系统复杂性测度参数确定的新方法及其应用

近似熵和样本熵的参数m和r对复杂度有重要影响,目前仍缺乏选取其共同最优参数m和r的有效方法.利用两种复杂度比较时的一致性要求及其曲线存在交点的特性,基于相关系数,提出确定其共同最优参数m和r的交叉点新方法.以泾河流域1956-2010年张家山水文站径流及其控制流域的降水为研究对象.结果表明:径流和降水两种复杂度的共同最优参数为m=2和r=0.11倍的序列标准差;降水和径流复杂度均呈现显著的递增趋势;径流或降水与其复杂度之间存在显著的递减关系,降水的递减趋势对径流复杂度的增加有重要影响.近似熵在描述序列的变化趋势方面优于样本熵,而样本熵在辨识序列的峰谷值变化方面强于近似熵.本研究提出的交叉点新方法具有较好的适用性.

A new method for determining parameters of system complexity measures and its application

The parameters of m and r for approximate entropy (ApEn) and sample entropy (SampEn) have important influences on complexities. Effective approaches for selecting the common optimal parameters of m and r for ApEn and SampEn are still absent. The consistency requirement of comparisons between ApEn and SampEn and the characteristics of intersection between the two curves of ApEn and SampEn were considered. A new intersection method for determining the common optimal parameters of m and r was presented in terms of coefficients of correlation. The time series of runoff at the Zhangjiashan station and the precipitation above the station in the Jinghe watershed during 1956-2010 were taken as the object of investigation. Results show that:(I) The common optimal parameters were determined as the values of m=2 and r=0.11 times the standard deviation of time series for both ApEn and SampEn. (Ⅱ) The complexities of the precipitation and runoff present increasing significant trends. (Ⅲ) There are significant decreasing relationships between both runoff and precipitation and their complexities. The decreasing trend of precipitation impacts greatly the increase of runoff complexity. The ApEn is better than the SampEn for describing the general changing trends of time series; while the SampEn has a better performance than the ApEn for identifying the changes of peak and valley of time series. There is a good applicability for the new intersection method presented in this study for selecting the common optimal parameters of m and r for both ApEn and SapmEn.