Impulse noise active control method based on t distribution density function

Abstract

The invention provides an impulse noise active control method based on a t distribution density function, which comprises the following steps of: firstly, obtaining a secondary path estimated value by using an LMS (Least Mean Square) method, and initializing an active control filter; then calculating a reference filtering signal filtered by the secondary path estimated value; secondly, calculating an output signal of the secondary sound source at the current sampling moment and an error signal at the current sampling moment; and finally, on the basis of a cost function of the t distribution density function, calculating the active control filter updated at the (n + 1) th sampling moment. And when the sampling time reaches the set control time, the active control system stops active control, and the active control method is ended. Compared with a traditional method, the active noise control method has the advantages that the convergence speed is higher, the average noise reduction amount is larger in the impulse noise environment, the noise reduction effect of active noise control can be improved in the strong impulse noise environment, and the sound pressure level of an active noise control system at a monitoring point is minimum.

Description

Technical Field

[0001] The invention belongs to the field of acoustic technology, and in particular relates to an impulse noise active control method based on t-distribution density function. Background Art

[0002] Active Noise Control (ANC) is a noise control technology that uses the principle of destructive interference of sound waves to effectively control low-frequency noise. It effectively improves the performance of its own algorithm by designing cost functions suitable for different controlled noises. Its application scenarios include: environmental noise reduction of multi-functional lecture halls, conference rooms, car cabs, personal audio equipment, closed cabin acoustic environment evaluation, and audio design.

[0003] At present, the design of adaptive active noise control system revolves around adaptive filters and their corresponding algorithms. The minimum mean square error (MMSE) criterion is widely used due to its advantages such as low computational complexity and simplicity. Based on MMSE, Widrow and Hoff proposed a minimum mean square (LMS) algorithm optimized for Gaussian noise model, which has the advantages of simplicity and low computational complexity. The Filtered-x LMS (FxLMS) algorithm is favored in ANC systems for its low computational complexity and stable performance, and has become a widely used basic algorithm.

[0004] In real life, we often encounter impulse noise, such as the sound of piling at construction sites and the impact sound of mechanical processing in workshops. High-intensity impulse noise is more likely to damage human hearing than steady-state noise of the same intensity, so it is of great significance to study the active control of impulse noise. Impulse noise has the characteristics of low probability of occurrence and large amplitude, which is quite different from the common Gaussian distribution noise. Since the FxLMS algorithm is optimized based on the Gaussian noise model, the noise reduction performance of this algorithm is limited in the impulse noise environment.

[0005] Since there are significant differences in the probability distribution of the amplitudes of Gaussian noise and impulse noise, using the second-order moment (such as mean square error) as the cost function of the algorithm is not the optimal solution for impulse noise. Resetting the cost function is a common means to solve the above problems. For example, the Filtered-x Maximum Correntropy Criterion (FxMCC) algorithm and the Filtered-x Maximum Versoria Criterion (FxMVC) algorithm have been proposed and proven to be effective active control algorithms for impulse noise. However, the FxMCC algorithm has the disadvantages of large amount of calculation, slow convergence speed, and low noise reduction. Although the FxMVC algorithm reduces the amount of calculation on the basis of the FxMCC algorithm, it still has the disadvantage of low noise reduction. Therefore, designing an active control algorithm with fast convergence speed and large noise reduction is one of the key research directions of active control algorithm research. Since the change in the shape of the cost function will cause a large change in the convergence speed and noise reduction of the algorithm, how to design the optimal cost function is a difficult problem and a pain point in the active control of impulse noise. Summary of the invention

[0006] The purpose of the present invention is to solve the problems of slow convergence speed and low noise reduction in the existing pulse noise active control method, and to provide an pulse noise active control method based on t distribution density function.

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

[0008] An impulse noise active control method based on t distribution density function is provided. A single-channel active control system is constructed. The t distribution probability density function is used as the cost function of the active control method. The impulse noise active control method of the active control method includes the following steps:

[0009] Step 1: Use white noise as the excitation signal of the secondary sound source, use the LMS method to obtain the secondary path estimation value h(n) required by the active control method, and initialize the active control filter w(n);

[0010] Step 2: Use the reference microphone to collect the reference signal x(n) at the current sampling moment, and calculate the reference filtered signal x'(n) after filtering by the secondary path estimation value h(n);

[0011] Step 3: Based on the reference signal x(n) at the current sampling moment and the active control filter w(n), calculate the output signal y(n) of the secondary sound source at the current sampling moment;

[0012] Step 4: According to the responses of the primary sound source and the secondary sound source at the error point, the error signal e(n) at the error point at the current sampling time is obtained;

[0013] Step 5: Based on the cost function J(n) of the t-distribution density function and the reference filter signal x'(n), the stochastic gradient descent method is used to obtain the active control filter w(n+1) updated at the n+1th sampling time, as shown in the following formula:

[0014]

[0015] Where n represents the nth sampling time, w(n)=[w0(n),w1(n),...,w L-1 (n)] T , represents the gradient of J(n), μ represents the iterative step size of gradient descent, a represents the kernel width coefficient of the t distribution density function, and p represents the shape function;

[0016] Step 6: When the sampling time reaches the set control time, the active control system will stop active control and the active control method ends; when the sampling time does not reach the set control time, return to step 2 and repeat steps 2 to 6.

[0017] Furthermore, the reference filtered signal x'(n) after filtering by the secondary path estimated value h(n) is calculated by the following formula:

[0018]

[0019] Where x(n) = [x(n), x(n-1), ..., x(n-L+1)] T , L represents the length of the active control filter, M represents the length of the secondary path, and * represents the convolution operation.

[0020] Furthermore, in step 3, the output signal y(n) of the secondary sound source at the current sampling moment is calculated by the following formula:

[0021] y(n)=w T (n)x(n)

[0022] Among them, w T (n) represents the transpose of w(n).

[0023] Furthermore, in step 4, the error signal e(n) at the error point at the current sampling moment is calculated by the following formula:

[0024] e(n)=d(n)+y(n)*h(n)

[0025] =d(n)+wT (n)x'(n)

[0026] Where d(n) represents the primary signal generated by the primary sound source at the error point, h(n) represents the actual secondary path, and x'(n) = [x'(n), x'(n-1), ..., x'(n-L+1)] T ,y(n)=[y(n),y(n-1),...,y(n-L+1)] T , the output signal y(n) of the secondary sound source at sampling time n.

[0027] Furthermore, in step 5, the cost function J(n) of the probability density function of the t distribution is expressed as:

[0028]

[0029] For the kernel width coefficient a and shape function p of the t-distribution density function, according to probability theory, the kernel width coefficient a needs to be greater than 0 and can be adjusted according to actual needs. The larger the value of a, the faster the convergence speed of the algorithm, but the average noise reduction of the impulse noise will decrease; the smaller the value of a, the slower the convergence speed of the algorithm, but the average noise reduction of the impulse noise will increase. Changing the parameter a has no effect on the computational complexity of the algorithm. The value range of the shape function p needs to be greater than 1. A larger parameter p is conducive to the rapid convergence of the algorithm and improves the average noise reduction of the algorithm for impulse noise. However, a larger parameter p will increase the computational complexity of the algorithm. If p is too large, the real-time performance of the entire system will be affected, thereby affecting the final noise reduction effect. Therefore, a more practical hardware system is needed to select the appropriate kernel width coefficient a and shape function p.

[0030] The advantages of the present invention are:

[0031] Compared with the traditional method, the active control method proposed in the present invention has a faster convergence speed and more average noise reduction in an impulse noise environment, can improve the noise reduction effect of active noise control in a strong impulse noise environment, and minimize the sound pressure level of the active noise control system at the monitoring point. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The features and advantages of the present invention will become more readily understood through the following description with reference to the accompanying drawings, which are not drawn to scale and in which some features are exaggerated or minimized to show details of particular components:

[0033] Figure 1 is a block diagram of a single-channel active control system according to an embodiment of the present invention;

[0034] Figure 2 is a schematic diagram of the deployment of an active noise control system according to an embodiment of the present invention;

[0035] Figure 3 is a noise signal diagram actually measured in an embodiment of the present invention;

[0036] Figure 4 is a QQ graph of a primary noise signal according to an embodiment of the present invention;

[0037] Figure 5 is the amplitude probability density distribution of the primary noise signal in the embodiment of the present invention;

[0038] Figure 6 is a cost function diagram of an embodiment of the present invention;

[0039] Figure 7 is a cost function gradient graph of an embodiment of the present invention;

[0040] Figure 8 is an error signal diagram of three different algorithms in an industrial noise environment according to an embodiment of the present invention;

[0041] Fig. 9 is a time domain diagram of ANR of three different algorithms in an industrial noise environment in an embodiment of the present invention;

[0042] Fig.10 It is a spectrum comparison diagram of the noise reduction effects of three different algorithms in the embodiments of the present invention. DETAILED DESCRIPTION

[0043] The present invention will be described in detail below with reference to the accompanying drawings by means of exemplary embodiments of the present invention. It should be noted that the following detailed description of the present invention is only for the purpose of illustration, and is not intended to limit the present invention.

[0044] The present invention designs an active control method for pulse noise based on t distribution density function. First, a single-channel active control system is constructed as follows: Figure 1 As shown, p(n) represents the primary path from the reference measuring point to the error measuring point; d(n) represents the primary signal generated by the primary sound source at the error point, h(n) represents the secondary path from the secondary sound source to the error measuring point; h(n) represents the estimated value of the secondary path with a length of 200 obtained by secondary path modeling; w(n) represents an active control filter with a length of 200; x(n) represents the reference signal; x'(n) represents the reference filtered signal; y(n) represents the output signal of the secondary sound source; s(n) represents the secondary signal generated by the secondary sound source at the error point; e(n) represents the signal received by the error microphone at the error point (a mixed signal of d(n) and s(n)), that is, the error signal.

[0045] The effectiveness of the algorithm of the present invention is verified by an active impulse noise experiment. This experiment is carried out in an anechoic chamber. The primary sound source is placed at the front end of the anechoic chamber using nylon rope and wire, the secondary sound source is placed on a chair, the reference microphone is placed close to the primary noise source, and the error microphone and the detection microphone are placed above the secondary sound source. The layout of the active control system is shown in the figure below. Figure 2 shown.

[0046] The measured industrial impulse noise was used as the sound source to verify the effectiveness of the proposed algorithm in a laboratory environment. The experimental process was carried out in the following steps:

[0047] Step 1: Use white noise as the excitation signal of the secondary sound source, use the LMS algorithm to obtain the estimated value of the secondary path, and initialize the active control filter.

[0048] Specifically, the measured construction site slapping noise is used as the excitation signal of the primary sound source, which is the sound produced by the impact of hammers and wooden boards. The sampling frequency is set to 2000 Hz, and the error microphone is used to collect the noise signal of the primary sound field. Figure 3 As shown in the figure, the amplitude probability distribution analysis is performed to determine whether the noise signal conforms to the Gaussian distribution. QQ plots (Quantile-Quantile plots) are a commonly used method in statistics to determine whether a set of data comes from a certain distribution. The noise signal time domain data is used as the input sample for statistical analysis, and the QQ plot is drawn as shown in the figure. Figure 4 To more intuitively show the characteristics of the noise signal, the histogram of the noise signal data and the fitting curves of the normal distribution and the α stable distribution are plotted. Figure 5 It can be clearly seen that the noise signal is non-Gaussian.

[0049] Step 2: Use a reference microphone to collect a reference signal at the current sampling time n, and calculate a reference filtered signal x'(n) obtained by filtering the reference signal through an impulse response estimate of a secondary path.

[0050] The reference filtered signal x'(n) is calculated by the following formula:

[0051]

[0052] Where x(n) = [x(n), x(n-1), ..., x(n-L+1)] T , L = 200, M=200, * represents convolution operation.

[0053] Step 3: Based on the collected reference signal and the initialized active control filter, calculate the output signal of the secondary sound source at the current moment.

[0054] The output signal y(n) of the secondary sound source is calculated by the following formula:

[0055] y(n)=w T (n)x(n)

[0056] Among them, w T (n) represents the transpose of w(n), w(n) = [w0(n), w1(n), ..., w L-1 (n)] T .

[0057] Step 4: Use the error microphone to collect the error signal at the current moment, or calculate the error signal at the current moment according to the following formula;

[0058] Depend on Figure 1 It can be seen that the error signal e(n) is expressed as follows:

[0059] e(n)=d(n)+s(n)

[0060] =d(n)+y(n)*h(n)

[0061] And y(n)=w T (n)x(n), Therefore, the error signal e(n) is expressed as:

[0062] e(n)=d(n)+w T (n)x'(n)

[0063] Where h(n) represents the actual secondary path, x'(n) = [x'(n), x'(n-1), ..., x'(n-L+1)] T ,y(n)=[y(n),y(n-1),...,y(n-L+1)] T .

[0064] Step 5: Based on the cost function of the t-distribution density function, the stochastic gradient descent method is used to obtain the active control filter updated at the sampling point n+1, as shown in the following formula:

[0065]

[0066] Among them, J(n) represents the cost function of the t distribution density function, which is expressed as: The relationship between the cost function and the error signal e(n) is as follows Figure 6 As shown, Represents the gradient of J(n), and the relationship between the gradient and the error signal e(n) is as follows Figure 7 As shown, μ represents the iterative step size of gradient descent, a represents the kernel width coefficient of the t distribution density function, and p represents the shape function.

[0067] This experiment uses the average noise reduction (ANR) as the performance evaluation index of the proposed algorithm. The specific calculation formula is as follows:

[0068]

[0069] A e (n) = ηA e (n-1)+(1-η)|e(n)|

[0070] A d (n) = ηA d (n-1)+(1-η)|d(n)|

[0071] Where η represents the forgetting factor, set η = 0.999, A e (0) = 0, A d (0)=0.

[0072] ANR reflects the amount of noise reduction of the active control algorithm at the current moment. The faster the ANR decreases in the early stage of active noise reduction, the faster the active control system can reduce the noise of the environment, that is, the faster the convergence speed, the better the system performance. When the active control algorithm reaches a stable state, the smaller the ANR, the greater the noise reduction of the active control at the error point position, and the better the system performance.

[0073] The active control method proposed by the present invention is to Figure 7 It can be seen that since the error signal e(n) becomes particularly large, The value is very small, according to the formula Obviously, very small The update speed of the active control filter will be suppressed, greatly alleviating the problem of system divergence caused by the large error signal e(n). When the error signal e(n) is small (no pulse signal appears), The larger the value, the faster the active control filter updates, thus achieving fast convergence. When the error signal e(n) is close to 0, A very small value will again inhibit and slow down the active control filter update, keeping the steady-state error low (larger ANR).

[0074] The FxMTC algorithm proposed in the present invention is compared with the FxLMS algorithm and the FxMVC algorithm to verify the superiority of the FxMTC algorithm designed in the present invention.

[0075] The parameter settings of the active noise control system of the above three algorithms are as follows: the step size μ of the FxLMS algorithm is set to 0.000000001, the step size μ of the FxMVC algorithm is set to 0.000007, τ=0.5, p=2; the FxMTC algorithm sets two different parameters, which are a=2, p=2 and a=8, p=2, and the step sizes μ are 0.0000078 and 0.0000062 respectively. The larger the parameter p, the greater the noise reduction of the active control, but the slower the convergence speed of the algorithm. The larger the parameter a, the faster the convergence speed of the algorithm, and the more effective the noise reduction.

[0076] In the anechoic chamber environment, industrial noise is used as the primary sound source. The error signals of the three different algorithms are as follows: Figure 8 As shown, Fig. 9 and Fig.10 The time domain diagram and the diagram of the number of iterations and the amount of noise reduction are respectively shown for active noise reduction using the three different noise reduction algorithms mentioned above. It can be seen from the time domain waveform that the noise amplitude of the FxMTC algorithm proposed in the present invention is significantly smaller than that of the FxLMS and FxMVC algorithms. Fig. 9 It can be seen from the number of iterations and the average noise reduction that the FxMTC algorithm proposed in the present invention converges faster than other algorithms, and the noise reduction of the proposed algorithm is significantly greater than that of other algorithms. The larger the parameter a is, the faster the convergence speed of the algorithm will be, and the more noise reduction can be effectively increased. Fig.10 It can be seen from the spectrum diagram that the FxMTC algorithm proposed in the present invention has better average noise reduction than the other two algorithms, whether it is peak value or broadband spectrum.

[0077] In summary, compared with traditional methods, the impulse noise denoising algorithm based on the maximum t-distribution density function criterion proposed in the present invention has excellent impulse noise denoising effect and fast convergence speed, which is significantly better than the FxLMS and FxMVC algorithms. The denoising amount of the proposed algorithm is significantly greater than the above two algorithms. At the same time, it has wide applicability and can be applied to a variety of reproduction scenarios.

[0078] Finally, it should be noted that, without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, all of which fall within the scope of the present invention to be protected. The features mentioned and / or shown in the above description of the exemplary embodiments of the present invention may be combined in the same or similar manner into one or more other embodiments, combined with features in other embodiments or substituted for corresponding features in other embodiments. The technical solutions obtained by these combinations or substitutions shall also be deemed to be included in the protection scope of the present invention.

Claims

1. An active control method for impulse noise based on t-distribution density function, characterized in that: Using the t-distribution probability density function as the cost function of the active control method, the impulse noise active control method includes the following steps: Step 1: Use white noise as the excitation signal of the secondary sound source, use the LMS method to obtain the secondary path estimation value h(n) required by the active control method, and initialize the active control filter w(n); Step 2: Use the reference microphone to collect the reference signal x(n) at the current sampling moment, and calculate the reference filtered signal x'(n) after filtering by the secondary path estimation value h(n); Step 3: Based on the reference signal x(n) at the current sampling moment and the active control filter w(n), calculate the output signal y(n) of the secondary sound source at the current sampling moment; Step 4: According to the responses of the primary sound source and the secondary sound source at the error point, the error signal e(n) at the error point at the current sampling time is obtained; Step 5: Based on the cost function J(n) of the t-distribution density function and the reference filter signal x'(n), the stochastic gradient descent method is used to obtain the active control filter w(n+1) updated at the n+1th sampling time, as shown in the following formula: Where n represents the nth sampling moment, represents the gradient of J(n), μ represents the iterative step size of gradient descent, a represents the kernel width coefficient of the t distribution density function, and p represents the shape function; Step 6: When the sampling time reaches the set control time, the active control system will stop active control and the active control method ends; when the sampling time does not reach the set control time, return to step 2 and repeat steps 2 to 6.

2. The method for active control of impulse noise according to claim 1, characterized in that: In step 2, the reference filtered signal x'(n) after filtering by the secondary path estimated value h(n) is calculated by the following formula: Where x(n) = [x(n), x(n-1), ..., x(n-L+1)] T , L represents the length of the active control filter, M represents the length of the secondary path, and * represents the convolution operation.

3. The pulse noise active control method according to claim 2, characterized in that: In step 3, the output signal y(n) of the nth secondary sound source at the current sampling time is calculated by the following formula: y(n)=w T (n)x(n) Among them, w T (n) represents the transpose of w(n).

4. The method for active control of impulse noise according to claim 3, characterized in that: In step 4, the error signal e(n) at the error point at the current sampling moment is calculated by the following formula: e(n)=d(n)+y(n)*h(n) =d(n)+w T (n)x'(n) Where d(n) represents the primary signal generated by the primary sound source at the error point, h(n) represents the actual secondary path, and x'(n) = [x'(n), x'(n-1), ..., x'(n-L+1)] T ,y(n)=[y(n),y(n-1),...,y(n-L+1)] T , the output signal y(n) of the secondary sound source at sampling time n.

5. The pulse noise active control method according to claim 1, characterized in that: In step 5, the cost function J(n) of the probability density function of the t distribution is expressed as:

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