An engineering structure reliability monitoring and evaluation method based on the generalized Pareto distribution model

Abstract

The present invention discloses a method for monitoring and evaluating the reliability of engineering structures based on the generalized Pareto distribution model, which includes obtaining a strain monitoring data set, constructing a strain probability model, calculating the location parameter of the model according to the excess threshold mean chart method, Hill chart method, least mean square error method, and kurtosis method, constructing a likelihood equation set, obtaining the distribution function and probability density function of the strain probability model according to the selected parameter set, constructing a second cumulative distribution function of the strain data of the engineering structure exceeding the location parameter during the prediction period, constructing a bearing capacity function of the engineering structure, and calculating the failure probability and reliability value according to the Monte Carlo method, the probability density function of the structural resistance, and the second cumulative distribution function. According to the limited number of measured data of external load effects, the probability model of the extreme value of the external load effect of the engineering structure during the service period is predicted more accurately, and the accuracy of calculating the failure probability and reliability value of the engineering structure is improved.

Description

Technical Field

[0001] The present invention relates to the field of reliability monitoring and evaluation of engineering structures, and particularly to a method for monitoring and evaluating the reliability of engineering structures based on a generalized Pareto distribution model. Background Art

[0002] In the past more than 30 years, the civil engineering field has entered a stage of vigorous development. The total output value of the construction industry has increased from 80.8 billion yuan to 20 trillion yuan, and the cumulative completed area of residential buildings has exceeded 42 billion m 2 . As of 2021, the total mileage of highways has reached 5.28 million kilometers, and there are 76,157 urban bridges in total. Among them, there are some major projects that attract the attention of the world, such as the Donghai Bridge with a cost of 7.11 billion yuan (completed in 2005), the Three Gorges Dam project with a total investment of 248.537 billion yuan, etc. However, these major projects face many problems and challenges in engineering design, and the current design methods are difficult to ensure the long-term stability performance of engineering structures. Under harsh environmental conditions and complex load actions, engineering structures face problems such as component damage, material deterioration, and structural failure, and the reliability of the structure is gradually weakened, resulting in the actual service life of the engineering structure not reaching the design requirements. At present, most of the research on the reliability evaluation of structures is carried out from the perspective of safety, that is, the ultimate limit state of bearing capacity, and less directly uses the monitoring data of structural load effects to carry out the reliability monitoring and evaluation of engineering structures, lacking calculation methods for reliability indicators and failure probabilities for monitoring data such as stress, bending moment, and deflection at different positions of engineering structures. Summary of the Invention

[0003] The present invention provides a method for monitoring and evaluating the reliability of engineering structures based on a generalized Pareto distribution model to overcome the above technical problems.

[0004] A method for monitoring and evaluating the reliability of engineering structures based on a generalized Pareto distribution model includes:

[0005] Step 1: Obtain the strain data of sensors in the engineering structure, store the strain data in the strain monitoring data set, and construct a strain probability model based on the generalized Pareto distribution.

[0006] Step 2: Based on the strain monitoring data set, calculate the first location parameter in the strain probability model according to the excess threshold mean chart method, calculate the second location parameter in the strain probability model according to the Hill chart method, calculate the third location parameter in the strain probability model according to the least mean square error method, and calculate the fourth location parameter in the strain probability model according to the kurtosis method.

[0007] Step 3: Construct a likelihood equation system. Save the data in the strain monitoring dataset that exceeds the first location parameter into the first over-threshold sample set. Calculate the first shape parameter and the first scale parameter in the likelihood equation system based on the first over-threshold sample set. Save the first location parameter, the first shape parameter, and the first scale parameter as the first parameter set.

[0008] Save the data in the strain monitoring dataset that exceeds the second location parameter value into the second over-threshold sample set. Calculate the second shape parameter and the second scale parameter in the likelihood equation system based on the second over-threshold sample set. Save the second location parameter, the second shape parameter, and the second scale parameter as the second parameter set.

[0009] Save the data in the strain monitoring dataset that exceeds the third location parameter into the third over-threshold sample set. Calculate the third shape parameter and the third scale parameter in the likelihood equation system based on the third over-threshold sample set. Save the third location parameter, the third shape parameter, and the third scale parameter as the third parameter set.

[0010] Save the data in the strain monitoring dataset that exceeds the fourth location parameter into the fourth over-threshold sample set. Calculate the fourth shape parameter and the fourth scale parameter in the likelihood equation system based on the fourth over-threshold sample set. Save the fourth location parameter, the fourth shape parameter, and the fourth scale parameter as the fourth parameter set.

[0011] Step 4: Select one parameter set from the first parameter set, the second parameter set, the third parameter set, and the fourth parameter set. Selecting one parameter set from the first parameter set, the second parameter set, the third parameter set, and the fourth parameter set means taking the parameter set where the minimum value among the first location parameter, the second location parameter, the third location parameter, and the fourth location parameter is located as the selected parameter set. Obtain the first cumulative distribution function and the first probability density function of the strain probability model based on the generalized Pareto distribution according to the selected parameter set. Conduct a k-s test on the strain probability model based on the generalized Pareto distribution to obtain a probability model that satisfies the k-s test.

[0012] Step 5: Obtain the location parameter in the selected parameter set. Calculate the number of data in the strain dataset that exceeds the location parameter according to the location parameter. Set the prediction period. Construct the second cumulative distribution function of the strain data of the engineering structure exceeding the location parameter within the prediction period according to the selected parameter set, the number of data, and the prediction period.

[0013] Step 6: Construct a functional function for the bearing capacity of the engineering structure. Obtain the set of structural resistance limits of the engineering structure. Construct the probability density function of the structural resistance according to the set of structural resistance limits. Set the number of samplings. Calculate the failure probability and the reliability value of the engineering structure according to the Monte Carlo method, the probability density function of the structural resistance, and the second cumulative distribution function.

[0014] Preferably, the construction of the strain probability model based on the generalized Pareto distribution includes constructing the probability density function of the strain probability model according to formula (1).

[0015]

[0016] where σ is the scale parameter; ξ ∈ R is the shape parameter; μ ∈ R is the location parameter, and x is the strain data in the strain monitoring dataset.

[0017] Preferably, the construction of the likelihood equations includes constructing the likelihood equations according to formulas (2) and (3).

[0018]

[0019]

[0020] where σ is the scale parameter; ξ ∈ R is the shape parameter; μ ∈ R is the location parameter, X i is the strain data in the strain dataset, which is sorted in ascending order according to the values of the strain data. The strain data exceeding the location parameter is used as the threshold exceedance sample set, and k is the number of strain data in the threshold exceedance sample set.

[0021] Preferably, the construction of the engineering structure load-carrying capacity function includes constructing the engineering structure load-carrying capacity function according to formula (4).

[0022] Z = g(R, S) = R - S (4)

[0023] where R is the structural resistance of the engineering structure, S is the load effect of the engineering structure, Z > 0 indicates that the engineering structure is in a reliable state, Z < 0 indicates that the engineering structure is in a failure state, and Z = 0 indicates that the engineering structure is in a limit state.

[0024] Preferably, the obtaining of the set of structural resistance limits of the engineering structure includes obtaining the set of structural resistance limits by designing different loads on the engineering structure, or obtaining the set of structural resistance limits according to the design specifications of the engineering structure.

[0025] The present invention provides a method for monitoring and evaluating the reliability of engineering structures based on the generalized Pareto distribution model. By fitting the strain data, the location parameter, scale parameter, and shape parameter of the strain probability model are obtained, which solves the problem that when the arbitrary time-point distribution of the actual external load effect in engineering structures does not follow common probability distribution types, it is difficult for traditional methods to relatively accurately establish the extreme value probability model of the external load effect of engineering structures. Based on the probability model, the corresponding parameter set of the probability model, and the prediction period, the second cumulative distribution function and the second probability density function of the strain data exceeding the location parameter within the prediction period of the engineering structure are constructed. It is possible to relatively accurately predict the probability model of the extreme value of the external load effect of the engineering structure during the service reference period only based on a limited number of measured data of the external load effect. Finally, the failure probability and reliability index of the engineering structure are obtained through the Monte Carlo method, improving the calculation accuracy. Description of the Drawings

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0027] Figure 1 It is the flowchart of the method of the present invention;

[0028] Figure 2 It is the high-pile wharf model of the present invention;

[0029] Figure 3 It is the strain time-history curve under the action of the stacking load of the present invention;

[0030] Figure 4 It is the exceedance threshold mean value diagram of the present invention;

[0031] Figure 5 It is the enlarged view of the tail of the exceedance threshold mean value diagram of the present invention;

[0032] Figure 6 It is the threshold estimation diagram based on the Hill diagram method of the present invention;

[0033] Figure 7 It is the cdf diagram and pdf diagram of the generalized Pareto distribution of the present invention;

[0034] Figure 8 It is the prediction result of the strain extreme value of the present invention. Detailed Embodiments

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0036] Figure 1 This is the flowchart of the method of the present invention. As Figure 1 shown, the method of this embodiment may include:

[0037] An engineering structure reliability monitoring and evaluation method based on the generalized Pareto distribution model, including,

[0038] Step 1: Obtain the strain data of the sensors in the engineering structure, store the strain data of the sensors in the strain monitoring dataset. The strain data is the real-time data of the specific load effect at a certain monitoring position on the building structure obtained by the sensors, and construct a strain probability model based on the generalized Pareto distribution. The generalized Pareto distribution is an important branch of extreme value theory. According to extreme value statistical theory, the extreme value estimation result is usually only closely related to the right-tail distribution of the sample and has little to do with other aspects. The generalized Pareto distribution is a right-skewed distribution, parameterized using the shape parameter and the scale parameter. Its extreme value estimation result is usually only closely related to the right-tail distribution of the sample. Parametric distribution fitting of data sometimes results in a good fit of the model to the data in the high-density region, but a poor fit in the low-density region. These low-density regions are called the "tails" of the distribution. However, in many applications, the fitting of tail data is the main problem. The generalized Pareto distribution (GPD) can model the tails of various distributions based on theoretical parameters. A distribution fitting method using GPD is to use non-parametric fitting (such as the empirical cumulative distribution function) in the region where the observed values are dense, and use GPD fitting in the data tails.

[0039] The construction of the strain probability model based on the generalized Pareto distribution includes constructing the probability distribution function of the strain probability model according to formula (1),

[0040]

[0041] where σ is the scale parameter; ξ ∈ R is the shape parameter; μ ∈ R is the location parameter, and x is the strain data in the strain monitoring dataset;

[0042] Step 2: Based on the strain monitoring dataset, calculate the first location parameter in the strain probability model according to the over-threshold mean plot method. The over-threshold mean plot method is a commonly used method for selecting thresholds. This method selects the optimal threshold by establishing a relationship curve between the sample mean excess function and the threshold.

[0043] For the known datasets X1, X2, …, X n The empirical estimate of the sample mean excess function e n (μ) is:

[0044]

[0045] where N u represents the number of data points exceeding the threshold in the dataset. This defined point set {μ, e n (μ)} is called the over-threshold mean plot. Select an appropriate μ0 > 0 as the threshold in the plot such that when μ > μ0, the mean excess e n (μ) fluctuates approximately near a straight line, and μ0 is the first location parameter.

[0046] Calculate the second location parameter in the strain probability model according to the Hill plot method. The Hill estimator is suitable for heavy-tailed distributions and is a classical tail index estimator for Pareto-type distributions (ξ > 0). Assume X (n，n) <…<X (2，n) <X (1，n) is the order statistic of independent and identically distributed samples (X1, X2,..., X n ), and the Hill statistic of its tail index can be expressed as:

[0047]

[0048] The Hill plot is defined as the curve composed of points . Select the abscissa k of the starting point of the stable region where tends to be a constant in the Hill plot, and the corresponding data X k，n is the selected threshold μ, and μ is the second location parameter.

[0049] Calculate the third location parameter in the strain probability model according to the least mean square error method.

[0050] The process of determining the optimal threshold based on the least mean square error of the GPD shape parameter ξ is shown in Table 1. The optimal threshold is the third location parameter;

[0051] Table 1 Steps of the least mean square error method

[0052]

[0053]

[0054] Calculate the fourth position parameter in the strain probability model according to the kurtosis method. The principle of the kurtosis method is similar to the intersection method of the normal distribution and the heavy-tailed distribution. The calculation process is simple and easy to understand, which is convenient for practical application.

[0055] Suppose X (1，n) >X (2，n) >…X (n，n) is the descending order statistic of the observed sample (X1, X2,... X n ). The specific steps to determine the sample threshold using the kurtosis method are shown in Table 2:

[0056] Table 2 Steps of the kurtosis method

[0057]

[0058]

[0059] Step 3: Construct the likelihood equations. The probability density function of the GPD is:

[0060]

[0061] Suppose the random variable satisfies the condition X1≥X2≥......≥X k >μ>X k+1 ≥......≥X N . According to the above formula, the likelihood function of the excess-threshold sample {X1, X2,......, X k} is:

[0062]

[0063] Its log-likelihood function is:

[0064]

[0065] Take the first-order derivatives of the log-likelihood function with respect to the parameters σ and ξ respectively, and let The simplified likelihood equations are Formulas (7) and (8),

[0066]

[0067]

[0068] where σ is the scale parameter; ξ ∈ R is the shape parameter; μ ∈ R is the position parameter, X i is the strain data in the strain dataset. Sort the strain data in ascending order according to its value, and take the strain data exceeding the position parameter as the excess-threshold sample set. k is the number of strain data in the excess-threshold sample set;

[0069] Save the data in the strain monitoring dataset that exceeds the first position parameter into the first super-threshold sample set, calculate the first shape parameter and the first scale parameter in the likelihood equation set according to the first super-threshold sample set, and save the first position parameter, the first shape parameter, and the first scale parameter as the first parameter set;

[0070] Save the data in the strain monitoring dataset that exceeds the second position parameter value into the second super-threshold sample set, calculate the second shape parameter and the second scale parameter in the likelihood equation set according to the second super-threshold sample set, and save the second position parameter, the second shape parameter, and the second scale parameter as the second parameter set,

[0071] Save the data in the strain monitoring dataset that exceeds the third position parameter into the third super-threshold sample set, calculate the third shape parameter and the third scale parameter in the likelihood equation set according to the third super-threshold sample set, and save the third position parameter, the third shape parameter, and the third scale parameter as the third parameter set,

[0072] Save the data in the strain monitoring dataset that exceeds the fourth position parameter into the fourth super-threshold sample set, calculate the fourth shape parameter and the fourth scale parameter in the likelihood equation set according to the fourth super-threshold sample set, and save the fourth position parameter, the fourth shape parameter, and the fourth scale parameter as the fourth parameter set.

[0073] Step 4: Select one parameter set from the first parameter set, the second parameter set, the third parameter set, and the fourth parameter set. The selection of one parameter set from the first parameter set, the second parameter set, the third parameter set, and the fourth parameter set means taking the parameter set where the minimum value among the first position parameter, the second position parameter, the third position parameter, and the fourth position parameter is located as the selected parameter set. Obtain the first cumulative distribution function and the first probability density function of the strain probability model based on the generalized Pareto distribution according to the selected parameter set, and conduct a k-s test on the strain probability model based on the generalized Pareto distribution. The Kolmogorov-Smirnov test (k-s test) is a non-parametric test method that can theoretically test any distribution situation (not limited to normal distribution test). It is a test method for comparing a frequency distribution f(x) with a theoretical distribution g(x) or two observed value distributions.

[0074] Its null hypothesis H0: The two data distributions are consistent or the data conforms to the theoretical distribution. D = max|f(x) - g(x)|. When the actual observed value D > D(n, a), then reject H0, otherwise accept the H0 hypothesis. D(n, a) is the statistical quantity threshold when the degree of freedom is n and the significance level is a.

[0075] Obtain the probability model that satisfies the k-s test.

[0076] The variable actions in structure should preferably be described by a stochastic process probability model. The filtered Poisson process is a kind of stochastic point process and can be used as the probability model of the stochastic process of the external load effect of engineering structures. Its expression is:

[0077]

[0078] In the formula: {N(t), t≥0} is the Poisson process; N(t) is the number of events occurring within time t, that is, the number of data peaks generated within time t; {ζ k , k = 0, 1, 2,...} is a set of independent and identically distributed random sequences, independent of {N(t)}, and ζ k is the k-th strain peak, and T k is the time when the k-th data peak appears.

[0079] The response function is:

[0080]

[0081] Based on the above stochastic process theory, the cumulative probability distribution of the extreme value of the building within the prediction period T can be deduced as:

[0082]

[0083] In the formula: F(x) is the distribution function of any time point of the stochastic process X(t), that is, the sectional distribution; n is the Poisson process intensity, indicating the number of strain peaks generated per unit time.

[0084] Substituting the probability distribution function F(x) of the generalized Pareto distribution into F M (x), the probability distribution function of the extreme value caused by the external load within the remaining service life of the engineering structure can be obtained as:

[0085]

[0086] Step 5: Obtain the location parameter in the selected parameter set, calculate the number of data in the strain dataset that exceeds the location parameter according to the location parameter, set the prediction period. According to the above filtered Poisson process, it can be known that by constructing the second cumulative distribution function of the strain data of the engineering structure that exceeds the location parameter within the prediction period according to the selected parameter set, the data quantity, and the prediction period.

[0087] When the whole structure or a part of the structure exceeds a certain specific state, it cannot meet a certain functional requirement specified in the design. This specific state is called the limit state of the structure. The limit state of the structure is the critical state between reliable and unreliable operation of the structure. The reliability analysis and design of the structure are based on whether the structure reaches the limit state. The limit state can generally be divided into two categories: the ultimate limit state of bearing capacity and the serviceability limit state.

[0088] According to the functional requirements of the structure and the signs of the corresponding limit states, the functional function or limit state equation of the structure can be established. Let X=(X1, X2,..., X n ) T be the n basic random variables that affect the structure's function. X can be the geometric dimensions of the structure, the physical and mechanical parameters of the material, the actions applied to the structure, etc. The random function is called the functional function, failure function, or limit state function of the structure:

[0089] Z = g(X) = g(X1, X2,..., X n ) (13)

[0090] It is stipulated that Z>0 indicates that the structure is in a reliable state, Z<0 indicates that the structure is in a failure state, and Z = 0 indicates that the structure is in the limit state.

[0091] The structural resistance refers to the ability of the structure to resist failure or deformation, such as ultimate internal force, ultimate strength, ultimate stiffness, as well as anti-sliding force, anti-overturning moment, etc. In this calculation, the structural resistance can take the corresponding limit values according to the design code or adopt the calculated values under the design loads.

[0092] The load effect refers to the internal force, displacement, etc. of the structural members caused by the load. In this calculation, the generalized Pareto distribution obtained by fitting the sample data, and the probability distribution function F(x) of the extreme value can be obtained through the filtered Poisson process; the Markov chain Monte Carlo method is used to sample and calculate the probability distribution function F M (x) is the load effect.

[0093] Step 6: Construct the functional function of the bearing capacity of the engineering structure. The construction of the functional function of the bearing capacity of the engineering structure includes constructing the functional function of the bearing capacity of the engineering structure according to formula (14),

[0094] Z = g(R, S) = R - S (14)

[0095] where R is the structural resistance of the engineering structure, S is the load effect of the engineering structure, Z>0 indicates that the engineering structure is in a reliable state, Z<0 indicates that the engineering structure is in a failure state, and Z = 0 indicates that the engineering structure is in the limit state;

[0096] Monte Carlo simulation is also known as the stochastic simulation method or the random sampling technique. It is a numerical method based on probability theory and mathematical statistics that obtains an approximate solution to a problem through statistical experiments and random simulations of random variables. Its main idea is as follows: To solve a problem, a probability model or a stochastic process is established such that its parameters are equal to the solution of the problem; then, by observing or sampling the model or process, the statistical characteristics (such as the mean, probability, etc.) of the parameters to be solved are calculated as the numerical solution of the problem to be solved. Finally, an approximate value of the solution is given, and the accuracy of the solution can be represented by the variance of the estimated value.

[0097] In the Monte Carlo method, its core idea is the law of large numbers, which uses a large number of sample statistics to replace the probability of the population.

[0098] Let there be independent random variables X1, X2,..., X n , and their corresponding probability density functions are respectively The state equation is Y = g(X1, X2,..., X n ), and the failure probability P f The solution process is as follows:

[0099] (1) First, use random sampling to obtain the quantile values x1, x2,..., x n of each variable respectively.

[0100] (2) Calculate the state function value: Y i = g(x1, x2,..., x n ).

[0101] (3) Let the number of samplings be N, and among them, the number of times L when the state function value Y i corresponding to the quantile value of the sampling variable is less than 0. Then the failure probability of the structure is:

[0102]

[0103] The reliability index of an engineering structure: The ability of a structure to complete its intended function within a specified time and under specified conditions is called the reliability of the structure. The probability that a structure completes its intended function within a specified time and under specified conditions is called the reliability of the structure. The structural reliability is the probability measure of the structural reliability, and the reliability is represented by β.

[0104] The failure probability of an engineering structure: The probability that a structure cannot complete its intended function, that is, the probability that the structure function appears less than zero (Z < 0) is called the failure probability of the structure, represented by P f .

[0105] The relationship between the structural reliability index and the failure probability is:

[0106] Pf = φ(-β) (16)

[0107] Obtain the set of structural resistance limit values of the engineering structure. The obtaining of the set of structural resistance limit values of the engineering structure includes obtaining the set of structural resistance limit values by designing different loads on the engineering structure, or obtaining the set of structural resistance limit values according to the design specifications of the engineering structure;

[0108] Construct the probability density function of the structural resistance according to the set of structural resistance limits, set the number of sampling times, and calculate the failure probability and reliability value of the engineering structure according to the Monte Carlo method, the probability density function of the structural resistance, and the second cumulative distribution function. Among them, random sampling can also be performed on the second cumulative distribution function of the structural resistance based on the Markov chain Monte Carlo method to obtain a Markov chain with a stationary distribution,

[0109] The Markov chain Monte Carlo method (MCMC) is a random sampling method. Compared with traditional Monte Carlo methods such as the acceptance-rejection method and importance sampling method, the Markov chain Monte Carlo method is more suitable for situations where the random variables are multivariate, the density function is in a non-standard form, the components of the random variables are not independent, etc., and the sampling efficiency is higher. The MCMC method establishes a Markov chain with a stationary distribution through repeated sampling, thereby obtaining state samples of the system.

[0110] The basic idea of the Markov chain Monte Carlo method is as follows: Use a certain sampling method for repeated sampling to establish a Markov chain with a stationary distribution of p(x) to obtain samples of p(x), and then perform Monte Carlo simulation on these samples, that is, establish a Markov chain that always converges to the stationary distribution p(x) to obtain state samples of the target distribution.

[0111] Among them, the Metropolis-Hastings algorithm is the most basic Markov chain Monte Carlo method, and its specific sampling steps are as follows:

[0112] For the target sampling distribution π(x):

[0113] The first step: Randomly select a starting point x, and specify the burn-in period m and the stabilization period N.

[0114] The second step: Start sampling. In each round of sampling, generate a normal distribution with the sampling value x of the previous round as the mean and a variance of 1, and then randomly select a value x from this normal distribution with a certain probability * .

[0115] The third step: Randomly generate a number U in the uniform distribution of [0, 1], and specify the acceptance probability If U < a, then the new sampling value of this round is x = x *, otherwise the new sampling value for this round remains the x of the previous round.

[0116] Repeat the sampling process in the second step to the third step m + N times. After completion, retain the results of the latter sampling as the approximate sampling of the target distribution.

[0117] This embodiment takes a simple high-pile wharf model as an example to illustrate the feasibility of the reliability monitoring and evaluation method. The high-pile wharf deck is subjected to stacking load. The stacking load is a uniformly distributed load along the entire wharf surface and has symmetry. The model is as Figure 2 shown, where A is the pile, B is the wharf deck, C is the seawater model, and D is the loading load. Strain monitoring data can be obtained through the strain sensors installed on the piles, and the time history curve of the strain monitoring data is as Figure 3 shown.

[0118] Obtain 4000 samples of strain extreme value monitoring data according to the strain time history curve, and its specific data set is S X =(15.2462, 8.8402,..., 14.5411,..., 12.9840, 18.7836). It is planned to use the generalized Pareto distribution as the probability model of the measured exceedance data, and four threshold estimation methods are selected to estimate the parameter μ of the GPD.

[0119] First, use the exceedance mean plot method for estimation. For the known data set S X Substitute it into the formula: and plot the exceedance mean plot of the points {μ, e 4000 (μ)}, where the abscissa 0 < μ < 20.5. The plotted exceedance mean plot is shown in Figure 4 , Figure 5 is the enlarged tail figure. Observe the enlarged curve Figure 5 It can be seen that when the abscissa, that is, the threshold μ > 20.2232, the average excess e 4000 (μ) fluctuates approximately near a straight line. Determine its threshold μ1 = 20.2232, and this threshold is the first location parameter.

[0120] Use the Hill plot method to estimate the threshold. Sort the data set S X in descending order as (20.2537, 20.2218,..., 14.8075,..., 1.2189, -1.9515), and substitute it into the formula and plot the Hill plot of the points , where 0 < k < 4000. The plotted result is shown in Figure 6 shown. The abscissa k of the starting point of the stable region where the ordinate tends to be a constant in the Hill plot is 1218, and its corresponding data value X k，n= 16.0058, that is, the threshold μ2 = 16.0058, and this threshold is the second location parameter.

[0121] The minimum mean square error method is used to estimate the threshold.

[0122] (1) Denote the descending-ordered sample set as S = [20.2537, 20.2218,..., 14.8075,..., 1.2189, -1.9515]. Take k = 2603 and repeat the following steps;

[0123] (2) Select the first 2603 sample points from the S samples to form the initial sample S k = [20.2537, 20.2218,..., 14.8075,..., 13.8157, 13.8151]. Fit the initial sample S with GPD k , and calculate the shape parameter of GPD using the maximum likelihood estimation method where the location parameter, i.e., the threshold μ = 13.8151;

[0124] (3) Adopt the method of sampling with replacement to draw 2603 samples from the initial sample S k to obtain the bootstrap sample S k (i) = [14.9204, 14.1177,..., 14.5782];

[0125] (4) Fit the bootstrap sample S with GPD k (i) , and calculate the shape parameter of GPD using the maximum likelihood estimation method where the location parameter μ = 13.8151;

[0126] (5) Repeat steps (3) and (4) 200 times to obtain 200 estimated values of the shape parameter, denoted as {-0.4700, -0.4717,..., -0.4633};

[0127] (6) Calculate the mean square error of the GPD shape parameter estimated based on 2063 tail data (S k ). Substitute B = 200, and obtain

[0128]

[0129] (7) Repeat steps (2) to (6) 50 times to obtain the corresponding mean square errors, denoted as (0.0013, 3.1586×10 -4 ,..., 3.4923×10 -5), select the minimum value among them, min(MSE) = 3.4923×10 -5 , according to the minimum value of MSE, determine the corresponding μ value as 13.1998, that is, the threshold μ3 = 13.1998, and this threshold is the third location parameter.

[0130] Estimate the threshold using the kurtosis method. After removing the data in the samples several times, the calculated average value and the kurtosis coefficient K = 2.9936. Since K is less than 3 and meets the condition, take the largest sample among the remaining sample points as the threshold. The largest sample is 20.2357, that is, the threshold μ4 = 20.2357, and this threshold is the fourth location parameter.

[0131] After knowing the four thresholds, use the maximum likelihood estimation method to estimate their parameters respectively, and obtain the corresponding parameter values ξ and σ. Taking the threshold μ2 = 16.0058 calculated by the Hill diagram method as an example, according to the obtained threshold, the over-threshold samples s U ={X1, X2,......, X k}={20.2537, 20.2218,......, 16.0058}, substitute it into the equation system

[0132] to obtain the corresponding parameter values ξ = -0.3400 and σ = 1.5426. The current ξ is the second shape parameter, and σ is the second size parameter. The calculation steps of the other three methods are the same, and the obtained parameter sets are shown in Table 3.

[0133] Table 3 Generalized Pareto distribution parameter set

[0134] Method μ ξ σ Over-threshold mean chart method 20.2232 NaN 0 Hill chart method 16.0058 -0.3400 1.5426 Least mean square error method 13.1998 -0.5148 3.6403 Kurtosis method 20.2357 NaN 0

[0135] Among them, μ = 20.2232 in the second row is the first location parameter, ξ is NaN which is the first shape parameter, σ = 0 is the first size parameter. According to the first location parameter, the first shape parameter, and the first size parameter, the first parameter set is obtained.

[0136] In the third row, μ = 16.0058 is the second location parameter, ξ = -0.3400 is the second shape parameter, σ = 1.5426 is the second size parameter. According to the second location parameter, the second shape parameter, and the second size parameter, the second parameter set is obtained.

[0137] In the fourth row, μ = 13.1998 is the third location parameter, ξ = -0.5148 is the third shape parameter, σ = 3.6403 is the third size parameter. According to the third location parameter, the third shape parameter, and the third size parameter, the third parameter set is obtained.

[0138] In the fifth row, μ = 20.2357 is the fourth location parameter, ξ is NaN which is the fourth shape parameter, σ = 0 is the fourth scale parameter. The fourth parameter set is obtained based on the fourth location parameter, the fourth shape parameter, and the fourth scale parameter.

[0139] Since the values of the first location parameter and the fourth location parameter are relatively large, resulting in very few data exceeding the threshold, it is impossible to calculate the other two parameters. The value of the third shape parameter is less than -1 / 2, resulting in the confidence interval and standard error not being able to be calculated reliably. Therefore, the second parameter set is selected, that is, μ w = 16.0058, ξ = -0.3400, σ = 1.5426.

[0140] The cumulative distribution function of the generalized Pareto distribution obtained through the second parameter set is The probability density function is The plotted cumulative distribution function (CDF) graph and probability density function (PDF) graph are as Figure 7 shown.

[0141] The obtained GPD probability model is subjected to the k-s test and the fitting of the data exceeding the threshold. After testing, it can be obtained that using the GPD distribution as the probability model of the measured data exceeding the threshold can pass the k-s test.

[0142] After determining that the values of the parameters μ, ξ, and σ of the generalized Pareto distribution are the second parameter set, it is necessary to determine the parameters λ and T of the filtered Poisson process. λ is the number of data exceeding the given threshold within the unit time period. According to the above calculation results, λ = 1218 is taken. T is the prediction period, and here T = 50 is taken.

[0143] Based on the above parameters, the cumulative distribution function of the extreme value of the strain caused by the stacking load of the high-pile wharf during the prediction period T can be obtained as and the probability density function is The plotted curve graph is shown in Figure 8 shown.

[0144] Let the structural bearing capacity function be: Z = g(R, S) = R - S.

[0145] When calculating the reliability of the strain of the high-pile wharf structure caused by the stacking load in this time, it is assumed that the structural resistance obeys a normal distribution with μ R = 400, σ R = 60, and its probability density function is The sample random number collection of the normal distribution of the structural resistance R.

[0146] The probability distribution function F of the extreme value of the high-pile wharf caused by the stacking load during the prediction period is obtained MAfter (x), the Markov Chain Monte Carlo method can be used to sample and calculate the probability distribution function F(x), and finally a convergent and stationary probability distribution F is obtained. M The sample set of (x) is the load effect S.

[0147] According to the known performance function, the Monte Carlo method is used to calculate the reliability index and the failure probability. Let the number of samplings N = 40000, and the number of times the state function value Z < 0 is 1. The failure probability calculated according to the formula Its reliability index β = -φ -1 (P f ) = 4.0556.

[0148] Overall beneficial effects:

[0149] The present invention provides a method for monitoring and evaluating the reliability of engineering structures based on the generalized Pareto distribution model. By fitting the strain data, the location parameter, scale parameter, and shape parameter of the strain probability model are obtained, which solves the problem that when the arbitrary time point distribution of the actual external load effect in engineering structures does not follow the common probability distribution types, it is difficult for traditional methods to relatively accurately establish the extreme value probability model of the external load effect of engineering structures. Based on the probability model, the corresponding parameter set of the probability model, and the prediction period, the second cumulative distribution function of the strain data exceeding the location parameter within the prediction period of the engineering structure is constructed, and the probability model of the extreme value of the external load effect of the engineering structure within the service reference period can be relatively accurately predicted only based on a limited number of measured data of the external load effect. Finally, the failure probability and reliability index of the engineering structure are obtained through the Monte Carlo method, improving the calculation accuracy.

[0150] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A reliability monitoring and evaluation method for engineering structures based on the generalized Pareto distribution model, characterized in that, including Step 1: Obtain the strain data of sensors in the engineering structure, store the strain data in the strain monitoring dataset, and construct a strain probability model based on the Generalized Pareto Distribution. Step 2: Based on the strain monitoring dataset, calculate the first location parameter in the strain probability model according to the over-threshold mean chart method, calculate the second location parameter in the strain probability model according to the Hill chart method, calculate the third location parameter in the strain probability model according to the least mean square error method, and calculate the fourth location parameter in the strain probability model according to the kurtosis method. Step 3: Construct a likelihood equation set, save the data in the strain monitoring dataset that exceeds the first location parameter into the first over-threshold sample set, calculate the first shape parameter and the first scale parameter in the likelihood equation set according to the first over-threshold sample set, and save the first location parameter, the first shape parameter, and the first scale parameter as the first parameter set. Save the data in the strain monitoring dataset that exceeds the second location parameter value into the second over-threshold sample set, calculate the second shape parameter and the second scale parameter in the likelihood equation set according to the second over-threshold sample set, and save the second location parameter, the second shape parameter, and the second scale parameter as the second parameter set. Save the data in the strain monitoring dataset that exceeds the third location parameter into the third over-threshold sample set, calculate the third shape parameter and the third scale parameter in the likelihood equation set according to the third over-threshold sample set, and save the third location parameter, the third shape parameter, and the third scale parameter as the third parameter set. Save the data in the strain monitoring dataset that exceeds the fourth location parameter into the fourth over-threshold sample set, calculate the fourth shape parameter and the fourth scale parameter in the likelihood equation set according to the fourth over-threshold sample set, and save the fourth location parameter, the fourth shape parameter, and the fourth scale parameter as the fourth parameter set. Step 4: Select a parameter set from the first parameter set, the second parameter set, the third parameter set, and the fourth parameter set. Selecting a parameter set from the first parameter set, the second parameter set, the third parameter set, and the fourth parameter set means taking the parameter set where the minimum value among the first location parameter, the second location parameter, the third location parameter, and the fourth location parameter is located as the selected parameter set. Obtain the first cumulative distribution function and the first probability density function of the strain probability model based on the Generalized Pareto Distribution according to the selected parameter set, and conduct a k-s test on the strain probability model based on the Generalized Pareto Distribution to obtain a probability model that meets the k-s test. Step 5: Obtain the location parameter in the selected parameter set, calculate the number of data in the strain dataset that exceeds the location parameter according to the location parameter, set the prediction period, and construct the second cumulative distribution function of the strain data in the engineering structure that exceeds the location parameter within the prediction period according to the selected parameter set, the number of data, and the prediction period. Step 6: Construct the functional function of the engineering structure's bearing capacity, obtain the set of structural resistance limits of the engineering structure, construct the probability density function of the structural resistance according to the set of structural resistance limits, set the number of sampling times, and calculate the failure probability and reliability value of the engineering structure according to the Monte Carlo method, the probability density function of the structural resistance, and the second cumulative distribution function.

2. The engineering structure reliability monitoring and evaluation method based on the generalized Pareto distribution model according to claim 1, characterized in that, The construction of the strain probability model based on the generalized Pareto distribution includes constructing the probability distribution function of the strain probability model according to formula (1), where σ is the scale parameter; ξ ∈ R is the shape parameter; μ ∈ R is the location parameter, and x is the strain data in the strain monitoring dataset.

3. A reliability monitoring and evaluation method for engineering structures based on the generalized Pareto distribution model according to claim 1, characterized in that, The construction of the likelihood equations includes constructing the likelihood equations according to formulas (2) and (3), where, σ is the scale parameter; ξ ∈ R is the shape parameter; μ ∈ R is the position parameter, and X i is the strain data in the strain dataset, which is sorted in ascending order according to the values of the strain data. The strain data exceeding the position parameter is used as the set of over-threshold samples, and k is the number of strain data in the set of over-threshold samples.

4. A reliability monitoring and evaluation method for engineering structures based on the generalized Pareto distribution model according to claim 1, characterized in that, The construction of the functional function of the engineering structure's bearing capacity includes constructing the functional function of the engineering structure's bearing capacity according to formula (4), Z = g(R, S) = R - S (4) where R is the structural resistance of the engineering structure, S is the load effect of the engineering structure, Z > 0 indicates that the engineering structure is in a reliable state, Z < 0 indicates that the engineering structure is in a failure state, and Z = 0 indicates that the engineering structure is in a limit state.

5. A reliability monitoring and evaluation method for engineering structures based on the generalized Pareto distribution model according to claim 1, characterized in that, The obtaining of the set of structural resistance limits of the engineering structure includes obtaining the set of structural resistance limits by designing different loads on the engineering structure, or obtaining the set of structural resistance limits according to the design specifications of the engineering structure.

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