基于希尔伯特-黄变换的潮汐分析方法研究

Study of the Analysis of Tides Based on the HHT Method

经验模态分解(EMD)是希尔伯特-黄变换(HHT)的核心组成部分.在对传统HHT方法研究与分析的基础上,发展了改进的集合经验模态分解的方法(MEEMD)对海洋潮汐进行分析.MEEMD方法根据水位数据序列的特点,通过添加成对白噪声和计算排列熵的方式来剔除分解过程中出现的虚假本征模态函数(IMF),从而抑制了模态混叠现象.数值模拟和实测水位数据实验表明,MEEMD方法可以在有效抑制模态混叠现象的基础上,对含有噪声的原始水位序列实现自适应滤波.MEEMD方法分解得到的高频IMF1和IMF2分量占原始水位数据总能量的90%以上,IMF1和IMF2分量的平均周期和平均振幅分别与调和分析得到的半日分潮与全日分潮结果基本一致.通过分析认为,IMF1和IMF2之和是主要半日分潮、全日分潮以及浅海分潮的叠加.传统的潮汐调和分析方法有赖于长期的水位记录,且需要水位数据的一些先验知识,涉及到的天文知识与数学计算也较为复杂.准调和分析可以处理短期的水位数据,但仍然涉及天文知识与复杂数学计算,对数据的完整性也要求较高.当收集到的水位数据因为存在噪声或者信息缺失,不足以进行传统的调和或准调和分析时,可以使用HHT方法进行有效的补充分析,以获得主要半日分潮、全日分潮和余水位的幅值信息,因此,该方法可以作为一种很好的潮汐分析的补充方法.

Empirical mode decomposition(EMD)is the core component of the Hilbert-Huang transform(HHT).Based on research and analysis of the traditional HHT method,we developed a method known as modified ensemble empirical mode decomposition(MEEMD)to analyze ocean tides.With respect to the characteristics of a water-level data series,we used MEEMD method to eliminate the false intrinsic mode function(IMF)in the decomposition process by adding paired white noise and calculating the permutation entropy,thus suppressing the occurrence of mode aliasing.A comparison of the numerical simulation results with measured water-level data shows that MEEMD method can effectively suppress modal aliasing and realize adaptive filtering for original water-level sequences with noise.In this study,the high-frequency IMF1 and IMF2 components decomposed by MEEMD method accounted for more than 90% of the total energy of the original water-level data.The average period and amplitude of the IMF1 and IMF2 components were basically consistent with the results of the semidiurnal-constituent and diurnal-constituent tidal components obtained by harmonic analysis,respectively.The results show that the sum of IMF1 and IMF2 is the superposition of the main semidiurnal,diurnal and shallow water tidal components,respectively. Traditional tidal harmonic analysis methods rely on long-term water-level records and require some prior knowledge of the water-level data.The astronomical knowledge and mathematical calculations involved are also more complex.Quasi-harmonic analysis can process short-term water-level data,but still requires astronomical knowledge and complex mathematical calculations,as well as high data integrity.When the collected water-level data are inadequate for traditional harmonic or quasi-harmonic analysis due to noise or lack of information,the HHT method can be used for effective supplementary analysis to obtain the magnitude information of the main semidiurnal constituent,diurnal constituent,and residual water levels.Therefore,MEEMD-HHT method can be used as a good supplementary method for tidal analysis.