CN104599676A - Method of eliminating influence of comb-spectrum noise upon vibrational energy level - Google Patents

Abstract

The invention discloses a method of eliminating influence of comb-spectrum noise upon vibrational energy level and aims to solve the technical problem that the existing method of eliminating the comb-spectrum noise is poor in practicality. According to the technical scheme, the method includes: determining related technical parameters, and constructing a corresponding band-pass filter with a Fourier kernel function as a primary function; adding a frequency-shifting factor to obtain a comb band rejection filter which is satisfactory; combining a power spectrum of an original signal and the constructed comb band rejection filter, and filtering, under a frequency domain, periodic interfering components in the original signal; according to post-filtering spectral amplitude, performing calculating to obtain power spectral density, and performing calculating with the power spectral density according to a frequency band to obtain a one-third octave band spectrum. The method has the advantages that interfering signals distributed at equal intervals can be filtered; the vibrational energy level is directly calculated under the frequency domain, repeated testing done for false vibration alarm can be avoided by correcting the false alarm on the vibrational energy level, caused by interfering noise; test cycle can be shortened; the method is highly practical.

Description

Eliminate the method that comb spectrum noise affects vibrational energy level

Technical field

The present invention relates to a kind of method eliminating comb spectrum noise, particularly a kind of method eliminated comb spectrum noise and vibrational energy level is affected.

Background technology

Third-octave spectrum is a kind of frequency-domain analysis method constructed the response characteristic of sound according to people's ear, there is the feature of the few bandwidth of spectral line, be widely used in the analyzing and processing of acoustics and vibration signal, the level value (level/sound level of shaking) of third-octave passes judgment on the leading indicator of vibration noise size.Along with people increase day by day to the concern of noise and vibration, octave method also constantly obtains improvement.The Chinese patent " directly obtaining the method (patent No. is ZL 201110012751.1) with the multi-measuring point variable working condition octave spectrum battle array near operating mode " of authorizing for 2014 has carried out comprehensive review to the present Research of domestic and international octave method, indicate that early-stage Study is mainly improved from computational accuracy and wave filter digitizing standard octave algorithm, directly can only process multi-measuring point list operating mode vibration noise data, octave process can not be carried out exactly to multi-measuring point variable working condition vibration noise data, and propose accordingly a kind of can directly obtain arrange near same operating mode multi-measuring point variable working condition octave spectrum battle array method list measuring point variable working condition octave spectrum battle array and with near operating mode multi-measuring point variable working condition octave spectrum battle array.First block measuring point spectrum battle array and block time matrix is determined, next sets up operating mode time matrix and performance of operating condition mean parameter matrix, determine the start-stop data block block number that each steady working condition is corresponding subsequently again, finally determine single measuring point variable working condition octave spectrum battle array and compose battle array with the multi-measuring point variable working condition octave near operating mode.Compare and original method, the method greatly reduces data processing time, improves treatment effeciency.However, it is normal signal that such third-octave disposal route is all still with test signal, does not comprise premised on obviously interference, thus there is technological deficiency to a certain degree when processing band noise signal.

On-the-spot measured signal often comprises the periodic frequency content caused by the local defect of the such as parts such as gear, bearing, the PERIODIC INTERFERENCE spectral line that even not clear interference source is introduced, if do not carry out process to these periodic interfering frequency compositions just directly calculate vibrational energy level, result of calculation must be caused bigger than normal, the accuracy that impact is passed judgment on, light then revision test, heavy then qualitative be unacceptable product, greatly increase development cost.In order to eliminate PERIODIC INTERFERENCE spectral line, people construct multiple comb filter, and current comb filter is widely applied in mechanical fault diagnosis.The paper " improving the application of pectination envelope-demodulation method in rolling bearing fault diagnosis " being published in periodical coal mine machinery the 31st volume the 2nd phase for 2010 is summarized conventional comb filter building method, point out that Morlet small echo is " clock " shape curve that top magnitude is not 1 under frequency domain, the amplitude that thus can produce signal when filtering changes.Non-flat-top feature like this says the information causing accurately extracting signal spectrum, and filter effect is poor, thus the popularization of method for limiting.And by the wave filter of Fourier Kernel, there is under frequency domain " box-like " feature well, on the basis of this characteristic, just can by the passband bandpass filter that constructs and comb band-pass filter, directly effectively designing can the pectinate band-stop filter device of filtering PERIODIC INTERFERENCE spectral line.

Summary of the invention

In order to overcome the deficiency of the method poor practicability of existing elimination comb spectrum noise.The invention provides a kind of method eliminated comb spectrum noise and vibrational energy level is affected.First the method by observing the distribution situation of pectinate noise in original signal spectrum, determines associated technical parameters, then with the bandpass filter of Fourier kernel function for basis function structure correspondence.On this basis, the pectinate band-stop filter device of requirement is met by adding frequency-shifting operator.Be equivalent to according to convolution the principle that frequency domain is multiplied subsequently, the power spectrum of original signal and the pectinate band-stop filter device that constructs are combined, the periodic interference components under frequency domain in filtering original signal.According to filtered spectral magnitude, calculate power spectrum density, the center frequency value that reference international standard value provides is by Data Placement frequency range, power spectral density value is finally utilized to calculate third-octave spectrum by frequency range, and on this basis judge disappear dry after signal vibrational energy level whether up to standard, practical.

The technical solution adopted for the present invention to solve the technical problems is: a kind of method eliminated comb spectrum noise and affect vibrational energy level, is characterized in comprising the following steps:

Step 1, if original signal is x (t), 0 < t < T.First within the time period [0, T], Fourier transform is carried out to x (t), obtains corresponding frequency domain distribution curve X (ω),

$X\left(\mathrm{\&omega;}\right)={\&Integral;}_0^{T}x\left(t\right)e^{-\mathrm{j\&omega;t}}\mathrm{dt}---\left(1\right)$

Step 2, observes in frequency spectrum whether there is pectinate noise spectral profile.If exist, determine centre frequency and the interval width of periodic noise spectral line according to spectrum distribution, determine the centre frequency f of wave filter _cwith the bandwidth B of wave filter;

Step 3, with Fourier kernel function for basis function structure amplitude is flat top belt bandpass filter s (t) of 1,

$s\left(t\right)=\frac{\sin {\mathrm{\&omega;}}_{0}t}{\mathrm{\&pi;t}}---\left(2\right)$

Wherein, ω ₀the cutoff frequency of>=0 expression institute structural belt bandpass filter.

The frequency domain distribution characteristic that s (t) is corresponding is

$S\left(\mathrm{\&omega;}\right)=\left\{\begin{array}{c}1,\left|\mathrm{\&omega;}\right|\&le;{\mathrm{\&omega;}}_0\\ 0,\mathrm{\&omega;}>{\mathrm{\&omega;}}_0,\mathrm{\&omega;}<-{\mathrm{\&omega;}}_0\end{array}\right.---\left(3\right)$

The comb filter based on Fourier basis function be made up of multiple bandpass filter is constructed by arranging frequency-shifting operator;

To structure fundamental frequency be f _b, bandwidth is 2 ω ₀comb filter h _b(t), then by arranging frequency displacement because obtaining:

$h_b\left(t\right)=\frac{\sin {\mathrm{\&omega;}}_{0}t}{\mathrm{\&pi;t}}\&times;{\mathrm{\&Sigma;}}_{k=1}^n\exp \left(j2\mathrm{\&pi;k}{f}_{b}t\right)---\left(4\right)$

H _ht () can only be f by frequency _band the comb band-pass filter of frequency multiplication.Frequency f _athe passband bandpass filter h of structure in scope _a(t),

$h_a\left(t\right)=\frac{\sin 2\mathrm{\&pi;}(f_a/2)t}{\mathrm{\&pi;t}}\&times;\exp \left(j2\mathrm{\&pi;k}{f}_{a}t\right)---\left(5\right)$

The h obtained will be constructed _a(t) and h _bt (), carries out Fourier conversion and obtains H _a(ω) and H _b(ω).According to the characteristic of Fourier conversion, comb filter H _c(ω)=H _a(ω)-H _b(ω) will only to f _band frequency multiplication produces band-stop response, and to all the other frequency contents, there is bandpass characteristics.

Step 4, be equivalent to according to convolution the principle that frequency domain is multiplied, the signal spectrum W (ω) after comb filtering is by W (ω)=X (ω) × H _c(ω) calculate.

Step 5, calculates power spectrum density G (ω) according to frequency spectrum W (ω)

$G\left(\mathrm{\&omega;}\right)=\frac{2}{T}{\left|W\left(\mathrm{\&omega;}\right)\right|}^2---\left(6\right)$

Obtain thus, with f _ccentered by h frequency range [f of frequency _l, f _u] in, the mean value of power spectrum data is

$a_h=\frac{G\left(\mathrm{\&omega;}\right)}{n}---\left(7\right)$

In formula, n is spectral line number in frequency range.Centre frequency f _ctake from the recommendation of ISO (International Standards Organization) ISO, frequency range bound f _land f _ufollowing relation should be met

$\left\{\begin{array}{c}{f}_c=\sqrt{f_u\&CenterDot;f_l}\\ f_u/f_l=2^{1/3}\end{array}\right.$

If with a ₀for zero shellfish reference value, then a _henergy level be expressed as

L _h＝20log(a _h/a ₀) (9)。

The invention has the beneficial effects as follows: first by observing the distribution situation of pectinate noise in original signal spectrum, determine associated technical parameters, then with the bandpass filter of Fourier kernel function for basis function structure correspondence.On this basis, the pectinate band-stop filter device of requirement is met by adding frequency-shifting operator.Be equivalent to according to convolution the principle that frequency domain is multiplied subsequently, the power spectrum of original signal and the pectinate band-stop filter device that constructs are combined, the periodic interference components under frequency domain in filtering original signal.According to filtered spectral magnitude, calculate power spectrum density, the center frequency value provided with reference to international standard value, by Data Placement frequency range, finally utilizes power spectral density value to calculate third-octave spectrum by frequency range, and judge on this basis to disappear dry after signal vibrational energy level whether up to standard.The undesired signal that the filtering of the method energy is spacedly distributed, and then directly vibrational energy level is calculated under frequency domain, obtain the indeed vibrations energy level of tested body.The vibrational energy level wrong report caused by modifying factor interference noise, avoids, because the revision test brought is reported in vibration by mistake, being conducive to shortening the test period, practical.

Below in conjunction with the drawings and specific embodiments, the present invention is elaborated.

Accompanying drawing explanation

Fig. 1 is that the present invention eliminates the process flow diagram of comb spectrum noise on the method that vibrational energy level affects.

Fig. 2 (a) is the inventive method simulating signal frequency spectrum profile before treatment.

Fig. 2 (b) is pectinate band-stop filter device frequency spectrum profile.

Fig. 2 (c) is the simulating signal spectrogram after filtering process.

Fig. 2 (d) is the octave comparison diagram before and after simulating signal comb filtering.

Fig. 3 (a) is filtering original vibration signal time domain waveform before treatment and spectrogram.

Fig. 3 (b) is the power density spectrum comparison diagram before and after original vibration signal comb filtering.

Fig. 3 (c) is original signal octave and the octave comparison diagram of signal after comb filtering.

Embodiment

With reference to Fig. 1-3 (c).It is as follows that the present invention eliminates the method concrete steps that comb spectrum noise affects vibrational energy level:

Embodiment 1:

This example is the data containing noise at equal intervals obtained according to vibration data and performance data emulation, by carrying out filtering process to the described comb spectrum noise containing being spaced apart 10Hz, and calculates the vibrational energy level after eliminating interference.This analog vibration data sampling frequency is 100Hz, and sampling number is 2048.Third-octave spectrum centre frequency f used _cdistribute as follows,

f _c＝[1,1.25,1.6,2,2.5,3.15,4,5,6.3,8,10,12.5,16,20,25,31.5,40,50]

Concrete steps are as follows:

Step 1, to simulate signal x (t), according to

$X\left(\mathrm{\&omega;}\right)={\&Integral;}_0^{20.47}x\left(t\right)e^{-\mathrm{j\&omega;t}}\mathrm{dt}---\left(1\right)$

Carry out FFT and spectrum analysis, whether the regularity of distribution of observing abnormal spectral line meets the characteristic be spacedly distributed, according to the formation of simulating signal can find its spectrogram 10,20,30,40Hz punishment is furnished with equally spaced spectral line, and amplitude is much larger than the value of all the other frequency ranges.Can think to there is pectinate noise in signal, it may be necessary comb filter and noise filtering is carried out to it.

Step 2, the centre frequency f of the spectral line frequency corresponding according to comb spectrum in simulating signal frequency spectrum and interval width determination bandpass filter _c=10,20,30,40Hz, bandwidth B=2Hz, based on Fourier basis function, structure amplitude is the flat top belt bandpass filter of 1, may be defined as

$s\left(t\right)=\frac{\sin {\mathrm{\&omega;}}_{0}t}{\mathrm{\&pi;t}}---\left(2\right)$

Wherein cutoff frequency ω ₀>=0, ω in this simulating signal ₀=2 π.Because s (t) is the symmetric function of independent variable zero crossing, calculate if directly get t=0, correct numerical solution cannot be obtained, and then clear and definite proposition in the present invention operating limit method can solve, namely

$s\left(0\right)={\lim }_{t\&RightArrow;0}s\left(t\right)=\frac{2{\mathrm{\&omega;}}_0}{2\mathrm{\&pi;}}=2---\left(3\right)$

Step 3, on the bandpass filter basis that step 2 designs, arrange 10,20,30, frequency-shifting operator exp (j2 π the k10t) (j=1 of 40Hz, 2,3,4), the comb band-pass filter based on Fourier basis function corresponding with core frequency is at equal intervals constructed, wherein containing four passbands, namely

$h_b\left(t\right)=\frac{\sin 2\mathrm{\&pi;t}}{\mathrm{\&pi;t}}\&times;{\mathrm{\&Sigma;}}_{k=1}^n\exp \left(j2\mathrm{\&pi;k}{f}_{b}t\right)---\left(4\right)$

Now designed wave filter h _bt () can only be the comb spectrum of 2Hz by width near 10,20,30,40Hz.Retain all the other signals in order to these frequency band signals of filtering, the passband bandpass filter of a width at 0 ~ 46Hz can be constructed within the scope of the analysis frequency of 0 ~ 50Hz

$h_a\left(t\right)=\frac{\sin 2\mathrm{\&pi;}(46/2)t}{\mathrm{\&pi;t}}---\left(5\right)$

Next, to h _a(t) and h _b(t) according to

$H_a\left(\mathrm{\&omega;}\right)={\&Integral;}_0^{20.47}{h}_a\left(t\right)e^{-\mathrm{j\&omega;t}}\mathrm{dt}---\left(6\right)$

$H_b\left(\mathrm{\&omega;}\right)={\&Integral;}_0^{20.47}{h}_b\left(t\right)e^{-\mathrm{j\&omega;t}}\mathrm{dt}---\left(7\right)$

Carry out FFT, finally obtain respective spectrum distribution H _a(ω) and H _b(ω).

According to Fourier conversion characteristic, by under frequency domain according to

H _c(ω)＝H _a(ω)-H _b(ω) (8)

Just can obtain the pectinate band-stop filter device under frequency domain.

Step 4, is obtaining the spectrum H of pectinate band-stop filter device _c(ω), after, be equivalent to according to convolution the principle that frequency domain is multiplied, filtering can directly complete under frequency domain, that is:

W(ω)＝X(ω)×H _c(ω) (9)

Thus obtain the signal spectrum W (ω) after filtering noise, can find out with reference to Fig. 2 (b), periodically spectral line is obviously suppressed.

Step 5, according to power spectrum density computing formula, the length obtaining filtered signal in duration 20.47s is the power spectral density value G of 1024 ₂sequence,

G ₂＝[6.2e-6,1.7e-5,…,5.5e-11,1.3e-10,…,2.0e-10] (10)

Similar with it, the length using same procedure can obtain original signal is the power spectral density value G of 1024 ₁sequence,

G ₁＝[6.2e-6,1.7e-5,…,1.4e-3,1.9e-3,…,2.0e-10] (11)

Then in the analysis frequency of 1 ~ 40Hz, the average decibel value of two groups of power spectral density value in each centre frequency section is respectively with wherein n is the spectral line number in each centre frequency section, is specifically distributed as

n＝[5,7,8,11,13,17,21,27,34,41,51,71,82,102,133,174] (12)

If with a ₀=3*10 ^-4for zero shellfish reference value, then original signal L ₁with filtered signal L ₂vibrational energy level be

L ₁＝20log(a _h1/a ₀) (13)

L ₂＝20log(a _h2/a ₀) (14)

By being contrasted one by one by the vibrational energy level sequential value of two groups of signals, can verify that the vibration of filtered signal decreases.Clearly can see that from Fig. 2 (d) vibrational energy level obtains significant suppression in the 3rd centre frequency section reciprocal.

Embodiment 2:

The power test of propulsion system completely examines the most effective research technique of propulsion system performance by land.Once a certain performance assessment criteria is not up to standard, test of gently then reforming, increase cost, delay progress, heavy then qualitative be unacceptable product, cause heavy economic losses to factory.Vibration, as one of most important performance assessment criteria of power test, by the restriction of on-the-spot test condition, inevitably comprises various interference in vibration survey data.

In certain site test, the continuous power test evaluation point vibration signal several times wherein in a period of time all includes the PERIODIC INTERFERENCE being spaced apart 100Hz.Propulsion machine motion-activated frequency equals engine and turns point several times frequently or integral multiple, when a turn frequency for engine changes, the mechanical motion excitation frequency of propulsion system is inevitable to be changed thereupon, therefore, judge that the spike bunch of evaluation point rumble spectrum is not encouraged by the mechanical motion of tool component to produce, but come from external interference source.In order to avoid revision test, save testing expenses, must assess the impact of interference.

Step 1, original signal strength is 128010, sample frequency 25600Hz.First FFT is carried out to it, obtain frequency domain spectral line X (ω), that is:

$X\left(\mathrm{\&omega;}\right)={\&Integral;}_0^{T}x\left(t\right)e^{-\mathrm{j\&omega;t}}\mathrm{dt}---\left(1\right)$

Wherein duration be about 5s.Can find by observing, the pectination interference spectral line in problem is concentrated and is appeared in the scope of 4500Hz ~ 6100Hz, there is the spectral line at equal intervals of about 100Hz, thus mainly will take filtering process for this segment data and be analyzed.

Step 2, in conjunction with spectral profile, determines each centre frequency f of comb filter _c=4547Hz, 4647Hz ..., 6047Hz, bandwidth B=20Hz.Fourier basis function is utilized to construct the bandpass filter met the demands on this basis wherein filter cutoff frequency ω ₀=5*2 π, then obtain s (0)=10 according to limit algorithm.

Step 3, on the basis of constructed bandpass filter, by adding the frequency-shifting operator exp (j2 π k100t) of 100Hz, can obtain the bandpass filter corresponding with centre frequency

$h_b\left(t\right)=\frac{\sin 10\mathrm{\&pi;t}}{\mathrm{\&pi;t}}\&times;\exp (2\mathrm{\&pi;}*4547*t)\&times;{\mathrm{\&Sigma;}}_{k=1}^n\exp \left(j2\mathrm{\&pi;k}100t\right)---\left(2\right)$

In formula, n is the pectination spectral line number in 4500Hz ~ 6100Hz frequency range.

In order to obtain trying to achieve pectinate band-stop filter device further, within the scope of the analysis frequency of 4500 ~ 6100Hz, construct the passband bandpass filter of a width at 4500 ~ 6100Hz

$h_a\left(t\right)=\frac{\sin 2\mathrm{\&pi;}(1500/2)t}{\mathrm{\&pi;t}}\&times;\exp (2\mathrm{\&pi;}*4500*t)---\left(3\right)$

Still utilize Fourier to convert subsequently, obtain the frequency domain distribution of two wave filters

$H_a\left(\mathrm{\&omega;}\right)={\&Integral;}_0^T{h}_a\left(t\right)e^{-\mathrm{j\&omega;t}}\mathrm{dt}---\left(4\right)$

$H_b\left(\mathrm{\&omega;}\right)={\&Integral;}_0^T{h}_b\left(t\right)e^{-\mathrm{j\&omega;t}}\mathrm{dt}---\left(5\right)$

Pass through H _c(ω)=H _a(ω)-H _b(ω) relation, just can be met the rejection filter H of requirement _c(ω) frequency domain representation.

Step 4, is obtaining H _c(ω), after, be equivalent to according to convolution the principle that frequency domain is multiplied, filtering by the realization that is multiplied under frequency domain,

W(ω)＝X(ω)×H _c(ω) (6)

After obtaining the frequency domain distribution W after filtering out interference (ω), just can calculate the power spectral density value of corresponding frequency spectrum further and its original signal power spectral density value with non-filtered is contrasted in Fig. 3 (b).

Step 5, finally according to power spectral density value and third-octave frequency domain algorithm

$a_h=\frac{G\left(\mathrm{\&omega;}\right)}{n}---\left(7\right)$

L＝20log(a _h/a ₀) (8)

Calculate the vibrational energy level of filtered signal, and its vibrational energy level with the original signal of non-filtered is contrasted in Fig. 3 (c).

By carrying out institute's image data effectively analyzing rear discovery, the vibrational energy level calculated after eliminating PERIODIC INTERFERENCE meets corresponding standard, avoids test of reforming, has saved testing expenses, shortened the test period, has proved the validity of this invention simultaneously.

Claims (1)

1. eliminate the method that comb spectrum noise affects vibrational energy level, it is characterized in that comprising the following steps:

Step 1, if original signal is x (t), 0 < t < T; First within the time period [0, T], Fourier transform is carried out to x (t), obtains corresponding frequency domain distribution curve X (ω),

$X\left(\mathrm{\&omega;}\right)={\&Integral;}_0^{T}x\left(t\right)e^{-\mathrm{j\&omega;t}}\mathrm{dt}---\left(1\right)$

Step 2, observes in frequency spectrum whether there is pectinate noise spectral profile; If exist, determine centre frequency and the interval width of periodic noise spectral line according to spectrum distribution, determine the centre frequency f of wave filter _cwith the bandwidth B of wave filter;

Step 3, with Fourier kernel function for basis function structure amplitude is flat top belt bandpass filter s (t) of 1,

$s\left(t\right)=\frac{\sin {\mathrm{\&omega;}}_{0}t}{\mathrm{\&pi;t}}---\left(2\right)$

Wherein, ω ₀the cutoff frequency of>=0 expression institute structural belt bandpass filter;

The frequency domain distribution characteristic that s (t) is corresponding is

$S\left(\mathrm{\&omega;}\right)=\left\{\begin{array}{c}1,\left|\mathrm{\&omega;}\right|\&le;{\mathrm{\&omega;}}_0\\ 0,\mathrm{\&omega;}>{\mathrm{\&omega;}}_0,\mathrm{\&omega;}<-{\mathrm{\&omega;}}_0\end{array}\right.---\left(3\right)$

The comb filter based on Fourier basis function be made up of multiple bandpass filter is constructed by arranging frequency-shifting operator;

To structure fundamental frequency be f _b, bandwidth is 2 ω ₀comb filter h _b(t), then by arranging frequency displacement because obtaining:

$h_b\left(t\right)=\frac{\sin {\mathrm{\&omega;}}_{0}t}{\mathrm{\&pi;t}}\&times;{\mathrm{\&Sigma;}}_{k=1}^n\exp \left(j2\mathrm{\&pi;k}{f}_{b}t\right)---\left(4\right)$

H _bt () can only be f by frequency _band the comb band-pass filter of frequency multiplication; Frequency f _athe passband bandpass filter h of structure in scope _a(t),

$h_a\left(t\right)=\frac{\sin 2\mathrm{\&pi;}(f_a/2)t}{\mathrm{\&pi;t}}\&times;\exp \left(j2\mathrm{\&pi;k}{f}_{a}t\right)---\left(5\right)$

The h obtained will be constructed _a(t) and h _bt (), carries out Fourier conversion and obtains H _a(ω) and H _b(ω); According to the characteristic of Fourier conversion, comb filter H _c(ω)=H _a(ω)-H _b(ω) will only to f _band frequency multiplication produces band-stop response, and to all the other frequency contents, there is bandpass characteristics;

Step 4, be equivalent to according to convolution the principle that frequency domain is multiplied, the signal spectrum W (ω) after comb filtering is by W (ω)=X (ω) × H _c(ω) calculate;

Step 5, calculates power spectrum density G (ω) according to frequency spectrum W (ω)

$G\left(\mathrm{\&omega;}\right)=\frac{2}{T}{\left|W\left(\mathrm{\&omega;}\right)\right|}^2---\left(6\right)$

Obtain thus, with f _ccentered by h frequency range [f of frequency _l, f _u] in, the mean value of power spectrum data is

$a_h=\frac{G\left(\mathrm{\&omega;}\right)}{n}---\left(7\right)$

In formula, n is spectral line number in frequency range; Centre frequency f _ctake from the recommendation of ISO (International Standards Organization) ISO, frequency range bound f _land f _ufollowing relation should be met

$\left\{\begin{array}{c}{f}_c=\sqrt{f_u\&CenterDot;f_l}\\ f_u/f_l=2^{1/3}\end{array}\right.---\left(8\right)$

If with a ₀for zero shellfish reference value, then a _henergy level be expressed as

L _h＝20log(a _h/a ₀) (9)。