CN111193497B - Secondary channel modeling method based on EMFNL filter - Google Patents

Abstract

The invention relates to the field of active noise control, and discloses a secondary channel modeling method based on an even mirror Fourier nonlinear with linear section (EMFNL, Even Mirror Fourier Nonlinear with Linear section) filter, including S1 generating Gaussian white Noise, and filter out the high-frequency part; S2 stimulates white noise in S1, constructs EMFNL filter taps and simplifies; S3 uses adaptive algorithm to identify coefficients for filter taps in S2; S4: Thinning the secondary channel in S3 Transfer function coefficients; S5: Compute the secondary channel estimation for the sparsified secondary channel. Compared with the prior art, the present invention can effectively model the nonlinear secondary channel situation in the active noise control system, making the nonlinear active noise control model more accurate, and the sparse coefficient method given at the same time can effectively reduce the The number of channel estimation coefficients can effectively reduce the complexity of the algorithm.

Description

A secondary channel modeling method based on EMFNL filter

Technical Field

The invention relates to the field of active noise control, and in particular to a secondary channel modeling method based on an Even Mirror Fourier Nonlinear with Linear section (EMFNL) filter.

Background Art

Active noise control (ANC) technology based on the superposition principle has been widely studied and applied due to its advantages such as low cost, significant low-frequency effect, and simple deployment and control. It is very likely to become the standard technology for noise reduction in enclosed spaces in the future.

Active noise control models are divided into models with secondary channels and models without secondary channels. In terms of models without secondary channels, Chinese patent CN 101393736 B discloses an active noise control method without secondary channel modeling, which uses a four-update direction search method to find the optimal coefficient, and has poor real-time performance. Chinese patent CN 103915091 A discloses a modeling method without secondary channels. This method requires statistics on the noise source signal and the error signal power, which is essentially a statistical method. It is difficult to achieve real-time in the initial stage of the system, and when the noise source changes, the system is difficult to respond quickly. Therefore, the model with secondary channels is still the main direction at present. International patent WO2017/048480 EN 2017.03.23 (Chinese patent CN 108352156A) and international patent WO2017/048481 EN 2017.03.23 (Chinese patent CN 108352157 A) disclose methods for estimating the amplitude and phase of secondary channels, which require estimation of different frequency components and have complex algorithms. Chinese patent CN 109448686 A discloses an online secondary modeling active noise control system, which uses a linear secondary channel model and is difficult to handle nonlinear secondary channel situations. Chinese patent CN 109379652 A discloses an offline identification method and system for secondary channels of active noise control of headphones, which uses an infinite impulse response (IIR) filter. Although this filter can approximate a linear filter with fewer coefficients, it is unstable.

In view of the problem that current nonlinear secondary modeling methods, especially the lack of modeling methods for strongly nonlinear situations, the present invention proposes a secondary channel modeling method based on a second-order even mirror Fourier nonlinear with linear section (EMFNL) filter, and provides a secondary channel estimation calculation method under the modeling coefficients.

Summary of the invention

Purpose of the invention: In view of the lack of nonlinear secondary modeling methods in the prior art, especially modeling methods for strongly nonlinear situations, the present invention proposes to provide a nonlinear secondary channel modeling method based on a second-order mirror Fourier nonlinear (EMFNL) filter with linear parts. The method can nonlinearly model secondary channels, and provides a method for calculating time-varying secondary channel estimates, and also provides a method for calculating sparse secondary coefficients and secondary estimates.

Technical solution: The present invention provides a secondary channel modeling method based on an EMFNL filter, comprising the following steps:

S1: Generate Gaussian white noise and filter out the high-frequency part;

S2: For the white noise in S1, construct and simplify the tap of the even-mirror Fourier nonlinear EMFNL filter with linear part;

S3: For the filter taps in S2, an adaptive algorithm is used to identify the coefficients;

S4: The secondary channel transfer function coefficients in the sparse S3;

S5: Calculate the secondary channel estimate for the sparse secondary channel.

Furthermore, the simplified filter tap implementation in S2 includes:

1) Remove some of the taps in the filter: if the secondary channel is very weakly nonlinear, only the linear part of the secondary channel coefficient s(n) is retained; if the system exhibits linear and triangular nonlinearity, only the linear, sine and cosine taps in the secondary channel coefficient s(n) are retained; or

2) The cross-tap partial diagonal structure is realized, and only part of the main diagonal channels are retained.

Furthermore, the sparseness in S4 refers to completing the sparseness by retaining coefficients with large contributions, and the sparseness method includes:

1) Sort the weight coefficients by contribution, and only update the first part of the weight coefficients sorted from large to small. The coefficients are sparsely populated during the update process. The sparse coefficient update algorithm is:

s _p (n+1)=s _p (n)+μe(n)f _c (n)

Where s _p is the first M/a coefficients in s(n) in contribution order, and a is 2 or 3; or,

2) Use a sparse threshold to retain only coefficient values greater than the threshold to complete coefficient sparseness.

Furthermore, in the sparseness method 2), the linear part and the nonlinear part sparseness thresholds are σ ₁ /4 and σ ₂ , wherein σ ₁ and σ ₂ are the variances of the linear part and the nonlinear part coefficients in s(n) respectively.

Furthermore, the secondary channel transfer function in S4 is expressed as follows:

Among them, R ₁ ≤M, R ₂ ≤M, R ₃ ≤M and R ₃ ≤M(M-1)/2 are the number of linear terms, sine terms, cosine terms and cross terms respectively, l _i , k _i , p _i and _qi are delay parameters, and s(n) = [a _i ^T ,b _i ^T ,c _i ^T ,d _i ^T ], where a _i = {a _i ,i = 1,2,…,R ₁ }, b _i = {b _i ,i = 1,2,…,R ₂ }, c _i = {c _i ,i = 1,2,…,R ₃ }, d _i = {d _i ,i = 1,2,…,R ₄ }.

Furthermore, the secondary channel after S5 sparseness is estimated as:

Among them, A _i ~ E _i are coefficient estimates, and l _i , k _i , p _i , _qi and r _i are delay parameters, which satisfy the following conditions:

Beneficial effects:

The present invention provides a nonlinear secondary channel modeling method based on a second-order band linear partial even image Fourier nonlinear (EMFNL) filter, which can nonlinearly model secondary channels, and provides a method for calculating time-varying secondary channel estimation, and also provides a method for calculating sparse secondary coefficients and secondary estimation. The nonlinear secondary channel modeling method can effectively model the nonlinear secondary channel situation in an active noise control system, making the nonlinear active noise control model more accurate, and the sparse coefficient method provided can effectively reduce the number of secondary channel estimation coefficients and reduce the amount of algorithm calculation.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a block diagram of an active noise reduction system;

FIG2 is a block diagram of an even-image Fourier nonlinear (EMFNL) filter with a linear portion;

FIG3 is a cross-term diagonal structure of an even mirror Fourier nonlinear (EMFNL) filter with a linear portion;

FIG4 is a block diagram of a secondary channel adaptive identification algorithm;

FIG. 5 is an identification curve of the secondary channel identified by the present invention and three other filters.

DETAILED DESCRIPTION

The present invention is described in detail below in conjunction with the accompanying drawings.

In the present invention, the secondary channel is the entire process from the output of a digital electrical signal by a digital signal processor (DSP) to the conversion of the digital signal into an acoustic signal that reaches the superposition point. As shown in Figure 1, in the secondary channel, the signal conversion process is as follows: the DSP outputs a digital electrical signal, which is converted into an analog signal by a digital analog converter (DAC), the analog signal is amplified by a power amplifier and then drives a secondary actuator (typically a loudspeaker) to move, generating an anti-noise signal, the acoustic signal is transmitted to the superposition point in the propagation medium, collected as an analog electrical signal by an error sensor, and converted into a digital error signal by an analog digital converter (ADC).

The present invention relates to the field of active noise control and discloses a nonlinear secondary channel modeling method in an active noise reduction system. The implementation steps include:

Step 1: Generate Gaussian white noise and filter out the high-frequency part.

There are various ways to generate Gaussian white noise, and engineers can generate it according to actual conditions. Since active noise control is mainly aimed at low-frequency noise, there is no need to use high-frequency excitation signals when identifying the system. A low-pass filter can be designed to filter out the high-frequency components in the excitation white noise. The reference value of the low-pass filter cutoff frequency is 1500 Hz.

Step 2: Construct an even mirror Fourier nonlinear (EMFNL) filter tap with linear part.

The current moment and M-1 previous moment signals of the excitation white noise are recorded as v(n) = [v(n), v(n-1), ..., v(n-M+1)], and the secondary channel length is M. The second-order band linear partial even mirror Fourier nonlinear (EMFNL) expansion is adopted, as shown in Figure 2, and the filter taps include:

C ₀₀ (n)=[v(n),v(n-1),v(n-2),…,v(n-M+1)] ^T ;

C ₁₀ (n)={sin[πv(n)/2],sin[πv(n)/2],…,sin[πv(n-M+1)/2]} ^T ;

C ₂₀ (n)={cos[πv(n)],cos[πv(n)],…,cos[πv(n-M+1)]} ^T ;

C ₂₁ (n)＝{sin[πv(n)/2]sin[πv(n-1)/2],…,sin[πv(n-M+2)/2]sin[πv(n-M +1)/2],

sin[πv(n)/2]sin[πv(n-2)/2],…,sin[πv(n-M+3)/2]sin[πv(n-M+1)/2],

…,

sin[πv(n)/2]sin[πv(n-M+1)/2} ^T .

According to the secondary channel characteristics, only the linear part coefficients and some nonlinear part coefficients are retained, which can effectively reduce the amount of calculation. Two simplified filter tap implementation forms are given below:

(1) Remove some taps from the filter. If the secondary channel is very weakly nonlinear, only the linear part of the secondary channel coefficient s(n) is retained; if the system exhibits linear and triangular nonlinearity, only the linear, sine and cosine taps in the secondary channel coefficient s(n) are retained.

(2) The cross-tap partial diagonal structure is implemented, and only some of the main diagonal channels are retained. As shown in Figure 3, when approximating a nonlinear system, the closer the kernel function is to the main diagonal channel in the cross-term part, the stronger the approximation ability of the system is. Therefore, the filter result can be simplified by retaining only the coarser main channels in the figure. The reference number of main channels to be retained is M/4, which is determined by engineers based on actual system requirements.

The function expansion tap of the filter is expressed in vector form:

f _c (n) = [C ₀₀ (n), C ₁₀ (n), C ₂₀ (n), C ₂₁ (n)] ^T (1)

Step 3: Use adaptive algorithm to identify coefficients.

The coefficients corresponding to the filter taps in the second step above are the secondary channel transfer function coefficients, which correspond to s(n)=[s ₀ (n),s ₁ (n),s ₂ (n),…,s _M+1 (n)] in Figure 2, with a length of (M ² +5M)/2 and initialized to 0. As shown in Figure 4, the adaptive least mean square error (LMS) algorithm is used to iteratively obtain the weight coefficients, and the iterative formula is:

s(n+1)＝s(n)+μe(n)f _c (n) (2)

Among them, μ is the step size, e(n) is the error signal after the two signals are superimposed, which is obtained by the following formula:

e(n)＝d(n)+d'(n)＝d(n)+f _c (n)*s(n) (3)

In the above formula, d(n) is the noise that reaches the error microphone after the white noise v(n) is transmitted through the secondary channel, which can be directly collected by the error sensor. The typical form of the sensor in active noise control is a microphone. d'(n) is the noise generated by the convolution of the identification EMFNL filter and the weight coefficient s(n). The processing process in the dotted box in Figure 4 is completed by a computing device, typically a DSP.

Step 4: Sparsify the secondary channel transfer function coefficients in step 3.

There may be a large number of near-zero terms in the coefficients, which may be noise in the identification process. Therefore, sparseness is achieved by retaining coefficients with greater contributions. The present invention discloses two sparseness methods:

(1) Only the items with larger contributions in the weight coefficients are updated, and the coefficients are sparsely distributed during the update process. The sparse coefficient update algorithm becomes:

s _p (n+1)＝s _p (n)+μe(n)f _c (n) (4)

Among them, s _p is the larger M/a coefficient in s(n), and the typical value of a is 2 or 3, which can be determined by the engineer according to actual needs.

(2) Use sparse thresholds to complete coefficient sparseness. After iteratively obtaining the complete secondary channel coefficients s(n), engineers select thresholds based on the actual system and only retain coefficient values greater than the threshold. Typical values of the thresholds are σ ₁ /4 and σ ₂ , where σ ₁ and σ ₂ are the variances of the linear and nonlinear coefficients in s(n), respectively.

Step 5: Calculate the secondary channel estimate for the sparse secondary channel.

The secondary channel transfer function is expressed as follows

Among them, R ₁ ≤M, R ₂ ≤M, R ₃ ≤M and R ₃ ≤M(M-1)/2 are the number of linear terms, sine terms, cosine terms and cross terms respectively, l _i , k _i , p _i and _qi are delay parameters, and s(n) = [a _i ^T ,b _i ^T ,c _i ^T ,d _i ^T ], where a _i = {a _i ,i = 1,2,…,R ₁ }, b _i = {b _i ,i = 1,2,…,R ₂ }, c _i = {c _i ,i = 1,2,…,R ₃ }, d _i = {d _i ,i = 1,2,…,R ₄ }.

The sparse secondary channel estimate s'(n) is:

Among them, A _i ~ E _i are coefficient estimates, l _i , k _i , p _i , q _i and r _i are delay parameters, satisfying the following formula:

If only the linear tap part of the filter is used in the secondary channel coefficient identification, then only _Ai is included in the secondary channel estimation. In this case, the secondary channel is a linear steady-state system, and the secondary channel coefficient estimation _Ai can be directly stored in the digital signal processor (DSP). If the secondary channel coefficient identification includes a nonlinear part, the secondary channel coefficient estimation is time-varying, and the secondary channel sparse estimation can be calculated in real time according to formula (7).

The following specific data are used to prove that the secondary channel modeling method of the present invention can effectively model the nonlinear secondary channel situation in the active noise control system and the model is more accurate.

Assume the transfer function of the secondary channel is:

Adaptive Chebyshev filter, second-order Volterra filter, function link artificial neural network (FLANN) filter and EMFNL filter are used to identify the secondary channel respectively. After identification, the normalized mean square error is used as the comparison standard. As shown in Figure 5, the Chebyshev, Volterra and FLANN filters can achieve identification results of about -13dB to -15dB, while the EMFNL filter can reach -27dB. This result shows that the EMFNL filter has a stronger characterization ability for the above secondary channels.

The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A secondary channel modeling method based on an Even Mirror Fourier non-Linear (EMFNL) filter with a Linear part is characterized by comprising the following steps:

s1: generating white gaussian noise and filtering out high frequency part;

s2: for white noise excited in S1, constructing and simplifying a tap of the even-image Fourier nonlinear EMFNL filter with the linear part;

s3: for the filter tap in the S2, adopting a self-adaptive algorithm to identify a coefficient;

s4: sparsifying the coefficients of the secondary channel transfer function in S3;

s5: a secondary channel estimate is computed for the thinned-out secondary channel.

2. The EMFNL filter-based secondary channel modeling method of claim 1, wherein the simplified filter tap implementation in S2 comprises:

1) Removing part of taps in the filter: if the secondary channel is a very weak non-linear case, only the linear part of the secondary channel coefficients s (n) is retained; if the system exhibits linear and triangular non-linear conditions, only the linear, sine and cosine taps in the secondary channel coefficients s (n) are retained; or

2) The cross-tap partial diagonal structure is implemented, and only partial main diagonal channels are reserved.

3. The EMFNL filter-based secondary channel modeling method according to claim 2, wherein the sparsification at S4 is performed by keeping coefficients contributing to a large amount, and the sparsification method comprises the following steps:

1) The contribution sizes of the weight coefficients are sorted, only the front part items of the weight coefficients, which are sorted from large to small, are updated, coefficient sparsification is completed in an updating link, and a sparsification coefficient updating algorithm is as follows:

s _p (n+1)＝s _p (n)+μe(n)f _c (n)

wherein s is _p M/a coefficients before the contribution sorting in s (n) are obtained, and a takes the value of 2 or 3; or,

2) And (4) using a sparse threshold value, only keeping coefficient values larger than the threshold value, and completing coefficient sparsification.

4. The EMFNL filter-based secondary channel modeling method according to claim 3, wherein the sparse threshold value of the linear part and the nonlinear part in the sparse method 2) is σ ₁ A/4 and a ₂ Wherein σ is ₁ And σ ₂ Respectively the variance of the linear part and non-linear part coefficients in s (n).

5. The EMFNL filter based secondary channel modeling method of claim 2, wherein the secondary channel transfer function in S4 is represented as follows:

wherein R is ₁ ≤M、R ₂ ≤M、R ₃ M and R are not more than ₃ M (M-1)/2 is less than or equal to the number of linear terms, sine terms, cosine terms and cross terms respectively, l _i ,k _i ,p _i And q is _i Is a time delay parameter, when s (n) = [ a _i ^T ,b _i ^T ,c _i ^T ,d _i ^T ]Wherein a is _i ＝{a _i ,i＝1,2,…,R ₁ }，b _i ＝{b _i ,i＝1,2,…,R ₂ }，c _i ＝{c _i ,i＝1,2,…,R ₃ }，d _i ＝{d _i ,i＝1,2,…,R ₄ }。

6. The EMFNL filter-based secondary channel modeling method of claim 5, wherein the S5 sparse secondary channel estimate is:

wherein A is _i ～E _i For coefficient estimation,/ _i ,k _i ,p _i ,q _i And r _i As a delay parameter, the following is satisfied:

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