PC bridge service state and vulnerability prediction method based on Bayesian theory

Abstract

The invention discloses a PC bridge service state and vulnerability prediction method based on the Bayesian theory, and relates to the technical field of bridge service state and vulnerability evaluation, and the method comprises the steps: building a three-dimensional finite element model of a bridge; key parameters influencing the service state of the bridge are determined, the three-dimensional finite element model is operated, the mid-span deflection value and the average prestress loss value of each bridge sample at different moments are obtained, and a database is formed; a GRU proxy model for prediction is obtained through database training; aiming at a to-be-studied bridge, obtaining an actually-measured midspan deflection measured value of the bridge; using the key parameters of the bridge and the GRU agent model to obtain a mid-span deflection prediction value of the bridge; performing Bayesian parameter estimation according to the measured value and the predicted value of the mid-span deflection of the bridge, and estimating bridge parameters of the bridge, which conform to posterior probability distribution; and substituting the estimated bridge parameters conforming to the posterior probability distribution into the GRU agent model to obtain a time-varying curve of the mid-span deflection value and the prestress average loss value of the bridge, and a time-varying vulnerability curve of the bridge. According to the method, the relatively accurate bridge key parameters are calculated through Bayesian parameter estimation, and more accurate prediction can be achieved.

Description

Technical Field

[0001] The invention relates to the technical field of bridge service status and vulnerability assessment, in particular to a PC bridge service status and vulnerability prediction method based on Bayesian theory. Background Art

[0002] Long-span prestressed concrete bridges (PC bridges) often suffer from cracking, deflection and other defects, which will reduce the bearing capacity and serviceability of the bridges and affect the safety and durability of the bridges. Therefore, it is of great significance to conduct long-term prediction and evaluation of the service status (health status) and vulnerability of bridges.

[0003] At present, finite element simulation is one of the common methods used to predict and evaluate the health status and vulnerability of PC bridges. Although, some scholars have proposed different constitutive models and fully considered various influencing factors such as nonlinear creep and prestress relaxation under complex service conditions, the prediction accuracy of finite element models has been further improved. However, the accuracy of finite element simulation is highly dependent on the accuracy of the input model parameters. If these parameters are not accurate enough, the simulation results may have large deviations. In addition, finite element simulation usually requires a lot of computing resources, including computing time and computing storage space. For large bridge structures, finite element simulation may require a long computing time and a large storage space, and the computing cost is high. Long-term prediction and evaluation of bridge structures require long simulations, which will further increase the computing cost. Therefore, it is crucial to quickly find the true values ​​of the key parameters of the actual bridge at a low cost. In addition, for the vulnerability of bridges, the traditional method is to evaluate based on the deflection of the bridge. However, this single indicator has certain limitations and cannot fully reflect the overall condition of the bridge. Summary of the invention

[0004] In order to overcome the defects in the above-mentioned prior art, the present invention provides a method for predicting the service status and vulnerability of a PC bridge based on Bayesian theory, which utilizes Bayesian parameter estimation to infer relatively accurate key parameters of the bridge, thereby enabling more accurate prediction.

[0005] To achieve the above object, the present invention adopts the following technical solutions, including:

[0006] The service status and vulnerability prediction method of PC bridges based on Bayesian theory includes the following steps:

[0007] S1, based on the constitutive model of the bridge, establish a three-dimensional finite element model of the bridge;

[0008] S2, determine the key parameters that affect the service status of the bridge, obtain several bridge samples with different key parameter values, run the three-dimensional finite element model, obtain the mid-span deflection value and the average prestress loss value of each bridge sample at different times, and form a database; use the database training to obtain GRU agent model 1 for predicting the mid-span deflection value at different times based on the key parameters and GRU agent model 2 for predicting the average prestress loss value at different times based on the key parameters;

[0009] S3, for the bridge to be studied, actually measuring the mid-span deflection value of the bridge at different times to obtain the measured value of the mid-span deflection of the bridge;

[0010] S4, using the key parameters of the bridge and the GRU agent model 1, obtain the predicted value of the mid-span deflection of the bridge;

[0011] S5, performing Bayesian parameter estimation based on the measured value of the mid-span deflection of the bridge and the predicted value of the mid-span deflection, and estimating the bridge parameters of the bridge that conform to the posterior probability distribution;

[0012] S6, substituting the bridge parameters that meet the posterior probability distribution estimated in step S5 into the GRU proxy model 1 and the GRU proxy model 2, respectively, to obtain a curve of the mid-span deflection value and the average prestress loss value of the bridge changing with time;

[0013] S7, substituting the bridge parameters that are estimated in step S5 and conforming to the posterior probability distribution into the GRU proxy model 2 to obtain the fragility curve of the bridge that changes over time.

[0014] Preferably, the specific process of step S5 is as follows:

[0015] S51, assuming that the initial value of the bridge parameter is θ 0 , with the current value of the bridge parameter, i.e., θ 0 As the center, set a distribution width w, the next candidate value of the bridge parameter θ 1 In (θ 0 -w,θ 0 +w) is randomly generated within the range;

[0016] S52, determine whether to accept the next candidate value θ of the bridge parameter j+1 , the acceptance criteria are:

[0017]

[0018] Among them, θ j represents the current value of the bridge parameter, θ j+1 represents the next candidate value of the bridge parameter, j = 1, 2, ....; p(θ j |y1,...,y k) means that when events y1,...,y k When the event θ occurs j The probability density function value of occurrence, that is, the bridge parameter θ j The posterior probability distribution of p(θ j+1 |y1,...,y k ) means that when events y1,...,y k When the event θ occurs j+1 The probability density function value of occurrence, that is, the bridge parameter θ j+1 The posterior probability distribution of Q(θ j ,θ j+1 ) represents the acceptance criterion, judging whether Q(θ j ,θ j+1 )>u, if it satisfies, then accept the next candidate value θ of the bridge parameter j+1 , and θ j+1 Continue to generate the next candidate value for the center. If it does not meet the requirement, the next candidate value of the bridge parameter θ is discarded. j+1 , continue with θ j Generate the next candidate value for the center; u is a random number in the range [0,1];

[0019] S53, repeating the sampling for multiple times in the manner of step S52, after the sampling is completed, a number of bridge parameters that conform to the posterior probability distribution are obtained.

[0020] Preferably, the posterior probability distribution p(θ|y1,...,y k ) is:

[0021]

[0022] Where K is a constant; bridge parameter θ = {x1, x2, x3, ..., x m ,s},x1,x2,x3,...,x m is the key parameter of the bridge, s is the noise; p(θ) represents the prior distribution of the bridge parameter θ; y k is the actual measured value of the mid-span deflection of the bridge at the kth moment, y k is the data containing noise; is the predicted value of the mid-span deflection of the bridge at the kth moment obtained by using the GRU proxy model 1 and the key parameters of the bridge. is the data without noise; k represents the kth moment, k=1,2,...,N data , a total of N data a moment;

[0023] Bridge parameters θ={x1,x2,x3,...,x m,s}, the prior distribution of each key parameter p(x1),p(x2),p(x3),...,p(x m ) and the prior distribution of noise p(s) need to be assumed. Assuming that all parameters are statistically independent, the prior joint probability density function of these parameters can be defined as:

[0024] p(θ)=p(x1)×p(x2)×p(x3)×...×p(x m )×p(s).

[0025] Preferably, all parameters of the bridge parameters are statistically independent, and the prior distribution of each key parameter is set as p(x1), p(x2), p(x3), ..., p(x m ) and the prior distribution of noise p(s), the prior distribution of the bridge parameter θ is:

[0026] p(θ)=p(x1)×p(x2)×p(x3)×...×p(x m )×p(s).

[0027] Preferably, in step S53, sampling is repeated multiple times in the manner of step S52. After the sampling is completed, the posterior probability distribution of each bridge parameter obtained is sorted in ascending order, the first 20% of the bridge parameters are discarded, and the remaining bridge parameters are considered to be bridge parameters that conform to the posterior probability distribution.

[0028] Preferably, in step S6, the various bridge parameters estimated in step S5 that conform to the posterior probability distribution are substituted into GRU proxy model 1 and GRU proxy model 2, respectively, to obtain the mid-span deflection value and the average prestress loss value of the bridge at different times under various bridge parameters, respectively. For each moment, the 5% and 95% quantiles of the mid-span deflection value, and the 5% and 95% quantiles of the average prestress loss value are selected, and images are drawn to obtain the 5% supremum and 95% infimum of the mid-span deflection value, as well as the 5% supremum and 95% infimum of the average prestress loss value.

[0029] Preferably, the specific process of step S7 is as follows:

[0030] S71: Define the service status of the bridge according to the average loss value of prestress, where less than 15% is a healthy state, less than 25% is a good state, less than 30% is a fair state, and greater than or equal to 30% is a poor state;

[0031] S72, substitute the various bridge parameters estimated in S5 that conform to the posterior probability distribution into the GRU proxy model 2, obtain the average prestress loss value of the bridge at different times under various bridge parameters, and count the proportion of the bridge in healthy, good, general, and poor conditions at each moment, so as to obtain the fragility curve.

[0032] Preferably, the key parameters of the bridge include: creep coefficient x1, shrinkage coefficient x2, concrete strength x3, prestress level x4 and ambient humidity x5.

[0033] Preferably, in step S2, Latin hypercube sampling is used to generate a plurality of bridge samples with different key parameter values.

[0034] The present invention also provides a computer program product, characterized in that it includes a computer program / instruction, which, when executed by a processor, implements the above-mentioned PC bridge service status and vulnerability prediction method based on Bayesian theory.

[0035] The advantages of the present invention are:

[0036] (1) The present invention provides a method for predicting the service status and vulnerability of a PC bridge based on Bayesian theory. First, a three-dimensional finite element model is established. Then, a database that can reflect the relationship between key parameters of the bridge and the prestress level and deflection of the bridge at different times is established by Latin hypercube sampling and running the three-dimensional finite element model. The GRU proxy model is trained. Then, based on the measured value of the early mid-span deflection of the bridge, Bayesian parameter estimation is performed to deduce relatively accurate key parameters of the bridge. Finally, the obtained bridge parameters are input into the trained GRU proxy model, thereby realizing the prediction of the service status of the PC bridge and drawing the bridge vulnerability curve.

[0037] (2) The present invention can calculate relatively accurate key parameters of the bridge based on the measured value of the mid-span deflection of the bridge.

[0038] (3) The present invention can realize the input of key parameters of the bridge, that is, the prestressing level of the bridge at different times can be predicted through the established GRU proxy model, thereby avoiding complex and expensive finite element simulations, reducing the time required for model prediction, improving prediction efficiency, reducing prediction costs, and being able to be used to predict future development trends.

[0039] (4) The present invention has good prediction accuracy and can obtain satisfactory results even for long-term predictions.

[0040] (5) The present invention uses the prestress loss value as an indicator for evaluating the vulnerability of the bridge, which can more comprehensively reflect the overall condition of the bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1The flowchart of the PC bridge service status and vulnerability prediction method based on Bayesian theory of the present invention.

[0042] Figure 2 Schematic diagram of deformation of concrete bridges. 1a is a schematic diagram of a concrete bridge without prestressing, 1b is a schematic diagram of deformation of a concrete bridge without prestressing under external load, 2a is a schematic diagram of a concrete bridge with prestressing, and 2b is a schematic diagram of deformation of a concrete bridge with prestressing under external load.

[0043] Figure 3 It is a schematic diagram of a three-dimensional finite element model of a bridge and related unit types established in the embodiment.

[0044] Figure 4 It is a real bridge used to verify the present invention in the examples.

[0045] Figure 5 It is a comparison chart of the measured deflection value and the predicted deflection value of the bridge in the embodiment.

[0046] Figure 6 It is the fragility curve of the bridge changing with time in the embodiment. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] Prestressing (prestressing forces) is to improve the performance of the structure during use. The prestressing stress during the use of the structure can fully or partially offset the tensile stress caused by the load and avoid structural damage. It is often used in concrete structures. Prestressed concrete structure is a structure that is prestressed before it is subjected to loads. When the external load acts, the internal force of the concrete in the tensile zone produces compressive stress to offset or reduce the tensile stress caused by the external load, so that the structure will not crack or crack later under normal use. Figure 2 As shown in the figure, 1a is a schematic diagram of a concrete bridge without prestressing; 1b is a schematic diagram of the deformation of a concrete bridge without prestressing under external load. A concrete bridge without prestressing is prone to cracking, deflection and other defects under normal use, i.e., under external load, which will reduce the bearing capacity and serviceability of the bridge; 2a is a schematic diagram of a concrete bridge with prestressing; 2b is a schematic diagram of the deformation of a concrete bridge with prestressing under external load.

[0049] Deflection refers to the linear displacement of the centroid of the cross-section along the direction perpendicular to the axis when the bridge is bent and deformed. In short, it is the maximum deformation of the bridge under load. It is usually expressed in terms of the vertical y-axis, that is, the vertical deformation of the bridge.

[0050] Depend on Figure 1 As shown, the PC bridge service status and vulnerability prediction method based on Bayesian theory of the present invention includes the following steps:

[0051] S1, based on the "cracking-time-varying-coupling" constitutive model of the bridge, a three-dimensional finite element model that can reflect the service and stress conditions of the bridge is established.

[0052] S2, determine the key parameters that affect the service status of the bridge, use Latin hypercube sampling to generate several bridge samples with different key parameter values, run the three-dimensional finite element model in step S1, obtain the mid-span deflection value and the average prestress loss value of each bridge sample at different times, and then form a "key parameter-mid-span deflection value at different times-average prestress loss value at different times" database, use the database to train a GRU proxy model that can replace the three-dimensional finite element model, including GRU proxy model 1 for predicting the mid-span deflection value at different times according to the key parameters and GRU proxy model 2 for predicting the average prestress loss value at different times according to the key parameters.

[0053] S3, actually measuring the mid-span deflection value of a bridge at different times to obtain the actual measured value of the mid-span deflection of the bridge.

[0054] S4, using the key parameters of the bridge and GRU agent model 1, predict the mid-span deflection value of the bridge, that is, obtain the predicted value of the mid-span deflection of the bridge.

[0055] S5, perform Bayesian parameter estimation based on the measured value and predicted value of the mid-span deflection to obtain the bridge parameters that conform to the posterior probability distribution;

[0056] S6, substitute the bridge parameters that conform to the posterior probability distribution estimated in step S5 into GRU proxy model 1 and GRU proxy model 2, respectively, and obtain the curves of the mid-span deflection value and the average prestress loss value of the bridge changing with time (including 5% supremum and 95% infimum).

[0057] S7, substituting the bridge parameters that are estimated in step S5 and conforming to the posterior probability distribution into the GRU proxy model 2 to obtain the fragility curve of the bridge that changes over time.

[0058] In step S1, the three-dimensional finite element model takes into account the coupling effects of early hydration heat and shrinkage creep of the bridge, and also takes into account the influence of relaxation of prestressed steel bars and ordinary steel bars.

[0059] In step S1, the “cracking-time-varying-coupling” constitutive model of the bridge is as follows:

[0060] The strain tensor ε is decomposed into the elastic strain ε e , plastic strain ε p 、Creep strain ε c and the contraction strain ε sh , as shown below:

[0061] ε=ε e +ε p +ε c +ε sh

[0062] Elastic strain ε e and the effective stress tensor The relationship is as follows:

[0063]

[0064] where C is the fourth-order lossless elastic stiffness tensor.

[0065] To calculate the plastic strain ε p , can be solved using the following tangential stiffness matrix expression:

[0066]

[0067] Where σ represents the stress tensor; denote the regularized tensile damage variable and compressive damage variable, respectively; denote the effective tensile stress and the effective compressive stress respectively; Δt denotes the time increment; η denotes the viscosity parameter; represents the derivative; ε represents the strain tensor.

[0068] With the expression of the tangential stiffness matrix, the plastic strain ε can be solved by combining existing technology and theory. p .

[0069] Calculate the creep strain ε c When , the following formula is used:

[0070] Δε c =Δε1n1+Δε2n2+Δε2n2

[0071] Among them, Δε1, Δε2, and Δε3 represent the three principal strain increments of concrete, n1, n2, and n3 represent the eigenvectors corresponding to the three principal strain increments; Δε c Represents the increase in creep strain.

[0072]

[0073] Among them, σ1, σ2, and σ3 are the three principal stresses respectively; is the internal state variable updated by the μth Kelvin unit in the previous time step, i.e., the n-1th time step; β μ Represents time-related parameters;

[0074] h(σ1), h(σ2), and h(σ3) respectively represent the influence of the three principal stresses on the increase of the creep coefficient. The specific calculation formula is as follows:

[0075]

[0076] Among them, f c,k is the concrete strength, a and c are two empirical parameters, and b is the threshold value.

[0077] Calculate the contraction strain ε at time t sh When , the following formula is used:

[0078]

[0079] Among them, t c is the drying start time; f and α are constants considering the shape and size of the component respectively; ε shu is the ultimate shrinkage strain, which is affected by humidity, volume-to-area ratio and wet curing time; I is the unit matrix.

[0080] The constitutive model of the present invention also takes into account the influence of ordinary steel bars. Ordinary steel bars are considered to be dispersed in the concrete unit, and the stress state of ordinary steel bars can be expressed by the following formula:

[0081] σ sx =ρ sx f sx

[0082] σ sy =ρ sy f sy

[0083] σ sz =ρ sz f sz

[0084] Among them, f sx 、f sy and f sz Respectively represent the axial stress of ordinary steel bars in the x, y and z directions; ρ sx , sy and ρ sz Respectively represent the reinforcement ratio of ordinary steel bars in the x, y and z directions; ρ sx , sy and σ szThey represent the average stress of the diffuse element of ordinary steel bars in the x, y and z directions respectively.

[0085] In the constitutive model of the present invention, the effect of prestressed tendon relaxation is also considered, where the relaxation rate ρ at time t is t It can be expressed by the following formula:

[0086]

[0087] Where t represents the time in hours; λ1 is equal to 1000 hours; ρ 1000 and k are both constants, and their values ​​depend on the grade of the prestressed tendons.

[0088] In step S2, Latin hypercube sampling is used to generate several bridge samples with different key parameter values, and the three-dimensional finite element model in S1 is run to obtain the mid-span deflection value and the average prestress loss value of each bridge sample at different times. The specific steps are as follows:

[0089] S21, select the required key parameters of the bridge, i.e. x1, x2, ..., x m The selection of key parameters depends on the actual needs of the bridge to be studied. The selection of key parameters also determines the scope of bridges to which the subsequent prediction model is applicable. m In this embodiment, the key parameters of the bridge include: creep coefficient, shrinkage coefficient, concrete strength, initial prestress level, and ambient humidity.

[0090] S22, assuming x1, x2, ..., x m are all independent and are assumed to obey normal distribution. A sample database of bridges is generated according to the Latin hypercube sampling method, i.e., the key parameters x1, x2, ..., x m .

[0091] S23, according to the design drawings, determine the length, cross-sectional form, elastic modulus, Poisson's ratio, density, boundary constraints and other geometric and physical parameters of the bridge structure, and then establish a three-dimensional finite element model of the bridge based on the drawings and with the help of finite element analysis software. Figure 3 As shown, C3D8 units are used for concrete and ordinary steel bars, and T3D2 units are used for prestressed tendons.

[0092] S24, based on the constitutive model, the 3D finite element model of the bridge was analyzed in the finite element analysis software to obtain the mid-span deflection value and the average prestress loss value of each bridge sample at different times.

[0093] In step S2, a neural network is used to establish GRU proxy model 1 and GRU proxy model 2. The input of GRU proxy model 1 is the key parameters and service time of the bridge, which are recorded as {x1, x2, x3, ..., x m ,t}, and the output is the mid-span deflection value y of the bridge. The input of GRU proxy model 2 is also the key parameters and service time of the bridge, that is, {x1,x2,x3,...,x m ,t}, the output is the prestress loss value P of the bridge.

[0094] In step S3, the mid-span deflection values ​​(measured mid-span deflection values) obtained by actual measurement of the bridge at different times are data containing noise s, denoted as y k , k represents the kth moment, y k represents the measured value of the mid-span deflection at the kth moment, k=1,2,...,N data , a total of N data The mid-span deflection value at the kth moment is t k .

[0095] In step S4, the GRU proxy model is used to predict the mid-span deflection of the bridge at different times according to the key parameters of the bridge, which is recorded as Prediction of mid-span deflection of bridges It is the data without noise (true value of mid-span deflection).

[0096] In step S5, it is assumed that the noise of each measurement follows a distribution of δ~N(0,s 2 ), we get the following formula:

[0097]

[0098] Among them, bridge parameters θ={x1,x2,x3,...,x m ,s},x1,x2,x3,...,x m is the key parameter of the bridge, s is the noise, s 2 is the standard deviation of the noise; p(y k |θ) represents the measured value of mid-span deflection y when the bridge parameter θ is given. k The probability density function value of .

[0099] Bayesian parameter estimation is performed based on the measured values ​​of the mid-span deflection of the bridge, as shown below:

[0100]

[0101] Among them, p(y1,...,y k ) is a constant, and p(y1,...,y k)=C;p(y1,...,y k ) represents the events y1,...,y k The probability density function value of occurrence; p(θ,y1,...,y k ) represents the events y1,...,y k The probability density function value of the event θ occurring simultaneously; p(θ|y1,...,y k ) means that when events y1,...,y k The probability density function value of event θ when it occurs; p(θ) represents the prior distribution of θ; p(y1,...,y k |θ) represents the event y1,...,y when event θ occurs k The probability density function value of occurrence.

[0102] Assuming that the measured values ​​of the mid-span deflection of the bridge obtained each time do not affect each other, the following formula can be obtained:

[0103]

[0104] Among them, p(y k |θ) means event y occurs when event θ occurs k The probability density function value of occurrence, that is, the measured value of mid-span deflection y when the bridge parameter θ is given k The probability density function value of ; It means that when the key parameters of the bridge are {x1,x2,x3,...,x m}, the predicted value of the mid-span deflection of the bridge at the i-th moment; y i is the measured value of the mid-span deflection of the bridge at the i-th moment.

[0105] Bridge parameters θ={x1,x2,x3,...,x m ,s}, the prior distribution of each key parameter p(x1),p(x2),p(x3),...,p(x m ) and the prior distribution of noise p(s) need to be assumed. Assuming that all parameters are statistically independent, the prior joint probability density function of these parameters can be defined as:

[0106] p(θ)=p(x1)×p(x2)×p(x3)×...×p(x m )×p(s)

[0107] Therefore, the final posterior probability distribution of bridge parameters p(θ|y1,...,y k )(that is, when events y1,...,y k The expression of the probability density function of event θ when it occurs is:

[0108]

[0109] Where K is a constant.

[0110] In the result of the Bayesian parameter estimation in step S5, an explicit expression of the posterior probability distribution is not directly given, but a Monte Carlo sampling method is used to obtain a set of bridge parameters θ that conform to the posterior probability distribution.

[0111] The specific process of step S5 is as follows:

[0112] S51, assuming that the initial value of the bridge parameter is θ 0 , with the current value of the bridge parameter, i.e., θ 0 Assuming a distribution width w, the next candidate value of the bridge parameter θ is centered at 1 will be in (θ 0 -w,θ 0 +w) is generated randomly within the range.

[0113] S52, determine whether to accept the next candidate value θ of the bridge parameter j+1 , the acceptance criteria are:

[0114]

[0115] Among them, θ j represents the current value of the bridge parameter, θ j+1 represents the next candidate value of the bridge parameter, j = 1, 2, ....; p(θ j |y1,...,y k ) means that when events y1,...,y k When the event θ occurs j The probability density function value of occurrence; p(θ j+1 |y1,...,y k ) means that when events y1,...,y k When the event θ occurs j+1 The probability density function value of occurrence; Q(θ j ,θ j+1 ) represents the acceptance criterion, judging whether Q(θ j ,θ j+1 )>u, if it satisfies, then accept the next candidate value θ of the bridge parameter j+1 , and θ j+1 Continue to generate the next candidate value for the center. If it does not meet the requirement, the next candidate value of the bridge parameter θ is discarded. j+1 , continue with θ j Generate the next candidate value for the center, where u is a random number in the range [0,1].

[0116] S53, repeat the sampling multiple times in the manner of step S52 to ensure that the obtained bridge parameters have a good consistency with the true posterior probability distribution. After the sampling is completed, the posterior probability distribution of each bridge parameter obtained is sorted in ascending order, the first 20% of the samples are discarded, and the remaining samples are considered to be bridge parameters that conform to the posterior probability distribution.

[0117] In step S6, the various bridge parameters estimated in step S5 that meet the posterior probability distribution are substituted into GRU proxy model 1 and GRU proxy model 2, respectively, to obtain the mid-span deflection value and the average prestress loss value of the bridge at different times under various bridge parameters. For each moment, the 5% and 95% quantiles of the mid-span deflection value, as well as the 5% and 95% quantiles of the average prestress loss value, are selected, and the images are drawn to obtain the 5% supremum and 95% infimum of the mid-span deflection value, as well as the 5% supremum and 95% infimum of the average prestress loss value. The 5% supremum and 95% infimum of the mid-span deflection value are as follows: Figure 5 shown.

[0118] In step S7, the fragility curve of the bridge changing with time is obtained, and the specific process is as follows:

[0119] S71, define the service status of the bridge according to the average loss value of prestress, where less than 15% is a healthy state, less than 25% is a good state, less than 30% is a general state, and greater than or equal to 30% is a poor state.

[0120] S72, the various bridge parameters estimated in S5 that meet the posterior probability distribution are substituted into the GRU proxy model 2 to obtain the average prestress loss value of the bridge at different times under various bridge parameters. The proportion of samples (bridge parameters) in healthy, good, general, and poor states at each time is counted to obtain the fragility curve. The fragility curve of the bridge changing over time is shown as follows: Figure 6 shown.

[0121] Example 1

[0122] like Figure 4 As shown, a certain type of continuous steel structure bridge is taken as an example to illustrate the specific implementation process of the present invention. This embodiment is used to predict the prestress level of a certain type of continuous steel structure bridge with different creep coefficients, shrinkage coefficients, concrete strengths, prestress levels and environmental humidity.

[0123] S101, firstly, a three-dimensional finite element model of a certain type of bridge is established with the help of finite element analysis software. The finite element model should be able to consider the "cracking-time-varying-coupling" effect and better reflect the stress conditions of the actual bridge.

[0124] The key parameters of the bridge to be studied are determined as follows: creep coefficient x1, shrinkage coefficient x2, concrete strength x3, prestressing level x4 and ambient humidity x5. Assuming that the above key parameters are independent and follow a normal distribution, 1000 groups of bridge samples with different parameters are generated according to the Latin hypercube sampling method. Each bridge sample data includes five key parameters: x1, x2, x3, x4 and x5.

[0125] Substitute each parameter sample into the three-dimensional finite element model, and perform analysis and calculation to obtain the prestress loss value P and mid-span deflection value y of each bridge sample at different times, and form X, where X = [x1, x2, x3, x4, x5, t], t represents the time corresponding to the prestress loss value P and the mid-span deflection value y;

[0126] S102, taking X as input and P as output, trains GRU proxy model 2 for predicting the average loss value of prestressing, and taking X as input and y as output, trains GRU proxy model 1 for predicting the mid-span deflection value.

[0127] S103, measure the mid-span deflection value of the bridge to be studied at different times (measured mid-span deflection value), recorded as (y k ,t k ), k=1,2,...,N data , measured value of mid-span deflection y k Contains noise s.

[0128] S104, using the GRU proxy model, the predicted values ​​of the mid-span deflection of the bridge at different times are predicted based on the key parameters of the bridge (x1, x2, x3, x4, x5) is the true value of the mid-span deflection without noise.

[0129] S105, assume the prior distribution of each key bridge parameter x1, x2, x3, x4, x5 and noise s, where the prior distribution of the key bridge parameters is assumed to be a uniform distribution with upper and lower bounds, and the distribution of the noise is assumed to be δ~N(0,s 2 )(other distributions can also be assumed), s 2 is the standard deviation of the noise, which is an unknown parameter. Assuming that the prior distribution of s is also a uniform distribution with upper and lower bounds, the bridge parameters of the measured bridge are θ={x1,x2,x3,...,x m ,s}, assuming that all parameters are statistically independent, the prior joint probability density function of these parameters can be defined as:

[0130] p(θ)=p(x1)×p(x2)×p(x3)×...×p(x m )×p(s)

[0131] Find the posterior probability distribution of bridge parameters. The expression of posterior probability distribution is:

[0132]

[0133] Among them, m=5.

[0134] Using Monte Carlo sampling, we get 12,000 sets of samples with values ​​of θ that match the posterior probability distribution. We discard the first 2,000 sets of samples. The remaining 10,000 sets of samples can be considered to be of good quality.

[0135] S106, according to the estimated results of the bridge parameters, each bridge parameter is substituted into the GRU proxy model 1 and 2, and each bridge parameter can obtain the mid-span deflection value and the average prestress loss value at different times. The 5% and 95% quantiles of the mid-span deflection value and the average prestress loss value at each time are selected and plotted, and the 5% supremum and 95% infimum of the mid-span deflection value and the average prestress loss value can be obtained. The 5% supremum and 95% infimum of the mid-span deflection value are as follows: Figure 5 shown.

[0136] S107, define the service state of the bridge according to the average loss value of prestress, where less than 15% is a healthy state, less than 25% is a good state, less than 30% is a general state, and greater than or equal to 30% is a poor state. Substitute each estimated bridge parameter into the GRU agent model 2, and each bridge parameter can obtain the average loss value of prestress at different times. The proportion of samples (bridge parameters) in healthy, good, general, and poor states at each time is counted to obtain the vulnerability curve. The vulnerability curve of the bridge over time is as follows: Figure 6 shown.

[0137] And, according to Figure 5 , 6 It can be seen that the prediction results are basically consistent with the actual situation and can better predict the situation of the actual bridge.

[0138] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting the service status and vulnerability of PC bridges based on Bayesian theory, characterized in that: The following steps are involved: S1, based on the constitutive model of the bridge, establish a three-dimensional finite element model of the bridge; S2, determine the key parameters that affect the service status of the bridge, obtain several bridge samples with different key parameter values, run the three-dimensional finite element model, obtain the mid-span deflection value and the average prestress loss value of each bridge sample at different times, and form a database; use the database training to obtain GRU agent model 1 for predicting the mid-span deflection value at different times based on the key parameters and GRU agent model 2 for predicting the average prestress loss value at different times based on the key parameters; S3, for the bridge to be studied, actually measuring the mid-span deflection value of the bridge at different times to obtain the measured value of the mid-span deflection of the bridge; S4, using the key parameters of the bridge and the GRU agent model 1, obtain the predicted value of the mid-span deflection of the bridge; S5, performing Bayesian parameter estimation based on the measured value of the mid-span deflection of the bridge and the predicted value of the mid-span deflection, and estimating the bridge parameters of the bridge that conform to the posterior probability distribution; S6, substituting the bridge parameters that meet the posterior probability distribution estimated in step S5 into the GRU proxy model 1 and the GRU proxy model 2, respectively, to obtain a curve of the mid-span deflection value and the average prestress loss value of the bridge changing with time; S7, substituting the bridge parameters that are estimated in step S5 and conforming to the posterior probability distribution into the GRU proxy model 2 to obtain the fragility curve of the bridge that changes over time.

2. The method for predicting the service status and vulnerability of PC bridges based on Bayesian theory according to claim 1 is characterized in that: The specific process of step S5 is as follows: S51, assuming that the initial value of the bridge parameter is θ 0 , with the current value of the bridge parameter, i.e., θ 0 As the center, set a distribution width w, the next candidate value of the bridge parameter θ 1 In (θ 0 -w,θ 0 +w) is randomly generated within the range; S52, determine whether to accept the next candidate value θ of the bridge parameter j+1 , the acceptance criteria are: Among them, θ j represents the current value of the bridge parameter, θ j+1 represents the next candidate value of the bridge parameter, j = 1, 2, ....; p(θ j |y1,...,y k ) means that when events y1,...,y k When the event θ occurs j The probability density function value of occurrence, that is, the bridge parameter θ j The posterior probability distribution of p(θ j+1 |y1,...,y k ) means that when events y1,...,y k When the event θ occurs j+1 The probability density function value of occurrence, that is, the bridge parameter θ j+1 The posterior probability distribution of Q(θ j ,θ j+1 ) represents the acceptance criterion, judging whether Q(θ j ,θ j+1 )>u, if it satisfies, then accept the next candidate value θ of the bridge parameter j+1 , and θ j+1 Continue to generate the next candidate value for the center. If it does not meet the requirement, the next candidate value of the bridge parameter θ is discarded. j+1 , continue with θ j Generate the next candidate value for the center; u is a random number in the range [0,1]; S53, repeating the sampling for multiple times in the manner of step S52, after the sampling is completed, a number of bridge parameters that conform to the posterior probability distribution are obtained.

3. The method for predicting the service status and vulnerability of PC bridges based on Bayesian theory according to claim 2 is characterized in that: The posterior probability distribution of the bridge parameter θ is p(θ|y1,...,y k ) is: Where K is a constant; bridge parameter θ = {x1, x2, x3, ..., x m ,s},x1,x2,x3,...,x m is the key parameter of the bridge, s is the noise; p(θ) represents the prior distribution of the bridge parameter θ; y k is the actual measured value of the mid-span deflection of the bridge at the kth moment, y k is the data containing noise; is the predicted value of the mid-span deflection of the bridge at the kth moment obtained by using the GRU proxy model 1 and the key parameters of the bridge. is the data without noise; k represents the kth moment, k=1,2,...,N data , a total of N data a moment; Bridge parameters θ={x1,x2,x3,...,x m ,s}, the prior distribution of each key parameter p(x1),p(x2),p(x3),...,p(x m ) and the prior distribution of noise p(s) need to be assumed. Assuming that all parameters are statistically independent, the prior joint probability density function of these parameters can be defined as: p(θ)=p(x1)×p(x2)×p(x3)×...×p(x m )×p(s)。 4. The method for predicting the service status and vulnerability of PC bridges based on Bayesian theory according to claim 3 is characterized in that: All parameters of the bridge parameters are statistically independent, and the prior distribution of each key parameter is set as p(x1), p(x2), p(x3), ..., p(x m ) and the prior distribution of noise p(s), the prior distribution of the bridge parameter θ is: p(θ)=p(x1)×p(x2)×p(x3)×...×p(x m )×p(s)。 5. The method for predicting the service status and vulnerability of PC bridges based on Bayesian theory according to claim 2 is characterized in that: Step S53, repeat the sampling multiple times in the manner of step S52. After the sampling is completed, the bridge parameters are sorted in ascending order according to the posterior probability distribution, and the first 20% of the bridge parameters are discarded. The remaining bridge parameters are considered to be bridge parameters that conform to the posterior probability distribution.

6. The method for predicting the service status and vulnerability of PC bridges based on Bayesian theory according to claim 2 is characterized in that: In step S6, the various bridge parameters estimated in step S5 that meet the posterior probability distribution are substituted into GRU proxy model 1 and GRU proxy model 2, respectively, to obtain the mid-span deflection value and the average prestress loss value of the bridge at different times under various bridge parameters, respectively. For each moment, the 5% and 95% quantiles of the mid-span deflection value, and the 5% and 95% quantiles of the average prestress loss value are selected, and images are drawn to obtain the 5% supremum and 95% infimum of the mid-span deflection value, as well as the 5% supremum and 95% infimum of the average prestress loss value.

7. The method for predicting the service status and vulnerability of PC bridges based on Bayesian theory according to claim 2 is characterized in that: The specific process of step S7 is as follows: S71: Define the service status of the bridge according to the average loss value of prestress, where less than 15% is a healthy state, less than 25% is a good state, less than 30% is a fair state, and greater than or equal to 30% is a poor state; S72, substitute the various bridge parameters estimated in S5 that conform to the posterior probability distribution into the GRU proxy model 2, obtain the average prestress loss value of the bridge at different times under various bridge parameters, and count the proportion of the bridge in healthy, good, general, and poor conditions at each moment, so as to obtain the fragility curve.

8. The method for predicting the service status and vulnerability of PC bridges based on Bayesian theory according to claim 1 or 3, characterized in that: The key parameters of the bridge include: creep coefficient x1, shrinkage coefficient x2, concrete strength x3, prestress level x4 and ambient humidity x5.

9. The method for predicting the service status and vulnerability of PC bridges based on Bayesian theory according to claim 1 is characterized in that: In step S2, Latin hypercube sampling is used to generate a number of bridge samples with different key parameter values.

10. A computer program product, characterized in that It includes a computer program / instruction, which, when executed by a processor, implements the PC bridge service status and vulnerability prediction method based on Bayesian theory as described in any one of claims 1 to 7.

Images