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

Continuous variational modal decomposition DWT denoising method for optical fiber sensing Download PDF

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CN113221692B
CN113221692B CN202110471496.0A CN202110471496A CN113221692B CN 113221692 B CN113221692 B CN 113221692B CN 202110471496 A CN202110471496 A CN 202110471496A CN 113221692 B CN113221692 B CN 113221692B
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邵向鑫
江虹
路天麒
刘成福
叶晗博
朱恒
徐伟进
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Changchun University of Technology
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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 modal decomposition DWT denoising method for optical fiber sensing
Technical Field
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.
Background
In a large-capacity FBG sensing network demodulation system, signal denoising is an important factor influencing the precise demodulation of the FBG sensing system. The fiber Bragg grating fbg (fiber Bragg grating) is used as a sensing element for measuring physical quantities such as temperature, strain force and the like. The method is widely applied to projects such as bridges, subways, structural health monitoring and the like.
For a large-capacity FBG sensing network measurement system, noise is generated due to factors such as human and environment in the process of collecting fiber bragg grating sensing signals, and interference is caused to the signals. How to remove noise to the maximum extent, improve wavelength resolution, and keep the accuracy and stability of demodulation signals is of great importance. Variational modal decomposition, VMD, was first proposed in 2014. The method overcomes the defects that EMD modal aliasing frequently occurs in empirical mode decomposition and mathematical theory is lacked when IMF (intrinsic mode functions) is extracted, has good basic theory and has stronger robustness on noise samples. One of the main problems of VMD is to set the number of decomposition levels K of the modal function (IMF) before the algorithm runs. High values of K may result in pattern mixing, while low values of K may result in pattern repetition.
Disclosure of Invention
In order to solve the problems, the continuous variational modal decomposition DWT denoising method for optical fiber sensing provided by the invention can complete signal decomposition without knowing the number of modes, and is combined with a wavelet threshold function with strong time-frequency analysis capability to process optical fiber sensing signals.
In order to achieve the purpose, the invention adopts the technical scheme that:
a continuous variation mode decomposition DWT denoising method for optical fiber sensing comprises
Step 1, acquiring an input signal, and performing 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.
Preferably, in step 1, after obtaining the BLIMF components, the BLIMF components of each layer are calculated and normalized.
As a matter of preference,
the input signal f (t) is decomposed into two signals: the kth mode uk(t) and a residual signal fr(t) and
f(t)＝uk(t)+fr(t) (1)；
wherein the residual signal fr(t) includes the sum of the previously obtained modes (Σ)i＝1:k-1ui(t)) and a signal unprocessed portion (f)u(t))，
Figure BDA0003045499220000021
To reduce the meterThe calculation quantity improves the calculation speed, avoids the occurrence of phenomena such as modal aliasing and the like, limits the constraint condition and enables sigmai＝1:k-1ui(t)＝0。
Preferably, there are 4 constraints, which are respectively:
constraint 1, kth mode minimization constraint:
Figure BDA0003045499220000022
wherein, ω iskIs the center frequency of the kth mode, which represents the convolution operation;
constraint 2, residual signal frU in (t)kThe frequency of (t) is under the minimization constraint:
Figure BDA0003045499220000031
Figure BDA0003045499220000032
wherein,
Figure BDA0003045499220000033
is an impulse response;
constraint 3 by establishing J2Similar methods of temporal use establish conditional constraints J3：
Figure BDA0003045499220000034
Figure BDA0003045499220000035
Wherein α is a parameter for balancing J1, J2, and J3;
constraint 4, reconstructed signal f (t):
Figure BDA0003045499220000036
finally, an updating formula of Lagrange multiplier lambda (t) is obtained through a dual rising method
Figure BDA0003045499220000037
Preferably, in step 2, a threshold function is introduced to the obtained BLIMF component,
Figure BDA0003045499220000038
wherein,
Figure BDA0003045499220000039
Figure BDA00030454992200000310
k, alpha are positive numbers for the adjustment factor;
since the wavelet transform coefficients of noise decrease with increasing scale, an adaptive threshold is used that can vary with the number of decomposition levels:
Figure BDA0003045499220000041
wherein j is the decomposition scale; n is the length of each layer of wavelet transform coefficient; σ is the variance of the noise.
Preferably, sym5 is selected as the wavelet basis with a wavelet decomposition level number of 6 when reconstructing the signal; the VMD parameters were chosen as follows: the balance parameter α is 200 and the convergence criterion tolerance tol is 1 × 10-7。
The beneficial effects of the invention are as follows:
1. the denoising method adopts a decomposition method capable of continuously extracting all IMFs, can complete signal decomposition without knowing the modal quantity, and is combined with a wavelet threshold function with strong time-frequency analysis capability to process optical fiber sensing signals.
2. In the denoising method, continuous variational modal decomposition is to avoid converging to a previously extracted mode by adding 4 constraint conditions on the basis of VMD, so that the number of modes can be determined in a self-adaptive manner, unnecessary calculation amount is reduced, and the calculation speed is increased.
3. In the denoising method, a new denoising threshold function is constructed, the self-adaptive threshold can change along with the change of the decomposition layer number, and the new function is high-order-derivable and is in the wj,kIs continuous, ± λ, and ωj,kAlong with the increase of the value of the threshold function, the constant deviation between the threshold value and the wavelet coefficient is better solved.
In summary, the denoising method adds 4 constraint conditions on the basis of the VMD algorithm to enable the VMD algorithm to extract the K value in a self-adaptive manner, greatly reduces the calculated amount of the VMD algorithm in a high mode, and then constructs a new threshold function 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. A signal-to-noise ratio (SNR) and a Root Mean Square Error (RMSE) are introduced to an MATLAB simulation experiment for comparison, the signal-to-noise ratio is improved compared with a soft threshold function and a hard threshold function and a current denoising method, and the root mean square error is reduced. Finally, temperature test experiments show that the method has good linear relation, can meet the actual engineering requirements and has good application value.
Drawings
FIG. 1 is a schematic diagram of a denoising function in the continuous variational modal decomposition DWT denoising method for optical fiber sensing according to the present invention.
FIG. 2 is a flow chart of the DWT denoising method for fiber sensing according to the continuous variation modal decomposition of the present invention.
FIG. 3 is a comparison graph of FBG signals and denoised signals in the continuous variational modal decomposition DWT denoising method for optical fiber sensing according to the present invention.
Detailed Description
In order to make the purpose, technical solution and advantages of the present technical solution more clear, the present technical solution is further described in detail below with reference to specific embodiments. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present teachings.
Example 1
As shown in fig. 1 to fig. 3, the continuous variational modal decomposition DWT denoising method for optical fiber sensing provided by the present invention adopts the following steps: obtaining an input signal, and carrying out variational modal decomposition on the input signal to obtain a BLIMF component; 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.
In particular, the Variation Modal Decomposition (VMD) is a self-adaptive, completely non-recursive method of modal variation and signal processing, and the key problem of improving the VMD is to constrain the intrinsic mode function components obtained by decomposition.
Continuous variational modal decomposition is to avoid converging to a previously extracted mode by adding some constraints on the basis of VMD. The number of the modes can be determined in a self-adaptive mode, unnecessary calculation amount is reduced, and calculation speed is increased.
Let the input signal f (t) be decomposed into two signals: the kth mode uk(t) and a residual signal fr(t)
f(t)＝uk(t)+fr(t) (1)
Wherein the residual signal fr(t) comprises two parts: sum of the previously obtained patterns (Σ)i＝1:k-1ui(t)) and a signal unprocessed portion (f)u(t))；
Figure BDA0003045499220000061
In order to reduce the calculation amount, improve the calculation speed and avoid the occurrence of the phenomena of mode aliasing and the like, 4 constraint conditions are determined to enable sigmai＝1:k-1ui(t)＝0。
Constraint 1: each mode should remain compact around its center frequency. So the Kth mode minimization constraint is;
Figure BDA0003045499220000062
wherein ω iskIs the center frequency of the k-th pattern, which represents the convolution operation.
Constraint 2: residual signal frU in (t)k(t) the frequency should be minimized, this constraint being achieved by appropriate filtering
Figure BDA0003045499220000063
To realize the purpose of the method, the device is provided with a plurality of sensors,
Figure BDA0003045499220000064
is an impulse response.
Figure BDA0003045499220000065
Figure BDA0003045499220000066
Constraint 3: by establishing J2Similar methods of temporal use establish conditional constraints J3；
Figure BDA0003045499220000071
Figure BDA0003045499220000072
Constraint 4: reconstructing the signal f (t);
Figure BDA0003045499220000073
where α is a parameter for balancing J1, J2, and J3, and finally solving the update formula of the lagrangian multiplier λ (t) by the dual-rise method:
Figure BDA0003045499220000074
wavelet threshold is widely used once it is proposed due to its powerful time frequency analysis capability. However, the traditional soft and hard threshold functions have the defects of large constant deviation and poor continuity. Scholars improve this problem by introducing an adjustment factor α, proposing a threshold function that compromises soft and hard thresholds. The improved threshold function achieves good effects, but the curve of the reconstructed signal at the critical threshold lambda is not smooth enough because the function cannot be derived in a high order. In view of the above problems, a new threshold function is proposed herein;
Figure BDA0003045499220000075
wherein,
Figure BDA0003045499220000076
Figure BDA0003045499220000077
for adjustment factors, k and α are positive numbers. The threshold function is shown in fig. 1.
Since the wavelet transform coefficients of noise decrease with increasing scale, an adaptive threshold is used that can vary with the number of decomposition levels:
Figure BDA0003045499220000081
wherein j is the decomposition scale; n is the length of each layer of wavelet transform coefficient; σ is the variance of the noise.
The new function is highly derivable and is at wj,k± λ is continuous. Omegaj,kAs the value of the threshold function increases closer to the hard threshold function. The problem of constant deviation between the threshold value and the wavelet coefficient is well solved.
Based on the successful application of the wavelet decomposition-EMD method, the method firstly carries out modal decomposition on an input original signal to obtain BLIMF component, then carries out wavelet decomposition on BLIMF, processes the signal by using a text threshold function, and finally carries out inverse wavelet transform to reconstruct the signal. The flow chart is shown in fig. 2.
Through self experiments and previous researches, sym5 is selected as a wavelet base, and the number of wavelet decomposition layers is 6. The VMD parameters were chosen as follows: the balance parameter α is 200 and the convergence criterion tolerance tol is 1 × 10-7。
Example 2
This example is an experiment and analysis of the continuous variational modal decomposition DWT denoising method for fiber sensing proposed in example 1.
1. Simulation experiment and analysis: testing the effect by using MATLAB software, simulating a noise-containing environment by adding a section of 5db Gaussian white noise to a section of reflection spectrum, and comparing the denoising effect by using a soft threshold, a hard threshold, a wavelet threshold-EMD method and a text method. The denoising effect is identified by the signal-to-noise ratio (SNR) and the Root Mean Square Error (RMSE).
Figure BDA0003045499220000082
Figure BDA0003045499220000091
Wherein f (t) represents the original signal,
Figure BDA0003045499220000092
representing the dessicated signal and n is the sample length.
The denoising effect of the method can be more intuitively seen from fig. 3. The signal denoised by the hard threshold function has a pseudo Gibbs phenomenon and contains more oscillation points. In comparison, the waveform denoised by the soft threshold function is smoother, but the distortion of the reconstructed signal is larger. Compared with the wavelet threshold-EMD method which has good effect, the method has the best denoising effect and reserves the most signal characteristics.
The new modal decomposition not only solves the problem of modal aliasing caused by selecting an excessively large or small K value, but also has great advantages (particularly obvious in high-modal) compared with a VMD algorithm in the aspect of computational efficiency (reducing the amount of computation and the computation time).
2. Temperature test experiment:
in order to verify the application effect of the method provided by the text in the FBG demodulation system, a temperature measurement experiment is carried out by adopting the sensing grating. The experimental platform adopts light source parameters: 500-2400 nm and 100mW of output power; the spectrometer selects a Yanghe AQ6370D-12-L1H/FC/RFC spectrometer, and the wavelength scanning range is the central wavelength of 1550nm waveband.
In the experiment, the FBG sensor is placed in a constant temperature bath isolated from the outside, the temperature is adjusted once from 5 ℃ to 60 ℃ at intervals of 5 ℃, the central wavelength is measured, each temperature point is measured for 5 times, and the average value is taken.
The foregoing is only a preferred embodiment of the present invention, and many variations in the specific embodiments and applications of the invention may be made by those skilled in the art without departing from the spirit of the invention, which falls within the scope of the claims of this patent.

Claims (2)

1. A DWT (continuous variation modal decomposition) denoising method for optical fiber sensing is characterized by comprising the following steps of: comprises that
Step 1, acquiring an input signal, and performing 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; performing wavelet inverse transformation on the processed signals and reconstructing the signals;
in the step 1, after BLIMF components are obtained, calculating BLIMF components of each layer and carrying out normalization processing;
the input signal f (t) is decomposed into two signals: the kth mode uk(t) and a residual signal fr(t) and
f(t)＝uk(t)+fr(t) (1)；
wherein the residual signal fr(t) includes the sum of the previously obtained modes (Σ)i＝1:k-1ui(t)) and a signal unprocessed portion (f)u(t))，
Figure FDA0003614014100000011
In order to reduce the calculation amount, improve the calculation speed and avoid the occurrence of the phenomena of mode aliasing and the like, constraint conditions are limited to enable sigmai＝1:k-1ui(t)＝0；
The number of the constraint conditions is 4, and the constraint conditions are respectively as follows:
constraint 1, kth mode minimization constraint:
Figure FDA0003614014100000012
wherein, ω iskIs the center frequency of the kth mode, indicates the convolution operation;
constraint 2, residual signal frU in (t)kThe frequency of (t) is under the minimization constraint:
Figure FDA0003614014100000021
Figure FDA0003614014100000022
wherein,
Figure FDA0003614014100000023
is an impulse response;
constraint 3 by establishing J2Similar methods of temporal use establish conditional constraints J3：
Figure FDA0003614014100000024
Figure FDA0003614014100000025
Wherein α is a parameter for balancing J1, J2, and J3;
constraint 4, reconstructed signal f (t):
Figure FDA0003614014100000026
finally, an updating formula for solving Lagrange multiplier lambda (t) by a dual rising method
Figure FDA0003614014100000027
In step 2, a threshold function is introduced to the obtained BLIMF component,
Figure FDA0003614014100000028
wherein,
Figure FDA0003614014100000029
Figure FDA00036140141000000210
k, alpha are positive numbers for the adjustment factor;
since the wavelet transform coefficients of noise decrease with increasing scale, an adaptive threshold is used that can vary with the number of decomposition levels:
Figure FDA0003614014100000031
wherein j is the decomposition scale; n is the length of each layer of wavelet transform coefficient; σ is the variance of the noise.
2. The DWT denoising method for fiber optic sensing according to claim 1, wherein: in reconstructing the signal, sym5 is selected as the wavelet basis, and the number of wavelet decomposition layers is 6; the VMD parameters were chosen as follows: the balance parameter α is 200 and the convergence criterion tolerance tol is 1 × 10-7。
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