CN113221692B - Continuous variational modal decomposition DWT denoising method for optical fiber sensing - Google Patents

Abstract

The application relates to the technical field of vibration signal processing, in particular to a continuous variational modal decomposition DWT denoising method for optical fiber sensing, which comprises the following steps of 1, obtaining an input signal, and carrying out variational modal decomposition on the input signal to obtain a BLIMF component; step 2, denoising the obtained BLIMF component by an adjustable semi-soft threshold; the processed signal is subjected to inverse wavelet transform and the signal is reconstructed. The denoising method can complete signal decomposition without knowing the number of modes, and can be used for processing optical fiber sensing signals by combining a wavelet threshold function with strong time-frequency analysis capability. The denoising method adds 4 constraint conditions on the basis of the VMD algorithm so that the K value can be extracted in a self-adaptive mode, the calculated amount of the K value is greatly reduced under a high mode, and then a new threshold function is constructed on the basis of a soft threshold function, a hard threshold function and a document to process FBG signals, so that the denoising effect is improved.

Description

Continuous Variational Mode Decomposition DWT Denoising Method for Optical Fiber Sensing

technical field

The present application relates to the technical field of vibration signal processing, in particular to a continuous variational mode decomposition DWT denoising method for optical fiber sensing.

Background technique

In the large-capacity FBG sensor network demodulation system, signal de-noising is an important factor affecting the accurate demodulation of the FBG sensor system. Fiber Bragg Grating FBG (Fiber Bragg Granting) is used as a sensing element to measure physical quantities such as temperature and strain. It has been widely used in bridges, subways, structural health monitoring and other projects.

For a large-capacity FBG sensor network measurement system, noise is usually generated due to human, environmental and other factors in the process of collecting fiber Bragg grating sensor signals, causing interference to the signal itself. How to remove the noise to the maximum extent, improve the wavelength resolution, and maintain the accuracy and stability of the demodulated signal is very important. Variational Mode Decomposition VMD was first proposed in 2014. It overcomes the shortcomings of the frequent occurrence of EMD mode aliasing and the lack of mathematical theory when extracting IMF (intrinsic mode functions). It has a good basic theory and is more robust to noise samples. One of the main problems of VMD is that the decomposition level K of the modal function (IMF) needs to be set before the algorithm runs. A high value of K may cause mode mixing, while a low value of K may cause mode duplication.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention proposes a continuous variational mode decomposition DWT denoising method for optical fiber sensing. The denoising method can complete the signal decomposition without knowing the number of modes. The wavelet threshold function with powerful time-frequency analysis capability is used to process optical fiber sensing signals.

For achieving the above object, the technical scheme adopted in the present invention is:

Continuous variational mode decomposition DWT denoising method for fiber optic sensing, including

Step 1. Obtain an input signal, and perform variational modal decomposition on the input signal to obtain a BLIMF component;

Step 2: Perform adjustable semi-soft threshold denoising on the obtained BLIMF component score; perform inverse wavelet transform on the processed signal, and reconstruct the signal.

Preferably, in step 1, after the BLIMF components are obtained, the BLIMF components of each layer are calculated and normalized.

As preferred,

decompose the input signal f(t) into two signals: the k-th mode _uk (t) and the residual signal _fr (t), and

f(t)=u _k (t)+f _r (t) (1);

where the residual signal f _r (t) contains the sum of the previously obtained patterns (∑ _i=1:k-1 u _i (t)) and the unprocessed part of the signal (f _u (t)),

In order to reduce the amount of calculation, improve the calculation speed and avoid the occurrence of modal aliasing and other phenomena, the constraints are limited to make ∑ _i=1:k-1 u _i (t)=0.

Preferably, there are four constraints, which are:

Constraint 1. The Kth mode minimizes the constraint:

Among them, ω _k is the center frequency of the k-th mode, and * represents the convolution operation;

Constraint 2, the frequency of _uk (t) in the residual signal _fr (t) is in the minimization constraint:

为脉冲响应；in,

is the impulse response;

Constraint 3. Condition constraint J ₃ is established by a similar method used when establishing J ₂ :

where α is the parameter used to balance J1, J2 and J3;

Constraint 4. Reconstructed signal f(t):

Finally, the updated formula of the Lagrange multiplier λ(t) is obtained by the dual ascent method

Preferably, in step 2, a threshold function is introduced into the obtained BLIMF components,

为调节因子，k,α为正数；in,

is the adjustment factor, k, α are positive numbers;

Since the wavelet transform coefficient of noise decreases with the increase of scale, an adaptive threshold that can change with the number of decomposition layers is adopted:

Among them, j is the decomposition scale; N is the length of the wavelet transform coefficient of each layer; σ is the variance of the noise.

Preferably, when reconstructing the signal, sym5 is selected as the wavelet base, and the number of wavelet decomposition layers is 6; the VMD parameters are selected as follows: the balance parameter α=200, and the convergence criterion tolerance tol=1×10 ⁻⁷ .

The beneficial effects of using the present invention are:

1. This denoising method adopts a decomposition method that can continuously extract all IMFs, and can complete the signal decomposition without knowing the number of modes. Combined with the wavelet threshold function with strong time-frequency analysis capability, it is used to process optical fiber sensing. Signal.

2. In this denoising method, the continuous variational modal decomposition is to add 4 constraints on the basis of VMD to avoid convergence to the previously extracted mode, which can adaptively determine the number of modes while reducing some unnecessary The amount of calculation is accelerated, and the calculation speed is accelerated.

3. In this denoising method, a new denoising threshold function is constructed, which is an adaptive threshold that can change with the number of decomposition layers. The new function is high-order derivable and continuous at w _j,k =±λ, and ω _j,k gets closer and closer to the hard threshold function as the value of the threshold function increases, which solves the problem of constant deviation between the threshold and the wavelet coefficients.

To sum up, this denoising method adds 4 constraints on the basis of VMD algorithm so that it can extract K value adaptively, and greatly reduces its calculation amount in high mode, and then uses soft and hard thresholds. On the basis of the function and the literature, a new threshold function is constructed to process the FBG signal and improve the denoising effect. In the MATLAB simulation experiment, the signal-to-noise ratio (SNR) and the root mean square error (RMSE) are introduced for comparison. reduce. Finally, the temperature test experiments show that this method has a good linear relationship, can meet the actual engineering needs, and has good application value.

Description of drawings

FIG. 1 is a schematic diagram of the denoising function in the continuous variational mode decomposition DWT denoising method for optical fiber sensing according to the present invention.

FIG. 2 is a flow chart of the continuous variational mode decomposition DWT denoising method for optical fiber sensing according to the present invention.

FIG. 3 is a comparison diagram of the effect of the continuous variational mode decomposition DWT denoising method for optical fiber sensing according to the present invention between the FBG signal and the signal after denoising.

Detailed ways

In order to make the purpose, technical solution and advantages of the technical solution more clear, the technical solution will be further described in detail below with reference to the specific embodiments. It should be understood that these descriptions are only exemplary and are not intended to limit the scope of the technical solution.

Example 1

As shown in Figures 1-3, the continuous variational mode decomposition DWT denoising method for optical fiber sensing proposed by the present invention is adopted, and the steps are as follows: acquiring an input signal, performing variational mode decomposition on the input signal, and obtaining BLIMF components; perform adjustable semi-soft threshold denoising on the obtained BLIMF component points; perform inverse wavelet transform on the processed signal, and reconstruct the signal.

Specifically, Variational Mode Decomposition (VMD) is an adaptive, completely non-recursive modal variation and signal processing method. The key problem in improving VMD is to constrain the eigenmode function components obtained by decomposition.

Continuous variational modal decomposition is achieved by adding some constraints on the basis of VMD to avoid convergence to previously extracted modes. The modal number can be determined adaptively while reducing some unnecessary computation and speeding up the computation.

Let the input signal f(t) be decomposed into two signals: the k-th mode _uk (t) and the residual signal fr ( _t )

f(t)=u _k (t)+f _r (t) (1)

where the residual signal fr ( _t ) contains two parts: the sum of the previously obtained patterns (∑ _i=1:k-1 u _i (t)) and the unprocessed part of the signal (f _u (t));

In order to reduce the amount of calculation, improve the calculation speed and avoid the occurrence of modal aliasing and other phenomena, four constraints are set to make ∑ _i=1:k-1 u _i (t)=0.

Constraint 1: Each mode should be compact around its center frequency. Therefore, the K-th mode minimization constraint is:

where ω _k is the center frequency of the k-th mode, and * denotes the convolution operation.

来实现，

为脉冲响应。Constraint 2: The frequency of _uk (t) in the residual signal _fr (t) should be minimized, and this constraint is filtered by appropriate filtering

to fulfill,

is the impulse response.

Constraint 3: Conditional constraint J ₃ is established by a similar method used when establishing J ₂ ;

Constraint 4: reconstructed signal f(t);

where α is the parameter used to balance J1, J2 and J3, and finally the updated formula of the Lagrangian multiplier λ(t) is obtained by the dual ascent method:

Wavelet threshold has been widely used because of its powerful time-frequency analysis ability. However, the traditional soft and hard threshold functions have the disadvantages of large constant deviation and poor continuity. Scholars have proposed a threshold function with a compromise between soft and hard thresholds to improve such problems by introducing the adjustment factor α. The improved threshold function achieves good results, but because the function cannot be high-order derivable, the curve of the reconstructed signal is not smooth enough at the critical threshold λ. Aiming at the above problems, this paper proposes a new threshold function;

为调节因子，k,α为正数。阈值函数如图1所示。in,

is the adjustment factor, and k and α are positive numbers. The threshold function is shown in Figure 1.

Since the wavelet transform coefficient of noise decreases with the increase of scale, an adaptive threshold that can change with the number of decomposition layers is adopted:

Among them, j is the decomposition scale; N is the length of the wavelet transform coefficient of each layer; σ is the variance of the noise.

The new function is higher-order differentiable and continuous at w _j,k =±λ. ω _j,k gets closer and closer to the hard threshold function as the value of the threshold function increases. It solves the problem of constant deviation between threshold and wavelet coefficients.

Based on the successful application of the wavelet decomposition-EMD method, the method in this paper firstly decomposes the input original signal to obtain the BLIMF component, then performs the wavelet decomposition on the BLIMF and uses the threshold function in this paper to process the signal, and finally performs the wavelet inverse transform to reconstruct the signal. . The flow chart is shown in Figure 2.

After our own experiments and previous researches, we choose sym5 as the wavelet base, and the number of wavelet decomposition layers is 6. The VMD parameters are selected as follows: the balance parameter α=200, the tolerance of the convergence criterion tol=1×10 ⁻⁷ .

Example 2

This embodiment is an experiment and analysis of the continuous variational mode decomposition DWT denoising method proposed in Embodiment 1 for optical fiber sensing.

1. Simulation experiment and analysis: Using MATLAB software to test the effect, by adding a section of 5db Gaussian white noise to a section of reflection spectrum to simulate a noisy environment, the soft threshold, hard threshold, wavelet threshold-EMD method and the method in this paper are used to compare the denoising effect of the signal. . The denoising effect was identified by signal-to-noise ratio (SNR) and root mean square error (RMSE).

表示去燥信号，n为采样长度。where f(t) represents the original signal,

represents the de-drying signal, and n is the sampling length.

From Figure 3, the denoising effect of this method can be seen more intuitively. The signal denoised by the hard threshold function has a pseudo-Gibbs phenomenon and contains many oscillation points. In comparison, the waveform after denoising by the soft threshold function is relatively smooth, but the reconstructed signal is relatively distorted. The wavelet threshold-EMD method has achieved good results. Compared with the method in this paper, the method in this paper achieves the best denoising effect and retains the most signal features.

The new modal decomposition not only solves the modal aliasing problem caused by the selection of a K value that is too large or too small, but also has great advantages over the VMD algorithm in terms of computational efficiency (reduces the amount of computation and reduces computation time). especially in high mode).

2. Temperature test experiment:

In order to verify the application effect of the method proposed in this paper in the FBG demodulation system, the temperature measurement experiment was carried out with the sensing grating. The experimental platform uses light source parameters: 500-2400nm, output power 100mW; the spectrometer selects Yokogawa AQ6370D-12-L1H/FC/RFC spectrum analyzer, and the wavelength scanning range is the central wavelength of the 1550nm band.

In the experiment, the FBG sensor was placed in a constant temperature bath isolated from the outside world, and the temperature was adjusted from 5°C to 60°C at intervals of 5°C, and the central wavelength was measured. Each temperature point was measured 5 times, and the average value was taken.

The above content is only the preferred embodiment of the present invention. For those of ordinary skill in the art, according to the idea of the technical content, many changes can be made in the specific implementation and application scope, as long as these changes do not depart from the concept of the present invention, All belong to the protection scope of this patent.

Claims (2)

1. Continuous variational mode decomposition DWT denoising method for optical fiber sensing, characterized in that: comprising: Step 1. Obtain an input signal, and perform variational modal decomposition on the input signal to obtain a BLIMF component; Step 2, performing adjustable semi-soft threshold denoising on the obtained BLIMF component score; performing wavelet inverse transformation on the processed signal, and reconstructing the signal; In step 1, after the BLIMF components are obtained, the BLIMF components of each layer are calculated and normalized; decompose the input signal f(t) into two signals: the k-th mode _uk (t) and the residual signal _fr (t), and f(t)=u _k (t)+f _r (t) (1); where the residual signal f _r (t) contains the sum of the previously obtained patterns (∑ _i=1:k-1 u _i (t)) and the unprocessed part of the signal (f _u (t)),

In order to reduce the amount of calculation, improve the calculation speed and avoid the occurrence of modal aliasing and other phenomena, the constraints are limited so that ∑ _i=1:k-1 u _i (t)=0; There are 4 constraints, which are: Constraint 1. The Kth mode minimizes the constraint:

Among them, ω _k is the center frequency of the k-th mode, and * represents the convolution operation; Constraint 2, the frequency of _uk (t) in the residual signal _fr (t) is in the minimization constraint:

in,

is the impulse response; Constraint 3. Condition constraint J ₃ is established by a similar method used when establishing J ₂ :

where α is the parameter used to balance J1, J2 and J3; Constraint 4. Reconstructed signal f(t):

Finally, the updated formula of the Lagrange multiplier λ(t) is obtained by the dual ascent method

In step 2, a threshold function is imported into the obtained BLIMF components,

in,

is the adjustment factor, k, α are positive numbers; Since the wavelet transform coefficient of noise decreases with the increase of scale, an adaptive threshold that can change with the number of decomposition layers is adopted:

Among them, j is the decomposition scale; N is the length of the wavelet transform coefficient of each layer; σ is the variance of the noise. 2. The continuous variational mode decomposition DWT denoising method for optical fiber sensing according to claim 1, characterized in that: when reconstructing the signal, sym5 is selected as the wavelet base, and the number of wavelet decomposition layers is 6; VMD The parameters are chosen as follows: the balance parameter α=200, the tolerance of the convergence criterion tol=1×10 ⁻⁷ .

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