CN102944252B - Method for processing fibber Bragg grating (FBG) signals based on translation invariant wavelet - Google Patents
Method for processing fibber Bragg grating (FBG) signals based on translation invariant wavelet Download PDFInfo
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Abstract
The invention relates to a method for processing FBG signals based on a translation invariant wavelet of an improved threshold value. The method includes providing an improved threshold function and combining the threshold function with the translation invariant wavelet to denoise the FBG noisy signals; and fitting denoised FBG spectral signals through a Gaussian fitting formula so as to position the peak wavelength. The wavelet denoising portion mainly includes performing cycle spinning on the FBG noisy signals, performing discrete wavelet decomposition on the spun signals to extract the wavelet coefficient in each layer, performing threshold value quantization on the wavelet coefficients by using improved threshold function, reconstructing the wavelet coefficients after the threshold value quantization, performing reverse cycle spinning on the reconstructed signals, and averaging the reconstructed signals at different spinning positions to obtain the final denoised signals. A Gaussian fitting peak searching algorithm mainly includes fitting the denooised signals through the Gaussian formula and obtaining the wavelength corresponding to the peak to finish demodulation of the FBG spectral signals.
Description
Technical Field
The invention relates to a signal processing method of optical fiber sensing, in particular to an FBG signal processing method based on translation invariant wavelet.
Background
As an optical fiber passive device, Fiber Bragg Gratings (FBGs) have been rapidly developed in the fields of optical fiber sensing, optical fiber communication, and the like in recent years, and the wavelength demodulation technology thereof is a key technology in sensing applications. The existence of noise seriously affects the wavelength demodulation precision, so that the demodulation precision of the measured physical quantity is affected, and therefore, the precise demodulation of the FBG signal can be realized only by combining the high-efficiency denoising method with the high-precision FBG peak searching algorithm.
Aiming at signal denoising, the denoising method based on wavelet analysis has a good effect in the field of signal processing. The wavelet threshold method denoising can almost completely inhibit noise, can well reserve the local characteristics of original signals, has high calculation speed and strong adaptability, and is the most widely applied wavelet denoising method. However, the classical soft and hard thresholding methods of threshold denoising have their drawbacks. The hard threshold method can obtain the optimal estimation of the signal, but a Pseudo-Gibbs (Pseudo-Gibbs) phenomenon can occur due to discontinuous functions; the estimated signal obtained by the soft threshold method is as smooth as the original signal, but has a constant deviation from the original signal.
In order to overcome the defects, in recent years, a plurality of researchers at home and abroad improve the threshold function in a targeted manner, and strive to set a continuous threshold function capable of eliminating constant deviation. Therefore, researchers propose threshold functions with soft and hard threshold function tradeoffs, and the effect of using the threshold functions for wavelet threshold denoising is improved. However, the expressions of the improved threshold function contain an adjustment factor, the adjustment factor has a value range, and in the value range, the minimum extreme value or the maximum extreme value of the adjustment factor corresponds to the expression of the hard threshold function or the soft threshold function. However, the optimal value of the adjustment factor has uncertainty, and the practical application has limitation.
Studies in recent years have shown that: the wavelet analysis is used for denoising the FBG sensing signals, good effect can be obtained, overlapped peaks can be processed, noise can be well eliminated, and the original spectrum is recovered. As a threshold quantitative denoising method with the widest wavelet denoising application, the threshold function has an improved space, so that aiming at the defects of the traditional soft and hard threshold functions and the defects of the existing improved threshold function, the invention provides the improved threshold function without the adjustment factor for the wavelet denoising; aiming at the oscillation phenomenon generated by the mismatch of breakpoints of the wavelet and the FBG processing signal during the wavelet denoising, the invention does not adopt the traditional wavelet threshold value quantization denoising method, but uses the Translation-invariant wavelet (TI) transform to process, and combines the improved threshold value function provided by the invention, provides the Translation-invariant wavelet based on the improved threshold value to denoise the collected FBG sensing signal, and estimates the signal closer to the original spectrum.
In the FBG signal processing, after the important step of denoising is completed, peak searching is also required to be performed on the denoised signal. At present, a plurality of peak searching algorithms exist, and the shape of the FBG reflection spectrum is approximately Gaussian distribution, so that the Gaussian fitting peak searching has high precision and good stability.
Therefore, the FBG signal processing method based on the translation invariant wavelet denoising combines wavelet denoising and Gaussian fitting, not only can effectively solve the noise problem of engineering measurement, but also can realize high-precision demodulation of parameters.
Disclosure of Invention
In view of this, the technical problem to be solved by the present invention is to provide a denoising method based on a translation invariant wavelet and an FBG spectral signal processing method based on a gaussian fitting model. The method overcomes the constant deviation between the estimated signal and the original signal generated by the traditional soft threshold denoising in wavelet analysis, eliminates the additional oscillation generated by the discontinuous function in the traditional hard threshold method, and solves the uncertainty and instability of the existing improved threshold function caused by the adjustment factor contained in the expression.
The purpose of the invention is realized as follows:
the invention provides a FBG signal processing method based on a translation invariant wavelet, which comprises the following steps:
s1: obtaining a length of 2NFBG spectral signal f (i) = s (i) + N (i), i =0,1,. N-1; wherein s (i) represents a de-noised signal, N (i) represents white gaussian noise, and N represents the length of the data sequence;
s2: the FBG spectral signals f (i) are subjected to a J-level shift invariant wavelet decomposition,wavelet coefficients w of each layer are obtainedj，kWherein J is the optimal decomposition layer number, the initial value is 1, J = J-1, k = N/2j；
S3: for each layer wavelet coefficient wj，kCarrying out threshold quantization processing;
s4: reconstructing the wavelet coefficient after threshold processing to obtain a denoising signal s (i);
s5: fitting the de-noised signal s (i) by a Gaussian formula to obtain an approximate signal;
s6: finding out the coordinates of the peak point of an approximate curve formed by the fitted approximate signals;
s7: and determining the wavelength value corresponding to the peak point.
Further, wavelet coefficients w of each layerj，kThe acquisition is specifically realized by the following steps:
s21: selecting a proper wavelet basis function;
s22: determining the decomposition layer number J by a self-adaptive method;
s23: circularly left-shifting the FBG spectral signal f (i) by 1 bit and 0 bit to obtain a first FBG spectral signal f (i,1) and a second FBG spectral signal f (i, 0);
s24: performing discrete wavelet transform on the first FBG spectral signal f (i,1) and the second FBG spectral signal f (i,0) to obtain a first wavelet coefficient w of each layer1j，kAnd a second wavelet coefficient w0j，k。
Further, the threshold quantization processing specifically includes the following steps:
s31: selecting a proper threshold criterion and determining a threshold;
s32: for the first wavelet coefficient w1j,kAnd a second wavelet coefficient w0j，kPerforming threshold quantization processing to obtain quantized wavelet coefficients;
s33: reconstructing according to the quantized wavelet coefficients to obtain a first signal s (i,1) and a second signal s (i, 0);
s34: cyclically right-shifting the first signal s (i,1) and the second signal s (i,0) by 1 bit and 0 bit, respectively;
s35: and averaging the first signal s (i,1) and the second signal s (i,0) after the right shift to obtain a final de-noised signal.
Further, the method for determining the optimal decomposition layer number specifically comprises the following steps:
s221: setting an initial value of the decomposition layer number as J = 1;
s222: performing one-layer wavelet decomposition on the acquired FBG spectral signals f (i) to obtain wavelet coefficients wj，k；
S223: for wavelet coefficient wj，kCarrying out whitening inspection;
s224: if the wavelet coefficient is white noise, adding 1 to the value of the decomposition layer number J, and returning to the step S222;
s225: if the wavelet coefficient is not white noise, the J value is output as the optimal number of decomposition layers.
Further, the threshold quantization processing adopts an improved threshold function processing, and the improved threshold function processing specifically includes the following steps:
s321: determining wavelet coefficients w of layersj，kA threshold λ of (2);
s322: judging wavelet coefficient w of each layerj，kWhether the following formula is satisfied:
|wj,k| ≧ λ; wherein, | wj,k| represents wavelet coefficient wj，kThe mold of (4);
s323: if not, let wj,kIf yes, wavelet coefficient w is calculated for each layerj，kThe calculation is made by the following formula: <math>
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s324: and reconstructing the quantized wavelet coefficients.
The invention has the advantages that: the invention adopts a denoising method based on translation invariant wavelet and an FBG spectral signal processing method based on a Gaussian fitting model. The method overcomes the constant deviation between an estimated signal and an original signal generated by wavelet analysis traditional soft threshold denoising, eliminates additional oscillation generated by function discontinuity of a traditional hard threshold method, solves the uncertainty and instability of the existing improved threshold function caused by the fact that an expression contains an adjustment factor, provides a continuous and high-order-guided improved threshold function without the adjustment factor, and is combined with the advantage of translation invariant wavelet processing of a signal containing a breakpoint to denoise an experimental FBG spectrum signal (sensing signal), thereby designing a high-efficiency denoising method based on wavelet analysis. And the denoising method is combined with a high-precision Gaussian fitting peak-searching algorithm, so that the demodulation precision of the FBG spectral signal is improved.
Fitting and peak finding are carried out on a de-noised signal (an FBG spectrum signal obtained after wavelet de-noising) by adopting a Gaussian fitting method, and the peak coordinate position of an FBG reflection spectrum is determined, namely the peak wavelength is demodulated; according to the magnitude relation between the peak wavelength of the FBG spectrum signal obtained at one time point and the peak wavelength of the FBG spectrum signal obtained at another time point, the variable quantity of the measured parameter and the immediate parameter value can be calculated according to the relational expression between the measured parameter and the wavelength variable quantity, so that the final demodulation of the FBG measured physical quantity is completed.
The invention adopts a fast translation invariant wavelet method, and a fast translation invariant wavelet denoising method with improved threshold value is adopted, so that the noise gram of the FBG sensing signal is well prepared, the global characteristic and the local characteristic of the original noise-free signal are reserved, the two evaluation indexes of signal-to-noise ratio and root-mean-square error are used for judging, and the efficiency is better than that of the traditional wavelet denoising method and the existing wavelet denoising method.
Drawings
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings, in which:
FIG. 1 is a flow chart of a FBG spectral signal processing method based on a translation invariant wavelet;
FIG. 2 is a flow chart of shift invariant wavelet denoising;
FIG. 3 is a flow chart of the adaptive method for determining the optimal number of decomposition levels;
fig. 4 is a flow diagram of an improved thresholding function thresholding process.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings; it should be understood that the preferred embodiments are illustrative of the invention only and are not limiting upon the scope of the invention.
Example 1
Fig. 1 is a flowchart of an FBG spectral signal processing method based on a translation invariant wavelet, fig. 2 is a flowchart of a translation invariant wavelet denoising process, fig. 3 is a flowchart of an adaptive method for determining an optimal decomposition layer number, and fig. 4 is a flowchart of an improved threshold function threshold processing, as shown in the figure: the invention provides a FBG signal processing method based on a translation invariant wavelet, which comprises the following steps:
s1: obtaining a length of 2NFBG spectral signal f (i) = s (i) + N (i), i =0,1,. N-1; wherein s (i) represents a de-noised signal, N (i) represents white gaussian noise, and N represents the length of the data sequence;
s2: performing J-layer translation invariant wavelet decomposition on FBG spectral signals f (i) to obtain wavelet coefficients w of each layerj，kWherein J is the optimal decomposition layer number, the initial value is 1, J = J-1, k = N/2j；
Wavelet coefficient w of each layerj，kThe acquisition is specifically realized by the following steps:
s21: selecting a proper wavelet basis function;
s22: determining the decomposition layer number J by a self-adaptive method;
the self-adaptive method for determining the optimal decomposition layer number specifically comprises the following steps:
s221: setting an initial value of the decomposition layer number as J = 1;
s222: performing one-layer wavelet decomposition on the acquired FBG spectral signals f (i) to obtain wavelet coefficients wj，k；
S223: for wavelet coefficient wj，kCarrying out whitening inspection;
s224: if the wavelet coefficient is white noise, adding 1 to the value of the decomposition layer number J, and returning to the step S222;
s225: if the wavelet coefficient is not white noise, the J value is output as the optimal number of decomposition layers.
S23: circularly left-shifting the FBG spectral signal f (i) by 1 bit and 0 bit to obtain a first FBG spectral signal f (i,1) and a second FBG spectral signal f (i, 0);
s24: performing discrete wavelet transform on the first FBG spectral signal f (i,1) and the second FBG spectral signal f (i,0) to obtain a first wavelet coefficient w of each layer1j,kAnd a second wavelet coefficient w0j，k。
S3: for each layer wavelet coefficient wj，kCarrying out threshold quantization processing;
the threshold quantization process specifically includes the steps of:
s31: selecting a proper threshold criterion and determining a threshold;
s32: for the first wavelet coefficient w1j，kAnd a second wavelet coefficient w0j，kPerforming threshold quantization processing to obtain quantized wavelet coefficients;
the threshold quantization processing adopts improved threshold function processing, and the improved threshold function processing specifically comprises the following steps:
s321: determining wavelet coefficients w of layersj，kA threshold λ of (2);
s322: judging wavelet coefficient w of each layerj，kWhether the following formula is satisfied:
|wj,k| ≧ λ; wherein, | wj,k| represents wavelet coefficient wj，kThe mold of (4);
s323: if not, let wj,kIf yes, wavelet coefficient w is calculated for each layerj，kThe calculation is made by the following formula: <math>
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s324: and reconstructing the quantized wavelet coefficients.
S33: reconstructing according to the quantized wavelet coefficients to obtain a first signal s (i,1) and a second signal s (i, 0);
s34: cyclically right-shifting the first signal s (i,1) and the second signal s (i,0) by 1 bit and 0 bit, respectively;
s35: and averaging the first signal s (i,1) and the second signal s (i,0) after the right shift to obtain a final de-noised signal.
S4: reconstructing the wavelet coefficient after threshold processing to obtain a denoising signal s (i);
s5: fitting the de-noised signal s (i) by a Gaussian formula to obtain an approximate signal;
s6: finding out the coordinates of the peak point of an approximate curve formed by the fitted approximate signals;
s7: and determining the wavelength value corresponding to the peak point.
Example 2
This embodiment 2 describes in detail the FBG signal processing method based on the shift invariant wavelet:
the data processing method provided by embodiment 2 of the present invention is provided for solving the problem that the wavelength demodulation accuracy is seriously affected by the noise contained in the FBG spectral signal. The wavelet denoising method with the improved threshold can well filter noise to obtain an optimal approximate signal of the FBG pure spectral signal; the Gaussian fitting peak searching algorithm can be well matched with FBG reflection spectrum signals, the peak value position is found, the precision is high, and the stability is good, so that the parameter value of the physical quantity measured by the FBG can be demodulated more accurately by combining a high-efficiency denoising method and a high-precision peak searching algorithm.
Fig. 1 shows a flow chart of the FBG spectral signal processing method, which includes the following steps:
step 1: firstly, a section of FBG spectral signal containing noise at a certain time point is collected, and is represented by F (i), and a data sequence f (i) with the length of N is extracted. It can be described as follows: the clean FBG spectral signal s (i) with length N is contaminated by noise N (i) to obtain FBG noise signal:
f (i) = s (i) + N (i) (i =0,1,2, …, N-1), wherein: n (i) is white gaussian noise subject to N (0, σ 2).
Step 2: performing wavelet threshold denoising on the FBG spectral signal f (i), wherein the denoising specific implementation process of the FBG signal sequence f (i) based on the translation invariant wavelet analysis is as follows (as shown in the attached figure 2):
1) according to the practical situation of denoising, selecting a wavelet basis function with proper support length and higher vanishing moment, and selecting a sym5 wavelet in the invention. An optimal decomposition layer number is determined by adopting a self-adaptive algorithm, and the specific steps are as follows (as shown in the attached figure 3):
(1) performing one-layer wavelet decomposition on the obtained FBG spectral signal sequence f (i) to obtain a wavelet coefficient wj，k；
(2) To wj，kCarrying out whitening detection, if the coefficient sequence is white noise, carrying out the step (3), otherwise, carrying out the step (4);
(3) adding 1 to the value of the decomposition layer number, and calculating the threshold value of the layer according to a threshold value criterion;
(4) subtracting 1 from the value of the decomposition layer number;
(5) the final J value is the optimal decomposition layer number;
2) based on the signal and noise characteristics, a suitable threshold function and threshold criteria are selected. In order to overcome the defects of the traditional soft threshold function and the traditional hard threshold function, the invention adopts an improved threshold function and a modified threshold criterion.
(1) A threshold function. Recent studies have shown that the hard thresholding method yields an optimal estimate of the original signal, but thatDiscontinuous function, thereby having Pseudo-Gibbs phenomenon, continuous soft threshold method function, smooth estimated signal same as original signal, but discontinuous derivative, wavelet coefficient wj，kAnd estimated wavelet coefficientsThere is a constant deviation which makes the reconstructed signal have unavoidable errors from the original signal. Aiming at the defects of soft and hard threshold methods, a plurality of researchers provide new threshold functions to enable estimated signals to be closer to original signals, the improved threshold methods are continuous in a wavelet domain but have some defects, function expressions all contain adjustment factors, and how to determine the values of the adjustment factors is critical.
Various improved threshold functions are researched to summarize a rule, and for a monotone function in a certain interval, the improved threshold method should meet two conditions: when | wj,kAs the amount of | is gradually increased,must gradually approach wj,k(ii) a When | wj,kAs | gradually approaches λIt must gradually go towards 0 or lambda. Based on these rules, the present invention proposes an improved threshold function without adjustment factors based on the previous research, as shown in the following formula:
wherein wj，kIs a function of the wavelet coefficients and is,λ is a threshold value for the quantized wavelet coefficients.
The threshold function is continuous and high-order derivative, and the function is faster to the hard threshold after the threshold point, so that the complexity is moderate, and the optimal estimation effect of the hard threshold and the advantages of the continuity and smoothness of the soft threshold are simultaneously achieved.
(2) A threshold criterion. The conventional threshold criterion isBut as the scale increases, the wavelet coefficients of the noise decrease in magnitude, and thus this is not optimal, the modified threshold is used in the present invention,where i is the decomposition scale where σ is the noise standard deviation, typicallyk=0,1,2，…,2j-1-1。
Therefore, the wavelet threshold denoising step of the present invention is to process the wavelet coefficients w of each layer by using the threshold functionj，k. First, calculate outA threshold value lambda of a certain layer, and wavelet coefficient w of the layerj,kIs compared to a threshold lambda. When | wj,kWhen | < lambda, the wavelet coefficient is set to zero; when | wj,kWhen | ≧ λ, the expression of the threshold function is used to express, and the estimated wavelet coefficient is obtainedThus, the improved threshold function denoising provided by the invention is completed.
3) Denoising the FBG spectral signal f (i) by using a translation invariant wavelet according to the determined wavelet basis, the decomposition layer number, the threshold function and the threshold criterion, and specifically comprising the following steps:
(1) the FBG spectral sequence f (i) is cyclically translated.
Defining Sh as a translation operator for circularly translating h bit, assuming left shift, and defining S for the FBG noisy signal f (i)hfiPerforming time domain translation for left shifting h bit on f (i), wherein the translation range is more than 0 and less than or equal to N, thereby obtaining N new signals with a certain phase difference with the input signal f (i)
Shfi＝f(i+h)0＜h≤N(2)
The corresponding cyclic inverse shift (right shift), i.e., inverse operation, can represent S-h＝(Sh)-1。
(2) And performing wavelet transformation on the translated signal, namely performing discrete wavelet decomposition on the basis of translation.
Discrete wavelet transform is carried out by using Mallet algorithm to obtain
Wherein S ishf (j, k) is a decomposed j-layer scale coefficient which is shifted to the left by h bits, Whf (j, k) is the decomposed wavelet coefficient of j layers shifted left by h bits, hereinafter denoted by wj，kDenotes Shf (0, k) represents FBG noisy signal translationh bits of the signal, J is the optimal scale, J =0,1,2, …, J-1, k is the number of wavelet coefficients of the J layer, k = N/2jAnd H and G are a low-pass filter of the scale function and a high-pass filter corresponding to the wavelet function respectively.
(3) And (4) threshold denoising, namely performing wavelet threshold quantization processing on the wavelet coefficients.
For wavelet coefficient wj，kPerforming threshold processing to obtain estimated wavelet coefficientSo thatThe value is minimal. The improved threshold function and modified threshold criteria provided by the present invention are used herein. When the modulus of the wavelet coefficients is greater than or equal to a threshold value, i.e. | wj,kIf ≧ λ, the wavelet coefficient is processed with an improved threshold function, as shown in equation (1), i.e., w isj，kBy usingIs expressed and the quantized wavelet coefficients are signedAnd when the modulus of the wavelet coefficient is less than the threshold, the wavelet coefficient is zeroed out (as shown in figure 4).
(4) And (3) wavelet reconstruction, namely reconstructing a wavelet coefficient after threshold quantization and a scale coefficient obtained after decomposition to obtain a signal sequence with the length of N.
For denoised wavelet coefficientPerforming discrete wavelet reconstruction to obtain reconstructed signalCan also be expressed asNamely, the original FBG spectral signal (including a noise signal) is subjected to wavelet de-noising and reconstructed signal after circularly shifting h bit.
(5) And (4) reverse cyclic translation, namely, the signal sequence is translated by the same number of bits in the reverse direction of the original translation.
The inverse cyclic shift operator S was mentioned previously-h＝(Sh)-1Here, the reconstructed signal is subjected to inverse cyclic translation (right shift) to obtain an estimated signal with the same phase as the original FBG spectral signal (noisy signal) f (i)The process can be represented as
(6) Averaging, averaging the signal sequence reconstructed by shifting different bits.
After one time of 'translation-denoising-inverse translation' is completed, averaging is carried out on all reconstruction signals which are translated by h bit and other bits. And as for what value should be taken by the value of h, the g.beykin finds that the wavelet coefficient set circularly translated by any odd digit is the same as the wavelet coefficient set circularly translated by 1 digit, and the wavelet coefficient set translated by any even digit is the same as the wavelet coefficient set translated by 0 digit, so that all wavelet coefficients in the TI algorithm can be obtained by calculating the original signal and the signal circularly translated by 1 digit. Thereby having a rapid TI transformation algorithm with the complexity ofO (nlog2n), greatly reducing the operation complexity of the original TI algorithm, adopting the rapid TI algorithm in the invention, thus h takes 1 and 0 to obtain two groups of reconstruction signals, and then taking the averageHerein, theAndand respectively representing a cyclic translation 0 bit and a translation 1 bit, and then obtaining a denoising signal through denoising and reverse translation.
Thereby completing the whole process of 'translation-denoising-inverse translation-averaging' to obtain the final denoised signalTo correspond to equation (2), the final denoised signal is usedTo indicate. The TI algorithm in the following represents the fast TI transform algorithm.
And 3, step 3: FBG (fiber Bragg Grating) noise-free spectral signal obtained after wavelet denoisingAnd fitting the spectral signal by adopting a peak searching algorithm and searching the coordinate position of the peak point. The curve approximation of the FBG signal without noise is obtained by fitting with a Gaussian formula, the approximate curve conforms to Gaussian distribution, so that the maximum point of the approximate curve, namely the peak point of the FBG signal, can be further obtained, the coordinate position of the peak point is determined, the abscissa and the ordinate of the point respectively represent the light intensity and the wavelength value, the demodulation purpose of the FBG sensing signal is to demodulate the wavelength value corresponding to the peak value of the FBG signal at a certain time point, and the wavelength value corresponds to the wavelength difference of the wavelength value demodulated at another time pointThe variable quantity of the physical quantity can be calculated according to the change rate of the FBG to the physical quantity, and therefore the FBG can demodulate the physical quantity.
In conclusion, the invention firstly adopts the translation invariant wavelet denoising method with the improved threshold value to effectively filter a great deal of noise of the FBG noisy spectrum signal and improve the signal-to-noise ratio; and then, a Gaussian approximation curve of the denoised FBG spectral signal is obtained by adopting Gaussian fitting, and the peak value coordinate of the approximation curve is found, so that the high-precision wavelength demodulation of the FBG spectral signal is completed.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and it is apparent that those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (3)
1. A FBG signal processing method based on a translation invariant wavelet is characterized in that: the method comprises the following steps:
s1: obtaining a length of 2NFBG spectral signal f (i) s (i) N (i), i 0, 1.. N-1; wherein s (i) represents a de-noised signal, N (i) represents white gaussian noise, and N represents the length of the data sequence;
s2: performing J-layer translation invariant wavelet decomposition on FBG spectral signals f (i) to obtain wavelet coefficients w of each layerj,kWherein J is the optimal decomposition layer number, the initial value is 1, J is J-1, k is N/2j；
S21: selecting a proper wavelet basis function;
s22: determining the decomposition layer number J by a self-adaptive method;
s221: setting the initial value of the decomposition layer number as J1;
s222: performing one-layer wavelet decomposition on the acquired FBG spectral signals f (i) to obtain wavelet coefficients wj,k；
S223: for wavelet coefficient wj,kCarrying out whitening inspection;
s224: if the wavelet coefficient is white noise, adding 1 to the value of the decomposition layer number J, and returning to the step S222;
s225: if the wavelet coefficient is not white noise, outputting the J value as the optimal decomposition layer number;
s23: circularly left-shifting the FBG spectral signal f (i) by 1 bit and 0 bit to obtain a first FBG spectral signal f (i,1) and a second FBG spectral signal f (i, 0);
s24: performing discrete wavelet transform on the first FBG spectral signal f (i,1) and the second FBG spectral signal f (i,0) to obtain a first wavelet coefficient w of each layer1j,kAnd a second wavelet coefficient w0j,k；
S3: for each layer wavelet coefficient wj,kCarrying out threshold quantization processing;
s4: reconstructing the wavelet coefficient after threshold processing to obtain a denoising signal s (i);
s5: fitting the de-noised signal s (i) by a Gaussian formula to obtain an approximate signal;
s6: finding out the coordinates of the peak point of an approximate curve formed by the fitted approximate signals;
s7: and determining the wavelength value corresponding to the peak point.
2. The method for processing the FBG signal based on the shift invariant wavelet as claimed in claim 1, wherein: the threshold quantization process specifically includes the steps of:
s31: selecting a proper threshold criterion and determining a threshold;
s32: for the first wavelet coefficient w1j,kAnd a second wavelet coefficient w0j,kPerforming threshold quantization to obtain quantized quantization scaleWave coefficient;
s33: reconstructing according to the quantized wavelet coefficients to obtain a first signal s (i,1) and a second signal s (i, 0);
s34: cyclically right-shifting the first signal s (i,1) and the second signal s (i,0) by 1 bit and 0 bit, respectively;
s35: and averaging the first signal s (i,1) and the second signal s (i,0) after the right shift to obtain a final de-noised signal.
3. The method for processing the FBG signal based on the shift invariant wavelet as claimed in claim 2, wherein: the threshold quantization processing adopts improved threshold function processing, and the improved threshold function processing specifically comprises the following steps:
s321: determining wavelet coefficients w of layersj,kA threshold λ of (2);
s322: judging wavelet coefficient w of each layerj,kWhether the following formula is satisfied:
|wj,k| ≧ λ; wherein, | wj,k| represents wavelet coefficient wj,kThe mold of (4);
s323: if not, let wj,kIf yes, wavelet coefficient w is calculated for each layerj,kThe calculation is made by the following formula:
s324: and reconstructing the quantized wavelet coefficients.
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| CN104048617B (en) * | 2014-07-09 | 2017-02-01 | 中国科学院半导体研究所 | Sensing modulating method for high-precision fiber bragg grating insensitive to polarization state changes |
| CN105787444B (en) * | 2016-02-24 | 2019-03-22 | 北方工业大学 | Signal denoising method based on V system |
| CN105783953B (en) * | 2016-03-25 | 2018-03-27 | 武汉烽理光电技术有限公司 | Quick Gauss curve fitting method applied to Fiber Bragg Grating FBG Wavelength demodulation |
| CN106226845B (en) * | 2016-08-11 | 2018-08-28 | 国家电网公司 | A method of identifying Hail distribution region from OPGW vibration signals |
| CN107490397B (en) * | 2016-09-14 | 2018-05-04 | 北京卫星环境工程研究所 | High-accuracy self-adaptation filters the quick Peak Search Method of FBG spectrum |
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