CN112115842A - Weak electric signal detection system and method based on improved lifting wavelet transformation and high-order autocorrelation processing - Google Patents
Weak electric signal detection system and method based on improved lifting wavelet transformation and high-order autocorrelation processing Download PDFInfo
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Abstract
The invention discloses a weak electric signal detection system and a method thereof based on improved lifting wavelet transformation and high-order autocorrelation processing, comprising the following steps: lifting the wavelet by adopting a wavelet lifting scheme; lifting the wavelet decomposition original signal to obtain each scale coefficient; processing wavelet coefficients of each layer by adopting an improved wavelet threshold function; carrying out inverse wavelet transform on wavelet coefficients of each layer processed by adopting an improved wavelet threshold function to obtain a reconstructed signal, and completing lifting wavelet threshold denoising of an original signal; performing multiple autocorrelation operations on the reconstructed signal to generate a high-order autocorrelation function, and selecting the number of repetition of the autocorrelation operations according to the improvement degree of the signal-to-noise ratio; finally, a time delay high-order autocorrelation demodulation method is adopted to detect the characteristics of the weak electric signal. The invention solves the distortion problem of the wavelet reconstruction signal and enlarges the detection range of the signal to noise ratio. The method has the advantages of low distortion degree of wavelet reconstruction signals, high signal-to-noise ratio improvement degree and the like.
Description
Technical Field
The invention belongs to the technical field of weak electric signal detection, and relates to a weak electric signal detection system and a method based on improved lifting wavelet transformation and high-order autocorrelation processing.
Background
For weak physical quantities such as measured vibration, sound, light and the like, the physical quantities are usually converted into micro-current or low-voltage signals through a vibration sensor or a sound sensor and the like, so that data acquisition is realized. The weak electric signal refers to a signal with a small amplitude value and a signal with an extremely low signal-to-noise ratio, and the detection essence is to adopt various signal processing methods to improve the signal-to-noise ratio of a target signal. In the fields of mechanical fault diagnosis, detection, communication, biomedical engineering and the like, the problem of weak electric signal detection under the background of strong noise is one of the hot problems which are widely concerned. Therefore, effectively improving the signal-to-noise ratio of the target signal is an important task for detecting the weak electric signal.
The research personnel carry out extensive research aiming at two problems of low signal-to-noise ratio and low amplitude in the actual detection process of the weak electric signal. In recent years, the wavelet threshold lifting denoising theory is increasingly widely applied to the fields of fault diagnosis, radar detection, spectral analysis, biomedical engineering and the like. For example, chinese patent "(ZL 200610113292.5) is a pulse signal processing method based on lifting wavelet, and the method uses lifting wavelet threshold to perform denoising processing on a signal to be detected, so when the low signal-to-noise ratio is low, the splitting operation in the lifting wavelet denoising process is likely to cause serious frequency aliasing. In addition, the denoising effect and the distortion degree are influenced by a plurality of factors such as the number of decomposition layers, wavelet basis functions, threshold functions and the like, and weak signals of useful components in the signals can be removed in the denoising process, so that the deviation between the denoised signals and target signals cannot be avoided. Resulting in limitations in the field of weak signal detection. Therefore, how to solve the problem of serious frequency aliasing caused by splitting operation in the lifting wavelet denoising process when the low signal-to-noise ratio is low is a problem which needs to be solved urgently.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a weak electric signal detection system and a method thereof based on improved lifting wavelet transformation and high-order autocorrelation processing. The method improves threshold noise reduction by improving lifting wavelet transformation, improves signal-to-noise ratio under the condition of reducing the distortion degree of a target signal, performs high-order autocorrelation operation on a wavelet reconstruction signal, performs envelope spectrum analysis on a high-order autocorrelation function, extracts the characteristics of a weak electric signal under the background of strong Gaussian noise, and can effectively solve the problem that the distortion degree of the lifting wavelet reconstruction signal is larger because the detected signal-to-noise ratio is not low enough in the existing method for detecting the weak electric signal by singly using the lifting wavelet transformation.
In order to achieve the technical purpose, the invention adopts the following technical scheme.
A weak electric signal detection system based on improved lifting wavelet transformation and high-order autocorrelation processing comprises:
the signal acquisition module is used for acquiring weak signals by adopting various sound, light, heat and displacement sensors and converting weak measured sound, light and heat physical quantities into micro-current or low-voltage signals;
the analog-to-digital conversion module is used for converting the micro-current or low-voltage signal collected by the sensor into a digital signal;
the weak electric signal characteristic extraction module is used for carrying out the following operations including improving lifting wavelet transformation, high-order autocorrelation processing and envelope spectrum demodulation;
the process of improving lifting wavelet transformation comprises the following steps: receiving a digital signal of a digital-to-analog conversion module, firstly adopting a wavelet lifting scheme to lift a wavelet, decomposing an original signal by the wavelet to obtain each scale coefficient, then updating a threshold value adjusting parameter u to obtain an optimal improved wavelet threshold value function to filter each layer of wavelet coefficient, and finally carrying out inverse small transformation on each layer of processed wavelet coefficient to obtain a reconstructed signal so as to finish lifting wavelet threshold value denoising the original signal;
the process of the high-order autocorrelation processing comprises the following steps: receiving a reconstructed signal of the signal noise reduction module, performing autocorrelation operation on the reconstructed signal once, performing autocorrelation operation on a signal obtained by the autocorrelation operation again, and repeating the autocorrelation operation for multiple times to further improve the signal-to-noise ratio;
the process of envelope spectrum demodulation comprises the following steps: and receiving a high-order autocorrelation function of the high-order autocorrelation module, and carrying out envelope spectrum analysis on the high-order autocorrelation function by adopting a time delay high-order autocorrelation demodulation method to obtain weak signal characteristics.
The invention discloses a weak electric signal detection method based on improved lifting wavelet transform and high-order autocorrelation processing, which adopts the weak electric signal detection system based on improved lifting wavelet transform and high-order autocorrelation processing, and comprises the following steps:
n is the signal length, sigma is the standard deviation of Gaussian white noise, and the estimation formula is shown as the formula (2):
σ＝med(|d1(k)|)/0.6745 (2)
wherein d is1(k) Performing median calculation for a first-layer wavelet coefficient sequence after lifting wavelet decomposition on an original signal by med (. -) representation;
step 3, improving a wavelet threshold function: searching an optimal adjusting parameter u to enable the performance of the improved wavelet threshold function to be optimal; comparing the denoising performance of the improved wavelet threshold function with the denoising performance of the soft threshold function and the denoising performance of the hard threshold function, and processing the wavelet coefficients w of each layer by adopting the improved wavelet threshold functionj,k. The specific process comprises the following steps: for each layer of wavelet coefficient wj,kPerforming threshold processing, improving the existing wavelet threshold function to obtain better denoising effect, and estimating wavelet coefficients by the improved wavelet threshold function
The expression is shown in formula (3):
updating the adjusting parameter u, and searching the optimal adjusting parameter u so as to obtain an optimal improved threshold function; the wavelet coefficient is preserved or reduced by adopting an improved wavelet threshold function; let S (n) be the original signal,
in order to improve the reconstructed signal after wavelet threshold denoising, the signal-to-noise ratio SNR and the root mean square error RMSE of the denoised signal are used as evaluation criteria, as shown in the formulas (4) and (5):
step 4, inverse wavelet transform: carrying out inverse wavelet transform on wavelet coefficients of each layer processed by adopting an improved wavelet threshold function to obtain a reconstructed signal, and completing lifting wavelet threshold denoising of an original signal;
step 5, high-order autocorrelation operation: after a reconstructed signal of noise reduction processing is obtained through inverse wavelet transform, autocorrelation operation is carried out on the reconstructed signal; then, performing autocorrelation operation on the signal after autocorrelation operation again; the autocorrelation operation is repeated a plurality of times to generate a high-order autocorrelation function, and the number of times of repetition of the autocorrelation operation is selected according to the degree of improvement in the signal-to-noise ratio. The specific process comprises the following steps:
the reconstructed signal obtained by the inverse wavelet transform is assumed to be:
Y(t)＝s(t)+q(t) (6)
wherein s (t) is a reconstructed target signal, and q (t) is a reconstructed noise signal; tau is delay time, after one time of delay autocorrelation is carried out on the reconstructed signal,
RYY(t)＝E[Y(t)·Y(t+τ)]＝Rss(τ)+Rsq(τ)+Rqq(τ) (7)
in the formula (7), the autocorrelation function R of the signalss(τ), cross-correlation function of signal and noise Rsq(τ), autocorrelation function R of noiseqq(tau) is obtained by calculation according to the formulas (8), (9) and (10) respectively, wherein T is sampling time,
Rsq(τ)＝E[s(t)·q(t+τ)]+E[s(t+τ)·q(t)] (9)
in the formula (9), if q (t) is standard white gaussian noise, E [ q (t) ] and E [ q (t + τ) ] are both 0, so that E [ s (t)). q (t + τ) ] and E [ s (t +. tau.). q (t)) ] are both 0;
in equation (10), in the case of white gaussian noise, the autocorrelation function of noise divided by τ is 0, and the autocorrelation functions of the remaining delay amounts are all 0;
theoretically, when the sampling time T is infinite, Rsq(τ)、Rqq(τ) both approach 0; in practical engineering, however, T cannot be infinite, so that both T and T always exist, and the denoising condition is not ideal; autocorrelation function R of signalss(τ) is regarded as a new periodic signal and has the same frequency as s (t), and R issq(τ)、Rqq(τ) treating as a new noise signal; repeating the autocorrelation operation to perform high-order autocorrelation analysis to obtain a high-order autocorrelation function; the number of times of repeating the autocorrelation operation to perform high-order autocorrelation analysis is not more than 4.
Step 6, envelope spectrum analysis: and performing Hilbert transform on a high-order autocorrelation function of the reconstructed signal by using a time-delay high-order autocorrelation demodulation method, constructing an envelope function on the transformed autocorrelation number, performing frequency spectrum analysis on the envelope function to obtain a time-delay high-order autocorrelation demodulation spectrum, and finally extracting weak signal characteristics.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the invention provides a new improved threshold function, which overcomes the defects of the traditional soft and hard threshold functions, obtains the optimal improved threshold function by adjusting a parameter u, has good adaptability, and is beneficial to the retention of a target signal wavelet coefficient and the filtration of a noise wavelet coefficient. The new improved threshold method can improve the signal-to-noise ratio of the signal, reduce the root mean square error, effectively eliminate the noise in the original signal and better reserve some important fault characteristics in the signal.
2. The invention combines the improved lifting wavelet transform and the high-order autocorrelation method to detect the weak electric signals, and combines the advantages of the lifting wavelet transform and the high-order autocorrelation. The problem that when the signal-to-noise ratio is low, severe frequency aliasing is easily caused by splitting operation in the wavelet denoising lifting process is solved.
3. The invention combines the improved lifting wavelet transform and the high-order autocorrelation method for detecting weak electric signals, overcomes the limitation of the single high-order autocorrelation method by the inherent function of the single high-order autocorrelation method, and can further improve the signal-to-noise ratio of output signals.
Drawings
Fig. 1 is a block diagram of a weak electrical signal detection system based on improved lifting wavelet transform and high-order autocorrelation processing according to an embodiment of the present invention.
FIG. 2 is a flowchart of a method according to an embodiment of the present invention.
FIG. 3 shows the root mean square error RMSE corresponding to the adjustment parameter u of the selection threshold function according to an embodiment of the present invention.
Fig. 4 is a time domain waveform of an original signal according to an embodiment of the present invention.
Fig. 5 is a time domain waveform of a signal after an improved lifting wavelet transform according to an embodiment of the present invention.
Fig. 6 is a time-delayed higher-order autocorrelation demodulation spectrum according to an embodiment of the present invention.
Fig. 7 is a time-delay high-order autocorrelation demodulation spectrum after wavelet reconstruction according to an embodiment of the present invention.
Detailed Description
The invention provides a weak electric signal detection method based on improved lifting wavelet transform and high-order autocorrelation processing, which comprises the steps of firstly, decomposing an original signal by adopting lifting wavelets to obtain each scale coefficient; then improving the wavelet threshold function, and searching an optimal adjusting parameter u to ensure that the performance of the improved wavelet threshold function is optimal; then, processing wavelet coefficients of each layer by adopting an improved wavelet threshold function, and obtaining a reconstructed signal through inverse wavelet transform to realize lifting wavelet denoising; then, carrying out time delay high-order autocorrelation on the reconstructed signal to further reduce noise and outputting a maximum signal-to-noise ratio; finally, a time delay high-order autocorrelation demodulation method is adopted to detect the characteristics of the weak electric signal.
The invention is described in further detail below with reference to the figures and specific embodiments. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that modifications may be made by persons skilled in the art without departing from the spirit of the invention. All falling within the scope of the present invention.
Referring to fig. 1, a block diagram of a weak electrical signal detection system based on an embodiment of improved lifting wavelet transform and high-order autocorrelation processing according to the present invention is shown, where the system of the embodiment includes:
the signal acquisition module: various sensors of sound, light, heat, displacement and the like are adopted to collect weak signals, and weak physical quantities of sound, light, heat and the like to be detected are converted into micro-current or low-voltage signals;
an analog-to-digital conversion module: converting the micro-current or low-voltage signal collected by the sensor into a digital signal;
the weak electric signal characteristic extraction module is used for carrying out the following operations, including: improving lifting wavelet transformation, high-order autocorrelation processing and envelope spectrum demodulation;
the process of improving lifting wavelet transformation comprises the following steps: receiving a digital signal of a digital-to-analog conversion module, firstly adopting a wavelet lifting scheme to lift a wavelet, decomposing an original signal by the wavelet to obtain each scale coefficient, then updating a threshold value adjusting parameter u to obtain an optimal improved wavelet threshold value function to filter each layer of wavelet coefficient, and finally carrying out inverse small transformation on each layer of processed wavelet coefficient to obtain a reconstructed signal so as to finish lifting wavelet threshold value denoising the original signal;
the process of the high-order autocorrelation processing comprises the following steps: receiving a reconstructed signal of the signal noise reduction module, performing autocorrelation operation on the reconstructed signal once, performing autocorrelation operation on a signal obtained by the autocorrelation operation again, and repeating the autocorrelation operation for multiple times to further improve the signal-to-noise ratio;
the process of envelope spectrum demodulation comprises the following steps: and receiving a high-order autocorrelation function of the high-order autocorrelation module, and carrying out envelope spectrum analysis on the high-order autocorrelation function by adopting a time delay high-order autocorrelation demodulation method to obtain weak signal characteristics.
Referring to fig. 2, a flow chart of a method according to an embodiment of the invention is shown. The implementation steps comprise:
various sensors of sound, light, heat, displacement and the like are adopted to collect weak signals, physical quantities of weak detected sound, light, heat, vibration signals and the like are converted into micro-current or low-voltage signals, and the micro-current or low-voltage signals are converted into digital signals for further processing. The example uses the fault signal in the rolling bearing database of the university of Kaiser storage, the data of which is derived from the website
http://csegroups.case.edu/bearingdatacenter/pages/download-data-file. The rolling bearing is selected to be a SKF6205-2RS JEM deep groove ball bearing. The outer ring bearing failure was chosen as an example. The number of the rolling balls is 9, the sampling frequency is 12kHz, the number of the sampling points N is 20000, the rotating speed r of the bearing is 1796r/min (29.93Hz), and the main calculation parameters of the rolling bearing are shown in the table 1:
TABLE 1 Rolling bearing details parameters (units: inches)
The failure frequency of the bearing outer ring can be calculated to be 107.3 Hz.
Step 1: lifting the wavelet by adopting a wavelet lifting scheme: and lifting the wavelet by adopting a wavelet lifting scheme.
Step 2: the method for obtaining each scale coefficient by lifting the original wavelet decomposition signal specifically comprises the following steps:
selection of wavelet basis functions: in the process of lifting wavelet transformation, the selection of wavelet basis function directly determines the quality of noise reduction effect. The Daubechies (dbN) wavelet has good regularity and good sensitivity for detecting signal mutation points. The db4 wavelet has the best temporal resolution and the shortest temporal window compared to the other dbN wavelets. The db4 wavelet was chosen for this example.
Selection of the number of decomposition layers: the larger the number of decomposition layers is obtained, the more obvious the different characteristics of the noise and the signal are shown, and the more favorable the separation of the two is. However, the larger the number of decomposition layers, the larger the distortion of the reconstructed signal, so that an appropriate decomposition scale needs to be selected. The distortion degree and the noise reduction effect of the reconstructed signal are comprehensively considered, and three decomposition layers are selected in the embodiment.
Selecting a threshold value: the wavelet coefficient threshold λ is chosen for this example. Using a universal threshold estimate:
in equation (1), N is the signal length, and σ is the standard deviation of white gaussian noise:
σ＝med(|d1(k)|)/0.6745 (2)
in the formula (2), d1(k) And (4) performing median calculation for the first-layer wavelet coefficient sequence after lifting wavelet decomposition on the original signal.
Lifting wavelet decomposition: lifting wavelet decomposition is carried out on the original signal containing the noise to obtain the wavelet coefficient wj,k。
And step 3: improving the wavelet threshold function: and searching an optimal adjusting parameter u to ensure that the performance of the improved wavelet threshold function is optimal, and comparing the denoising performance of the improved wavelet threshold function with the denoising performance of the soft threshold function and the denoising performance of the hard threshold function. The improved threshold function is shown in equation (3):
in formula (3):
are wavelet coefficients after thresholding.
And (4) updating the adjusting parameter u in the step (3), and searching the optimal adjusting parameter u so as to obtain the optimal improved threshold function.
In order to improve the reconstructed signal after wavelet threshold denoising, the Root Mean Square Error (RMSE) of the denoised signal is used as an evaluation standard, as shown in formula (4):
in order to measure the distortion of the reconstructed signal, the Root Mean Square Error (RMSE) of the reconstructed signal and the original signal is compared, and the value of the corresponding parameter u is the best when the RMSE value is the minimum, as can be seen from fig. 3, the best value of u is 1.
Improving threshold noise reduction processing: setting threshold value for high-frequency coefficient of each layer, and adopting improved wavelet threshold value function to make wavelet coefficient wj,kA reservation or reduction is made. Compared with the traditional threshold function, the new improved threshold function overcomes the defects of the traditional soft and hard threshold function, and the optimal improved threshold function is obtained by adjusting the parameter u, so that the method has good adaptability; the method is beneficial to the retention of the wavelet coefficient of the target signal and the filtering of the wavelet coefficient of the noise, can effectively eliminate the noise in the original signal, and better retains some important fault characteristics in the signal.
And 4, step 4: inverse wavelet transform: and carrying out inverse wavelet transform on the wavelet coefficients of each layer processed by adopting the improved wavelet threshold function to obtain a reconstructed signal, and completing lifting wavelet threshold denoising of the original signal. Assuming that a reconstructed signal y (t) obtained after the inverse wavelet transform process is:
Y(t)＝s(t)+q(t) (5)
in equation (5), s (t) is a reconstructed failure signal, and q (t) is a noise signal in the reconstructed signal.
And 5: and (4) performing high-order autocorrelation operation. After one time delay autocorrelation is carried out on the signal after the inverse wavelet reconstruction, tau is a time delay:
RYY(t)＝E[Y(t)·Y(t+τ)]＝Rss(τ)+Rsq(τ)+Rqq(τ) (6)
in the formula (6), the autocorrelation function R of the target signalss(τ), cross-correlation function R of target signal and noisesq(τ), autocorrelation function R of noiseqq(τ) is calculated according to equations (7), (8) and (9), and T is a sampling time:
Rsq(τ)＝E[s(t)·q(t+τ)]+E[s(t+τ)·q(t)] (8)
reconstructing the autocorrelation function R of the signal from the inverse waveletss(τ) as a new periodic signal with the same frequency as s (t), Rsq(τ)、Rqq(τ) is considered as a new noise signal. And (4) repeating the autocorrelation operation of the step (3) to perform high-order autocorrelation analysis, and improving the output signal-to-noise ratio. The present embodiment employs quadratic autocorrelation operation.
By combining the improved lifting wavelet transform and the high-order autocorrelation method, the limitation of a single high-order autocorrelation method by an inherent function of the single high-order autocorrelation method is overcome, and the signal-to-noise ratio of an output signal can be further improved. In addition, the problem that when the signal-to-noise ratio is low, the splitting operation in the lifting wavelet denoising process is easy to cause serious frequency aliasing is solved.
Step 6: and (4) analyzing an envelope spectrum. Performing Hilbert transform on the quadratic autocorrelation coefficient obtained in the step 5 by adopting a time delay high-order autocorrelation demodulation method, constructing an envelope function on the transformed autocorrelation function, performing frequency spectrum analysis on the envelope function to obtain a time delay high-order autocorrelation demodulation spectrum, and extracting the fault frequency and frequency multiplication of the outer ring rolling bearing.
FIG. 3 shows the root mean square error RMSE corresponding to the adjustment parameter u of the selection threshold function according to an embodiment of the present invention. By selecting different adjusting parameters u, the Root Mean Square Error (RMSE) of the reconstructed signal and the original signal is compared, and the value of the corresponding parameter u is optimal when the RMSE value is minimum, as can be seen from fig. 3, the optimal value of u is 1.
Fig. 4 is a time domain waveform of an original signal according to an embodiment of the present invention. Fig. 5 is a time domain waveform of an improved lifting wavelet transformed signal according to an embodiment of the present invention. Comparing the time domain waveform diagrams of fig. 3 and fig. 4, the inverse wavelet reconstructed signal obtains good noise reduction effect without losing the characteristics of the fault signal.
As shown in fig. 6 and 7, the weak electrical signal detection method based on the improved lifting wavelet transform and the high-order autocorrelation adopted in the present embodiment is compared with the experimental result obtained by singly adopting the lifting wavelet threshold denoising method. Through comparative analysis, the envelope spectrum of the outer circle quadratic autocorrelation function can clearly observe the fault signal characteristic frequency of 107.7Hz, and obtain the fault signal double frequency of 215.2Hz, triple frequency of 322.9Hz, quadruple frequency of 430.5Hz, quintuple frequency of 538.2Hz, sextuple frequency of 645.7Hz and the like. This detection result is more prominent than the corresponding frequency components of the envelope spectrum of fig. 6, and the influence of noise can be greatly reduced.
In a word, the wavelet is firstly lifted by adopting a wavelet lifting scheme; then improving a wavelet threshold function, and decomposing and reconstructing the original signal by adopting an improved wavelet transformation method; and then, carrying out time delay high-order autocorrelation processing on the wavelet reconstructed signal, outputting the maximum signal-to-noise ratio, and finally detecting the characteristics of the weak electric signal by adopting a time delay high-order autocorrelation demodulation method on the obtained high-order autocorrelation function. The invention relates to a detection method and practical application, aiming at the problem that the distortion degree of a reconstructed signal of lifting wavelets is larger due to the fact that the signal-to-noise ratio of the detection is not low enough in the existing weak electric signal detection by singly using the lifting wavelet transformation, and the noise-containing signal is subjected to threshold denoising by adopting the improved lifting wavelet transformation method. And the inverse wavelet reconstruction signal is further processed by combining a high-order autocorrelation method, so that the problem that when the low signal-to-noise ratio is low, the splitting operation in the wavelet denoising lifting process is easy to cause serious frequency aliasing is solved, and the limitation of a single high-order autocorrelation method by a function is overcome.
Claims (5)
1. A weak electric signal detection system based on improved lifting wavelet transformation and high-order autocorrelation processing is characterized by comprising:
the signal acquisition module is used for acquiring weak signals by adopting various sound, light, heat and displacement sensors and converting weak measured sound, light and heat physical quantities into micro-current or low-voltage signals;
the analog-to-digital conversion module is used for converting the micro-current or low-voltage signal collected by the sensor into a digital signal;
the weak electric signal characteristic extraction module is used for carrying out the following operations including improving lifting wavelet transformation, high-order autocorrelation processing and envelope spectrum demodulation;
the process of improving lifting wavelet transformation comprises the following steps: receiving a digital signal of a digital-to-analog conversion module, firstly adopting a wavelet lifting scheme to lift a wavelet, decomposing an original signal by the wavelet to obtain each scale coefficient, then updating a threshold value adjusting parameter u to obtain an optimal improved wavelet threshold value function to filter each layer of wavelet coefficient, and finally carrying out inverse small transformation on each layer of processed wavelet coefficient to obtain a reconstructed signal so as to finish lifting wavelet threshold value denoising the original signal;
the process of the high-order autocorrelation processing comprises the following steps: receiving a reconstructed signal of the signal noise reduction module, performing autocorrelation operation on the reconstructed signal once, performing autocorrelation operation on a signal obtained by the autocorrelation operation again, and repeating the autocorrelation operation for multiple times to further improve the signal-to-noise ratio;
the process of envelope spectrum demodulation comprises the following steps: and receiving a high-order autocorrelation function of the high-order autocorrelation module, and carrying out envelope spectrum analysis on the high-order autocorrelation function by adopting a time delay high-order autocorrelation demodulation method to obtain weak signal characteristics.
2. A weak electric signal detection method based on improved lifting wavelet transform and high-order autocorrelation processing is characterized in that a weak electric signal detection system based on improved lifting wavelet transform and high-order autocorrelation processing is adopted, and the method comprises the following steps:
the signal acquisition module is used for acquiring weak signals by adopting various sound, light, heat and displacement sensors and converting weak measured sound, light and heat physical quantities into micro-current or low-voltage signals;
the analog-to-digital conversion module is used for converting the micro-current or low-voltage signal collected by the sensor into a digital signal;
the weak electric signal characteristic extraction module is used for carrying out the following operations including improving lifting wavelet transformation, high-order autocorrelation processing and envelope spectrum demodulation;
the process of improving lifting wavelet transformation comprises the following steps: receiving a digital signal of a digital-to-analog conversion module, firstly adopting a wavelet lifting scheme to lift a wavelet, decomposing an original signal by the wavelet to obtain each scale coefficient, then updating a threshold value adjusting parameter u to obtain an optimal improved wavelet threshold value function to filter each layer of wavelet coefficient, and finally carrying out inverse small transformation on each layer of processed wavelet coefficient to obtain a reconstructed signal so as to finish lifting wavelet threshold value denoising the original signal;
the process of the high-order autocorrelation processing comprises the following steps: receiving a reconstructed signal of the signal noise reduction module, performing autocorrelation operation on the reconstructed signal once, performing autocorrelation operation on a signal obtained by the autocorrelation operation again, and repeating the autocorrelation operation for multiple times to further improve the signal-to-noise ratio;
the process of envelope spectrum demodulation comprises the following steps: receiving a high-order autocorrelation function of a high-order autocorrelation module, and carrying out envelope spectrum analysis on the high-order autocorrelation function by adopting a time delay high-order autocorrelation demodulation method to obtain weak signal characteristics;
the method comprises the following steps:
step 1, lifting wavelets by adopting a wavelet lifting scheme: lifting the wavelet by adopting a wavelet lifting scheme;
step 2, lifting the wavelet decomposition original signal to obtain each scale coefficient: selecting proper wavelet basis function, wavelet decomposition layer number and threshold value according to signal characteristics and noise characteristics, and then obtaining wavelet coefficient w of each layerj,kThe threshold λ is selected by using a general threshold estimation, and the expression thereof is shown as the following formula (1):
n is the signal length, sigma is the standard deviation of Gaussian white noise, and the estimation formula is shown as the formula (2):
σ＝med(|d1(k)|)/0.6745 (2)
wherein d is1(k) Performing median calculation for a first-layer wavelet coefficient sequence after lifting wavelet decomposition on an original signal by med (. -) representation;
step 3, improving a wavelet threshold function: searching an optimal adjusting parameter u to enable the performance of the improved wavelet threshold function to be optimal; comparing the denoising performance of the improved wavelet threshold function with the denoising performance of the soft threshold function and the denoising performance of the hard threshold function, and processing the wavelet coefficients w of each layer by adopting the improved wavelet threshold functionj,k；
Step 4, inverse wavelet transform: carrying out inverse wavelet transform on wavelet coefficients of each layer processed by adopting an improved wavelet threshold function to obtain a reconstructed signal, and completing lifting wavelet threshold denoising of an original signal;
step 5, high-order autocorrelation operation: after a reconstructed signal of noise reduction processing is obtained through inverse wavelet transform, autocorrelation operation is carried out on the reconstructed signal; then, performing autocorrelation operation on the signal after autocorrelation operation again; repeating the autocorrelation operation for multiple times to generate a high-order autocorrelation function, and selecting the repetition times of the autocorrelation operation according to the improvement degree of the signal-to-noise ratio;
step 6, envelope spectrum analysis: and (3) carrying out envelope spectrum demodulation on the high-order autocorrelation function by adopting a time delay high-order autocorrelation demodulation method to obtain weak signal characteristics.
3. The method for detecting weak electric signals based on the improved lifting wavelet transform and the high-order autocorrelation processing as claimed in claim 2, wherein: in step 3, wavelet coefficients w are applied to each layerj,kPerforming threshold processing, improving the existing wavelet threshold function to obtain better denoising effect, and estimating wavelet coefficients by the improved wavelet threshold function
The expression is shown in formula (3):
updating the adjusting parameter u, and searching the optimal adjusting parameter u so as to obtain an optimal improved threshold function; the wavelet coefficient is preserved or reduced by adopting an improved wavelet threshold function; let S (n) be the original signal,
in order to improve the reconstructed signal after wavelet threshold denoising, the signal-to-noise ratio SNR and the root mean square error RMSE of the denoised signal are used as evaluation criteria, as shown in the formulas (4) and (5):
4. the method for detecting weak electric signals based on the improved lifting wavelet transform and the high-order autocorrelation processing as claimed in claim 2, wherein: the specific process of the step 5 is as follows: the reconstructed signal obtained by the inverse wavelet transform is assumed to be:
Y(t)＝s(t)+q(t) (6)
wherein s (t) is a reconstructed target signal, and q (t) is a reconstructed noise signal; tau is delay time, after one time of delay autocorrelation is carried out on the reconstructed signal,
RYY(t)＝E[Y(t)·Y(t+τ)]＝Rss(τ)+Rsq(τ)+Rqq(τ) (7)
in the formula (7), the autocorrelation function R of the signalss(τ), cross-correlation function of signal and noise Rsq(τ), autocorrelation function R of noiseqq(tau) is obtained by calculation according to the formulas (8), (9) and (10) respectively, wherein T is sampling time,
Rsq(τ)＝E[s(t)·q(t+τ)]+E[s(t+τ)·q(t)] (9)
in the formula (9), if q (t) is standard white gaussian noise, E [ q (t) ] and E [ q (t + τ) ] are both 0, so that E [ s (t)). q (t + τ) ] and E [ s (t +. tau.). q (t)) ] are both 0;
in equation (10), in the case of white gaussian noise, the autocorrelation function of noise divided by τ is 0, and the autocorrelation functions of the remaining delay amounts are all 0;
theoretically, when the sampling time T is infinite, Rsq(τ)、Rqq(τ) both approach 0; in practical engineering, however, T cannot be infinite, so that both T and T always exist, and the denoising condition is not ideal; autocorrelation function R of signalss(τ) is regarded as a new periodic signal and has the same frequency as s (t), and R issq(τ)、Rqq(τ) treating as a new noise signal; repeating the autocorrelation operation to perform high-order autocorrelation analysis to obtain a high-order autocorrelation function; the number of times of repeating the autocorrelation operation to perform high-order autocorrelation analysis is not more than 4.
5. The method for detecting weak electric signals based on the improved lifting wavelet transform and the high-order autocorrelation processing as claimed in claim 2, wherein: in step 6, the envelope spectrum analysis process is as follows: and performing Hilbert transform on a high-order autocorrelation function of the reconstructed signal by adopting a time delay high-order autocorrelation demodulation method, constructing an envelope function on the transformed autocorrelation number, performing frequency spectrum analysis on the envelope function to obtain a time delay high-order autocorrelation demodulation spectrum, and finally extracting weak signal characteristics.
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