阅读说明：本技术 一种基于最大相关熵准则的主动噪声控制算法 (Active noise control algorithm based on maximum correlation entropy criterion ) 是由 李晨 彭诺蒙 曾毓敏 姚天楠 于萍 徐谨 李彬 于 2021-07-30 设计创作，主要内容包括：本发明提出一种基于最大相关熵准则的主动噪声控制算法,该方法包括以下步骤：(1)使用α稳定分布来产生脉冲噪声,参考传声器采集脉冲噪声,脉冲噪声序列可表示为x(n)＝[x(1),x(2),...,x(n)]～(T),n为正实数,表示时间序列,α称为位置参数,其表示α稳定分布函数的分布均值或者中值；(2)对脉冲噪声使用滤波-x算法结合单通道前馈结构,通过次级传声器产生次级噪声来抑制脉冲噪声；(3)根据脉冲噪声的冲击特性,将最大相关熵(MCC)算法与(2)中的滤波-x算法结构组合为最大相关熵算法(FXMCC)抑制脉冲噪声的离散点；(4)将两个最大相关熵算法(FXMCC)使用凸组合结构(CONVEX)并行组合,有脉冲噪声时,两个算法并行工作,分别控制降噪系统的降噪速度和降噪量。(The invention provides an active noise control algorithm based on a maximum correlation entropy criterion, which comprises the following steps: (1) using the alpha stationary profile to generate impulse noise, the reference microphone collects the impulse noise, and the impulse noise sequence may be denoted as x (n) ═ x (1), x (2),.., x (n)] T N is a positive real number and represents a time series, and alpha is called a position parameter and represents a distribution mean value or a median value of an alpha stable distribution function; (2) the pulse noise is suppressed by generating secondary noise through a secondary microphone by using a filter-x algorithm in combination with a single-channel feedforward structure; (3) according to the impulse characteristics of impulse noise, combining the maximum correlation entropy (MCC) algorithm and the filter-x algorithm structure in the step (2) into discrete points of the maximum correlation entropy algorithm (FXMCC) for suppressing the impulse noise; (4) and (3) combining the two maximum correlation entropy algorithms (FXMCC) in parallel by using a CONVEX combined structure (CONVEX), wherein when impulse noise exists, the two algorithms work in parallel to respectively control the noise reduction speed and the noise reduction amount of the noise reduction system.)

1. An active noise control algorithm based on a maximum correlation entropy criterion, the method comprising the steps of:

(1) using the alpha stationary profile to generate impulse noise, the reference microphone collects the impulse noise, and the impulse noise sequence may be denoted as x (n) ═ x (1), x (2),.., x (n)]^TN is a positive real number and represents a time series, and alpha is called a position parameter and represents a distribution mean value or a median value of an alpha stable distribution function;

(2) the pulse noise is suppressed by generating secondary noise through a secondary microphone by using a filter-x algorithm in combination with a single-channel feedforward structure;

(3) according to the impulse characteristics of impulse noise, combining the maximum correlation entropy (MCC) algorithm and the filter-x algorithm structure in the step (2) into discrete points of the maximum correlation entropy algorithm (FXMCC) for suppressing the impulse noise;

(4) and (3) combining the two maximum correlation entropy algorithms (FXMCC) in parallel by using a CONVEX combined structure (CONVEX), wherein when impulse noise exists, the two algorithms work in parallel to respectively control the noise reduction speed and the noise reduction amount of the noise reduction system.

2. The active noise control algorithm based on the maximum correlation entropy criterion as claimed in claim 1, wherein in step (1), the method for generating impulse noise by using the alpha stable distribution is as follows: this impulse noise is modeled using a standard Symmetric Stable distribution (S α Stable, S α S) with a characteristic function of:

3. the active noise control algorithm based on the maximum correlation entropy criterion as claimed in claim 1 or 2, wherein in step (2), the workflow based on the filter-x algorithm combined with the single-channel feedforward structure is as follows:

(2.1) generating impulse noise by a noise source, and acquiring a reference input signal x (n) by a reference microphone and inputting the reference input signal x (n) into an adaptive filtering algorithm;

(2.2) after the reference input signal x (n) passes through the primary path, obtaining a d (n) signal;

d(n)＝x(n)*p

wherein p is a primary path coefficient;

(2.3) y (n) is the output signal of the secondary microphone after the reference signal x (n) passes through the adaptive filter;

y(n)＝w(n)x(n)

wherein w (n) represents the weight coefficient of the filter in the active noise reduction system;

(2.4) y' (n) is the secondary output signal after y (n) has passed through the secondary path;

y'(n)＝y(n)*s

(2.5) counteracting y' (n) and d (n) at the error sensor to obtain an error signal e (n);

e(n)＝d(n)-y'(n)

(2.6) the weight update formula of the finally obtained filter-x algorithm is as follows:

w(n+1)＝w(n)+2μe(n)x(n)s

where s is the secondary channel coefficient and μ is the step size parameter.

4. The active noise control algorithm based on the maximum correlation entropy criterion of claim 3, wherein in step (3), the maximum correlation entropy algorithm (FXMCC) is shown as follows:

(3.1) the maximum cross-correlation entropy is a measure of the similarity between two random variables X, Y, κ (·,) is a kernel that maps data into a non-linear space, the kernel employs a gaussian kernel:

wherein σ is the nucleus width;

(3.2) after the cross-correlation entropy is empirically estimated, the filter weight parameters are optimized by maximizing the cross-correlation entropy between the desired signal and the secondary filter output, with a cost function of:

in the formula (I), the compound is shown in the specification,for the correlation entropy cost function, σ is the kernel width, e is the error function, e ═ x-y, e²Is containing noise information;

(3.3) using a stochastic gradient algorithm on the function of equation (5), the following is derived:

in the formula, W_nIs the weighting coefficient, W, of the filter at the previous time_n+1And the weighting coefficient at the later moment of the filter, mu is a step size parameter, sigma is a kernel width, e is an error signal, x is a reference signal, and s is a secondary channel coefficient.

5. The active noise control algorithm based on the maximum correlation entropy criterion as claimed in claim 4, wherein in the step (4), the convex combination method is constructed as follows, and the output of the overall combination filter adopts the following:

y₁＝x*w₁,y₁′＝y₁*s

y₂＝x*w₂,y₂′＝y₂*s

y＝λy₁′+(1-θ)y₂′

w＝λw₁+(1-λ)w₂

in the formula, w₁A first kernel width filter; w is a₂Is a second kernel width filter, the second kernel width being smaller than the first kernel width, y₁Is the output signal of the first kernel width filter, y₁' is y₁The signal is obtained after the signal passes through the secondary channel; y is₂Is the output signal of the second kernel width filter, y₂' is y₂And (3) obtaining a signal after the signal passes through a secondary channel, wherein s is a secondary channel coefficient, c is a real number between-4 and 4, and lambda is a parameter with a value between 0 and 1.

6. The active noise control algorithm according to claim 5, wherein λ is an arctangent function:

λ＝β[arctan(γ)+m]

in the formula, arctan is an arctangent function, and β, m are real number parameters.

Technical Field

The invention belongs to the field of signal processing, and particularly relates to an active noise control algorithm based on a maximum correlation entropy criterion.

Background

Due to the demands of the advancement and development of technology, noise has attracted attention and prevention. Compared with the conventional passive noise control, Active Noise Control (ANC) can effectively suppress low-frequency noise and has been applied to noise reduction in an aircraft cabin, noise reduction in an automobile, noise reduction in a duct, and the like.

In real life, many noises usually show a pulse-like non-gaussian nature, such as baby incubator noise, device piling sound and some artificial noises, and the waveform has many sharp protrusions and many outlier sample values from the aspect of time domain sampling. This type of noise is mathematically described by a model of the stationary distribution. The algorithm based on the minimum mean square error criterion can have the condition of maladjustment or non-convergence under the condition, so the research on the impulse noise active control algorithm can improve the performance of the white adaptive controller in eliminating impulse noise and meet the requirement of people on comfortable environment.

The maximum correlation entropy criterion is used as a cost function (MCC) and is applied to an improved convex combination active noise control structure, so that the ANC system can realize quick convergence and better noise reduction at the same time.

Disclosure of Invention

The purpose of the invention is as follows: aiming at the problem of the existing pulse noise interference, the invention provides an improved convex combination maximum correlation entropy (CSMCC) algorithm. The CSMC algorithm has better robustness, high convergence rate and good noise reduction effect in an impulse noise environment.

The technical scheme is as follows: in order to achieve the object of the present invention, the present invention provides an active noise control algorithm based on the maximum correlation entropy criterion, the method includes the following steps:

(1) root of herbaceous plantAccording to the method, a time domain in life shows pulse-shaped noise, a stable distribution of alpha is used for generating pulse noise, a reference microphone collects the pulse noise, and a pulse noise sequence can be expressed as x (n) ([ x (1), x (2) ], x (n))]^TN is a positive real number and represents a time series, and alpha is called a position parameter and represents a distribution mean value or a median value of an alpha stable distribution function;

(2) the pulse noise is suppressed by generating secondary noise through a secondary microphone by using a filter-x algorithm in combination with a single-channel feedforward structure;

(3) according to the impulse characteristics of impulse noise, combining the maximum correlation entropy (MCC) algorithm and the filter-x algorithm structure in the step (2) into discrete points of the maximum correlation entropy algorithm (FXMCC) for suppressing the impulse noise;

(4) and (3) combining the two maximum correlation entropy algorithms (FXMCC) in parallel by using a CONVEX combined structure (CONVEX), wherein when impulse noise exists, the two algorithms work in parallel to respectively control the noise reduction speed and the noise reduction amount of the noise reduction system.

In the step (1), the method for generating impulse noise by alpha stable distribution is as follows:

in practical environments, impulse noise is generally a large amplitude interfering signal with a low probability. In experimental simulations, such impulse noise is usually modeled using a standard Symmetric Stable distribution (S α Stable, S α S) with a characteristic function of

The larger the alpha value is, the closer the alpha value is to normal distribution, and the smaller the impact property is; conversely, the smaller the α value, the greater the impact resistance. As in fig. 1, a time domain image of impulse noise is shown, α is 1.4;

in the step (2), the overall working structure of the basic classical filtering-x algorithm combined with the single-channel feedforward structure is as follows:

fig. 2 shows a block diagram of a filter-x single channel feedforward active noise reduction system. Wherein P (z), S (z) are the primary and secondary channel transfer functions, as measured, and w (z) is the controller,for the secondary channel compensation coefficients, which are generally equal to s (z), d (n) is the primary channel output, y (n) is the secondary channel output, y' (n) is the secondary microphone output signal, and e (n) is the error signal obtained after cancellation.

(2.1) in the algorithm, a noise source generates impulse noise, and a reference microphone acquires a reference input signal x (n) and inputs the reference input signal x (n) into a later-stage adaptive filtering algorithm;

(2.2) simultaneously, after the reference input signal x (n) passes through a primary path, obtaining a d (n) signal;

d(n)＝x(n)*p (1)

wherein p is the primary path coefficient.

(2.3) y (n) is the output signal of the secondary microphone after the reference signal x (n) passes through the adaptive filter;

y(n)＝w(n)x(n) (2)

where w (n) represents the weighting coefficients of the filter in the active noise reduction system.

(2.4) y' (n) is the secondary output signal after y (n) has passed through the secondary path;

y'(n)＝y(n)*s (3)

and (2.5) counteracting y' (n) and d (n) at the error sensor to obtain an error signal e (n), wherein the counteracting error signal is smaller and smaller, and the noise reduction is better and better.

e(n)＝d(n)-y'(n) (4)

(2.6) finally, the weight updating formula of the obtained classical filtering-x algorithm is as follows:

w(n+1)＝w(n)+2μe(n)x(n)s (5)。

in step (3), the maximum correlation entropy algorithm (FXMCC) is shown as follows:

(3.1) the maximum cross-correlation entropy is a measure of the similarity between two random variables X, Y, κ (·,) is a kernel that maps data into a non-linear space, where the kernel uses a gaussian kernel:

where σ is the nucleus width.

(3.2) after empirical estimation of the cross-correlation entropy, the filter weight parameters are optimized by maximizing the cross-correlation entropy (similarity) between the desired signal and the secondary filtered output, where the cost function is:

in the formula (I), the compound is shown in the specification,for the correlation entropy cost function, σ is the kernel width, e is the error function, e ═ x-y, e²Is noisy information, then (e)²Is much greater than 0, we include after gradient update, derivation of equation (5)Of (e)²Is much greater than 0, thenIs trending towards 0 and therefore noisy individuals have little effect on gradient updates.

(3.3) Using a stochastic gradient algorithm on the function of equation (5), the following is derived

In the formula, W_nIs the weighting coefficient, W, of the filter at the previous time_n+1And the weighting coefficient at the later moment of the filter, mu is a step size parameter, sigma is a kernel width, e is an error signal, x is a reference signal, and s is a secondary channel coefficient.

Further, in the step (4), the convex combination method is constructed as follows:

the algorithm (CSMCC) combines two adaptive filters with different kernel widths, and the larger the kernel width value is, the faster the convergence speed is, and the steady-state error of the algorithm is increased; the smaller the value of the kernel width, the opposite is true.

A block diagram of a convex combination of two adaptive filters is shown in fig. 3. The output of the overall combined filter is taken as follows:

in the formula, w₁A first kernel width filter; w is a₂Is a second kernel width filter, the second kernel width being smaller than the first kernel width, y₁Is the output signal of the first kernel width filter, y₁' is y₁The signal is obtained after the signal passes through the secondary channel; y is₂Is the output signal of the second kernel width filter, y₂' is y₂And (3) obtaining a signal after the signal passes through a secondary channel, wherein s is a secondary channel coefficient, c is a real number between-4 and 4, and lambda is a parameter with a value between 0 and 1.

In step (5), the improved function is as follows:

compared with the lambda (n) function in the step (4), the step improves the function, adopts the arctangent function, and reduces the complexity of the whole operation, wherein the arctangent function is as follows:

λ＝β[arctan(γ)+m] (8)

in the formula, arctan is an arctangent function, gamma is an independent variable, and beta and m are real number parameters.

The working principle of the structure is that when the error value is large initially, the algorithm with large step length works to accelerate convergence; when the error value after convergence is smaller, the steady-state error is reduced after the algorithm with small step length works, and the two algorithms work simultaneously to solve the contradiction between the convergence speed and the steady-state error.

Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:

aiming at the feedforward active noise control of standard S alpha S distributed non-Gaussian noise, the maximum correlation entropy criterion is taken as a target function, and a convex combination structure is combined on the basis; the complexity of the whole algorithm is reduced by taking a new function as a joint adjustment parameter. The effect of the algorithm is verified through theoretical derivation and simulation, the problem of limitation that convergence speed and steady-state error cannot be obtained simultaneously is solved well, and the noise reduction effect is better.

Drawings

FIG. 1 shows a time domain image of impulse noise;

FIG. 2 is a block diagram of a feed-forward single-channel active noise reduction system;

FIG. 3 is an active noise reduction system based on a convex composite structure;

figure 4 is a graph comparing Sigmoid function and arctan function of the present invention.

Detailed Description

The specific implementation details of each part of the invention are as follows:

(1) in the algorithm, a noise source generates impulse noise, and a reference microphone acquires a reference input signal x (n) and inputs the reference input signal x (n) into a later-stage adaptive filtering algorithm;

(2) the acquisition signal x (n) is input into a filter, and the output anti-noise signal is as follows:

in the formula, w^T(n)＝[w₀(n),w₁(n),...,w_N-1(n)]^TIs the weight coefficient at time n.

(3) The output anti-noise signal is offset with the original signal to generate an error signal:

wherein d (n) is x (n) after passing through the primary channel.

(4) Further based on the error signal, the weight coefficient update process of the basic classical filter-x algorithm can be expressed as:

w(n+1)＝w(n)-μe(n)x(n)s (4)

where e (n) is the error signal at time n, x (n) is the impulse noise signal, and s is the measured secondary channel transfer coefficient.

(5) Maximum correlation entropy algorithm (FXMCC), discrete points are suppressed by introducing a gaussian kernel function.

The cost function of the maximum correlation entropy algorithm is as follows:

where κ (·,. cndot.) is the gaussian kernel used in the present invention.

(6) The No. 1 filter and the No. 2 filter work in parallel to respectively generate two offset signals which are then based on

The combination of parameters produces the final cancellation signal:

y₁＝x*w₁,y₁′＝y₁*s

y₂＝x*w₂,y₂'＝y₂*s (7)

y＝λy₁'+(1-λ)y₂'

where λ is the combining function that combines the two filters, and used in the present invention is the arctangent function, y₁Is the output signal of filter No. 1, y'₁Is y₁The signal after passing through the secondary channel is the same as the signal of the No. 2 filter; y (n) is the total output signal after the combination of the No. 1 and No. 2 filters.

(7) After parallel combination, according to the maximum correlation entropy algorithm in the step (6), the two adaptive filter weight updating equations are respectively as follows:

in the formula, mu₁,μ₂Respectively step length parameters.

Finally, the weight update equation for the whole system is:

w＝λw1+(1-λ)w2 (10)

in the formula, w1 is the filter weight No. 1, w2 is the filter weight No. 2, and w is the combined weight of the filter No. 1 and the filter No. 2.

The two adaptive filters respectively control the convergence speed and the steady-state error, and are adjusted according to the error signals under the control of the intermediate parameter lambda (n) so as to achieve a faster convergence speed and a larger steady-state error.

(8) A new less complex lambda function is proposed.

Due to the high complexity of the sigmoid function, the new arctan function proposed herein is shown in comparison with fig. 4.

λ＝β[arctan(γ)+m] (11)

In the formula, gamma is an independent variable, beta and m are real parameters. The fitting degree of the arctan function and the original Sigmoid function is good, the intermediate transition part is more sensitive to the change of gamma, and the response time is reduced; the stability of the boundary value is better, and the stable state can be reached quickly for the burst pulse.

As shown in fig. 4, the arctan function used is compared with the conventional Sigmoid function. The fitting degree of the arctan function and the original Sigmoid function is better, the intermediate transition part is more sensitive to the change of gamma, and the response time is reduced; the stability of the boundary value is better, and the stable state can be reached quickly for the burst pulse.