CN105678049A - End effect suppression method based on improved SVR continuation - Google Patents

Abstract

The present invention discloses an end effect suppression method based on improved SVR continuation. The end effect suppression method comprises the following steps of preprocessing a signal, and obtaining maximum and minimum value sequences; calculating and obtaining an average extremum sequence, and continuing the calculated average extremum sequence forwardly and backwardly with a finite number of average extremums by utilization of support vector regression; reversely deriving the corresponding maximum value and the minimum value according to the average extremums; and performing interpolation processing on the calculated extremum sequence by utilization of a cubic spline curve. The problem that ends of the signal are still uncertain after the original signal is continued by the support vector regression is solved, and the end effect suppression method has a good effect on suppressing end effects of empirical mode decomposition.

Description

Based on the end effect suppressing method improving SVR continuation

Technical field

The present invention relates to signal processing technology field, particularly to a kind of based on the end effect suppressing method improving SVR continuation.

Technical background:

Empirical mode decomposition (EmpiricalModeDecomposition, EMD) non-stationary, nonlinear properties can be processed preferably, compared with believing processing method with other time-frequencies, this method has lot of advantages, such as posteriority, intuitive and adaptivity etc. Being primarily due to this conversion and be based on a kind of decomposition method of data itself, therefore it has better performance. Although EMD method has good effect when analyzing non-stationary signal, but there is the more serious problem of ratio, i.e. an end effect in actual applications.

At present, the method solving end effect is broadly divided into two classes: one is select other reliable interpolation methods that extreme point is interpolated calculating, and another kind of is that the two ends to original signal carry out continuation process to obtain more extreme point. Equations of The Second Kind method can be divided into again end effect, neutral net continuation, AR model continuation and support vector regression (SupportVectorRegression, SVR) continuation etc. according to the difference of continuation algorithm. End effect is had certain rejection ability by these continuation methods, but these methods are due to itself and reason all having some limitations property of application conditions.

Summary of the invention

The invention aims to solve the deficiency that existing method exists, it is provided that a kind of based on the end effect suppressing method improving SVR continuation.

In order to achieve the above object, insight of the invention is that and first signal is carried out pretreatment, obtain very big, minimum sequence, calculate again and obtain mean pole value sequence, utilize support vector regression to calculated mean pole value sequence respectively forwardly limited the average extreme value of continuation backward, again by the anti-maximum point releasing correspondence of these average extreme values and minimum point, finally utilize cubic spline curve that the extreme point sequence after calculating is interpolated process.

Conceiving according to foregoing invention, the technical solution used in the present invention is:

A kind of based on the end effect suppressing method improving SVR continuation, comprise the following steps:

1) obtain all extreme points in primary signal, respectively constitute maximum sequence and minimum sequence, calculate the average avr (i) and mean difference σ of corresponding maximum point and minimum point:

$avr\left(i\right)=\frac{\max \left(i\right)+\min \left(i\right)}{2}$ 1≤i≤N

$\mathrm{\σ}=\underset{i=1}{\overset{N}{\Σ}}\frac{max\left(i\right)-\min \left(i\right)}{2N}$

Wherein max (i) is the maximum of i-th point, and min (i) is the minimum of i-th point, and N is sampling number, thus obtaining mean pole value sequence avr (1), and avr (2) ..., avr (N);

2) determining the sample number of training, and select suitable penalty factor and precision parameter ε, (x, y, f), and select suitable kernel function, thus produces a training set L={ (x to select loss function e₁,y₁),…,(x_l,y_l), wherein l is number of training, (x_i,y_i) for i-th training sample, specific formula for calculation is x_i=[avr (i) avr (i+1) ... avr (N-l+i-1)]^T, y_i=avr (N-l+i);

3) obtain the model based on SVR, use this model to be obtained in that the m-th data point avr (N+M) that the prediction of continuation backward obtains; Calculate in conjunction with the data obtained after continuation and mean difference σ and obtain corresponding m-th maximum point max (N+M) and minimum point min (N+M);

4) maximum sequence and minimum sequence to obtaining after calculating are sequentially carried out interpolation processing, it is thus achieved that corresponding envelope;

5) envelope after continuation is utilized to suppress the generation of end effect in EMD catabolic process.

The present invention compared with prior art has the following advantages:

1, the present invention utilizes the method for the support vector regression continuation of improvement that the mean pole value sequence of envelope is carried out continuation, it is proposed that a kind of new method suppressing EMD end effect.

2, the invention solves the problem that after the EMD caused by end effect decomposes, distorted signals is more serious.

Accompanying drawing explanation

Fig. 1 is the method flow diagram of the embodiment of the present invention.

Fig. 2 is that the embodiment of the present invention is without the emulation signal schematic representation suppressing end effect to process.

Fig. 3 is embodiment of the present invention emulation signal schematic representation after improving SVR continuation.

Detailed description of the invention:

Below in conjunction with accompanying drawing, technical scheme is specifically described.

As it is shown in figure 1, a kind of based on the end effect suppressing method improving SVR continuation, specifically include following steps:

1) choosing input signal x (t)=2sin (20 π t)+cos (10 π t)+sin (5 π t), this signal is the cosine signal by frequency to be the sinusoidal signal of 20 π Hz, frequency be 10 π Hz and the sinusoidal signal that frequency is 5 π Hz is formed by stacking. Sample frequency is 1000Hz, and the sampling time is 2s, and its time domain waveform and upper and lower envelope are as shown in Figure 2. Solid line in figure is the waveform of primary signal, and the dotted line in figure is the envelope up and down of this signal. As can be seen from the figure process, through cubic spline interpolation, the envelope obtained and do not comprise whole data, all occur in that distortion phenomenon in various degree at the two ends, left and right of coenvelope line and the right-hand member of lower envelope line, this generates end effect.

2) obtain all extreme points in primary signal, respectively constitute maximum sequence and minimum sequence, calculate the average avr (i) and mean difference σ of corresponding maximum point and minimum point:

$avr\left(i\right)=\frac{\max \left(i\right)+\min \left(i\right)}{2}$ 1≤i≤N

$\mathrm{\σ}=\underset{i=1}{\overset{N}{\Σ}}\frac{max\left(i\right)-\min \left(i\right)}{2N}$

Wherein max (i) is the maximum of i-th point, and min (i) is the minimum of i-th point, and N is sampling number, thus obtaining mean pole value sequence avr (1), and avr (2) ..., avr (N);

3) adopt support vector regression algorithm that mean pole value sequence is carried out continuation, determine the sample number of training, and to choose penalty factor be C=∞, precision parameter is ε=0, loss function e (x, y, f) linear insensitive function is selected, kernel function selects linear kernel function, and number of training is set to l=100, thus produces an average extreme value training set.

4) obtain the model based on SVR, use this model to be just obtained in that the m-th data point avr (N+M) that the prediction of continuation backward obtains. Just can calculate in conjunction with the data obtained after continuation and mean difference σ and obtain corresponding m-th maximum point max (N+M) and minimum point min (N+M).

5) maximum sequence and minimum sequence to obtaining after calculating are sequentially carried out interpolation processing, it is possible to obtaining corresponding envelope, result is as shown in Figure 3. In figure, solid line is the signal after improved SVR algorithm continuation, and dotted line is its upper and lower envelope.

To the comparison of Fig. 2 and Fig. 3 it is found that adopt innovatory algorithm that signal is carried out end extending, while ensureing that original signal is basically unchanged so that envelope curve optimizes significantly, it is possible to comprise all of data in signal, successfully inhibit end effect.

Claims (1)

1. the end effect suppressing method based on improvement SVR continuation, it is characterised in that comprise the following steps:

1) obtain all extreme points in primary signal, respectively constitute maximum sequence and minimum sequence, calculate the average avr (i) and mean difference σ of corresponding maximum point and minimum point:

$avr\left(i\right)=\frac{max\left(i\right)+\min \left(i\right)}{2},1\≤i\≤N$

$\mathrm{\σ}=\underset{i=1}{\overset{N}{\Σ}}\frac{max\left(i\right)-\min \left(i\right)}{2N}$

Wherein max (i) is the maximum of i-th point, and min (i) is the minimum of i-th point, and N is sampling number, thus obtaining mean pole value sequence avr (1), and avr (2) ..., avr (N);

2) determining the sample number of training, and select suitable penalty factor and precision parameter ε, (x, y, f), and select suitable kernel function, thus produces a training set L={ (x to select loss function e₁,y₁),…,(x_l,y_l), wherein l is number of training, (x_i,y_i) for i-th training sample, specific formula for calculation is x_i=[avr (i) avr (i+1) ... avr (N-l+i-1)]^T, y_i=avr (N-l+i);

3) obtain the model based on SVR, use this model to be obtained in that the m-th data point avr (N+M) that the prediction of continuation backward obtains; Calculate in conjunction with the data obtained after continuation and mean difference σ and obtain corresponding m-th maximum point max (N+M) and minimum point min (N+M);

4) maximum sequence and minimum sequence to obtaining after calculating are sequentially carried out interpolation processing, it is thus achieved that corresponding envelope;

5) envelope after continuation is utilized to suppress the generation of end effect in EMD catabolic process.