A method, apparatus, equipment and medium for assessing the time-varying reliability of bridges

Abstract

This application discloses a method, apparatus, equipment, and medium for assessing the time-varying reliability of bridges. This method quantifies and propagates the numerical uncertainty caused by observations of finite time-varying limit state functions. It measures the numerical uncertainty caused by finite observations by obtaining the posterior mean and upper bound of the posterior standard deviation of the time-varying failure probability through Bayesian inference. If the ratio of the upper bound of the posterior standard deviation to the posterior mean does not meet the iteration termination condition, a new sample point is selected and observed on the limit state function by constructing an objective function based on the contribution of the upper bound of the posterior standard deviation, resulting in new observation values. Then, Bayesian inference is performed again based on the new observation values ​​and existing observation values, realizing an active learning process. The selected new observation points can accelerate the satisfaction of the iteration termination condition, and the active learning process of selecting sample points can reduce the number of observation points, thereby improving the accuracy and efficiency of bridge time-varying reliability assessment.

Description

Technical Field

[0001] This application relates to the field of bridge reliability analysis technology, and in particular to a method, apparatus, equipment and medium for assessing the time-varying reliability of bridges. Background Technology

[0002] During construction, service, and maintenance, bridges inevitably face multi-source uncertainties caused by factors such as material properties, random loads, and geometric characteristics. Under the combined effects of harsh environments and external loads, the structural performance of bridges gradually degrades over time. To accurately assess their structural safety, especially considering multi-source uncertainties and degradation parameters, time-varying reliability analysis is crucial. Compared to traditional time-invariant reliability analysis, time-varying reliability analysis, by incorporating the time dimension, significantly increases the computational burden due to the time-varying characteristics of structural properties, loading conditions, and failure events, making the analysis process more challenging.

[0003] Currently, surrogate models are commonly used to evaluate the time-varying reliability of bridges. However, existing surrogate model methods ignore the numerical uncertainty of time-varying failure probabilities, resulting in low computational accuracy and efficiency. Summary of the Invention

[0004] This application aims to address at least one of the technical problems existing in the prior art. To this end, this application proposes a method, apparatus, device, and medium for assessing the time-varying reliability of bridges, which can quantify and propagate the numerical uncertainties caused by the observation of finite time-varying limit state functions, thereby improving the accuracy and efficiency of bridge time-varying reliability assessment.

[0005] A bridge time-varying reliability assessment method according to a first aspect embodiment of this application, the method comprising:

[0006] Obtain the observation set of the h-th iteration step, and use the observation set of the h-th iteration step as the target observation set. The observation set of the h-th iteration step includes multiple observation points, which are obtained by observing sample points on the limit state function. The limit state function is constructed by the structural parameters of the bridge and the limit state of the bridge. h is a positive integer.

[0007] Obtain the sample set of the h-th iteration step, and use the sample set of the h-th iteration step as the target sample set, wherein the sample set of the h-th iteration step includes multiple sample points generated according to the probability density function;

[0008] Perform a Bayesian inference process, which includes:

[0009] Generate the posterior distribution of the limiting state function based on the target observation set, and infer the integral expression of the posterior mean of the time-varying failure probability corresponding to the limiting state function and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability based on the posterior distribution of the limiting state function.

[0010] as well as,

[0011] Based on the target sample set, the integral expression of the posterior mean of the time-varying failure probability, and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, estimate the posterior mean of the time-varying failure probability and the upper bound of the posterior standard deviation of the time-varying failure probability corresponding to the limiting state function.

[0012] If the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability does not meet the first threshold, then according to the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, an objective function is generated to characterize the contribution of the sample point to the upper bound of the posterior standard deviation. A new observation point with the largest contribution is selected according to the objective function, and the new observation point and the observation set of the h-th iteration step are combined to form the observation set of the h+1-th iteration step. The observation set of the h+1-th iteration step is used as the target observation set and the Bayesian inference process is executed.

[0013] If the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies the first threshold, then the reliability of the bridge is evaluated based on the posterior mean of the time-varying failure probability.

[0014] According to a second aspect embodiment of the present application, a bridge time-varying reliability assessment apparatus includes:

[0015] The observation set calculation module is used to obtain the observation set of the h-th iteration step and use the h-th iteration step observation set as the target observation set. The h-th iteration step observation set includes multiple observation points, which are obtained by observing sample points on the limit state function. The limit state function is constructed by the structural parameters of the bridge and the limit state of the specified bridge. h is a positive integer.

[0016] The sample set calculation module is used to obtain the sample set of the h-th iteration step and use the sample set of the h-th iteration step as the target sample set, wherein the sample set of the h-th iteration step includes multiple sample points generated according to the probability density function;

[0017] The Bayesian analysis module is used to perform the Bayesian inference process, which includes:

[0018] Generate the posterior distribution of the limiting state function based on the target observation set, and infer the integral expression of the posterior mean of the time-varying failure probability corresponding to the limiting state function and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability based on the posterior distribution of the limiting state function.

[0019] as well as,

[0020] Based on the target sample set, the integral expression of the posterior mean of the time-varying failure probability, and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, estimate the posterior mean of the time-varying failure probability and the upper bound of the posterior standard deviation of the time-varying failure probability corresponding to the limiting state function.

[0021] The new observation point selection module is used to generate an objective function to characterize the contribution of sample points to the upper bound of the posterior standard deviation of the time-varying failure probability if the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability does not meet a first threshold. The module then selects the new observation point with the largest contribution based on the objective function, and combines the new observation point and the observation set of the h-th iteration step to form the observation set of the (h+1)-th iteration step. The observation set of the (h+1)-th iteration step is then used as the target observation set, and the Bayesian inference process is executed.

[0022] The reliability assessment module is used to assess the reliability of the bridge based on the posterior mean of the time-varying failure probability if the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies the first threshold.

[0023] An electronic device according to a third aspect of this application includes at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, the instructions being executed by the at least one control processor to enable the at least one control processor to perform the bridge time-varying reliability assessment method described above.

[0024] A computer-readable storage medium according to a fourth aspect of this application stores computer-executable instructions for causing a computer to perform the above-described bridge time-varying reliability assessment method.

[0025] The bridge time-varying reliability assessment method according to the embodiments of this application has at least the following beneficial effects:

[0026] This method quantifies and propagates the numerical uncertainty caused by observations of the finite time-varying limit state function. It measures the numerical uncertainty caused by these observations by obtaining the posterior mean and upper bound of the posterior standard deviation of the time-varying failure probability through Bayesian inference. If the ratio of the upper bound of the posterior standard deviation to the posterior mean does not satisfy the iteration termination condition, a new sample point is selected and observed on the limit state function by constructing an objective function that contributes to the upper bound of the posterior standard deviation, resulting in new observations. Then, Bayesian inference is performed again based on these new observations and the observations from the h-th iteration step, realizing an active learning process. The selected new observation points accelerate the satisfaction of the iteration termination condition, improving the accuracy and efficiency of bridge time-varying reliability assessment.

[0027] Other features and advantages of this application will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing this application. Attached Figure Description

[0028] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0029] Figure 1 This is a flowchart illustrating an embodiment of the bridge time-varying reliability assessment method provided in this application;

[0030] Figure 2 This is a flowchart illustrating another embodiment of the bridge time-varying reliability assessment method provided in this application;

[0031] Figure 3 This is a schematic diagram of an embodiment of the tied arch bridge provided in this application;

[0032] Figure 4 This is a schematic diagram of an embodiment of the finite element model of the tied arch bridge provided in this application;

[0033] Figure 5 This is a schematic diagram of the time-varying failure probability of the under-deck tied arch bridge provided in this application;

[0034] Figure 6 This is a schematic diagram of the bridge time-varying reliability assessment device provided in this application;

[0035] Figure 7 This is a schematic diagram of the structure of the electronic device provided in this application. Detailed Implementation

[0036] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0037] In the description of this application, the use of terms such as "first," "second," etc., is for the purpose of distinguishing technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of the technical features indicated.

[0038] In the description of this application, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0039] In the description of this application, it should be noted that, unless otherwise explicitly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0040] like Figure 1 One embodiment of this application provides a method for evaluating the time-varying reliability of bridges, the method comprising:

[0041] Step S110: Obtain the observation set of the h-th iteration step and use the observation set of the h-th iteration step as the target observation set. The observation set of the h-th iteration step includes multiple observation points. The observation points are obtained by observing the sample points on the limit state function. The limit state function is constructed by the structural parameters of the bridge and the limit state of the specified bridge. h is initially 1.

[0042] Step S120: Obtain the sample set of the h-th iteration step and use the sample set of the h-th iteration step as the target sample set, wherein the sample set of the h-th iteration step includes multiple sample points generated according to the probability density function;

[0043] Step S130: Perform the Bayesian inference process, which includes:

[0044] Generate the posterior distribution of the limit state function based on the target observation set, and infer the integral expression of the posterior mean of the time-varying failure probability corresponding to the limit state function, and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability based on the posterior distribution of the limit state function.

[0045] as well as,

[0046] Based on the target sample set, the integral expression of the posterior mean of the time-varying failure probability and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, estimate the posterior mean of the time-varying failure probability and the upper bound of the posterior standard deviation of the time-varying failure probability corresponding to the limit state function.

[0047] Step S140: If the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability does not meet the first threshold, then according to the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, an objective function is generated to characterize the contribution of the sample point to the upper bound of the posterior standard deviation. The new observation point with the largest contribution is selected according to the objective function, and the new observation point and the observation set of the h-th iteration step are combined to form the observation set of the h+1-th iteration step. The observation set of the h+1-th iteration step is used as the target observation set and the Bayesian inference process is executed.

[0048] If the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies the first threshold, then the reliability of the bridge is assessed based on the posterior mean of the time-varying failure probability.

[0049] In step S110, assuming the bridge provided in the embodiment is a tied-arch bridge with under-deck construction, the problem is to assess the deflection reliability of the tied-arch bridge. The random input parameters of the bridge include, but are not limited to, the cross-sectional area of ​​the hangers, the cross-sectional area of ​​the arch ribs, and the moment of inertia of the main beam section. The limit state of the bridge is: the mid-span deflection of the main beam does not exceed a specified threshold of 10cm. The limit state function is used for subsequent Bayesian inference.

[0050] In this embodiment, h represents the iteration step. It is assumed that h is 1 initially. A certain number of initial sample points are generated by sampling using the Sobol sequence and observed on the limit state function to form the observation set of the h=1th iteration step.

[0051] It is important to note that only the observation set of the first iteration is obtained based solely on the initial sample points; when h is a positive integer greater than 1, the observation set of the h-th iteration step is obtained by adding new observation points to the observation set of the (h-1)-th iteration step.

[0052] In step S120, during the first iteration, a set number of samples can be generated based on the probability density function to form a sample set.

[0053] It should be noted that when h is a positive integer greater than 1, the sample set of the h-th iteration step is obtained by adding new sample points to the sample set of the (h-1)-th iteration step.

[0054] In step S130, Bayesian inference uses Bayes' theorem to combine new data and prior probabilities to obtain the posterior probability distribution.

[0055] In this embodiment, the posterior distribution of the limiting state function is first generated based on the target observation set. Then, based on the posterior distribution of the limiting state function, the integral expression for the posterior mean of the time-varying failure probability corresponding to the limiting state function and the integral expression for the upper bound of the posterior standard deviation of the time-varying failure probability are inferred. Finally, based on the target sample set, the integral expression for the posterior mean, and the integral expression for the upper bound of the posterior standard deviation, the posterior mean and the upper bound of the posterior standard deviation of the time-varying failure probability are estimated. For detailed procedures, please refer to subsequent embodiments.

[0056] In step S140, it is first determined whether the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability meets the first threshold. If it does not meet the threshold, it indicates that the time-varying failure probability has a large degree of uncertainty, and new observation points need to be generated again for Bayesian inference.

[0057] Then, this embodiment proposes to generate an objective function based on the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability. This objective function can reflect the degree of contribution of the sample points to the upper bound of the posterior standard deviation. That is, the sample points with the highest contribution can be selected through this objective function, and then new observation points can be obtained based on the observation of the sample points in the limit state function.

[0058] Then, based on the new observation point and the observation set of the h-th iteration step, the observation set of the h+1-th iteration step is formed, and the process of step S130 is executed again to obtain the posterior mean of the time-varying failure probability and the upper bound of the posterior standard deviation of the time-varying failure probability of the Bayesian inference. The judgment is made again, and so on.

[0059] Finally, if the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability in a certain iteration satisfies the first threshold, the reliability of the bridge can be inferred based on the posterior mean of the time-varying failure probability output in that iteration. This embodiment measures the numerical uncertainty of the time-varying failure probability based on the posterior mean and the upper bound of the posterior standard deviation of the time-varying failure probability. Because the number of observation points is limited—for example, the observation set in the first iteration step only has a set number of observation points—the posterior distribution of the limit state function generated based on the target observation set is used to estimate the posterior mean and upper bound of the posterior standard deviation of the time-varying failure probability. It is then determined whether the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies the first threshold. If not, an objective function is generated based on the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability. This objective function reflects the contribution of the sample points to the upper bound of the posterior standard deviation, allowing the selection of the sample points with the highest contribution. Based on the observations of the limit state function at these sample points, new observation points are obtained. The new observation points are then added to the observation set of the h-th iteration step, and the next iteration is performed to reach the iteration termination condition as quickly as possible. This process continues until the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies the first threshold. Finally, the posterior mean of the time-varying failure probability is taken as the final result.

[0060] The beneficial effects of this embodiment include:

[0061] This embodiment quantifies and propagates the numerical uncertainty caused by observations of the finite time-varying limit state function, obtaining the posterior mean and upper bound of the standard deviation of the time-varying failure probability. By constructing an objective function to assess the contribution of the upper bound of the posterior standard deviation, new sample points are selected and observed on the limit state function to obtain new observations. Then, based on the new observations and the observations at the h-th iteration step, Bayesian inference is performed again, realizing an active learning process. The selected new observation points can accelerate the satisfaction of the iteration termination condition, improving the accuracy and efficiency of bridge time-varying reliability assessment.

[0062] In some embodiments of this application, step S140, if the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies a first threshold, then assessing the reliability of the bridge based on the posterior mean of the time-varying failure probability includes:

[0063] Step S1410: If the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies the first threshold, and the variability of the posterior mean of the time-varying failure probability is greater than or equal to the second threshold, then new sample points are generated according to the probability density function, and the new sample points and the sample set of the h-th iteration step are combined to form the sample set of the h+1-th iteration step. The sample set of the h+1-th iteration step is used as the target sample set and the Bayesian inference process is executed.

[0064] Step S1420: If the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies the first threshold, and the variability of the posterior mean of the time-varying failure probability is less than the second threshold, then the reliability of the bridge is evaluated based on the posterior mean of the time-varying failure probability.

[0065] In this embodiment, if the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability meets the first threshold, the variability of the posterior mean of the time-varying failure probability is also judged. If the coefficient of variation of the posterior mean of the time-varying failure probability is greater than or equal to the second threshold, it indicates that the posterior mean estimate of the time-varying failure probability output by the Bayesian inference process in step S130 above has a large uncertainty. New sample points need to be generated to increase the sample size, and the Bayesian inference process is performed again until the accuracy requirement is met.

[0066] In this embodiment, if the variability of the posterior mean of the time-varying failure probability is less than the second threshold, it indicates that the uncertainty of the posterior mean of the time-varying failure probability output by the Bayesian inference process in step S130 is small. At this time, the accuracy meets the requirements, and the reliability of the bridge can be directly evaluated using the posterior mean of the time-varying failure probability.

[0067] This embodiment allows for control over the accuracy of the posterior mean of the time-varying failure probability output by the Bayesian inference process in step S130. If the accuracy requirement is not met, the uncertainty of the posterior mean of the time-varying failure probability can be reduced by increasing the number of sample points and performing the Bayesian inference process until a satisfactory posterior mean of the time-varying failure probability is obtained for evaluating the bridge's reliability. This embodiment improves the accuracy of bridge time-varying reliability assessment.

[0068] like Figures 2 to 5 To facilitate understanding, taking a tied-arch bridge as an example, a tied-arch bridge inevitably experiences structural deflection under the coupled effects of dynamic loads and deterioration parameters. Excessive deflection can easily lead to problems such as bridge cracking, instability, and reduced driving comfort. Therefore, preventing excessive deflection in tied-arch bridges is a key issue in ensuring the safe operation of this type of bridge. An embodiment of a time-varying reliability assessment method for bridges is provided, specifically including the following:

[0069] Step S911, construct the limit state function;

[0070] A certain tied-arch bridge with a span of 125m and a rise-to-span ratio of 1:5 has 34 hangers with a spacing of 6.8m. As the bridge ages, the hangers will corrode, and traffic volume will continue to increase. Considering the worst-case scenario of heavy load, i.e., the mid-span section experiences a concentrated force F(t) that increases over time, this is modeled as a stochastic process. The tied-arch bridge with a span... Figure 3 As shown;

[0071] Under the combined action of live load and dead load, the arch bridge will experience mid-span deflection. The mid-span deflection of the main girder should not exceed a specified threshold Δ. lim =10cm as the normal service limit state, the limit state function of the arch bridge is established as: g(X,F(t),t)=Δ lim -Δ(A(t),E1,A2,E2,I y ,F1,F(t)), where X=[A1,E1,A2,E2,I y [F1], the structural parameters include the following: A(t) = A1 × (1 - 0.007t) is the cross-sectional area of ​​the hanger, A1 and E1 are the initial cross-sectional area and elastic modulus of the hanger, respectively, t∈[0,50] is the time parameter; A2 and E2 are the cross-sectional area and elastic modulus of the arch rib, respectively; I y F1 is the moment of inertia of the main beam section; F1 is the sum of dead and live loads; F(t) is the concentrated load at mid-span, characterized as a non-stationary Gaussian process. Statistical information of each structural parameter is shown in Table 1.

[0072] Table 1

[0073]

[0074] Δ(·) is obtained through finite element model calculation. In this embodiment, OpenSEES is used to construct the finite element model of the entire bridge. The main beam, hangers, and arch ribs are all simulated using elastic beam-column elements, and the concrete slab of the bridge deck system is simulated using plate fiber elements with a thickness of 0.4m. The model contains a total of 241 nodes and 439 elements. The finite element model is as follows: Figure 4 As shown.

[0075] Step S912, initialize parameters;

[0076] The initial number of observation points in the target observation set is set to n0 = 12, and the initial number of sample points in the target sample set is set to ΔN0 = 10. 5 Number of discrete time nodes n t =501, the first threshold of the stopping criterion is ∈ U =5%, the second threshold for the coefficient of variation of the Monte Carlo simulation estimator is ∈ N =5%, let the number of iterations be h, and the number of sample points in the target sample set be N. tot =ΔN0.

[0077] Step S913, discrete random process F(t);

[0078] Using n t Equally spaced time nodes Discretize the time interval [0, 50] into n. t-1 subintervals. The series optimal linear estimation method (EOLE) is used to represent the stochastic process F(t) as a function of a series of independent random variables and time parameters. Specifically:

[0079]

[0080] Where μ(t) and σ(t) are the mean and standard deviation functions of the stochastic process F(t), respectively; p is the number of terms in the expansion of the stochastic process F(t), corresponding to the number of principal eigenvalues ​​and the number of independent standard normal variables ξ. i The number of; Let ρ be the correlation vector. Y (t1,t2) is the autocorrelation function; λ and φ i These are the principal eigenvalues ​​and eigenvectors of the correlation matrix C, respectively. The correlation matrix C is:

[0081]

[0082] Step S914: Construct the target observation set (i.e., the observation set of the h-th iteration step, initially h=1);

[0083] An initial sample of n0 is generated using Sobol sequence sampling, and observations are made on the limiting state function g(X,F(t),t) to form the target observation set.

[0084] Step S915: Generate the target sample set (i.e., the sample set for the h-th iteration step);

[0085] Based on the probability density function f X (x) and the standard normal density generate N tot The target sample set is formed from the samples.

[0086] Step S916: Perform Bayesian inference of time-varying failure probability;

[0087] Step S916 includes the following:

[0088] Step S9161: Infer the posterior distribution of the limit state function;

[0089] Let [x,y(t),t]=v, the target observation set is represented as Assign a Gaussian process prior to the limit state function g(v), denoted as:

[0090] Where g0 is the prior distribution of g(·), and Let these be the prior mean and covariance function, respectively, and take them as constants and Gaussian kernels, i.e. and in s is a constant 2 Indicates process variance; Let l be a diagonal matrix. i >0 indicates the length scale of the i-th dimension, and d = n + 2 is the dimension of the input variable.

[0091] Based on the target observation set The posterior distribution of the limiting state function is obtained by estimating the hyperparameter θ using maximum likelihood estimation.

[0092] in, Let g(·) be the posterior mean function of the limit state function. Let be the posterior covariance function, where Both are n×1 dimensional covariance vectors, and the i-th element is respectively and The i-th element is The n0×1 dimensional mean vector.

[0093] Step S9162: Infer the posterior mean and upper bound of the posterior standard deviation of the time-varying failure probability;

[0094] Define the posterior indicator function as follows:

[0095]

[0096] Where (v|t) represents the time trajectory; the indicator function I n The probability that (v|t) is 0 corresponds to n t Each time point g n The probability that (v) is greater than 0, that is:

[0097] Obviously, It follows a multivariate normal distribution, that is:

[0098]

[0099] in, and g n n t ×1 dimensional mean vector and n t ×n t The covariance matrix is ​​expressed as follows:

[0100]

[0101] Let the probability that the time trajectory (v|t) is safe be... The corresponding failure probability is p s (v|t) can be further expressed as:

[0102]

[0103] The above formula involves n t High-dimensional integrals, although estimated using Monte Carlo simulations, have computational time that varies with the number of time points (n). t The increase is rapid due to the increase in p. To address this issue, [further details are needed regarding p]. s (v|t) has been simplified without affecting its calculation accuracy. First, a coefficient λ is introduced to make the following equation hold:

[0104]

[0105] Due to the inequality This holds true for all cases, therefore λ should be between 0 and 1. To effectively simplify p... s The calculation of (v|t) will involve p s (v|t) is taken as

[0106] The posterior mean and posterior variance of the indicator function are expressed as follows: and The posterior distribution of the indicator function I n (v|t) will cause a time-varying failure probability p f The posterior distribution of (0,50) (denoted as p) f,n (0,50)), the posterior mean integral and posterior variance integral of the time-varying failure probability:

[0107]

[0108] Construct the upper bound integral of the posterior variance of the time-varying failure probability based on the Cauchy-Schwarz inequality, i.e.:

[0109]

[0110] Step S917: Estimate the posterior mean and upper bound standard deviation of the time-varying failure probability;

[0111] Based on the generated target sample set N tot For each sample, the posterior mean and upper bound of the posterior standard deviation of the time-varying failure probability are estimated based on the formula in step S916. The estimator is expressed as: and

[0112] Step S918: Determine whether the stopping criterion is met;

[0113] Constructing a stopping criterion using the posterior mean and upper bound estimator of the time-varying failure probability. Where, ∈ U The specified first threshold is used; if it is not met, proceed to the next step; otherwise, proceed to step S920.

[0114] This application sets It is an important indicator for measuring the uncertainty of time-varying failure probability (due to a small number of observations), when A relatively large value indicates that the posterior mean of the time-varying failure probability is likely inaccurate and cannot be used as the final result; when A smaller value indicates that the uncertainty of the time-varying failure probability is relatively small, and the posterior mean of the time-varying failure probability is highly likely to be accurate. Therefore, by judging... To determine whether new observation points need to be added.

[0115] Step S919: Identify sample points and expand the observation set;

[0116] To quickly reduce The integrand in the integral of the posterior upper bound standard deviation of the time-varying failure probability measures the contribution of a certain position v to the posterior upper bound. An objective function characterizing this contribution to the posterior upper bound is proposed, namely:

[0117] UPSTDC(x)=[p s (x)(1-p s (x))] 1 / 2 f X (x) (12)

[0118] First, identify the time trajectory with the maximum UPSTDC. Select the instant with the greatest predictive uncertainty Here, we choose the classic U-function to determine this. The strategy is expressed as: the newly identified sample points are in The new observation point is obtained by observing the new sample point on the limiting state function.

[0119] Combine the observation set of the h-th iteration step with the new observation point to form a new observation set. Let h = h + 1, then the new observation set is the observation set of the h-th iteration step, and this is used as the target observation set.

[0120] Return the target observation set to step S916.

[0121] This embodiment has two loops. This is the first loop, which determines whether the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability is less than a first threshold. If it is not satisfied, a new observation point is selected using the objective function.

[0122] Step S920: Determine whether the variability of the posterior mean of the time-varying failure probability is satisfied;

[0123] The coefficient of variation for calculating the posterior mean of the time-varying failure probability Where, ∈ N The specified second threshold is used. If satisfied, the posterior mean of the final time-varying failure probability is returned. The final time-varying failure probability P f If not satisfied, then let the target sample set N be... tot =N tot +ΔN0, return to step S915.

[0124] This embodiment has two loops; this is the second loop. The second loop is the outer loop of the first loop, which determines whether the sampling variability of the posterior mean of the time-varying failure probability is less than a specified threshold. If it is not satisfied, new sample points are added. Once both conditions are met, the accurate posterior mean of the time-varying failure probability is obtained.

[0125] The time-varying failure probability and reliability index of the under-arch bridge in t∈[0,50] are as follows: Figure 5 As shown, the reliability index is based on β = Φ -1 (1-P f The reliability index of the arch bridge gradually decreases with the increase of its service life and tends to degrade linearly. As can be seen from the figure, the reliability index in year 50 (3.15) decreased by 32.77% compared with year 0 (4.51), which reflects the necessity of time-varying reliability analysis for this type of bridge.

[0126] Because tied arch bridges inevitably experience structural deflection under the coupled effects of dynamic loads and deterioration parameters, excessive deflection can easily lead to problems such as component cracking, instability, and reduced driving comfort. Therefore, preventing excessive deflection in tied arch bridges is a key issue in ensuring the safe operation of this type of bridge.

[0127] Therefore, this embodiment obtains the posterior mean and upper bound of the standard deviation of the time-varying failure probability by quantifying and propagating the numerical uncertainty caused by the observation of the finite limit state function. Based on this, an objective function and stopping criterion are constructed to realize the active learning process, thereby improving the accuracy and efficiency of bridge time-varying reliability assessment.

[0128] like Figure 6 This embodiment provides a time-varying reliability assessment device for bridges, the device comprising:

[0129] The observation set calculation module 1100 is used to obtain the observation set of the h-th iteration step and use the h-th iteration step observation set as the target observation set. The h-th iteration step observation set includes multiple observation points, which are obtained by observing the sample points on the limit state function. The limit state function is constructed by the structural parameters of the bridge and the limit state of the specified bridge; h is a positive integer.

[0130] The sample set calculation module 1200 is used to obtain the sample set of the h-th iteration step and use the sample set of the h-th iteration step as the target sample set, wherein the sample set of the h-th iteration step includes multiple sample points generated according to the probability density function.

[0131] The Bayesian analysis module 1300 is used to perform the Bayesian inference process, which includes:

[0132] Generate the posterior distribution of the limit state function based on the target observation set, and infer the integral expression of the posterior mean of the time-varying failure probability corresponding to the limit state function, and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability based on the posterior distribution of the limit state function.

[0133] as well as,

[0134] Based on the target sample set, the integral expression of the posterior mean of the time-varying failure probability and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, estimate the posterior mean of the time-varying failure probability and the upper bound of the posterior standard deviation of the time-varying failure probability corresponding to the limit state function.

[0135] The new observation point selection module 1400 is used to generate an objective function to characterize the contribution of sample points to the upper bound of the posterior standard deviation of the time-varying failure probability if the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability does not meet the first threshold. The module then selects the new observation point with the largest contribution based on the objective function, and combines the new observation point and the observation set of the h-th iteration step to form the observation set of the h+1-th iteration step. The observation set of the h+1-th iteration step is then used as the target observation set and the Bayesian inference process is executed.

[0136] The reliability assessment module 1500 is used to assess the reliability of the bridge based on the posterior mean of the time-varying failure probability if the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies a first threshold.

[0137] It should be noted that the bridge time-varying reliability assessment device provided in this embodiment is based on the same inventive concept as the bridge time-varying reliability assessment method described above. Therefore, the relevant content of the bridge time-varying reliability assessment method described above also applies to the content of the bridge time-varying reliability assessment device, and will not be repeated here.

[0138] like Figure 7 Based on the same inventive concept, this application also provides an electronic device.

[0139] Electronic devices may include a processor 401 and a memory 402 storing computer programs or instructions.

[0140] Specifically, the processor 401 may include a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of the present invention.

[0141] Memory 402 may include mass storage for data or instructions. For example, and not limitingly, memory 402 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 402 may include removable or non-removable (or fixed) media. Where appropriate, memory 402 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 402 is non-volatile solid-state memory. Memory may include read-only memory (ROM), random access memory (RAM), disk storage media devices, optical storage media devices, flash memory devices, electrical, optical, or other physical / tangible memory storage devices. Therefore, typically, a memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described in the bridge time-varying reliability assessment method provided in the above embodiments.

[0142] The processor 401 reads and executes computer program instructions stored in the memory 402 to implement the time-varying reliability assessment method for any bridge in the above embodiments.

[0143] In one example, the electronic device may also include a communication interface 403 and a bus 410. The processor 401, memory 402, and communication interface 403 are connected via the bus 410 and communicate with each other.

[0144] The communication interface 403 is mainly used to realize communication between various modules, devices, units and / or devices in the embodiments of the present invention.

[0145] Bus 410 includes hardware, software, or both, that couples components of an electronic device together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI Express (PCI X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 410 may include one or more buses. While specific buses are described and illustrated in embodiments of the invention, the invention contemplates any suitable bus or interconnect.

[0146] The electronic device can execute the data processing method described in the embodiments of the present invention, thereby achieving... Figure 1 Any method for assessing the time-varying reliability of a bridge as described.

[0147] Furthermore, in conjunction with the bridge time-varying reliability assessment method in the above embodiments, this invention can be implemented using a readable storage medium. This readable storage medium stores program instructions; when these program instructions are executed by a processor, they implement any of the bridge time-varying reliability assessment methods in the above embodiments.

[0148] It should be clarified that the present invention is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present invention is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of the present invention.

[0149] The functional blocks shown in the above-described structural diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this invention are programs or code segments used to perform the required tasks. The programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried in a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0150] It should also be noted that the exemplary embodiments mentioned in this invention describe methods or systems based on a series of steps or apparatus. However, this invention is not limited to the order of the steps described above; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0151] The aspects of this application have been described above with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It should be understood that each block in the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that these instructions, executable via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by dedicated hardware performing the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0152] The above description is merely a specific embodiment of the present invention. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the protection scope of the present invention.

Claims

1. A method for evaluating the time-varying reliability of bridges, characterized in that, The method includes: Obtain the observation set of the h-th iteration step and use the observation set of the h-th iteration step as the target observation set. The observation set of the h-th iteration step includes multiple observation points, which are obtained by observing sample points on the limit state function. The limit state function is constructed by the structural parameters of the bridge and the limit state of the bridge. h is initially 1. Obtain the sample set of the h-th iteration step, and use the sample set of the h-th iteration step as the target sample set, wherein the sample set of the h-th iteration step includes multiple sample points generated according to the probability density function; Perform a Bayesian inference process, which includes: Generate the posterior distribution of the limiting state function based on the target observation set, and infer the integral expression of the posterior mean of the time-varying failure probability corresponding to the limiting state function and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability based on the posterior distribution of the limiting state function. as well as, Based on the target sample set, the integral expression of the posterior mean of the time-varying failure probability, and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, estimate the posterior mean of the time-varying failure probability and the upper bound of the posterior standard deviation of the time-varying failure probability corresponding to the limiting state function. If the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability does not meet the first threshold, then according to the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, an objective function is generated to characterize the contribution of the sample point to the upper bound of the posterior standard deviation. A new observation point with the largest contribution is selected according to the objective function, and the new observation point and the observation set of the h-th iteration step are combined to form the observation set of the (h+1)-th iteration step. The observation set of the (h+1)-th iteration step is used as the target observation set, and the Bayesian inference process is executed. The objective function includes: UPSTDC(x)=[p s (x)(1-p s (x))] 1 / 2 f X (x) Where UPSTDC(x) represents the objective function, p s (x) is the safety probability at point x, 1-p s (x) represents the failure probability at point x, where x is a variable, and f X (x) is the probability density function; The step of selecting the new observation point with the greatest contribution based on the objective function includes: The time trajectory that contributes most to the upper bound of the posterior standard deviation of the time-varying failure probability is determined based on the objective function. The instant with the greatest prediction uncertainty is selected from the time trajectory based on the U function; New sample points are generated based on the instantaneous time. New observation points are obtained by observing the new sample points on the limiting state function; If the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies the first threshold, then the reliability of the bridge is evaluated based on the posterior mean of the time-varying failure probability.

2. The bridge time-varying reliability assessment method according to claim 1, characterized in that, If the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability does not satisfy a first threshold, then, based on the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, an objective function is generated to characterize the contribution of the sample points to the upper bound of the posterior standard deviation. A new observation point with the largest contribution is selected according to the objective function, and the new observation point and the observation set of the h-th iteration step are combined to form the observation set of the (h+1)-th iteration step. The observation set of the (h+1)-th iteration step is used as the target observation set, and the Bayesian inference process is executed, including: Calculate the first ratio between the upper bound of the posterior standard deviation of the time-varying failure probability and the posterior mean of the time-varying failure probability; If the first ratio is greater than or equal to the first threshold, then according to the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, an objective function is generated to characterize the contribution of the sample point to the upper bound of the posterior standard deviation. Based on the objective function, a new observation point with the largest contribution is selected, and the new observation point and the observation set of the h-th iteration step are combined to form the observation set of the h+1-th iteration step. The observation set of the h+1-th iteration step is used as the target observation set and the Bayesian inference process is executed.

3. The bridge time-varying reliability assessment method according to claim 2, characterized in that, If the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies the first threshold, then the reliability of the bridge is evaluated based on the posterior mean of the time-varying failure probability, including: If the first ratio is less than the first threshold, calculate the coefficient of variation of the posterior mean of the time-varying failure probability; If the coefficient of variation of the posterior mean of the time-varying failure probability is less than the second threshold, the reliability of the bridge is evaluated based on the posterior mean of the time-varying failure probability.

4. The bridge time-varying reliability assessment method according to claim 3, characterized in that, After calculating the variability of the posterior mean of the time-varying failure probability, the method further includes: If the first ratio is less than the first threshold and the variability of the posterior mean of the time-varying failure probability is greater than or equal to the second threshold, new sample points are generated according to the probability density function, and the new sample points and the sample set of the h-th iteration step are combined to form the sample set of the h+1-th iteration step. The sample set of the h+1-th iteration step is used as the target sample set and the Bayesian inference process is executed.

5. A time-varying reliability assessment device for bridges, characterized in that, The device includes: The observation set calculation module is used to obtain the observation set of the h-th iteration step and use the h-th iteration step observation set as the target observation set. The h-th iteration step observation set includes multiple observation points, which are obtained by observing sample points on the limit state function. The limit state function is constructed by the structural parameters of the bridge and the limit state of the specified bridge. h is a positive integer. The sample set calculation module is used to obtain the sample set of the h-th iteration step and use the sample set of the h-th iteration step as the target sample set, wherein the sample set of the h-th iteration step includes multiple sample points generated according to the probability density function; The Bayesian analysis module is used to perform the Bayesian inference process, which includes: Generate the posterior distribution of the limiting state function based on the target observation set, and infer the integral expression of the posterior mean of the time-varying failure probability corresponding to the limiting state function and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability based on the posterior distribution of the limiting state function. as well as, Based on the target sample set, the integral expression of the posterior mean of the time-varying failure probability, and the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, estimate the posterior mean of the time-varying failure probability and the upper bound of the posterior standard deviation of the time-varying failure probability corresponding to the limiting state function. The new observation point selection module is used to generate an objective function characterizing the contribution of sample points to the upper bound of the posterior standard deviation of the time-varying failure probability if the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability does not meet a first threshold. Based on the integral expression of the upper bound of the posterior standard deviation of the time-varying failure probability, the module selects the new observation point with the largest contribution according to the objective function, and combines the new observation point and the observation set of the h-th iteration step to form the observation set of the (h+1)-th iteration step. The observation set of the (h+1)-th iteration step is then used as the target observation set, and the Bayesian inference process is executed. The objective function includes: UPSTDC(x)=[p s (x)(1-p s (x))] 1 / 2 f X (x) Where UPSTDC(x) represents the objective function, p s (x) is the safety probability at point x, 1-p s (x) represents the failure probability at point x, where x is a variable, and f X (x) is the probability density function; The step of selecting the new observation point with the greatest contribution based on the objective function includes: The time trajectory that contributes most to the upper bound of the posterior standard deviation of the time-varying failure probability is determined based on the objective function. The instant with the greatest prediction uncertainty is selected from the time trajectory based on the U function; New sample points are generated based on the instantaneous time. New observation points are obtained by observing the new sample points on the limiting state function; The reliability assessment module is used to assess the reliability of the bridge based on the posterior mean of the time-varying failure probability if the ratio of the upper bound of the posterior standard deviation of the time-varying failure probability to the posterior mean of the time-varying failure probability satisfies the first threshold.

6. An electronic device, characterized in that: It includes at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, which, when executed by the at least one control processor, enables the at least one control processor to perform the bridge time-varying reliability assessment method according to any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions for causing a computer to perform the bridge time-varying reliability assessment method according to any one of claims 1 to 4.

8. A computer program product, characterized in that, When the instructions in the computer program product are executed by the processor of the electronic device, the electronic device performs the bridge time-varying reliability assessment method as described in any one of claims 1 to 4.

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