Robust active noise control method based on minimum mean square Lp norm

Abstract

The invention relates to the technical field of active noise control, in particular to a robust active noise control method based on a minimum mean square Lp norm, which comprises the following steps: capturing a reference signal x (n) through a reference microphone at any moment n, and expanding the reference signal x (n) by using a trigonometric function FLN module to form an expanded input signal xe (n); a signal xe is input through a digital filter for filtering processing, and a signal y (n) is output to an amplifier driving circuit to control a loudspeaker to emit main disturbance d (n); carrying out filtering-x signal calculation on the input signal xe (n) through a self-adaptive controller to obtain xs as an input signal of a secondary channel; and calculating the input signal xs and the error signal e (n) according to an algorithm to obtain a new filter weight w (n + 1), and inputting the new filter weight w (n + 1) into a digital filter for subsequent filtering processing, the method shows excellent performance in various same-noise environments, enhances the robustness of the system, and can be used as an effective solution for relieving the output saturation problem.

Description

Technical Field

[0001] The present invention relates to the technical field of active noise control, and particularly to a robust active noise control method based on the least mean square Lp norm. Background Art

[0002] In recent years, the extensive practical applications of active noise control (ANC) have attracted great attention and extensive research. The ANC technology is a method for eliminating noise, which cancels unwanted noise sources by generating anti-noise waves with equal amplitudes but opposite phases. The filtered-x least mean square (FxLMS) algorithm and the filtered-x affine projection (FxAP) algorithm are mature and classical ANC algorithms that utilize the mean square error (MSE) criterion. These algorithms are commonly used in ANC applications with Gaussian reference input signals. However, nonlinear distortion may affect the primary or secondary channels in the ANC system, resulting in poor performance of the FxLMS and FxLMS algorithms in a nonlinear environment.

[0003] To overcome the above challenges, a method called the filtered LMS (FsLMS) algorithm has been proposed, which uses a functional link network (FLN) to handle a nonlinear environment. FLNs and their variant adaptive exponential FLN variants have been proven to be powerful tools for nonlinear modeling and have been applied to various nonlinear ANC scenarios. However, signals in the real world usually have various non-Gaussian noise characteristics, such as chaotic noise, impulse noise, binary noise, and uniform noise. The presence of these non-Gaussian noises will degrade the performance of algorithms based on the MSE criterion.

[0004] In the field of physical systems, the ANC system often exhibits output saturation, which may lead to system instability. To solve this problem and limit the system power, various algorithms have been developed in the past few decades. Notable methods include the clipping algorithm, the rescaling algorithm, and the optimal leaky FxLMS (OLFxLMS) algorithm. However, these methods all have their limitations. For example, if the update direction of the control filter remains unchanged, the clipping algorithm may encounter a coefficient overflow problem. On the other hand, the rescaling algorithm performs well under output limit conditions but also brings fluctuations in the maximum output power. In addition, the OLFxLMS algorithm increases the computational requirements related to the update equation of the control filter due to the addition of a leakage factor.

[0005] Therefore, it is necessary to provide a robust active noise control method based on the least mean square Lp norm to solve the above technical problems. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides an active noise control method based on a robust algorithm.

[0007] A robust active noise control method based on the least mean square Lp norm provided by the present invention specifically comprises the following steps:

[0008] S1. At any time n, a reference signal x(n) is captured by a reference microphone, and the reference signal x(n) is extended by using a trigonometric function FLN module to form an extended input signal x e(n) ;

[0009] S2. The input signal x e(n) is filtered by a digital filter in combination with a filter weight w(n), and a signal y(n) is output to an amplifier drive circuit;

[0010] S3. After receiving the output signal y(n), the amplifier drive circuit controls a loudspeaker to emit a main disturbance d(n);

[0011] S4. An input signal x e(n) is filtered by an adaptive controller to calculate a filtered - x signal, and x s is obtained as an input signal of a secondary channel;

[0012] S5. The input signal x s and an error signal e(n) are calculated according to an algorithm to obtain a new filter weight w(n + 1), which is input into the digital filter for subsequent filtering processing.

[0013] Preferably, in S1, the reference signal x(n) is extended by using a trigonometric function FLN module to form an extended input signal x e(n) , and the specific formula is:

[0014]

[0015] where P represents the order of FLN.

[0016] Preferably, in S2, the input signal x e(n) is filtered, and a signal y(n) is output to an amplifier drive circuit, and the specific formula is:

[0017]

[0018] where represents the filter weight, and L=(2P + 1)M represents the order of the digital filter.

[0019] Preferably, in S4, the input signal x is filtered and the -x signal is calculated through an adaptive controller to obtain x e as the input signal of the secondary channel. The specific formula is: s

[0020] x s (n) = s T (n) * x e (n)

[0021] where s T (n) represents the impulse response of the secondary channel or the impulse response of the z - transfer function S(z). z represents the transformation of discrete - time signals and uses the convolution operator.

[0022] Preferably, in S5, the input signal x s and the error signal e(n) are calculated according to the algorithm to obtain the specific formula for the new filter weight w(n + 1) as:

[0023]

[0024] where μ represents the learning rate, z(n) is the loss function, and the loss function z(n) is defined as

[0025]

[0026] where λ represents the control parameter, the parameter p ∈ (0, 2), and e(n) is the error signal.

[0027] Preferably, the specific formula for the error signal e(n) is:

[0028] e(n) = d(n) - y s (n) = d(n) - s T (n) * y(n).

[0029] where y s (n) is the secondary disturbance, y s (n) = s T (n) * y(n). The noise emitted by the speaker is used as the anti - noise source, that is, it has the same amplitude as the main disturbance but the opposite phase.

[0030] Preferably, Δ w z(n) = -pe p-1 (n) sign[e(n)] x s (n), and the sign function sign[·] represents the sign function;

[0031] Therefore, the update equation for the new filter weight w(n + 1) is

[0032] w(n + 1) = w(n) + μe​p-1 (n) sign[e(n)]x s (n) - λy(n)x e (n).

[0033] Compared with the related technologies, a robust active noise control method based on the least mean square Lp norm provided by the present invention has the following beneficial effects:

[0034] The present invention proposes a robust active noise control method based on the least mean square Lp norm, which can effectively achieve active noise control in a non-Gaussian environment. The algorithm uses the fractional-order low-order criterion as its underlying framework and combines the minimum output variance technique to address the challenges brought by the output saturation scenario. A large number of simulations clearly confirm the limitations of existing algorithms (such as FsLMS, RFsLMS, FsqLMP, and MOV-FsLMS). It is worth noting that the new algorithm proposed by the present invention shows superior performance in various noise environments, outperforming its counterparts. The algorithm can not only enhance the robustness of the system but also serve as an effective solution to alleviate the output saturation problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a schematic flow chart of a robust active noise control method based on the least mean square Lp norm provided by the present invention;

[0036] Figure 2 is the ANR curve of each algorithm under SαS noise;

[0037] Figure 3 is the performance comparison of each algorithm under different λ values;

[0038] Figure 4 is the ANR curve of each algorithm under chaotic noise;

[0039] Figure 5 is the ANR curve of each algorithm under Gaussian noise;

[0040] Figure 6 is the ANR curve of each algorithm when S(z) changes (α = 1.9);

[0041] Figure 7 is the ANR curve of each algorithm when the noise source changes (minimum-phase secondary path). DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein can be arranged and designed in a variety of different configurations.

[0043] Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0044] The following describes in detail the specific implementation of a robust active noise control method based on the least mean square Lp norm in combination with specific embodiments.

[0045] Reference Figures 1 to 6 , a robust active noise control method based on the least mean square Lp norm provided by the present invention, the specific steps are as follows:

[0046] S1. At any moment n, the reference signal x(n) is captured by the reference microphone, and the reference signal x(n) is expanded by using the trigonometric function FLN module to form an expanded input signal x e(n) ;

[0047] S2. The input signal x e is filtered by the digital filter in combination with the filter weight w(n), and the signal y(n) is output to the amplifier drive circuit;

[0048] S3. After receiving the output signal y(n), the amplifier drive circuit controls the speaker to emit the main disturbance d(n);

[0049] S4. The input signal x e(n) is calculated by the adaptive controller to obtain the filtered - x signal x s as the input signal of the secondary channel;

[0050] S5. The input signal x s and the error signal e(n) are calculated according to the algorithm to obtain a new filter weight w(n + 1), which is input into the digital filter for subsequent filtering processing.

[0051] In the embodiment of the present invention, in S1, the reference signal x(n) is expanded by using the trigonometric function FLN module to form an expanded input signal x e , and the specific formula is:

[0052]

[0053] Where P represents the order of the FLN.

[0054] In an embodiment of the present invention, in S2, the input signal x e is filtered, and the signal y(n) is output to the amplifier drive circuit. The specific formula is:

[0055]

[0056] Where represents the filter weight, and L=(2P + 1)M represents the order of the digital filter.

[0057] In an embodiment of the present invention, in S4, the input signal x e is used to calculate the filtered - x signal through an adaptive controller, and x s is obtained as the input signal of the secondary channel. The specific formula is:

[0058] x s (n)=s T (n)*x e (n)

[0059] Where s T (n) represents the impulse response of the secondary channel or the impulse response of the z - transfer function S(z). z represents the transformation of the discrete - time signal, and the convolution operator is used.

[0060] In an embodiment of the present invention, in S5, the input signal x s and the error signal e(n) are calculated according to the algorithm to obtain the specific formula for the new filter weight w(n + 1) as:

[0061]

[0062] Where μ represents the learning rate, z(n) is the loss function, and the loss function z(n) is defined as

[0063]

[0064] Where λ represents the control parameter, the parameter p∈(0,2), and e(n) is the error signal.

[0065] In an embodiment of the present invention, the specific formula for the error signal e(n) is:

[0066] e(n)=d(n)-y s (n)=d(n)-s T (n)*y(n)

[0067] Where ys (n) is the secondary perturbation, y s (n) = s T (n) * y(n). The noise emitted by the speaker serves as the anti-noise source, that is, it has the same amplitude as the main perturbation but the opposite phase.

[0068] In the embodiment of the present invention, the Δ w z(n) = -pe p-1 (n) sign[e(n)]x s (n). The sign sign[·] represents the sign function;

[0069] Therefore, the updated equation for the new filter weight w(n + 1) is

[0070] w(n + 1) = w(n) + μe p-1 (n) sign[e(n)]x s (n) - λy(n)x e (n) #(10).

[0071] The new algorithm proposed by the present invention is called the Minimum Output Variance FsLMP (MOVFsLMP) algorithm, which is specifically designed to cope with non-Gaussian noise environments. The MOV method in the ANC system has several key advantages. It can effectively control the output power, ensure a quiet and comfortable environment, and at the same time maintain stable performance, thus achieving long-term stable noise reduction effects. In addition, its computational efficiency makes it very practical in real-time applications. This algorithm is based on the fractional lower order criterion and utilizes the power of the Functional Link Network (FLN) to achieve non-linear modeling functions. It should be noted that the MOV-FsLMP algorithm is essentially based on the combination of the L2 norm and the Lp norm components, enabling it to effectively capture and process signals with various statistical characteristics. In addition, the MOV-FsLMP algorithm also has the remarkable feature of constraining the output variance, thus enhancing the effectiveness of system control. Through the comprehensive analysis of simulation and experimental results, it can be clearly seen that the proposed algorithm outperforms existing similar algorithms in various noise environments, further demonstrating its excellent performance and unparalleled potential.

[0072] Analysis of the new algorithm (MOV-FsLMP algorithm)

[0073] (I) Convergence analysis

[0074] Introduce the weight-error vector as follows

[0075]

[0076] Here, the symbol w o represents the optimal weight vector. Therefore, the calculation formula for the error signal is

[0077]

[0078] Then, the posterior error signal is defined as

[0079]

[0080] Substituting (12) and (13) into (10) gives

[0081]

[0082] Taking the expected value and Euclidean norm on both sides of (14), we get

[0083]

[0084] where

[0085]

[0086] Meanwhile If the algorithm converges, it needs to satisfy:

[0087]

[0088] If the inequality (19) is solvable in the real number domain, it can be divided into two cases

[0089] Case 1: If b 2 (n) - 4a(n)c(n) = 0, the solution is

[0090] Case 2: If b 2 (n) - 4a(n)c(n) > 0, the solution is

[0091]

[0092] Therefore, the sufficient condition for convergence can be derived as:

[0093]

[0094] where "inf" is the infimum.

[0095] (II) Computational complexity

[0096] For algorithms based on the FIR filter structure, the main difference in their computational complexity lies in the update formula of each algorithm. Therefore, we only focus on the computational complexity when updating the weight vector. Table 1 summarizes the computational complexity related to the weight vector update process in each algorithm. Since the Filtered-s type algorithms in Table 1 are all triangular FLNs expansions, they all involve L - 1 additions and L multiplications to calculate the controller output y(n). Due to the introduction of the output power constraint, compared with other algorithms (FsLMS, RFsLMS, and FsLMP), the computational burden of the MOV type algorithms has increased slightly, but it is still at an acceptable level.

[0097] (III) Optimal control parameter λ

[0098] To analyze the optimal control parameter, assume that the filter converges to obtain the optimal weight vector 2, and the steady-state filter output is y o (n) at this time. To avoid non-linearity in the steady state, the L∞ norm is used as

[0099]

[0100] where "sup" is the highest. When the steady-state reference signal is lower than the maximum available range ρ of the input signal amplitude applicable to the system, if Equation (22) is satisfied, the following conditions need to be met

[0101]

[0102] where [·] i is the i-th element of the vector, and γ is the maximum control signal amplitude. Therefore, the optimal λ is

[0103]

[0104] Algorithm Multiplication Addition <![CDATA[L p Norm]]> FsLMS L+1 L - RFsLMS L+7 L+8 - FsLMP L+2 L L MOV-FsLMS 2L+2 2L - MOV-FsLMP 2L+3 3L L

[0105] Table 1: Computational complexity required to evaluate weight vector update.

[0106] Simulation results of the new algorithm (MOV - FsLMP algorithm)

[0107] A comparative analysis of the proposed new algorithm in the field of ANC was carried out, and it was benchmarked against FsLMS, RFsLMS, FsqLMP, and MOVFsLMS. The experimental results presented are the average of 100 independent runs. The order of the FLN is P = 3, the memory length of the reference input signal is M = 9, and the number of filter weight coefficients is L = 63. To evaluate the performance of each algorithm, we use the metric of average noise reduction (ANR).

[0108]

[0109] Where A e A(n) = βA(n - 1)+(1 - β)|e(n)|#(26) e

[0110] A d A(n) = βA(n - 1)+(1 - β)|d(n)|,#(27) d

[0111] Where β = 0.99, the main disturbance can be described as

[0112] d(n)=u(n - 2)+δu(n - 2)-δu(n - 1)#(28) 1 u 2 2 u 3

[0113] Where δ 1 = 0.08, δ 2 = 0.04, u(n)=x(n)*p(n), p(n) represents the impulse response of the main transfer function P(z)=z - 0.3z+0.2z T T -3 -4 -5 Subsequently, the original disturbance is affected by additive white Gaussian noise, characterized by a signal - to - noise ratio (SNR) of 30 dB. The transfer function of the minimum - phase quadratic path is for the case where the source of the standard α - stable distribution noise (SαS)

[23] ,

[24] (i.e., the input signal x(n) is α - stable noise) has a characteristic exponent of α = 1.9. The performance of each algorithm is as

[0114] shown. Since both the FsLMS and MOV - FsLMS algorithms are MSE - based algorithms, they diverge in the initial convergence stage. In contrast, the MOV - FsLMP algorithm has the lowest steady - state ANR. Changing the noise source to a chaotic noise source, whose generation formula is Figure 2

[0115] x(n)=θx(n - 6)[1 - x(n - 6)]#(29)

[0116] Where θ = 4.

[0117] Figure 3 The performance of the proposed algorithm for different values of λ is compared. As shown in the figure, a larger control factor reduces the gain of the control filter, resulting in a decrease in the noise reduction performance. On the contrary, a very small control factor produces a weak output constraint and may lead to output saturation. Therefore, we choose to fix λ at 0.01.

[0118] Figure 4 ​​​​​​​​​The ANR curves of each algorithm under the chaotic noise source are shown. At the same steady-state ANR level, the MOV algorithms (i.e., MOV-fslms and MOV-fslmp) have the highest convergence rate; followed by the FsLMS algorithm.

[0119] To verify the effectiveness of the proposed MOV-FsLMP algorithm in different noise environments, Figure 5 The ANR curves of the proposed algorithm and other algorithms under the Gaussian noise source are shown. In this case, the MOV-FsLMP algorithm still maintains the lowest steady-state ANR, followed by MOV-FsLMS, FsLMS, FsqLMP, and RFsLMS. To evaluate the tracking ability of the algorithms, a test was conducted. At the midpoint of the iteration, the secondary path was modified to have a transfer function S(z)=z -2 +1.5z -3 -z -4 . A non-minimum phase system with such characteristics.

[0120] Figure 6 The performance of each algorithm in response to the above-mentioned change in the secondary path is given. Due to the existence of the impulsive noise environment, the divergence of the MSE-based algorithm is not surprising. However, when the phase of the secondary path changes, the RFsLMS algorithm also shows poor tracking performance. In contrast, the proposed MOV-FsLMP algorithm has the lowest steady-state ANR in this case. During the iteration under the minimum-phase secondary path, the characteristic exponent of the SαS noise source changes from 1.9 to 1.8 at the midpoint.

[0121] The final performance of each algorithm is as Figure 7 shown. In this case, the RFsLMS and FsqLMP algorithms still maintain convergence after changing the impulse intensity, but their steady-state ANRs are much higher than that of the MOV-FsLMP algorithm. Obviously, the MOV-FsLMP algorithm shows excellent tracking performance in all scenarios.

[0122] The above are only embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structure or equivalent process transformation made by using the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present invention.

Claims

1. A robust active noise control method based on the least mean square Lp norm, characterized in that: The specific steps are: S1. At any time n, the reference signal x(n) is captured by the reference microphone. The reference signal x(n) is expanded by using the trigonometric function FLN module to form the expanded input signal X e(n) ; S2, through the digital filter combined with the filter weight w (n) to the input signal x e(n) Perform filtering and output signal y(n) to the amplifier driving circuit; S3, after receiving the output signal y(n), the amplifier driving circuit emits the main disturbance d(n) by controlling the speaker; S4, through the adaptive controller to the input signal x e Perform filter-x signal calculation to get x s As the input signal of the secondary channel; S5, for input signal x s The error signal e(n) is calculated according to the algorithm to obtain a new filter weight w(n+1), which is input into the digital filter for subsequent filtering processing.

2. The robust active noise control method based on the least mean square Lp norm according to claim 1, characterized in that: In S1, the reference signal x(n) is expanded by using the trigonometric function FLN module to form an expanded input signal x e , the specific formula is: x e (n)={x(n),…,x(n-M+1), sin[πx(n)],…, sin[πx(n-M+1)],…, sin[Pπx(n)],…,sin[Pπx(n-M+1)], Cos[πx(n)],…, cos[πx(n-M+1)],…, Where P represents the order of FLN.

3. The robust active noise control method based on the least mean square Lp norm according to claim 1, characterized in that: The input signal x in S2 e Perform filtering and output signal y(n) to the amplifier driving circuit. The specific formula is: in represents the filter weight, and L=(2P+1)M represents the order of the digital filter.

4. The method for robust active noise control based on the least mean square Lp norm according to claim 1, characterized in that: In S4, the input signal x is controlled by an adaptive controller. e Perform filter-x signal calculation to get x s As the input signal of the secondary channel, the specific formula is: x s (n)=s T (n)*x e (n) Among them, s T (n) represents the impulse response of the sub-channel or the impulse response of the z transfer function S(z), and z represents the transformation of the discrete-time signal using the convolution operator.

5. The method for robust active noise control based on the least mean square Lp norm according to claim 1, characterized in that: The input signal x in S5 s The specific formula for calculating the error signal e(n) according to the algorithm to obtain the new filter weight w(n+1) is: Where μ represents the learning rate, z(n) is the loss function, and the loss function z(n) is defined as Among them, λ represents the control parameter, parameter p∈(0,2), and e(n) is the error signal.

6. The method for robust active noise control based on the least mean square Lp norm according to claim 5, characterized in that: The specific formula of the error signal e(n) is: e(n)=d(n)-y s (n)=d(n)-s T (n)*y(n) where y s (n) is the secondary disturbance.

7. The method for robust active noise control based on the least mean square Lp norm according to claim 6, characterized in that: The Δ w z(n)=-pe p-1 (n)sign[e(n)]x s (n), The symbol sign[·] represents a sign function; Therefore, the new filter weight w(n+1) update equation is w(n+1)=w(n)+μe p-1 (n)sign[e(n)]x s (n)-λy(n)x e (n)。

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