Natural gas pipeline time-varying reliability prediction method considering corrosion correlation

Abstract

The invention discloses a natural gas pipeline time-varying reliability prediction method considering corrosion correlation, and relates to the field of natural gas pipeline safety assessment, and the method comprises the steps: collecting finite continuous ILI data of a natural gas pipeline, building a logarithmic normal probability model of pipeline corrosion defect geometric parameters, and calculating the corrosion defect geometric parameters of the pipeline; acquiring distribution parameters and correlation coefficients of the geometric parameters; based on the distribution parameters and the correlation coefficients, constructing a covariance matrix, and performing Cholesky decomposition to generate an initial corrosion random sample of the pipeline; based on limited continuous ILI data, constructing a gamma process growth model, and performing defect evolution prediction on the initial corrosion random sample to obtain a prediction result; on the basis of the prediction result, the bursting pressure of the natural gas pipeline at the prediction time point is calculated, a limit state equation is constructed, and the time-varying failure probability of the pipeline is calculated through a PHI2 method; through the four steps, the accuracy and scientificity of pipeline corrosion safety risk decision making under the condition of limited detection data are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of natural gas pipeline safety assessment, in particular to a time-varying reliability prediction method for natural gas pipeline considering corrosion correlation. BACKGROUND

[0002] Currently, for the integrity assessment and residual life prediction of corroded natural gas pipelines, the engineering and academic communities mainly rely on rule-based assessment methods (such as ASME B31G, CSA Z662, etc.) and probabilistic reliability models. These traditional methods usually simplify corrosion defects into regular geometric shapes (such as rectangles or ellipses), and use deterministic or random models to independently model and predict single defect parameters. With further research, random field theory and gamma process are introduced to characterize the spatial variability and temporal variability of corrosion defects, and internal inspection (ILI) data is used to provide measured support.

[0003] However, these existing technologies still have many limitations:

[0004] In terms of defect correlation modeling: Most methods fail to systematically consider the cross-correlation between corrosion defect geometric parameters (length, width, depth) and the spatial correlation of defect distribution along the pipeline axis. Even though some studies attempt to build multivariate models, they often have problems such as complex models, low computational efficiency, or difficulty in directly embedding into time-varying reliability analysis frameworks when dealing with three-dimensional spatial correlation and parameter estimation under limited ILI data conditions. At the same time, the lack of a practical modeling framework that considers both geometric parameter correlation and spatial distribution correlation leads to biases in the assessment of corrosion aggregation areas and synergistic evolution effects.

[0005] In terms of practical data application: Due to the high cost and long implementation period of ILI detection, the available data is limited and there are measurement errors. Traditional parameter estimation methods are difficult to accurately construct the correlation structure between multiple defects and multiple parameters, and cannot effectively describe the non-stationary growth characteristics of corrosion over time, resulting in large uncertainties in evolution prediction.

[0006] In terms of time-varying reliability analysis, although Monte Carlo simulation, first-order reliability method (FORM), etc. have been widely applied, their computational efficiency is low, and most methods do not strictly follow the non-stationary random process theory, making it difficult to accurately represent the failure probability evolution process of the pipeline throughout its life cycle.

[0007] The above defects result in a lack of systematization in the overall assessment framework, limiting the engineering applicability and decision support capability of the assessment results. These defects not only affect the accuracy of pipeline safety assessment, but also bring additional costs and risks to operation and maintenance. SUMMARY

[0008] The application aims to provide a natural gas pipeline corrosion defect three-dimensional time-varying reliability analysis method which is accurate and efficient.

[0009] To achieve the above-mentioned purpose, a natural gas pipeline time-varying reliability prediction method considering corrosion correlation is established, and the method comprises the following steps:

[0010] Step one: collect limited continuous ILI data of the natural gas pipeline, construct a lognormal probability model of the pipeline corrosion defect geometric parameters based on the initial ILI data, quantify the cross correlation between the geometric parameters and the spatial correlation along the pipeline axial direction, obtain the distribution parameters and correlation coefficients of the geometric parameters;

[0011] Step two: construct a covariance matrix based on the distribution parameters and the correlation coefficients, perform Cholesky decomposition on the covariance matrix, generate an initial corrosion random field of the pipeline, and obtain initial corrosion random samples;

[0012] Step three: construct a gamma process growth model based on the limited continuous ILI data, perform defect evolution prediction on the initial corrosion random samples based on the gamma process growth model, and obtain a prediction result;

[0013] Step four: calculate the burst pressure of the natural gas pipeline at the prediction time point based on the prediction result, construct a limit state equation based on the burst pressure, and calculate the time-varying failure probability of the pipeline by using PHI2 method based on the limit state equation;

[0014] The geometric parameters include the length, width and depth of the corrosion defect.

[0015] The corrosion defect of the natural gas pipeline has spatial correlation in the three-dimensional parameters of length, width and depth, and its evolution is a time-varying process. Traditional prediction methods often simplify the defect geometric shape or ignore the correlation between parameters, resulting in significant deviation in long-term reliability prediction.

[0016] In step one, the scheme is based on the initial ILI data to construct a lognormal probability model of geometric parameters covering three dimensions of length, width and depth, to obtain the distribution parameters and correlation coefficients, and to solve the problem of incomplete characterization of initial corrosion morphology statistical characteristics and spatial correlation in the traditional method; step two is to construct a covariance matrix based on these distribution parameters and correlation coefficients and to perform Cholesky decomposition to generate an initial corrosion random sample, which can accurately reproduce the three-dimensional distribution characteristics and aggregation effect of corrosion defects in the axial, circumferential and radial directions, solve the problem of spatial correlation estimation bias under small sample, make the corrosion morphology simulation more in line with the actual working conditions, and provide reliable geometric parameter input for subsequent reliability analysis; step three is to construct a gamma process growth model based on limited continuous ILI data, the gamma process conforms to the physical properties changing with time, and can intuitively reflect the trend of parameter change with time. In addition, the independent non-negative increment and monotonic increment characteristics of the gamma distribution can characterize the time variation of corrosion geometric parameters, and combined with the gamma process, the monotonic cumulative growth characteristics of corrosion defects along the axial, radial and circumferential directions can be accurately simulated, the defect size distribution at different time nodes can be quantified, and the corrosion evolution prediction accuracy is greatly improved, providing timely and reliable state prediction basis for pipeline life cycle integrity management. Finally, step four is to calculate the pipeline burst pressure at the future time point based on the gamma prediction result, and to construct the limit state equation, and then to calculate the time-varying failure probability by PHI2 method,

[0017] The complex dynamic reliability problem is converted into a cross-time domain integral problem that can be efficiently solved, avoiding the defects of high calculation cost or theoretical misuse of traditional Monte Carlo simulation method. Through the above four steps, the accuracy and scientificity of pipeline corrosion safety risk decision-making under the condition of limited detection data are significantly improved.

[0018] Further, the distribution parameters include a log mean and a log standard deviation;

[0019] The calculation formula of the log mean μ xi is as follows:

[0020] ;

[0021] The calculation formula of the log standard deviation σ xi is as follows:

[0022] ;

[0023] Wherein, is the mean of lnxi, is the standard deviation of lnxi, is the total sample size, is the geometric parameter dimension identifier x ifor the geometric parameters, j = 1, 2, …, N.

[0024] Further, the calculation formula of the correlation coefficient is as follows:

[0025]

[0026] wherein, ρ XY is the correlation coefficient of X i and Y i , , ρ XY = ρ YX , X i,j is the measured value of X i in the jth sample, Y i，j is the measured value of parameter Y i in the jth sample, μ Xi is the logarithmic mean of X i in all samples, and μ Yi is the logarithmic mean of Y i in all samples.

[0027] Further, in step two, the covariance matrix is ∑, wherein:

[0028]

[0029] wherein, is the variance of the length of the corrosion defect, is the variance of the width of the corrosion defect, is the variance of the depth of the corrosion defect, l is the length of the corrosion defect, d is the depth of the corrosion defect, w is the width of the corrosion defect, ρ wl is the correlation coefficient of w and , is the correlation coefficient of d and l, is the correlation coefficient of and w, ρ dw is the correlation coefficient of d and w, ρ ld is the correlation coefficient of l and d, is the correlation coefficient of and d, is the logarithmic standard deviation of w, is the logarithmic standard deviation of l, is the logarithmic standard deviation of d.

[0030] Further, in step two, the calculation formula of the initial corrosion random sample is as follows:

[0031]

[0032] ​​​wherein S xi is the initial corrosion random field sample, x i is the geometric parameter, x i = l, d, w, l is the length of the corrosion defect, d is the depth of the corrosion defect, w is the width of the corrosion defect, μ xi is the logarithmic mean of x i , σ xi is the logarithmic standard deviation of x i , is the inverse function of the probability density function of the geometric parameter, Z xi is the correlation standardized sample based on the lower triangular matrix U transformation, obtained by Cholesky decomposition of the covariance matrix, wherein .

[0033] Further, the gamma process growth model is constructed based on the limited continuous ILI data, comprising:

[0034] Based on the limited continuous ILI data, the actual geometric parameter mean and the actual geometric parameter standard deviation of all corrosion defects at each acquisition time point are calculated and obtained;

[0035] The gamma process growth model is constructed, the shape parameter and the rate parameter of the gamma process growth model are defined, and the predicted geometric parameter mean and the predicted geometric parameter standard deviation of all corrosion defects at each acquisition time point are derived based on the shape parameter and the rate parameter;

[0036] An optimization objective function is constructed, which is used to minimize the difference between the actual geometric parameter mean and the predicted geometric parameter mean, and the difference between the actual geometric parameter standard deviation and the predicted geometric parameter standard deviation;

[0037] The optimization objective function is solved to obtain the optimal value of the shape parameter and the rate parameter;

[0038] The optimal value is substituted into to complete the construction of the gamma process growth model.

[0039] The actual geometric parameter mean and actual geometric parameter standard deviation of all corrosion defects at each detection time point are calculated based on the limited continuous ILI data, and these statistics objectively reflect the real collective behavior and dispersion degree of corrosion defects in three-dimensional space over time; then, a gamma process growth model is constructed and key time-varying parameters, i.e., a shape parameter and a rate parameter, are defined, based on the theoretical properties of the two parameters, the predicted geometric parameter mean and predicted geometric parameter standard deviation generated by the model at the same time point can be derived; then, an optimization objective function is constructed, and the core objective of the function is to minimize the difference between the model prediction value and the actual observation value, which makes the calibration process of the model into a mathematical optimization problem with the goal of matching the statistical characteristics of historical data; by solving the optimization objective function, the optimal values of the shape parameter and the rate parameter under the current data conditions can be obtained; finally, the two optimal parameters are substituted into the model, and the construction of the gamma process growth model is completed. The present scheme estimates the time-varying parameters directly based on the statistical characteristics of the continuous ILI data by optimizing the model, without complex prior assumptions, so as to accurately capture the monotonic cumulative growth characteristics of corrosion defects in three-dimensional space, and greatly improve the precision and reliability of predicting future corrosion morphology evolution from limited historical data.

[0040] Further, the probability density function of the gamma process growth model is , wherein:

[0041] ;

[0042] , wherein: is the shape parameter at t time, is the rate parameter, is the increment of the corrosion defect geometric parameter in the time interval , and is the gamma function.

[0043] Further, in step four, the formula for calculating the burst pressure of the natural gas pipeline at the predicted time point is:

[0044] ;

[0045] , wherein: is the pipeline burst pressure at t time, is the yield strength of the pipeline, D is the outer diameter of the pipeline, δ is the wall thickness, d(t) is the depth of the corrosion defect at t time, w(t) is the width of the corrosion defect at t time, is the length of the corrosion defect at t time, m is the first fitting parameter, n is the second fitting parameter, and r is the third fitting parameter

[0046] Further, the limit state equation is:

[0047] ;

[0048] wherein, is the limit state function value at time t, is the pipe burst pressure at time t, P0 is the internal working pressure of the pipe, which is the pressure generated by the natural gas transported in the pipe on the inner wall of the pipe during normal service of the natural gas pipe, and X is a set of static random variables, is a set of time-varying random parameters, and ω is a sampling point in the initial corrosion random sample space.

[0049] Further, the PHI2 method is used to calculate the time-varying failure probability of the pipe based on the limit state equation, comprising:

[0050] based on the limit state function value at time t , a reliability index at time t is calculated and obtained;

[0051] based on the limit state function value at time t , a reliability index at time t is calculated and obtained; correlation between G(t, X(t, ω) and G(t+Δt, X(t+Δt, ω) is calculated, and a correlation coefficient

[0052] is obtained;

[0053] based on β(t), and ρ(t, t+Δt), a bivariate normal distribution function is used to calculate a crossing rate;

[0054] the crossing rate is time-integrated to obtain the time-varying failure probability .

[0055] wherein, β(t) and quantify the safety margin of the pipe at two consecutive time points t and respectively, and characterizes the statistical association characteristics of the pipe failure process at consecutive time points; the crossing rate refers to the average probability that the performance of the pipe first crosses from a safe state to a failure state between two time points, and by time-integrating these discrete crossing rates in the entire service period, the time-varying failure probability evolution law of the pipe in the running period can be obtained.

[0056] The one or more technical solutions provided by the present application have at least the following technical effects or advantages:

[0057] ​1. The application adopts a three-dimensional lognormal random field model, combines Cholesky decomposition technology, and constructs a 3D corrosion random field containing length, width and depth based on limited ILI data. The spatial correlation is represented by an exponential function to generate relevant samples that retain the original statistical characteristics and spatial structure. Compared with the traditional method of simplifying defect geometry and ignoring parameter correlation, this scheme fully excavates the spatial correlation information in the limited detection data, accurately reproduces the three-dimensional distribution characteristics and aggregation effect of corrosion defects in the axial, circumferential and radial directions, solves the problem of spatial correlation estimation bias under small sample, makes the corrosion morphology simulation more in line with the actual working conditions, and provides reliable geometric parameter input for subsequent reliability analysis.

[0058] 2. The application adopts a three-dimensional gamma process to construct a corrosion growth model, and includes the dynamic changes of length, width and depth in the modeling category. The time-varying shape parameters and rate parameters are directly estimated based on the mean and standard deviation of continuous ILI data by optimizing the model, without complex prior assumptions. Future defect size prediction is achieved through cumulative increments. Traditional models mostly only focus on depth growth and use linear parameters to simplify the process, which cannot reflect the multi-dimensional coordinated evolution law. The application can accurately capture the monotonic cumulative growth characteristics of corrosion defects in three-dimensional space, quantify the defect size distribution at different time nodes, and greatly improve the corrosion evolution prediction accuracy, providing timely and reliable state prediction basis for pipeline life cycle integrity management.

[0059] 3. The application introduces the PHI2 method to carry out time-varying reliability analysis. By defining a burst pressure limit state equation containing three-dimensional defect parameters, the time-varying reliability problem is converted into a cross-time domain traversal rate integral calculation, and the failure probability is solved by combining the bivariate normal distribution function. Traditional methods such as Monte Carlo simulation have problems of high calculation cost or insufficient accuracy, and some research violates the random process theory. However, this scheme can accurately quantify the failure probability evolution law of the pipeline during the service period by strictly following the random process theory, and improve the calculation efficiency through time-invariant reliability conversion. It effectively solves the contradiction between the accuracy and efficiency of traditional methods, and provides scientific quantitative support for corrosion pipeline safety risk decision-making. BRIEF DESCRIPTION OF DRAWINGS

[0060] The drawings described herein are used to provide further understanding of the embodiments of the application, constitute a part of the application, and do not constitute a limitation on the embodiments of the application;

[0061] Figure 1 is a flowchart of a time-varying reliability prediction method for a natural gas pipeline considering corrosion correlation in the application. DETAILED DESCRIPTION

[0062] In order to enable the above-mentioned objects, features and advantages of the present application to be more clearly understood, the following further describes the present application with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0063] In the following description, many specific details are set forth in order to provide a thorough understanding of the present application. However, the present application can be practiced in other manners that are not consistent with the details described herein, and the scope of the present application is not limited to the specific embodiments disclosed herein.

[0064] Embodiment one

[0065] Please refer to Figure 1 The embodiment one of the present application provides a time-varying reliability prediction method for a natural gas pipeline considering corrosion correlation, and the method comprises the following steps:

[0066] Step one: collect limited continuous ILI data of the natural gas pipeline, based on initial ILI data therein, construct a lognormal probability model of geometric parameters of corrosion defects of the pipeline, quantify cross correlation between the geometric parameters and spatial correlation thereof along the axial direction of the pipeline, and obtain distribution parameters and correlation coefficients of the geometric parameters;

[0067] Step two: construct a covariance matrix based on the distribution parameters and the correlation coefficients, perform Cholesky decomposition on the covariance matrix, generate an initial corrosion random field of the pipeline, and obtain initial corrosion random samples;

[0068] Step three: based on the limited continuous ILI data, construct a gamma process growth model, perform defect evolution prediction on the initial corrosion random samples based on the gamma process growth model, and obtain a prediction result;

[0069] Step four: based on the prediction result, calculate a burst pressure of the natural gas pipeline at a prediction time point, construct a limit state equation based on the burst pressure, and calculate a time-varying failure probability of the pipeline by using a PHI2 method based on the limit state equation;

[0070] The geometric parameters comprise a length of the corrosion defect, a width of the corrosion defect and a depth of the corrosion defect.

[0071] In the embodiment, an ILI detection tool is used to perform ILI detection on the natural gas pipeline in a detection period, and the detection period can be set as needed, such as once every half year or once every year. The initial ILI data are data obtained at the first detection, and the limited continuous ILI data are obtained.

[0072] The distribution parameters comprise a log mean value and a log standard deviation.

[0073] Wherein, the logarithmic mean μ xi The calculation formula is as follows:

[0074] ;

[0075] Log-standard deviation σ xi The calculation formula is as follows:

[0076] ;

[0077] in, , where is the mean of lnxi. , where is the standard deviation of ln xi, N is the total sample size, i is the geometric dimension identifier, and x is the standard deviation of ln xi. i Let j be the geometric parameters, j = 1, 2, ..., N.

[0078] The probability density function of the geometric parameters of corrosion defects can be expressed as f μ, ∑ (xi), where:

[0079] ;

[0080] Where ∑ is the covariance matrix, [xi]=[l,w,d] T μ [xi] Let μ be the logarithmic mean vector of the geometric parameters. [xi] =[μ l , μ w , μ d ] T T is the transpose.

[0081] in:

[0082] ;

[0083] Where is the variance of the length of the corrosion defect. The variance of the width of the corrosion defect. Let Variance be the variance of the depth of the corrosion defect. Let d be the length of the corrosion defect, d be the depth of the corrosion defect, w be the width of the corrosion defect, and ρ be the length of the corrosion defect. wl The correlation coefficient between w and l The correlation coefficient between d and l, Let ρ be the correlation coefficient between l and w. dw ρ is the correlation coefficient between d and w. ld The correlation coefficient between l and d. The correlation coefficient between w and d. Let w be the logarithmic standard deviation. Let l be the logarithmic standard deviation. Let be the logarithmic standard deviation of d.

[0084] The spatial correlation of the initial corrosion random field is expressed using the following exponential correlation function. It means that, among them:

[0085] ;

[0086] Where x and x' represent two spatial points along the natural gas pipeline, This represents the spatial correlation length of the initial erosion random field.

[0087] In step two, the formula for calculating the initial corrosion random sample is as follows:

[0088] ;

[0089] Among them, S xi For the initial corrosion random field sample, Here are the geometric parameters: l is the length of the corrosion defect, d is the depth of the corrosion defect, w is the width of the corrosion defect, and μ is the depth of the corrosion defect. xi For x i The logarithmic mean, For x i The logarithmic standard deviation, Z is the inverse function of the probability density function of the geometric parameters. xi The standardized samples are based on the transformation of the lower triangular matrix U, which is obtained by performing Cholesky decomposition on the covariance matrix, where... .

[0090] in, , Let them be independent standard normal random variables. The values ​​corresponding to the length, depth, and width of the corrosion defect are obtained independently from the standard normal distribution using the Monte Carlo random sampling method. These independent random variables are then linearly transformed using the Cholesky decomposition matrix to generate samples of corrosion defect geometric parameters with cross-correlation.

[0091] The construction of the gamma process growth model based on the finite continuous ILI data includes:

[0092] Based on the aforementioned finite continuous ILI data, the mean and standard deviation of the actual geometric parameters of all corrosion defects at each acquisition time point were calculated.

[0093] A gamma process growth model is constructed, and the shape parameters and rate parameters of the gamma process growth model are defined. Based on the shape parameters and rate parameters, the mean and standard deviation of the predicted geometric parameters of all corrosion defects at each acquisition time point are derived.

[0094] Construct an optimization objective function, which is used to minimize the difference between the mean of the actual geometric parameters and the mean of the predicted geometric parameters, and between the standard deviation of the actual geometric parameters and the standard deviation of the predicted geometric parameters;

[0095] Solve the optimization objective function to obtain the optimal values ​​of the shape parameter and the rate parameter;

[0096] Substituting the optimal value into the model, the gamma process growth model is constructed.

[0097] The formula for calculating the mean of the actual geometric parameters is as follows:

[0098] ;

[0099] in, The mean of the actual geometric parameters at time t is used to characterize the actual distribution center of the geometric parameters at that time point. Let be the geometric parameters of the j-th corrosion defect at time t, where j = 1, 2, ..., n, and n is the sample size of the ILI data corresponding to time t.

[0100] The formula for calculating the standard deviation of the actual geometric parameters is as follows:

[0101] ;

[0102] in, The standard deviation of the actual geometric parameters at time t. Let be the geometric parameter for time t.

[0103] The probability density function of the gamma process growth model is: ,in:

[0104] ;

[0105] in, The shape parameter is given at time t. For the rate parameter, Time interval The increment of the geometric parameters of the corrosion defects This is a gamma function.

[0106] The derivation formula for the mean of the predicted geometric parameters is as follows:

[0107] ;

[0108] wherein, is the predicted geometric parameter mean value of time;

[0109] The derivation formula of the predicted geometric parameter standard deviation is:

[0110] ;

[0111] wherein, is the predicted geometric parameter standard deviation of time t.

[0112] The optimization objective function is wherein:

[0113] ;

[0114] Specifically, based on the solved optimal shape parameter and the rate parameter β, 10 6 times of random sampling are performed from the gamma process probability density function 6 to generate 10 corrosion increment samples . Each increment sample represents the growth amount of the i-th type of geometric parameter (corrosion defect length, depth and width) within the time interval Δt. By accumulating these random increments to the initial measured values, the predicted values of the corrosion defect geometric parameters at different future time points can be obtained, thereby realizing the probabilistic prediction of the pipeline corrosion evolution.

[0115] wherein, in step four, the formula for calculating the burst pressure of the natural gas pipeline at the predicted time point is:

[0116] ;

[0117] wherein, is the pipeline burst pressure at time t, UST is the yield strength of the pipeline, D is the outer diameter of the pipeline, δ is the wall thickness, d(t) is the depth of the corrosion defect at time t, is the width of the corrosion defect at time t, is the length of the corrosion defect at time t, m is the first fitting parameter, n is the second fitting parameter, and r is the third fitting parameter, m, n and r are obtained by fitting the finite element calculation data, and take values of 0.1075, -0.4102 and 0.2504, respectively.

[0118] wherein, the limit state equation is:

[0119] ;

[0120] wherein, Let be the limit state function value at time t. Let Pt be the pipeline burst pressure at time t, P0 be the internal working pressure of the pipeline (the pressure exerted on the inner wall of the pipeline by the natural gas being transported during normal operation), and X be a set of static random variables. It is a time-varying set of random parameters, where ω is a sampling point in the initial corrosion random sample space.

[0121] The calculation of the time-varying failure probability of the pipeline using the PHI2 method based on the limit state equation includes:

[0122] Limit state function value based on time t Calculate the reliability index of the time. ;

[0123] based on Time-limiting state function value Calculation obtained Time reliability indicators ;

[0124] Calculate the correlation between G(t,X(t, ω) and G(t+Δt,X(t+Δt, ω) to obtain the correlation coefficient. ;

[0125] Based on β(t), and The crossing rate was calculated using a bivariate normal distribution function.

[0126] Integrating the crossing rate over time yields the time-varying failure probability P. f (0,t).

[0127] In the specific calculation, , , yes standard deviation yes The standard deviation. Calculate. At that time, based on the aforementioned gamma process growth model, the predicted 10 6 Geometric parameter sample of corrosion defects Combined with pipe material parameters (such as yield strength) The distribution parameters of other random variables such as P0 were calculated using the Monte Carlo method. 6 These 10 limit state function values, through the analysis of these 10 6 By statistically analyzing the limit state function values, we obtain σ(t). Similarly, we can obtain the standard deviation of time t+Δt. .

[0128] in, is the normal vector of the design point in the standard normal space, u*(t) is the design point of the limit state surface in the standard normal space at time t, the method of finding the design point is the classical prior art in the field of structural reliability analysis—FORM method (First Order Reliability Method), in the structural reliability analysis, the design point (Design Point) is also called the most likely failure point. Specifically, the physical space variable is converted to the standard normal space through the equal probability transformation, in the standard normal space, the design point u*(t) is defined as the point closest to the origin on the limit state surface . The calculation method is also the classical prior art under the framework of the FORM method. The normal vector is the core component of the FORM method, and together with the design point u*(t) constitutes the basic elements of reliability analysis. In the FORM method, the normal vector is defined as the unit vector in the standard normal space, which points to the safe domain direction at the design point.

[0129] is the normal vector of the design point in the standard normal space, related to time , u*(t+Δt) is the design point of the limit state surface in the standard normal space at time t+Δt, the design point is a specific point on the limit state surface (defined by the time-varying limit state equation) in the standard normal space.

[0130] wherein, the calculation formula of the crossing rate is as follows:

[0131] ;

[0132] wherein, Prob represents the probability of the structure transitioning from a safe state to a failure state between time t and t+Δt. is the bivariate standard normal cumulative distribution function.

[0133] wherein, the calculation formula of the time-varying failure probability is as follows: .

[0134] After calculating the failure probability, the corresponding reliability index can be calculated: .

[0135] wherein, represents the inverse function of the standard normal cumulative distribution function.

[0136] ​​While the preferred embodiments of the application have been described, additional variations and modifications can be made to these embodiments by those skilled in the art once they have the benefit of the present disclosure without departing from the spirit and scope of the application. Accordingly, it is intended that the appended claims include all such modifications and variations as fall within the scope of the present application.

[0137] It is apparent that those skilled in the art can make various changes and modifications to the application without departing from the spirit and scope of the application. It is therefore intended that the present application cover all such changes and modifications that are within its scope.

Claims

1. A time-varying reliability prediction method for natural gas pipelines considering corrosion correlation, characterized in that, The method includes the following steps: Step 1: Collect finite continuous ILI data of the natural gas pipeline. Based on the initial ILI data, construct a log-normal probability model of the geometric parameters of pipeline corrosion defects, quantify the cross-correlation between the geometric parameters and their spatial correlation along the pipeline axis, and obtain the distribution parameters and correlation coefficients of the geometric parameters. Step 2: Construct a covariance matrix based on the distribution parameters and the correlation coefficient, perform Cholesky decomposition on the covariance matrix to generate the initial corrosion random field of the pipeline, and obtain the initial corrosion random sample; Step 3: Based on the finite continuous ILI data, construct a gamma process growth model, and predict the defect evolution of the initial corrosion random sample based on the gamma process growth model to obtain the prediction results; Step 4: Based on the prediction results, calculate the burst pressure of the natural gas pipeline at the predicted time point, construct the limit state equation based on the burst pressure, and calculate the time-varying failure probability of the pipeline using the PHI2 method based on the limit state equation. The geometric parameters include the length, width, and depth of the corrosion defect.

2. The time-varying reliability prediction method for natural gas pipelines considering corrosion correlation according to claim 1, characterized in that, The distribution parameters include the logarithmic mean and the logarithmic standard deviation; Among them, the logarithmic mean The calculation formula is as follows: ， Log-standard deviation The calculation formula is as follows: ， in, ,for The mean, ,for standard deviation Let be the total sample size, and i be the dimension identifier of the geometric parameter. The geometric parameters are... .

3. The time-varying reliability prediction method for natural gas pipelines considering corrosion correlation according to claim 2, characterized in that, The formula for calculating the correlation coefficient is as follows: ； in, for and The correlation coefficient, , , , For the first In each sample The measured value, For the first Parameters in each sample The measured value, For all samples The logarithmic mean, For all samples The logarithmic mean.

4. The time-varying reliability prediction method for natural gas pipelines considering corrosion correlation according to claim 3, characterized in that, In step two, the covariance matrix is ,in: ； in, Let V be the variance of the length of the corrosion defect. Let Variance be the width of the corrosion defect. Let Variance be the variance of the depth of the corrosion defect. Let d be the length of the corrosion defect, d be the depth of the corrosion defect, and w be the width of the corrosion defect. for and The correlation coefficient, for and The correlation coefficient, for and The correlation coefficient, for The correlation coefficient between w and w for and The correlation coefficient, The correlation coefficient between w and d. Let w be the logarithmic standard deviation. for The logarithmic standard deviation, for The logarithmic standard deviation.

5. The time-varying reliability prediction method for natural gas pipelines considering corrosion correlation according to claim 1, characterized in that, In step two, the calculation formula for the initial corrosion random sample is as follows: , in, For the initial corrosion random field sample, The geometric parameters are... , Let d be the length of the corrosion defect, d be the depth of the corrosion defect, and w be the width of the corrosion defect. for The logarithmic mean, for The logarithmic standard deviation, It is the inverse function of the probability density function of the geometric parameters. Based on lower triangular matrix The relevant standardized samples of the transformation The covariance matrix was obtained by performing Cholesky decomposition. .

6. The time-varying reliability prediction method for natural gas pipelines considering corrosion correlation according to claim 1, characterized in that, The construction of a gamma process growth model based on finite continuous ILI data includes: Based on the aforementioned finite continuous ILI data, the mean and standard deviation of the actual geometric parameters of all corrosion defects at each acquisition time point were calculated. A gamma process growth model is constructed, and the shape parameters and rate parameters of the gamma process growth model are defined. Based on the shape parameters and rate parameters, the mean and standard deviation of the predicted geometric parameters of all corrosion defects at each acquisition time point are derived. Construct an optimization objective function, which is used to minimize the difference between the mean of the actual geometric parameters and the mean of the predicted geometric parameters, and between the standard deviation of the actual geometric parameters and the standard deviation of the predicted geometric parameters; Solve the optimization objective function to obtain the optimal values ​​of the shape parameter and the rate parameter; Substituting the optimal value into the model, the gamma process growth model is constructed.

7. The time-varying reliability prediction method for natural gas pipelines considering corrosion correlation according to claim 6, characterized in that, The probability density function of the gamma process growth model is ,in: ； in, The shape parameter is given at time t. For the rate parameter, Time interval The increment of the geometric parameters of the corrosion defects This is a gamma function.

8. The time-varying reliability prediction method for natural gas pipelines considering corrosion correlation according to claim 1, characterized in that, In step four, the formula for calculating the burst pressure of the natural gas pipeline at the predicted time point is: ； in, Let t be the pipeline burst pressure. Let D be the yield strength of the pipe, and D be the outer diameter of the pipe. For pipe wall thickness, Let t be the depth of the corrosion defect at time t. Let t be the width of the corrosion defect. Let t be the length of the corrosion defect. m The first fitted parameter is... n The second fitting parameter, r This is the third fitting parameter.

9. A time-varying reliability prediction method for natural gas pipelines considering corrosion correlation according to claim 1, characterized in that, The limiting state equation is: ； in, Let be the limit state function value at time t. Let t be the pipeline burst pressure. Let X be the internal working pressure of the pipeline, and let X be a set of static random variables. It is a time-varying set of random parameters, and w is a sampling point in the initial corrosion random sample space.

10. A method for predicting the time-varying reliability of natural gas pipelines considering corrosion correlation according to claim 9, characterized in that, Based on the aforementioned limit state equations, the time-varying failure probability of the pipeline is calculated using the PHI2 method, including: Limit state function value based on time t Calculate the reliability index at time t. ; based on Time-limiting state function value Calculation obtained Time reliability indicators ; calculate and To obtain the correlation coefficient between them. ; based on , and The crossing rate was calculated using a bivariate normal distribution function. Integrating the crossing rate over time yields the time-varying failure probability. .

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