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A new method for detecting mutation of hydrological sequence based on matrix-based Renyi's α order entropy
QIAN Longxia, WANG Hongrui, WU Wanqing, DANG Suzhen, SONG Shuhong
Systems Engineering - Theory & Practice
2023, 43 (1):
295-308.
DOI: 10.12011/SETP2021-1391
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.
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