Research On EMD Algorithm And Its Application In Signal Denoising

Empirical Mode Decomposition (EMD) is a time-frequency analysis method to process non-linear and non-stationary signals. According to the characteristics of input signals, this method can decompose the original signal to a sum of some intrinsic mode functions adaptively without any prior knowledge. It is considered to be a great breakthrough of traditional time-frequency analysis methods such as Fourier analysis and wavelet analysis which are based on the hypothesis of linear and stationary. In the course of development after many years of EMD method, it gradually shows the unique advantage in processing non-stationary signals. EMD method not only has the important theoretical research value but also has wide application prospect. Moreover, it has enormous application value in mechanical fault diagnosis, feature extraction, information detection, biomedical signal analysis, image signal analysis, communication radar signal analysis and other fields at present.In this paper, further research on the whole theory of EMD is made, and taking the inherent disadvantages of EMD algorithm as breakthrough points, a lot of research work is done about the problems of end effect and mode mixing in EMD algorithm. At the same time, the corresponding solution program are given From the angle of application, adaptive filtering characteristics of EMD algorithm is deeply researched, and it is used in the signal filtering and noise reduction. Moreover, two new methods of noise elimination are given. The main contents and innovative points of the paper are as follows:Firstly, aiming at the problem of end effect in EMD algorithm, the mechanism of generating end effect is described, and the respective characteristics of methods to restrain end effect are analyzed. At the same time, the conceptions of matching distance and waveform similarity coefficient are introduced. A method of data continuation which is based on the nearest similarity distance is proposed. This method finds the matching section which has the minimum differences of the shape and amplitude in the original signal to extend the data of endpoints, so the smooth transition at the juncture between extended data and original signal is realized. Meanwhile, this method just needs one time to extend the data of endpoints, and it not only can solve two kinds of end effect effectively but also have very fast running speed.Secondly, aiming at the problem of mode mixing in EMD algorithm, the reasons of generating EMD mode mixing are analyzed. According to the problem of mode mixing which is caused by discrete events, the changing characteristics of time characteristic scale and extremum characteristic scale are analyzed, and the conceptions of smoothness of time characteristic scale and extremum characteristic scale are introduced. Two methods which are based on smoothness of time characteristic scale and extremum characteristic to solve the problem of mode mixing scale are proposed. Through simulation experiments, the effectiveness of two methods is verified in this paper, and in some cases the limitations of these methods are pointed out. According to these, anther method to solve mode mixing which is based on combined smoothness is proposed. The judgement criterion of two kinds of smoothness is comprehensively considered in this method, so judgment accuracy is enhanced, and problem of mode mixing which is caused by discrete events is solved effectively.Thirdly, aiming at the problem of the mode mixing which is brought by mutual reaction among signals, the condition and basis to separate two signals from each other correctly are analyzed, then a method is presented to resolve this problem. Meanwhile, theoretical derivation and proof are given. Based on the characteristics of Fourier-transform and the relationship of spectrum between original signal and its analytic signal, an effective and reversible evolution process is constructed in this method. The signal which does not satisfy the condition of EMD decomposition after positive evolving, EMD decomposing and reverse evolving, the components of EMD decomposition which don't have mode mixing are obtained. This method not only solves the problem of mode mixing which is caused by mutual reaction among signals very well but also fits for the situation of multiple signals, and it provides a new idea to solve the problem of mode mixing.Finally, EMD algorithm which is used in signal filtering and noise reduction is researched. Aiming at the disadvantage of poor stability which is caused by using energy criterion to judge dividing point and relying on the difference of respective autocorrelation function's characteristics of noise and signal, a new de-noising method based on characteristic of autocorrelation function is proposed. In this method, a new criterion to judge dividing point is constructed, and aiming at the noise modes which have been judged. A method which is similar to wavelet soft-threshold de-noising is used to remove noise. The useful signal components which maybe exist in noise modes are reserved better. Through simulation experiments, the de-noising effects of two methods are compared, whether on the fact of stability or de-noising precision is better than the old method. In addition, the statistical characteristics of noise and each component obtained by EMD decomposition are discussed. Under the premise that the first component is assumed as a noise, a new de-noising method based on EMD statistical characteristics of noise is proposed. In this method, the new component is gotten by the first component using random sort each time, and the reconstructing signal is the sum of each new component and other components, then the sum of all the reconstructing signals are got. At last, the average value of the sum is calculated, because of the random characteristic of noise, the signal component whose signal-to-noise ratio is improved is obtained. After that, the new signal component is decomposed, and this operation is repeated several times, so the signal component whose noise power has been restrained is obtained. This method can be simplified as:random sorting, reconstructing, accumulating, calculating the average value, further decomposing, and repeating aforementioned operation.Generally speaking, the EMD algorithm and its application in signal filtering and noise reduction are researched, and aiming at the disadvantage of EMD algorithm, the corresponding improvement of EMD algorithm is done. Meanwhile, aiming at the characteristic of de-noising in EMD, two de-noising methods are proposed. Through the simulation experiments, the effect of algorithm that has been improved in the paper...