A method for tracking and suppressing waterbed effect in an adaptive feedback active control system

Abstract

The present invention discloses a method for tracking and suppressing the waterbed effect of an adaptive feedback active control system, comprising the following steps: secondary path modeling; synthesizing a reference signal x(n) by using an error signal e(n) picked up by an error sensor minus a control signal y(n) fed to a secondary sound source filtered by a secondary path model; calculating a filtered-x signal r(n) by using the secondary path model and the reference signal; performing linear prediction on an initial noise signal to obtain a whitening filter of the initial noise; filtering the error signal e(n) by a whitening filter to obtain a filtered-e signal e'(n); filtering the filtered-x signal r(n) by a whitening filter to obtain a filtered-r signal r'(n); iterating the control filter coefficients, and at the same time minimizing the cost function. The present invention can track and suppress the noise amplification caused by the "waterbed" effect in real time without knowing the location of the "waterbed" in advance.

Description

Technical Field

[0001] The invention belongs to the technical field of active noise control, and in particular relates to a method for tracking and suppressing a waterbed effect of an adaptive feedback active control system. Background Art

[0002] Active Noise Control (ANC) has been widely used in active noise reduction headphones, active noise reduction in cars, machine noise reduction, active sound barriers and indoor noise reduction. It also has application prospects in human-computer interaction situations, such as reducing the noise in the robot's operating environment and improving its ability to recognize speech.

[0003] Active noise control structures can be divided into feedforward active noise control and feedback active noise control, where the performance of the former depends on the coherence between the reference signal and the primary noise signal. In many ANC system application scenarios, it is impossible to obtain a high-quality reference signal, the noise reduction performance is weak or no noise reduction can be achieved, and a feedback active control system can be used. However, the feedback system has a "water bed" effect, that is, while reducing noise in a specific frequency band, it will cause noise amplification in other frequency bands.

[0004] A common method to solve this problem is to use an offline algorithm to design a control filter. The noise amplification caused by the water bed effect is considered as a constraint in the offline algorithm design. ∞ Design method (B. Rafaely and SJ Elliott, “H2 / H ∞active control of sound in a headrest: design and implementation,” IEEE T.Contr.Syst.T.7(1), 79-84(1999)), constructs a convex optimization problem with “water bed” suppression and robust stability as constraints, and then uses a sequential quadratic programming algorithm to solve the optimal filter, obtaining a control filter that meets the constraints and effectively reduces noise. For example, Zhang proposed a numerical solution algorithm that does not require complex weight parameter selection and optimization. By widening the noise amplification frequency band as much as possible and uniformly amplifying the noise within the noise amplification frequency band, the noise amplification peak is limited to a given limit to improve the “water bed” effect (L.Zhang, L.Wu, and X.Qiu, “An intuitive approach for feedback active noise controller design,” Appl. Acoust. 74 (1), 160-168 (2013)). However, these algorithms are not suitable for real-time adaptive systems. In real-time adaptive feedback systems, the internal model control (IMC) structure is generally adopted, and the basic filter-x least mean square (FxLMS) algorithm is used to calculate the control filter. Due to the "waterbed" effect, it may cause large noise amplification in certain frequency bands. The use of the leakage filter-x least mean square (LFxLMS) algorithm can reduce the size of the full-band output signal and achieve "waterbed" suppression. However, this algorithm can only constrain the full-band control filter with the same weight. Generalized leaky filter-x least mean square (GLFxLMS) algorithm (L.Wu, X.Qiu, and Y.Guo, “A generalized leaky FxLMS algorithm for tuning the waterbed effect of feedback active noise control systems,”Mech.Syst.Signal.Pr.106,13-23(2018)) and the frequency band constrained filtered-x least mean square (FcFxLMS) algorithm (C.Zhou,H.Zou,and X.Qiu,“A frequency band constrained filtered–x least meansquare algorithm for feedback active control systems,”JACOUST SOC AM,148(4),1947-1951(2020)) can suppress the noise amplification caused by the water bed effect by suppressing the amplitude of the control filter in a specific frequency band, and the noise reduction effect is higher than that of the LFxLMS algorithm.However, both algorithms require knowing the frequency band where the "water bed" appears in advance. When the noise spectrum changes, both algorithms cannot constrain the newly appearing "water bed" in real time.

[0005] Based on this, it is necessary to provide an algorithm for feedback active noise control system, which can track and suppress the noise amplification caused by the water bed effect in real time when the noise spectrum changes and the noise amplification frequency band caused by the water bed effect changes accordingly. Summary of the invention

[0006] Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a method for tracking and suppressing the waterbed effect of an adaptive feedback active control system, which can track and suppress the noise amplification caused by the "waterbed" effect in real time without knowing the location of the "waterbed" in advance.

[0007] Technical solution: To achieve the above purpose, the technical solution adopted by the present invention is:

[0008] A method for tracking and suppressing a waterbed effect of an adaptive feedback active control system comprises the following steps:

[0009] Step 1: Measure the unit impulse response of the secondary path transfer function of the active control system and obtain the secondary path estimation function z is a complex variable.

[0010] Step 2: Use the error signal e(n) picked up by the error sensor minus the control signal y(n) fed to the secondary sound source to estimate the secondary path function After filtering, we get the reference signal x(n), x(n) = [x(n), x(n-1), ..., x(n-M+1)] T , n is the time index, and M is the unit impulse response order of the secondary path.

[0011] Step 3, calculate the filtered-x signal r(n) through the reference signal x(n), Where r(n) is the filtered-x signal, r(n) = [r(n), r(n-1), ..., r(n-L+1)] T , L is the length of the control filter, and T is the transposed sign.

[0012] Step 4: Perform linear prediction on the initial noise p(n) to obtain the whitening filter F(z) of the initial noise.

[0013] Step 5: Filter the error signal e(n) through a whitening filter F(z) to obtain a filtered-e signal e'(n).

[0014] Step 6: Filter the filtered-x signal r(n) through the whitening filter F(z) to obtain the filtered-r signal r'(n), r'(n) = [r'(n), r'(n-1), ..., r'(n-L+1)] T .

[0015] Step 7, update the control filter coefficient w(n) through the iterative formula, the iterative formula is:

[0016] w(n+1)=γw(n)-2μ[e(n)r(n)+αe′(n)r′(n)]

[0017] Among them, μ is the iteration step size, α is the weight factor of the constrained water bed effect, γ = 1-2μβ, and β is the weight factor of the constrained control filter output.

[0018] Step 8, continuously iteratively control the filter coefficient w(n) to minimize the cost function. The cost function is:

[0019] J=E[p 2 (n)+αp′ 2 (n)]+2w T (P+αP′)+w T (R+αR′+βI)w

[0020] Where J is the cost function value, E is the expected calculation, p(n) is the initial noise, p'(n) is the signal after the initial noise is filtered by the whitening filter F(z), R is the autocorrelation matrix of the filter-x signal r(n), R' is the autocorrelation matrix of the filter-r signal r'(n), P is the cross-correlation vector of p(n) and r(n), P' is the cross-correlation vector of p'(n) and r'(n), I is the unit matrix, and w is the abbreviation of the control filter coefficient.

[0021] Preferred: Use variable weight factors for sensitivity magnitude constraints:

[0022]

[0023] Among them, α is the weight factor of the constrained water bed effect, α0 is a non-negative constant, N is the block length in the MFBLMS algorithm, and e LP is the error vector in the kth block of the adaptive linear prediction process.

[0024] Preferred: The error vector e in the kth block of the adaptive linear prediction process LP :

[0025] e LP =[e LP (kN),e LP (kN+1),…,e LP (kN+N-1)]T

[0026] Wherein, k represents the data block number.

[0027] Preferred: The cross-correlation vector P of p(n) and r(n):

[0028] P=E[p(n)r(n)]

[0029] Where P is the cross-correlation vector of p(n) and r(n).

[0030] Preferably: the signal after the initial noise signal is filtered by the whitening filter F(ω):

[0031] p′(n)=f(n)*p(n)

[0032] Where p'(n) is the signal after the initial noise signal is filtered by the whitening filter F(ω).

[0033] Preferred: Filter-r signal:

[0034] r′(n)=f(n)*r(n)

[0035] Where r'(n) represents the filtered -r signal.

[0036] Preferred: Autocorrelation matrix of the filtered-x signal r(n):

[0037] R = E[r(n)r T (n)]

[0038] Where R is the autocorrelation matrix of the filtered-x signal r(n).

[0039] Preferred: The cross-correlation vector of p'(n) and r'(n):

[0040] P′=E[p′(n)r′(n)]

[0041] Where P' is the cross-correlation vector of p'(n) and r'(n).

[0042] Preferred: Autocorrelation matrix of the filtered-r signal r'(n):

[0043] R′=E[r′(n)r′ T (n)]

[0044] Where R' is the autocorrelation matrix of the filtered-r signal r'(n).

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] (1) Compared with the non-adaptive filter design method, the method proposed in the present invention can be used in real-time adaptive systems.

[0047] (2) Compared with the LFxLMS algorithm, the present invention does not limit the control filter amplitude of all frequency bands, but only performs water bed suppression on the frequency band where noise is amplified, resulting in a better noise reduction effect.

[0048] (3) Compared with the GLFxLMS algorithm and the FcFxLMS algorithm, the present invention can track and suppress the noise amplification caused by the water bed effect in real time when the noise spectrum changes, resulting in a change in the noise amplification frequency band caused by the water bed effect of the system. There is no need to know the frequency band where the "water bed" appears in advance, and the algorithm can be applied in a wider range. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a block diagram of the present invention.

[0050] Figure 2 is the amplitude-frequency response of the whitening filter in the embodiment of the present invention.

[0051] Figure 3 It is a comparison diagram of the power spectral density of the noise signal before and after noise reduction by the present invention and the traditional FxLMS algorithm and LFxLMS algorithm when the noise signal and the secondary path remain unchanged.

[0052] Figure 4 It is a comparison diagram of the amplitude-frequency response of the steady-state filter of the present invention, the traditional FxLMS algorithm and the LFxLMS algorithm.

[0053] Figure 5 Schematic diagram of different movements of the head and torso model in the active noise reduction headrest system.

[0054] Figure 6 It is a comparison diagram of the power spectral density of the noise signal before and after noise reduction by the present invention and the traditional FxLMS algorithm and LFxLMS algorithm when the noise signal changes.

[0055] Figure 7 It is a MSE convergence curve diagram of the whitening filter and the control filter when the noise signal changes in the present invention. DETAILED DESCRIPTION

[0056] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0057] A method for tracking and suppressing the waterbed effect of an adaptive feedback active control system, such as Figure 1 As shown, the following steps are included:

[0058] Step 1: Measure the unit impulse response of the secondary path transfer function of the active control system and obtain the secondary path estimation function z is a complex variable.

[0059] Step 2: Use the error signal e(n) picked up by the error sensor to subtract the control signal y(n) fed to the secondary sound source to obtain the initial noise p(n). The initial noise p(n) is estimated by the secondary path estimation function After filtering, the reference signal x(n) is obtained, where x(n) = [x(n), x(n-1), ..., x(n-M+1)] T , n is the time index, and M is the unit impulse response order of the secondary path.

[0060] Step 3, calculate the filtered-x signal r(n) through the reference signal x(n), Where r(n) is the filtered-x signal, r(n) = [r(n), r(n-1), ..., r(n-L+1)] T , L is the length of the control filter, and T is the transposed sign.

[0061] Step 4: Perform linear prediction on the initial noise p(n) to obtain the whitening filter F(z) of the initial noise.

[0062] Step 5: Filter the error signal e(n) through a whitening filter F(z) to obtain a filtered-e signal e'(n).

[0063] Step 6: Filter the filtered-x signal r(n) through the whitening filter F(z) to obtain the filtered-r signal r'(n), r'(n) = [r'(n), r'(n-1), ..., r'(n-L+1)] T .

[0064] Step 7, update the control filter coefficient w(n) through the iterative formula, the iterative formula is:

[0065] w(n+1)=γw(n)-2μ[e(n)r(n)+αe′(n)r′(n)]

[0066] Among them, μ is the iteration step size, α is the weight factor of the constrained water bed effect, γ = 1-2μβ, and β is the weight factor of the constrained control filter output.

[0067] Step 8, continuously iteratively control the filter coefficient w(n) to minimize the cost function. The cost function is:

[0068] J=E[p 2 (n)+αp′ 2 (n)]+2w T (P+αP′)+wT (R+αR′+βI)w

[0069] Where J is the cost function value, E is the expected calculation, p(n) is the initial noise, p'(n) is the signal after the initial noise is filtered by the whitening filter F(z), R is the autocorrelation matrix of the filter-x signal r(n), R' is the autocorrelation matrix of the filter-r signal r'(n), P is the cross-correlation vector of p(n) and r(n), P' is the cross-correlation vector of p'(n) and r'(n), and w is the abbreviation of the control filter coefficient.

[0070] Figure 1 The block diagram of the FxLMS algorithm (hereinafter referred to as the basic algorithm) of the feedback ANC system based on internal model control is outside the dotted frame. The algorithm of the present invention has been improved on the basic algorithm, as shown in the dotted frame.

[0071] Figure 1 The outside of the dotted box e(n) is the error signal, y(n) is the signal output to the secondary source after the reference signal x(n) passes through the control filter W(z), and y(n) is superimposed with the initial noise signal p(n) through the secondary path C(z) to obtain the error signal e(n). is the estimation function of the secondary path function C(z), and the reference signal x(n) is the estimation of the initial noise signal, which is obtained by subtracting the error signal e(n) from the y(n) fed to the secondary source. The filtered signal is obtained.

[0072] The dotted box F(z) is the whitening filter of the initial noise p(n), e'(n) is the signal after the error signal e(n) is filtered by the whitening filter F(z), which is called the filtered-e signal; r(n) is the reference signal x(n) after being filtered by the whitening filter F(z). The filtered-x signal obtained after filtering, r'(n) is the filtered-x signal r(n) filtered by the whitening filter F(z) to obtain the filtered-r signal. The coefficient f(n) of the whitening filter F(z) can be obtained by linear prediction of the initial noise signal p(n). There are many ways to achieve linear prediction, such as the frequency-domain block LMS (Frequency-domain Block Least Mean Square, MFBLMS) algorithm or the improved frequency-domain block LMS algorithm.

[0073] Depend on Figure 1 As shown, the time domain form of the cost function of the present invention is:

[0074] J=E[e 2 (n)+αe′ 2 (n)]+βw(n) T w(n) (1)

[0075] The expression of e(n) is:

[0076] e(n)=p(n)+w T (n)r(n) (2)

[0077] Where r(n) = [r(n), r(n-1), ..., r(n-L+1)] T is the filtered-x signal vector, To filter the -x signal, x(n) = [x(n), x(n-1), ..., x(n-M+1)] T is the reference signal vector, L is the length of the control filter, and M is the secondary path estimated unit impulse response Length.

[0078] The expression of e'(n) is:

[0079] e′(n)=f(n)*e(n) (3)

[0080] Among them, f(n) is the filter coefficient of the whitening filter F(z), and * represents the convolution operation.

[0081] Let P p (ω) is the power spectral density of the initial noise, and F(ω) is the whitening filter frequency response of the initial noise p(n), that is:

[0082]

[0083] According to the Wiener-Khinchin theorem, the frequency domain form of the cost function expressed by equation (1) is:

[0084]

[0085] It is known that the sensitivity function of the feedback ANC system is defined as S(ω)=E(ω) / P(ω), where E(ω) represents the error noise signal e(n), P(ω) represents the Fourier transform of the initial noise p(n), and P e (ω) is the power spectral density of the error signal e(n), P p (ω) is the power spectral density of the initial noise signal p(n). When |S(ω)|>1, the noise is amplified, which means that the "water bed effect" causes noise amplification. When |S(ω)|<1, the noise is attenuated.

[0086] Put |S(ω)| 2 =P e (ω) / P p Substituting (ω) and equation (4) into equation (5), the frequency domain form of the cost function changes to:

[0087]

[0088] It can be seen that the second term in the brackets of the cost function can constrain the amplitude of the sensitivity function |S(ω)| of the feedback ANC system, reduce the size of |S(ω)|, and by setting a suitable weight factor α, the noise amplification caused by the "water bed" effect can be suppressed without affecting the noise reduction performance. The third term in the brackets of the cost function constrains the amplitude of the control filter of the feedback ANC system, which is similar to the LFxLMS algorithm. The difference is that in the present invention, the role of this term is not to constrain the water bed effect, but to ensure the stability of system convergence, so the weight factor β used is much smaller than the LFxLMS algorithm.

[0089] Substituting equation (2) and equation (3) into equation (1), we get:

[0090]

[0091] Where p'(n) is the signal after the initial noise signal is filtered by the whitening filter F(ω), I is the unit matrix, R and R' are the autocorrelation matrices of the filtered-x signal r(n) and the filtered-r signal r'(n), respectively, P is the cross-correlation vector of p(n) and r(n), and P' is the cross-correlation vector of p'(n) and r'(n), which are defined as follows:

[0092] p′(n)=f(n)*p(n) (8)

[0093] r′(n]=f(n)*r(n) (9)

[0094] P=E[p(n)r(n)] (10)

[0095] R = E[r(n)r T (n)] (11)

[0096] P′=E[p′(n)r′(n)] (12)

[0097] R′=E[r′(n)r′ T (n)] (13)

[0098] According to formula (7), the cost function J is a convex function of the control filter coefficient w(n), so there is a global optimal solution. The instantaneous gradient of formula (1) is:

[0099]

[0100] According to the stochastic gradient descent method, the iterative formula for controlling the filter coefficients is:

[0101]

[0102] in, is the instantaneous gradient, μ is the iteration step size, and γ = 1-2μβ.

[0103] The present invention filters the error signal to realize the constraint of the sensitivity function of the feedback ANC system, which is hereinafter referred to as the sensitivity constrained FeLMS (Sensitivity constrained Filtered-e Least Mean Square) algorithm, or ScFeLMS algorithm for short.

[0104] The whitening filter coefficient f(n) can be obtained by linear prediction of the initial noise signal p(n), and the prediction speed and accuracy will affect the algorithm performance. The following example illustrates how to obtain f(n) through linear prediction. A publicly disclosed improved frequency-domain block LMS algorithm (J. Lu, X. Qiu, and H. Zou, "A modified frequency-domain block LMS algorithm with guaranteed optimal steady-state performance," Signal Processing. 104, 27-32 (2014)) can converge to the Wiener solution in a non-causal situation. This example uses the algorithm to adaptively iterate the whitening filter coefficient f(n), that is, the real-time update process of the whitening filter coefficient is embedded in the proposed algorithm, so that the algorithm of the present invention can adaptively update the whitening filter and control the filter when the noise spectrum characteristics change. In the adaptive iteration process of f(n), the error of linear prediction decreases from large to small, and finally reaches stability. If the weight factor α is kept unchanged, in the initial stage of iteration, due to the inaccuracy of f(n), the algorithm has the risk of divergence. The embodiment of the present invention uses a variable weight factor for the sensitivity amplitude constraint, which is defined as follows:

[0105]

[0106] Among them, α is the weight factor of the constrained water bed effect, α0 is a non-negative constant, N is the block length in the MFBLMS algorithm, and e LP is the error vector in the kth block of the adaptive linear prediction process.

[0107] The error vector e in the kth block of the adaptive linear prediction process is LP :

[0108] e LP =[e LP (kN),e LP (kN+1),…,e LP (kN+N-1)] T

[0109] Wherein, k represents the data block number.

[0110] The variable weight factor shown in formula (16) can constrain the e'(n) signal with a smaller weight when the whitening filter does not converge, thereby ensuring the stability of the present invention. After the whitening filter converges, the value of the weight factor shown in formula (16) remains stable, thereby ensuring the performance of the present invention.

[0111] The effect of the present invention is illustrated below by taking an active noise reduction headrest system as an example. The active noise reduction headrest system is generally arranged near the human ear, and a loudspeaker is used as a secondary sound source. By reducing the noise of the error microphone near the human ear, a quiet zone is generated near the human ear. Each ear uses a control channel, which includes a secondary sound source and an error microphone. The error microphone is 8 cm away from the center of the secondary sound source diaphragm. There are 2 channels for 2 ears. Generally speaking, the 2 channels of the active noise reduction headrest system are weakly coupled, and each channel can be regarded as a single-channel system. The active noise reduction headrest system is usually used to reduce low-frequency noise. When the feedback adaptive active control algorithm is applied, noise amplification will occur in the mid- and high-frequency bands due to the water bed effect. If the water bed is not constrained, a higher water bed may appear in certain frequency bands, causing greater noise amplification and affecting the sense of hearing. The above steps 1-8 can be used to implement the present invention to track and suppress the noise amplification caused by the water bed effect.

[0112] In order to illustrate the performance of the method of the present invention, the steady-state performance of the traditional FxLMS algorithm, the LFxLMS algorithm and the ScFeLMS algorithm proposed in the present invention are compared and verified by simulation. The above active noise reduction head is used to simulate the transfer function measured by the system, and a speaker is used as the primary sound source. The primary noise is a square with a variance of 10 －10 The white noise passes through a transfer function of H(z)=[(1-2z -2 +z -4 ) / (1-3.91z -1 +5.76z -2 -3.79z -3 +0.94z -4 )] after the signal is filtered by the bandpass filter. The adaptive control filter length L = 512, the whitening filter length is 513, and the block length N and iteration step size in the MFBLMS algorithm are 513 and 1.1×10 -4 , the constant weight factors α0 and β are 2.6 and 1.0 respectively, and the control filter iteration step size μ is 6.0×10 -8 The constraint weight of the filter coefficient of the comparison algorithm LFxLMS is set to 2.0×10 2, which is 200 times the filter constraint weight of the ScFeLMS algorithm. It can be seen that the ScFeLMS algorithm mainly reflects the constraint on the amplitude of the system sensitivity function in the second term in the brackets of the cost function of formula (6), rather than the constraint on the filter amplitude. In the simulation, it is assumed that the secondary path model is accurately estimated, that is, equal to C(z). The sampling rate is set to 16kHz.

[0113] The amplitude-frequency response of the converged whitening filter F(ω) in the ScFeLMS algorithm is as follows: Figure 2 shown. Figure 3 The power spectral density of the noise signal before and after noise reduction is given, and compared with the results after noise reduction using the FxLMS algorithm and the LFxLMS algorithm. In the legend, "Primary" represents the noise signal before noise reduction. Although the FxLMS algorithm can achieve the maximum noise reduction of 18.6dB, it produces a large noise amplification in the frequency bands below 100Hz and above 1000Hz, and the peak value of noise amplification in the entire frequency band is 10.8dB. Both the LFxLMS algorithm and the ScFeLMS algorithm can effectively suppress noise amplification, but the amount of noise reduction is reduced. The specific values ​​are shown in Table 1. The amplitude-frequency response of the control filter after convergence of each algorithm is shown in Figure 4 The LFxLMS algorithm reduces the noise amplification caused by the "water bed" effect by suppressing the amplitude of the full-band control filter. The noise reduction is 9.0dB, and the peak value of the noise amplification in the full-band is 4.4dB. The amplitude-frequency response of the control filter after convergence is shown in the figure below. Figure 4 The ScFeLMS algorithm directly constrains the sensitivity function to reduce noise amplification. The noise reduction in the entire frequency band is 12.0 dB, and the noise amplification peak is 4.2 dB. After convergence, the amplitude-frequency response of the control filter is as follows: Figure 4 Shown by the solid red line.

[0114] Table 1 Noise reduction and noise amplification peak of different algorithms when the noise and secondary path remain unchanged

[0115]

[0116] When is not equal to C(z), the reference signal synthesized in IMC is no longer an accurate estimate of the primary noise signal, so there will be a certain error in the estimation of the whitening filter in the ScFeLMS algorithm. Figure 5 The layout diagram of the active headrest system is given in four different cases: the head and torso model (hereinafter referred to as the artificial head) is in the middle of the headrest system (state 1), the artificial head is moved 5 cm to the right (state 2), the artificial head is moved 5 cm to the left (state 3), and there is no artificial head (state 4). The performance of the ScFeLMS algorithm under the change of the secondary path is analyzed by measuring the secondary path transfer function from the left secondary source to the left error microphone in these four different cases.

[0117] by Figure 5 The secondary path transfer function when the human head is located in the middle of the system (state 1) is the secondary path model in the ScFeLMS algorithm. The secondary paths of these four cases are used as the real secondary paths to calculate the noise reduction effect of the ScFeLMS algorithm to simulate the change of the secondary path in the actual active head system. It can be seen from Table 2 that when the secondary path changes, the noise reduction amount of the ScFeLMS algorithm does not change substantially, and its range is 12.0dB to 12.2dB. The noise amplification peak value increases relative to before the change, and its range is 4.2dB to 5.3dB. It can be seen that the algorithm of the present invention has good robustness for the change of the secondary path.

[0118] Table 2 Noise reduction and noise amplification peak of ScFeLMS algorithm when the secondary path changes

[0119]

[0120] The ScFeLMS algorithm proposed in the present invention has a built-in real-time update process of the whitening filter coefficient, so it can update the whitening filter coefficient and the control filter coefficient in real time when the noise changes, thereby tracking and suppressing the noise amplification caused by the water bed effect. The performance of the ScFeLMS algorithm after the noise spectrum changes is analyzed below. The noise is set to change from a center frequency of 300Hz and noise energy mainly concentrated in 200-450Hz to a center frequency of 200Hz and noise energy concentrated in 90-400Hz after 100s. The total duration of the noise signal is 200s. The power spectral density before and after the noise change is as follows: Figure 6 The black circle marker line and the blue triangle marker line are shown in the figure. The parameter settings in the simulation are consistent with the previous article. The normalized MSE convergence curves of the whitening filter update and the control filter update in the ScFeLMS algorithm are shown in Figure 2. Figure 7 As shown by the blue dotted line and the red solid line, the MSE curve from 0s to 100s in the figure uses the mean square value of the noise signal before the noise changes as the normalization factor, and the MSE curve from 100s to 200s uses the mean square value of the noise signal after the noise changes as the normalization factor. Before the noise spectrum changes from 0s to 100s, the whitening filter MSE and the control filter iteration MSE converge. When the noise spectrum changes from 100s to 101s, the whitening filter iteration MSE and the control filter iteration MSE both increase, then gradually decrease, and then converge.

[0121] Figure 6To count the power spectral density of the noise signal before and after noise reduction from 195s to 200s, the black circular marker line in the figure represents the noise signal before the noise changes, and the blue triangle marker line represents the noise signal after the noise changes. The green cross marker line, the purple square marker line and the red solid line represent the power spectral density of the noise signal after noise reduction by the FxLMS algorithm, the LFxLMS algorithm and the ScFeLMS algorithm, respectively. After the noise changes, the noise reduction amount and noise amplification peak of each algorithm from 195s to 200s are shown in Table 3. The FxLMS algorithm can obtain the largest 19.3dB noise reduction among all algorithms, but it has a large noise amplification in the frequency band from 1000Hz to 2500Hz, among which the noise amplification value at 1527Hz is 10.8dB. Both the LFxLMS algorithm and the ScFeLMS algorithm can track and constrain the noise amplification caused by the "water bed" effect after the noise changes. LFxLMS can reduce the noise amplification peak to 7.0dB by constraining the amplitude of the full-band control filter, and the noise reduction is also reduced to 11.9dB. The ScFeLMS algorithm can reduce the noise amplification peak to 7.0 dB and the noise reduction is 15.0 dB by real-time constraining the sensitivity function amplitude.

[0122] It can be seen that when the noise spectrum changes, the whitening filter coefficients are adaptively updated through linear prediction by the MFBLMS algorithm, and the ScFeLMS algorithm can update the constraints on the amplitude of the sensitivity function in real time, which is equivalent to the noise amplification peak of the LFxLMS algorithm, but improves the noise reduction amount.

[0123] Table 3 Steady-state noise reduction and noise amplification peak of different algorithms after the noise spectrum changes

[0124]

[0125] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for tracking and suppressing the waterbed effect of an adaptive feedback active control system, characterized in that , including the following steps: Step 1: Measure the unit impulse response of the secondary path transfer function of the active control system and obtain the secondary path estimation function z is a complex variable; Step 2: After the reference signal x(n) passes through the control filter W(z), the signal output to the secondary source is recorded as the control signal y(n) fed to the secondary sound source; the initial noise p(n) is obtained by subtracting the control signal y(n) fed to the secondary sound source from the error signal e(n) picked up by the error sensor. The initial noise p(n) is estimated by the secondary path estimation function After filtering, we get the reference signal x(n), x(n) = [x(n), x(n-1), ..., x(n-M+1)] T , n is the time index, M is the unit impulse response order of the secondary path; Step 3, calculate the filtered-x signal r(n) through the reference signal x(n), Where r(n) is the filtered-x signal, r(n) = [r(n), r(n-1), ..., r(n-L+1)] T , L is the length of the control filter, T is the transposed sign; Step 4, linearly predict the initial noise p(n) to obtain the whitening filter F(z) of the initial noise; Step 5, filtering the error signal e(n) through a whitening filter F(z) to obtain a filtered-e signal e'(n); Step 6: Filter the filtered-x signal r(n) through the whitening filter F(z) to obtain the filtered-r signal r'(n), r'(n) = [r'(n), r'(n-1), ..., r'(n-L+1)] T ; Step 7, update the control filter coefficient w(n) through the iterative formula, the iterative formula is: w(n+1)=γw(n)-2μ[e(n)r(n)+αe′(n)r′(n)] Among them, μ is the iteration step size, α is the weight factor of the constrained water bed effect, γ = 1-2μβ, β is the weight factor of the constrained control filter output; Use a variable weight factor for the sensitivity magnitude constraint: Among them, α is the weight factor of the constrained water bed effect, α0 is a non-negative constant, N is the data block length in the linear prediction algorithm, and e LP is the error vector in the kth block of the adaptive linear prediction process; The error vector e in the kth block of the adaptive linear prediction process is LP : have been LP =[ie LP (kN), ie LP (kN+1),…,e LP (kN+N-1)] T Wherein, k represents the data block number; Step 8, continuously iteratively control the filter coefficient w(n) to minimize the cost function. The cost function is: J=E[p 2 (n)+αp′ 2 (n)]+2w T (P+αP′)+w T (R+αR′+βI)w Where J is the cost function value, E is the expected calculation, p(n) is the initial noise, p'(n) is the signal after the initial noise is filtered by the whitening filter F(z), R is the autocorrelation matrix of the filter-x signal r(n), R' is the autocorrelation matrix of the filter-r signal r'(n), P is the cross-correlation vector of p(n) and r(n), P' is the cross-correlation vector of p'(n) and r'(n), I is the unit matrix, and w is the abbreviation of the control filter coefficient.

2. The method for tracking and suppressing the waterbed effect of an adaptive feedback active control system according to claim 1 is characterized in that: The cross-correlation vector P of p(n) and r(n): P=E[p(n)r(n)] Where P is the cross-correlation vector of p(n) and r(n).

3. The method for tracking and suppressing the waterbed effect of an adaptive feedback active control system according to claim 2, characterized in that: The signal after the initial noise signal is filtered by the whitening filter F(ω): p′(n)=f(n)*p(n) Where p'(n) is the signal after the initial noise signal is filtered by the whitening filter F(ω).

4. The method for tracking and suppressing the waterbed effect of an adaptive feedback active control system according to claim 3 is characterized in that: Filter-r signal: r′(n)=f(n)*r(n) Where r'(n) represents the filtered -r signal.

5. The method for tracking and suppressing the waterbed effect of an adaptive feedback active control system according to claim 4, characterized in that: The autocorrelation matrix of the filtered-x signal r(n): R=E[r(n)r T (n)] Where R is the autocorrelation matrix of the filtered-x signal r(n).

6. The method for tracking and suppressing the waterbed effect of an adaptive feedback active control system according to claim 5, characterized in that: The cross-correlation vector of p'(n) and r'(n): P′=E[p′(n)r′(n)] Where P' is the cross-correlation vector of p'(n) and r'(n).

7. The method for tracking and suppressing the waterbed effect of an adaptive feedback active control system according to claim 6, characterized in that: The autocorrelation matrix of the filtered-r signal r'(n): R′=E[r′(n)r′ T (n)] Where R' is the autocorrelation matrix of the filtered-r signal r'(n).

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