矿井通风系统可靠性的马氏链分析

Markov Chain Analysis of Reliability of Mine Ventilation

为保证井下正常通风,从可靠度的角度对矿井通风系统的稳定性进行分析。首先以通风系统的维修率作为实测对象,在概率统计理论和以往经验性规律的基础上,得出矿井通风系统的可靠度服从指数分布这一规律的结论。然后运用马尔可夫过程对通风系统的有效度进行分析,建立了通风系统的失效模型,运用此模型可预测通风系统的有效度、平均寿命和平均维修时间。并且针对目前普遍采用的遍历点法求解矿井通风系统可靠度问题中,存在耗时耗力、只适用于小型通风网路的弊端,提出了邻接矩阵法求解最小路集的不交最小路法,适用于手算简单通风系统的可靠性。最后以一个工程实例作为模型的算例,结果表明:矿井通风系统为可修复系统,可以用马尔可夫过程对其进行分析,求出通风网络的有效度、平均寿命和平均修复时间等可靠度指标。

In order to ensure the normally well ventilation,would study the reliability of mine ventilation from the view of reliability. At first, the maintenance rate of the mine ventilation was regard as the measured object. Basing on the mathematical statistics theory and previous experiences, draws a conclusion that the reliability of mine ventilation obeys index distribution. Then, the Markov chain was applied into analyzing the stability of mine ventilation. Forming and using failure models of mine ventilation can predict its stability, average life and mean time to repair. In the study of the reliability of mine ventilation, adopt going all through points to solve the problem. But the method wastes much time and effort. In addition, it is only suited to compact mine ventilation. However, adopts adjacent matrix to solve the problem which can avoid those disadvantages and suit human to do. At last, draws a conclusion from a engineering example which is regarded as the case of the model. The conclusion is that mine ventilation is rock repairable system. So that the Markov process can be applied to analyze the system to obtain its stability,mean life,mean time to repair and other indexes.