CN113947121A - Wavelet basis function selection method and system based on modular maximum denoising evaluation - Google Patents
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Abstract
The application discloses a wavelet basis function selection method and a system based on modular maximum denoising evaluation, wherein a signal set needing wavelet basis selection is determined, and first-order, second-order and third-order Gaussian function derivatives are respectively used as wavelet basis functions to perform denoising processing on signals in the signal set; and determining the wavelet basis function of the first signal according to the processed signal waveform curve and the spectrum analysis diagram. The noise reduction algorithm based on wavelet coefficient modulus maximum evaluation can obviously keep singular components in original signals and eliminate noise parts. Since the wavelet basis functions with different vanishing moments can identify different types of singular points, the waveform change of the denoised signals of the wavelet basis functions with different vanishing moments, the corresponding frequency spectrum curve and the signal-to-noise ratio result can be adopted through comprehensive contrast analysis to judge which wavelet basis function can more comprehensively extract the singularity information of the corresponding signals.
Description
Technical Field
The application relates to the technical field of signal analysis and processing, in particular to a wavelet basis function selection method and system based on modular maximum noise reduction evaluation.
Background
In engineering practice, the condition monitoring and fault diagnosis of the working equipment are required, but the fault equipment generates impact due to the unstable operation of the equipment, or the acquired signals are complex and non-stable signals due to the influence of environmental noise. Particularly, when detecting the tool state of a machine tool, the change of the indirect signal of the cutting process is used for analyzing and evaluating the wear state of the tool, however, because the traditional Fourier transform is only suitable for the analysis of a stable signal, a method for analyzing a non-stable signal is needed.
Wavelet transform enables analysis of signals according to different size factors and therefore has a unique advantage in the processing of non-stationary signals. The difficulty encountered at present is the selection of wavelet basis functions, and the higher the requirement on analysis precision is, the more obvious the importance of accurate selection is.
The wavelet basis selection method used at present mainly measures the similarity between the signal to be analyzed and the wavelet basis function with scale factor and translation factor on the basis of the basic characteristics of the known wavelet basis function, and the method is subjective and qualitative. It is therefore desirable to find objective criteria for the selection method of wavelet basis functions for extracting the components of the detected signal to avoid distortion and low accuracy of the result due to improper wavelet basis selection when performing signal analysis using wavelet transform.
Disclosure of Invention
In order to solve the technical problems, the following technical scheme is provided:
in a first aspect, an embodiment of the present application provides a wavelet basis function selection method based on a modulo maximum denoising evaluation, where the method includes: determining a signal set which needs wavelet base selection, wherein the signal set comprises a plurality of signals of different types; respectively utilizing first-order, second-order and third-order Gaussian function derivatives as wavelet basis functions to perform noise reduction processing on the signals in the signal set; and determining a wavelet basis function of a first signal according to the processed signal waveform curve and the spectrum analysis chart, wherein the first signal is any one signal in the signal set.
By adopting the implementation mode, the noise reduction algorithm based on wavelet coefficient modulus maximum evaluation can obviously keep singular components in the original signal and eliminate the noise part. Since the wavelet basis functions with different vanishing moments can identify different types of singular points, the waveform change of the denoised signals of the wavelet basis functions with different vanishing moments, the corresponding frequency spectrum curve and the signal-to-noise ratio result can be adopted through comprehensive contrast analysis to judge which wavelet basis function can more comprehensively extract the singularity information of the corresponding signals.
With reference to the first aspect, in a first possible implementation manner of the first aspect, the performing denoising processing on the signals in the signal set by using first, second, and third gaussian function derivatives as wavelet basis functions respectively includes: determining that the mode maximum point is generated by signals or noise according to the change rule of the mode maximum point of the signals along the scale s in the (u, s) (space u, scale s) plane; if the mode maximum value point is generated by noise, setting a screening threshold value on the maximum scale; screening a mode maximum value point caused by noise through the screening threshold; and setting the modulus maximum point with the value of the modulus maximum point wavelet coefficient smaller than the screening threshold value to zero.
With reference to the first possible implementation manner of the first aspect, in a second possible implementation manner of the first aspect, the determining that a module maximum point is a signal or noise generation according to a variation rule of the module maximum point of the signal along a dimension s in a (u, s) (space u, dimension s) plane includes: if the wavelet coefficient value of the module maximum value point is reduced along with the reduction of the scale s and finally converged, the maximum value line communicated with the module maximum value point corresponds to a signal point containing singular information and generates a signal; alternatively, if the value of the corresponding wavelet coefficient of the modulo maximum point increases with decreasing scale, the modulo maximum point is noise-producing.
With reference to the first or second possible implementation manner of the first aspect, in a third possible implementation manner of the first aspect, the screening threshold is:
wherein Z is a constant and the discrete scale s is 2jJ is the maximum value of the discrete scale coefficient, and M is the maximum value of all the modulus maxima on the maximum scale.
With reference to the first aspect, in a fourth possible implementation manner of the first aspect, the determining a wavelet basis function of the first signal according to the processed signal waveform curve and the spectrum analysis chart includes: determining smoothness of a signal waveform curve of the first signal and noise energy of a high frequency portion in the spectral analysis chart; and if the fine sawtooth waveform in the signal waveform curve is eliminated and the noise energy of the high-frequency part disappears, determining that the derivative of the current-order Gaussian function is the wavelet basis function of the first signal.
In a second aspect, an embodiment of the present application provides a wavelet basis function selection system based on a modulo maximum denoising evaluation, the system including: the device comprises a first determining module, a second determining module and a third determining module, wherein the first determining module is used for determining a signal set which needs wavelet base selection, and the signal set comprises a plurality of signals of different types; the noise reduction processing module is used for performing noise reduction processing on the signals in the signal set by respectively using first-order, second-order and third-order Gaussian function derivatives as wavelet basis functions; and the second determining module is used for determining the wavelet basis function of the first signal according to the processed signal waveform curve and the spectrum analysis chart, wherein the first signal is any one signal in the signal set.
With reference to the second aspect, in a first possible implementation manner of the second aspect, the noise reduction processing module includes: a first determining unit, configured to determine that a mode maximum point of a signal is signal or noise generation according to a variation rule of the mode maximum point of the signal along a scale s in a (u, s) (space u, scale s) plane; a setting unit, configured to set a screening threshold on a maximum scale if the modulo maximum point is noise generation; the screening unit is used for screening the mode maximum value points caused by the noise through the screening threshold value; and the processing unit is used for setting the modulus maximum point with the value of the modulus maximum point wavelet coefficient smaller than the screening threshold value to zero.
With reference to the first possible implementation manner of the second aspect, in a second possible implementation manner of the second aspect, the first determining unit includes: the first determining subunit is used for determining that a maximum line communicated with the modulus maximum point corresponds to a signal point containing singularity information and generating a signal if the value of the wavelet coefficient of the modulus maximum point is reduced along with the reduction of the scale s and finally converged; a second determining subunit, configured to, if a value of the corresponding wavelet coefficient to the modulo maximum point increases with decreasing scale, generate noise for the modulo maximum point.
With reference to the first or second possible implementation manner of the second aspect, in a third possible implementation manner of the second aspect, the screening threshold is:
wherein Z is a constant and the discrete scale s is 2jJ is the maximum value of the discrete scale coefficient, and M is the maximum value of all the modulus maxima on the maximum scale.
With reference to the second aspect, in a fourth possible implementation manner of the second aspect, the second determining module includes: a second determination unit for determining smoothness of a signal waveform curve of the first signal and noise energy of a high frequency portion in the spectral analysis chart; and a third determining unit, configured to determine that the derivative of the current-order gaussian function is the wavelet basis function of the first signal if the fine sawtooth waveform in the signal waveform curve is eliminated and the noise energy of the high-frequency part disappears.
Drawings
Fig. 1 is a schematic flowchart of a wavelet basis function selection method based on modulo maximum denoising evaluation according to an embodiment of the present application;
fig. 2 is a schematic diagram illustrating a noise reduction effect of a vibration signal according to an embodiment of the present application;
fig. 3 is a schematic diagram illustrating a noise reduction effect of an acoustic signal according to an embodiment of the present application;
FIG. 4 is a schematic diagram of a noise reduction effect of a cutting force signal according to an embodiment of the present application
Fig. 5 is a schematic diagram of a wavelet basis function selection system based on a modulo maximum noise reduction evaluation according to an embodiment of the present application.
Detailed Description
The present invention will be described with reference to the accompanying drawings and embodiments.
Fig. 1 is a schematic flowchart of a wavelet basis function selection method based on a modulo maximum denoising evaluation provided in an embodiment of the present application, and referring to fig. 1, the wavelet basis function selection method based on the modulo maximum denoising evaluation in the embodiment includes:
s101, determining a signal set which needs wavelet base selection and contains a plurality of signals of different types.
The signal to be subjected to wavelet basis selection is collected, and in the present application, sound, cutting force, and vibration signals of a cutting tool in a cutting process are taken as an illustrative example, and are collected by a sensor.
And S102, performing noise reduction processing on the signals in the signal set by respectively using first-order, second-order and third-order Gaussian function derivatives as wavelet basis functions.
Because the normalization of the gaussian function can ensure that all the detected modulus maximum lines can be extended to the minimum scale, and simultaneously, the first-order, second-order, third-order and higher-order derivatives of the gaussian function respectively have first-order, second-order, third-order and higher-order vanishing moments, the following contents all use the derivatives of the gaussian function as wavelet basis functions to carry out wavelet transformation. According to the experience of data processing and the consideration of calculation efficiency, the singularity type of most sensor signals can be determined by respectively carrying out modulus maximum noise reduction calculation by using the first third order Gaussian function derivative.
And respectively using first-order, second-order and third-order Gaussian function derivatives as wavelet basis functions to perform noise reduction treatment on the collected sound, cutting force and vibration signals in the cutting process.
The lee index of noise is usually negative, so it can be distinguished whether the mode maximum point is generated by noise or signal by judging the change rule of the mode maximum point along the scale s in the (u, s) (space u, scale s) plane.
If there is a modulo maximum point, its wavelet coefficient value decreases with decreasing scale s and eventually converges to u of the u-axis0At the coordinate point, the maximum line communicated with the module maximum point corresponds to a signal point containing singularity information; if, on the other hand, the value of the corresponding wavelet coefficient for a modulo maximum increases significantly with decreasing scale, then that point is typically the point dominated by noise,
therefore, a threshold value T (formula 1) is set on the maximum scale to screen the modulus maximum value points caused by noise, if the value of the wavelet coefficient of the modulus maximum value points is smaller than T, the modulus maximum value points are set to be zero, and then the tower algorithm of Mallat is used for reconstructing signals by utilizing the wavelet coefficient. The Mallat algorithm is actually a fast algorithm of orthogonal wavelet transform based on multiresolution analysis, which performs a tower-like multiple decomposition and reconstruction of a measurement signal through a wavelet filter, decomposes the measurement signal into subband signals from a frequency domain, and synthesizes the subband signals into new signals through a synthesis filter after processing.
The noise reduction algorithm based on wavelet coefficient modulus maximum evaluation is referred to as modulus maximum noise reduction method hereinafter.
Where Z is a constant, here taken to be 2, and the discrete scale s is 2jJ is the maximum value of the discrete scale coefficient, and a relatively large scale coefficient may cause some loss of locally important singularity information, where J is 5, and M is the maximum value of all the modulus maxima on the maximum scale. The method can effectively and reliably remove noise and simultaneously reserve useful components in the signal.
S103, determining a wavelet basis function of a first signal according to the processed signal waveform curve and the spectrum analysis chart, wherein the first signal is any one signal in the signal set.
By analyzing and sorting the above-mentioned results, 3 kinds of noise-reduced waveform graphs are obtained for each signal as shown in fig. 2(b) to (d), fig. 3(b) to (d), and fig. 4(b) to (d), and spectral analysis graphs are shown in fig. 2(f) to (h), fig. 3(f) to (h), and fig. 4(f) to (h).
As can be seen from a comprehensive observation of fig. 2(b) to (d) and fig. 3(b) to (d), the curves of the vibration signals after noise reduction with an increase in the vanishing moment of the wavelet basis function become smoother in the cut-vibration signals and the sound signals, and after the mode maximum noise reduction with the wavelet basis function having the first-order vanishing moment, there are many fine and jagged fluctuations in the signal waveform, and it can be seen that high noise energy still exists in the high frequency portion by a comprehensive observation of the corresponding spectral graphs 2(f) to (h) and fig. 3(f) to (h).
Compared with the noise reduction effect of the wavelet basis function of the first order vanishing moment, the small and saw-toothed fluctuation on the curve of the waveform curve obtained by comparing and observing the wavelet basis function noise reduction of the second order vanishing moment is basically and effectively removed, and the noise energy of the high-frequency part on the corresponding frequency spectrum curve is also basically disappeared.
Finally, the wavelet basis function of the third-order vanishing domain and the wavelet basis function of the second-order vanishing domain are longitudinally compared, so that the change of the wavelet basis functions is small on a waveform curve of a noise reduction effect, the noise energy of a high-frequency part shown on a corresponding frequency spectrum curve is further inhibited, and the reduction degree is limited.
In the cutting force signal, as shown in fig. 3(b) to (d), the smoothing degrees of the waveform curves of the three wavelet basis functions after noise reduction are basically the same, and meanwhile, the spectral graphs 3(f) to (h) are longitudinally and comprehensively observed, and the difference among the three wavelet basis functions is very small.
In order to further quantify the Noise reduction effect of performing the module maximum Noise reduction processing on each order derivative of the representation gaussian function, the Signal-to-Noise Ratio (SNR') which can be achieved by the corresponding original Signal is calculated respectively, which is shown in table 1.
It can be seen from table 1 that, in terms of cutting vibration signals, after the gaussian second derivative of the second vanishing moment is used for noise reduction, the signal-to-noise ratio result is greatly reduced from the result of using the first small moment, and the amplitude is 14.59%, while after the gaussian third derivative is used for noise reduction, the relative reduction amplitude of the signal-to-noise ratio result is limited, and is only 2.96%.
In terms of sound signals, the signal-to-noise ratio is reduced by 18.67% when the second-order Gaussian derivative is used for noise reduction, and is reduced by 7.44% when the third-order Gaussian derivative is used for noise reduction.
In the aspect of cutting force signals, after noise reduction is carried out by adopting higher-order Gaussian function derivatives, the reduction range of the signal-to-noise ratio result of the cutting force signals is respectively 3.78% and 1.54%, and the reduction degree can be basically ignored.
The comprehensive analysis according to the previous results can conclude that the singularity dominant in the cutting vibration signal and the sound signal is the second type of singularity, and the singularity dominant in the cutting force signal is the first type of singularity, so the wavelet basis function with the second-order vanishing moment is the best choice for analyzing the singularities of the cutting vibration signal and the sound signal, and the wavelet basis function of the first-order vanishing domain is the best choice for analyzing the singularity of the cutting force signal.
TABLE 1 SNR (db) results for different noise reduction algorithms
In summary, the following conclusions can be drawn: the dominant singularity information in the cutting force signal is the first type of singularity, and the wavelet basis function with the first-order vanishing moment is the best choice for analyzing the singularity of the cutting force signal. Meanwhile, the wavelet basis function selection method based on the modulus maximum denoising evaluation can be proved to be capable of effectively and reliably evaluating and qualifying unknown singularity types of sensor signals so as to complete determination of the optimal wavelet basis function vanishing moment in singularity analysis.
The wavelet basis functions with higher-order vanishing moments can identify more kinds of singular points, which can show that more kinds of singular points can be identified along with the increase of the order of the vanishing moments in the process of modular maximum denoising, and the noise points removed are increased by carrying out threshold analysis, so that the signal-to-noise ratio is reduced. But the degree of the decrease of the signal-to-noise ratio result depends on which kind of singular points in the original signal are dominant: if the first-class singular points in the signals are dominant, only a few higher-order singular points can be identified even if wavelet bases with higher-order vanishing moments are adopted, so that threshold elimination is carried out on the identified first-class singular points and the higher-order singular points, the final signal-to-noise ratio result is reduced, but the reduction amplitude is limited; if the second singular point in the signal is dominant, when the wavelet base with the second-order vanishing moment is adopted for identifying the modulus maximum, because more dominant second singular points are identified, the modulus maximum denoising algorithm can compare the threshold of more modulus maximum points, so that the number of the eliminated noise points is increased sharply, and finally the signal-to-noise ratio is reduced greatly, and the like.
The method establishes a singularity analysis theory based on wavelet transformation, forms a signal denoising algorithm based on wavelet transformation coefficient modulus maximum evaluation, realizes denoising while retaining singularity characteristics in original signals, can effectively and reliably evaluate and qualify unknown singularity types of sensor signals, and determines the optimal wavelet basis function vanishing moment in singularity analysis.
Corresponding to the wavelet basis function selection method based on the modular maximum denoising evaluation provided by the embodiment, the application also provides an embodiment of a wavelet basis function selection system based on the modular maximum denoising evaluation.
Referring to fig. 5, a wavelet basis function selection system 20 based on modulo maximum denoising evaluation includes: a first determination module 201, a noise reduction processing module 202 and a second determination module 203.
The first determining module 201 is configured to determine a signal set that needs wavelet basis selection, where the signal set includes a plurality of signals of different types. And the denoising module 202 is configured to perform denoising processing on the signals in the signal set by using first, second, and third order gaussian function derivatives as wavelet basis functions, respectively. A second determining module 203, configured to determine a wavelet basis function of a first signal according to the processed signal waveform curve and the spectrum analysis diagram, where the first signal is any signal in the signal set.
In this embodiment, the denoising module 202 includes: the device comprises a first determining unit, a setting unit, a screening unit and a processing unit.
And the first determining unit is used for determining that the module maximum point is signal or noise generation according to the change rule of the module maximum point of the signal along the scale s in the (u, s) (space u, scale s) plane. And the setting unit is used for setting a screening threshold value on the maximum scale if the mode maximum value point is generated by noise. And the screening unit is used for screening the mode maximum value point caused by the noise through the screening threshold value. And the processing unit is used for setting the modulus maximum point with the value of the modulus maximum point wavelet coefficient smaller than the screening threshold value to zero.
Further, the first determination unit includes: a first determining subunit and a second determining subunit.
And the first determining subunit is used for generating a signal if the wavelet coefficient value of the module maximum point is reduced along with the reduction of the scale s and finally converged, wherein the maximum line communicated with the module maximum point corresponds to a signal point containing singularity information. A second determining subunit, configured to, if a value of the corresponding wavelet coefficient to the modulo maximum point increases with decreasing scale, generate noise for the modulo maximum point.
In this embodiment, the screening threshold is:
in the formulaZ is constant and the discrete scale s is 2jJ is the maximum value of the discrete scale coefficient, and M is the maximum value of all the modulus maxima on the maximum scale.
The second determining module includes: a second determination unit and a third determination unit.
A second determining unit for determining smoothness of a signal waveform curve of the first signal and noise energy of a high frequency portion in the spectral analysis chart. A third determination unit for determining a derivative of a current order Gaussian function as a wavelet basis function of the first signal if a fine sawtooth waveform in the signal waveform curve is removed and noise energy of a high frequency part disappears
It is noted that, in this document, relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
Claims (10)
1. A method for wavelet basis function selection based on a modulo maximum denoising assessment, the method comprising:
determining a signal set which needs wavelet base selection, wherein the signal set comprises a plurality of signals of different types;
respectively utilizing first-order, second-order and third-order Gaussian function derivatives as wavelet basis functions to perform noise reduction processing on the signals in the signal set;
and determining a wavelet basis function of a first signal according to the processed signal waveform curve and the spectrum analysis chart, wherein the first signal is any one signal in the signal set.
2. The method of claim 1, wherein denoising the signals in the set of signals using first, second and third order gaussian function derivatives as wavelet basis functions comprises:
determining that the mode maximum point is generated by signals or noise according to the change rule of the mode maximum point of the signals along the scale s in the (u, s) (space u, scale s) plane;
if the mode maximum value point is generated by noise, setting a screening threshold value on the maximum scale;
screening a mode maximum value point caused by noise through the screening threshold;
and setting the modulus maximum point with the value of the modulus maximum point wavelet coefficient smaller than the screening threshold value to zero.
3. The method of claim 2, wherein determining that a mode maxima point is a signal or noise occurrence according to a rule of variation of the mode maxima point of the signal along a dimension s in a (u, s) (space u, dimension s) plane comprises:
if the wavelet coefficient value of the module maximum value point is reduced along with the reduction of the scale s and finally converged, the maximum value line communicated with the module maximum value point corresponds to a signal point containing singular information and generates a signal;
or,
if the value of the corresponding wavelet coefficient of the modulo maximum point increases with decreasing scale, the modulo maximum point is noise-producing.
4. The method of selecting wavelet basis function based on modulo maximum noise reduction evaluation of claim 2 or 3, wherein the filtering threshold is:
wherein Z is a constant and the discrete scale s is 2jJ is the maximum value of the discrete scale coefficient, and M is the maximum value of all the modulus maxima on the maximum scale.
5. The method of claim 1, wherein determining wavelet basis functions for the first signal from the processed signal profile and the spectral analysis plot comprises:
determining smoothness of a signal waveform curve of the first signal and noise energy of a high frequency portion in the spectral analysis chart;
and if the fine sawtooth waveform in the signal waveform curve is eliminated and the noise energy of the high-frequency part disappears, determining that the derivative of the current-order Gaussian function is the wavelet basis function of the first signal.
6. A wavelet basis function selection system based on a modulo maximum denoising evaluation, the system comprising:
the device comprises a first determining module, a second determining module and a third determining module, wherein the first determining module is used for determining a signal set which needs wavelet base selection, and the signal set comprises a plurality of signals of different types;
the noise reduction processing module is used for performing noise reduction processing on the signals in the signal set by respectively using first-order, second-order and third-order Gaussian function derivatives as wavelet basis functions;
and the second determining module is used for determining the wavelet basis function of the first signal according to the processed signal waveform curve and the spectrum analysis chart, wherein the first signal is any one signal in the signal set.
7. The wavelet basis function selection system based on modulo maximum denoising evaluation of claim 6, wherein the denoising processing module comprises:
a first determining unit, configured to determine that a mode maximum point of a signal is signal or noise generation according to a variation rule of the mode maximum point of the signal along a scale s in a (u, s) (space u, scale s) plane;
a setting unit, configured to set a screening threshold on a maximum scale if the modulo maximum point is noise generation;
the screening unit is used for screening the mode maximum value points caused by the noise through the screening threshold value;
and the processing unit is used for setting the modulus maximum point with the value of the modulus maximum point wavelet coefficient smaller than the screening threshold value to zero.
8. The method of selecting wavelet basis functions based on modulo maximum denoising evaluation according to claim 7, wherein the first determining unit comprises:
the first determining subunit is used for determining that a maximum line communicated with the modulus maximum point corresponds to a signal point containing singularity information and generating a signal if the value of the wavelet coefficient of the modulus maximum point is reduced along with the reduction of the scale s and finally converged;
a second determining subunit, configured to, if a value of the corresponding wavelet coefficient to the modulo maximum point increases with decreasing scale, generate noise for the modulo maximum point.
9. The system of claim 7 or 8, wherein the filtering threshold is:
wherein Z is a constant and the discrete scale s is 2jJ is the maximum value of the discrete scale coefficient, and M is the maximum value of all the modulus maxima on the maximum scale.
10. The modulus maxima denoising evaluation-based wavelet basis function selection system of claim 6, wherein the second determination module comprises:
a second determination unit for determining smoothness of a signal waveform curve of the first signal and noise energy of a high frequency portion in the spectral analysis chart;
and a third determining unit, configured to determine that the derivative of the current-order gaussian function is the wavelet basis function of the first signal if the fine sawtooth waveform in the signal waveform curve is eliminated and the noise energy of the high-frequency part disappears.
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