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Hilbert-Huang Transform end effect inhibition method based on grey theory

A technology based on gray theory and endpoint effects, applied in complex mathematical operations, etc., can solve the problems of not being able to obtain the Hilbert spectrum of the intrinsic mode function and effectively extracting the essential characteristics of the signal, and achieve high short-term prediction accuracy, fast calculation speed, The effect of reducing endpoint effects

Inactive Publication Date: 2011-08-31
HARBIN INST OF TECH
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Problems solved by technology

[0005] The present invention is to solve the problem that the existing Hilbert-Huang transform method cannot effectively extract the essential characteristics of the signal due to the interference of the endpoint effect, and cannot obtain accurate eigenmode functions and Hilbert spectrum, and provides a gray theory-based Hilbert-Huang Transform Endpoint Effect Suppression Method

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  • Hilbert-Huang Transform end effect inhibition method based on grey theory
  • Hilbert-Huang Transform end effect inhibition method based on grey theory
  • Hilbert-Huang Transform end effect inhibition method based on grey theory

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specific Embodiment approach 1

[0020] Specific implementation mode 1: Combination figure 1 To explain this embodiment, the method for suppressing the end effect of the Hilbert-Huang transform based on the gray theory described in this embodiment, the specific steps are:

[0021] Step 1: Initialize p=1; q=1; r q (t)=s(t); h pq (t)=s(t); c q (t)=s(t); SD=1000; where, (t∈N + ) Is the given signal to be processed; where p represents the number of inner cycles, q represents the number of outer cycles, r q (t) represents the function of the residual error of the qth cycle, h pq (t) represents the function of the intermediate variables generated in the p-th inner loop and the q-th outer loop, c q (t) represents the qth IMF, SD represents the termination criterion;

[0022] Step 2: Judge r q (t) Whether it is monotonous, if yes, go to step 8; otherwise, go to step 3;

[0023] Step 3: Take 0.2≤ε≤0.3, judge whether SD>ε holds, if yes, go to step 7; otherwise, go to step 4; where ε represents the selected threshold;

[0024]...

specific Embodiment approach 2

[0044] Specific implementation manner 2: This implementation manner is an example of a method for suppressing the Hilbert-Huang transform endpoint effect based on gray theory. Select a nonlinear non-stationary complex signal s(t) as the original signal of this embodiment, s(t)=15*sin((t / 80) 1.5 *π)+3*sin((t / 100) 0.8 *π)+(t / 500+5), t=1:1:3000.

[0045] Step 1: Initialize p=1; q=1; r q (t)=s(t); h pq (t)=s(t); c q (t)=s(t); SD=1000; among them, the original signal to be processed is (t∈[1,3000]∩N + ); where p represents the number of inner loops, q represents the number of outer loops, r q (t) represents the function of the residual error of the qth cycle, h pq (t) represents the function of the intermediate variables generated in the p-th inner loop and the q-th outer loop, c q (t) represents the qth IMF, SD represents the termination criterion;

[0046] Step 2: Judge r q (t) Whether it is monotonous, if yes, go to step 8; otherwise, go to step 3;

[0047] Step 3: Take ε=0.2, judge w...

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Abstract

The invention discloses a Hilbert-Huang Transform end effect inhibition method based on a grey theory, and relates to a characteristic extracting method in the field of signal processing. The method aims at solving the problems that a current Hilbert-Huang Transform method is interfered by the end effect and can not effectively extract the substantive characteristics of a signal and can not obtain accurate intrinsic modal functions and Hilbert spectrums. The method is as follows: on the one hand, the grey theory is adopted to predict an extreme point worked out by traditional EMD (Empirical Mode Decomposition) to the left and right; and an original extreme point and the predicted extreme point are used for solving the envelope and calculating the accurate intrinsic component IMF of an original signal; on the other hand, the grey theory is used to extend the data at the two ends of each IMF worked out by the EMD (empirical mode decomposition), and then implement Hilbert transform to obtain the Hilbert spectrums. The Hilbert-Huang Transform end effect inhibition method based on the grey theory has the advantages of less input data volume required by the grey model, high short period prediction precision, rapid calculation speed, and effective processing on nonlinear or nonstationary signals. The Hilbert-Huang Transform end effect inhibition method is applied to the field of signal processing.

Description

Technical field [0001] The invention relates to a method for suppressing the Hilbert-Huang transform endpoint effect based on gray theory. Background technique [0002] In 1998, Huang E of the National Space Administration (NASA) and others proposed the Hilbert-Huang transform (HHT). This method is different from the traditional Fourier analysis. It does not have a strict mathematical theoretical framework. It is an adaptive signal processing algorithm driven entirely by data. The core idea of ​​HHT is: through Empirical Mode Decomposition (EMD), the signal is decomposed into a small number of intrinsic mode functions (Intrinsic Mode Function, IMF) and a final residual sum, and then IMF is Hill Hilbert Transform (HT) obtains the instantaneous frequency and amplitude of the signal, and finally calculates the Hilbert spectrum. [0003] Although the proposal of HHT is a major breakthrough in the field of signal processing, Huang E et al. emphasized the seven public theoretical issue...

Claims

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Application Information

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IPC IPC(8): G06F17/14
Inventor 沈毅贺智王强张淼
Owner HARBIN INST OF TECH
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