基于最大熵原理的多失效模式下煤巷锚杆支护结构体系可靠度模型

煤巷锚杆支护结构中包含多个相关的失效模式，传统的煤巷锚杆支护结构可靠度分析方法没有考虑多个失效模式之间的相关性，使得煤巷锚杆支护结构的可靠度被低估.为此，提出多失效模式下的煤巷锚杆支护结构分析方法，建立考虑多失效模式相关的煤巷锚杆支护结构体系可靠度分析模型.同时，采用最大熵原理推断煤巷锚杆支护结构参数的统计特征，利用对数正态分布描述岩石和煤体的粘聚力和内摩擦角.并采用Monte Carlo模拟法进行多失效模式下结构体系可靠度计算. 研究结果表明：采用最大熵原理能有效推断煤巷锚杆支护结构基本变量统计特征；多失效模式相关的结构可靠度模型所得到的可靠度值 比传统单一不相关模式下所计算的结果更加科学、准确；在MATLAB环境下采用Monte Carlo模拟法编程计算煤巷锚杆支护结构体系可靠度，无需将功能函数线性化，随机变量正态化，不需要求解近似联合密度函数，不需要进行复杂变换，编程过程简单，精度高.

Reliability model on bolt support structure systems of coal roadway considering multiple correlated failure modes based on maximal entropy principle

There are some correlated failure modes in blot support structure of coal roadway. The traditional reliability method of blot support structure of coal roadway had not considered the relativities between the failure modes, which lead to the reliabilities were underestimated. Therefore, an analysis method with multiple correlated failure modes for blot support structure of coal roadway is put forward, and a reliability analysis mode considering multiple correlated failure modes of blot support structure systems of coal roadway is established. Meanwhile, the maximal entropy principle is used to infer the statistical property of random variable of blot support structure of coal roadway. The lognormal distribution is used for the cohesion and the friction angle of rock and coal. And this structure system's reliabilities are calculated by Monte Carlo simulation method. It indicates that the statistical property of random variable of blot support structure of coal roadway can be inferred effectively by the maximal entropy principle. And the results calculated by the multiple correlated failure modes are more scientific and reliable, in comparison with those calculated by the traditional single uncorrelated mode. Taking Monte Carlo simulation methods to calculate the reliabilities of blot support structure systems of coal roadway in Matlab makes the programming process easier. This method, with a high precision, is not only easy to program and without solving the joint probability density function and without complicated transforms, but also without the limit of nonlinear functions and non-normal random variables.