CN107832261B - Wavelet transform-based non-stationary exhaust noise signal order quantitative extraction method - Google Patents
Wavelet transform-based non-stationary exhaust noise signal order quantitative extraction method Download PDFInfo
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Abstract
A wavelet transform-based non-stationary exhaust noise signal order quantitative extraction method comprises the following steps: 1) calculating a rotating speed curve through the rotating speed pulse signal, and obtaining a corresponding time sequence; 2) smoothing the rotating speed curve by adopting a cubic spline curve to obtain a smooth rotating speed curve; 3) establishing a standard windowed wavelet function for correlation transformation calculation; 4) performing time domain correlation transformation on the non-stationary exhaust noise signal by adopting a windowed wavelet function to obtain time domain fluctuation signals of each order; 5) and performing sound pressure level transformation on the time domain order fluctuation signals to obtain sound pressure level curves of all orders. The invention can overcome the problems of frequency spectrum leakage, order aliasing and the like; simplifying the process of order extraction; more accurate sound quality analysis is realized; the time domain fluctuation signals of all order components can be freely combined and can be converted into order sound pressure levels, so that a foundation is laid for the research of the quality of exhaust noise and the quantitative comparison and analysis of the silencing effect of different structures.
Description
Technical Field
The invention relates to a method for analyzing and processing non-stationary noise signal orders, in particular to a method for quantitatively extracting time domain orders of an automobile exhaust noise signal under an acceleration working condition.
Background
The order noise occupies main components in the automobile exhaust noise and has important influence on the automobile sound quality, and meanwhile, the quantitative extraction of the order components is the basis of the analysis design of the exhaust silencing structure. The order analysis method is mainly classified into a hardware order tracking method and a computed order tracking method (COT). The hardware order tracking method is complex in operation, and the calculation order tracking method gradually becomes the mainstream along with the development of computer technology. The calculation order tracking method adopts time domain equidistant original digital signals, and a plurality of processing methods have been formed through years of development. The order analysis method based on short-time fourier transform proposed by Gabor in 1946 can perform time (rotation speed) -frequency representation on unsteady signals, but cannot reconstruct the time domain waveform of order components, and cannot quantitatively calculate order sound pressure level. The order analysis method based on equiangular resampling was first proposed by Potter, and although this method enables time (rotational speed) -order representation, it cannot reconstruct the time-domain waveform of the order component. In 1993, Vold first provides a Vold-Kalman order tracking algorithm based on angular velocity on the basis of a Kalman filter, the order tracking analysis method can adaptively adjust the rotation speed change, avoids phase shift caused by time-frequency transformation and resampling, can realize time domain waveform reconstruction of order components, but cannot perform time-frequency representation on signals, and simultaneously needs large-scale decoupling calculation and is difficult to realize online processing. In 2001, Albright and Qian propose order tracking analysis based on Gabor time-frequency transformation based on Gabor development idea, and the method can perform time-domain representation on signals and also perform waveform reconstruction according to coefficients extracted from order components on a time-frequency graph to obtain time-domain waveforms of order components, thereby analyzing order noise more comprehensively. However, the order component of the method after time-frequency transformation has offset on the phase, and the width of the time window of the method is irrelevant to the frequency, so that the method is a constant resolution analysis, and therefore, accurate order analysis and extraction are difficult to be carried out on non-stationary time-varying signals, and the application of the method is limited. In recent years, some patents have proposed methods for extracting and analyzing order signals. For example, in patent No. CN201510715768.1 (a method for extracting and analyzing nonlinear order components of an engine, 10/2015 and 29), a three-dimensional spectrogram is obtained by discrete fourier transform DFT calculation, and then a linear order curve on the spectrogram is extracted. In an invention patent with the patent number CN201610219654.2 (a real-time extraction method of an active suspension passive side acceleration primary vibration signal, 2016, 4, month and 11), a peak value of a signal spectrum is obtained by fast fourier transform FFT processing, and then time domain reconstruction of the primary signal is performed, so that the primary signal is successfully extracted.
The above order analysis techniques are based on fourier transform, which is a constant resolution analysis, and when used for analyzing nonlinear time-varying signals, problems such as frequency leakage and order aliasing occur, so that a large error occurs in an analysis result. The automobile exhaust noise in acceleration driving is a nonlinear time-varying signal, and a nonlinear variable resolution analysis method is needed to accurately track and extract the order noise component of the automobile exhaust noise. In the invention patent No. CN201510685473.4 (order tracking method based on non-linear frequency-modulated wavelet transform, 2015, 10/month and 22 days), the vibration signal is subjected to time-frequency analysis by using the non-linear frequency-modulated wavelet transform, and then the order tracking of the signal is finally completed by using means such as maximum search of spectral peak, least square fitting, envelope demodulation, equal-angle resampling, and the like. The method analyzes the order components on the basis of the time domain diagram, cannot reconstruct the time domain waveform of the order components, and cannot accurately and quantitatively extract the order components. The invention provides a wavelet transform-based nonlinear multiresolution refined analysis and calculation method, which is used for quantitative extraction and analysis of order components and accurate extraction of order components in exhaust noise, thereby providing a standard and reliable signal processing means for further deep research on the sound quality of the exhaust noise and quantitative comparison and analysis of silencing effects of different structures.
Disclosure of Invention
The invention aims to provide a wavelet transform-based nonlinear multiresolution refined analysis and calculation method for quantitative extraction and analysis of order components. The method can effectively solve the problems of frequency spectrum leakage, order aliasing and the like existing in an order extraction method based on Fourier transform, accurately extracts the time domain fluctuation signal of the order component in the exhaust noise, and is convenient for analysis and quantitative comparison research.
In order to achieve the purpose, the invention adopts the following technical scheme.
A non-stationary exhaust noise signal order quantitative extraction method based on wavelet transformation comprises the following steps:
step (1) obtaining an engine rotating speed pulse signal through a rotating speed measuring instrument, and setting the serial number of the ith pulse appearing in the rotating speed pulse signal in a signal sequence to be sn(i) The time interval Δ T between the ith pulse and the (i + 1) th pulse is:
ΔT(i)＝[sn(i+1)-sn(i)]/fs(1)
in the formula (1), fsIs the sampling frequency. The calculation formula of the instantaneous rotational speed of the engine is as follows:
in the formula (2), n' (t) represents the engine speed, and z represents the number of pulses per revolution.
And (3) calculating an engine rotating speed curve by the joint type (1) and the formula (2). The time sequence corresponding to each point on the engine speed curve can be represented by the formula tn＝sn(i)/fsAnd (6) obtaining.
And (2) smoothing the engine speed curve by adopting a cubic spline curve to eliminate fluctuation on the engine speed curve to obtain a smooth engine speed curve n (t).
And (3) constructing a wavelet basis function through a band-pass filter. The frequency domain transfer function expression of the real-even ideal band-pass filter is shown as the formula (3).
The time domain impulse response function expression of the ideal band-pass frequency domain transfer function can be realized by using a sinc function, as shown in formula (4).
hB(t)＝2FLHsinc(2FLHt)-2FLLsinc(2FLLt) (4)
Wherein the content of the first and second substances,FLHis the upper cut-off frequency, F, of an ideal band-pass filterLLThe lower cut-off frequency of an ideal band-pass filter is determined by two parameters, namely the center frequency and the bandwidth of the band-pass filter, and the mathematical description of the lower cut-off frequency can be expressed by an equation (5).
Wherein wp(τ) is the bandwidth of the bandpass filter, and fc(τ) is the order center frequency, τ is the correlation versus time system. And (3) calculating the central frequency of each order from the rotating speed curve n (t) of the engine in the step (2), wherein the central frequency is shown as a formula (6).
In the formula (6), the order is the order, and the general engine ignition order and the frequency multiplication thereof are places where the acoustic energy is concentrated.
And (4) connecting three formulas (4), (5) and (6), so that a time domain expression of an ideal band-pass impulse response function can be obtained, as shown in formula (7).
Constructed according to the invention
As wavelet basis functions for order extraction analysis. Constructed wavelet basis functions
The stretching scale is related to the rotating speed and the bandwidth of the rotating equipment, and the bandwidth value and the rotating speed value on a relevant comparison time system can construct a mapping relation according to the signal analysis requirement, so that the simultaneous local multi-resolution refined analysis on a time domain and a frequency domain in the order analysis is realized, and the order components in the non-stationary noise signal are accurately extracted.
And (4) analyzing and processing the signals only by using a time-domain limited function in engineering. Therefore, the wavelet basis function is intercepted by adopting the cosine window function, so that the wavelet basis function has time domain limitation. The window function is shown in equation (8).
Wherein Wβ(T) is a cosine window function, β is a window lifting rate, TwIs the truncated window width.
The expression of the wavelet function intercepted by the window function is shown as a formula (9).
In the formula (9)
The standard windowed wavelet function constructed in the invention is used for order tracking extraction of automobile exhaust non-stationary noise signals in engineering.
And (5) acquiring exhaust radiation noise under an acceleration condition through real vehicle test, and performing time domain correlation transformation on the exhaust radiation noise and the acquired windowed wavelet function to acquire time domain fluctuation signals of each order, wherein the formula is shown as (10).
The acquired time domain fluctuation signals can be independently played in a listening room, so that more accurate sound quality analysis is realized.
And (6) carrying out sound pressure level transformation on the time domain order fluctuation signals so as to facilitate quantitative comparison and analysis of the order signals. The effective sound pressure calculation formula of the non-stationary noise signal is shown as formula (11).
In the formula pe(τ) is the effective acoustic pressure of the time-varying signal,
is a time-varying fluctuating signal, TpRepresenting a selected average time period. The sound pressure level conversion formula is shown in formula (12).
Ls(τ)＝10log10(pe 2(τ)/p0 2) (12)
In the formula Ls(τ) represents the sound pressure level, p, of a time-varying sound pressure signal0Representing a reference sound pressure. The acquired sound pressure level curves of all the orders can be used for carrying out quantitative comparative analysis on the order silencing effects of different exhaust silencing structures, so that the improvement of the silencing structures is effectively guided.
Due to the adoption of the technical scheme, the invention has the following advantages: 1. the order extraction and analysis method based on wavelet transformation can perform nonlinear multiresolution refinement analysis aiming at non-stationary signals, and effectively solves the problems of frequency spectrum leakage, order aliasing and the like caused by Fourier transformation; 2. the standard wavelet basis function for order component extraction is constructed through an ideal band-pass impact response function, so that the order extraction process is simplified, the signal processing efficiency is improved, and the method is suitable for online processing; 3. the order analysis method provided by the invention directly obtains the time domain fluctuation signals of each order component, and can be independently played in a listening room, thereby realizing more accurate sound quality analysis; 4. the time domain fluctuation signals of all order components obtained by the invention can be freely combined and can be converted into order sound pressure levels, thereby laying a foundation for further deep research on the sound quality of the exhaust noise and quantitative comparison and analysis of the silencing effects of different structures.
Drawings
FIG. 1 is a schematic diagram of a tail pipe radiation noise real vehicle testing device under a motion condition of the invention. Wherein, I is the test vehicle, II is the installing support, III is the microphone, IV is the balloon.
FIG. 2 is a plot of instantaneous engine speed calculated from the pulse signal of the present invention.
FIG. 3 is a plot of the non-stationary exhaust noise signal and the smoothed engine speed of the present invention (a) the non-stationary exhaust noise signal and (b) the smoothed engine speed curve.
Fig. 4 is a graph of the ideal band-pass transfer function and impulse response function of the present invention (a) an ideal band-pass frequency domain transfer function curve, and (b) an ideal band-pass time domain impulse response function curve.
FIG. 5 shows the structure of the cosine window bandpass impulse response function of the present invention, which is (a) an ideal bandpass time domain impulse response function, (b) a cosine window function, and (c) a windowed bandpass time domain impulse response function.
FIG. 6 is a time domain fluctuation signal of each order component in the exhaust noise of the present invention (a) a second order signal, (b) a fourth order signal, and (c) a sixth order signal.
Fig. 7 shows the time domain total sound pressure level and order sound pressure level curves of the present invention (a) noise time domain total sound pressure level curve (weighted by a) and (b) order time domain sound pressure level curve (weighted by C).
FIG. 8 is a three-dimensional chromatogram of the original exhaust noise signal and the signals of each order of the present invention (a) a three-dimensional chromatogram of the exhaust noise signal, and (b) a three-dimensional chromatogram of the signals of each order.
Detailed Description
The present invention is described in detail below with reference to the attached drawings. It is to be understood, however, that the drawings are provided solely for the purposes of promoting an understanding of the invention and that they are not to be construed as limiting the invention.
The invention discloses a wavelet transform-based non-stationary exhaust noise signal order quantitative extraction method, which comprises the following steps of:
1) the serial number of the ith pulse appearing in the rotating speed pulse signal in the signal sequence is sn(i) Then the time interval Δ T between the ith pulse and the (i + 1) th pulse is:
ΔT(i)＝[sn(i+1)-sn(i)]/fs(1)
in the formula (1), fsIs the sampling frequency. The calculation formula of the instantaneous rotational speed of the engine is as follows:
in the formula (2), n' (t) represents the engine speed, and z represents the number of pulses per revolution.
The engine speed curve can be calculated by the pulse signals through the joint formula (1) and the formula (2). The time sequence corresponding to each point on the engine speed curve can be represented by the formula tn＝sn(i)/fsAnd (6) obtaining.
2) Because of electrical interference, a rotating speed curve calculated by a rotating speed pulse signal generally has fluctuation, and in order to eliminate the fluctuation on the rotating speed curve of the engine, a cubic spline curve is adopted to carry out smoothing treatment on the rotating speed curve of the engine, so that a smooth rotating speed curve n (t) of the engine is obtained.
3) The order extraction of the time-varying exhaust noise signal is carried out by tracking the order center frequency converted by the rotating speed signal and carrying out time-varying band-pass filtering to obtain each order component, so that a wavelet basis function is constructed from the band-pass filter. The frequency domain transfer function expression of the real-even ideal band-pass filter is shown as the formula (3).
The time domain impulse response function expression of the ideal band-pass frequency domain transfer function can be realized by using a sinc function, as shown in formula (4).
hB(t)＝2FLHsinc(2FLHt)-2FLLsinc(2FLLt) (4)
Wherein, FLHIs the upper cut-off frequency, F, of an ideal band-pass filterLLThe lower cut-off frequency of the ideal band-pass filter.
However, when filtering the order components in the time-varying signal, it is necessary to implement multi-resolution refinement analysis of the signal through shifting the center frequency of the band-pass transfer function and stretching the bandwidth, that is, the center frequency and the bandwidth of the band-pass filter need to change along with the change of the correlation ratio to the time τ, and the mathematical description thereof can be expressed by equation (5).
Wherein wp(τ) is the bandwidth of the bandpass filter, and fc(τ) is the order center frequency, τ is the correlation versus time system. The center frequency of each order is calculated from the engine speed, as shown in equation (6).
In the formula (6), the order is the order, and the general engine ignition order and the frequency multiplication thereof are places where the acoustic energy is concentrated.
The three formulas of (4), (5) and (6) are combined, and an expression of an ideal band-pass impulse response function can be obtained, as shown in formula (7).
4) The engineering needs time-domain limited functions to analyze and process signals. Wavelet basis function
The method has no time domain limitation, and the time domain waveform length is limited by window function interception. The expression of the window function for intercepting the wavelet basis function in the invention is as follows:
wherein Wβ(T) is a cosine window function, β is a window lifting rate, TwIs the truncated window width.
The expression of the wavelet function intercepted by the window function is shown as a formula (9).
In the formula (9)
Namely, the standard windowed wavelet function constructed in the invention is used for order tracking extraction of non-stationary noise signals.
5) Exhaust radiation noise under an acceleration condition is obtained through real vehicle testing, and time domain related transformation is carried out on the obtained windowed wavelet function, so that time domain fluctuation signals of all orders can be obtained. For the time-domain filtering system, the time-domain correlation transformation between the compared signals can be converted into a correlation inner product operation, as shown in equation (10).
And (4) comparing and calculating according to the formula (10) to extract time domain fluctuation signals of all orders. The acquired time domain fluctuation signals can be independently played in a listening room, so that more accurate sound quality analysis is realized.
6) In order to facilitate quantitative comparison and analysis of the order signal, the time-domain order fluctuation signal needs to be subjected to sound pressure level conversion, and the conversion formula is shown as formula (11).
In the formula pe(τ) is the effective acoustic pressure of the time-varying signal,
is whenVarying the wave signal, TpRepresenting a selected average time period. The sound pressure level conversion formula is shown in formula (12).
Ls(τ)＝10log10(pe 2(τ)/p0 2) (12)
In the formula Ls(τ) represents the sound pressure level, p, of a time-varying sound pressure signal0Representing a reference sound pressure. The obtained sound pressure level curve of each order can carry out quantitative comparative analysis on the order silencing effects of different exhaust silencing structures.
The time domain digital weighting method for non-stationary noise signals of the present invention is explained in detail by the following specific embodiments:
according to the invention, a certain 1.5L four-cylinder engine of an automobile is adopted to collect tail pipe radiation noise, a microphone is mounted on a support at the tail end of the automobile, and the support and the automobile body are firmly welded, as shown in figure 1, wherein L is 0.5m, theta is 45 degrees +/-10 degrees, and L is not less than 0.2. And meanwhile, a rotating speed measuring instrument is adopted to obtain the rotating speed pulse of the engine through the cigarette lighter. When exhaust noise is collected, the running condition of the automobile is a two-gear full-accelerator pedal acceleration condition. The method provided by the invention is adopted to extract the order of the exhaust radiation noise under the acceleration working condition, and the specific process is as follows:
1) the rotating speed pulse signal is obtained by sampling by a data acquisition unit at equal intervals, and the serial number of the ith pulse appearing in the rotating speed pulse signal in a signal sequence is set as sn(i) Then the time interval between the ith pulse and the (i + 1) th pulse is:
ΔT(i)＝[sn(i+1)-sn(i)]/fs(1)
in the formula fsFor sampling frequency, f in this embodimentsIs 16384 Hz.
The calculation formula of the instantaneous rotational speed of the engine is as follows:
in the formula (2), n' (t) represents the engine speed, and z represents the number of pulses per revolution. The combination of the vertical type (1) and the formula (2) can calculate the pulse intervalAverage engine speed of (2). The time sequence corresponding to each rotation speed point can be represented by the formula tn＝sn(i)/fsAnd (6) obtaining. The engine speed curve obtained by calculation is shown in fig. 2.
2) It can be seen from fig. 2 that in the interval with higher rotation speed, the calculated engine rotation speed curve may fluctuate due to the interference of the electrical signal of the electrical appliance on the vehicle. The cubic spline curve can ensure continuous position, continuous slope and continuous change of curvature on the curve, so that the cubic spline curve is adopted to carry out smoothing treatment on the rotating speed curve. Acquired raw noise signal psFig. 3 shows (t) and the smoothed engine speed n (t).
3) The order extraction of the time-varying exhaust noise signal is carried out by tracking the order center frequency converted by the rotating speed signal and carrying out time-varying band-pass filtering to obtain each order component, so that a wavelet basis function is constructed from the band-pass filter. The frequency domain transfer function expression of the real-even ideal band-pass filter is shown as the formula (3).
The time domain impulse response function expression of the ideal band-pass frequency domain transfer function can be realized by using a sinc function, as shown in formula (4).
hB(t)＝2FLHsinc(2FLHt)-2FLLsinc(2FLLt) (4)
Wherein, FLHIs the upper cut-off frequency, F, of an ideal band-pass filterLLThe lower cut-off frequency of the ideal band-pass filter. The frequency domain transfer function curve and the time domain function curve of the ideal band-pass filter are shown in fig. 4.
However, when filtering the order components in the time-varying signal, it is necessary to implement multi-resolution refinement analysis of the signal through shifting the center frequency of the band-pass transfer function and stretching the bandwidth, that is, the center frequency and the bandwidth of the band-pass filter need to change along with the change of the correlation ratio to the time τ, and the mathematical description thereof can be expressed by equation (5).
Wherein wp(τ) is the bandwidth of the bandpass filter, and fc(τ) is the order center frequency, τ is the correlation versus time system. The central frequency of each order is calculated from the rotating speed curve n (t) of the engine, and is shown as a formula (6).
In the formula (6), the order is the order, and the general engine ignition order and the frequency multiplication thereof are places where the acoustic energy is concentrated. In the present embodiment, a four-stroke four-cylinder engine is used, and thus the 2, 4, and 6 stages are the stages that need to be focused.
The three formulas of (4), (5) and (6) are combined, and an expression of an ideal band-pass impulse response function can be obtained, as shown in formula (7).
Constructed as used in this example
As a standard wavelet basis function, for extraction of order noise. Because the energy of the order component in the exhaust noise is concentrated in a narrow frequency band under the condition of automobile acceleration, and the bandwidth of the order component basically does not change along with time, the bandwidth parameter in the wavelet basis function in the embodiment is constant, namely wp(τ)＝15Hz。
4) In engineering, a time-domain limited function is required to analyze and process signals, so that windowing processing needs to be performed on wavelet basis functions. Hamming windows (hamming) in cosine windows can significantly reduce spectral leakage while the frequency resolution is relatively high. Therefore, in this embodiment, a hamming window (hamming) is used to intercept the wavelet basis function, and the expression of the window function is as follows:
wherein Wβ(T) is a cosine window function, β is a window lifting rate, β is 0.54/0.46, TwIs the window width intercepted, the size of which directly determines the transition bandwidth of the band-pass filter, T in this embodimentw＝0.2s。
The expression of the wavelet function intercepted by the window function is shown as a formula (9).
In the formula (9)
Namely, the standard windowed wavelet function constructed in the present embodiment is used for order tracking extraction of non-stationary noise signals. The wavelet basis functions, the window functions, and the windowed wavelet functions in this embodiment are shown in fig. 5.
5) Exhaust radiation noise under an acceleration condition is obtained through real vehicle testing, and time domain related transformation is carried out on the exhaust radiation noise and the obtained windowed wavelet function, so that time domain fluctuation signals of all orders can be obtained. For the time-domain filtering system, the time-domain correlation transformation between the compared signals can be converted into a correlation inner product operation, as shown in equation (10).
In this embodiment, time domain fluctuation signals of each order can be extracted by performing comparison calculation according to equation (10), as shown in fig. 5. The acquired time domain fluctuation signals can be independently played in a listening room, so that more accurate sound quality analysis is realized.
6) In order to facilitate quantitative comparison and analysis of the order signal, the time-domain order fluctuation signal needs to be subjected to sound pressure level conversion, and the conversion formula is shown as formula (11).
In the formula pe(τ) is the effective acoustic pressure of the time-varying signal,
is a time-varying fluctuating signal, TpRepresents a selected average time period, T in this examplep＝0.125s。
The sound pressure level conversion formula is shown in formula (12).
Ls(τ)＝10log10(pe 2(τ)/p0 2) (12)
In the formula Ls(τ) represents the sound pressure level, p, of a time-varying sound pressure signal0Represents a reference sound pressure, p0＝2×10-5Pa。
The order sound pressure level curves obtained according to equations (11) and (12) are shown in fig. 6. The obtained sound pressure level curve of each order can carry out quantitative comparative analysis on the order silencing effects of different exhaust silencing structures.
In order to verify the correctness of the order extraction method proposed by the present invention, a short-time fourier transform is used to obtain a three-dimensional chromatogram of the original noise signal and each order signal, as shown in fig. 7. As can be seen from fig. 7, the order noise components of 2, 4 and 6 orders are clearly shown in (b), (c) and (d), other irrelevant noises are all filtered, and the order noise components are well matched with the corresponding order graph in the original exhaust noise spectrogram in fig. 7(a), so that the order extraction method provided by the invention is fully demonstrated to accurately separate the order components.
The above examples are only for illustrating the present invention, and the implementation steps of the method and the like can be changed, and all equivalent changes and modifications based on the technical scheme of the present invention should not be excluded from the protection scope of the present invention.
Claims (1)
1. A non-stationary exhaust noise signal order quantitative extraction method based on wavelet transformation is characterized by comprising the following steps:
step (1): the engine speed pulse signal obtained by the speed measuring instrument is provided with the ith pulse appearing in the speed pulse signalThe sequence number in the signal sequence being sn(i) The time interval Δ T between the ith pulse and the (i + 1) th pulse is:
ΔT(i)＝[sn(i+1)-sn(i)]/fs(1)
in the formula (1), fsIs the sampling frequency; the calculation formula of the instantaneous rotational speed of the engine is as follows:
in the formula (2), n' (t) is the engine speed, and z is the number of pulses per revolution;
calculating an engine rotating speed curve by the joint vertical type (1) and the formula (2), and calculating a time sequence corresponding to each point on the engine rotating speed curve by the formula tn＝sn(i)/fsObtaining;
step (2): smoothing the engine speed curve by adopting a cubic spline curve to obtain a smooth engine speed curve n (t);
and (3): wavelet basis functions are constructed by band pass filters: the frequency domain transfer function expression of the real-even ideal band-pass filter is shown as the formula (3):
the time domain impulse response function expression of the ideal band-pass frequency domain transfer function is realized by using a sinc function, as shown in formula (4):
hB(t)＝2FLHsinc(2FLHt)-2FLLsinc(2FLLt) (4)
wherein, FLHIs the upper cut-off frequency, F, of an ideal band-pass filterLLThe lower cut-off frequency of an ideal band-pass filter is determined by two parameters of the center frequency and the bandwidth of the band-pass filter, and the mathematical description thereof can be expressed by equation (5):
wherein wp(τ) is the bandwidth of the bandpass filter, and fc(tau) is order center frequency, tau is correlation comparison time system; calculating the central frequency of each order from the engine speed curve n (t) in the step (2), wherein the formula (6) is as follows:
in the formula (6), the order is;
the time domain expression of the ideal band-pass impulse response function obtained by the three formulas of the joint type (4), (5) and (6) is shown as the formula (7):
and (4): intercepting the wavelet basis function by adopting a cosine window function to enable the wavelet basis function to have time domain limitation; the window function is shown in equation (8):
wherein Wβ(T) is a cosine window function, β is a window lifting rate, TwIs the window width intercepted;
the expression of the windowed wavelet function after the window function is intercepted is shown as the formula (9):
acquiring exhaust radiation noise under an acceleration condition through real vehicle test, and performing time domain correlation transformation on the exhaust radiation noise and the acquired windowed wavelet function to acquire time domain fluctuation signals of each order, wherein the formula (10) is shown;
step (6) to facilitate quantitative comparison and analysis of the order signals, sound pressure level conversion is carried out on the time domain order fluctuation signals; the effective sound pressure calculation formula of the non-stationary noise signal is shown as formula (11):
in the formula pe(τ) is the effective acoustic pressure of the time-varying signal,
is a time-varying fluctuating signal, TpRepresenting a selected average time period; the sound pressure level transformation formula is shown in formula (12):
Ls(τ)＝10log10(pe 2(τ)/p0 2) (12)
in the formula Ls(τ) represents the sound pressure level, p, of a time-varying sound pressure signal0Represents a reference sound pressure; and carrying out quantitative comparative analysis on the order silencing effects of different exhaust silencing structures by using the acquired sound pressure level curves of each order, thereby guiding the improvement of the silencing structures.
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