CN111490753A - Design method of low-pass filter for collecting characteristic signals of rotating equipment - Google Patents
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Abstract
The invention discloses a design method of a low-pass filter for collecting characteristic signals of rotating equipment, which comprises the following steps: s1, acquiring a characteristic signal of the rotating equipment, a highest frequency component needing to be reserved for low-pass filtering and a lowest frequency component needing to be filtered; s2, designing a group of low-pass filters according to the highest frequency component required to be reserved and the lowest frequency component required to be filtered; s3, respectively filtering the characteristic signals of the rotating equipment by adopting a low-pass filter, and determining an optimal low-pass filter and a corresponding differential equation thereof; and S4, establishing a low-pass filter difference equation comparison table under different filtering requirements. The invention avoids the problem that the derivation of the analog filter is difficult to solve when converting the digital filter, and simultaneously optimizes the current situation that two parameters of the passband cut-off frequency and the stopband cut-off frequency of the filter are selected by depending on experience in the prior art; and a difference equation comparison table is established, so that the difference equation of the corresponding filter can be directly selected when the actual engineering needs, and the purposes of high efficiency and strong feasibility are achieved.
Description
Technical Field
The invention relates to the technical field of filters, in particular to a design method of a low-pass filter for collecting characteristic signals of rotating equipment.
Background
Digital filtering of signals/data is generally a prerequisite and fundamental for signal processing, and useful components in the filtered signals can be more prominent in the characteristics of the signals. When the fault diagnosis of the rotating equipment is carried out, noise influence such as vibration signals, frequency multiplication components of current signals and the like are effectively removed or suppressed in real time through a digital filter, and the fault diagnosis method has important significance for further researching the fault characteristics of the rotating equipment.
The digital filter can be generally classified into: infinite Impulse Response (IIR) digital filters and Finite Impulse Response (FIR) digital filters; the method can be divided into the following steps according to different amplitude-frequency response characteristics: low-pass digital filters, high-pass digital filters, band-stop digital filters, and the like. Compared with a finite-length impulse response (FIR) digital filter, the design method of the infinite-length impulse response (IIR) digital filter utilizes the research result of an analog filter, is simple and effective, and can obtain good amplitude characteristics.
The main idea of designing an Infinite Impulse Response (IIR) digital filter is to design an analog filter meeting the conditions according to the design indexes of the filter and then convert the analog filter into a digital filter. The design method has standard formula steps, but in practical application, how to meet the real-time requirement and obtain the digital analytic formula still hopes to simplify the problems: the design steps are integrated into a generalized formula, so that the corresponding filter difference equation can be obtained by directly substituting the formula according to the actual signal frequency component and the filtering requirement. However, in the derivation process, the step of converting the analog filter into the digital filter by the impulse response invariant method or the bilinear transformation method is difficult to implement, and the higher order filter is difficult to convert, so that the generalized formula cannot be solved due to complex calculation. In addition, there is no general method for selecting two parameters of the passband cut-off frequency and the stopband cut-off frequency of the optimal low-pass filter according to actual needs to achieve a good filtering effect.
In summary, how to provide a technical solution with high efficiency and strong feasibility under different signal frequency components and filtering requirements is a problem to be solved by those skilled in the art.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a design method of a low-pass filter for acquiring a characteristic signal of rotating equipment.
The design method of the low-pass filter for collecting the characteristic signal of the rotating equipment comprises the following steps:
s1, acquiring a characteristic signal of the rotating equipment, a highest frequency component needing to be reserved for low-pass filtering and a lowest frequency component needing to be filtered;
s2, designing a group of low-pass filters according to the highest frequency component needing to be reserved and the lowest frequency component needing to be filtered of the low-pass filter obtained in the step S1;
s3, respectively filtering the characteristic signals of the rotating equipment by adopting the low-pass filter designed in the step S2, and determining an optimal low-pass filter and a corresponding difference equation thereof according to the filtering result;
and S4, repeating the steps S1, S2 and S3, and establishing a low-pass filter difference equation comparison table under different filtering requirements.
Preferably, in step S1, the acquisition of the highest frequency component that needs to be retained and the lowest frequency component that needs to be filtered by the low-pass filtering are artificially set according to actual needs.
Preferably, in step S2, a set of low-pass filters is designed according to the highest frequency component required to be retained and the lowest frequency component required to be filtered by the low-pass filtering acquired in step S1 by a cyclic frequency search method.
Preferably, in step S3, the specific step of determining the optimal low-pass filter and the corresponding difference equation is: and (4) respectively filtering the characteristic signals of the rotating equipment by adopting a group of low-pass filters designed in the step (S2), carrying out fast Fourier transform on the filtered signals, comparing amplitudes of the filtered signals at the highest frequency component required to be reserved and the lowest frequency component required to be filtered by different low-pass filters, and determining the optimal low-pass filter and a corresponding differential equation thereof by combining the order of the low-pass filter.
Preferably, in step S1, after acquiring the rotating device characteristic signal, the highest frequency component that needs to be retained by low-pass filtering, and the lowest frequency component that needs to be filtered out, the method further includes the steps of: the passband maximum attenuation and the stopband minimum attenuation of the low-pass filter are set empirically.
Preferably, the method for designing the low-pass filter for acquiring the characteristic signal of the rotating equipment comprises the following steps:
s1', acquiring the characteristic signal of the rotating equipment, the highest frequency component required to be reserved for low-pass filtering and the lowest frequency component required to be filtered, and then setting the maximum attenuation of a pass band and the minimum attenuation of a stop band according to experience;
s2 ', according to the highest frequency component needing to be reserved, the lowest frequency component needing to be filtered, the set maximum attenuation of the pass band and the set minimum attenuation of the stop band of the low-pass filtering acquired in the step S1', a group of low-pass filters are designed through a cyclic frequency search method;
s3 ', respectively filtering the rotating equipment characteristic signals by adopting the low-pass filter designed in the step S2', and determining the optimal low-pass filter and the corresponding difference equation thereof according to the filtering result;
and S4 ', repeating the steps S1', S2 'and S3', and establishing a comparison table of low-pass filter difference equations under different filtering requirements.
Preferably, in step S2 ″, the designing of the set of low-pass filters specifically includes the following steps: generating a set of pass band cut-off frequency parameters and a set of stop band cut-off frequency parameters according to the highest frequency component required to be reserved and the lowest frequency component required to be filtered in the low-pass filtering acquired in the step S1 by a cyclic frequency search method, then designing a set of low-pass analog filters by combining the set pass band maximum attenuation and stop band minimum attenuation, and then converting the low-pass analog filters into a set of low-pass digital filters.
Preferably, the method for determining the optimal low-pass filter and the corresponding difference equation thereof according to the filtering processing result is determined by comparing the filtering effect and combining the filter order comprehensive consideration.
Preferably, the analog filter is a butterworth filter, and the method of conversion is a bilinear transformation method.
Compared with the prior art, the invention has the following beneficial effects:
according to the invention, a group of low-pass filters are designed by a cyclic frequency search method according to the highest frequency component required to be reserved for low-pass filtering, the lowest frequency component required to be filtered and the set maximum attenuation of a pass band and the minimum attenuation of a stop band of the low-pass filters, the optimal filters meeting the requirements and the corresponding difference equations thereof are selected, and then a comparison table of the difference equations of the low-pass filters under different filtering requirements is established to facilitate the actual engineering requirements, so that the problem that the derivation of an analog filter and the conversion of a digital filter are difficult to solve is avoided, and the current situation that two parameters of the pass band cut-off frequency and the stop band cut-off frequency of; the establishment of the comparison table of the differential equations is convenient for directly selecting the corresponding filter differential equations when in actual engineering needs, thereby achieving the purposes of high efficiency and strong feasibility.
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FIG. 1 is a flow chart of a design method of the present invention;
fig. 2 is a schematic diagram of the amplitude characteristic of the low-pass filter according to the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the accompanying drawings and the specific embodiments, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
Referring to fig. 1, the method for designing a low-pass filter for collecting a characteristic signal of a rotating device according to this embodiment includes the following steps:
s1', acquiring characteristic signals of the rotating equipment, the highest frequency component needing to be reserved for low-pass filtering, the lowest frequency component needing to be filtered, the maximum attenuation of a pass band and the minimum attenuation of a stop band;
it should be noted here that the acquired characteristic signal of the rotating equipment contains various frequency components, such as power frequency, frequency multiplication, noise, and other components, and these unimportant components need to be filtered out in the actual fault diagnosis, and only useful components are retained for analysis, which is the purpose of low-pass filtering; the purpose of acquiring the highest frequency component required to be reserved and the lowest frequency component required to be filtered in the low-pass filtering is to acquire the upper frequency limit required to be reserved and the lower frequency limit required to be filtered; the maximum attenuation of the passband and the minimum attenuation of the stopband are set by human experience;
s2 ', according to the highest frequency component needing to be reserved, the lowest frequency component needing to be filtered, the set maximum attenuation of the pass band and the set minimum attenuation of the stop band of the low-pass filtering acquired in the step S1', a group of low-pass filters are designed through a cyclic frequency search method;
it should be noted that, in the embodiment of the present invention, a set of passband cutoff frequency parameters and a set of stopband cutoff frequency parameters are generated by the cyclic frequency search method according to the highest frequency component required to be retained and the lowest frequency component required to be filtered by low-pass filtering, and are used to design a low-pass filter, and then a set of butterworth low-pass analog filters are designed by combining the set passband maximum attenuation and the set stopband minimum attenuation, and are converted into a set of low-pass digital filters by using a bilinear transformation method;
s3 ', respectively filtering the rotating equipment characteristic signals by adopting the low-pass filter designed in the step S2', comparing the filtering effect and combining the filter order, and determining the optimal low-pass filter and the corresponding difference equation under the current filtering requirement;
and S4 ', repeating the steps S1', S2 'and S3', and establishing a comparison table of low-pass filter difference equations under different filtering requirements.
It should be noted that different filtering requirements refer to the difference between the highest frequency component that needs to be retained and the lowest frequency component that needs to be filtered out in the low-pass filtering.
In order to quickly acquire a proper low-pass filter as required in actual engineering, the invention adjusts the highest frequency component which needs to be reserved and the lowest frequency component which needs to be filtered out by low-pass filtering for many times according to the filtering requirement under the normal condition, and repeats the steps to obtain a low-pass filter difference equation comparison table expanded by the optimal filter difference equation so as to directly acquire the proper low-pass filter from the comparison table as required.
According to the invention, a group of low-pass filters are designed by a cyclic frequency search method according to the highest frequency component required to be reserved for low-pass filtering, the lowest frequency component required to be filtered and set parameters (maximum attenuation of a pass band and minimum attenuation of a stop band), the optimal filter meeting the requirements and the corresponding differential equation thereof are selected and determined from the low-pass filters, and then a low-pass filter differential equation comparison table under different filtering requirements is established, so that the actual engineering requirements are facilitated, the problem that the derivation of an analog filter conversion digital filter is difficult to solve is avoided, and the current situation that two parameters of the pass band cut-off frequency and the stop band cut-off frequency of the filter are usually selected by experience; the establishment of the difference equation comparison table is beneficial to the staff to simply, conveniently and efficiently obtain the required filter, and the feasibility is strong.
Referring to fig. 2, the amplitude characteristic of the low pass filter is shown. Where H (f) is the filter system transfer function, fpIs the passband cut-off frequency, fsIs the stop band cut-off frequency, fcIs the sampling frequency;pis the amplitude of the passband ripple and,sis the stop band ripple amplitude (both a factor less than 1). The pass band frequency range is more than or equal to 0 and less than or equal to fpRequiring (1) in the pass bandp) Less than | H (f) | less than or equal to 1; stop band frequency range of fs≤f≤(fcPer 2), in the stop band, the requirement is that | H (f) | is less than or equal tos. From fpTo fsReferred to as the transition zone, is generally monotonically decreasing.
Wherein f isp、fsThe closer the distance, the narrower the transition band of the filter and the higher the order of the filter. For signals with the highest frequency components needing to be reserved and the lowest frequency components needing to be filtered out, the closer the two parameters are set, the better the two parameters are; for signals with the highest frequency to be preserved and the lowest frequency to be filtered away, the two parameters are not necessarily set so close, becauseThe narrower the transition band and the higher the filter order, the larger the amount of calculation required, and the two cannot be brought into infinite proximity in the actual simulation. While the pass band cut-off frequency f is chosen to be optimal for the characteristics of the signal to be processedpStop band cut-off frequency fsAnd then the optimal filter under the current signal processing requirement is obtained, at present, the optimal filter is mainly selected by experience, and a general method is not available.
The embodiment of the invention provides a design method of a low-pass filter for collecting a characteristic signal of rotating equipment, which comprises the following steps of after acquiring the characteristic signal of the rotating equipment, a highest frequency component needing to be reserved for low-pass filtering and a lowest frequency component needing to be filtered, designing a group of low-pass filters by a cyclic frequency search method, and specifically comprising the following steps:
according to the filtering requirement of the current rotating equipment characteristic signal, the highest frequency component needing to be reserved is set as fhF is the lowest frequency component to be filteredlBecause of the low pass filtering, f is necessaryl＞fhWith fhAs passband cut-off frequency fpAt the start of the cycle of (c) in the form of [ (f)h+fl)/2-2]Hz is taken as the terminal point, 1Hz (optionally 0.5Hz or less if the precision is higher) is taken as the step length to sequentially increase and generate a passband cut-off frequency array [ fh,fh+1,fh+2,…,(fh+fl)/2-3,(fh+fl)/2-2](ii) a With flAs stop band cut-off frequency fsAt the start of the cycle of (c) in the form of [ (f)h+fl)/2+2]Hz is taken as the terminal point, 1Hz (optionally 0.5Hz or less if the precision is higher) is taken as the step length to sequentially decrease to generate a stop band cut-off frequency array [ fl,fl-1,fl-2,…,(fh+fl)/2+3,(fh+fl)/2+2]. Taking a pair of f of two arrays of identical index positions each timep、fsA low pass filter is designed and a set of digital filters is finally obtained.
In selecting the type of low pass filter, the design method of an Infinite Impulse Response (IIR) digital filter utilizes the Finite Impulse Response (FIR) digital filter as compared to the FIR digital filterThe research result of the analog filter is simple and effective in design method, good amplitude characteristics can be obtained, and particularly, a bilinear transformation method is popular because of no spectrum aliasing, so that an IIR digital filter is used. The method comprises the steps of firstly converting the technical index of a low-pass filter into the corresponding technical index of an analog filter, then designing the analog filter meeting the technical index, and finally converting the designed analog filter into a digital filter meeting the technical index. When designing the low-pass filter, the analog filter is a Butterworth filter, and the method used for converting the analog filter into the digital filter is a bilinear transformation method. Technical indicators of analog low-pass filters are: cut-off angular frequency omega of pass bandpStop band cut-off angular frequency omegas: the two angular frequencies can be respectively determined by the cut-off frequency f of the digital technical index passbandpStop band cut-off frequency fsCalculated, pass band maximum attenuation αpMinimum stop band attenuation αsBoth of which are set by human experience.
The following is a design method of a low-pass filter used in the embodiment of the present invention, and the specific steps are as follows:
firstly, solving the cutoff frequency omega of the analog domain passband by adopting a bilinear transformation methodpAnalog stop band cut-off frequency omegas。
Wherein T is a sampling period, and T is 1/fc，fcIs the sampling frequency.
And (3) solving the order N of the filter according to the passband and stopband cutoff frequency of the analog domain obtained by the formulas (1) and (2) in combination with the maximum attenuation of the passband and the minimum attenuation of the stopband.
λsp＝Ωs/Ωp(3)
Solving for the 3dB cutoff frequency omega according to the stop band cutoff frequency and the stop band minimum attenuation obtained by the formula (2)c。
The pole s of the analog filter is obtained from the 3dB cutoff frequency obtained from equation (6) and the filter order obtained from equation (5)kAnd determining the system function H of the analog filter based on the polesa(s)。
Wherein the content of the first and second substances,
transfer function H of analog filter by bilinear transformation methoda(s) conversion to a low pass filter transfer function H (z):
the design method of the low-pass filter for collecting the characteristic signal of the rotating equipment provided by the embodiment of the invention can further comprise the following steps after the group of filters are obtained through the steps:
and correspondingly recording to obtain a group of orders corresponding to each filter, filtering the rotating equipment characteristic signals by using each filter to obtain a group of filtered signals, and performing fast Fourier transform on each filtered signal to obtain a frequency spectrum.
In the present invention, since it is desired to ensure the relation fhAnd signal components of frequencies below f, and filtering out f as much as possiblelAnd signals of frequencies above itThe order of the low-pass filter is kept from being too high (after a certain degree, the improvement of the order of the filter is not obvious to improve the filtering effect and the calculation amount is increased), so that the low-pass filter designed in the foregoing needs to be compared with the f in the frequency spectrumhRetention of amplitude at frequency component, for flAnd (3) filtering the amplitude at the frequency component, combining the order of the filter, selecting the filter which is most suitable for the current filtering requirement from the group of filters, and obtaining a corresponding filter difference equation.
In order to quickly obtain a proper low-pass filter as required in practical engineering, the highest frequency component f to be reserved is usually required to be reserved according to different filtering requirements (the frequency components to be reserved and filtered in the low-pass filtering are different)hTaking 20Hz as a starting point, 110Hz as an end point, and taking 10Hz as a step length to increase progressively; at fhFixed, lowest frequency component f to be filteredlWith (f)h+10) Hz as the starting point, 120Hz as the end point, and 10Hz as the step length for increasing progressively; the highest frequency component f to be reserved in the cyclic frequency search method is adjusted for multiple timeshAnd the lowest frequency component f to be filteredlAnd repeating the steps of designing and optimally selecting the filter, wherein the embodiment determines the parameters and difference equations of the low-pass filter under different filtering requirements, and provides a comparison table of the difference equations of the low-pass filter under different requirements (see attached table 1-attached table 10), wherein fhFor the highest frequency component (unit: Hz), f, to be retainedlFor the lowest frequency component (unit: Hz), f, to be filteredlThe contents in the corresponding (x, y, z) format in the column represent: x-passband cut-off frequency f corresponding to the optimum low-pass filterp(unit: Hz), y-corresponds to the stopband cut-off frequency f of the optimum low-pass filters(unit: Hz), z-corresponds to the order N of the optimal low-pass filter. Such a look-up table can basically meet the requirements of filtering components such as power frequency, frequency multiplication, noise and the like in actual engineering, and when low-pass filtering needs to be carried out on rotating equipment characteristic signals in the actual engineering problem, the low-pass filtering can be directly selected according to the requirements, so that the purposes of high efficiency and strong feasibility are achievedThe purpose of (1).
Attached Table 1 fhDifference equation comparison table under 20Hz
Attached Table 2 fhDifference equation comparison table under 30Hz
Attached Table 3 fhDifference equation comparison table under 40Hz
Attached table 4 fhComparison table of difference equation at 50Hz
Attached table 5 fhDifference equation comparison table under 60Hz
Attached table 6 fhDifference equation comparison table under 70Hz
Attached table 7 fhDifference equation comparison table under 80Hz
Attached table 8 fhComparison table of difference equation at 90Hz
Attached Table 9 is fhDifference equation comparison table at 100Hz
Attached table 10 fhDifference equation comparison table under 110Hz
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
Claims (9)
1. The design method of the low-pass filter for collecting the characteristic signal of the rotating equipment is characterized by comprising the following steps of:
s1, acquiring a characteristic signal of the rotating equipment, a highest frequency component needing to be reserved for low-pass filtering and a lowest frequency component needing to be filtered;
s2, designing a group of low-pass filters according to the highest frequency component needing to be reserved and the lowest frequency component needing to be filtered of the low-pass filter obtained in the step S1;
s3, respectively filtering the characteristic signals of the rotating equipment by adopting the low-pass filter designed in the step S2, and determining an optimal low-pass filter and a corresponding difference equation thereof according to the filtering result;
and S4, repeating the steps S1, S2 and S3, and establishing a low-pass filter difference equation comparison table under different filtering requirements.
2. The method of claim 1, wherein in step S1, the highest frequency component to be retained and the lowest frequency component to be filtered are obtained by the low-pass filtering, which is manually set according to actual needs.
3. The method of claim 1, wherein in step S2, a set of low pass filters is designed according to the highest frequency component required to be retained and the lowest frequency component required to be filtered out in the low pass filtering obtained in step S1 by a cyclic frequency search method.
4. The method of claim 1, wherein in step S3, the specific steps of determining the optimal low-pass filter and the corresponding difference equation are as follows: and (4) respectively filtering the characteristic signals of the rotating equipment by adopting a group of low-pass filters designed in the step (S2), carrying out fast Fourier transform on the filtered signals, comparing amplitudes of the filtered signals at the highest frequency component required to be reserved and the lowest frequency component required to be filtered by different low-pass filters, and determining the optimal low-pass filter and a corresponding differential equation thereof by combining the order of the low-pass filter.
5. The method for designing a low pass filter for collecting a rotating equipment characteristic signal according to claim 1, wherein in step S1, after obtaining the rotating equipment characteristic signal, the highest frequency component to be retained for low pass filtering and the lowest frequency component to be filtered, the method further comprises the steps of: the passband maximum attenuation and the stopband minimum attenuation of the low-pass filter are set empirically.
6. The method for designing a low-pass filter for acquiring a rotating apparatus signature signal as claimed in claim 5, wherein the method comprises the steps of:
s1', acquiring the characteristic signal of the rotating equipment, the highest frequency component required to be reserved for low-pass filtering and the lowest frequency component required to be filtered, and then setting the maximum attenuation of a pass band and the minimum attenuation of a stop band according to experience;
s2 ', according to the highest frequency component needing to be reserved, the lowest frequency component needing to be filtered, the set maximum attenuation of the pass band and the set minimum attenuation of the stop band of the low-pass filtering acquired in the step S1', a group of low-pass filters are designed through a cyclic frequency search method;
s3 ', respectively filtering the rotating equipment characteristic signals by adopting the low-pass filter designed in the step S2', and determining the optimal low-pass filter and the corresponding difference equation thereof according to the filtering result;
and S4 ', repeating the steps S1', S2 'and S3', and establishing a comparison table of low-pass filter difference equations under different filtering requirements.
7. The method as claimed in claim 6, wherein the step S2 "includes the following steps: generating a set of pass band cut-off frequency parameters and a set of stop band cut-off frequency parameters according to the highest frequency component required to be reserved and the lowest frequency component required to be filtered in the low-pass filtering acquired in the step S1 by a cyclic frequency search method, then designing a set of low-pass analog filters by combining the set pass band maximum attenuation and stop band minimum attenuation, and then converting the low-pass analog filters into a set of low-pass digital filters.
8. The method for designing a low-pass filter for acquiring a signature signal of a rotating device according to claim 1 or 6, wherein the optimal low-pass filter and the corresponding difference equation are determined by comparing filtering effects and considering filter orders comprehensively according to the filtering processing results.
9. The method of claim 6, wherein the analog filter is a butterworth filter, and the method of conversion is a bilinear transform.
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Application publication date: 20200804 |