Distributed Active Noise Control Method Based on Block Diffusion Filtered Least Mean Square Algorithm

Abstract

The present invention discloses a distributed active noise control method based on a block diffusion filtering least mean square algorithm. The method comprises the following steps: (1) building a plurality of identical distributed node systems and assigning node numbers; (2) arranging communication links of each node according to the building environment of a multi-channel active noise control system, and two nodes establishing a communication link are called neighborhood nodes; (3) identifying secondary paths of the multi-channel active noise control system; (4) an adaptive estimation stage based on neighborhoods; (5) a communication stage: distributing the combined adaptive estimation block vectors to neighborhood nodes interactively through the communication links; (6) a fusion estimation stage based on nodes; (7) a sampling stage; (8) optimizing and adjusting an adaptive step size. The method of the present invention can be applied to a multi-channel active noise control system, and has the advantages of low computational complexity, high stability and high noise reduction performance compared with the current multi-channel active noise control system.

Description

Technical Field

[0001] The present invention belongs to the field of active noise control, and particularly relates to an adaptive optimization method for a distributed active noise control system based on a block vector diffusion update strategy and an optimal adaptive step size criterion under steady-state operation. Background Art

[0002] Multi-channel active noise control (ANC) systems are widely used in the attenuation of low-frequency noise in the whole space. The centralized filtered-x least mean square (CFxLMS) algorithm has become the most classical benchmark algorithm adopted by multi-channel active noise processors due to its excellent noise reduction and convergence performance. The CFxLMS algorithm collects the error sound signals of all channels to iteratively update all control filter coefficients within a single calculation cycle, and its high computational burden has been widely criticized in practical applications. Different from the centralized strategy, the decentralized FxLMS (DCFxLMS) algorithm divides the multi-channel active noise control system into independent ANC subsystems. The subsystem processor uses a single error sound signal within the system to update the subsystem control filter to achieve noise reduction. However, the decentralized strategy ignores the acoustic coupling between subsystems, introducing an inherent instability problem while greatly reducing the computational burden.

[0003] Recently, distributed signal processing methods based on wireless acoustic information processing networks have been applied to multi-channel ANC systems. The distributed active noise control system uses a distributed node processor network to allocate the high computational burden of the entire system. The classical distributed active noise control system based on the multi-task diffusion FxLMS (MDFxLMS) algorithm first requires each node processor to update the node filter coefficients according to the node error signal during the adaptive stage, which is equivalent to decentralized control; secondly, in the fusion stage, the adaptive update results are mutually transmitted according to the established node communication network and the result space smoothing is performed to finally obtain the distributed update result of the node filter. In addition, the fusion communication also reduces the system instability risk.

[0004] However, spatial smoothing forces the weight vectors of different control filters to be similar, which will greatly reduce the noise reduction performance of a multi-channel ANC system under an asymmetric primary acoustic path. In the case of a weakly asymmetric path, such drawbacks can be alleviated (but not eliminated) by applying variable combination weights (J. Chen, C. Richard, and A. H. Sayed (2015) “Diffusion LMS over multitask networks,” IEEE Trans. Signal Process., vol. 63, no. 11, pp. 2733-2748.) and a spatial regularization term (Y. Chu, S. C. Chan, C. M. Mak, and M. Wu (2021) “A diffusion FxLMS algorithm for multi-channel active noise control and variable spatial smoothing,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., Toronto, ON, Canada, pp. 4695-4699.). However, in practical applications, the primary acoustic path between the primary noise source and the error microphones is usually significantly different for each channel, which goes beyond the assumptions of the above methods. Recently, for distributed ANC systems, node-specific incremental algorithms (J. Plata-Chaves, A. Bertrand, and M. Moonen (2016) “Incremental multiple error filtered-X LMS for node-specific active noise control over wireless acoustic sensor networks,” in Proc. IEEE Sensor Array Multichannel Signal Process. Workshop (SAM), Rio de Janeiro, Brazil, pp. 1-5.) and group diffusion LMS algorithms (Y. Dong, J. Chen, and W. Zhang (2020) “Distributed wave-domain active noise control based on the diffusion adaptation,” IEEE / ACM Trans. Audio, Speech, Lang. Process., vol. 28, pp. 2374-2385.) have been studied to eliminate the inherent bias in the MDFxLMS algorithm.However, the former is sensitive to communication link failures and is based on an unrealistic assumption that each faulty microphone only receives control sounds from its adjacent nodes; while the latter requires additional computational burden to process complex spherical harmonic functions and restricts the placement positions of the speakers.

[0005] In summary, through research, it is found that existing multi-channel ANC systems cannot meet the dual requirements of low computational complexity and system stability when the noise source location is unknown or the primary sound paths are inconsistent. Therefore, it is of great significance to design a new multi-channel ANC system with low computational load, strong robustness, and high noise reduction performance. Summary of the Invention

[0006] The present invention proposes a distributed multi-channel active noise control method based on the Block Diffusion FxLMS (BDFxLMS) algorithm, which can obtain the noise reduction performance equivalent to that of a traditional multi-channel ANC system based on the CFxLMS algorithm with low computational complexity in the case of unknown noise source location or strong asymmetric primary paths.

[0007] The technical solution adopted by the present invention is as follows:

[0008] The distributed active noise control method based on the block diffusion filtering least mean square algorithm includes the following steps:

[0009] Step 1, build multiple identical distributed node systems and assign node numbers to facilitate subsequent standardized placement;

[0010] Step 2, arrange the communication links of each node according to the building environment of the multi-channel active noise control system, and the two nodes establishing the communication link are called neighborhood nodes;

[0011] Step 3, identify the secondary paths of the multi-channel active noise control system. Each node sequentially uses the offline secondary path modeling method to obtain the secondary sound paths between itself and the neighborhood nodes;

[0012] Step 4, the first stage of noise reduction of the multi-channel active noise control system, that is, the neighborhood-based adaptive estimation stage: each node independently estimates the control filter coefficients of the neighborhood nodes according to its own error sound signal to obtain a joint adaptive estimation block vector;

[0013] Step 5, the second stage of noise reduction of the multi-channel active noise control system, that is, the communication stage: distribute the joint adaptive estimation block vector to the neighborhood nodes interactively through the communication link;

[0014] Step 6, the third stage of noise reduction in the multi-channel active noise control system, i.e., the node-based fusion estimation stage: Each node independently smooths the received joint adaptive block vector according to the node number using the fusion criterion to obtain the fusion estimation result;

[0015] Step 7, the fourth stage of noise reduction in the multi-channel active noise control system, i.e., the extraction value stage: Each node independently extracts the block vector corresponding to its own node number from the fusion estimation result as the update value of the control filter coefficient of its own node to drive the secondary speaker to achieve noise reduction, and waits for the system to stabilize to obtain the minimized residual noise under the current system parameter conditions;

[0016] Step 8, optimize and adjust the adaptive step size, and repeat Steps 4 to 7 to further optimize the noise reduction performance of the system.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0018] The present invention proposes a BDFxLMS algorithm based on neighborhood-based adaptive estimation and node-based fusion estimation, and designs a new type of distributed ANC system on this basis. In the case where the noise source position is unknown or the primary path is strongly asymmetric, the noise reduction performance of the new type of ANC system is equivalent to that of the traditional lumped active noise reduction scheme, and it makes up for the defects of the high computational complexity of the existing lumped scheme, the low system stability of the decentralized scheme, and the low noise reduction performance of the distributed scheme. Description of the Drawings

[0019] Figure 1 is a schematic flow chart of the method of the present invention.

[0020] Figure 2 is a schematic diagram of the K-channel ANC system of the method of the present invention.

[0021] Figure 3 is a schematic diagram of the node communication network of the method of the present invention.

[0022] Figure 4 is an example diagram of the execution process of the BDFxLMS algorithm based on neighborhood-based adaptive estimation and node-based fusion estimation, where (a) represents Figure 3 the neighborhood-based adaptive estimation process of node 3 in Figure 3 and (b) represents

[0023] Figure 5It is the configuration diagram of the multi-channel ANC system in the simulation experiment of the embodiment. Among them, (a) shows the placement positions of the secondary speaker array and the error microphone array of the multi-channel ANC system, (b) shows the communication link of the distributed network of the multi-channel ANC system, and (c) shows the noise source distributions in the cases of symmetric primary sound paths, weakly asymmetric primary sound paths, and strongly asymmetric primary sound paths.

[0024] Figure 6 It is the result of the normalized residual noise under the symmetric primary path in the simulation experiment of the embodiment. Abscissa: Iteration time / second, Ordinate: Normalized residual noise / dB; (a) Single-frequency primary noise; (b) Multi-frequency primary noise; (c) Narrowband primary noise, the three curves from top to bottom at -25 dB to -30 dB are the results of the MDFxLMS, BDFxLMS, and CFxLMS algorithms respectively; (d) Wideband primary noise, the convergence curves of the BDFxLMS and CFxLMS algorithms overlap.

[0025] Figure 7 It is the result of the normalized residual noise under the weakly asymmetric primary path in the simulation experiment of the embodiment. Abscissa: Iteration time / second, Ordinate: Normalized residual noise / dB; (a) Single-frequency primary noise; (b) Multi-frequency primary noise; (c) Narrowband primary noise; (d) Wideband primary noise.

[0026] Figure 8 It is the result of the normalized residual noise under the strongly asymmetric primary path in the simulation experiment of the embodiment. Abscissa: Iteration time / second, Ordinate: Normalized residual noise / dB; (a) Single-frequency primary noise; (b) Multi-frequency primary noise; (c) Narrowband primary noise; (d) Wideband primary noise.

[0027] Figure 9 It is the global control filter coefficient vector under the strongly asymmetric primary path in the simulation experiment of the embodiment. Abscissa: Filter tap number, Ordinate: Filter tap value; (a) CFxLMS algorithm; (b) DCFxLMS algorithm; (c) MDFxLMS algorithm; (d) BDFxLMS algorithm. Specific implementation manner

[0028] As Figure 2 shown in the schematic diagram of the K-channel ANC system, the processor updates the control filter w based on different adaptive strategies k to drive the secondary speaker to generate the control signal u k , and reduces the primary noise signal d at the error microphone through the acoustic superposition effect via the secondary sound path k . The primary noise signal refers to the interference sound signal that the output noise of the primary noise source propagates to the error microphone through the corresponding primary sound path. As Figure 1As shown in the figure, the design of a distributed multi-channel ANC system based on BDFxLMS includes the following steps:

[0029] Step 1: Build multiple identical distributed node systems. Each system contains 1 error microphone (or residual noise microphone), 1 secondary speaker, and 1 node processor with both communication and data processing functions. Different node numbers are assigned to each node.

[0030] Step 2: Arrange the communication links of each node according to the building environment of the ANC system. The two nodes that establish a communication link are called neighborhood nodes.

[0031] Step 3: Identify the secondary path of the ANC system. Each node sequentially uses the offline secondary path modeling method to obtain the secondary acoustic path between itself and the neighborhood nodes.

[0032] Step 4: The first stage of noise reduction in the ANC system, that is, the neighborhood-based adaptive estimation stage, to ensure unbiased estimation and low computational complexity: Each node independently estimates the control filter coefficients of the neighborhood nodes according to its own error acoustic signal to obtain the joint adaptive estimation block vector.

[0033] Step 5: The second stage of noise reduction in the ANC system, that is, the communication stage: Distribute the joint adaptive estimation block vector to the neighborhood nodes through the communication link in an interoperable manner.

[0034] Step 6: The third stage of noise reduction in the ANC system, that is, the node-based fusion estimation stage, to ensure the stability of adaptive iteration: Each node independently smooths the received joint adaptive block vector according to the node number using the fusion criterion to obtain the fusion estimation result.

[0035] Step 7: The fourth stage of noise reduction in the ANC system, that is, the decimation stage: Each node independently extracts the block vector corresponding to its own node number from the fusion estimation result as the update value of the control filter coefficient of its own node to drive the secondary speaker to achieve noise reduction, and waits for the system to stabilize to obtain the minimum residual noise under the current system parameter conditions.

[0036] Step 8: Optimize and adjust the adaptive step size to ensure the fastest convergence while achieving the optimal noise reduction performance. Repeat steps 4 - 7 to further optimize the noise reduction performance of the system.

[0037] The control method of a distributed multi-channel ANC system based on the block diffusion filtering least mean square algorithm mainly includes the following parts:

[0038] 1. Build a multi-node distributed ANC system and establish a two-way communication link. As shown in the appendix Figure 3 Taking a 9-node communication network as an example, the neighborhood nodes of node 3 include nodes 2, 3, 4, 5, and 9.

[0039] 2. ANC system secondary path identification process: The secondary path reflects the configuration relationship of the multi-channel ANC system and is the key to the successful execution of the filtering reference class adaptive algorithm. The secondary path identification of the ANC system can use the offline modeling method: when the primary noise source is silent, the secondary speaker is excited with a broadband white noise signal and the LMS algorithm is used to estimate the secondary acoustic path between the current secondary speaker and different error microphones (characterized as the time-domain unit impulse response), where k is the number of the secondary speaker, i is the number of the error microphone, and the length of the secondary acoustic path is set to J (S. Elliott (2001) Signal Processing for Active Control. London, U.K.: Academic, pp. 103 - 270.).

[0040] 3. Define the cost function of the distributed multi-channel ANC system based on the BDFxLMS algorithm for adaptive optimization:

[0041]

[0042] where the subscript k on the left side of the equal sign represents the k-th node; the first term on the right side of the equation is the local error estimation term, and the second term is the vector Euclidean norm deviation term; the operator represents the mathematical expectation, and e k (n) represents the error acoustic signal of the k-th node at time n; the non-negative parameter α k is used to balance the local error estimation and the spatial regularization, and the index set represents the neighborhood node numbers of the k-th node including the k-th node, and the index set represents the neighborhood node numbers of the l-th node including the l-th node; the non-negative parameter {b klp} represents the weight of the information of each neighborhood node on the block vector estimation of the k-th node, and the operator ||·|| 2 represents the Euclidean norm; v k represents the block vector of the k-th node, which contains all the control filter coefficients within the neighborhood φ p represents the block vector estimation value of the p-th node; the selection matrix is used to select the control filter coefficient of the l-th node from the block vector of the k-th node, where the operator represents the Kronecker product, is a column vector with a unique non-zero element 1 only in the q-th row and the matrix I L is the identity matrix of dimension L, and L represents the length of the control filter coefficient w l ; similarly, the selection matrix The control filter coefficients used to select the l-th node from the p-node block vector.

[0043] 4. Applying the stochastic gradient descent method to minimize the above cost function, the update equation for the k-th node can be obtained as:

[0044]

[0045] where is the neighborhood-based filtering reference signal vector of the k-th node at time n, and its inner sub-vector x F,kl (n) = s kl X T (n), X(n) = [x(n) x(n - 1) … x(n - J + 1)] T is the reference signal at time n, T is the transpose operator, and the sub-vector x(n) in X(n) = [x(n) x(n - 1) … x(n - L + 1)] T ; ▽ is the partial derivative operator of the cost function J k with respect to the variable at time n; μ k represents the adaptive step size of the k-th node.

[0046] 5. Divide the above update equation into two parts, successively:

[0047]

[0048] and

[0049]

[0050] It can be found that the first update equation is the adaptive estimation under local error information, where is the joint adaptive estimation block vector at time n + 1 iteratively updated by the k-th node according to the local error sound signal e k (n) obtained by itself, and the sub-vector represents the estimated value of the l-th filter coefficient vector obtained by the k-th node at time n + 1 through iterative calculation based on the error sound signal; the second update equation is the fusion result of the neighborhood adaptive vector.

[0051] 6. Replace v k (n) and φ p (n) in the second item of step 5 with ψ k (n + 1) and ψ p (n + 1) respectively to ensure that the fusion process includes the residual noise information at the latest time (i.e., time n + 1), and at the same time, restrict that the p nodes participating in the calculation in the above fusion stage must be the neighborhood nodes of the k-th node, that is, the first-order communication restriction where ∩ represents the intersection of two index sets; we can further simplify it to:

[0052] (1) Neighborhood-based Adaptive Estimation Phase of the Distributed ANC System:

[0053]

[0054] Among them, affected by the first-order communication limitation, the estimated value φ k (n) replaces the actual filter coefficient v k (n). This phase is as Figure 4 (a) shown. Node 3 estimates the control filter coefficients of its neighborhood based on its own error sound signal, that is, the jointly adaptive estimation block vector.

[0055] (2) Node-based Fusion Estimation Phase of the Distributed ANC System:

[0056]

[0057] Among them, the intermediate variable α k and {b klp} are transformed into the fusion coefficient matrix:

[0058]

[0059] Among them represents the identity matrix of dimension , p represents the node communicating with node k, and p′ represents the common neighborhood nodes of node p and node k; the fusion coefficient matrix can be expressed as the Kronecker product:

[0060]

[0061] Among them represents the sum of the elements of the index set , represents the sum of the elements of the index set , and the above non-negative fusion coefficients satisfy the "node-based fusion estimation" property, that is:

[0062]

[0063] Among them, Let \(K\) be the total number of nodes. Classical fusion criteria, such as the Averaging rule (V.D. Blondel, J.M. Hendrickx, A. Olshevsky, and J.N. Tsitsiklis (2005) “Convergence in multiagent coordination, consensus, and flocking,” in Proc. 44th IEEE Conf. Decision Control, Seville, Spain, pp. 2996 - 3000.), the Relative - variance rule (S.-Y. Tu and A.H. Sayed (2011) “Optimal combination rules for adaptation and learning over networks,” in Proc. 4th IEEE Int. Workshop Comput. Adv. Multi - Sensor Adapt. Process., San Juan, PR, USA, pp. 317 - 320.), and the maximum - degree rule (L. Xiao, S. Boyd, and S. Lall (2005) “A scheme for robust distributed sensor fusion based on average consensus,” in Proc. Fourth Int. Symp. Inform. Process. Sensor Netw., Boise, ID, USA, pp. 63 - 70.)) can be used to calculate the above - mentioned fusion coefficients. As Figure 4 shown above the dotted line in (b), the fusion is carried out in the node order.

[0064] (3) The downsampling stage of the distributed ANC system:

[0065]

[0066] where \(w\) k (n + 1) represents the control filter coefficients of the \(k\) - th node updated according to the information at the \(n\) - th moment at the \((n + 1)\) - th moment to drive the secondary loudspeaker to generate a control sound signal to reduce the primary noise signal at the error microphone. As Figure 4 shown below the dotted line in (b), its own control filter coefficients are extracted from the fused block vector through downsampling to drive the secondary loudspeaker.

[0067] 7. Calculate the optimal adaptive step size to ensure system steady state and faster convergence. The global adaptation and fusion sums and variables are defined as follows:

[0068] Ψ B (n) = col{ψ 1 (n) ψ 2 (n) … ψ K (n)}

[0069] And

[0070] Φ B (n) = col{φ 1 (n) φ 2 (n) … φ K (n)}

[0071] Secondly, the global filtering reference matrix and the channel filtering reference matrices of the BDFxLMS algorithm of the present invention are defined as follows:

[0072]

[0073] And

[0074]

[0075] Where It is easy to obtain

[0076]

[0077] Where the transformation matrix Γ B Is:

[0078]

[0079] The submatrix T B,k Satisfies:

[0080]

[0081] The global fusion matrix is defined as:

[0082]

[0083] Where O represents a matrix of all zeros.

[0084] The global step size matrix is:

[0085]

[0086] Finally, based on the iterative update equations in the adaptation and fusion phases, and the above-defined global variables, it is easy to obtain the global update equation on the distributed network as:

[0087]

[0088] Taking the expectation on both sides of the above equation, the steady-state convergence solution is obtained:

[0089] Φ B (∞) = -[I Σ +C B Ξ - C B ) -1 C B Z μ Γ B N Xd ,

[0090] where Ξ = Z μ Γ B N XX G B , the global selection matrix subscript represents the dimension of the identity square matrix I, and the global filtering reference matrix at time n is:

[0091]

[0092] Subtracting the steady-state convergence solution from both sides of the global update equation on the distributed network and taking the expectation, we can obtain:

[0093]

[0094] where Further arranging, the iterative update formula at the mean level is obtained:

[0095]

[0096] To ensure convergence rather than divergence, the step size parameter should satisfy:

[0097] λ(C B (I Σ - Ξ)) < 1

[0098] where the operator λ(·) represents the spectral radius of the internal matrix.

[0099] Embodiment

[0100] Next, in combination with the attached drawings, in the form of a simulation experiment, the advantages of the distributed active noise control system based on the block diffusion filtering least mean square algorithm proposed by the present invention in terms of noise reduction performance and computational complexity are highlighted:

[0101] 1. Simulation experiment parameter settings

[0102] In the embodiment, a 10-channel ANC system under free field conditions is selected for the simulation experiment. The configuration of the ANC system is asFigure 5 As shown in (a), the radii of the concentric circular arrays of the secondary loudspeaker and the error microphone are 1.5 m and 1.2 m respectively. Each node is equipped with 1 error microphone, 1 secondary loudspeaker, and 1 node processor with signal processing and external communication functions. Figure 5 The solid lines in (b) represent the communication links between distributed nodes. Specifically, the communication links between Node 1 - Node 6 and Node 5 - Node 9 are established to verify the network universality of the proposed algorithm. The adaptive algorithms for comparison include the traditional CFxLMS, DCFxLMS, and MDFxLMS algorithms, and the fusion criterion of the diffusion algorithm is selected as the average criterion.

[0103] All primary paths, secondary paths, and control filters are respectively set as FIR filters with 64, 64, and 260 taps. To compare the noise reduction performance of the proposed algorithm and current traditional algorithms under different primary paths, we set the following three primary paths, that is, different primary noise source distributions under the same secondary path configuration:

[0104] Configuration 1: Symmetric primary path. The primary noise source is placed at the center of the circular array (x p , y p ) = (0, 0) m, as shown by the triangle in Figure 5 (c);

[0105] Configuration 2: Weakly asymmetric acoustic path. The primary noise source is placed at a position slightly offset from the center of the array (x p , y p ) = (0, 0.05) m, as shown by the diamond in Figure 5 (c);

[0106] Configuration 3: Strongly asymmetric acoustic path. The primary noise source is placed at a position far from the center of the array (x p , y p ) = (0, 2.0) m, as shown by the star in Figure 5 (c).

[0107] In addition, single - frequency, multi - frequency, narrow - band, and wide - band primary noises are selected to test the noise reduction performance of different algorithms. The single - frequency signal is a sine wave of 400 Hz with zero initial phase and unit amplitude; the multi - frequency signal is a combined sine wave of 200, 300, and 400 Hz with an amplitude ratio of 1:3:6; the narrow - band random noise is Gaussian white noise filtered by a 100 - order FIR filter with a bandwidth of 400 Hz - 410 Hz; the wide - band random noise is Gaussian white noise filtered by a 100 - order FIR filter with a bandwidth of 100 Hz - 1500 Hz. The sampling rate of the system is 5 kHz, and the signal - to - noise ratio of all microphones is set to 30 dB. The output signal of the primary noise source is used as the ideal reference for the simulation experiment. The following normalized residual noise is used to evaluate the global noise control performance of different algorithms:

[0108]

[0109] All the simulation experiment results for random narrowband and wideband noise reduction are smoothed by 500 Monte Carlo methods, and all the simulation experiment results for periodic single-frequency and multi-frequency noise reduction are smoothed by a single experiment with a 40-window-length moving average window. The adaptive step sizes of different algorithms are summarized in the following table, and the adaptive step sizes have been adjusted to the optimal to ensure the fastest convergence while maximizing noise reduction. The adaptive step size of the DCFxLMS algorithm is the same as that of the proposed BDFxLMS algorithm to verify whether the proposed algorithm can improve the system stability.

[0110] Adaptive step sizes under different primary paths and primary noises

[0111]

[0112] 2. Simulation experiment results

[0113] The normalized residual noise results under the symmetric primary path (Configuration 1) are as Figure 6 shown. For the single-frequency and multi-frequency noise reduction results shown in Figure 6 (a) and (b), the reference signal is highly correlated with the primary noise signal at the error microphone. Therefore, except for the DCFxLMS algorithm that diverges due to inherent instability, other algorithms converge to the sampling floor noise of -30 dB. For the narrowband and wideband random noises shown in Figure 6 (c) and (d), the normalized residual noise is higher than -30 dB. In addition, the noise reduction performance of the MDFxLMS algorithm is slightly inferior to that of the CFxLMS and BDFxLMS algorithms because the MDFxLMS algorithm uses neighborhood-based spatial smoothing to force all control filters to tend to be the same. At this time, even if the primary noise sources are placed at the center of the array to form a symmetric primary path, the random sampling noises of different error microphones cannot be the same, resulting in a deterioration of the noise reduction performance.

[0114] The normalized residual noise results under the weak asymmetric primary path (Configuration 2) are as Figure 7 shown. Comparing Figure 6 with Figure 7 , the CFxLMS algorithm converges quickly and the DCFxLMS algorithm still diverges. However, the noise reduction performance of the MDFxLMS algorithm deteriorates significantly. For Figure 7For all the primary noises shown, the noise reduction performance of the MDFxLMS algorithm deteriorates by more than 10 dB for all types of primary noises under a weak non - symmetric primary path. By comparative observation, it can be found that the noise reduction effect of the proposed BDFxLMS algorithm on all types of primary noises is the same as that of the CFxLMS algorithm. Therefore, the proposed algorithm solves the instability of the DCFxLMS algorithm and the estimation deviation problem of the MDFxLMS algorithm simultaneously.

[0115] The normalized residual noise results under a strong non - symmetric primary path (Configuration 3) are as Figure 8 shown. It can be observed that the CFxLMS and BDFxLMS algorithms converge to results similar to the previous experiments, while the DCFxLMS algorithm diverges, and the MDFxLMS algorithm shows worse performance than Figure 7 in all types of primary noises. To further reveal the advantages of the BDFxLMS algorithm, Figure 9 the steady - state convergence results of the global control filter vector for broadband primary noise under a strong non - symmetric primary path are given. As can be clearly seen from Figure 9 (a), when the primary noise source is placed far from the center of the array, the deviation between the control filters of different nodes is large to match different primary sound paths. However, affected by spatial smoothing, the different control filters obtained by the iterative MDFxLMS algorithm are similar to each other ( Figure 9 (c)), revealing the essential reason for the poor noise reduction performance of the MDFxLMS algorithm under a strong non - symmetric path. In contrast, Figure 9 the control filters of the proposed algorithm in (d) converge to results similar to those of the CFxLMS algorithm.

[0116] The computational complexities of a single processor and all processors based on different adaptive algorithms for one iteration in the above - mentioned simulation experiments are summarized below. It should be noted that since each node has different neighboring nodes, the computational complexity of each node is different. The computational complexity statistical results show that the computational complexity of the proposed BDFxLMS algorithm is higher than that of the MDFxLMS algorithm but lower than that of the CFxLMS.

[0117] Computational complexity of a single processor

[0118] Algorithm Multiplication Addition CFxLMS 63600 60790 DCFxLMS 845 841 MDFxLMS 1625～1885 1361～1621 BDFxLMS 3833～5197 3565～4927

[0119] Computational complexity of all processors

[0120] Algorithm Multiplication Addition CFxLMS 63600 60790 DCFxLMS 8450 8410 MDFxLMS 17290 14650 BDFxLMS 43786 41098

[0121] The above results show that, regardless of the noise type and system configuration, the BDFxLMS algorithm proposed by the present invention can converge to the optimal lumped solution and reduce the computational burden. Compared with the DCFxLMS and MDFxLMS algorithms, the BDFxLMS algorithm of the present invention overcomes the instability problem and the estimation bias problem respectively at the cost of a higher computational complexity.

Claims

1. A distributed active noise control method based on the block diffusion filtering least mean square algorithm, characterized in that, the method comprises the following steps: Step 1, build a plurality of identical distributed node systems and assign node numbers for subsequent standardized placement; Step 2, arrange the communication links of each node according to the building environment of the multi-channel active noise control system, and the two nodes establishing the communication link are called neighborhood nodes; Step 3, identify the secondary paths of the multi-channel active noise control system. Each node sequentially obtains the secondary acoustic path between itself and the neighborhood nodes by using the offline secondary path modeling method; Step 4, the first stage of noise reduction of the multi-channel active noise control system, i.e., the neighborhood-based adaptive estimation stage: each node independently estimates the control filter coefficients of the neighborhood nodes according to its own error sound signal to obtain a joint adaptive estimation block vector; Step 5, the second stage of noise reduction of the multi-channel active noise control system, i.e., the communication stage: distribute the joint adaptive estimation block vector to the neighborhood nodes interactively through the communication link; Step 6, the third stage of noise reduction of the multi-channel active noise control system, i.e., the node-based fusion estimation stage: each node independently smooths the received joint adaptive block vector according to the node number by using the fusion criterion to obtain a fusion estimation result; Step 7, the fourth stage of noise reduction of the multi-channel active noise control system, i.e., the decimation stage: each node independently extracts the block vector corresponding to its own node number from the fusion estimation result as the update value of the control filter coefficient of its own node to drive the secondary loudspeaker to achieve noise reduction, and waits for the system to stabilize to obtain the minimized residual noise under the current system parameter conditions; Step 8, optimize and adjust the adaptive step size, and repeat Steps 4 to 7 to further optimize the noise reduction performance of the system.

2. The distributed active noise control method based on the block diffusion filtering least mean square algorithm according to Claim 1, characterized in that, in Step 1, the distributed node system includes 1 error microphone for detecting residual noise, 1 secondary loudspeaker for generating a control sound signal, and 1 node processor for both data processing and external communication.

3. The distributed active noise control method based on the block diffusion filtering least mean square algorithm according to Claim 1, characterized in that, in Step 4, a joint cost function based on local error estimation and vector Euclidean norm deviation is used as the cost function for adaptive estimation: where the subscript \(k\) on the left side of the equal sign represents the \(k\)-th node; the first term on the right side of the equation is the local error estimation term, and the second term is the vector Euclidean norm deviation term; the operator denotes the mathematical expectation, and \(e\) k (n) represents the error sound signal of the \(k\)-th node at time \(n\); the non-negative parameter \(\alpha\) k is used to balance local error estimation and spatial regularization, and the index set represents the neighborhood node numbers of the \(k\)-th node including the \(k\)-th node, and the index set represents the neighborhood node numbers of the \(l\)-th node including the \(l\)-th node; the non-negative parameter \(\{b\) klp} represents the weights of the information of each neighborhood node on the block vector estimation of the \(k\)-th node, and the operator \(\|\cdot\|\) 2 denotes the Euclidean norm; \(v\) k represents the block vector of the \(k\)-th node, which contains all the control filter coefficients \(w\) l in the neighborhood: \(v\) k =\(col\{w\) l \},\) \(\varphi\) p represents the block vector estimate of the \(p\)-th node; the selection matrix is used to select the control filter coefficient of the \(l\)-th node from the block vector of the \(k\)-th node, where the operator denotes the Kronecker product, is a column vector with a unique non-zero element 1 only in the \(q\)-th row, and the matrix \(I\) L is the identity matrix of dimension \(L\), and \(L\) represents the length of the control filter coefficient \(w\) l ; similarly, the selection matrix is used to select the control filter coefficient of the \(l\)-th node from the block vector of the \(p\)-th node.

4. The distributed active noise control method based on the block diffusion filtering least mean square algorithm according to Claim 3, characterized in that, in Step 4, the joint adaptive estimation block vector is: Among them is the combined adaptive estimation block vector at time n+1 iteratively updated by the k-th node based on the local error sound signal e k (n), and the sub-vector represents the estimated value of the l-th filter coefficient vector obtained by the k-th node through iterative calculation based on the error sound signal at time n+1; φ k (n) is the result of the fusion block vector obtained by the k-th node at time n; μ k represents the adaptive step size of the k-th node; represents the filtering reference signal vector based on the neighborhood of the k-th node at time n.

5. The distributed active noise control method based on the block diffusion filtering least mean square algorithm according to Claim 4, characterized in that, in Step 6, the sub-vectors with the same node number in the joint adaptive estimation block vector received at the n + 1 moment are fused to obtain the fusion block vector result of the k node at the n + 1 moment: where the intermediate variable C kp is the fusion coefficient matrix, expressed in the form of a Kronecker product: where represents the sum of elements of the index set , represents the sum of elements of the index set , and the non - negative fusion coefficients satisfy the following conditions: Among them, K is the total number of nodes.

6. The distributed active noise control method based on the block diffusion filtering least mean square algorithm according to Claim 5, characterized in that, In the said step 8, the criterion for optimizing and adjusting the adaptive step size is as follows: where the operator λ(·) represents the spectral radius of the internal matrix; C B represents the global fusion matrix; the subscript represents the dimension of the identity matrix I, Z μ is the global step matrix, Γ B is the transformation matrix, the operator represents the mathematical expectation, is the diagonalized global filtering reference matrix at time n, X F (n) is the global filtering reference matrix at time n, G B is the global selection matrix.

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