水文序列分析中基于信息熵理论的消噪方法

为准确有效地识别和分离水文时间序列中的噪声成分，应用信息熵理论并结合小波消噪概念，建立了小波系数阈值优选熵准则和水文序列消噪新方法。该方法首先应用熵函数H值描述噪声成分的不确定度，并应用信息量系数(information cost function ICF)值描述主序列的复杂度；然后通过分析不同小波系数阈值对应的噪声成分H值和主序列ICF值的变化规律，可优选出合理的小波系数阈值；最后对小波系数进行阈值量化处理，即可实现水文序列消噪。通过对不同特性模拟序列和不同实测水文序列分别进行分析，并通过与常用小波消噪方法(FT、SURE、MAXMIN)的消噪结果对比，验证了该阈值优选熵准则的合理性和适用性。分析结果显示，水文序列中的噪声成分具有偏态特性，因此本文应用偏态分布线型(P_Ⅲ型分布)对噪声成分进行描述更为合理，而且小波系数阈值优选熵准则所得的阈值是基于信息熵理论而确定的，因此是整体上最优值。

Information entropy theory based noise reduction method for hydrologic series data analysis

Base on information entropy theory and the concept of wavelet for noise reduction an improved entropy criterion for optimal selection of wavelet coefficient threshold is established and a new method for noise reduction of hydrologic series is proposed. First, the entropy value H is applied to describe the andom characteristics of noise, and the information cost function is used to describe the complexity degrees of the main series. Then, the reasonable wavelet coefficient threshold can be optimized by analyzing the corresponding H value of wavelet coefficient threshold and the variation law of information cost function of main series. Finally, the selected thresholds are used to deal with the wavelet coefficients and the accurate separation of noise can be realized. The effectiveness of the proposed method is verified by comparing the analyses on two different synthetic series and two different observed hydrologic series with traditional methods. It is found that generally the hydrologic noises exhibit skew characteristics, so that it is reasonably to use skew probability distribution to describing the noise components, and the wavelet coefficient threshold obtained by optimal entropy criterion based on information entropy theory in the global optimum.