矩阵Renyi α阶熵水文序列变异诊断新方法

A new method for detecting mutation of hydrological sequence based on matrix-based Renyi’s α order entropy

水文序列的变异诊断研究能够为各类水利、土木工程规划和管理决策提供依据和参考.针对水文序列动力学结构变异难以诊断的问题,本文提出一种基于矩阵Renyi α阶熵的变异诊断方法.首先,引入矩阵Renyi α阶熵理论描述水文序列的动力学结构;其次,利用数据滑动技术构造滑动移除矩阵Renyi α阶熵序列,用来刻画水文系统动力学结构的演变;最后,利用Pettitt检验诊断出滑动移除矩阵Renyi α阶熵序列的变异点及显著性水平.以渭河流域、洮河流域、窟野河流域和西柳沟流域的水沙序列为例开展应用研究,并与Shannon熵、Mann-Kendall检验和滑动T检验等方法进行对比分析.研究结果表明:咸阳站、状头站和红李区间年径流序列均没有发生变异,其它站年径流序列均发生了变异,变异概率大于90%;咸阳站、张家山站和状头站年输沙量序列均在20世纪80年代发生了变异,其它站点在20世纪90年代末发生变异,变异发生的概率均大于95%.通过与现有研究成果比对分析发现,本文提出的Renyi α阶熵方法的诊断结果与实际情况基本吻合,而其它方法的诊断结果与实际情形差异较大.

Study on variation diagnosis of hydrological series can provide basis and reference for various water conservancy and civil engineering planning and management decisions. It is difficult to detect the sudden change of dynamic structure of hydrological series. This paper presents a new method for detecting the variation of a hydrological sequence based on matrix-based Renyi’s alpha order entropy. First, the matrix-based Renyi’s alpha order entropy is introduced to describe dynamic structure of the hydrologic sequence. Second, a sequence of moving cut matrix-based Renyi’s alpha order entropy is constructed by the moving window technique;it is used to describe the evolution of dynamic structure of hydrological system. Finally, Pettitt test is applied to detect the change point and the level of significance of the moving cut sequence. Taking runoff and sediment sequences in Weihe River, Taohe River, Kuye River and Xiliugou River as examples,researches on detection of change point are performed, and the results of Shannon entropy,Mann Kendell and moving T test are also included for comparison. The results indicate that no mutation occurred in the runoff sequences at Xianyang Station, Zhuangtou Station and Red Li interval, while all the annual runoff sequences changed at Zhangjiashan Station, Huaxian Station,Wenjiachuan Station and Longtouguai Station. Moreover, all the probabilities of mutation are greater than 90%. There are change points in the 1980s for the annual sediment discharge sequences at Xianyang Station, Zhangjiashan Station and Zhuangtou Station, while the change points at other stations are in the late 1990s. All the probabilities of the mutation are greater than 95%. Compared with some researches, the results generated by the matrix-based Renyi’s alpha order entropy are basically consistent with the actual situations, while those generated by the other methods are quite different from the actual situations.