Research Article
Wavelet Adaptive Algorithm and Its Application to
MRE Noise Control System
Zhang Yulin and Zhao Xiuyang
School of Information Science and Engineering, University of Jinan, Jinan 250022, China
Correspondence should be addressed to Zhao Xiuyang; zhaoxy@ujn.edu.cn
Received January ; Accepted March
Academic Editor: Seung-Bok Choi
Copyright © Z. Yulin and Z. Xiuyang. is is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
To address the limitation of conventional adaptive algorithm used for active noise control (ANC) system, this paper proposed and
studied two adaptive algorithms based on Wavelet. e twos are applied to a noise control system including magnetorheological
elastomers (MRE), which is a smart viscoelastic material characterized by a complex modulus dependent on vibration frequency
and controllable by external magnetic elds. Simulation results reveal that the Decomposition LMS algorithm (D-LMS) and
Decomposition and Reconstruction LMS algorithm (DR-LMS) based on Wavelet can signicantly improve the noise reduction
performance of MRE control system compared with traditional LMS algorithm.
1. Introduction
e most popular algorithm used to adapt FIR lters is
the Widrow-Ho LMS [], which is shown in Figure .Its
popularity is due to its low computational complexity and
robustness to implementation errors.
As in Figure , (), (), (),and()denote the refer-
ence of system, disturbance, control error, and control signal,
respectively. e system control signal can be expressed as
(
)
=
𝑇
(
)
(
)
,
()
where ()=[
0
,
1
,...,
𝑁−1
]
𝑇
istheweightvectorofthe
order control lter,
𝑇
()=()∑
𝑁−1
𝑖=0
−𝑖
,anddenotes
the vectors transpose. e goal is to minimize the output
error:
(
)
=
(
)
−
(
)
.
()
According to the Widrow-Ho LMS algorithm [], the
weightofcontrolltercanbeadjustedby
(
+1
)
=
(
)
+2
(
)
(
)
,
()
where is the step-size parameter. e convergence rate
of this algorithm depends on the condition numbers of
the autocorrelation
𝑥
of the reference signal. When the
eigenvalues of
𝑥
arewidelyspread,theexcessmeansquare
error produced by LMS algorithm is primarily determined by
the largest eigenvalue, and the time taken by the average tap-
weight vector [
()]to converge is limited by the smallest
eigenvalue. However, the speed of convergence of the mean
square error is aected by the spread of the eigenvalues of
𝑥
.
e speed of convergence of the LMS algorithm may
slow down when the correlation matrix of the inputs is
ill-conditioned, which implies that the control system with
Widrow-Ho LMS adaptive algorithm might become unsta-
ble when inputs change indenitely. In order to enhance
the performance of the algorithm, Wavelet Transform is
proposed in this study due to its time-frequency localization
[, ]. is paper presents two kinds of adaptive wavelet
algorithm: Decomposition LMS algorithm (D-LMS) and
Decomposition and Reconstruction LMS algorithm (DR-
LMS).
2. Decomposition LMS Algorithm (D-LMS)
In D-LMS algorithm, the input signal is decomposed
into various wavelet spaces according to various scales to
form the input vector, and then the adaptive lter weight
Hindawi Publishing Corporation
Shock and Vibration
Volume 2015, Article ID 968082, 8 pages
http://dx.doi.org/10.1155/2015/968082
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