Transient signal detection method combining principal component analysis and hilbert-huang transform

Abstract

The application provides a transient signal detection method combining principal component analysis with Hilbert-Huang transform, and relates to the field of optical cable identification signal detection. The method comprises the following steps: performing empirical mode decomposition on an original signal, taking a plurality of IMF components obtained by the decomposition as column vectors to construct a sample matrix; performing principal component analysis on the sample matrix in a singular value decomposition manner, selecting principal components according to singular values or cumulative contribution rates, and completing first noise reduction; performing empirical mode decomposition on the signal after the first noise reduction again, screening effective IMF components to reconstruct the signal, and realizing second noise reduction; and calculating the instantaneous amplitude of the signal after the noise reduction according to the Hilbert-Huang transform algorithm, and taking the instantaneous amplitude as a detection statistic to make a binary decision on whether the transient signal exists. The method has strong self-adaptive noise reduction capability and is suitable for transient signal detection in a low signal-to-noise ratio environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical cable identification signal detection, and particularly relates to a transient signal detection method combining principal component analysis and Hilbert-Huang transform. BACKGROUND

[0002] Optical cable line reconstruction and optical cable fault repair caused by machine room relocation, network expansion and upgrading, etc. are emerging, and it is necessary to quickly and effectively identify the target optical cable. The technology based on optical coherent demodulation to identify the target optical cable in specific application, the operator knocks the optical cable to cause the amplitude and phase of the light field to change, and the base station personnel judges whether the knocked optical cable is the target optical cable by detecting the amplitude change of the echo interference signal. The transient echo interference signal generated by knocking the optical cable has a short duration, and is a typical nonlinear and non-stationary signal. The Fourier transform based on harmonic basis function and the wavelet transform based on wavelet basis function have their limitations in analyzing such signals. In addition, in the case of serious environmental noise, such as the target optical cable being fixedly pressed at a certain place, the target optical cable being twisted together with other cables and knocking each other, and the coherence of the used laser source being poor, etc., the accuracy of optical cable identification cannot be guaranteed. How to adaptively reduce noise and effectively complete the time-frequency analysis method of transient signal detection is attracting more and more attention.

[0003] At present, the empirical mode decomposition method is commonly used for nonlinear and non-stationary signal analysis. This method does not need to set the basis function in advance, but adaptively completes the decomposition according to the time scale characteristics of the signal itself. The decomposition result is the sum of several IMF components and the residual representing the local characteristics of different time scales, and the signal is reconstructed by appropriately selecting the IMF components according to the detection requirements, highlighting the characteristics in a certain frequency range. However, the IMF components inevitably have the phenomenon of modal aliasing of useful components and noise, resulting in the loss of useful components in the reconstructed signal and poor noise reduction effect.

[0004] In view of this, the present application is proposed. SUMMARY

[0005] The purpose of the present application is to provide a signal detection method with strong adaptive noise reduction capability, which can highlight certain transient characteristics of the original signal.

[0006] The technical scheme adopted by the present application is:

[0007] A transient signal detection method combining principal component analysis and Hilbert-Huang transform, comprising the following steps:

[0008] Step 1: performing empirical mode decomposition on the original signal to obtain multiple IMF components and a residual;

[0009] Step 2, construct a sample matrix with each IMF component as a column vector, perform principal component analysis on each column vector by singular value decomposition, obtain singular values, and select principal component IMF components according to singular value size or cumulative contribution rate to complete the first noise reduction;

[0010] Step 3, perform empirical mode decomposition on the signal after the first noise reduction again, screen effective IMF components, complete the second noise reduction and reconstruct the signal;

[0011] Step 4, calculate the instantaneous amplitude of the reconstructed signal based on the Hilbert-Huang transform algorithm as a detection statistic, and make a binary decision on the presence or absence of transient signals.

[0012] Further, step 2 specifically includes:

[0013] Step 201, construct a sample matrix with each IMF component as a column vector, and normalize each component of the column vector Obtain a new sample matrix Z = (z1, z2, z3,..., zn) n ); wherein x i is a certain IMF component of the column vector, m is the number of sampling points contained in the IMF component, and n is the number of IMF components contained in the column vector;

[0014] Step 202, calculate the correlation coefficient matrix of the normalized sample matrix

[0015] Step 203, let the eigenvalue be λ i , the singular value be σ i , the left singular vector be u i , and the right singular vector be v i , then list the characteristic equation of matrix C, and obtain each singular value and singular vector:

[0016] Cv i = λ i v i

[0017]

[0018]

[0019] Step 204, calculate the cumulative contribution rate of the first p singular values:

[0020]

[0021] Select the IMF component with a cumulative contribution rate of singular values exceeding a threshold value or a singular value greater than 1 as an effective signal, and the remaining IMF components are considered as noise.

[0022] Further, in step 3, the number of effective IMF components is selected according to the number of principal IMF components selected in step 2.

[0023] The present application is based on principal component analysis algorithm, and the cumulative contribution rate of singular value is used to reduce the dimension of sample matrix composed of IMF components, so as to realize the first noise reduction. Then, the signal after the first noise reduction is subjected to empirical mode decomposition again, the effective IMF components are screened for the second noise reduction, the noise suppression performance is improved, and the accuracy of transient feature detection is improved. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 The flow chart of the transient signal detection of the embodiment of the present application is shown.

[0025] Figure 2 The original signal detected in the embodiment of the present application is shown.

[0026] Figure 3 The EMD decomposition result of the original signal in the embodiment of the present application is shown.

[0027] Figure 4 The signal after the first noise reduction in the embodiment of the present application is shown.

[0028] Figure 5 The EMD decomposition result of the signal after the first noise reduction in the embodiment of the present application is shown.

[0029] Figure 6 The signal after the second noise reduction in the embodiment of the present application is shown.

[0030] Figure 7 The instantaneous amplitude curve after the Hilbert transform in the embodiment of the present application is shown. DETAILED DESCRIPTION

[0031] The present application will be further described below with reference to the accompanying drawings.

[0032] A transient signal detection method combining principal component analysis and Hilbert-Huang transform, the detection flow is shown in Figure 1 .

[0033] Step 1, the original signal is subjected to empirical mode (EMD) decomposition to obtain a plurality of IMF components and a residual.

[0034] (1) find the maximum value point and the minimum value point of the original signal, respectively fit the upper envelope line and the lower envelope line, and calculate the average envelope line;

[0035] (2) subtract the average envelope line from the original signal to obtain the first IMF component; the original signal is shown in Figure 2 .

[0036] (3) Subtract the IMF component generated in step (2) from the original signal to obtain a new signal to be detected. Return the new signal to be detected to step (1) as the original signal and repeat the whole process until the residual is a monotonic function.

[0037] After multiple decompositions, the original signal can be expressed as

[0038]

[0039] Where: IMFi is the i-th IMF component; r n is the residual, and n is the number of IMF components obtained.

[0040] The empirical mode decomposition results of the original signal are as follows: Figure 3 shown.

[0041] Step 2: Use each IMF component as a column vector to construct a sample matrix, perform principal component analysis on each column vector in the form of singular value decomposition, obtain each singular value, and select the principal component IMF component according to the size of the singular value or the cumulative contribution rate to complete the first denoising. The EMD decomposition result of the signal after the first denoising is shown in the figure below: Figure 5 shown.

[0042] Assume that after the original signal is decomposed into n groups of IMF components, each group of IMF components contains m sampling points. The sample matrix is ​​represented as X(X∈R m×n )。 X=(x1,x2,x3,......,x n ), where x1=IMF1,x2=IMF2,……,x n =IMFn. The specific steps of principal component analysis are as follows:

[0043] 1) Normalize each component of the column vector Get the new sample matrix Z=(z1,z2,z3,......,z n );

[0044] 2) Calculate the correlation coefficient matrix of the standardized sample matrix

[0045] 3) Let the eigenvalue be λ i , the singular value is σ i , the left singular vector is u i , the right singular vector is v i , we can list the characteristic equation of the matrix C and find the singular values ​​and singular vectors:

[0046] Cv i =λ i v i (2)

[0047]

[0048]

[0049] 4) The number of the final selected principal components is determined according to the cumulative contribution rate of singular values. The contribution rate of singular values and the cumulative contribution rate of the first p singular values are defined as follows:

[0050]

[0051]

[0052] In this embodiment, the singular values of each principal component and its contribution rate are shown in Table 1.

[0053]

[0054] The cumulative contribution rate of singular values is more than 80%, or the principal component with singular value greater than 1 is considered as an effective signal, and the rest of the principal components are considered as noise. Thus, the first three principal components are selected as useful components, and the rest of the principal components are discarded. Figure 4 The signal after the first denoising.

[0055] Step 3: The signal after the first denoising is again subjected to empirical mode decomposition, and the effective IMF components are screened to complete the second denoising and reconstruct the signal.

[0056] The number of effective IMF components in this step is selected according to the number of principal component IMF components selected in step 2. In this embodiment, the first three principal components are selected in step 2, so the first three IMF components are selected in this step to reconstruct the signal and complete the second denoising. Figure 6 The signal after the second denoising.

[0057] The signal-to-noise ratio is calculated according to S / N = 20LOG(V S / V N ), where V S and V N represent the amplitudes of the signal and the noise, respectively. In this embodiment, the amplitudes of the original signal and the signal after the second denoising and the signal-to-noise ratio are shown in Table 2. After denoising, the signal-to-noise ratio is optimized from 6.29 dB to 8.30 dB.

[0058]

[0059] Step 4: The instantaneous amplitude of the reconstructed signal is calculated based on the Hilbert-Huang transform algorithm and used as a detection statistic for binary decision of the presence or absence of a signal. When the instantaneous amplitude is greater than a threshold value, a transient signal is detected. The instantaneous amplitude curve after Hilbert transform is shown in Figure 7The threshold value for judging whether there is a transient signal is adjusted according to the amplitude of the actual test data. In this embodiment, the threshold value is set to 0.15, and if the transient amplitude exceeds 0.15, it is judged that a transient signal is detected.

Claims

1. A transient signal detection method combining principal component analysis and Hilbert-Huang transform, characterized in that: The following steps are involved: Step 1: Perform empirical mode decomposition on the original signal to obtain multiple IMF components and residuals; Step 2: Use each IMF component as a column vector to construct a sample matrix. Perform principal component analysis on each column vector using singular value decomposition to obtain each singular value. Then, select the principal component IMF component according to the size of the singular value or the cumulative contribution rate to complete the first noise reduction. Step 3: Perform empirical mode decomposition on the signal after the first denoising again, screen the effective IMF components, complete the second denoising and reconstruct the signal; Step 4: Calculate the instantaneous amplitude of the reconstructed signal based on the Hilbert-Huang transform algorithm and use it as a detection statistic to make a binary decision on whether a transient signal exists.

2. The transient signal detection method combining principal component analysis and Hilbert-Huang transform according to claim 1, characterized in that: Step 2 specifically includes: Step 201: construct a sample matrix using each IMF component as a column vector and normalize each component of the column vector. Get the new sample matrix Z=(z1,z2,z3,......,z n ); where x i is an IMF component of the column vector, m is the number of sampling points contained in the IMF component, and n is the number of IMF components contained in the column vector; Step 202: Calculate the correlation coefficient matrix of the standardized sample matrix Step 203: Set the eigenvalue to λ i , the singular value is σ i , the left singular vector is u i , the right singular vector is v i , then list the characteristic equation of matrix C and find the singular values ​​and singular vectors: Cv i =λ i v i Step 204: Calculate the cumulative contribution rate of the first p singular values: The IMF components whose cumulative contribution rate of singular values ​​exceeds the threshold or whose singular values ​​are greater than 1 are considered as valid signals, and the remaining IMF components are considered as noise.

3. The transient signal detection method combining principal component analysis and Hilbert-Huang transform according to claim 1, characterized in that: When screening the effective IMF components of the second empirical mode decomposition in step 3, the number of effective IMF components is selected according to the number of principal component IMF components selected in step 2.

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