灰色Markov过程改进预测模型及其应用  

Gray Markov Process Amended Prediction Model and Its Application

作　　者：张磊 李世民 庞坤 徐礼[3] 

机构地区：[1]32134部队 [2]63963部队 [3]75130部队

出　　处：《信息工程大学学报》2017年第4期454-457,463,共5页Journal of Information Engineering University

基　　金：国防重点实验室预研基金项目(9140C900104150C90384)

摘　　要：针对传统灰色Markov链残差修正预测模型在实际运用中存在的不足,运用时间连续且状态离散的Markov过程对其进行了改进。将灰色GM(1,1)模型的预测结果与数据的残差进行对比分析,根据残差的分布情况划分状态区间并确定区间状态值。由各区间状态的转换情况得到Markov模型的一步转移概率矩阵,论证并运用Kolmogorov微分方程求解了各状态概率的时间函数并建立状态概率预测式,最后通过求解状态数学期望值的方式得到残差修正值。对比发现与一般灰色GM(1,1)模型和传统Markov链预测模型相比,Markov过程改进模型的预测精度有了稳定提高。同时,改进模型的预测精度会随Markov模型状态数的增加而提高;由状态区间内残差的均值作为区间的状态值更能反应区间内残差的分布状况,并提高预测精度。According to the defects of traditional gray Markov chain residual error correction model,Time-continuous and state-discrete Markov process is used to improve the GM(1,1).By comparison and analysis about GM(1,1) prediction results and its residual errors,the state intervals are divided,and the state-values are solved.Besides,the one-step transition matrix is calculated by states transition.Kolmogorov differential equations are discussed and used,the time functions of state probability are obtained and the prediction equations are constructed.The mean of state values is regarded as the final correction value.The results comparison shows that the prediction precision of the amended model is better than general GM(1,1) model and traditional Markov chain model,and cases analysis shows that the results of the amended prediction model will be more precise when the number of Markov states increases.Besides,the distribution of residual errors can be reflected more precisely when the mean value of residual errors is taken as the state-value,and the results will be more precise.

关 键 词：Makov模型 GM(1 1)模型 Kolmogorov微分方程 预测精度 

分 类 号：O29[理学—应用数学]