A novel adaptive neural controller for narrowband active noise control systems

A Novel Adaptive Neural Controller for Narrowband Active Noise Control Systems A novel adaptive neural controller for narrowband active noise control systems Minh Canh Huynh Dept of Electrical Enginee[.]

2021 8th NAFOSTED Conference on Information and Computer Science (NICS) A novel adaptive neural controller for narrowband active noise control systems Minh-Canh Huynh Dept of Electrical Engineering Chung Yuan Christian University Taoyuan City, Taiwan Cheng-Yuan Chang Dept of Electrical Engineering Chung Yuan Christian University Taoyuan City, Taiwan ccy@cycu.edu.tw Dept of Electrical Engineering Eastern International University Binh duong Province, Viet Nam canh.huynh@eiu.edu.vn Abstract—This paper proposes a novel adaptive neural network controller which can operate effectively in both linear and nonlinear narrowband active noise control systems The advantage of the proposed method is a simple structure with three network layers, which its adaptive coefficients are updated online Algorithm analysis of the proposed method is presented in this paper The improved performance is verified by computer simulations through comparison with the traditional method structure with fast learning algorithm and is shown by the algorithm analysis The performance of the proposed algorithm is considered based on the simulation results The rest of this paper is as follows The traditional method is analyzed in Section II The proposed method is also analyzed in Section III The simulation results are shown in Section IV The conclusions are presented in Section V Keywords—Active noise control, narrowband active noise control, adaptive neural controller II TRADITIONAL METHOD ANALYSIS I INTRODUCTION Noise reduction using the active noise control (ANC) method gives high efficiency at low frequencies While the method of passive noise reduction using sound-proof materials is cumbersome and only effective at high frequencies [1] Hence, the ANC method has been chosen as an effective solution to cancel noise at low frequencies in industrial applications [2] The filtered-x least mean square (FXLMS) algorithm is commonly performed in ANC systems, because it is simple and effective for linear ANC systems Many studies using the FXLMS algorithm for the linear ANC controllers have been published [3-5] However, practical ANC systems may exhibit nonlinear behaviors due to the effects of external circumstances such as measurement noise, temperature, the frequency content As a result, the efficiency of linear ANC controllers is significantly reduced Therefore, several works have developed nonlinear adaptive controllers in ANC systems Lu et al proposed an adaptive Volterra filter for nonlinear ANC system [6] Haseeb et al mentioned a fuzzy controller to calculate the instantaneous gain for auxiliary noise based on two inputs [7] Functional link artificial neural network (FLANN)[8, 9] has been used to cope with nonlinear ANC systems Zhang et al introduced adaptive nonlinear neurocontroller to cancel the non-Gaussian noises [10] Thai et al proposed variable step-size for adaptive neural controller based on FXLMS algorithm for feedback ANC systems [11] Markedly, Thai’s method approached a fast learning algorithm with two adaptive filters without pre-training for the neural network This paper is developed based on the adaptive neural controller in [11] The difference of the proposed method uses only one adaptive controller at the output layer The adaptive weights of the hidden layer are copied from the weights of the output layer This method has a simple 978-1-6654-1001-4/21/$31.00 ©2021 IEEE In this content, the algorithm of the traditional method is analyzed The Figure illustrates the ANC system using the traditional method The A( z ) and P( z ) are the secondary path and primary path transfer functions, respectively And x j (n)  cos( j n ) is the j th reference signal obtained from signal generator, where  j is the angular frequency of the reference signal The error signal is defined by (1) e(n)  d (n)  u (n), with d (n) is the primary noise signal, u (n)  a (n)  u ( n) and a ( n) is the impulse response of A( z ) , “  ” denotes linear convolution operation The u (n) is determined by k u ( n )   u j ( n ) , j  1, 2,3 , k (2) j 1 The output signal of j th adaptive filter is defined by N 1 u j (n )   w j ( n) x j (n  l )  w Tj (n ) x j (n ), (3) l 0 T with x j (n)  [ x j (n), x j (n -1), , x j (n  N  1)] is the input signal vector and w j (n)  [ w j ,0 (n), w j ,1 (n), , w j , N 1 (n)]T is the weight vector The filtered reference signal is computed as: xj (n)  M 1  aˆ (n) x (n  m)  aˆ j m0 T (4) ( n) x j (n), where aˆ ( n)  [ aˆ0 ( n), aˆ ( n), , aˆ M 1 (n )]T The weights are updated by adaptive law as: w j (n  1)  w j (n)  t e(n) xj (n), where t is step (5) size and xj (n)  [ xj (n), xj (n -1), , xj (n  N  1)] is the filtered signal vector 504 T 2021 8th NAFOSTED Conference on Information and Computer Science (NICS) The e(n) is error signal d ( n) + P( z ) Non-acoustic Sensor Signal generator Wj x j ( n)  - e( n) , cˆ j (n)  [cˆ j (n), cˆ j (n  1), , cˆ j (n  N  1)]T the u1 (n)  u ( n) Noise source LMS III PROPOSED METHOD ANALYSIS Algorithm analysis of the proposed method is shown in this section u ( n )   u j ( n ) , j  1, 2,3 , k (10) with B is the bias parameter, the activation function is defined by (11) c j ( n)  sigmoid (b j (n ))  b ( n ) 1 e j The output layer: N 1 L3j (n)  u j ( n)   w j (n)c j (n  l ) (12) l 0 The filtered signal is computed as: T (n)c j ( n), (13) where aˆ ( n)  [ aˆ0 ( n ), aˆ ( n), , aˆ M 1 ( n)]T is the filter vector A( z ) uk ( n )  B b j ( n) c j ( n) Sigmoid function Aˆ ( z ) 1 w j , N 1 cˆ j (n) wj u j ( n) LMS e( n) j th copy Layer Layer Layer L1j  n  L2j  n  L3j  n  Figure 3: Structure of adaptive neural controller IV SIMULATION RESULTS Simulation results are performed in linear and nonlinear ANC systems to consider the responsiveness of the proposed method Concerning the setting of parameters for the ANC system in both cases as: The sampling frequency Fs  KHz The length of the adaptive filters is 150 A Case This experiment is performed on a linear ANC system P( z ) and A( z ) are obtained by estimating in [1] with the length of 200 The noisy signal is the sum of two narrowband sinusoidal signals, including a white noise signal (amplitude 0.01) combined with two tonal signals at frequencies of 220Hz , and 440Hz (amplitude 1) The step size of the traditional method is t  15  10 6 The learning rate of the proposed method is  p   10 4 and the bias parameter B  105 The parameters of the proposed method are determined by the trial and error method Figure illustrates the cancellation of the tonal signals, including the tonal signals d (n) (gold), the error signals of proposed (red) and traditional (blue) methods Obviously, both the proposed and traditional methods eliminate noise completely at frequencies of 220Hz and 440Hz and c j (n)  [c j ( n), c j (n  1), , c j (n  M  1)]T The weights of the output layer are updated by w j ( n  1)  w j (n)   p e(n)cˆ j (n) , u(n) u ( n)  (9) l 0 j w j ,3  (7) N 1  aˆ (n)c (n  m)  aˆ w j ,2 x j (n  N  1) where b j ( n)   ( w j (n) x j (n  l )  B), m0 w j ,1 z 1 x j ( n  2) z where d ( n) is the primary noise signal The structure of adaptive neural controller is displayed in Figure The controller has three-layer perceptron The input layer is Layer 1, the hidden layer is layer The sigmoid activation function is located at the output of the hidden layer The weights of the hidden layer are copied by the weights of the output layer Layer is the output layer, which has only an adaptive filter Aˆ ( z ) is an estimate of A( z ) The algorithm of the proposed method is built by The input layer: (8) L1j ( n)  x j ( n) at the j th channel M 1 x j (n  1) x j (n  3) j 1 The hidden layer: L2j ( n )  c j (b j ( n)),  w j ,0 z 1 (6) The error signal is defined, e(n)  d (n)  u (n), j th u1 (n) e( n ) z 1 obtained from the signal generator, A( z ) and P( z ) are the secondary path and primary path transfer functions, respectively The u (n) is the sum of the anti-noise signals as k Adaptive neural controller  - Figure 2: The block diagram of the proposed algorithm x j ( n) Firstly, the block diagram of the proposed method is illustrated by Figure The x j (n) is the j th reference signal cˆ j (n)  Non-acoustic Sensor x j ( n) Figure 1: Traditional method d ( n) + P( z) Signal generator xj (n) filtered signal vector,  p is the learning rate u( n) A( z ) uk ( n) Aˆ ( z ) is is and  Noise source where the weight vector w j ( n)  [ w j ,0 (n), w j ,1 ( n), , w j , N 1 ( n)]T (14) 505 2021 8th NAFOSTED Conference on Information and Computer Science (NICS) The proposed method cancels noise completely at frequencies of 160Hz , 320Hz and 480Hz -10 Through two experiments with different ANC systems from linear to nonlinear, the proposed method is superior to the traditional method The proposed method reduces noise significantly in both linear and nonlinear ANC systems, while the traditional method is only effective for the linear ANC system However, the computational cost of the proposed method is higher than that of the traditional method -20 -30 -40 -50 -60 -70 I CONCLUSIONS -80 The simulation results of this paper have proved that the proposed method has outstanding performance in both linear and nonlinear ANC systems The advantage of the proposed method is a simple algorithm, which has been shown through the mathematical analysis The weights of the controller are directly updated without prior training for the neural network Although the proposed method is computationally burdensome, the performance trade-off needs to be considered 100 200 300 400 500 Frequency (Hz) Figure 4: Tonal signals cancellation, including the tonal signals d (n) (gold line), the error signals of proposed (red line) and traditional (blue line) methods B Case The ANC system in this case is nonlinear The nonlinear primary and secondary paths are selected as in [12] The primary acoustic path is d (n)  f (n  2)  0.08  f (n  2)  0.04  f (n  2) , REFERENCES [1] [2] and f ( n)  x ( n  2)  0.9 x ( n  3)  0.01x ( n  5) The secondary acoustic path is given by [3] u (n)  u (n)  0.35u (n  1)  0.09u (n  2)  0.5u (n)u (n  1) 0.4u (n)u (n  2) [4] [5] Magnitude (dB) [6] [7] [8] [9] [10] Figure 5: Tonal signals cancellation, including the tone signal d (n) is the gold line, the error signals of proposed (red) and traditional (blue) methods This experiment changes the frequency of the noisy signals including 160Hz , 320Hz and 480Hz with amplitude 1, and a white noise signal is added as in case The bias parameter is B  0.001 and the learning rate of the proposed method is  p  15  10 4 The step size of the [11] [12] traditional method is t   10 6 The cancellation of tonal signals is displayed in Figure Here, it can be seen that the traditional method is not efficient for nonlinear ANC system 506 S M Kuo and D R Morgan, Active noise control systems: Algorithms 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