Empirical Mode Decomposition

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1 Empirical Mode Decomposition
专题11 Empirical Mode Decomposition

2 Outline Introduction Decomposition Composition Conclusion

3 传统的信号分析与处理都是建立在傅立叶分析的基础上的，它有三个基本的假设：线性、高斯性和平稳性，建立的是一种理想的模型。傅立叶分析在科学与技术的所有领域中发挥着十分重要的作用，但是它使用的是一种全局的变换，因此无法表述信号的时频局部性能，而这种性质恰恰是非平稳(时变)信号最根本和最关键的性质，因此就不适合用于分析非平稳信号。现实生活中存在的自然或是人工的信号大多是非平稳信号，如语音信号、机械振动信号、心电信号、雷达信号及地震信号等。因此为了分析和处理非平稳(时变)信号，人们对傅立叶分析进行了推广乃至根本性的革命，提出并发展了一系列新的信号分析与处理理论，即非平稳(时变)信号分析与处理。

4 Introduction: Background
经验模式分解(Empirical Mode Decomposition, EMD)是一种完全由数据驱动的自适应非线性时变信号分解方法,它将数据分解成具有物理意义的几个内蕴模式函数分量。 Crude oil is one of the most important energy in the world. a 1% increase in price of oil = 0.6 to 2.5 GDP growth percentage points

5 It is difficult to analyze and predict crude oil price.
Crude oil price is basically determined by its supply and demand; But strongly influenced by many irregular past/present/future events. Crude oil market today Keep rising Fluctuate dramatically. The most volatile among all the markets, except NASDAQ. (Maurice ,1994)

6 Introduction: Challenge
An objective data analysis method should be developed not only to help discover the characteristics of the data but also help understand the underlying rules. The Empirical Mode Decomposition method (EMD), which is proposed by Huang et al. (1998), is one such method.

7 Empirical Mode Decomposition (EMD)
Empirical Mode Decomposition (EMD) is a generally nonlinear, nonstationary data processing method developed by Huang et al. (1998).黄锷 Norden E Huang receiver signal source 1 signal source 2 Overall Signal

8 The principle of EMD The generic principle of the EMD is to decompose any time series into a set of simple intrinsic modes of oscillations in the data itself, based on scale separation. The intrinsic modes are called Intrinsic Mode Function (IMF) and defined as: have the same numbers of extrema and zero-crossings or differ at most by one; are symmetric with respect to local zero mean. When the IMFs and the residual are summed together they form the original time series.

9 在物理上，如果瞬时频率有意义，那么函数必须是对称的，局部均值为零，并且具有相同的过零点和极值点数目。在此基础上，NordneE
在物理上，如果瞬时频率有意义，那么函数必须是对称的，局部均值为零，并且具有相同的过零点和极值点数目。在此基础上，NordneE.Huang等人提出了本征模态函数(Intrinsic Mode Function，简称IMF)的概念。本征模函数任意一点的瞬时频率都是有意义的。Hunag等人认为任何信号都是由若干本征模态函数组成，任何时候，一个信号都可以包含若干个本征模态函数，如果本征模函数之间相互重叠，便形成复合信号。EMD分解的目的就是为了获取本征模态函数，然后再对各本征模态函数进行希尔伯特变换，得到希尔伯特谱。

10 EMD方法假设任何信号都由不同的本征模态函数(IMF)组成，每个IMF可以是线性的，也可以是非线性的，IMF分量必须满足下面两个条件：一是其极值点个数和过零点数相同或最多相差一个，二是其上下包络关于时间轴局部对称。这样任何一个信号就可以分解为有限个IMF之和。 分解过程基于以下假设：(1)信号最少有一个极大值和一个极小值；(2)时域特性由极值间隔决定；(3)如果数据序列完全缺乏极值但是仅包含拐点，那么它也可通过求导一次或多次来揭示极值点，而最终结果可以由这些成分求积分来获得。具体方法是由一个“筛选”过程完成的：

11 EMD Algorithm

12

13 SIFTING

14 SIFTING

15 SIFTING

16 SIFTING

17 SIFTING

18 SIFTING

19 SIFTING

20 SIFTING

21 SIFTING

22 SIFTING

23 SIFTING

24 SIFTING

25 Current Applications of EMD
Limited to natural and engineering fields Non-destructive evaluation for structural health monitoring Vibration, speech, and acoustic signal analyses Earthquake engineering Bio-medical applications Cosmological gravitational wave and planets hunting Only two significant applications in social sciences Financial market data analysis examine the changeability of the markets by Huang et al. (2003). Epidemics transmission show the existence of a spatial–temporal traveling wave in the incidence of dengue hemorrhagic fever in Thailand DOT: department of transportation NSWC: Naval Surface Warfare Center DFRC:NASA - Dryden Flight Research Center KSC:NASA - Kennedy Space Center FBI :Federal Bureau of Investigation Defense Advanced Research Projects Agency University of California, San Diego The Johns Hopkins University National Oceanic & Atmospheric Administration

26 Advantages of EMD EMD can reduce any data from non-stationary and nonlinear process into simple independent intrinsic mode functions; Only extrema are needed in the sifting process, so it is local and adaptive; The inductive basis is posterior rather than prior and, therefore, it is physically meaningful; The IMFs have a clear definition of instantaneous frequency as the derivative of the phase function, so Hilbert transformation can be applied to the IMFs, allowing us to analyze the data in a time-frequency space.

27 Data: WTI oil price 1、第一个平稳期( 年)：这一时期，国际油价非常平稳，平均价格2.84美元/桶，世界处于典型的“低油价时代”。 2、第一个暴涨期( 年)：该时期国际油价暴涨的导火线是第四次中东战争。油价暴涨引起了西方国家的经济衰退，引发了战后最严重的世界性经济危机。 3、第二个平稳期( 年)：这个时期原油平均价格13.27美元/桶，国际油价相对平稳，对于世界各国经济走出“滞胀”起到了一定的促进作用。 4、第二个暴涨期( 年)：1979年，伊朗为报复美国支持伊朗旧国王，宣布石油禁运，石油生产急剧减少。1980年，两伊战争爆发引起世界石油市场的动荡和供应紧张，国际油价从1979年1月的14.85美元/桶窜升至1980年4月的39.5美元/桶。 5、第三个平稳期( 年)：这个时期国际油价稳中下降，从1982年初的38美元/桶跌至1989年末的14美元/桶。此外，油价波动性明显增大。 6、第三个暴涨期( 年)：该时期国际油价暴涨的导火索是1990年8月的伊拉克入侵科威特事件。1991年1月，第一次海湾战争爆发，伊、科石油业遭到严重破坏，国际市场供给短缺高达9%，油价一路飞涨。 7、第四个平稳期( 年)：由于伊拉克很快战败投降，战争很快结束，加上沙特阿拉伯等多国配合增产，OECD各国也动用石油储备平抑油价，国际油价迅速平稳。 8、第四个持续暴涨期(1998至今)： 年初，欧佩克三次减产，国际油价再次剧升。2001年美国遭受“9·11”恐怖袭击后，开始陈兵海湾。2003年3月，美军再次进军伊拉克。加之美元贬值，世界油价步入长时间上行通道。2005年7月伊朗重启核浓缩计划，国际油价一度突破67美元/桶。由于伊朗核问题迟迟得不到解决，2006年4月，国际油价突破70美元/桶。目前国际油价仍在高位徘徊。这个时期的油价波动急剧扩大，极大地影响了世界经济的发展。 Figure 1 The observed time series of WTI oil price from Jan.1946 to May, 2006

28 WTI oil price decomposition

29 Decomposition

30 Why Composition? Scale-mixing in Decomposition
Help focus on components of different characteristics

31 EMD with Intermission(1): original signal

32 EMD with Intermission(2): Decomposition Results

33 EMD with Intermission(3):Comparision

34 Three Components

35 Trend: deterministic force in the long run
The deterministic force for oil price evolution in the long run. holds a high correlation with the original price accounts for more than 70% percent of variability, The long term trend of crude oil price may be determined by global economic development The continuing increasing trend is consistent with the economic development of the world. Figure World GDP and the trends in oil price. The solid line is the annual world GDP measured by constant 2000 US$ from 1960 to The data is from the World Economic Indicators Database. The dotted line is the trend from 1960 to The yearly trend value is defined as the average of monthly residue in the same year

36 Trend: Is there a sudden structure change in 1973?
The trend line can be fitted accurately with a quadratic function. But it will drift while changing the sample range due to the end effect in decomposition. This finding is similar to what Pindyck (1999) found for real crude oil price.

37 Effects of Significant Events: the causes of large fluctuations in medium term
Described by IMF4 to IMF7 The mean periods range from 3.5 years to 30 years The amplitudes at some data points could be more than $10 or even higher, suggesting the effects of some significant events on oil price may be very serious. .

38 Normal Market Disequilibrium: important for short term forecasting
Have no serious impact on oil price –generally within $5. But these events are becoming more and more frequent and have become the fundamental impetus for oil prices going up recently.

39 low frequency component
residue It is also described as the “trend” in EMD, could represent the major trend of oil price in the long run. low frequency component It can be treated as the effect of significant events. It is the main reason for the dramatic oil price variability in the medium term. high frequency component It should be explained as normal market fluctuations or events which only bring a short term impact to crude oil price. the price of $70.84/barrel in May 2006 = a trend price ($36.26)+ a significant event price ($32.63)+ and a normal fluctuation of $1.21.

40 Thanks!!!