A time-varying reliability prediction method for natural gas pipelines considering corrosion correlation

Abstract

The application discloses a kind of time-varying reliability prediction methods of natural gas pipeline considering corrosion correlation, it is related to natural gas pipeline safety evaluation field, the method includes: collecting the finite continuous ILI data of natural gas pipeline, constructs the lognormal probability model of pipeline corrosion defect geometric parameter, obtains the distribution parameter and correlation coefficient of the geometric parameter;Based on the distribution parameter and the correlation coefficient, covariance matrix is constructed, and Cholesky decomposition is carried out, to generate the initial corrosion random sample of pipeline;Based on finite continuous ILI data, construct a gamma process growth model, defect evolution prediction is carried out to the initial corrosion random sample, and the prediction result is obtained;Based on the prediction result, the burst pressure of natural gas pipeline at the prediction time point is calculated, the limit state equation is constructed, and the time-varying failure probability of pipeline is calculated using PHI2 method;The application improves the accuracy and scientificity of pipeline corrosion safety risk decision under the condition of limited detection data through the above four steps.

Description

Technical Field

[0001] This invention relates to the field of natural gas pipeline safety assessment, and more specifically, to a method for predicting the time-varying reliability of natural gas pipelines that takes corrosion correlation into account. Background Technology

[0002] Currently, for integrity assessment and remaining 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 typically simplify corrosion defects into regular geometric shapes (such as rectangles or ellipses) and use deterministic or stochastic models to independently model and predict individual defect parameters. With further research, random field theory and gamma processes have been introduced to characterize the spatial and temporal variability of corrosion defects and to provide experimental support using internal inspection (ILI) data.

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

[0004] Regarding defect correlation modeling: most methods fail to systematically consider the cross-correlation between the geometric parameters (length, width, depth) of corrosion defects, as well as the spatial correlation of defect distribution along the pipe axis. Even some studies attempt to construct multivariate models, but when dealing with parameter estimation under conditions of three-dimensional spatial correlation and limited ILI data, they often suffer from problems such as model complexity, low computational efficiency, or difficulty in directly embedding into time-varying reliability analysis frameworks. Furthermore, the lack of a practical modeling framework that unifies the consideration of geometric parameter correlation and spatial distribution correlation leads to biases in the assessment of corrosion accumulation regions and co-evolution effects.

[0005] In practical data application, ILI detection is costly and time-consuming, resulting in limited available data and measurement errors. Traditional parameter estimation methods struggle to accurately construct the correlation structure between multiple defects and parameters, and are unable to effectively describe the non-stationary growth characteristics of corrosion over time, leading to significant uncertainty in evolution prediction.

[0006] At the level of time-varying reliability analysis, although Monte Carlo simulation and the first-order reliability method (FORM) have been widely used, their computational efficiency is low, and most methods fail to strictly follow the theory of non-stationary random processes, and cannot accurately characterize the failure probability evolution process of pipelines throughout their entire life cycle.

[0007] These deficiencies result in a lack of systematic approach in the overall assessment framework, limiting the engineering applicability and decision support capabilities of the assessment results. These deficiencies not only affect the accuracy of pipeline safety assessments but also introduce additional costs and risks to operation and maintenance. Summary of the Invention

[0008] The purpose of this invention is to provide a precise and efficient three-dimensional time-varying reliability analysis method for corrosion defects in natural gas pipelines.

[0009] To achieve the above objectives, a time-varying reliability prediction method for natural gas pipelines considering corrosion correlation is established. The method includes the following steps:

[0010] 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.

[0011] 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.

[0012] 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;

[0013] 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.

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

[0015] Corrosion defects in natural gas pipelines exhibit spatial correlation in three-dimensional parameters of length, width, and depth, and their evolution is a time-varying process. Traditional prediction methods often simplify the geometry of defects or ignore the correlation between parameters, leading to significant deviations in long-term reliability predictions.

[0016] In step one, this scheme constructs a log-normal probability model covering geometric parameters in three dimensions (length, width, and depth) based on the initial ILI data, and obtains its distribution parameters and correlation coefficients, solving the problem of incomplete representation of the initial corrosion morphology statistical characteristics and spatial correlation in traditional methods. In step two, a covariance matrix is ​​constructed based on these distribution parameters and correlation coefficients, and Cholesky decomposition is performed to generate initial random corrosion samples. These initial random corrosion samples can accurately reproduce the three-dimensional distribution characteristics and clustering effects of corrosion defects in the axial, circumferential, and radial directions, solving the problem of spatial correlation estimation bias under small sample conditions, making the corrosion morphology simulation more consistent with actual working conditions, and providing reliable geometric parameter input for subsequent reliability analysis. In step three, a gamma process growth model is constructed based on finite continuous ILI data. The gamma process conforms to the physical properties that change over time, and can intuitively reflect the trend of parameter changes over time. Furthermore, the independent non-negative and monotonic increments of the gamma distribution can characterize the temporal changes in corrosion geometry parameters. Combined with the gamma process, it can accurately simulate the monotonic cumulative growth characteristics of corrosion defects along the axial, radial, and circumferential directions, quantify the defect size distribution at different time points, significantly improve the accuracy of corrosion evolution prediction, and provide timely and reliable state prediction basis for pipeline integrity management throughout its entire life cycle. Finally, step four calculates the pipeline burst pressure at future time points based on the gamma prediction results, constructs the limit state equation, and then uses the PHI2 method to calculate the time-varying failure probability.

[0017] This invention transforms complex dynamic reliability problems into efficiently solvable cross-time domain integral problems, avoiding the high computational costs or theoretical misuse inherent in traditional methods such as Monte Carlo simulations. Through these four steps, the invention significantly improves the accuracy and scientific rigor of pipeline corrosion safety risk decision-making under conditions of limited detection data.

[0018] Furthermore, the distribution parameters include the logarithmic mean and the logarithmic standard deviation;

[0019] Wherein, the logarithmic mean μ xi The calculation formula is as follows:

[0020] ;

[0021] Log-standard deviation σ xi The calculation formula is as follows:

[0022] ;

[0023] in, , where is the mean of lnxi. , where is the standard deviation of lnxi. The total sample size is... x is the dimension identifier for the geometric parameter. iLet j be the geometric parameters, j = 1, 2, ..., N.

[0024] Furthermore, the formula for calculating the correlation coefficient is as follows:

[0025] ;

[0026] Where, ρ XY For X i and Y i The correlation coefficient, , , ρ XY =ρ YX X i,j For the j-th sample, X i The measured value of Y i，j For the parameter Y in the j-th sample i The measured value, μ Xi For all samples X i The logarithmic mean, μ Yi For all samples Y i The logarithmic mean.

[0027] Furthermore, in step two, the covariance matrix is ​​∑, where:

[0028] ;

[0029] in, Let V be the variance of the length of the corrosion defect. Let Variance be the width of the corrosion defect. Let be the variance of the depth of the corrosion defect, l 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 variance of the depth of the corrosion defect. wl For w and The correlation coefficient, For d and The correlation coefficient of l for The correlation coefficient between ρ and w dw ρ is the correlation coefficient between d and w. ld The correlation coefficient between l and d. for The correlation coefficient between and d Let w be the logarithmic standard deviation. Let l be the logarithmic standard deviation. Let be the logarithmic standard deviation of d.

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

[0031] ;

[0032] Among them, S xi For the initial corrosion random field sample, x i Let x be the geometric parameter. 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 For x i The logarithmic mean, σ xi 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 based on the lower triangular matrix U-transform are obtained by performing Cholesky decomposition on the covariance matrix, where... .

[0033] Furthermore, the construction of the gamma process growth model based on the finite continuous ILI data includes:

[0034] 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.

[0035] 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.

[0036] 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;

[0037] Solve the optimization objective function to obtain the optimal values ​​of the shape parameter and the rate parameter;

[0038] Substituting the optimal value into the model, the gamma process growth model is constructed.

[0039] This scheme, based on the finite continuous ILI data, calculates the mean and standard deviation of the actual geometric parameters of all corrosion defects at each detection time point. These statistics objectively reflect the true collective behavior and dispersion of corrosion defects in three-dimensional space over time. Next, a gamma process growth model is constructed, defining its key time-varying parameters: shape and rate. Based on the theoretical properties of these two parameters, the mean and standard deviation of the predicted geometric parameters generated by the model at the same time point can be derived. Then, an optimization objective function is constructed, the core objective of which is to minimize the difference between the model's predicted values ​​and the actual observed values. This transforms the model calibration process into a mathematical optimization problem aimed at matching the statistical characteristics of historical data. By solving this optimization objective function, the optimal values ​​of the shape and rate parameters under the current data conditions can be obtained. Finally, substituting these two optimal parameters into the model completes the construction of the gamma process growth model. This scheme estimates time-varying parameters directly based on the statistical characteristics of continuous ILI data by optimizing the model, without the need for complex prior assumptions. This allows for the accurate capture of the monotonic cumulative growth characteristics of corrosion defects in three-dimensional space, significantly improving the accuracy and reliability of predicting future corrosion morphology evolution from limited historical data.

[0040] Furthermore, the probability density function of the gamma process growth model is: ,in:

[0041] ;

[0042] 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.

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

[0044] ;

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

[0046] Furthermore, the limiting state equation is:

[0047] ;

[0048] in, 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.

[0049] Furthermore, the calculation of the time-varying failure probability of the pipeline using the PHI2 method based on the limit state equation includes:

[0050] Limit state function value based on time t Calculate the reliability index of the time obtained;

[0051] based on Time-limiting state function value Calculate the reliability index of the time obtained;

[0052] Calculate the correlation between G(t,X(t, ω) and G(t+Δt,X(t+Δt, ω) to obtain the correlation coefficient. ;

[0053] Based on β(t), The crossing rate is obtained by calculating ρ(t, t+Δt) using a bivariate normal distribution function;

[0054] Integrating the crossing rate over time yields the time-varying failure probability. .

[0055] Where, β(t) and The two consecutive time points t and t were quantized respectively. Safety margin of pipelines, It characterizes the statistical correlation characteristics of pipeline failure process at continuous time points; the crossing rate refers to the average probability that the pipeline performance first crosses from a safe state to a failure state between two time points. By integrating these discrete crossing rates over the entire service cycle, the evolution law of time-varying failure probability of the pipeline during the operation cycle can be obtained.

[0056] One or more technical solutions provided by this invention have at least the following technical effects or advantages:

[0057] 1. This invention employs a three-dimensional log-normal random field model, combined with Cholesky decomposition technology, to construct a 3D corrosion random field containing length, width, and depth based on finite ILI data. Spatial correlation is characterized by an exponential function, generating relevant samples that retain the original statistical characteristics and spatial structure. Compared to traditional methods that simplify defect geometry and ignore parameter correlations, this approach fully exploits the spatial correlation information in finite detection data, accurately reproducing the three-dimensional distribution characteristics and clustering effects of corrosion defects in the axial, circumferential, and radial directions. It solves the problem of spatial correlation estimation bias under small sample sizes, making corrosion morphology simulation more closely resemble actual working conditions and providing reliable geometric parameter input for subsequent reliability analysis.

[0058] 2. This invention employs a three-dimensional gamma process to construct a corrosion growth model, incorporating the dynamic changes in length, width, and depth into the modeling scope. By optimizing the model, it directly estimates time-varying shape and rate parameters based on the mean and standard deviation of continuous ILI data, without requiring complex prior assumptions. Furthermore, it predicts future defect sizes through cumulative increments. Traditional models mostly focus only on depth growth and use linear parameters to simplify the process, failing to reflect the multi-dimensional collaborative evolutionary laws. This invention can accurately capture the monotonic cumulative growth characteristics of corrosion defects in three-dimensional space, quantify the defect size distribution at different time points, significantly improve the accuracy of corrosion evolution prediction, and provide timely and reliable status prediction basis for pipeline integrity management throughout its entire life cycle.

[0059] 3. This invention introduces the PHI2 method for time-varying reliability analysis. By defining a burst pressure limit state equation that includes three-dimensional defect parameters, the time-varying reliability problem is transformed into a cross-time domain crossing rate integral calculation, combined with a bivariate normal distribution function to solve for the failure probability. Traditional methods such as Monte Carlo simulation suffer from high computational costs or insufficient accuracy, and some studies violate stochastic process theory. This approach, however, strictly adheres to stochastic process theory to accurately quantify the evolution of pipeline failure probability during its service life, while improving computational efficiency through time-invariant reliability transformation. It effectively resolves the contradiction between accuracy and efficiency inherent in traditional methods, providing scientific quantitative support for safety risk decision-making in corroded pipelines. Attached Figure Description

[0060] The accompanying drawings, which are provided to further illustrate embodiments of the invention and constitute a part of this invention, are not intended to limit the scope of the invention.

[0061] Figure 1 This is a flowchart illustrating a time-varying reliability prediction method for natural gas pipelines that considers corrosion correlation, as described in this invention. Detailed Implementation

[0062] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, where there is no conflict, the embodiments of the present invention and the features thereof can be combined with each other.

[0063] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0064] Example 1

[0065] Please refer to Figure 1 Embodiment 1 of the present invention provides a time-varying reliability prediction method for natural gas pipelines considering corrosion correlation. The method includes the following steps:

[0066] 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.

[0067] 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.

[0068] 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;

[0069] 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.

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

[0071] In this embodiment, a magnetic flux leakage (MFL) detection tool is used to perform ILI (Intra-Low Liquidity) detection on the natural gas pipeline within a detection cycle. The detection cycle can be set as needed, such as once every six months or once a year. The initial ILI data is the data from the first detection, obtaining a limited continuous ILI data.

[0072] The distribution parameters include the logarithmic mean and the logarithmic 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] in, The mean of the predicted geometric parameters for time;

[0109] The derivation formula for the standard deviation of the predicted geometric parameters is as follows:

[0110] ;

[0111] in, Let be the standard deviation of the predicted geometric parameters at time t.

[0112] The optimization objective function is: ,in:

[0113] ;

[0114] Specifically, based on the optimal shape parameters obtained from the solution And the rate parameter β, using the Monte Carlo method from the probability density function of the gamma process 10 6 Random sampling was performed to generate 10 6 One corrosion increment sample Each incremental sample represents the increase in the i-th type of geometric parameter (corrosion defect length, depth, and width) within a time interval Δt. By accumulating these random increments to the initial measured values, predicted values ​​of the corrosion defect geometric parameters at different future time points can be obtained, thereby achieving probabilistic prediction of pipeline corrosion evolution.

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

[0116] ;

[0117] in, Let be the burst pressure of the pipeline at time t, UST be the yield strength of the pipeline, D be the outer diameter of the pipeline, δ be the pipe wall thickness, and d(t) be the depth of the corrosion defect at time t. Let t be the width of the corrosion defect. Let m be the length of the time-corrosion defect, n be the first fitting parameter, and r be the third fitting parameter. m, n, and r are obtained by fitting the data from finite element analysis and have values ​​of 0.1075, -0.4102, and 0.2504, respectively.

[0118] The limiting state equation is as follows:

[0119] ;

[0120] in, 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 of . 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, = , This is the normal vector of the time-dependent design point in the standard normal space. Let u*(t) be the design point of the limit state surface in the standard normal distribution space at time t. The method for finding the design point is the classic existing technique in structural reliability analysis—the FORM (First Order Reliability Method). In structural reliability analysis, the design point is also called the most likely failure point. Specifically, the physical space variables are transformed to the standard normal space through an equal probability transformation. In the standard normal space, the design point u*(t) is defined as the limit state surface. The point closest to the origin. Normal vector. The calculation method is also a classic existing technique within the FORM framework. Normal vector It is a core component of the FORM method, and together with the design point u*(t), it constitutes the basic elements of reliability analysis. In the FORM method, the normal vector... Defined as a unit vector pointing in the direction of the safety region at the design point in standard normal space.

[0129] For standard normal space and time The normal vector of the relevant design point, u*(t+Δt) is the design point of the limit state surface in the standard normal distribution 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 distribution space.

[0130] Among them, crossing rate The calculation formula is:

[0131] ;

[0132] Here, Prob represents the probability that the structure transitions from a safe state to a failure state between times t and t+Δt. It is a bivariate standard normal cumulative distribution function.

[0133] The formula for calculating the time-varying failure probability is as follows: .

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

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

[0136] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.

[0137] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

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 of the corrosion defect, the width of the corrosion defect, and the depth of the corrosion defect; 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.

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 The total sample size is... As a dimension identifier for geometric parameters, 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. The length of the corrosion defect, The depth of the corrosion defect, The width of the corrosion defect, for and The correlation coefficient, for and The correlation coefficient, for and The correlation coefficient, for and The correlation coefficient, for and The correlation coefficient, for and The correlation coefficient, for 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... , The length of the corrosion defect, The depth of the corrosion defect, 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 probability density function of the gamma process growth model is: ,in: ； in, for The shape parameters of time, For the rate parameter, Time interval The increment of the geometric parameters of the corrosion defects This is a gamma function.

7. 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, for The pressure of time-induced pipe bursting. The yield strength of the pipeline. The outer diameter of the pipe. For pipe wall thickness, for The depth of time-corrosion defects, for The width of time-corrosion defects, for The length of the time-corrosion defect, m is the first fitting parameter, n is the second fitting parameter, and r is the third fitting parameter.

8. The 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, for The time-limiting state function value, for The pressure of time-induced pipe bursting. The internal working pressure of the pipeline. For a set of static random variables, It is a set of time-varying random parameters. This is a sampling point in the initial corrosion random sample space.

9. A time-varying reliability prediction method for natural gas pipelines considering corrosion correlation according to claim 8, 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: based on Time-limiting state function value Calculation obtained Time reliability indicators ; 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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