Signal prediction based on empirical mode decomposition and artificial neural networks

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Geodesy and Geodynamics 2012,3 ( 1) :52 -56

http://www. jgg09. com

Doi:10.3724/SP.J.1246.2012.00052

Signal prediction based on empirical mode decomposition and

artificial neural networks

Wang Y ong1 , Liu Y anping2 and Yang Jing3

1 _{School of Surveying}

& Umd lnfonnation EngiMering, Henan Polyteclmic University, Ji.oozuo 454000, China 2

School of Civil Engineering, Central South University, Changsha 410075, China 3

College of Mining EngiMering, Hebei United University, Tangslw.n 063009 , Chino

Abstract: In view of the usefulness of Empirical Mode Decomposition ( EMD) , Artificial Neural Networks ( ANN) , and Most Relevant Matching Extension ( MRME) methods in dealing with nonlinear signals , we pro-pose a new way of combining these methods to deal with signal prediction. We found the results of combining EMD with either ANN or MRME to have higher prediction precision for a time series than the result of using EMD alone.

Key words: EMD (Empirical Mode Decomposition); ANN (Artificial Neural Networks); MRME (Most Rel-evant Matching Extension) ; IMF (Intrinsic Mode Function) ; endpoint problem; RBF ( Radial Basis Func-tion)

1 Introduction

Empirical mode decomposition ( EMD) is a method of transforming an empirical time series into a few Intrin-sic Mode Function ( IMF) components and a tendency term, which is the final drab and smooth part of the o-riginal sequence['-'l. It is usually applied to deal with some nonlinear or non stationary series. Because of its certain characteristics , such as parallel processing, self adaptivity, self-organization, associative memory,

fault

tolerance , robustness , it is suitable for application to prediction studies.

In this paper, we show how to use EMD to decom-pose a simulation signal into several IMF components and a tendency , how to treat the endpoint problem in two ways, how to do signal prediction by using RBF

Received,2012.()2.05; Aooepted,2012.Q2·12

Corresponding author: Tel: + 86-13785091437, E-mail: Wangyongiz@ 126. com

This work was supporteal. by the Notional Natural Scince Foundation of

Hebei Provinoe ( 0201000921)

(Radial Basis Function) neural network for each com-ponent separately, and how to reconstroct the final pre-diction results.

2 EMD and endpoint problem

During the EMD decomposition, the resultant IMF components must meet the following conditions : 1 ) The number of maximum and minimum points and the number of zero-crossing in different directions must be approximately equal; 2) the mean value of the

maxi-mum and minimaxi-mum at any point must be zero. The decomposition process is as follows[3J :

1) For a signal x ( t) , connecting all the maxima

with a 3 -order spline curve to get the upper envelope , and from the minima to get a lower envelope similarly. Generating a new signal by subtracting the mean of the upper and lower envelope from the original signal.

2) Checking whether the new signal meets the a-bove-mentioned basic requirement of IMF, or whether the residual r is a monotonic function. IT not, repeating step1).

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4 Conclusion

The neural network extension and the most relevant match extension methods are both good solutions to the endpoint-effect problem. EMD decomposition can sup-ply input variables with higher quality to the RBF neu-ral network. The new prediction method presented here can achieve higher precision.

References

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[3]

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( in Chinese)

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