Esmd Method _ Mathematics Science

Monograph "The method of pole symmetry mode decomposition--The new way of data analysis and scientific exploration" has been published in 2015.5, please pay attention to.
Http://blog.sciencenet.cn/blog-686810-898163.html

The latest free esmd software download: Previously released trial version, the probationary period ended on December 30, 2013. has never been updated since. Because of the interest in the Esmd method and hope to continue to use a lot of people, we decided to release it, provided for free use. The software is developed for the ESMD data analysis method, which can be attempted by scientific explorers who are concerned with data analysis.

Please refer to science net Li Zongjun Blog "Release the latest free esmd4j_v1.2 software (2016.7.20 update)"

Link Address: http://blog.sciencenet.cn/blog-460365-992979.html

"Science Nets" May 27 to "Qingdao University of Science and Technology research and development of new data processing" as the title of the School of Sciences Wang Jinliang and Li Zongjun Two teachers to develop the Esmd method was reported (http://news.sciencenet.cn/htmlnews/2013/5/ 278345.shtm); Then, May 30 the school newspaper and the "Our school teacher research and development of data processing new methods of concern" as the title of the follow-up report (HTTP://NEWS.QTECH.EDU.CN/ARTICLE.PHP?ARTICLEID=24900); July 3 Report officially published in the "China Science Daily" (4th edition 2013-07-03 International), titled "Qingdao Science and Technology invention data Processing New method" (http://news.sciencenet.cn/sbhtmlnews/2013/7/274855.shtm )。

The ESMD method is the abbreviation [1] of the "pole symmetric mode Decomposition method", and is a new development of the famous Hilbert-huang transformation [2], which can be used in the fields of information science, marine and Atmospheric Sciences, economics, ecology, medicine and seismology, all involving data processing in scientific research and engineering applications. From our preliminary trial results [3], the ESMD method is suitable for the study of the Hai-gas flux, which is better than the separation of turbulence and non turbulent components of the observed wind velocity. In addition, some oceanographic experts ' feedback show that the method has a good trial effect.

The research and development of this method lasted two years, completed in April 2012, and was published in March 2013. Related papers can be downloaded through the ARXIV electronic paper public website for free Download Lookup "Http://arxiv.org/abs/1303.6540,ESMD method for Data analysis.pdf"

The official thesis [1] was published in the August in the regular international journal Advances in Adaptive Data analysis.

The core of high technology is "mathematical technology", and "mathematical technology" is the main means of numerical simulation and data processing. Problems with mature mathematical models are applicable to numerical simulations, and problems with no mathematical model can only depend on data processing. In particular, the study relies on observational experiments for the process of unclear physical mechanisms. The way of exploration is to decompose random observational data into different frequencies of modal, and find the possible change rule.

In the field of stochastic data analysis, the classical method is based on the linear superposition principle of Fourier transform. It maps an observation time sequence to the frequency-energy spectral space, and each mode is a sine function with constant amplitude and constant frequency. The disadvantage is that it is only suitable for stationary signals for linear change, and wavelet transform is a popular method at present, it decomposes the signal by taking the local finite wavelet base, which makes up the defect of Fourier transform and can express the time-varying of frequency. However, the theory is based on the linear superposition principle, which is only applicable to non-stationary signals for linear change, and the Hilbert-huang transform based on empirical mode decomposition (EMD) is a popular method at present, it is a kind of data adaptive processing method, which does not require a predetermined base function or window length, The decomposed modes are variable in frequency and variable amplitude, and are suitable for nonlinear non-stationary signals. The main problems are: The number of screening is difficult to determine [5], the decomposition of the trend function is too rough, Hilbert spectral analysis has limitations, such as [1].

The fundamental problem of random data processing lies in its non-stationary, one is the change of the trend, the other is the amplitude and the frequency is sometimes denatured. How to extract a global EMA is the most important issue when there is a big trend change. Fourier transformation at the beginning of the view that the global moving average is zero, "least squares" must have a priori function form, "sliding averaging method" in the time window and weight function selection is lack of basis, the wavelet transform is actually a sliding average. Only the global EMA is better filtered than the rest can be seen as the pulsation amount.

The proposed ESMD method uses EMD's idea to change the outer envelope interpolation to the internal pole symmetry interpolation, and uses the idea of "least squares" to optimize the last remaining mode to make it become the "adaptive global average" of the whole data, and thus to determine the best filtering times. Considering that all integral transformations including Hilbert transform have inherent defects in analyzing time-frequency variation, we discard the traditional idea that spectrum analysis relies on integral transformation and creatively propose a direct interpolation (DI) method for data. This can not only visually reflect the amplitude and frequency of each modal time-varying, but also can be clearly known to the total energy change (here "energy" is generalized, to the temperature of the intensity of the fluctuation). In fact, the output of the software program based on the "direct interpolation" of the time-varying spectrum is more intuitive and more reasonable than the Hilbert spectrum, because not only the frequency is the change of the total energy is also changed deliberately to see energy as constant and mapping it to a set of fixed frequencies is far-fetched.

Esmd method Modal Decomposition Example:

Example 1. A signal synthesized by a sine function, a weighted periodic function, and a parabola:

The modal decomposition test is carried out. The optimal number of filters is 29, which corresponds to the minimum variance ratio (indicating that the last remaining modal R is the best adaptive global EMA for the data). At this point, the corresponding decomposition is also the best, three function curves are clearly separated (see Figure 2).

Figure 1: Variance ratio varies with the number of filters (29 times Best)

Figure 2:ESMD corresponds to the decomposition result of the filter number 29 (where the first is a synthetic signal)

Example 2. The modal decomposition test of the measured temperature data from 2008.05.10 to 2011.11.03 provided by the United States Climate Data center was carried out. At this time the best filter number is 30, the corresponding decomposition see Figure 3. Among them, the residual modal R is the best adaptive global ema corresponding to the interannual temperature variation (Fig. 4 shows that r can fit the data well), and the 5th, 4, 3 modes correspond to the average period of approximately 66 days, 35 days, and 17 days of temperature fluctuations respectively. In particular, we can determine the frequency bands and the time (Fig. 3, fig. 6) Where the temperature anomaly occurs by varying the amplitude of each modal. In this case, the modal 5 amplitude change is small and the modal 4 amplitude changes greatly, which indicates that the temperature anomaly mainly occurs in the time scale of 35 days, and the anomalous time is mainly concentrated in 2009 1 to March. In addition, the software program can output a time-varying spectrum based on the "direct interpolation method" (Fig 5), it is more intuitive and more reasonable than the Hilbert spectrum, because not only is the total energy of the change also changing (Fig 7), energy can not be viewed as a constant and mapped to a series of fixed frequencies. The final fig. 8 reflects the fluctuation of the filtering EMA, which is better than the "least squares" method and the "sliding average" method.

Figure 3:ESMD corresponds to the decomposition result of the filter number 30 (the horizontal coordinate represents the time/day)

Figure 4: Optimal Adaptive Global moving average R to fit the data

Figure 5: Time-varying Spectrogram (a line representing the frequency change of a modal)

Figure 6: time-varying graphs of modal frequencies and amplitudes (f and A, respectively, representing frequencies and amplitudes)

Figure 7: time-varying diagram of total modal energy

Figure 8: Filtering unless a stationary adaptive global EMA is followed by a fluctuating amount

This blog post has been organized into a formal paper:

Wang Jinliang, Li Zongjun. A esmd method that can be used for climate data analysis, "Climate Change Research Letters," 2014,3,1-5.

http://www.hanspub.org/Journal/PaperInformation.aspx?paperID=12981

Reference documents:

[1] Jin-liang Wang and Zong-jun Li extreme-point symmetric Mode decomposition method for the Data analysis.  Advances in Adaptive Data Analysis, vol. 5, No.3 (2013), 1350015 (36pages). [doi:10.1142/s1793536913500155] http://arxiv.org/abs/1303.6540,

Esmd method for Data analysis.pdf

[2] N. E. Huang et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary. Proc. R. Soc. Lond. A, 454:903c995, 1998.

[3] Hui-feng Li, Jin-liang Wang and Zong-jun Li, application of Esmd method to Air-sea Flux. International Journal of Geosciences, 4, 2013, p8-11.
HTTP://DX.DOI.ORG/10.4236/IJG.2013.45B002 application of Esmd method 2013.pdf

[4] Scilab Scientific Computing software platform use instructions http://www.scilab.org/

[5] Jin-liang Wang and Zong-jun Li. What about the asymptotic behavior of the intrinsic mode functions as the sifting times tend to infinity? Advances in adaptive Data Analysis, 4 (1 & 2), 1250008 (17pages), 2012.

What about the asymptotic behavior of the Imf.pdf

http://www.worldscientific.com/doi/abs/10.1142/S1793536912500082

Extreme-point symmetric Mode decomposition for the Data Analysis summary:

an extreme-point symmetric mode decomposition  (ESMD)  method is  proposed to improve the hilbert-huang transform  (HHT)  through the  following prospects:  (1)  the sifting process is implemented by  the aid of 1, 2, 3 or more inner interpolating curves,  which classifies the methods into esmd_i, esmd_ii, esmd_iii, and  so on;  (2)  the last residual is defined as an optimal  curve possessing a certain number of extreme points, instead  of general trend with at most one extreme point, which  allows the optimal sifting times and decompositions;  (3)  the  extreme-point symmetry is applied instead of the envelop symmetry;  (4)  The data-based  direct interpolating approach is developed to compute the  instantaneous frequency and amplitude. one advantage of the esmd  Method is to determine an optimal global mean curve in an  adaptive way which is better than the common least-square  Method and running-mean approach; another one is to determine the  instantaneous frequency and amplitude in a direct way which  is better than the hilbert-spectrum method. these will improve  the adaptive analysis of the data from atmospheric and  Oceanic sciences, inforMatics, economics, ecology, medicine, seismology, and so on.

Keyword:extreme-point symmetric mode decomposition  (esmd); empirical mode  decomposition  (EMD);
hilbert-huang transform  (HHT); direct interpolating  (DI); adaptive  global mean  (AGM);
intrinsic mode function  (IMF); data  (Signal)  processing  

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