining structural life. Existing fatigue damage assessment methods for steel bridges mainly consider factors such as stress ratio, stress amplitude, and loading frequency, rarely considering the coupled effects of welding residual stress and corrosion pit stress concentration. Therefore, there is an urgent need to conduct refined modeling research on crack propagation in welded details under corrosion-fatigue coupling.

[0003] Furthermore, the growth rate and path of corrosion fatigue cracks exhibit significant randomness, and a universal theoretical physical model for the entire service life of a structure has not yet been established. Key monitoring information of the in-service structure can provide the most accurate information for subsequent service life prediction. Combining limited measured information with prior information will help reduce the impact of subjective uncertainties and improve the accuracy of corrosion fatigue damage prediction for steel bridges. Bayesian networks can be used to characterize the complex uncertainties of model parameters and can fuse multi-source information such as experimental data, physical models, and monitoring data. However, traditional Bayesian methods mainly update based on observation point data, making it difficult to incorporate posterior moments and interval constraints of experimental material parameters, which are highly beneficial for diagnosing fatigue damage in steel bridges. Information entropy methods can effectively handle various information such as point, interval, and moment estimations through additional constraints. Therefore, how to combine Bayesian information entropy data fusion theory to construct a framework for the inversion and updating of corrosion fatigue damage in steel bridges has become an urgent technical challenge. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-source information fusion method for assessing corrosion fatigue damage of steel bridges, effectively solving the above-mentioned technical problems.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] The present invention provides a multi-source information fusion method for assessing corrosion fatigue damage in steel bridges, comprising the following steps:

[0007] Step 1: Based on the effective stress intensity factor and stress threshold value of the welding crack, establish the corrosion fatigue crack propagation model as shown in equation (1.1):

[0008]

[0009] In the formula, a is the crack length, N is the number of fatigue load cycles, and ΔK eff ΔK is the effective stress intensity factor. th is the stress threshold value, m is the crack propagation material parameter, taken as 3.0; C is a parameter to be determined, which is related to the mechanical properties of the weld material and can be obtained through corrosion fatigue crack propagation rate tests on welded CT specimens;

[0010] Step 2: Obtain a series of direct measured data of the undetermined parameter C in the corrosion fatigue crack propagation model through corrosion fatigue crack propagation rate tests, and establish the prior distribution of the undetermined parameter C;

[0011] Step 3: Based on Step 1 and Step 2, construct a Bayesian network model for corrosion fatigue crack propagation according to the Bayesian network principle, and characterize the uncertainty relationship between variables, undetermined parameter C, and observation data in the corrosion fatigue crack propagation model.

[0012] Step 4: Based on the corrosion fatigue crack propagation Bayesian network model obtained in Step 3, obtain the direct measured data of the parameter moments and parameter intervals of the undetermined parameter C during the service of the steel bridge. Integrate the parameter moments and interval information to obtain the constraints of the posterior model for the undetermined parameter C. Construct the likelihood function of the undetermined parameter C based on the indirect information of crack observation points obtained during the service of the steel bridge. Integrate the prior distribution and likelihood function of the undetermined parameter C to establish the posterior model of the undetermined parameter C. Use the maximum entropy criterion to obtain the posterior model and calibrate the undetermined parameter C. The parameter moment constraints are solved by constructing a Lagrangian function; the parameter interval constraints limit the upper and lower bounds of the undetermined parameter C.

[0013] Step 5: Substitute the calibration result of the undetermined parameter C obtained in Step 4 into the corrosion fatigue crack propagation model, predict the corrosion fatigue crack length at the current moment based on the number of vehicle load cycles borne by the welded details during the service of the steel bridge, and predict the corrosion fatigue crack propagation life of the welded details of the steel bridge based on the critical crack size.

[0014] Furthermore, in step one, the effective stress intensity factor and stress threshold value are determined as follows:

[0015] The residual stress distribution at the crack tip is obtained. The effective stress ratio of the crack is determined based on the maximum and minimum values ​​of the stress intensity factor. The crack opening stress ratio is determined based on the effective stress ratio. The effective stress intensity factor and stress threshold value are then obtained based on the effective stress ratio, opening stress ratio, welding angle correction parameter, and geometric parameter correction factor.

[0016] Furthermore, the effective stress ratio of the crack is calculated according to equation (1.2):

[0017]

[0018] In the formula, R eff The effective stress ratio of the crack; This represents the maximum effective stress intensity factor. This is the minimum effective stress intensity factor. and Determine according to formulas (1.3) and (1.4):

[0019]

[0020]

[0021] In the formula, K max K min These are the maximum and minimum values ​​of the stress intensity factor caused by the external load, respectively; K res For the distribution of welding residual stress, K res Determine according to formula (1.5):

[0022]

[0023] In the formula, denoted as the residual stress at the crack tip, a as the crack length, and b and l as the transverse positions of the weld corresponding to the points of maximum residual tensile and compressive stress, respectively.

[0024] Furthermore, the crack opening stress ratio is calculated according to equation (1.6):

[0025]

[0026] In the formula, U is the crack opening stress ratio; f' is the crack closure effect function, and f' is calculated according to formula (1.7):

[0027]

[0028] In the formula, A0, A1, A2, and A3 are constants of the crack closure effect function, determined according to equations (1.8) to (1.11), respectively:

[0029] A0 = (0.825 - 0.34α + 0.05α) 2 )[cos(πσ max / 2σ f )] 1 / α (1.8)

[0030] A1=(0.415-0.071α)σ max / σ f (1.9)

[0031] A2 = 1 - A0 - A1 - A3 (1.10)

[0032] A3 = 2A0 + A1 - 1 (1.11)

[0033] In the formula, σ f For flow stress, σ f =1.15(σ y +σ u ) / 2; α is the stress-strain constant, which has a value of 1 under plane stress and a value of 3 under plane strain, σ max For the maximum stress, σ y For yield strength, σ u This represents the ultimate tensile strength.

[0034] Furthermore, the effective stress intensity factor is determined according to equation (1.12):

[0035]

[0036] In the formula, ΔK eff Δσ is the effective stress intensity factor. eff Δσ represents the effective stress range for welding. eff =Uσ max (1-R eff ), d is the pit depth, K t This represents the stress concentration factor at the tip of the pit. G(θ) is the geometric parameter correction factor, and G(θ) is the welding angle correction parameter. G(θ) and G(θ) are determined according to equations (1.13) and (1.14), respectively:

[0037]

[0038]

[0039] In the formula, q is the weld angle coefficient, q=ln[(11.584-0.0588θ) / 2.30], θ is the weld angle, and B is the thickness of the welded plate.

[0040] K t Determine according to formula (1.15):

[0041] K t =GPR[w,l,d] (1.15)

[0042] In the formula, w, l, and d represent the length, width, and depth of the erosion pit, respectively, and GPR is a Gaussian process regression model.

[0043] Furthermore, the Gaussian process regression model was obtained as follows: The maximum and minimum values ​​of the pit stress distribution under no fewer than 40 different dimensional parameters were obtained through finite element simulation, and their ratio σ was calculated respectively. max / σ0, where σ0 is the average stress of the steel wire without pitting. The pit length w, width l, and depth d are used as inputs to the GPR model, and the stress concentration factor K at the pit tip is used. t As the model output, the GPR model is trained to establish a trained GPR model for assessing corrosion fatigue damage of steel bridges. This model is then used to predict the stress concentration factor at the tip of the corrosion pit.

[0044] Furthermore, the stress threshold value is determined according to equation (1.16):

[0045]

[0046] In the formula, ΔK th This is the stress threshold value; a th a is the threshold for corrosion fatigue crack growth. th Determine according to formula (1.17):

[0047]

[0048] In the formula, b1 is the corrosion fatigue strength coefficient, b1=-1 / m; m is the material parameter for crack propagation, which is taken as 3.0.

[0049] Furthermore, in step two, the undetermined parameter C in the corrosion fatigue crack propagation rate test is a single-point continuous random variable, and the statistical prior distribution of its directly measured data follows a normal distribution, that is, the prior distribution of the undetermined parameter C is expressed by equation (2.1):

[0050]

[0051] In the formula, p0(lnC) is the prior distribution of the parameter lnC, and lnC T Let μ be the direct measured value of parameter lnC at time T. lnC σ lnC The parameters are lnC respectively. T The mean and standard deviation.

[0052] Furthermore, in step three, the Bayesian network model for corrosion fatigue crack propagation is constructed as follows:

[0053] The effective stress intensity factor, fatigue crack growth length, and fatigue crack calculation length are determined as functional nodes; fatigue load, effective welding stress range, welding residual stress, stress concentration factor, stress threshold value, crack propagation material parameters and undetermined parameter C of the fatigue crack propagation model, initial crack size, and geometric dimensions are determined as continuous nodes; the number of fatigue load cycles and fatigue crack observation length are determined as observation nodes; the mutual physical dependencies of each node at the same time and the temporal dependencies of each node between adjacent time points are determined, ultimately forming a Bayesian network structure that considers multivariate physical relationships.

[0054] Furthermore, in step four, the moment constraint of parameter C during the service of the steel bridge is expressed by equations (4.1) and (4.2) as follows:

[0055] p1(lnC)∝p0(lnC)×exp(βf(lnC)) (4.1)

[0056] βf(lnC)=-β1lnC-β2(lnC) 2 (4.2)

[0057] In the formula, p1(lnC) is the posterior distribution of the parameters after moment constraints; β, β1, and β2 are Lagrange factors, and solving for the value of β requires satisfying the expectation constraints of the mean and variance as shown in equation (4.3):

[0058]

[0059] In the formula, E(lnC) is the mean constraint of lnC, ∑(lnC) is the variance constraint of lnC, and μ lnC Let lnC be the mean. Let lnC be the variance.

[0060] Furthermore, in step four, the interval constraint of parameter C during the service of the steel bridge is expressed by equation (4.4):

[0061] lnC∈[(lnC) - ,(lnC) + (4.4)

[0062] In the formula, (lnC) - (lnC) + These are the lower and upper limits of the interval for lnC, respectively.

[0063] Furthermore, in step four, based on the indirect information provided by the crack observation point data obtained during the service of the steel bridge, which is the crack observation length during the service of the steel bridge, a likelihood function is constructed according to equation (4.5):

[0064]

[0065] In the formula, Let lnC be the likelihood function of the parameter. σ e For model error, σ a For measurement error; a T To calculate the crack length at time T in tests with different corrosion fatigue crack propagation rates based on the welding corrosion fatigue crack propagation model. The crack length observed at time T; a T Determine according to formulas (4.6) and (4.7):

[0066]

[0067]

[0068] In the formula, Δa T The crack growth length during the time interval T-1 to T; N is the initial crack length at time T; T The number of corrosion fatigue load cycles during the time period from 0 to T, N T-1 The number of fatigue load cycles during the time period from 0 to T-1; The effective stress intensity factor at time T. This represents the stress threshold value at time T.

[0069] Furthermore, in step four, the parameter moments and parameter intervals of the undetermined parameter C during the service of the steel bridge are used as constraints for the posterior model of the undetermined parameter C. The prior distribution and likelihood function of the undetermined parameter C in the corrosion fatigue crack propagation model are also integrated to obtain the probability distribution of the posterior model of the undetermined parameter C, expressed as Equation (4.8). Equation (4.8) can be calculated by Markov Monte Carlo simulation sampling.

[0070]

[0071] In the formula, p n (lnC) is the posterior distribution of the parameter lnC.

[0072] Furthermore, in step five, the length of the corrosion fatigue crack in the weld details at the current moment during the service of the steel bridge is predicted according to formula (5.1):

[0073]

[0074] In the formula, a T N represents the predicted length of welding corrosion fatigue crack at time T. T The number of corrosion fatigue load cycles borne by the welded details of the steel bridge during the time period from 0 to T. This is the calibration value for the parameter C to be determined.

[0075] Furthermore, in step five, the corrosion fatigue crack propagation life of the steel bridge weld details is predicted according to equation (5.2):

[0076]

[0077] In the formula, N f The corrosion fatigue crack propagation life of the welded details of the steel bridge is defined as the number of corrosion fatigue load cycles that the welded details of the steel bridge endure during the period from the initial crack development to the critical crack. a0 is the initial crack size; a c Let a be the critical crack size. c Determine according to formula (5.3):

[0078]

[0079] In the formula, K IC σ represents the fracture toughness of the material. c This is the critical stress.

[0080] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0081] This invention discloses a multi-source information fusion method for assessing corrosion fatigue damage in steel bridges, including parameter updating and damage prediction for a corrosion fatigue crack propagation model. Specifically: a corrosion fatigue crack propagation model for steel bridges is established based on the influence mechanism of welding residual stress and crack closure on corrosion fatigue crack propagation; a series of direct measured data for undetermined parameters are obtained through corrosion fatigue crack propagation rate tests, and a prior distribution of the undetermined parameter C in the corrosion fatigue crack propagation model is established; based on Bayesian network principles, the uncertainties of variables, parameters, and observation data in the corrosion fatigue crack propagation model are characterized; considering the moment information, interval direct measured information, and indirect information from crack observation points of the undetermined parameters, the posterior calibration of the undetermined parameter C is achieved through the maximum entropy principle; based on the calibration results of the undetermined parameter C and statistical information such as the actual number of load cycles, corrosion fatigue damage assessment and remaining life prediction for welded details of the steel bridge are realized. This invention combines Bayesian network principles and the information entropy method to fuse limited indirect observation data from the service life of steel bridges with multi-source information such as moment information and interval information of the undetermined parameter C. This overcomes the limitation of traditional Bayesian methods, which can only update data based on observation points. It helps to reduce the influence of chance and cognitive uncertainty in the damage assessment of steel bridges, and achieves high prediction accuracy for corrosion fatigue damage. The prediction method of this invention is reasonable, computationally efficient, and highly scalable, making it suitable for bridge structural safety assessment and intelligent operation and maintenance. Attached Figure Description

[0082] Figure 1 This is a flowchart of the multi-source information fusion method for assessing corrosion fatigue damage of steel bridges as described in this invention.

[0083] Figure 2Diagram of the Bayesian network model for corrosion fatigue crack propagation;

[0084] Figure 2 middle:

[0085] (1) The symbols are explained in the table below:

[0086]

[0087] In the table, the geometric parameters include the weld angle θ and the weld plate thickness B;

[0088] (2) Graphical explanation:

[0089] Elliptical nodes are continuous nodes, representing continuous random variables; inverted triangle nodes are functional nodes, representing deterministic function variables; rectangular nodes are observation nodes, representing observed variables; nodes are connected by arrows, with parent nodes pointing to child nodes, representing their conditional dependencies; solid arrows represent the relationships between nodes at a certain time, while dashed arrows represent the temporal dependencies of continuous random variables between adjacent time points;

[0090] (3) Construction principle:

[0091] Based on the welding details and geometry of the rusted steel bridge Ω T and cyclic load (F T , Effective stress at the crack tip during welding under the action of ) Residual stress Stress concentration factor Effective stress intensity factor Combined stress threshold value Crack propagation material parameter C T With m T Calculate the crack growth length Δa T The parameter C is to be determined. T C can be obtained through crack propagation rate tests. After integrating parametric moments, parameter ranges, and observation point information to establish a posterior model and its constraints, information about parameter C can be obtained. T The posterior probability distribution with the highest entropy; combined with the initial crack length at the current moment. and crack growth length Δa T Obtain the crack calculation length a T The crack length is observed at the current moment. The Bayesian entropy multi-source information fusion technology was used to calibrate the undetermined parameter C of the corrosion fatigue crack propagation model, and the corrosion fatigue damage of the steel bridge was predicted based on the calibration results. Detailed Implementation

[0092] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0093] Example 1;

[0094] like Figure 1-2 This embodiment provides a method for assessing corrosion fatigue damage of steel bridges based on multi-source information fusion, including the following steps:

[0095] Step 1: Based on the effective stress intensity factor and stress threshold value of the welding crack, establish the corrosion fatigue crack propagation model as shown in equation (1.1):

[0096]

[0097] In the formula, a is the crack length, N is the number of fatigue load cycles, and ΔK eff ΔK is the effective stress intensity factor. th is the stress threshold value, m is the crack propagation material parameter, taken as 3.0; C is a parameter to be determined, which is related to the mechanical properties of the weld material and can be obtained through corrosion fatigue crack propagation rate tests on welded CT specimens;

[0098] It should be noted that the effective stress intensity factor and stress threshold value are determined according to the following method:

[0099] The residual stress distribution at the crack tip is obtained. The effective stress ratio of the crack is determined based on the maximum and minimum values ​​of the stress intensity factor. The crack opening stress ratio is determined based on the effective stress ratio. The effective stress intensity factor and stress threshold value are then obtained based on the effective stress ratio, opening stress ratio, welding angle correction parameter, and geometric parameter correction factor.

[0100] It should be noted that the effective stress ratio of the crack is calculated according to formula (1.2):

[0101]

[0102] In the formula, R eff The effective stress ratio of the crack; This represents the maximum effective stress intensity factor. This is the minimum effective stress intensity factor. and Determine according to formulas (1.3) and (1.4):

[0103]

[0104]

[0105] In the formula, K max K min These are the maximum and minimum values ​​of the stress intensity factor caused by the external load, respectively; K res For the distribution of welding residual stress, K res Determine according to formula (1.5):

[0106]

[0107] In the formula, denoted as the residual stress at the crack tip, a as the crack length, and b and l as the transverse positions of the weld corresponding to the points of maximum residual tensile and compressive stress, respectively.

[0108] It should be noted that the crack opening stress ratio is calculated according to formula (1.6):

[0109]

[0110] In the formula, U is the crack opening stress ratio; f' is the crack closure effect function, calculated according to formula (1.7):

[0111]

[0112] In the formula, A0, A1, A2, and A3 are constants of the crack closure effect function, determined according to equations (1.8) to (1.11), respectively:

[0113] A0 = (0.825 - 0.34α + 0.05α) 2 )[cos(πσ max / 2σ f )] 1 / α (1.8)

[0114] A1=(0.415-0.071α)σ max / σ f (1.9)

[0115] A2 = 1 - A0 - A1 - A3 (1.10)

[0116] A3 = 2A0 + A1 - 1 (1.11)

[0117] In the formula, σ f For flow stress, σ f =1.15(σ y +σ u ) / 2; α is the stress-strain constant, which has a value of 1 under plane stress and a value of 3 under plane strain, σ max For the maximum stress, σ y For yield strength, σ uThis represents the ultimate tensile strength.

[0118] It should be noted that the effective stress intensity factor is determined according to equation (1.12):

[0119]

[0120] In the formula, ΔK eff Δσ is the effective stress intensity factor. eff Δσ represents the effective stress range for welding. eff =Uσ max (1-R eff ), d is the pit depth, K t This represents the stress concentration factor at the tip of the pit. G(θ) is the geometric parameter correction factor, and G(θ) is the welding angle correction parameter. G(θ) and G(θ) are determined according to equations (1.13) and (1.14), respectively:

[0121]

[0122]

[0123] In the formula, q is the weld angle coefficient, q=ln[(11.584-0.0588θ) / 2.30], θ is the weld angle, and B is the thickness of the welded plate.

[0124] K t Determine according to formula (1.15):

[0125] K t =GPR[w,l,d] (1.15)

[0126] In the formula, w, l, and d represent the length, width, and depth of the erosion pit, respectively, and GPR is a Gaussian process regression model.

[0127] It should be noted that the Gaussian process regression model was obtained as follows: the maximum and minimum values ​​of the pit stress distribution under 120 different size parameters were obtained through finite element simulation, and their ratio σ was calculated respectively. max / σ0, where σ0 is the average stress of the steel wire without pitting. The pit length w, width l, and depth d are used as inputs to the GPR model, and the stress concentration factor K at the pit tip is used. t As the model output, the GPR model is trained to establish a trained GPR model for assessing corrosion fatigue damage of steel bridges. This model is then used to predict the stress concentration factor at the tip of the corrosion pit.

[0128] It should be noted that the stress threshold value is determined according to formula (1.16):

[0129]

[0130] In the formula, ΔK th This is the stress threshold value; a th a is the threshold for corrosion fatigue crack growth. th Determine according to formula (1.17):

[0131]

[0132] In the formula, b1 is the corrosion fatigue strength coefficient, b1=-1 / m; m is the material parameter for crack propagation, taken as 3.0;

[0133] Substituting equations (1.12) and (1.16) into equation (1.1) yields equation (1.18):

[0134]

[0135] Step 2: Obtain a series of direct measured data of the undetermined parameter C in the corrosion fatigue crack propagation model through corrosion fatigue crack propagation rate tests, and establish the prior distribution of the undetermined parameter C;

[0136] It should be noted that the undetermined parameter C in the corrosion fatigue crack propagation rate test is a single-point continuous random variable, and the statistical prior distribution of its directly measured data follows a normal distribution. The directly measured data of the undetermined parameter C refers to the measured value of parameter C that can be directly determined according to different corrosion fatigue crack propagation rate tests. The prior distribution of the undetermined parameter C is expressed by equation (2.1):

[0137]

[0138] In the formula, p0(lnC) is the prior distribution of the parameter lnC, and lnC T Let μ be the direct measured value of parameter lnC at time T. lnC σ lnC The parameters are lnC respectively. T The mean and standard deviation.

[0139] Step 3: Based on Step 1 and Step 2, construct a Bayesian network model for corrosion fatigue crack propagation according to the Bayesian network principle, and characterize the uncertainty relationship between variables, undetermined parameter C, and observation data in the corrosion fatigue crack propagation model.

[0140] It should be noted that the Bayesian network model for corrosion fatigue crack propagation is constructed as follows:

[0141] The effective stress intensity factor, fatigue crack growth length, and fatigue crack calculation length are determined as functional nodes; fatigue load, effective welding stress range, welding residual stress, stress concentration factor, stress threshold value, crack propagation material parameters and undetermined parameter C of the fatigue crack propagation model, initial crack size, and geometric dimensions are determined as continuous nodes; the number of fatigue load cycles and fatigue crack observation length are determined as observation nodes; the mutual physical dependencies of each node at the same time and the temporal dependencies of each node between adjacent time points are determined, ultimately forming a Bayesian network structure that considers multivariate physical relationships.

[0142] Step 4: Based on the corrosion fatigue crack propagation Bayesian network model obtained in Step 3, obtain direct measured data of the parametric moments and parameter intervals of the undetermined parameter C during the service of the steel bridge. Integrate the parametric moments and interval information to obtain the constraints of the posterior model for the undetermined parameter C. Construct the likelihood function of the undetermined parameter C based on the indirect information of crack observation points obtained during the service of the steel bridge. Integrate the prior distribution and likelihood function of the undetermined parameter C to establish the posterior model of the undetermined parameter C. Use the maximum entropy criterion to obtain the posterior model and calibrate the undetermined parameter C. The parametric moment constraints are solved by constructing a Lagrangian function; the parameter interval constraints limit the upper and lower bounds of the undetermined parameter C.

[0143] It should be noted that the moment constraint of parameter C during the service of the steel bridge is expressed by equations (4.1) and (4.2) as follows:

[0144] p1(lnC)∝p0(lnC)×exp(βf(lnC)) (4.1)

[0145] βf(lnC)=-β1lnC-β2(lnC) 2 (4.2)

[0146] In the formula, p1(lnC) is the posterior distribution of the parameters after moment constraints; β, β1, and β2 are Lagrange factors, and solving for the value of β requires satisfying the expectation constraints of the mean and variance as shown in equation (4.3):

[0147]

[0148] In the formula, E(lnC) is the mean constraint of lnC, ∑(lnC) is the variance constraint of lnC, and μ lnC Let lnC be the mean. Let lnC be the variance.

[0149] It should be noted that the interval constraint of parameter C during the service of the steel bridge is expressed by equation (4.4):

[0150] lnC∈[(lnC) - ,(lnC) + (4.4)

[0151] In the formula, (lnC) - (lnC) + These are the lower and upper limits of the interval for lnC, respectively.

[0152] It should be noted that, based on the indirect information provided by the crack observation point data, which is the crack observation length during the service of the steel bridge, the likelihood function is constructed according to equation (4.5):

[0153]

[0154] In the formula, Let lnC be the likelihood function of the parameter. σ e For model error, σ a For measurement error; a T To calculate the crack length at time T in tests with different corrosion fatigue crack propagation rates based on the welding corrosion fatigue crack propagation model. The crack length observed at time T; a T Determine according to formulas (4.6) and (4.7):

[0155]

[0156]

[0157] In the formula, Δa T The crack growth length during the time interval T-1 to T; N is the initial crack length at time T; T The number of corrosion fatigue load cycles during the time period from 0 to T, N T-1 The number of fatigue load cycles during the time period from 0 to T-1; The effective stress intensity factor at time T. This represents the stress threshold value at time T.

[0158] It should be noted that the parametric moments and parameter intervals of the undetermined parameter C during the service of the steel bridge are used as constraints for the posterior model of the undetermined parameter C. The prior distribution and likelihood function of the undetermined parameter C in the corrosion fatigue crack propagation model are also integrated to obtain the probability distribution of the posterior model of the undetermined parameter C, expressed as Equation (4.8). Equation (4.8) can be calculated by Markov Monte Carlo simulation sampling.

[0159]

[0160] In the formula, p n (lnC) is the posterior distribution of the parameter lnC;

[0161] Based on the experimental data from different corrosion fatigue crack propagation rates, Equation (4.8) is sampled and calculated. According to the maximum entropy principle, the posterior distribution with the largest entropy in Equation (4.8) can be obtained. The direct observation value of parameter C corresponding to this posterior distribution is the calibration value of parameter C.

[0162] Step 5: Substitute the calibration result of the undetermined parameter C obtained in Step 4 into the corrosion fatigue crack propagation model, predict the welding corrosion fatigue crack length at the current moment based on the number of vehicle load cycles borne by the welded details during the service of the steel bridge, and predict the corrosion fatigue life of the welded details during the service of the steel bridge based on the critical crack size.

[0163] It should be noted that the length of the weld corrosion fatigue crack at the current moment during the service of the steel bridge is predicted according to formula (5.1):

[0164]

[0165] In the formula, a T N represents the predicted length of corrosion fatigue cracks in the weld details at time T. T The number of corrosion fatigue load cycles borne by the welded details of the steel bridge during the time period from 0 to T. The calibration value for the parameter C to be determined;

[0166] According to equation (1.18), we can further obtain:

[0167]

[0168] It should be noted that the corrosion fatigue crack propagation life of the welded details of the steel bridge is predicted according to formula (5.2):

[0169]

[0170] In the formula, N f The corrosion fatigue crack propagation life of the welded details of the steel bridge is defined as the number of corrosion fatigue load cycles that the welded details of the steel bridge endure during the period from the initial crack development to the critical crack; a0 is the initial crack size; a c This is the critical crack size;

[0171] According to equation (1.18), we can further obtain:

[0172]

[0173] Among them, a c Determine according to formula (5.3):

[0174]

[0175] In the formula, KIC σ represents the fracture toughness of the material. c This is the critical stress.

[0176] The beneficial effects of this embodiment compared to the prior art are as follows: This invention discloses a multi-source information fusion method for assessing corrosion fatigue damage in steel bridges, including updating corrosion fatigue crack propagation model parameters and damage prognosis. Specifically, based on the influence mechanism of welding residual stress and crack closure on corrosion fatigue crack propagation, a corrosion fatigue crack propagation model for steel bridge welding is established; a series of direct measured data of the undetermined parameters are obtained through corrosion fatigue crack propagation rate tests, and a priori distribution of the undetermined parameter C of the corrosion fatigue crack propagation model is established; based on the Bayesian network principle, the uncertainties of variables, parameters, and observation data in the corrosion fatigue crack propagation model are characterized; considering the moment information, interval direct measured information, and indirect information of crack observation points of the undetermined parameters, the posterior calibration of the undetermined parameter C is achieved through the maximum entropy principle; based on the calibration results of the undetermined parameter C and statistical information such as the actual number of load cycles, the corrosion fatigue damage assessment and remaining life prediction of the steel bridge welding details are realized. This invention combines Bayesian network theory and the information entropy method to fuse limited indirect observation data from the service life of steel bridges with multi-source information such as moment information and interval information of the undetermined parameter C. This overcomes the limitation of traditional Bayesian methods, which can only update data based on observation points. It helps to reduce the influence of chance and cognitive uncertainty in the damage assessment of steel bridges, and achieves high prediction accuracy for corrosion fatigue damage. The prediction method of this invention is reasonable, computationally efficient, and highly scalable, and can be widely applied to bridge structural safety assessment and intelligent operation and maintenance.

[0177] The applicant further declares that while the above embodiments illustrate the implementation method of the present invention, the present invention is not limited to the above-described embodiments, meaning that the present invention does not necessarily rely on the above methods and structures for implementation. Those skilled in the art should understand that any improvements to the present invention, equivalent substitutions for the selected implementation methods, additions to steps, and selections of specific methods all fall within the protection and disclosure scope of the present invention.

[0178] This invention is not limited to the above-described embodiments. All embodiments that use similar structures and methods to achieve the purpose of this invention are within the scope of protection of this invention.

Claims

1. A method for assessing corrosion fatigue damage of steel bridges based on multi-source information fusion, characterized in that: Includes the following steps: Step 1: Based on the effective stress intensity factor and stress threshold value of the welding crack, establish the corrosion fatigue crack propagation model as shown in equation (1.1): (1.1) In the formula, a is the crack length, and N is the number of fatigue load cycles. The effective stress intensity factor, is the stress threshold value, m is the crack propagation parameter, and C is a parameter to be determined; Step 2: Obtain a series of direct measured data of the undetermined parameter C in the corrosion fatigue crack propagation model through corrosion fatigue crack propagation rate tests, and establish the prior distribution of the undetermined parameter C; Step 3: Based on Step 1 and Step 2, construct a Bayesian network model for corrosion fatigue crack propagation to characterize the uncertainties of variables, undetermined parameter C, and observed data in the corrosion fatigue crack propagation model. Step 4: Based on the corrosion fatigue crack propagation Bayesian network model obtained in Step 3, obtain the direct measured data of the parameter moments and parameter intervals of the undetermined parameter C during the service of the steel bridge. Integrate the parameter moments and interval information to obtain the constraints of the posterior model of the undetermined parameter C. Construct the likelihood function of the undetermined parameter C based on the indirect information of crack observation points obtained during the service of the steel bridge. Integrate the prior distribution and likelihood function of the undetermined parameter C to establish the posterior model of the undetermined parameter C. Use the maximum entropy criterion to obtain the posterior model and calibrate the undetermined parameter C. Step 5: Substitute the calibration result of the undetermined parameter C obtained in Step 4 into the corrosion fatigue crack propagation model, predict the corrosion fatigue crack length at the current moment based on the number of vehicle load cycles borne by the welded details during the service of the steel bridge, and predict the corrosion fatigue crack propagation life of the welded details of the steel bridge based on the critical crack size. In step one, the effective stress intensity factor is determined according to equation (1.12): (1.12) In the formula, For the effective stress range, d represents the pit depth, K t This represents the stress concentration factor at the tip of the pit. For geometric parameter correction factors, For welding angle correction parameters; and Determine according to equations (1.13) and (1.14) respectively: (1.13) (1.14) In the formula, Here, θ is the weld angle coefficient, and θ is the weld angle. For the thickness of the welding plate; K t Determine according to formula (1.15): (1.15) In the formula, w, l, and d represent the length, width, and depth of the pit, respectively, and GPR is a Gaussian process regression model; In step one, the stress threshold value is determined according to formula (1.16): (1.16) In the formula, a th The threshold for corrosion fatigue crack growth. Determine according to formula (1.17): (1.17) In the formula, b1 is the corrosion fatigue strength coefficient. ; In step two, the prior distribution of the undetermined parameter C is expressed by equation (2.1): (2.1) In the formula, Let lnC be the prior distribution of the parameter. Parameters at time T The direct measured value, , They are respectively The mean and standard deviation; In step three, the Bayesian network model for corrosion fatigue crack propagation is constructed as follows: The effective stress intensity factor, fatigue crack growth length, and fatigue crack calculation length are defined as functional nodes; fatigue load, effective welding stress range, welding residual stress, stress concentration factor, stress threshold value, crack propagation material parameters and undetermined parameter C of the fatigue crack propagation model, initial crack size, and geometric dimensions are defined as continuous nodes; the number of fatigue load cycles and fatigue crack observation length are defined as observation nodes; the mutual physical dependencies of each node at the same time and the temporal dependencies of each node between adjacent time points are determined, ultimately forming a Bayesian network structure that considers multivariate physical relationships. In step four, the moment constraint of parameter C during the service of the steel bridge is expressed by equations (4.1) and (4.2) as follows: (4.1) (4.2) In the formula, p1(lnC) is the posterior distribution of the parameters after moment constraints. Let lnC be the prior distribution of the parameter; β, , Given the Lagrange factor, solve for β. , The values ​​must satisfy the expected constraints of mean and variance as shown in equation (4.3): (4.3) In the formula, For the mean constraint of lnC, For the variance constraint of lnC, Let lnC be the mean. Let lnC be the variance; The interval constraint of parameter C during the service of the steel bridge is expressed by equation (4.4): (4.4) In the formula, , These are the lower and upper limits of the interval lnC, respectively; In step four, based on the indirect information provided by the crack observation data obtained during the service of the steel bridge, the likelihood function is constructed according to equation (4.5): (4.5) In the formula, Let lnC be the likelihood function of the parameter. , σ e For model error, σ a For measurement error; To calculate the crack length at time T in tests with different corrosion fatigue crack propagation rates based on the corrosion fatigue crack propagation model. The crack length observed at time T; Determine according to formulas (4.6) and (4.7): (4.6) (4.7) In the formula, The crack growth length during the time period T-1 to T; Let T be the initial length of the crack. ; The number of corrosion fatigue load cycles during the time period from 0 to T. The number of fatigue load cycles within the time period from 0 to T-1; The effective stress intensity factor at time T. This represents the stress threshold value at time T.

2. The method for assessing corrosion fatigue damage of steel bridges based on multi-source information fusion according to claim 1, characterized in that: In step four, the prior distribution and likelihood function of the undetermined parameter C in the corrosion fatigue crack propagation model are combined to obtain the probability distribution of the posterior model of the undetermined parameter C, expressed by equation (4.8): (4.8) In the formula, Let lnC be the posterior distribution of the parameter. Let lnC be the prior distribution of the parameter. Let lnC be the likelihood function of the parameter.

3. The multi-source information fusion method for assessing corrosion fatigue damage of steel bridges according to any one of claims 1-2, characterized in that: In step five, the length of weld corrosion fatigue cracks at the current moment during the service of the steel bridge is predicted according to formula (5.1): (5.1) In the formula, The predicted length of welding corrosion fatigue crack at time T. The number of corrosion fatigue load cycles borne by the welded details of the steel bridge during the time period from 0 to T. The calibration value for parameter C to be determined.

4. The method for assessing corrosion fatigue damage of steel bridges based on multi-source information fusion according to claim 3, characterized in that: In step five, the corrosion fatigue crack propagation life of the steel bridge weld details is predicted according to formula (5.2): (5.2) In the formula, For the corrosion fatigue crack propagation life of the steel bridge weld details, a0 is the initial crack size; a c a is the critical crack size. c Determine according to formula (5.3): (5.3) In the formula, K IC σ represents the fracture toughness of the material. c This is the critical stress.

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