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[.]
Trang 1A novel adaptive neural controller for narrowband
active noise control systems
Minh-Canh Huynh
Dept of Electrical Engineering
Chung Yuan Christian University
Taoyuan City, Taiwan
Dept of Electrical Engineering
Eastern International University
Binh duong Province, Viet Nam
canh.huynh@eiu.edu.vn
Cheng-Yuan Chang Dept of Electrical Engineering Chung Yuan Christian University Taoyuan City, Taiwan ccy@cycu.edu.tw
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
Keywords—Active noise control, narrowband active noise
control, adaptive neural controller
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
neuro-controller 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
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
II TRADITIONAL METHOD ANALYSIS
In this content, the algorithm of the traditional method is analyzed
The Figure 1 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 nj( ) cos( jn)is the j reference signal obtained th from signal generator, where is the angular frequency of j the reference signal The error signal is defined by
withd 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 ( )
1
j
The output signal of jthadaptive filter is defined by
1 0
l
with ( ) [ ( ), ( -1), , ( 1)]T
j n x n x nj j x n Nj
signal vector and ( ) [ ,0( ), ,1( ), , , 1( )]T
the weight vector
The filtered reference signal is computed as:
1
0
ˆ ˆ
m
where ˆ( ) [ ( ), a ( ), , aˆ0 ˆ1 ˆ 1( )] T
M
The weights are updated by adaptive law as:
( ) [ ( ), ( -1), , ( 1)]T
signal vector
Trang 2Thee n is error signal ( )
Noise
( )
e n +
-Signal generator
LMS
( )
A z ˆ( )
A z
( )
j
x n
( )
j
x n
1 ( )
u n ( )
k
u n
( )
u n u n( )
j
W
Non-acoustic
Sensor
Figure 1: Traditional method III PROPOSED METHOD ANALYSIS
Algorithm analysis of the proposed method is shown in
this section
Firstly, the block diagram of the proposed method is
illustrated by Figure 2 Thex n is the j( ) j reference signal th
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 ( )
1
j
The error signal is defined,
whered n is the primary noise signal The structure of ( )
adaptive neural controller is displayed in Figure 3 The
controller has three-layer perceptron The input layer is
Layer 1, the hidden layer is layer 2 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 3 is the output layer, which has only an
adaptive filter ˆ( )A z is an estimate of ( )A z The algorithm of
the proposed method is built by
The input layer:
The hidden layer:
2j( ) j( ( )),j
0
l
with B is the bias parameter, the activation function is
defined by
( )
1
e
The output layer:
1 3
0
l
The filtered signal is computed as:
1
0
ˆ
m
where ˆ( ) [ ( ), a ( ), , aˆ0 ˆ1 ˆ 1( )]T
M
j n c n c nj j c n Mj
The weights of the output layer are updated by
ˆ
ˆ ( ) [ ( ), (ˆ ˆ 1), , (ˆ 1)]T
j n c n c nj j c n Nj
signal vector, p is the learning rate
Noise
( )
e n +
neural controller ( )
j
x n
th
j
( )
A z
1 ( )
u n
( )
k
u n
( )
u n u n( )
Non-acoustic Sensor
Figure 2: The block diagram of the proposed algorithm
1
z 1
z 1
z 1
z
copy
( )
e n
( )
j
c n
ˆ( )
A z
ˆ ( )j
c n
( )
j
u n
( )
j
x n
j
j
j
x n
,0 j
w
,1 j
w
,2 j
w
,3 j
j
( )
j
b n
j
w
1 j
j
j
L n
j
x n N w j N ,1
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 Fs4KHz The length of the adaptive filters is 150
A Case 1 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
traditional method is t 15 10 6 The learning rate of the proposed method is p 3 10 4 and the bias parameter 5
10
B The parameters of the proposed method are determined by the trial and error method Figure 4 illustrates the cancellation of the tonal signals, including the tonal signalsd n (gold), the error signals of proposed (red) and ( ) traditional (blue) methods Obviously, both the proposed and traditional methods eliminate noise completely at frequencies
Trang 30 100 200 300 400 500
Frequency (Hz)
-80
-70
-60
-50
-40
-30
-20
-10
0
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 2
The ANC system in this case is nonlinear The nonlinear
primary and secondary paths are selected as in [12] The
primary acoustic path is
and f n( )x n( 2) 0.9 ( x n 3) 0.01 (x n5)
The secondary acoustic path is given by
0.4 ( ) ( 2)
u n u n
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 1
The bias parameter is B0.001and the learning rate of the
proposed method is p15 10 4 The step size of the
traditional method is t 2 10 6 The cancellation of tonal
signals is displayed in Figure 5 Here, it can be seen that the
traditional method is not efficient for nonlinear ANC system
The proposed method cancels noise completely at frequencies of 160Hz, 320Hzand 480Hz
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
I CONCLUSIONS
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
REFERENCES [1] S M Kuo and D R Morgan, Active noise control systems:
Algorithms and DSP Implementation New York, NY, USA: Wiley, 1996
[2] T Tsuei, A Srinivasa, and S M Kuo, "An adaptive feedback
active noise control system," in Proceedings of the 2000 IEEE International Conference on Control Applications Conference Proceedings (Cat No 00CH37162), 2000: IEEE, pp 249-254 [3] Y Xiao, "A new efficient narrowband active noise control
system and its performance analysis," IEEE Trans Audio Speech Lang Process., vol 19, no 7, pp, 1865-1874, 2010 [4] S M Kuo and A B Puvvala, "Effects of frequency separation
in periodic active noise control systems," IEEE Trans Audio Speech Lang Process., vol 14, no 5, pp, 1857-1866, 2006 [5] J Shin, H J Baek, B Y Park, and J Cho, "A Sequential
Selection Normalized Subband Adaptive Filter with Variable Step-Size Algorithms," Mathematical Problems in Engineering, vol 2018, 2018
[6] L Lu and H Zhao, "Adaptive Volterra filter with continuous
lp-norm using a logarithmic cost for nonlinear active noise control," J Sound Vib., vol 364, pp, 14-29, 2016
[7] A Haseeb, M Tufail, and S Ahmed et al., "A Fuzzy
Logic-Based Gain Scheduling Method for Online Feedback Path Modeling and Neutralization in Active Noise Control Systems," Fluctuation and Noise Letters, vol 19, no 01, p 2050008,
2020
[8] H Zhao, X Zeng, Z He, S Yu, and B Chen, "Improved
functional link artificial neural network via convex combination for nonlinear active noise control," Applied Soft Computing, vol
42, pp, 351-359, 2016
[9] L Luo and J Sun, "A novel bilinear functional link neural
network filter for nonlinear active noise control," Applied Soft Computing, vol 68, pp, 636-650, 2018
[10] X Zhang, X Ren, J Na, B Zhang, and H Huang, "Adaptive
nonlinear neuro-controller with an integrated evaluation algorithm for nonlinear active noise systems," J Sound Vib., vol 329, no 24, pp, 5005-5016, 2010
[11] N Le Thai, X Wu, J Na, and Y Guo et al., "Adaptive variable
step-size neural controller for nonlinear feedback active noise control systems," Applied Acoustics, vol 116, pp, 337-347,
2017
[12] M.-C Huynh and C.-Y Chang, "Nonlinear Neural System for
Active Noise Controller to Reduce Narrowband Noise," Mathematical Problems in Engineering, vol 2021, 2021