CN107832261A - A kind of quantitative extracting method of non-stationary exhaust noise signal order based on wavelet transformation - Google Patents
A kind of quantitative extracting method of non-stationary exhaust noise signal order based on wavelet transformation Download PDFInfo
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Abstract
A kind of quantitative extracting method of non-stationary exhaust noise signal order based on wavelet transformation, including：1) speed curves, and time series corresponding to acquisition are calculated by rotational speed pulse signal；2) speed curves are smoothed using cubic spline curve, obtain smooth speed curves；3) the standard adding window wavelet function calculated for correlating transforms is established；4) time domain correlating transforms are carried out to non-stationary exhaust noise signal using adding window wavelet function, obtains the time domain fluctuation signal of each order；5) sound pressure level conversion is carried out to time domain order fluctuation signal, obtains each order sound pressure level curve.The present invention can overcome the problems such as spectrum leakage, order aliasing；Simplify the process of order extraction；Realize that more accurately sound quality is analyzed；The time domain fluctuation signal of each order component can carry out independent assortment, while can be exchanged into order sound pressure level, so as to be laid the foundation for exhaust noise product Quality Research and different structure soundproof effect Comparative and Quantitative Analysis.
Description
Technical field
The present invention relates to a kind of nonstationary noise signal order analysis processing method, particularly automobile exhaust under accelerating mode
The quantitative extracting method of the time domain order of noise signal.
Background technology
Order noise occupies main component in automobile exhaust noise, has important influence to automobile sound quality, simultaneously
The quantitative extraction of order composition is the basis of exhausting silencer structural analysis design.Order analysis method be broadly divided into hardware order with
Track method and calculating order tracking technique method (COT, computed order tracking).The operation of hardware order tracking technique method is complex,
With the development of computer technology, calculate order tracking technique method and be increasingly becoming main flow.Order tracking technique method is calculated all using time domain
Equidistant raw digital signal, a variety of processing methods are formd by years development.Rank based on Fourier Tranform in short-term
Secondary analysis method is proposed that (rotating speed)-frequency is represented, but can not weighed when can be carried out to unstable signal by Gabor in nineteen forty-six
The time domain waveform of structure order component, it can not quantify and calculate order sound pressure level.Order analysis method based on angularly resampling is most
It is early to be proposed by Potter, although this method can carry out the time (rotating speed)-order expression, order component can not be reconstructed
Time domain waveform.1993, Vold proposed the Vold-Kalman ranks based on angular speed on the basis of Kalman filter first
Secondary tracking algorithm, this order tracking technique analysis method can adaptively be adjusted to rotation speed change, avoided due to time-frequency conversion
With phase offset caused by resampling, it is possible to achieve the reconstruct of the time domain waveform of order component, but when can not be carried out to signal-frequency
Represent, while need to carry out large-scale decoupling computation, it is more difficult to realize online processing.2001, Albright and Qian from
Gabor expansion thought is set out, and proposes the order tracking technique analysis based on Gabor time-frequency conversions, and this method can be carried out to signal
When-domain representation, the time domain ripple that Waveform Reconstructing obtains order component can be also carried out according to the coefficient of order constituents extraction on time-frequency figure
Shape, so as to analyze order noise more fully hereinafter.But this method order component after time-frequency conversion has partially in phase
Move, and the width of the time window of this method is unrelated with frequency, is a kind of permanent resolution analysis, thus be difficult to believe non-stationary time-varying
Number accurate order analysis and extraction are carried out, limit the application of this method.In recent years, partial monopoly also proposes order letter
Number extraction and analytical method.Such as a kind of Patent No. CN201510715768.1 patent of invention (non-linear order of engine point
Measure extraction and analytical method, on October 29th, 2015), calculated using discrete Fourier transform DFT and obtain three-dimensional spectrogram, it is then right
Linear order curve on spectrogram is extracted.(active engine mount is passive for Patent No. CN201610219654.2 patent of invention
The main order vibration signal real time extracting method of latax, on April 11st, 2016), obtained using Fast Fourier Transform (FFT) FFT processing
The peak value of signal spectrum is taken, then carries out the time domain reconstruction of main order signal, so as to successfully extract main order signal.
Above order analysis technology is all based on Fourier transform, and Fourier Tranform is linear transformation, is a kind of
Permanent resolution analysis, during for analyzing nonlinear time varying signal, it may appear that the problems such as frequency leakage, order aliasing, so that
Obtain analysis result and larger error occur.Automobile exhaust noise in giving it the gun is nonlinear time varying signal, it is necessary to a kind of non-
The analysis method of linear variable resolution ratio carries out accurate tracking extraction to its order noise contribution.Patent No.
CN201510685473.4 patent of invention (Order Tracking based on nonlinear frequency modulation wavelet transformation, October 22 in 2015
Day), time frequency analysis is carried out to vibration signal using nonlinear frequency modulation wavelet transformation, then utilizes spectral peak maximum value search, minimum
Square law fitting, angularly envelope demodulation, the means such as resampling, it is finally completed the order tracking technique of signal.The method is with time domain
Order composition is analyzed based on figure, it is impossible to the time domain waveform of order component is reconstructed, can not accurate quantitative analysis extraction order point
Amount.The present invention proposes a kind of refinement analysis calculation method of the non-linear multiresolution based on wavelet transformation, for order component
Quantitative extraction and analysis, the order composition in exhaust noise is accurately extracted, so as to further for exhaust noise sound quality
Further investigation and different structure soundproof effect Comparative and Quantitative Analysis provide the reliable signal processing means of standard.
The content of the invention
The purpose of the present invention is to propose to a kind of refinement analysis calculation method of the non-linear multiresolution based on wavelet transformation,
Quantitative extraction and analysis for order component.This method can effectively solve the problem that the order extracting method institute based on Fourier Tranform
The problems such as existing spectrum leakage, order aliasing, the time domain fluctuation signal of the order component in exhaust noise is accurately extracted, just
In analysis and quantitative contrast research.
To achieve the above object, the present invention takes following technical scheme.
A kind of quantitative extracting method of non-stationary exhaust noise signal order based on wavelet transformation, comprises the following steps：
The engine speed pulse signal that step (1) is obtained by tachometer of measuring, if occur in rotational speed pulse signal
Serial number s of i-th of pulse in signal sequencen(i), the time interval Δ T between i-th of pulse and i+1 pulse is：
Δ T (i)=[sn(i+1)-sn(i)]/fs (1)
In formula (1), fsFor sample frequency.The calculation formula of the transient speed of engine is as follows：
In formula (2), n'(t) it is engine speed, z turns umber of pulse to be every.
Simultaneous formula (1) and formula (2) calculate engine speed graph.Time in engine speed graph corresponding to each point
Sequence, can be by formula tn=sn(i)/fsTry to achieve.
Step (2) is bent to engine speed using cubic spline curve in order to eliminate the fluctuation in engine speed graph
Line is smoothed, and obtains smooth engine speed graph n (t).
Step (3) builds mother wavelet function by bandpass filter.The frequency domain transfer function of real even ideal bandpass filter
Shown in expression formula such as formula (3).
The time domain impulse receptance function expression of preferable band logical frequency domain transfer function can be realized with Sinc function, such as formula
(4) shown in.
hB(t)=2FLH sinc(2FLHt)-2FLL sinc(2FLLt) (4)
Wherein, FLHFor ideal bandpass filter upper cut-off frequency, FLLFor ideal bandpass filter lower-cut-off frequency,
Determined by two parameters of centre frequency and bandwidth of bandpass filter, its mathematical description can use formula (5) to represent.
Wherein wp(τ) is the bandwidth of bandpass filter, and fc(τ) is order centre frequency, and τ is correlation ratio to time system.
Each order centre frequency is calculated by the speed curves n (t) of the engine of step (2), as shown in formula (6).
In formula (6), ε is order number, and general engine ignition order and its frequency multiplication are the places that acoustic energy is concentrated.
Simultaneous formula (4), (5), (6) three formulas, the time-domain expression of available preferable band logical impulse response function,
As shown in formula (7).
The present invention is using structureMother wavelet function as order extraction and analysis.The mother wavelet function of structureFlexible yardstick it is relevant with the rotating speed and bandwidth of slewing, and in correlation ratio to bandwidth value in time system and rotating speed
Value can need to build mapping relations according to signal analysis, in time domain and frequency domain while local more in order analysis so as to realize
Resolution ratio refinement analysis, the accurate order composition extracted in nonstationary noise signal.
The function of time-domain finite is needed to carry out the analysis and processing of signal in step (4) engineering.Thus the present invention adopts
Mother wavelet function is intercepted with cosine window function, it is possessed time-domain finite.Shown in window function such as formula (8).
Wherein Wβ(t) it is cosine window function；β is window enhancing rate；TwIt is the window width of interception.
Shown in wavelet function expression formula such as formula (9) after window function interception.
In formula (9)It is the standard adding window wavelet function built in the present invention, it is non-for automobile exhaust in engineering
The order tracking technique extraction of stationary noise signal.
Step (5) by real steering vectors obtain accelerating mode under exhaust emission noise, and with the adding window wavelet function of acquisition
Carry out time domain correlating transforms, you can the time domain fluctuation signal of each order is obtained, as shown in formula (10).
The time domain fluctuation signal of acquisition can carry out independent play-out in listening room, so as to realize more accurately sound quality point
Analysis.
Step (6) carries out sound pressure level conversion for ease of the Comparative and Quantitative Analysis of order signal to time domain order fluctuation signal.
Shown in the effective acoustic pressure calculation formula such as formula (11) of nonstationary noise signal.
P in formulae(τ) is the effective acoustic pressure of time varying signal,It is time-varying fluctuation signal, TpRepresent the average time chosen
Cycle.Shown in sound pressure level transformation for mula such as formula (12).
Ls(τ)=10log10(pe 2(τ)/p0 2) (12)
L in formulas(τ) represents the sound pressure level of time-varying sound pressure signal, p0Represent reference sound pressure.Each order sound pressure level obtained is bent
Line, can be that the order soundproof effect of different exhausting silencer structures carries out Comparative and Quantitative Analysis, so as to effectively instruct noise elimination structure
Improve.
For the present invention due to taking above technical scheme, it has advantages below：1st, it is proposed by the present invention to be based on wavelet transformation
Order extraction and analytical method, non-stationary signal can be directed to and carry out the refinement analysis of non-linear multiresolution, effectively overcome Fu Li
Caused by leaf transformation the problems such as spectrum leakage, order aliasing；2nd, the present invention is built by preferable band logical impulse response function
For the standard mother wavelet function of order constituents extraction, simplify the process of order extraction, improve the efficiency of signal transacting, be applied to
Online processing；3rd, order analysis method proposed by the present invention directly obtains the time domain fluctuation signal of each order component, can listen
Tone chamber carries out independent play-out, so as to realize more accurately sound quality analysis；4th, the time domain for each order component that the present invention obtains
Fluctuation signal can carry out independent assortment, while can be exchanged into order sound pressure level, so as to be the further of exhaust noise sound quality
Further investigation and different structure soundproof effect Comparative and Quantitative Analysis lay the foundation.
Brief description of the drawings
Fig. 1 is tail pipe radiated noise real steering vectors schematic device under motion operating mode of the invention.Wherein, I is instruction carriage
, II is mounting bracket, and III is microphone, and IV is wind ball.
Fig. 2 is the instant engine speed curves that the pulse signal of the present invention calculates.
Fig. 3 is the non-stationary exhaust noise signal of the present invention and smooth engine speed graph (a) non-stationary exhaust noise
Signal, (b) smooth rear engine speed curves.
Fig. 4 is that the preferable band logical transmission function of the present invention and the preferable band logical frequency domain of impulse response function curve (a) transmit letter
Number curve, (b) preferable band logical time domain impulse response function curve.
Fig. 5 is that the Cosine Window band logical impulse of the present invention rings the preferable band logical time domain impulse response function of composition (a) of function,
(b) cosine window function, (c) adding window band logical time domain impulse response function.
Fig. 6 is time domain fluctuation signal (a) second order signal of each order composition in exhaust noise of the invention, and (b) quadravalence is believed
Number, (c) six rank signal.
Fig. 7 is the time domain overall sound pressure level and order sound pressure level curve (a) noise time domain overall sound pressure level curve (A meters of the present invention
Power), (b) order time domain sound pressure level curve (C weighteds).
Fig. 8 is the former exhaust noise signal of the present invention and three dimensional chromatogram (a) the exhaust noise signal three of each order signal
Tie up chromatogram, the three dimensional chromatogram of (b) each order signal.
Embodiment
Come to carry out the present invention detailed description below in conjunction with accompanying drawing.It should be appreciated, however, that accompanying drawing has been provided only more
Understand the present invention well, they should not be interpreted as limitation of the present invention.
The quantitative extracting method of the non-stationary exhaust noise signal order based on wavelet transformation of the present invention, including following step
Suddenly：
1) the engine speed pulse signal obtained by tachometer of measuring, if i-th occurred in rotational speed pulse signal
Serial number s of the pulse in signal sequencen(i), then the time interval Δ T between i-th of pulse and i+1 pulse is：
Δ T (i)=[sn(i+1)-sn(i)]/fs (1)
In formula (1), fsFor sample frequency.The calculation formula of the transient speed of engine is as follows：
In formula (2), n'(t) it is engine speed, z turns umber of pulse to be every.
Simultaneous formula (1) and formula (2), you can engine speed graph is calculated by pulse signal.In engine speed graph
Time series corresponding to each point, can be by formula tn=sn(i)/fsTry to achieve.
2) due to electrical Interference, the speed curves calculated by rotational speed pulse signal can typically have fluctuation situation, be
The fluctuation in engine speed graph is eliminated, using cubic spline curve engine speed graph is smoothed, from
And obtain smooth engine speed graph n (t).
3) time-varying exhaust noise signal order extraction, its essence is tracking tach signal conversion order centre frequency,
Carry out time-varying bandpass filtering and obtain each order composition, thus first build mother wavelet function from bandpass filter.It is real even preferable
Shown in the frequency domain transfer function expression formula such as formula (3) of bandpass filter.
The time domain impulse receptance function expression of preferable band logical frequency domain transfer function can be realized with Sinc function, such as formula
(4) shown in.
hB(t)=2FLH sinc(2FLHt)-2FLL sinc(2FLLt) (4)
Wherein, FLHFor ideal bandpass filter upper cut-off frequency, FLLFor ideal bandpass filter lower-cut-off frequency.
But, it is necessary to pass through band logical transmission function centre frequency when carrying out the filtering process of order composition in time varying signal
The flexible of skew and bandwidth realizes the refinement analysis of signal multiresolution, i.e., the centre frequency of bandpass filter and bandwidth need with
Change with related comparison time τ change, its mathematical description can use formula (5) to represent.
Wherein wp(τ) is the bandwidth of bandpass filter, and fc(τ) is order centre frequency, and τ is correlation ratio to time system.
Each order centre frequency is calculated by the rotating speed of engine, as shown in formula (6).
In formula (6), ε is order number, and general engine ignition order and its frequency multiplication are the places that acoustic energy is concentrated.
Simultaneous formula (4), (5), (6) three formulas, the expression formula of available preferable band logical impulse response function, such as formula
(7) shown in.
Flexible yardstick it is relevant with the rotating speed and bandwidth of slewing, and in correlation ratio to bandwidth in time system
Value and tachometer value can need to build mapping relations according to signal analysis, same in time domain and frequency domain so as to realize in order analysis
When the refinement analysis of part multiresolution.Using structure in the present inventionMother wavelet function as order extraction and analysis.
4) function of time-domain finite is needed to carry out the analysis and processing of signal in engineering.Mother wavelet functionAlso
Do not possess time-domain finite, it is necessary to limit its time domain waveform length by window function interception.It is used to intercept mother wavelet in the present invention
The window function expression formula of function is as follows：
Wherein Wβ(t) it is cosine window function；β is window enhancing rate；TwIt is the window width of interception.
Shown in wavelet function expression formula such as formula (9) after window function interception.
In formula (9)It is the standard adding window wavelet function built in the present invention, for nonstationary noise signal
Order tracking technique extracts.
5) exhaust emission noise under accelerating mode is obtained by real steering vectors, and with the progress of adding window wavelet function will be obtained to obtain
Time domain correlating transforms, you can obtain the time domain fluctuation signal of each order.For time-domain filtering system, the time domain phase between signal is compared
Related inner product operation can be converted into by closing conversion, as shown in formula (10).
The time domain fluctuation signal for calculating and can extract each order is compared by formula (10).The time domain fluctuation signal of acquisition can
To carry out independent play-out in listening room, so as to realize more accurately sound quality analysis.
6) for ease of the Comparative and Quantitative Analysis of order signal, time domain order fluctuation signal need to be subjected to sound pressure level conversion, become
Change shown in formula such as formula (11).
P in formulae(τ) is the effective acoustic pressure of time varying signal,It is time-varying fluctuation signal, TpRepresent the average time chosen
Cycle.Shown in sound pressure level transformation for mula such as formula (20).
Ls(τ)=10log10(pe 2(τ)/p0 2) (12)
L in formulas(τ) represents the sound pressure level of time-varying sound pressure signal, p0Represent reference sound pressure.Each order sound pressure level obtained is bent
Line, Comparative and Quantitative Analysis can be carried out to the order soundproof effect of different exhausting silencer structures.
The time-domain digital weighted method of the nonstationary noise signal of the present invention is carried out below by specific embodiment detailed
Explanation：
Microphone is arranged on the tailstock by the present invention using the automobile collection tail pipe radiated noise of certain 1.5L four cylinder engine
On the support at end, support is firm with automobile body welding, as shown in figure 1, wherein, L 0.5m, θ are 45 ° ± 10 °, l≤0.2.Simultaneously
The tacho-pulse of engine is obtained by cigar lighter using tachometer of measuring.When gathering exhaust noise, vehicle operational mode two
The full accelerator pedal accelerating mode of shelves.Order is carried out using method proposed by the present invention to the exhaust emission noise under accelerating mode to carry
Take, detailed process is as follows：
1) rotational speed pulse signal is that acquisition is equidistantly sampled by data acquisition unit, if occur in rotational speed pulse signal i-th
Serial number s of the individual pulse in signal sequencen(i), then the time interval between i-th of pulse and i+1 pulse is：
Δ T (i)=[sn(i+1)-sn(i)]/fs (1)
F in formulasFor sample frequency, f in the present embodimentsFor 16384Hz.
The calculation formula of the transient speed of engine is as follows：
In formula (2), n'(t) it is engine speed, z turns umber of pulse to be every.Simultaneous formula (1) and formula (2) can calculate respectively
Engine mean speed in pulse section.And the time series corresponding to each rotating speed point, can be by formula tn=sn(i)/fsTry to achieve.
It is as shown in Figure 2 to calculate the engine speed graph obtained.
2) as seen from Figure 2, in the higher section of rotating speed, due to the interference of electrical equipment electric signal on automobile, calculate
Engine speed graph can have fluctuation situation.Cubic spline curve can guarantee that on curve continuous position, slope rate continuity and song
Rate consecutive variations, thus speed curves are smoothed using cubic spline curve.The original noise p of collections(t)
And it is smooth after engine speed n (t) it is as shown in Figure 3.
3) time-varying exhaust noise signal order extraction, its essence is tracking tach signal conversion order centre frequency,
Carry out time-varying bandpass filtering and obtain each order composition, thus first build mother wavelet function from bandpass filter.It is real even preferable
Shown in the frequency domain transfer function expression formula such as formula (3) of bandpass filter.
The time domain impulse receptance function expression of preferable band logical frequency domain transfer function can be realized with Sinc function, such as formula
(4) shown in.
hB(t)=2FLH sinc(2FLHt)-2FLL sinc(2FLLt) (4)
Wherein, FLHFor ideal bandpass filter upper cut-off frequency, FLLFor ideal bandpass filter lower-cut-off frequency.
Ideal bandpass filter frequency domain transfer function curve and time domain function curve are as shown in Figure 4.
But, it is necessary to pass through band logical transmission function centre frequency when carrying out the filtering process of order composition in time varying signal
The flexible of skew and bandwidth realizes the refinement analysis of signal multiresolution, i.e., the centre frequency of bandpass filter and bandwidth need with
Change with related comparison time τ change, its mathematical description can use formula (5) to represent.
Wherein wp(τ) is the bandwidth of bandpass filter, and fc(τ) is order centre frequency, and τ is correlation ratio to time system.
Each order centre frequency is calculated by the speed curves n (t) of engine, as shown in formula (6).
In formula (6), ε is order number, and general engine ignition order and its frequency multiplication are the places that acoustic energy is concentrated.This implementation
Using four stroke four cylinder engines in example, thus 2,4,6 ranks are the orders for needing to pay close attention to.
Simultaneous formula (4), (5), (6) three formulas, the expression formula of available preferable band logical impulse response function, such as formula
(7) shown in.
Using structure in the present embodimentAs the mother wavelet function of standard, the extraction for order noise.By
Order multicomponent energy in the case of automobile acceleration in exhaust noise concentrates on narrower frequency band, its bandwidth not anaplasia at any time substantially
Change, thus the bandwidth parameter in the present embodiment in mother wavelet function takes constant, i.e. wp(τ)=15Hz.
4) function of time-domain finite is needed in engineering could carry out the analysis and processing of signal, thus need to mother wavelet letter
Number carries out windowing process.Hamming window (hamming) in Cosine Window can be substantially reduced spectrum leakage, while frequency resolution
It is of a relatively high.Thus using Hamming window (hamming) interception mother wavelet function, the following institute of window function expression formula in the present embodiment
Show：
Wherein Wβ(t) it is cosine window function；β is window enhancing rate, β=0.54/0.46；TwIt is the window width of interception, its size is straight
The transition band width for determining bandpass filter is connect, T in the present embodimentw=0.2s.
Shown in wavelet function expression formula such as formula (9) after window function interception.
In formula (9)It is the standard adding window wavelet function built in the present embodiment, for nonstationary noise signal
Order tracking technique extraction.Mother wavelet function, window function and adding window wavelet function in the present embodiment is as shown in Figure 5.
5) by real steering vectors obtain accelerating mode under exhaust emission noise, and with obtain adding window wavelet function carry out when
Domain correlating transforms, you can obtain the time domain fluctuation signal of each order.For time-domain filtering system, the time domain compared between signal is related
Conversion can be converted into related inner product operation, as shown in formula (10).
The time domain fluctuation signal for calculating and can extract each order is compared by formula (10) for the present embodiment, as shown in Figure 5.Obtain
The time domain fluctuation signal taken can carry out independent play-out in listening room, so as to realize more accurately sound quality analysis.
6) for ease of the Comparative and Quantitative Analysis of order signal, time domain order fluctuation signal need to be subjected to sound pressure level conversion, become
Change shown in formula such as formula (11).
P in formulae(τ) is the effective acoustic pressure of time varying signal,It is time-varying fluctuation signal, TpRepresent the average time chosen
Cycle, T in the present embodimentp=0.125s.
Shown in sound pressure level transformation for mula such as formula (20).
Ls(τ)=10log10(pe 2(τ)/p0 2) (12)
L in formulas(τ) represents the sound pressure level of time-varying sound pressure signal, p0Represent reference sound pressure, p0=2 × 10-5Pa。
It is as shown in Figure 6 according to the order sound pressure level curve that formula (11) and formula (12) obtain.Each order sound pressure level obtained is bent
Line, Comparative and Quantitative Analysis can be carried out to the order soundproof effect of different exhausting silencer structures.
In order to verify the correctness of order extracting method proposed by the present invention, former noise is obtained using Fourier Tranform in short-term
The three dimensional chromatogram of signal and each order signal, as shown in Figure 7.It can be seen from figure 7 that (b), (c), (d) are appeared clearly from
2nd, the order noise contribution of 4,6 ranks, other uncorrelated noises are all filtered out, and with the former exhaust noise spectrogram in Fig. 7 (a)
Corresponding order figure coincide it is good, absolutely prove order extracting method proposed by the present invention be precisely separating out each order into
Point.
Above-described embodiment is merely to illustrate the present invention, and wherein each implementation steps of method etc. can be all varied from,
Every equivalents carried out on the basis of technical solution of the present invention and improvement, should not be excluded in protection scope of the present invention
Outside.
Claims (1)
- A kind of 1. quantitative extracting method of non-stationary exhaust noise signal order based on wavelet transformation, it is characterized in that including following step Suddenly：Step (1)：The engine speed pulse signal obtained by tachometer of measuring, if occur in rotational speed pulse signal i-th Serial number s of the individual pulse in signal sequencen(i), the time interval Δ T between i-th of pulse and i+1 pulse is：Δ T (i)=[sn(i+1)-sn(i)]/fs (1)In formula (1), fsFor sample frequency；The calculation formula of the transient speed of engine is as follows：<mrow> <msup> <mi>n</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>60</mn> <mfrac> <mn>1</mn> <mrow> <mi>z</mi> <mo>&CenterDot;</mo> <mi>&Delta;</mi> <mi>T</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>In formula (2), n'(t) it is engine speed, z turns umber of pulse to be every；Simultaneous formula (1) and formula (2) calculate engine speed graph, the time sequence in engine speed graph corresponding to each point Row, by formula tn=sn(i)/fsTry to achieve；Step (2)：Engine speed graph is smoothed using cubic spline curve, obtains smooth engine speed Curve n (t)；Step (3)：Mother wavelet function is built by bandpass filter：The frequency domain transfer function expression of real even ideal bandpass filter Shown in formula such as formula (3)：<mrow> <msub> <mi>H</mi> <mi>B</mi> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mo>(</mo> <mo>|</mo> <mi>f</mi> <mo>|</mo> <mo>&Element;</mo> <mo>&lsqb;</mo> <msub> <mi>F</mi> <mi>L</mi> </msub> <mo>,</mo> <msub> <mi>F</mi> <mi>H</mi> </msub> <mo>&rsqb;</mo> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>(</mo> <mi>e</mi> <mi>l</mi> <mi>s</mi> <mi>e</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>The time domain impulse receptance function expression of preferable band logical frequency domain transfer function is realized with Sinc function, as shown in formula (4)：hB(t)=2FLH sinc(2FLHt)-2FLL sinc(2FLL t) (4)Wherein, FLHFor ideal bandpass filter upper cut-off frequency, FLLFor ideal bandpass filter lower-cut-off frequency, by band logical Two parameters of centre frequency and bandwidth of wave filter determine that its mathematical description can use formula (5) to represent：<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>L</mi> <mi>H</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mi>w</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>L</mi> <mi>L</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mi>w</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>Wherein wp(τ) is the bandwidth of bandpass filter, and fc(τ) is order centre frequency, and τ is correlation ratio to time system；Each rank Subcenter frequency is calculated by the engine speed graph n (t) of step (2), as shown in formula (6)：<mrow> <msub> <mi>f</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>&epsiv;</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> </mrow> <mn>60</mn> </mfrac> <mo>,</mo> <mrow> <mo>(</mo> <mi>&epsiv;</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>...</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>In formula (6), ε is order number；Simultaneous formula (4), (5), (6) three formula, the time-domain expression of obtained preferable band logical impulse response function, such as formula (7) It is shown：<mrow> <msubsup> <mover> <mi>h</mi> <mo>~</mo> </mover> <mi>B</mi> <mi>&epsiv;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo>&lsqb;</mo> <mn>2</mn> <mi>&pi;</mi> <mi>&epsiv;</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mi>t</mi> <mo>/</mo> <mn>30</mn> <mo>&rsqb;</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mo>&lsqb;</mo> <msub> <mi>&pi;w</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mi>t</mi> <mo>&rsqb;</mo> </mrow> <mrow> <mi>&pi;</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>Step (4)：Mother wavelet function is intercepted using cosine window function, it is possessed time-domain finite；Window function such as formula (8) shown in：Wherein Wβ(t) it is cosine window function；β is window enhancing rate；TwIt is the window width of interception；Shown in adding window wavelet function expression formula such as formula (9) after window function interception：<mrow> <msubsup> <mover> <mi>h</mi> <mo>~</mo> </mover> <mrow> <mi>w</mi> <mi>B</mi> </mrow> <mi>&epsiv;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>W</mi> <mi>&beta;</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msubsup> <mover> <mi>h</mi> <mo>~</mo> </mover> <mi>B</mi> <mi>&epsiv;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>Step (5) obtains exhaust emission noise under accelerating mode by real steering vectors, and is carried out with the adding window wavelet function of acquisition Time domain correlating transforms, you can the time domain fluctuation signal of each order is obtained, as shown in formula (10).<mrow> <msub> <mi>p</mi> <mi>&epsiv;</mi> </msub> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <mi>&tau;</mi> <mo>-</mo> <msub> <mi>T</mi> <mi>w</mi> </msub> <mo>/</mo> <mn>2</mn> </mrow> <mrow> <mi>&tau;</mi> <mo>+</mo> <msub> <mi>T</mi> <mi>w</mi> </msub> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <mi>p</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msubsup> <mover> <mi>h</mi> <mo>~</mo> </mover> <mrow> <mi>w</mi> <mi>B</mi> </mrow> <mi>&epsiv;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&tau;</mi> <mo>,</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>Step (6) carries out sound pressure level conversion for ease of the Comparative and Quantitative Analysis of order signal to time domain order fluctuation signal；It is non-flat Shown in the effective acoustic pressure calculation formula such as formula (11) of steady noise signal：<mrow> <msubsup> <mi>p</mi> <mi>e</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>&tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mi>p</mi> </msub> </mfrac> <msubsup> <mo>&Integral;</mo> <mrow> <mi>&tau;</mi> <mo>-</mo> <msub> <mi>T</mi> <mi>p</mi> </msub> <mo>/</mo> <mn>2</mn> </mrow> <mrow> <mi>&tau;</mi> <mo>+</mo> <msub> <mi>T</mi> <mi>p</mi> </msub> <mo>/</mo> <mn>2</mn> </mrow> </msubsup> <msup> <mover> <mi>p</mi> <mo>~</mo> </mover> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>P in formulae(τ) is the effective acoustic pressure of time varying signal,It is time-varying fluctuation signal, TpRepresent the average time period chosen； Shown in sound pressure level transformation for mula such as formula (12)：Ls(τ)=10log10(pe 2(τ)/p0 2) (12)L in formulas(τ) represents the sound pressure level of time-varying sound pressure signal, p0Represent reference sound pressure；Each order sound pressure level curve obtained, it is The order soundproof effect of different exhausting silencer structures carries out Comparative and Quantitative Analysis, so as to effectively instruct the improvement of noise elimination structure.
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