基于柯西分布的水文序列异常值检测方法

针对基于正态分布的检测算法在窗口中出现偏差较大的极端异常值时，检测模型出现不稳定的现象，提出一种基于柯西分布的异常检测算法。通过试验发现，用滑动窗口内的中位数以及中位数绝对偏差来代替均值以及标准差，可以较好地消除滑动窗口内极端异常值对检测算法的影响。探讨了算法中滑动窗口以及置信度的设置，并通过实例对算法进行验证。结果表明，所提算法的检出率在窗口以及置信度设置恰当的情况下保持较高水平。与其他算法对比表明，所提算法对于处理局部波动剧烈的流量时间序列展现出较好的适用性以及鲁棒性。

Outlier detection method of hydrological time series based on Cauchy distribution

When the algorithm based on the normal distribution is applied in the sliding window, the detection model will yield an extreme outlier and exhibit unstable phenomenon. To address this issue, this study proposed an algorithm based on the Cauchy distribution for detecting outliers in hydrological time series. Test results indicate that using the median and median absolute deviation in the sliding window instead of the mean and standard deviation can well eliminate the influence of extreme outliers. The setup of the sliding window and the confidence in the algorithm were analyzed. Examples were used to verify this method and the results indicate that the detection rate of the proposed algorithm maintains a high level when the window and confidence settings are appropriate. The comparison with other algorithms shows that the proposed algorithm exhibits good applicability and robustness for dealing with time series with severe local fluctuations.