CN113947121B - Wavelet basis function selection method and system based on mode maximum noise reduction evaluation - Google Patents
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Abstract
The application discloses a wavelet basis function selection method and a system based on mode maximum noise reduction evaluation, which are used for determining a signal set needing wavelet basis selection, and respectively utilizing first-order, second-order and third-order Gaussian function derivatives as wavelet basis functions to perform noise reduction treatment on signals in the signal set; and determining a wavelet basis function of the first signal according to the processed signal waveform curve and the spectrum analysis chart. The noise reduction algorithm based on wavelet coefficient modulus maximum value evaluation can remarkably retain singular components in the original signal and remove noise parts. The wavelet basis functions with different vanishing moments can identify different types of singular points, so that the waveform change, the corresponding spectrum curve and the signal-to-noise ratio result of the signals after noise reduction by adopting the wavelet basis functions with different vanishing moments can be comprehensively compared and analyzed to judge which wavelet basis function can more comprehensively extract the singular 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 mode maximum noise reduction evaluation.
Background
In engineering practice, state monitoring and fault diagnosis are required for working equipment, but the fault equipment is impacted due to unstable operation of the equipment or the acquired signal is a complex non-stationary signal due to the influence of environmental noise. In particular, when detecting the tool state of a machine tool, the change in the signal indirect to the cutting process is used to analyze and evaluate the wear state of the tool, however, since the conventional fourier transform is only suitable for the analysis of stationary signals, a method for analyzing non-stationary signals is required.
Wavelet transformation enables analysis of signals according to different size factors and thus has unique advantages in the processing of non-stationary signals. The difficulty encountered at the present stage is the selection of wavelet basis functions, and the higher the analysis precision requirement is, the more obvious the importance of accurate selection is.
The wavelet basis selection method currently used is mainly to measure the similarity between the signal to be analyzed and the wavelet basis function with scale factors and translation factors on the basis of the basic characteristics of the known wavelet basis functions, which is subjective and qualitative. Therefore, objective criteria need to be found on the selection method of the wavelet basis functions for extracting the detected signal components, so as to avoid the result distortion and low accuracy caused by improper wavelet basis selection when the wavelet transformation is used for signal analysis.
Disclosure of Invention
In order to solve the technical problems, the application provides the following technical scheme:
In a first aspect, an embodiment of the present application provides a wavelet basis function selection method based on a mode maximum noise reduction evaluation, where the method includes: determining a set of signals requiring wavelet base selection, the set of signals comprising a plurality of different types of signals; respectively using the derivatives of the first-order, second-order and third-order Gaussian functions as wavelet basis functions to perform noise reduction treatment on 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 graph, wherein the first signal is any signal in the signal set.
By adopting the implementation mode, the noise reduction algorithm based on wavelet coefficient modulus maximum value evaluation can obviously reserve singular components in the original signal and remove noise parts. The wavelet basis functions with different vanishing moments can identify different types of singular points, so that the waveform change, the corresponding spectrum curve and the signal-to-noise ratio result of the signals after noise reduction by adopting the wavelet basis functions with different vanishing moments can be comprehensively compared and analyzed to judge which wavelet basis function can more comprehensively extract the singular information of the corresponding signals.
With reference to the first aspect, in a first possible implementation manner of the first aspect, the performing noise reduction processing on signals in the signal set by using derivatives of first-order, second-order and third-order gaussian functions 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 point is noise generation, setting a screening threshold on the maximum scale; screening a mode maximum value point caused by noise through the screening threshold; and setting the mode maximum value point of which the value of the mode maximum value point wavelet coefficient is smaller than the screening threshold value to be 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, according to a rule of change of a scale s in a (u, s) (spatial u, scale s) plane of a mode maximum point of a signal, that the mode maximum point is a signal or noise generation includes: if the wavelet coefficient value of the mode maximum point is reduced along with the reduction of the scale s and finally converges, the maximum line communicated with the mode maximum point corresponds to a signal point containing singular information, and the signal point is generated; or if the value of the wavelet coefficient corresponding to the mode maximum point increases with the decrease of the scale, the mode maximum point is noise generation.
With reference to the first aspect or the first or the second possible implementation manners, in a third possible implementation manner of the first aspect, the screening threshold is:
Where Z is a constant, the discrete scale s=2 j (j=0, 1,2,..j), J is the maximum value of the discrete scale coefficient, and M is the maximum value of all the mode maxima at 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 the smoothness of a signal waveform curve of the first signal and the noise energy of a high-frequency part in the spectrum analysis chart; if the fine sawtooth waveform in the signal waveform curve is eliminated and the noise energy of the high frequency part is disappeared, determining the derivative of the current-order Gaussian function as 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 mode maximum noise reduction evaluation, the system including: a first determining module, configured to determine a signal set that needs to perform wavelet base selection, where the signal set includes a plurality of signals of different types; the noise reduction processing module is used for carrying out noise reduction processing on signals in the signal set by using the derivatives of the first-order, second-order and third-order Gaussian functions as wavelet basis functions respectively; and the second determining module is used for determining a wavelet basis function of a first signal according to the processed signal waveform curve and the spectrum analysis graph, wherein the first signal is any 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 the mode maximum point is signal or noise generation according to a change rule of the mode maximum point of the signal along the scale s in the (u, s) (space u, scale s) plane; a setting unit, configured to set a screening threshold on a maximum scale if the mode maximum point is noise generation; the screening unit is used for screening the mode maximum value points caused by noise through the screening threshold; and the processing unit is used for setting the mode maximum value point of which the value of the mode maximum value point wavelet coefficient is 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: a first determining subunit, configured to generate a signal for a signal point including singular information corresponding to a maximum line that is connected to the mode maximum point if the value of the wavelet coefficient of the mode maximum point decreases with a decrease in the scale s and finally converges; and the second determination subunit is used for generating noise if the value of the wavelet coefficient corresponding to the mode maximum value point increases along with the reduction of the scale.
With reference to the first or the second possible implementation manner of the second aspect, in a third possible implementation manner of the second aspect, the screening threshold is:
Where Z is a constant, the discrete scale s=2 j (j=0, 1,2,..j), J is the maximum value of the discrete scale coefficient, and M is the maximum value of all the mode maxima at 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 determining unit, configured to determine smoothness of a signal waveform curve of the first signal and noise energy of a high-frequency part in the spectrum analysis chart; and a third determining unit for determining that the derivative of the gaussian function of the current order is a 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 is disappeared.
Drawings
FIG. 1 is a schematic flow chart of a wavelet basis function selection method based on a mode maximum noise reduction evaluation according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a vibration signal noise reduction effect according to an embodiment of the present application;
Fig. 3 is a schematic diagram of a noise reduction effect of a sound signal according to an embodiment of the present application;
FIG. 4 is a schematic diagram showing the noise reduction effect of the cutting force signal according to the embodiment of the present application
Fig. 5 is a schematic diagram of a wavelet basis function selection system based on a mode maximum noise reduction evaluation according to an embodiment of the present application.
Detailed Description
The present invention is described below with reference to the drawings and the detailed description.
Fig. 1 is a flow chart of a wavelet basis function selection method based on a mode maximum noise reduction evaluation according to an embodiment of the present application, referring to fig. 1, the wavelet basis function selection method based on the mode maximum noise reduction evaluation in the embodiment includes:
S101, determining a signal set needing wavelet base selection, wherein the signal set comprises a plurality of signals of different types.
The signal to be subjected to wavelet base selection is collected, and the sound, cutting force and vibration signals of the cutting tool during cutting processing are taken as an illustrative example in the application, and the collection is performed by using a sensor.
S102, noise reduction processing is carried out on signals in the signal set by using the derivatives of the first-order, second-order and third-order Gaussian functions as wavelet basis functions respectively.
The normalization of the gaussian function can ensure that all the detected mode maximum lines can be extended to the minimum scale, and meanwhile, the first-order, second-order, third-order and higher-order derivatives of the gaussian function respectively have vanishing moments of the first-order, second-order, third-order and higher-order, so that wavelet transformation is carried out by using the derivatives of the gaussian function as wavelet basis functions. The singular types of most sensor signals are typically determined by performing a modulo maximum noise reduction calculation using the first third order gaussian function derivatives, respectively, based on experience with the data processing and in view of computational efficiency.
And respectively using the derivatives of the first-order, second-order and third-order Gaussian functions as wavelet basis functions to perform noise reduction treatment on the collected sound, cutting force and vibration signals in the cutting machining process.
The li index of noise is usually negative, so that whether the mode maximum point is generated by noise or signal can be distinguished by judging the rule of variation of the mode maximum point along the scale s in the (u, s) (space u, scale s) plane.
If a mode maximum point exists, the value of a wavelet coefficient of the mode maximum point is reduced along with the reduction of the scale s and finally converges at a u 0 coordinate point of a u axis, and a maximum line communicated with the mode maximum point corresponds to a signal point containing singular information; in contrast, if the value of the modulus maxima corresponding to the wavelet coefficients increases significantly with decreasing scale, then the points are typically all points controlled by noise,
For this purpose, a threshold T (equation 1) is set at the maximum scale to screen the mode maxima caused by noise, if the values of the mode maxima wavelet coefficients are smaller than T, these mode maxima are zeroed out, and then the signal is reconstructed using the tower algorithm of Mallat with wavelet coefficients. The Mallat algorithm is actually a fast algorithm of orthogonal wavelet transformation based on multi-resolution analysis as a basic theoretical basis, and performs multiple decomposition and reconstruction like a graph tower on a measurement signal through a wavelet filter, decomposes the measurement signal from a frequency domain into subband signals, and synthesizes the subband signals into a new signal through a synthesis filter after processing.
The noise reduction algorithm based on the wavelet coefficient modulo maximum value estimation is hereinafter simply referred to as a modulo maximum value noise reduction method.
Where Z is a constant, here taken as 2, the discrete scale s=2 j (j=0, 1,2,..j) where J is the maximum value of the discrete scale factor, typically a relatively large scale factor may lead to some loss of locally significant singularity information, where j=5 is chosen and m is the maximum of all the mode maxima at the maximum scale. The method can effectively and reliably remove noise and simultaneously retain 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 graph, wherein the first signal is any signal in the signal set.
By analyzing and sorting the results obtained above, 3 types of waveform graphs after noise reduction 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 spectrum analysis diagrams, as shown in fig. 2 (f) to (h), fig. 3 (f) to (h) and fig. 4 (f) to (h).
As can be seen from comprehensive observation of fig. 2 (b) to (d) and fig. 3 (b) to (d), the curves of the vibration signal after noise reduction with an increase in the vanishing moment of the wavelet basis function become smoother in the cutting-vibration signal and the sound signal, and after the mode maximum noise reduction by the wavelet basis function having the first-order vanishing moment, there are many fine and saw-tooth-like fluctuations in the signal waveform, and at the same time, the corresponding spectral graphs 2 (f) to (h) and fig. 3 (f) to (h) are comprehensively observed, so that high noise energy still exists in the high-frequency portion.
The noise reduction effect of the waveform curve obtained by comparing and observing the wavelet basis function noise reduction of the second-order vanishing moment relative to the wavelet basis function of the first-order vanishing moment is tiny and saw-tooth-shaped fluctuation on the curve is basically eliminated, and the noise energy of a high-frequency part on the corresponding frequency spectrum curve is basically eliminated.
Finally, the change of the wavelet basis function of the longitudinal comparison third-order vanishing domain and the wavelet basis function of the second-order vanishing domain on the waveform curve of the noise reduction effect can be seen to be smaller, and the noise energy of the high-frequency part displayed on the corresponding frequency spectrum curve is further suppressed, but the reduction degree is limited.
In the cutting force signals, as shown in fig. 3 (b) to (d), the smoothness of the waveform curves after noise reduction of the three wavelet basis functions is basically the same, and meanwhile, the differences among the three waveform curves can be observed very little by comprehensively observing the spectrum graphs 3 (f) to (h) in the longitudinal direction.
In order to further quantify the Noise reduction effect of the mode maximum Noise reduction processing of the derivatives of the gaussian function, signal-Noise Ratio (SNR') which can be achieved by the corresponding original Signal is calculated, respectively, as shown in table 1.
As can be seen from the observation of table 1, in terms of the cutting vibration signal, the signal-to-noise ratio result is greatly reduced by 14.59% compared with the result obtained by using the first-order hour moment after the noise reduction by using the gaussian function second derivative of the second vanishing moment, and the relative reduction of the signal-to-noise ratio result is limited by only 2.96% after the noise reduction by using the gaussian function third derivative.
In terms of sound signals, the signal-to-noise ratio result after noise reduction by using the second-order Gaussian derivative is 18.67% lower than that by using the first-order Gaussian derivative, and the signal-to-noise ratio result after noise reduction by using the third-order Gaussian derivative is only 7.44% lower than that by using the second-order Gaussian derivative.
In the aspect of cutting force signals, the reduction amplitude of the signal-to-noise ratio result of the cutting force signals is 3.78% and 1.54% respectively after the higher-order Gaussian function derivative is used for noise reduction, and the reduction degree is basically negligible.
According to the previous result comprehensive analysis, the dominant singularities in the cutting vibration signal and the sound signal are inferred to be the second type singularities, and the dominant singularities in the cutting force signal are inferred to be the first type singularities, so that 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 singularities of the cutting force signal.
TABLE 1 Signal-to-noise ratio (db) results for different noise reduction algorithms
From the analysis, the following conclusions can be drawn: the dominant singularity information in the cutting force signal is the first type of singularities, and the wavelet basis function with the first order vanishing moment is the best choice for analyzing the singularities of the cutting force signal. Meanwhile, the wavelet basis function selection method based on the mode maximum noise reduction evaluation can be proved to be capable of effectively and reliably evaluating and qualifying unknown singular types of sensor signals so as to finish the determination of the optimal wavelet basis function vanishing moment in singular analysis.
The wavelet basis function with higher order vanishing moment can identify more kinds of singular points, which can be shown as increasing the order of vanishing moment in the process of mode maximum noise reduction, the method can identify more mode maximum points, and the noise points removed are increased by carrying out threshold analysis, so that the signal to noise ratio is reduced. The degree to which the signal-to-noise ratio results drop depends on which type of singular point in the original signal dominates: if the first kind of singular points in the signal are dominant, even if a wavelet base with higher order vanishing moment is adopted, only fewer singular points with higher order can be identified, then threshold value elimination is carried out in the identified singular points with the first kind and the singular points with higher order, and the final signal-to-noise ratio result is reduced, but the reduction amplitude is limited; if the second kind of singular points in the signal are dominant, when the wavelet basis with the second order vanishing moment is adopted for identifying the mode maximum value, as more dominant second kind of singular points are identified, the mode maximum value noise reduction algorithm can perform threshold comparison on more mode maximum value points, so that the number of the noise points to be removed is increased sharply, the result of the signal to noise ratio is reduced greatly finally, and the like.
The application establishes a singular analysis theory based on wavelet transformation, forms a signal noise reduction algorithm based on wavelet transformation coefficient mode maximum evaluation, realizes noise reduction while retaining singular characteristics in the original signal, and can effectively and reliably evaluate and qualify unknown singular types of sensor signals so as to complete the determination of optimal wavelet basis function vanishing moment in singular analysis.
Corresponding to the wavelet basis function selection method based on the mode maximum noise reduction evaluation provided by the embodiment, the application also provides an embodiment of the wavelet basis function selection system based on the mode maximum noise reduction evaluation.
Referring to fig. 5, the wavelet basis function selection system 20 based on a modulo maximum noise reduction evaluation includes: a first determination module 201, a noise reduction processing module 202, and a second determination module 203.
A first determining module 201 is configured to determine a signal set that needs to be selected based on a wavelet, where the signal set includes a plurality of signals of different types. The noise reduction processing module 202 is configured to perform noise reduction processing on signals in the signal set by using derivatives of first-order, second-order and third-order gaussian functions as wavelet basis functions, respectively. The second determining module 203 is configured to determine a wavelet basis function of a first signal according to the processed signal waveform curve and the spectrum analysis chart, where the first signal is any signal in the signal set.
In this embodiment, the noise reduction processing module 202 includes: the device comprises a first determining unit, a setting unit, a screening unit and a processing unit.
A first determining unit, configured to determine that the mode maximum point is signal or noise generation according to a change rule of the mode maximum point along the scale s in the (u, s) (space u, scale s) plane of the signal. 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 points caused by noise through the screening threshold value. And the processing unit is used for setting the mode maximum value point of which the value of the mode maximum value point wavelet coefficient is smaller than the screening threshold value to zero.
Further, the first determination unit includes: a first determination subunit and a second determination subunit.
And the first determination subunit is used for generating a signal if the value of the wavelet coefficient of the mode maximum point is reduced along with the reduction of the scale s and finally converges, and the maximum line communicated with the mode maximum point corresponds to the signal point containing the singularity information. And the second determination subunit is used for generating noise if the value of the wavelet coefficient corresponding to the mode maximum value point increases along with the reduction of the scale.
In this embodiment, the screening threshold is:
Where Z is a constant, the discrete scale s=2 j (j=0, 1,2,..j), J is the maximum value of the discrete scale coefficient, and M is the maximum value of all the mode maxima at the maximum scale.
The second determining module includes: a second determination unit and a third determination unit.
And the second determining unit is used for determining the smoothness of the signal waveform curve of the first signal and the noise energy of the high-frequency part in the spectrum analysis chart. A third determination unit for determining that the derivative of the current 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 is eliminated
It should be noted that in this document, relational terms such as "first" and "second" and the like are 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. Moreover, 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 one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
Claims (4)
1. A wavelet basis function selection method based on a mode maximum noise reduction evaluation, the method comprising:
determining a set of signals requiring wavelet base selection, the set of signals comprising a plurality of different types of signals;
and respectively utilizing the derivatives of the first-order, second-order and third-order Gaussian functions as wavelet basis functions to perform noise reduction processing on signals in the signal set, wherein the noise reduction processing comprises the following steps:
Determining that the mode maximum point is generated by the signal or noise according to the change rule of the mode maximum point of the signal along the scale s in the (u, s) plane, wherein: u is space, s is scale;
If the mode maximum point is noise generation, setting a screening threshold on the maximum scale;
screening a mode maximum value point caused by noise through the screening threshold;
setting zero to the mode maximum value point of which the value of the wavelet coefficient of the mode maximum value point is smaller than the screening threshold value;
the determining that the mode maximum point is signal or noise generation according to the change rule of the mode maximum point of the signal along the scale s in the (u, s) plane comprises the following steps:
if the wavelet coefficient value of the mode maximum point is reduced along with the reduction of the scale s and finally converges, the maximum line communicated with the mode maximum point corresponds to a signal point containing singular information, and the signal point is generated;
Or alternatively
If the value of the wavelet coefficient corresponding to the mode maximum point increases along with the reduction of the scale, the mode maximum point is generated by noise;
the screening threshold is:
Wherein Z is a constant, the discrete scale s=2 j, j=0, 1,2,., J is the maximum value of the discrete scale coefficient, M is the maximum value of all the mode maxima at the maximum scale;
And determining a wavelet basis function of a first signal according to the processed signal waveform curve and the spectrum analysis graph, wherein the first signal is any signal in the signal set.
2. The method for wavelet basis function selection based on mode maximum noise reduction estimation according to claim 1, wherein said determining the wavelet basis function of the first signal based on the processed signal waveform profile and the spectrum analysis map comprises:
determining the smoothness of a signal waveform curve of the first signal and the noise energy of a high-frequency part in the spectrum analysis chart;
if the fine sawtooth waveform in the signal waveform curve is eliminated and the noise energy of the high frequency part is disappeared, determining the derivative of the current-order Gaussian function as the wavelet basis function of the first signal.
3. A wavelet basis function selection system based on a modulo maximum noise reduction evaluation, the system comprising:
A first determining module, configured to determine a signal set that needs to perform wavelet base selection, where the signal set includes a plurality of signals of different types;
the noise reduction processing module is used for carrying out noise reduction processing on signals in the signal set by using the derivatives of the first-order, second-order and third-order Gaussian functions as wavelet basis functions respectively;
The noise reduction processing module includes:
A first determining unit, configured to determine that the mode maximum point is a signal or noise generation according to a change rule of the mode maximum point of the signal along a scale s in a (u, s) plane, where: u is space, s is scale;
A setting unit, configured to set a screening threshold on a maximum scale if the mode maximum point is noise generation;
the screening unit is used for screening the mode maximum value points caused by noise through the screening threshold;
The processing unit is used for setting the modulus maximum value point of which the value of the modulus maximum value point wavelet coefficient is smaller than the screening threshold value to zero;
The first determination unit includes:
a first determining subunit, configured to generate a signal for a signal point including singular information corresponding to a maximum line that is connected to the mode maximum point if the value of the wavelet coefficient of the mode maximum point decreases with a decrease in the scale s and finally converges;
A second determining subunit, configured to, if a value of a wavelet coefficient corresponding to a mode maximum point increases with a decrease in scale, generate noise for the mode maximum point;
the screening threshold is:
Wherein Z is a constant, the discrete scale s=2 j, j=0, 1,2,., J is the maximum value of the discrete scale coefficient, M is the maximum value of all the mode maxima at the maximum scale;
And the second determining module is used for determining a wavelet basis function of a first signal according to the processed signal waveform curve and the spectrum analysis graph, wherein the first signal is any signal in the signal set.
4. A wavelet basis function selection system based on modular maximum noise reduction assessment according to claim 3, wherein said second determination module comprises:
a second determining unit, configured to determine smoothness of a signal waveform curve of the first signal and noise energy of a high-frequency part in the spectrum analysis chart;
and a third determining unit for determining that the derivative of the gaussian function of the current order is a 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 is disappeared.
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