信度马尔科夫链预测模型及应用

Reliability Markov Chain Prediction Model and Its Application

马尔科夫链在随机过程理论中具有重要的地位并获得了广泛的应用。文章提出了一种改进状态间的转移矩阵的方法,通过引入D-S理论对原始数据所处的状态进行处理得到与之对应的信度函数值,并给出了连续状态信度函数值确定的一般方法;再通过基于后退偏差平方和加权的方法对信度函数值进行权重分配形成转移矩阵,使得该转移矩阵考虑状态间影响的累积效应。通过实例分析,对比不同模型下状态间的回代误差,得到了较好的预测结果。

Markov chain plays an important role in the theory of stochastic processes and has been widely used. This paper presents a method of improving transition matrix of the states relationship. By introducing the D-S theory the paper deals with the state of the original data to obtain the reliability function and the corresponding value. And then it gives a general method to deter- mine the value of the continuous-state reliability function. By use of the method of the weighted sum of back squared deviations, the paper distributes different weight to the values of the reliability function to construct a transition matrix, and gives consider- ation to the cumulative effect between different states of this transition matrix. Finally through example analysis and comparison of the back substitution errors between states under different models, a better prediction result is achieved.