基于Copula相依性建模的运营地铁盾构隧道结构安全分析

吴浩

摘 要

运营地铁盾构隧道赋存于复杂的地下环境中，其结构安全受到了众多具有相依性影响因素的长期耦合作用，导致隧道结构服役能力随着时间的推移不断劣化。如何在考虑了各种影响因素相依性的条件下，基于现场监测的有限数据，实现对运营地铁结构安全准确、动态的分析，从而为运营地铁结构安全管控决策提供有效的信息支持，是地铁运维管理需要解决的实际工程问题。本文针对以上问题，基于Copula相依性建模理论，以运营地铁盾构隧道结构安全分析为对象，开展了一系列研究工作。

1、从结构安全影响因素分析角度，介绍了运营地铁盾构隧道结构安全常见的几类影响因素及产生原因，归纳总结了影响因素的特性，从理论层面证实常见的几种影响因素存在的复杂相依关系。

2、从结构安全可靠性分析角度，提出了基于Vine Copula模型的运营地铁盾构隧道结构安全可靠性分析方法。基于Vine Copula相依性建模理论，建立多维影响因素参数的联合概率分布函数，在精准表征多种影响因素相依关系的条件下，实现对运营地铁盾构隧道结构安全可靠性分析。

3、从结构安全动态分析角度，提出了基于PCBN模型的运营地铁盾构隧道结构安全动态分析方法。首先通过模糊综合评价法获取PCBN模型的关键参数，然后基于PCBN相依性建模理论，捕捉动态变化的相依性影响因素与隧道整体结构安全状态之间的非线性映射关系，最后结合贝叶斯网络推理、GM（1,1）时间序列预测模型、多项式回归分析技术，实现对运营地铁盾构隧道结构安全状态的动态分析。

本文以武汉地铁某区间运营盾构隧道为案例开展实证分析，分析结果表明，本文提出的运营地铁盾构隧道结构安全的一系列分析方法，不仅能较为敏感的捕捉到多种影响因素的相依关系，而且能够实现对地铁结构安全准确、动态的分析，为运营地铁盾构隧道结构安全管控决策提供了信息支持。

关键词：运营地铁结构安全；Vine Copula；PCBN；可靠性分析；动态分析

Abstract

Operating subway shield tunnel exists in a complex underground environment, and it’s structural safety is subject to long-term coupling effects of many dependent factors, which leads to the continuous deterioration of the tunnel structure's service capacity over time. Under the condition of considering the dependence of various influencing factors, how to accurately and dynamically analyze the safety of the operating subway structure based on the limited data monitored on site, so as to provide effective information support for the safety management and control decision of the operating subway structure，which is an actual engineering problem that needs to be solved in the operation and maintenance management of the subway. Aiming at the above problems, based on Copula's dependency modeling theory, a series of research work has been carried out on the safety analysis of operating subway shield tunnels.

1. From the perspective of analysis of influencing factors of structural safety, introduced several common influencing factors and causes of structural safety of operating subway shield tunnels, summarized the characteristics of influencing factors, and from the theoretical level, it is confirmed that there are complex interdependencies among several common influencing factors.

2. From the perspective of structural safety and reliability analysis, a method for analyzing the structural safety and reliability of operating subway shield tunnels based on Vine Copula model is proposed. Based on the Vine Copula dependency modeling theory, a joint probability distribution function of multi-dimensional influencing factor parameters is established. Under the condition of accurately characterizing the dependence of multiple influencing factors, the safety and reliability analysis of the operating subway shield tunnel structure is realized.

3. From the perspective of dynamic analysis of structural safety, a method for dynamic analysis of structural safety of operating subway shield tunnels based on PCBN model is proposed. First, the key parameters of the PCBN model are obtained by fuzzy comprehensive evaluation method, and then based on the PCBN dependency modeling theory, the nonlinear mapping relationship between the dynamically changing dependency factors and the overall structural safety state of the tunnel is captured., and finally the combination of Bayesian network inference and GM (1,1) time series prediction model and polynomial regression analysis technology to realize the dynamic analysis of the safety status of operating subway structures.

In this paper, an empirical analysis is carried out by taking the operation of a shield tunnel in Wuhan Metro Line 3 as an example, and the analysis results show that the series of analysis methods for the structural safety of the subway shield tunnel proposed in this paper can not only capture the dependence of various influencing factors more sensitively, but also realize the accurate and dynamic analysis of the subway structure safety, which provide information support for the safety management and control decisions of operating subway shield tunnels.

Key words：Operational subway structure safety; Vine Copula; PCBN; reliability analysis; dynamic analysis