考虑多缺陷相关性的输气管段结构可靠性评价

doi:10.16265/j.cnki.issn1003-3033.2025.12.1701

摘要/Abstract

摘要：

针对输气管段多缺陷间相互联系的特点以及多缺陷高度非线性耦合作用难以量化的问题,提出基于Copula函数的含多缺陷输气管段结构可靠性评价方法。首先,基于不同缺陷对应的管段极限状态方程,采用蒙特卡罗法(MC)计算单缺陷作用下管段的失效概率和概率分布;其次,将各缺陷概率分布作为随机变量,通过Copula函数研究不同缺陷间相关性对管段失效概率的影响,得到2缺陷耦合作用下管段的联合失效概率;然后,基于二阶窄界理论确定含多缺陷输气管段可靠度;最后,探究腐蚀和裂纹缺陷间相关性对输气管段结构可靠性的影响,分析在不同缺陷深度和壁厚之比(0.2~0.8)条件下管段可靠度的变化。结果表明:在缺陷失效概率量级一致且相差不大的条件下,同种缺陷相关性更强且耦合作用对管段失效概率影响更大;相较于传统串联方法考虑缺陷间相互独立低估管段的可靠度,文中方法管段结构可靠性评价结果更符合实际需要,可为含多缺陷输气管段的稳定运行提供理论支持。

Abstract:

A structural reliability evaluation method for gas pipeline segments with multiple defects, based on Copula functions, was proposed to address the characteristics of the interrelationship between defects and the difficulty in quantifying the highly nonlinear coupling effects of multiple defects. First, based on the limit state equations of pipeline segments corresponding to different defects, Monte Carlo (MC) method was used to calculate the failure probability and probability distribution of pipeline segments under the influence of a single defect. Second, the probability distribution of each defect were treated as random variables, and the Copula functions were employed to study the impact of the correlation between different defects on the pipeline failure probability. The joint failure probability of the pipeline segment under the coupling effect of two defects was obtained. Third, the reliability of the pipeline segment with multiple defects was determined based on the second-order narrow-bound theory. Finally, using this method, the impact of the correlation between corrosion and crack defects on the structural reliability of gas pipeline segments was explored, and the variation of pipeline reliability was analyzed under different defect depths and wall thickness ratios (0.2-0.8). The results show that, under the condition that the failure probabilities of the defects are at the same order of magnitude and do not differ significantly, the correlation of the same type of defects is stronger, and the coupling effect has a greater impact on the pipeline failure probability. Compared with traditional series methods that assume independence between defects, which underestimate the pipeline reliability, the results of this method are more consistent with practical needs. This approach provides theoretical support for the stable operation of gas pipeline segments with multiple defects.

Key words: multiple defects, correlation, gas pipeline segments, structural reliability, reliability assessment, Copula functions, failure probability

中图分类号:

X944.4

彭卫远, 彭世亮, 陈朋超, 苏怀, 张宏, 张劲军. 考虑多缺陷相关性的输气管段结构可靠性评价[J]. 中国安全科学学报, 2025, 35(12): 147-153.

PENG Weiyuan, PENG Shiliang, CHEN Pengchao, SU Huai, ZHANG Hong, ZHANG Jinjun. Structural reliability assessment of gas pipeline segments considering multiple defects correlation[J]. China Safety Science Journal, 2025, 35(12): 147-153.

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Copula 函数类型	相关参数α	分布函数 ${C}_{\alpha }({u}_{1},{u}_{2};\alpha )$	Kendall Rank 相关系数 τ与α的关系	函数特性
Gaussian	$\alpha \in [-\mathrm{1,1}]$	${\Phi }_{2}\left({\Phi }^{-1}\right({u}_{1}),{\Phi }^{-1}({u}_{2});\alpha )$	$\tau =\frac{2}{\pi }arcsin\left(\alpha \right)$	对称相关性不作边缘分布相关假设
Student t	$\alpha \in (-\mathrm{1,1})$	${T}_{\upsilon }\left({{t}_{\upsilon }}^{-1}\right({u}_{1}),{{t}_{\upsilon }}^{-1}({u}_{2});\alpha,\upsilon )$	$\tau =\frac{2}{\pi }arcsin\left(\alpha \right)$	对称尾部相关性
Gumbel	$\alpha \in \left(\mathrm{0,1}\right]$	$exp\left(-{\left[(-ln{u}_{1}{)}^{\frac{1}{\alpha }}+(-ln{u}_{2}{)}^{\frac{1}{\alpha }}\right]}^{\alpha }\right)$	$\tau =1-\alpha $	非对称性上尾部相关性变化敏感
Frank	$\alpha \ne \left\{0\right\}$	$-\frac{1}{\alpha }ln\left(1+\frac{\left(exp\right(-\alpha {u}_{1})-1)\left(exp\right(-\alpha {u}_{2})-1)}{{e}^{-\alpha }-1}\right)$	$\begin{array}{l}\tau =1+\\ \frac{4}{\alpha }\left[{D}_{1}\right(\alpha )-1]\end{array}$	对称性描述非负和负相关性的随机变量
Clayton	$\begin{array}{l}\alpha \in (-\mathrm{1,0})\bigcup \\ (0,+\infty )\end{array}$	$max\left(({{u}_{1}}^{-\alpha }+{{u}_{2}}^{-\alpha }{-1)}^{-\frac{1}{\alpha }},0\right)$	$\tau =\frac{\alpha }{2+\alpha }$	非对称性下尾部相关性变化敏感

随机变量	分布类型	均值	变异系数
屈服强度σ_y/MPa	正态	467	0.07
抗拉强度σ_u/MPa	对数正态	576	0.07
管段壁厚t/mm	正态	19.05	0.03
管段外径D/mm	正态	1219.2	0.03
运行压力p/MPa	I型广义极值	6~16	0.02
腐蚀深度d/mm	正态	(20%~80%)t	0.1
腐蚀长度l/mm	正态	200	0.05
裂纹深度a/mm	正态	(20%~80%)t	—
裂纹半长c/mm	—	25~100	—
夏比冲击值C_v/J	正态	200	0.16

缺陷	可靠度	失效概率
腐蚀z₁	0.997 8	0.002 2
腐蚀z₂	0.998 6	0.001 4
裂纹z₃	0.997 8	0.002 2
裂纹z₄	0.997 0	0.003 0

拟合模型	τ	AIC	联合失效概率
Gaussian	0.847	-2 720	0.002089
Student t		-2 741	0.002 134
Clayton		-2 451	0.002 187
Gumbel		-2 831	0.002 18
Frank		-2 607	0.000 152 7
Indep	0	0	6.561×10^-6

缺陷组合	拟合模型	τ	α	联合失效概率
z₁z₂	Frank	0.89	35	1.01×10^-4
z₁z₃	Indep	0.00	0	4.48×10^-6
z₁z₄	Indep	0.00	0	6.6×10^-6
z₂z₃	Indep	0.00	0	3.08×10^-6
z₂z₄	Indep	0.00	0	4.2×10^-6
z₃z₄	Gumbel	0.98	50	2.18×10^-3