CN117150863A - Multi-source information fusion steel bridge corrosion fatigue damage assessment method - Google Patents
Multi-source information fusion steel bridge corrosion fatigue damage assessment method Download PDFInfo
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Abstract
The invention discloses a multi-source information fusion steel bridge corrosion fatigue damage assessment method, which comprises the following steps: establishing a corrosion steel bridge welding fatigue crack propagation model containing undetermined parameters; obtaining measured data of undetermined parameters through a corrosion fatigue crack propagation test, and establishing prior distribution of the parameters; establishing a corrosion fatigue crack propagation Bayesian network model to characterize uncertainty relation among variables, undetermined parameters and observed data; fusion of multi-source information such as parameter moment, interval and observation point information, and the posterior calibration of the parameter is realized through a maximum entropy criterion; based on the calibrated parameters, the corrosion fatigue damage assessment of the steel bridge welding detail and the structure residual life prediction are realized. The invention fuses the limited indirect observation information with the multisource information in the service process of the steel bridge, and reduces the influence of cognitive uncertainty in the damage evaluation process of the steel bridge. The method is reasonable, high in prediction accuracy and high in calculation efficiency, and is suitable for bridge structure safety evaluation and intelligent operation and maintenance.
Description
Technical Field
The invention relates to the field of safety evaluation of service bridges, in particular to a method for evaluating corrosion fatigue damage of a steel bridge by multi-source information fusion.
Background
With the continuous increase of the axle weight and traffic volume of vehicles, fatigue damage is becoming one of the key problems affecting the service safety of steel bridges. The welding detail is a weak structure of the steel bridge, and the steel bridge continuously bears repeated vehicle load in the service process. Meanwhile, due to the influence of welding quality, the material has the defects of oxidization, impurities, non-uniformity and the like. The defect part often has stress concentration, and crack initiation is easy to be induced under the action of fatigue load. In addition, in the service process of the steel bridge, the fatigue fracture process of welding details can be further accelerated by long-term environmental corrosion, and the residual service life of the structure is obviously reduced. The existing steel bridge fatigue damage assessment method mainly considers the influence factors such as stress ratio, stress amplitude, loading frequency and the like, and rarely considers the influence of concentrated coupling of welding residual stress and etching pit stress, so that the development of detailed modeling research on welding detail crack expansion under corrosion fatigue coupling is needed.
In addition, the corrosion fatigue crack growth rate and the path have great randomness, and a general theoretical physical model of the whole structure service process is not established at present. The service structure key monitoring information can provide the truest information for the subsequent service life prediction. If the limited actual measurement information can be combined with the prior information, the subjective uncertainty influence can be reduced, and the prediction accuracy of the corrosion fatigue damage of the steel bridge can be improved. The Bayesian network can be used for representing complex uncertainty of model parameters and can be used for fusing multi-source information such as experimental data, physical models, monitoring data and the like. However, the traditional Bayesian method is mainly combined with the data of the observation points to update, so that constraint information such as posterior moment and interval of the parameters of the test materials are difficult to integrate, and the posterior moment and interval information of the parameters of the damage characterization of the materials are very beneficial to the diagnosis of the fatigue damage of the steel bridge. The information entropy method can effectively process various information such as point, interval and moment estimation through additional constraint, so that how to combine the Bayesian information entropy data fusion theory to construct a steel bridge corrosion fatigue damage inversion and update framework becomes a technical problem to be solved urgently.
Disclosure of Invention
The invention aims to provide a multi-source information fusion steel bridge corrosion fatigue damage assessment method which effectively solves the technical problems.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the invention discloses a multi-source information fusion steel bridge corrosion fatigue damage assessment method, which comprises the following steps:
step one: according to the effective stress intensity factor and the stress threshold value of the welding crack, a corrosion fatigue crack propagation model is established as shown in the formula (1.1):
wherein a is the crack length, N is the cycle of fatigue load, and DeltaK eff As an effective stress intensity factor, ΔK th Taking the stress threshold value, m is a crack propagation material parameter, and taking 3.0; c is a parameter to be determined, which is related to the mechanical property of the welding line material and can be obtained through a corrosion fatigue crack propagation rate test of a welding CT test piece;
step two: acquiring a series of direct actual measurement data of the undetermined parameter C in the corrosion fatigue crack propagation model through a corrosion fatigue crack propagation rate test, and establishing prior distribution of the undetermined parameter C;
step three: constructing a corrosion fatigue crack propagation Bayesian network model according to the Bayesian network principle, and characterizing the uncertainty relation among variables, undetermined parameters C and observed data in the corrosion fatigue crack propagation model;
step four: based on the corrosion fatigue crack propagation Bayesian network model obtained in the step three, obtaining parameter moment and parameter interval direct actual measurement data of the undetermined parameter C in the service process of the steel bridge, fusing parameter moment and interval information to obtain constraint conditions of a posterior model of the undetermined parameter C, constructing a likelihood function of the undetermined parameter C according to crack observation point indirect information obtained in the service process of the steel bridge, fusing prior distribution and likelihood function of the undetermined parameter C to establish the posterior model of the undetermined parameter C, and obtaining the posterior model according to a maximum entropy criterion to calibrate the undetermined parameter C; the parameter moment constraint is solved by constructing a Lagrangian function; the parameter interval constraint limits the upper and lower limit intervals of the undetermined parameter C;
step five: substituting the calibration result of the undetermined parameter C obtained in the step four into a corrosion fatigue crack extension model, predicting the corrosion fatigue crack length at the current moment according to the number of vehicle load cycles born by welding details in the service process of the steel bridge, and predicting the corrosion fatigue crack extension life of the welding details of the steel bridge according to the critical crack size.
Further, in the first step, the effective stress intensity factor and the stress threshold value are determined according to the following method:
and obtaining the distribution of the welding residual stress at the tip of the crack, determining the effective stress ratio of the crack according to the maximum value and the minimum value of the stress intensity factor, determining the crack opening stress ratio according to the effective stress ratio, and obtaining the effective stress intensity factor and the stress threshold value according to the effective stress ratio, the opening stress ratio, the welding angle correction parameter and the geometric parameter correction factor.
Further, the crack effective force ratio is calculated according to formula (1.2):
wherein R is eff Effective force ratio for cracks;is the maximum value of the effective stress intensity factor; />Is the effective stress intensity factor minimum, < ->And->Determined according to the formulas (1.3), (1.4):
wherein K is max 、K min Respectively the maximum and minimum values of stress intensity factors caused by external load; k (K) res K for welding residual stress distribution res Determined according to formula (1.5):
in the method, in the process of the invention,and (3) welding residual stress for the crack tip, wherein a is the crack length, and b and l are the transverse positions of the welding seam corresponding to the maximum points of the residual tensile stress and the compressive stress respectively.
Further, the crack opening stress ratio is calculated according to formula (1.6):
wherein U is the crack opening stress ratio; f 'is a crack closure effect function, f' being calculated according to formula (1.7):
wherein A is 0 、A 1 、A 2 、A 3 The constants for the crack closure effect function are determined according to formulas (1.8) to (1.11), respectively:
A 0 ＝(0.825-0.34α+0.05α 2 )[cos(πσ max /2σ f )] 1/α (1.8)
A 1 ＝(0.415-0.071α)σ max /σ f (1.9)
A 2 ＝1-A 0 -A 1 -A 3 (1.10)
A 3 ＝2A 0 +A 1 -1 (1.11)
in sigma f For flow stress, sigma f ＝1.15(σ y +σ u ) 2; alpha is a stress-strain constant, and has a value of 1 in a plane stress state and a value of 3 and sigma in a plane strain state max For maximum stress, sigma y Is of yield strength, sigma u Is ultimate tensile strength.
Further, the effective stress intensity factor is determined according to formula (1.12):
in the formula, deltaK eff As an effective stress intensity factor, Δσ eff For welding effective stress range Δσ eff ＝Uσ max (1-R eff ) D is the depth of the etching pit, K t To etch pit tip stress concentration coefficient,g (theta) is a welding angle correction parameter; />And G (θ) are respectively determined according to formulas (1.13), (1.14):
where q is the weld angle coefficient, q=ln [ (11.584-0.0588 θ)/2.30 ], θ is the weld angle, and B is the weld plate thickness.
K t Determined according to formula (1.15):
K t ＝GPR[w,l,d] (1.15)
wherein w, l and d are the length, width and depth of the etching pit respectively, and GPR is a Gaussian process regression model.
Further, the Gaussian process regression model is obtained as follows: obtaining the maximum value and the minimum value of the stress distribution of the etching pit under at least 40 groups of parameters with different sizes through finite element simulation, and respectively calculating the ratio sigma max /σ 0 ，σ 0 The average stress of the steel wire without etching pits is input by taking the length w, the width l and the depth d of the etching pits as GPR models, and the stress concentration coefficient K of the tip of the etching pits t And training the GPR model as model output so as to establish a trained GPR model for evaluating corrosion fatigue damage of the steel bridge, and predicting the stress concentration coefficient of the etching pit tip by adopting the model.
Further, the stress threshold is determined according to equation (1.16):
in the formula, deltaK th Is a stress threshold value; a, a th For corrosion fatigue crack growth threshold, a th Determined according to formula (1.17):
wherein b is 1 To corrosion fatigue strength coefficient b 1 -1/m; m is crack propagation materialParameters, take 3.0.
Further, in the second step, the undetermined parameter C in the corrosion fatigue crack growth rate test is a single-point continuous random variable, and the statistical prior distribution of the direct actually measured data is subjected to normal distribution, that is, the prior distribution of the undetermined parameter C is expressed as follows in the formula (2.1):
wherein p is 0 (lnC) is an a priori distribution of the parameters lnC, lnC T As the direct measured value of the T moment parameter lnC, mu lnC 、σ lnC Respectively parameters lnC T Mean and standard deviation of (a).
Further, in the third step, the corrosion fatigue crack propagation Bayesian network model is constructed according to the following method:
determining an effective stress intensity factor, a fatigue crack growth length and a fatigue crack calculation length as functional nodes; the fatigue load, the welding effective stress range, the welding residual stress, the stress concentration coefficient, the stress threshold value, the crack propagation material parameter and undetermined parameter C of the fatigue crack propagation model, the initial crack size and the geometric size are determined to be continuous nodes; determining the fatigue load cycle times and the fatigue crack observation length as an observation node; and determining the mutual physical dependency relationship of all nodes in the same moment and the time dependency relationship of all nodes in adjacent moments, and finally forming the Bayesian network structure considering the multivariable physical relationship.
Further, in the fourth step, the moment constraint of the parameter C in the service process of the steel bridge is expressed as following formulas (4.1) and (4.2):
p 1 (lnC)∝p 0 (lnC)×exp(βf(lnC)) (4.1)
βf(lnC)＝-β 1 lnC-β 2 (lnC) 2 (4.2)
wherein p is 1 (lnC) is a post-moment-constrained parametric posterior distribution; beta, beta 1 、β 2 To solve for the Lagrangian factor, the beta value needs to satisfy the mean and the square as in equation (4.3)Poor desired constraint:
where E (lnC) is the mean constraint of lnC, sigma (lnC) is the variance constraint of lnC, μ lnC Is the average value of lnC and is equal to,is lnC.
Further, in the fourth step, the interval constraint of the parameter C in the service process of the steel bridge is expressed as formula (4.4):
lnC∈[(lnC) - ,(lnC) + ] (4.4)
in (lnC) - 、(lnC) + A lower and an upper interval limit of lnC, respectively.
In the fourth step, according to indirect information provided by crack observation point data obtained in the service process of the steel bridge, the indirect information is crack observation length in the service process of the steel bridge, and a likelihood function is constructed according to a formula (4.5):
in the method, in the process of the invention,is a likelihood function of the parameter lnC, +.>σ e For model error, sigma a Is the measurement error; a, a T For calculating the crack calculation length at time T in the test of different corrosion fatigue crack growth rates according to the welding corrosion fatigue crack growth model +.>Observing the length of the crack at the moment T; a, a T Determined according to formulas (4.6), (4.7):
wherein Δa T Is the crack growth length in the time period of T-1 to T;the initial length of the crack at the moment T; n (N) T Is the cycle of corrosion fatigue load in the period of 0 to T, N T-1 The fatigue load is cycled for a cycle in the time period of 0-T-1; />Is the effective stress intensity factor at the moment T +.>The stress threshold value at the moment T.
Further, in the fourth step, the parameter moment and the parameter interval information of the undetermined parameter C in the service process of the steel bridge are fused to serve as constraint conditions of a posterior model of the undetermined parameter C, the prior distribution and likelihood functions of the undetermined parameter C of the corrosion fatigue crack propagation model are fused to obtain probability distribution of the posterior model of the undetermined parameter C, the probability distribution is expressed according to a formula (4.8), and the formula (4.8) can be calculated through simulation sampling by a Markov Monte Carlo method:
wherein p is n (lnC) is the posterior distribution of the parameter lnC.
In the fifth step, the length of the welding detail corrosion fatigue crack at the current moment in the service process of the steel bridge is predicted according to (5.1):
wherein a is T Predicting the length of the welding corrosion fatigue crack at the moment T and N T The corrosion fatigue load born by the welding detail of the steel bridge in the time period of 0-T is cycled for a round,is the calibrated value of the pending parameter C.
Further, in the fifth step, the corrosion fatigue crack growth life of the steel bridge welding detail is predicted according to the formula (5.2):
wherein N is f For the corrosion fatigue crack propagation life of the steel bridge welding detail, i.e. the cycle of the corrosion fatigue load born by the steel bridge welding detail during the period of the corrosion fatigue crack from the initial crack to the critical crack, a 0 Is the initial crack size; a, a c A is critical crack size, a c Determined according to formula (5.3):
wherein K is IC Fracture toughness of the material; sigma (sigma) c Is critical stress.
Compared with the prior art, the invention has the beneficial effects that:
the invention discloses a multi-source information fusion steel bridge corrosion fatigue damage assessment method, which comprises the steps of updating corrosion fatigue line expansion model parameters and prognosis of damage, namely: according to the influence mechanism of welding residual stress and crack closure on corrosion fatigue crack growth, a steel bridge corrosion fatigue crack growth model is established; obtaining a series of direct measured data of undetermined parameters through a corrosion fatigue crack propagation rate test, and establishing prior distribution of undetermined parameters C of a corrosion fatigue crack propagation model; based on the Bayesian network principle, the uncertainties such as variables, parameters and observation data in the corrosion fatigue crack propagation model are characterized; considering moment information, interval direct actual measurement information and crack observation point indirect information of the undetermined parameter, and realizing posterior calibration of the undetermined parameter C through a maximum entropy principle; based on the calibration result of the undetermined parameter C, the actual load cycle times and other statistical information, the corrosion fatigue damage assessment and the residual life prediction of the steel bridge welding detail are realized. According to the invention, the Bayesian network principle and the information entropy method are combined, the limited indirect observation data information in the service process of the steel bridge is fused with the multisource information such as the moment information and the interval information of the undetermined parameter C, the defect that the traditional Bayesian can only be updated by combining with the observation point data is overcome, the influence of accidental and cognitive uncertainty in the damage evaluation process of the steel bridge is reduced, and the prediction precision of corrosion fatigue damage of the steel bridge is higher; the prediction method is reasonable, high in calculation efficiency and strong in popularization, and is suitable for bridge structure safety evaluation and intelligent operation and maintenance.
Drawings
FIG. 1 is a flow chart of a method for evaluating corrosion fatigue damage of a steel bridge with multisource information fusion.
FIG. 2 is a diagram of a Bayesian network model for corrosion fatigue crack propagation;
in fig. 2:
(1) The symbols are explained in the following table:
in the table, the geometrical parameters include the weld angle θ and the weld plate thickness B;
(2) Graphic interpretation:
the elliptic nodes are continuous nodes and represent continuous random variables; the inverted triangle node is a functional node and represents deterministic function variables; rectangular nodes are observation nodes and represent observation variables; the nodes are connected through arrow lines, and the parent node points to the child node to represent the condition dependency relationship; the solid arrow indicates the interrelation of each node at a certain moment, and the dotted arrow indicates the time dependency of continuous random variables between adjacent moments;
(3) The construction principle is as follows:
according to the geometric dimension omega of the welding detail of the rusted steel bridge T Cyclic loading (F) T 、) Effective stress of crack tip welding under action +.>Residual stress->Stress concentration coefficient->Effective stress intensity factor->Combined stress thresholdCrack propagation Material parameter C T And m is equal to T Calculation of crack growth Length Δa T Wherein the parameter C is pending T The method can be obtained through a crack propagation rate test, and a posterior model and constraint conditions thereof are established by fusing parameter moment, parameter interval and observation point information to obtain a related parameter C T The posterior probability distribution with the greatest entropy; combined with the initial length of the crack at the current moment->And crack growth length Δa T Obtaining the calculated crack length a T Length of crack observation by the current moment +.>And (3) adopting a Bayesian entropy multisource information fusion technology to calibrate the undetermined parameter C of the corrosion fatigue crack expansion model, and predicting the corrosion fatigue damage of the steel bridge according to a calibration result.
Detailed Description
The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the embodiments and the accompanying drawings, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1;
1-2, the embodiment provides a method for evaluating corrosion fatigue damage of a steel bridge by multi-source information fusion, which comprises the following steps:
step one: according to the effective stress intensity factor and the stress threshold value of the welding crack, a corrosion fatigue crack propagation model is established as shown in the formula (1.1):
wherein a is the crack length, N is the cycle of fatigue load, and DeltaK eff As an effective stress intensity factor, ΔK th Taking the stress threshold value, m is a crack propagation material parameter, and taking 3.0; c is a parameter to be determined, which is related to the mechanical property of the welding line material and can be obtained through a corrosion fatigue crack propagation rate test of a welding CT test piece;
the effective stress intensity factor and the stress threshold value are determined according to the following method:
and obtaining the distribution of the welding residual stress at the tip of the crack, determining the effective stress ratio of the crack according to the maximum value and the minimum value of the stress intensity factor, determining the crack opening stress ratio according to the effective stress ratio, and obtaining the effective stress intensity factor and the stress threshold value according to the effective stress ratio, the opening stress ratio, the welding angle correction parameter and the geometric parameter correction factor.
The crack effective force ratio was calculated according to formula (1.2):
wherein R is eff Effective force ratio for cracks;is the maximum value of the effective stress intensity factor; />Is the effective stress intensity factor minimum, < ->And->Determined according to the formulas (1.3), (1.4):
wherein K is max 、K min Respectively the maximum and minimum values of stress intensity factors caused by external load; k (K) res K for welding residual stress distribution res Determined according to formula (1.5):
in the method, in the process of the invention,and (3) welding residual stress for the crack tip, wherein a is the crack length, and b and l are the transverse positions of the welding seam corresponding to the maximum points of the residual tensile stress and the compressive stress respectively.
The crack opening stress ratio was calculated according to formula (1.6):
wherein U is the crack opening stress ratio; f' is a crack closure effect function calculated according to equation (1.7):
wherein A is 0 、A 1 、A 2 、A 3 The constants for the crack closure effect function are determined according to formulas (1.8) to (1.11), respectively:
A 0 ＝(0.825-0.34α+0.05α 2 )[cos(πσ max /2σ f )] 1/α (1.8)
A 1 ＝(0.415-0.071α)σ max /σ f (1.9)
A 2 ＝1-A 0 -A 1 -A 3 (1.10)
A 3 ＝2A 0 +A 1 -1 (1.11)
in sigma f For flow stress, sigma f ＝1.15(σ y +σ u ) 2; alpha is a stress-strain constant, and has a value of 1 in a plane stress state and a value of 3 and sigma in a plane strain state max For maximum stress, sigma y Is of yield strength, sigma u Is ultimate tensile strength.
The effective stress intensity factor is determined according to formula (1.12):
in the formula, deltaK eff As an effective stress intensity factor, Δσ eff For welding effective stress range Δσ eff ＝Uσ max (1-R eff ) D is the depth of the etching pit, K t To etch pit tip stress concentration coefficient,g (theta) is a welding angle correction parameter; />And G (θ) are respectively determined according to formulas (1.13), (1.14):
where q is the weld angle coefficient, q=ln [ (11.584-0.0588 θ)/2.30 ], θ is the weld angle, and B is the weld plate thickness.
K t Determined according to formula (1.15):
K t ＝GPR[w,l,d] (1.15)
wherein w, l and d are the length, width and depth of the etching pit respectively, and GPR is a Gaussian process regression model.
It should be noted that, the gaussian process regression model is obtained by the following method: obtaining the maximum value and the minimum value of the stress distribution of the etching pit under 120 groups of parameters with different sizes through finite element simulation, and respectively calculating the ratio sigma max /σ 0 ，σ 0 The average stress of the steel wire without etching pits is input by taking the length w, the width l and the depth d of the etching pits as GPR models, and the stress concentration coefficient K of the tip of the etching pits t And training the GPR model as model output so as to establish a trained GPR model for evaluating corrosion fatigue damage of the steel bridge, and predicting the stress concentration coefficient of the etching pit tip by adopting the model.
The stress threshold value is determined according to the formula (1.16):
in the formula, deltaK th Is a stress threshold value; a, a th For corrosion fatigue crack growth threshold, a th Determined according to formula (1.17):
wherein b is 1 To corrosion fatigue strength coefficient b 1 -1/m; m is a crack propagation material parameter, and 3.0 is taken;
substitution of formulas (1.12), (1.16) into formula (1.1) can give formula (1.18):
step two: acquiring a series of direct actual measurement data of the undetermined parameter C in the corrosion fatigue crack propagation model through a corrosion fatigue crack propagation rate test, and establishing prior distribution of the undetermined parameter C;
it should be noted that, the undetermined parameter C in the corrosion fatigue crack growth rate test is a single-point continuous random variable, the statistical prior distribution of the direct actually measured data is compliant with normal distribution, the direct actually measured data of the undetermined parameter C refers to the actually measured value of the parameter C which can be directly measured according to different corrosion fatigue crack growth rate tests, and the prior distribution of the undetermined parameter C is expressed as follows in the formula (2.1):
wherein p is 0 (lnC) is an a priori distribution of the parameters lnC, lnC T As the direct measured value of the T moment parameter lnC, mu lnC 、σ lnC Respectively parameters lnC T Mean and standard deviation of (a).
Step three: constructing a corrosion fatigue crack propagation Bayesian network model according to the Bayesian network principle, and characterizing the uncertainty relation among variables, undetermined parameters C and observed data in the corrosion fatigue crack propagation model;
the corrosion fatigue crack propagation Bayesian network model is constructed according to the following method:
determining an effective stress intensity factor, a fatigue crack growth length and a fatigue crack calculation length as functional nodes; the fatigue load, the welding effective stress range, the welding residual stress, the stress concentration coefficient, the stress threshold value, the crack propagation material parameter and undetermined parameter C of the fatigue crack propagation model, the initial crack size and the geometric size are determined to be continuous nodes; determining the fatigue load cycle times and the fatigue crack observation length as an observation node; and determining the mutual physical dependency relationship of all nodes in the same moment and the time dependency relationship of all nodes in adjacent moments, and finally forming the Bayesian network structure considering the multivariable physical relationship.
Step four: based on the corrosion fatigue crack propagation Bayesian network model obtained in the step three, obtaining the parameter moment and the direct actual measurement data of a parameter interval of the undetermined parameter C in the service process of the steel bridge, fusing the parameter moment and the interval information to obtain the constraint condition of a posterior model of the undetermined parameter C, constructing a likelihood function of the undetermined parameter C according to the crack observation point indirect information obtained in the service process of the steel bridge, fusing the prior distribution and the likelihood function of the undetermined parameter C to establish the posterior model of the undetermined parameter C, and obtaining the posterior model according to the maximum entropy criterion to calibrate the undetermined parameter C; the parameter moment constraint is solved by constructing a Lagrangian function; the parameter interval constraint limits the upper and lower limit intervals of the undetermined parameter C;
note that, the moment constraint of the parameter C in the service process of the steel bridge is expressed as following formulas (4.1), (4.2):
p 1 (lnC)∝p 0 (lnC)×exp(βf(lnC)) (4.1)
βf(lnC)＝-β 1 lnC-β 2 (lnC) 2 (4.2)
wherein p is 1 (lnC) is a post-moment-constrained parametric posterior distribution; beta, beta 1 、β 2 To solve for the Lagrangian factor, the beta value needs to satisfy the desired constraints of mean and variance as in equation (4.3):
where E (lnC) is the mean constraint of lnC, sigma (lnC) is the variance constraint of lnC, μ lnC Is the average value of lnC and is equal to,is lnC.
It should be noted that, the interval constraint of the parameter C in the service process of the steel bridge is expressed as formula (4.4):
lnC∈[(lnC) - ,(lnC) + ] (4.4)
in (lnC) - 、(lnC) + A lower and an upper interval limit of lnC, respectively.
The method is characterized in that according to indirect information provided by crack observation point data, the indirect information is crack observation length in the service process of the steel bridge, and a likelihood function is constructed according to a formula (4.5):
in the method, in the process of the invention,is a likelihood function of the parameter lnC, +.>σ e For model error, sigma a Is the measurement error; a, a T For calculating the crack length at time T in the test of different corrosion fatigue crack growth rates according to the welding corrosion fatigue crack growth model +.>Observing the length of the crack at the moment T; a, a T Determined according to formulas (4.6), (4.7):
wherein Δa T Is the crack growth length in the time period of T-1 to T;the initial length of the crack at the moment T; n (N) T Is the cycle of corrosion fatigue load in the period of 0 to T, N T-1 The fatigue load is cycled for a cycle in the time period of 0-T-1; />Is the effective stress intensity factor at the moment T +.>The stress threshold value at the moment T.
It should be noted that, the parameter moment and parameter interval information of the undetermined parameter C in the service process of the steel bridge are fused as constraint conditions of the posterior model of the undetermined parameter C, the prior distribution and likelihood function of the undetermined parameter C of the corrosion fatigue crack propagation model are fused, the probability distribution of the posterior model of the undetermined parameter C is obtained, the probability distribution is expressed according to the formula (4.8), and the formula (4.8) can be calculated by simulating sampling through a markov monte carlo method:
wherein p is n (lnC) is the posterior distribution of parameter lnC;
according to the test data of different corrosion fatigue crack growth rate tests, sampling and calculating the formula (4.8), and obtaining the posterior distribution with the maximum entropy in the formula (4.8) according to the maximum entropy principle, wherein the direct observation of the parameter C corresponding to the posterior distributionThe value is the calibrated value of the parameter C
Step five: substituting the calibration result of the undetermined parameter C obtained in the step four into a corrosion fatigue crack propagation model, predicting the length of a welding corrosion fatigue crack at the current moment according to the number of vehicle load cycles born by welding details in the service process of the steel bridge, and predicting the corrosion fatigue life of the welding details in the service process of the steel bridge according to the critical crack size;
it should be noted that, the length of the welding detail corrosion fatigue crack at the current moment in the service process of the steel bridge is predicted according to (5.1):
wherein a is T Predicting length of corrosion fatigue crack for welding detail at moment T, N T The corrosion fatigue load born by the welding detail of the steel bridge in the time period of 0-T is cycled for a round,a calibration value for the parameter C to be determined;
further obtainable according to formula (1.18):
it should be noted that the corrosion fatigue crack growth life of the steel bridge welding detail is predicted according to the formula (5.2):
wherein N is f For corrosion fatigue crack propagation life of steel bridge welding details, i.e. cycle of corrosion fatigue load to which the steel bridge welding details are subjected during the period of the corrosion fatigue crack developing from the initial crack to the critical crackCarrying out cycle times; a, a 0 Is the initial crack size; a, a c Is critical crack size;
further obtainable according to formula (1.18):
wherein a is c Determined according to formula (5.3):
wherein K is IC Fracture toughness of the material; sigma (sigma) c Is critical stress.
The beneficial effects of this embodiment different from prior art are: the invention discloses a multi-source information fusion steel bridge corrosion fatigue damage assessment method, which comprises the steps of updating corrosion fatigue line expansion model parameters and prognosis of damage, namely: according to the influence mechanism of welding residual stress and crack closure on corrosion fatigue crack growth, a steel bridge welding corrosion fatigue crack growth model is established; obtaining a series of direct measured data of undetermined parameters through a corrosion fatigue crack propagation rate test, and establishing prior distribution of undetermined parameters C of a corrosion fatigue crack propagation model; based on the Bayesian network principle, the uncertainties such as variables, parameters and observation data in the corrosion fatigue crack propagation model are characterized; considering moment information, interval direct actual measurement information and crack observation point indirect information of the undetermined parameter, and realizing posterior calibration of the undetermined parameter C through a maximum entropy principle; based on the calibration result of the undetermined parameter C, the actual load cycle times and other statistical information, the corrosion fatigue damage assessment and the residual life prediction of the steel bridge welding detail are realized. According to the invention, a Bayesian network theory and an information entropy method are combined, and limited indirect observation data information in the service process of the steel bridge is fused with multisource information such as moment information and interval information of undetermined parameters C, so that the defect that the traditional Bayesian can only be updated by combining with observation point data is overcome, the influence of accidental and cognitive uncertainties in the damage evaluation process of the steel bridge is reduced, and the prediction precision of corrosion fatigue damage of the steel bridge is higher; the prediction method is reasonable, high in calculation efficiency and strong in popularization, and can be widely applied to bridge structure safety evaluation and intelligent operation and maintenance.
The applicant has further stated that the present invention is illustrated by the above examples as a method of implementing the invention, but the invention is not limited to the above embodiments, i.e. it is not meant to imply that the invention must be implemented in dependence on the above methods and structures. It should be apparent to those skilled in the art that any modification of the present invention, equivalent substitutions for the implementation method selected by the present invention, addition of steps, selection of specific modes, etc., fall within the scope of the present invention and the scope of the disclosure.
The present invention is not limited to the above embodiments, and all embodiments adopting a structure similar to the present invention and a method thereof to achieve the object of the present invention are within the scope of the present invention.
Claims (10)
1. The method for evaluating corrosion fatigue damage of the steel bridge by multi-source information fusion is characterized by comprising the following steps of: the method comprises the following steps:
step one: according to the effective stress intensity factor and the stress threshold value of the welding crack, a corrosion fatigue crack propagation model is established as shown in the formula (1.1):
wherein a is the crack length, N is the cycle of fatigue load, and DeltaK eff As an effective stress intensity factor, ΔK th The stress threshold value is represented by m, the crack propagation parameter is represented by m, and the undetermined parameter is represented by C;
step two: acquiring a series of direct actual measurement data of the undetermined parameter C in the corrosion fatigue crack propagation model through a corrosion fatigue crack propagation rate test, and establishing prior distribution of the undetermined parameter C;
step three: constructing a corrosion fatigue crack propagation Bayesian network model according to the first step and the second step, and characterizing the uncertainty relation among variables, undetermined parameters C and observed data in the corrosion fatigue crack propagation model;
step four: based on the corrosion fatigue crack propagation Bayesian network model obtained in the step three, obtaining parameter moment and parameter interval direct actual measurement data of the undetermined parameter C in the service process of the steel bridge, fusing parameter moment and interval information to obtain constraint conditions of a posterior model of the undetermined parameter C, constructing a likelihood function of the undetermined parameter C according to crack observation point indirect information obtained in the service process of the steel bridge, fusing prior distribution and likelihood function of the undetermined parameter C to establish the posterior model of the undetermined parameter C, and obtaining the posterior model according to a maximum entropy criterion to calibrate the undetermined parameter C;
step five: substituting the calibration result of the undetermined parameter C obtained in the step four into a corrosion fatigue crack extension model, predicting the corrosion fatigue crack length at the current moment according to the number of vehicle load cycles born by welding details in the service process of the steel bridge, and predicting the corrosion fatigue crack extension life of the welding details of the steel bridge according to the critical crack size.
2. The multi-source information fusion steel bridge corrosion fatigue damage assessment method according to claim 1, wherein the method is characterized by comprising the following steps: the effective stress intensity factor is determined according to formula (1.12):
in the formula delta sigma eff For effective stress range, Δσ eff ＝Uσ max (1-R eff ) The method comprises the steps of carrying out a first treatment on the surface of the d is the depth of the etching pit, K t To etch pit tip stress concentration coefficient,g (theta) is a welding angle correction parameter;
and G (θ) are respectively determined according to formulas (1.13), (1.14):
wherein q is a weld angle coefficient, θ is a weld angle, and B is a weld plate thickness;
K t determined according to formula (1.15):
K t ＝GPR[w,l,d] (1.15)
wherein w, l and d are the length, width and depth of the etching pit respectively, and GPR is a Gaussian process regression model.
3. The multi-source information fusion steel bridge corrosion fatigue damage assessment method according to claim 2, wherein the method is characterized by comprising the following steps: the stress threshold is determined according to equation (1.16):
wherein a is th For corrosion fatigue crack growth threshold, a th Determined according to formula (1.17):
wherein b is 1 To corrosion fatigue strength coefficient b 1 ＝-1/m。
4. The multi-source information fusion steel bridge corrosion fatigue damage assessment method according to claim 1, wherein the method is characterized by comprising the following steps: in step two, the a priori distribution of the undetermined parameter C is expressed as in equation (2.1):
wherein p is 0 (lnC) is an a priori distribution of the parameters lnC, lnC T As the direct measured value of the T moment parameter lnC, mu lnC 、σ lnC lnC respectively T Mean and standard deviation of (a).
5. The multi-source information fusion steel bridge corrosion fatigue damage assessment method according to claim 4, wherein the method is characterized by comprising the following steps: in the third step, a corrosion fatigue crack propagation Bayesian network model is constructed according to the following method:
determining an effective stress intensity factor, a fatigue crack growth length and a fatigue crack calculation length as functional nodes; the fatigue load, the welding effective stress range, the welding residual stress, the stress concentration coefficient, the stress threshold value, the crack propagation material parameter and undetermined parameter C of the fatigue crack propagation model, the initial crack size and the geometric size are determined to be continuous nodes; determining the fatigue load cycle times and the fatigue crack observation length as an observation node; and determining the mutual physical dependency relationship of all nodes in the same moment and the time dependency relationship of all nodes in adjacent moments, and finally forming the Bayesian network structure considering the multivariable physical relationship.
6. The multi-source information fusion steel bridge corrosion fatigue damage assessment method according to claim 1, wherein the method is characterized by comprising the following steps: in the fourth step, the moment constraint of the parameter C in the service process of the steel bridge is expressed as the following formulas (4.1) and (4.2):
p 1 (lnC)∝p 0 (lnC)×exp(βf(lnC)) (4.1)
βf(lnC)＝-β 1 lnC-β 2 (lnC) 2 (4.2)
wherein p is 1 (lnC) is a post-moment-constrained parameter posterior distribution, p 0 (lnC) is an a priori distribution of the parameters lnC; beta, beta 1 、β 2 Solving beta, beta for Lagrangian factor 1 、β 2 The values are required to satisfy the desired constraints of mean and variance as in equation (4.3):
where E (lnC) is the mean constraint of lnC, sigma (lnC) is the variance constraint of lnC, μ lnC Is the average value of lnC and is equal to,is lnC.
The interval constraint of the parameter C in the service process of the steel bridge is expressed as shown in a formula (4.4):
lnC∈[(lnC) - ,(lnC) + ] (4.4)
in (lnC) - 、(lnC) + A lower and an upper interval limit of lnC, respectively.
7. The multi-source information fusion steel bridge corrosion fatigue damage assessment method according to claim 1, wherein the method is characterized by comprising the following steps: in the fourth step, according to indirect information provided by crack observation point data obtained in the service process of the steel bridge, a likelihood function is constructed according to a formula (4.5):
in the method, in the process of the invention,is a likelihood function of the parameter lnC, +.>σ e For model error, sigma a Is the measurement error; a, a T For calculating crack calculation lengths at time T in different corrosion fatigue crack growth rate tests according to corrosion fatigue crack growth models +.>Observing the length of the crack at the moment T; a, a T Determined according to formulas (4.6), (4.7):
wherein Δa T Is the crack growth length in the time period of T-1 to T;for the initial crack length at time T->N T Is the cycle of corrosion fatigue load in the period of 0 to T, N T-1 The fatigue load is cycled for a cycle in the time period of 0-T-1; />Is the effective stress intensity factor at the moment T +.>The stress threshold value at the moment T.
8. The multi-source information fusion steel bridge corrosion fatigue damage assessment method according to claim 1, wherein the method is characterized by comprising the following steps: in the fourth step, the priori distribution and likelihood function of undetermined parameters C of the corrosion fatigue crack propagation model are fused, the probability distribution of a posterior model of undetermined parameters C is obtained, and the probability distribution is expressed according to a formula (4.8):
wherein p is n (lnC) is the posterior distribution of parameter lnC, p 0 (lnC) is an a priori distribution of the parameters lnC,is a likelihood function of the parameter lnC.
9. The multi-source information fusion steel bridge corrosion fatigue damage assessment method according to any one of claims 1-8, wherein: in the fifth step, the length of the welding corrosion fatigue crack at the current moment in the service process of the steel bridge is predicted according to (5.1):
wherein a is T Predicting the length of the welding corrosion fatigue crack at the moment T and N T The corrosion fatigue load born by the welding detail of the steel bridge in the time period of 0-T is cycled for a round,is the calibrated value of the pending parameter C.
10. The multi-source information fusion steel bridge corrosion fatigue damage assessment method according to any one of claims 1-8, wherein: in the fifth step, the corrosion fatigue crack extension life of the steel bridge welding detail is predicted according to the formula (5.2):
wherein N is f Corrosion fatigue crack growth life for steel bridge welding detail, a 0 Is the initial crack size; a, a c A is critical crack size, a c Determined according to formula (5.3):
wherein K is IC Fracture toughness of the material; sigma (sigma) c Is critical stress.
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