CN111121955A - Vibration signal wavelet analysis trend term removing method adaptive to threshold frequency - Google Patents
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Abstract
The invention provides a method for removing a trend term by wavelet analysis of a vibration signal with self-adaptive threshold frequency, belonging to the field of pretreatment of the vibration signal of a mechanical system. The method comprises the steps of firstly establishing a criterion W for eliminating the trend effect, preferably selecting five wavelet functions with higher accuracy rate based on a good threshold frequency self-adaptive screening rule of a W curve, comprehensively judging the optimal threshold frequency by utilizing the W curve screening results, then setting the threshold frequency, screening the optimal wavelet function based on the W curve, and completing the self-adaptive setting of the threshold frequency and the wavelet function. According to the method, the optimal threshold frequency and the wavelet function can be determined in a self-adaptive manner without depending on experience to compare the actual effects of various threshold frequencies and wavelet functions in signal processing. The method has better self-adaptability and practicability and higher calculation efficiency, and improves the self-adaptability of the wavelet analysis of the vibration signal.
Description
Technical Field
The invention relates to the field of mechanical system vibration signal preprocessing, in particular to a vibration signal wavelet analysis trend term removing method of self-adaptive threshold frequency.
Background
In the state monitoring and fault diagnosis of a mechanical system, under the influence of factors such as unstable low-frequency performance outside the frequency of a sensor, zero drift of an amplifier along with temperature change, interference of the surrounding environment and the like, an actually measured vibration signal is often deviated from a base line, a constant is generated due to nonalignment of zero when signal types are converted, a straight line is formed after integration, and low-frequency noise becomes a slowly changing trend component after the integration and amplification. The existence of the trend term can seriously affect the signal time domain correlation analysis and the frequency domain power spectrum estimation precision, and the serious trend term interference can even seriously distort the low frequency spectrum.
At present, methods for removing signal trend terms are more, wherein the least square curve fitting method, the high-pass filtering method, the piecewise polynomial fitting method, the moving average method and other methods generally need to presuppose the trend term type in the signal, and are not suitable for processing non-stationary signals with complex variation trend or random variation trend, and the application range is severely restricted. Although the effective component extraction technology based on EMD can realize the self-adaptive decomposition of the non-stationary signal without considering the trend item type, the decomposed trend function is rough under the influence of modal aliasing and end effect, and the extraction precision of the effective component of the signal is restricted. Therefore, the method of removing trend terms, which is widely applied, is a method based on wavelet transform, but the method based on wavelet transform has many challenges at present.
Wavelet transformation requires the pre-selection of wavelet functions and the number of decomposition layers according to a priori knowledge. The more similar a signal is to a wavelet function, the easier it is to extract the signal features. The upper frequency limit of the trend term removed from the signal is called the threshold frequency, which determines the number of wavelet decomposition levels in relation to: l ═ floor (log2(fs/ftr)), where: l is the number of decomposition layers, fs is the sampling rate, ftr is the threshold frequency, and the function of the floor () function is to round down one decimal. The trend item component of the collected signal is uncertain usually, and the upper limit of the frequency is difficult to predict, so in engineering application, the applicability of the threshold frequency and the wavelet function is generally judged by comparing the actual effect of various threshold frequencies and wavelet functions in signal processing, so that the traditional wavelet analysis trend item removing method is greatly influenced by human selection factors and has no self-adaptability.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a vibration signal wavelet analysis trend item removing method capable of self-adapting to the threshold frequency, which can self-adaptively judge the threshold frequency and the wavelet function, and has better self-adaptability and practicability and higher calculation efficiency.
The invention is realized by the following steps:
a method for removing a trend term from a wavelet analysis of a vibration signal with adaptive threshold frequency, comprising:
installing a sensor along the vibration direction of the mechanical structure to obtain an acceleration signal, and converting the acceleration signal through signal types to obtain a vibration signal containing a trend item;
carrying out frequency domain analysis on the vibration signal containing the trend term to obtain the frequency F of the vibration signal;
establishing a vanishing and trending effect criterion W through array operation;
performing self-adaptive screening according to the vanishing and trending effect criterion W to obtain self-adaptive threshold frequency, wherein the screening range of the self-adaptive threshold frequency is 0.1-F/2;
setting a threshold frequency as the self-adaptive threshold frequency, and then carrying out self-adaptive screening according to the vanishing and trending effect criterion W to obtain a self-adaptive wavelet function;
and performing wavelet analysis and trend item removing processing on the vibration signal containing the trend item by utilizing the self-adaptive threshold frequency and the self-adaptive wavelet function.
Further, the establishing of the vanishing and trending effect criterion W through array operation specifically includes:
s301, calculating the difference D1 between the maximum value and the minimum value in the input signal;
s302, storing all maximum values in the input signal into an array L1 according to the time sequence;
s303, storing all minimum values in the input signal into an array L2 according to the time sequence;
s304, judging whether the first appearing in the input signal is a maximum value, if so, entering a step 305, otherwise, deleting a first element in L2, and then entering the step 305;
s305, subtracting the array L2 from the array L1 to obtain an array L3, and calculating the average value D2 of all elements in the L3;
and S306, the vanishing effect criterion W is D1-D2.
Further, the self-adaptive screening is performed according to the vanishing and trending effect criterion W to obtain a self-adaptive threshold frequency, which specifically includes:
s401, setting an initial value of a threshold frequency to be 0.1 Hz;
s402, selecting n wavelet functions, and performing wavelet analysis and trend item removing processing on the vibration signals containing the trend items for n times by using the wavelet functions to obtain n first signals;
s403, establishing vanishing and approaching effect criterion W by using n first signals as input signals through array operation1、W2、W3、……、Wn(ii) a Then, respectively storing the results into an array 1 to an array n;
s404, adding 0.1Hz to the threshold frequency;
s405, repeating S402 to S404, and executing ((F multiplied by 10)/2) times;
s406, solving the positions of the minimum values of the arrays 1 to n and storing the positions into an array L;
s407, solving the element S with the largest occurrence frequency in the array L;
s408, calculating the adaptive threshold frequency P ═ S + 1)/10.
Preferably, the n wavelet functions are specifically: db4, db6, coif1, coif2 and sym8, n is 5.
Further, the setting of the threshold frequency as the adaptive threshold frequency, and then performing adaptive screening according to the vanishing and trending effect criterion W to obtain an adaptive wavelet function specifically includes:
s501, selecting m wavelet functions, sequentially numbering J from 0 to m-1, and selecting a wavelet function with the number J of 0 from the initial wavelet function;
s502, setting a threshold frequency as the self-adaptive threshold frequency, and performing wavelet analysis and trend item removing processing on the vibration signal containing the trend item by using a J wavelet function to obtain a second signal;
s503, taking the second signal as an input signal, solving a cancellation effect criterion W, and continuously storing a result into an array 6;
s504, adding 1 to the number J of the wavelet function;
s505, repeating S502-S504, and executing for m times;
s506, solving the position C where the minimum value in the array 6 is located, wherein the self-adaptive wavelet function is the Cth wavelet function.
Preferably, the m wavelet functions are specifically: db2, db3, db4, db5, db6, db7, db8, db9, db10, db11, db12, db13, db14, coif1, coif2, coif3, coif4, coif5, sym2, sym3, sym4, sym5, sym6, sym7, and sym8, where m is 25.
The invention has the following advantages:
the method effectively solves the problems that the traditional wavelet analysis trend item removing method depends on experience and has no self-adaptability, can adaptively judge the threshold frequency and the wavelet function by only inputting the vibration signal containing the trend item, thereby obtaining the vibration signal without the trend item without manual multiple tests, and has the advantages of strong self-adaptability, simplicity, easy implementation, wide application range, good trend removing effect and the like.
Drawings
The invention will be further described with reference to the following examples with reference to the accompanying drawings.
FIG. 1 is a schematic flowchart of a method for removing a trend term in wavelet analysis of a vibration signal with adaptive threshold frequency according to an embodiment of the present application;
fig. 2 is a schematic view of a construction process of the vanishing and trending effect criterion W in the embodiment of the application;
FIG. 3 is a flowchart of an algorithm for adaptively setting a threshold frequency and a wavelet function according to an embodiment of the present application;
FIG. 4 is a general flowchart of a method for removing trend terms in wavelet analysis by adaptively setting threshold frequency and wavelet function according to an embodiment of the present application;
fig. 5(a) and 5(b) are a vibration acceleration signal after primary integration and a vibration displacement signal after secondary integration according to an embodiment of the present application, respectively;
FIG. 6 is a threshold frequency-W plot for one embodiment of the present application;
FIG. 7 is a graph of wavelet function versus W for one embodiment of the present application;
fig. 8(a), 8(b) and 8(c) are schematic diagrams respectively showing the results of removing the trend term by the least square method and the high-pass filtering method in the embodiment of the present application.
Detailed Description
Referring to fig. 1 to 7, an embodiment of the present specification discloses a method for removing a trend term in wavelet analysis of a vibration signal with adaptive threshold frequency, which may include the following steps:
s10, mounting a sensor along the vibration direction of the mechanical structure to obtain an acceleration signal, and converting the acceleration signal through signal types to obtain a vibration signal containing a trend term;
an acceleration sensor can be installed along the vibration direction of the mechanical structure, an acceleration signal of the mechanical structure is obtained through testing, and the acceleration signal is converted through signal types (such as primary integration and/or secondary integration) so as to obtain a speed signal containing a trend term and/or a displacement signal containing the trend term, namely a vibration signal containing the trend term;
s20, carrying out frequency domain analysis on the vibration signal containing the trend term to obtain the frequency F of the vibration signal;
s30, establishing a vanishing and trending effect criterion W through array operation; the method specifically comprises the following steps:
s301, calculating the difference D1 between the maximum value and the minimum value in the input signal;
s302, storing all maximum values in the input signal into an array L1 according to the time sequence;
s303, storing all minimum values in the input signal into an array L2 according to the time sequence;
s304, judging whether the first appearing in the input signal is a maximum value, if so, entering a step 305, otherwise, deleting a first element in L2, and then entering the step 305;
s305, subtracting the array L2 from the array L1 to obtain an array L3, and calculating the average value D2 of all elements in the L3;
and S306, the vanishing effect criterion W is D1-D2.
In the embodiment of the present specification, the input signal is a signal obtained by performing wavelet analysis and trend removing item processing on the vibration signal containing the trend item by using a wavelet function, and the advantage and disadvantage of the trend removing effect can be judged according to the calculated value by calculating the trend removing effect criterion W on the input signal.
The maximum value is a local maximum value in the input signal, namely a peak in a section of signal; the minimum value is a local minimum value in the input signal, namely a wave trough in a section of signal; whether the input signal appears first is judged to be a maximum value, so that each maximum value is subtracted by the immediately following minimum value, and the situation that each maximum value is subtracted by the preceding minimum value is avoided.
The array L2 is subtracted from the array L1 to obtain the array L3, for example, when the existing arrays a, b, c are (9,8,7,6), b is (1,2,3,4), c is (3,4,5), and d is (6,5), then a-b is (9-1,8-2,7-3,6-4) is (8,6,4,2), a-c is (9-3,8-4,7-5) is (6,4,2), and d-c is (6-3,5-4) is (3, 1).
In the embodiment of the specification, a vanishing and trending effect criterion W is firstly established, the vanishing and trending effect criterion takes the minimum value when the threshold frequency and the wavelet function are optimal, and the vanishing and trending effect criterion has good threshold frequency and wavelet function adaptive screening rules, so that the vanishing and trending effect criterion can be used for carrying out adaptive screening on the threshold frequency and the wavelet function.
S40, carrying out self-adaptive screening according to the vanishing and trending effect criterion W to obtain self-adaptive threshold frequency, wherein the screening range of the self-adaptive threshold frequency is 0.1-F/2; the method specifically comprises the following steps:
s401, setting an initial value of a threshold frequency to be 0.1 Hz;
s402, selecting 5 wavelet functions db4, db6, coif1, coif2 and sym8, and respectively performing n-time wavelet analysis and trend item removing processing on the vibration signals containing the trend items by utilizing the wavelet functions to obtain 5 first signals;
s403, establishing vanishing and approaching effect criterion W by using 5 first signals as input signals through array operation1、W2、W3、W4、W5(ii) a Then, respectively storing the results into an array 1 to an array 5;
s404, adding 0.1Hz to the threshold frequency;
s405, repeating S402 to S404, and executing ((F multiplied by 10)/2) times;
s406, solving the positions of the minimum values of the arrays 1 to 5 and storing the positions into an array L;
s407, solving the element S with the largest occurrence frequency in the array L;
s408, calculating the adaptive threshold frequency P ═ S + 1)/10.
The 5 wavelet functions selected in the embodiment of the present application are one of possible implementations, and other wavelet functions less than 5 or more than 5 may also be selected according to actual situations to perform the filtering of the adaptive threshold frequency.
S50, setting a threshold frequency as the self-adaptive threshold frequency, and then carrying out self-adaptive screening according to the vanishing and trending effect criterion W to obtain a self-adaptive wavelet function; the method specifically comprises the following steps:
s501, selecting 25 wavelet functions db2, db3, db4, db5, db6, db7, db8, db9, db10, db11, db12, db13, db14, coif1, coif2, coif3, coif4, coif5, sym2, sym3, sym4, sym5, sym6, sym7 and sym8, sequentially numbering J between 0 and 24, and selecting a wavelet function with the number J being 0 as an initial wavelet function;
s502, setting a threshold frequency as the self-adaptive threshold frequency, and performing wavelet analysis and trend item removing processing on the vibration signal containing the trend item by using a J wavelet function to obtain a second signal;
s503, taking the second signal as an input signal, solving a cancellation effect criterion W, and continuously storing a result into an array 6;
s504, adding 1 to the number J of the wavelet function;
s505, repeating S502-S504, and executing for 25 times;
s506, solving the position C where the minimum value in the array 6 is located, wherein the self-adaptive wavelet function is the Cth wavelet function.
The 25 wavelet functions selected in the embodiment of the present application are one of possible implementations, and other wavelet functions less than 25 or more than 25 may also be selected according to actual situations to perform the screening of the adaptive wavelet functions.
And S60, performing wavelet analysis and trend item removing processing on the vibration signal containing the trend item by using the adaptive threshold frequency and the adaptive wavelet function.
In one embodiment, the steps of the adaptive threshold frequency vibration signal wavelet analysis detrending term method are shown in FIG. 3 and comprise: firstly, mounting an acceleration sensor along the vibration direction of a mechanical structure, testing to obtain an acceleration signal of the mechanical structure, and performing primary integration or secondary integration on the acceleration signal to obtain a speed signal containing a trend term or a displacement signal containing the trend term, wherein the speed signal or the displacement signal containing the trend term is collectively called as a vibration signal containing the trend term; secondly, carrying out frequency domain analysis on the vibration signal containing the trend term to obtain the frequency F of the vibration signal; thirdly, establishing a vanishing and trending effect criterion W through array operation, wherein the vanishing and trending effect criterion is taken to be the minimum value when the optimal threshold frequency and the optimal wavelet function are obtained as shown in fig. 6 and 7, and the vanishing and trending effect criterion has a good threshold frequency and wavelet function self-adaptive screening rule; fourthly, obtaining self-adaptive threshold frequency P based on a threshold frequency self-adaptive screening rule with a good W curve, wherein the screening range of the self-adaptive threshold frequency is 0.1-F/2; fifthly, setting a threshold frequency as the adaptive threshold frequency in the fourth step, and screening the adaptive wavelet function based on a wavelet function adaptive screening rule with a good W curve; and sixthly, performing wavelet analysis and trend item removal processing on the vibration signal containing the trend item by using the self-adaptive threshold frequency and the wavelet function which are selected by self-adaptation, and further applying the vibration signal without the trend item instead of the vibration signal containing the trend item.
One specific embodiment of the application in the vibrating machine industry is as follows: firstly, mounting an acceleration sensor along the vibration direction of a mechanical structure, testing to obtain an acceleration signal of the mechanical structure, performing primary integration or secondary integration on the acceleration signal to obtain a speed signal containing a trend term or a displacement signal containing the trend term as shown in fig. 5(a), and collectively obtaining a vibration signal containing the trend term, wherein the vibration displacement signal is shown in fig. 5 (b); secondly, carrying out frequency domain analysis on the vibration signal containing the trend term to obtain the frequency F of the vibration signal; thirdly, setting the screening range of the self-adaptive threshold frequency to be 0.1-F/2, and obtaining the self-adaptive threshold frequency P based on the good threshold frequency self-adaptive screening rule of the W curve; as shown in fig. 6, the threshold frequency-W curves of the 5 wavelet functions all start to take the minimum value of W at the threshold frequency of 3.6Hz, and the adaptive threshold frequency is 3.6 Hz; fourthly, setting a threshold frequency as the adaptive threshold frequency in the third step, and screening an adaptive wavelet function based on a wavelet function adaptive screening rule with a good W curve, wherein the wavelet function-W curve takes a W minimum value at a 17 th wavelet function, and the adaptive wavelet function is the wavelet function coif5 with the number 17; and fifthly, performing wavelet analysis and trend term removal processing on the vibration signal containing the trend term by using the threshold frequency and the wavelet function which are selected in the self-adaption mode, wherein the result is shown in fig. 8 (a).
Fig. 8(a), fig. 8(b) and fig. 8(c) are diagrams illustrating the result of removing the trend term by the embodiment of the present application, the least square method and the high-pass filtering method, respectively, and it can be seen that the trends of 99.9%, 95% and 92% are removed by the three methods, respectively, and it can be seen that the effect of the method for removing the trend term by wavelet analysis of the vibration signal with adaptive threshold frequency of the embodiment of the present application is optimal.
The invention effectively solves the problems that the traditional wavelet analysis trend item removing method depends on experience and has no self-adaptability, and by utilizing the method, the threshold frequency and the wavelet function can be adaptively judged only by inputting the vibration signal containing the trend item, so that the vibration signal without the trend item is obtained, manual multiple tests are not needed, and the method has the advantages of strong self-adaptability, simplicity and practicability, wide application range, good trend removing effect and the like.
Although specific embodiments of the invention have been described above, it will be understood by those skilled in the art that the specific embodiments described are illustrative only and are not limiting upon the scope of the invention, and that equivalent modifications and variations can be made by those skilled in the art without departing from the spirit of the invention, which is to be limited only by the appended claims.
Claims (6)
1. A method for removing a trend term from a wavelet analysis of a vibration signal with adaptive threshold frequency, comprising:
installing a sensor along the vibration direction of the mechanical structure to obtain an acceleration signal, and converting the acceleration signal through signal types to obtain a vibration signal containing a trend item;
carrying out frequency domain analysis on the vibration signal containing the trend term to obtain the frequency F of the vibration signal;
establishing a vanishing and trending effect criterion W through array operation;
performing self-adaptive screening according to the vanishing and trending effect criterion W to obtain self-adaptive threshold frequency, wherein the screening range of the self-adaptive threshold frequency is 0.1-F/2;
setting a threshold frequency as the self-adaptive threshold frequency, and then carrying out self-adaptive screening according to the vanishing and trending effect criterion W to obtain a self-adaptive wavelet function;
and performing wavelet analysis and trend item removing processing on the vibration signal containing the trend item by utilizing the self-adaptive threshold frequency and the self-adaptive wavelet function.
2. The method of claim 1, wherein: the method for establishing the vanishing and trending effect criterion W through the array operation specifically comprises the following steps:
s301, calculating the difference D1 between the maximum value and the minimum value in the input signal;
s302, storing all maximum values in the input signal into an array L1 according to the time sequence;
s303, storing all minimum values in the input signal into an array L2 according to the time sequence;
s304, judging whether the first appearing in the input signal is a maximum value, if so, entering a step 305, otherwise, deleting a first element in L2, and then entering the step 305;
s305, subtracting the array L2 from the array L1 to obtain an array L3, and calculating the average value D2 of all elements in the L3;
and S306, the vanishing effect criterion W is D1-D2.
3. The method according to claim 1 or 2, characterized in that: the self-adaptive screening is carried out according to the vanishing and trending effect criterion W to obtain a self-adaptive threshold frequency, and the method specifically comprises the following steps:
s401, setting an initial value of a threshold frequency to be 0.1 Hz;
s402, selecting n wavelet functions, and performing wavelet analysis and trend item removing processing on the vibration signals containing the trend items for n times by using the wavelet functions to obtain n first signals;
s403, establishing vanishing and approaching effect criterion W by using n first signals as input signals through array operation1、W2、W3、……、Wn(ii) a Then, respectively storing the results into an array 1 to an array n;
s404, adding 0.1Hz to the threshold frequency;
s405, repeating S402 to S404, and executing ((F multiplied by 10)/2) times;
s406, solving the positions of the minimum values of the arrays 1 to n and storing the positions into an array L;
s407, solving the element S with the largest occurrence frequency in the array L;
s408, calculating the adaptive threshold frequency P ═ S + 1)/10.
4. The method of claim 3, wherein: the n wavelet functions are specifically: db4, db6, coif1, coif2 and sym8, n is 5.
5. The method according to claim 1 or 2, wherein the setting of the threshold frequency as the adaptive threshold frequency and then performing adaptive screening according to the vanishing and trending effect criterion W to obtain an adaptive wavelet function specifically comprises:
s501, selecting m wavelet functions, sequentially numbering J from 0 to m-1, and selecting a wavelet function with the number J of 0 from the initial wavelet function;
s502, setting a threshold frequency as the self-adaptive threshold frequency, and performing wavelet analysis and trend item removing processing on the vibration signal containing the trend item by using a J wavelet function to obtain a second signal;
s503, taking the second signal as an input signal, solving a cancellation effect criterion W, and continuously storing a result into an array 6;
s504, adding 1 to the number J of the wavelet function;
s505, repeating S502-S504, and executing for m times;
s506, solving the position C where the minimum value in the array 6 is located, wherein the self-adaptive wavelet function is the Cth wavelet function.
6. The method of claim 5, wherein: the m wavelet functions are specifically: db2, db3, db4, db5, db6, db7, db8, db9, db10, db11, db12, db13, db14, coif1, coif2, coif3, coif4, coif5, sym2, sym3, sym4, sym5, sym6, sym7, and sym8, where m is 25.
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