A Novel Approach to Active Noise Control using Normalized Clipped ...
76 International Journal of Manufacturing, Materials, and Mechanical Engineering, 3(3), 76-88, July-September 2013
A Novel Approach to Active Noise Control using Normalized Clipped Adaptive Algorithm A. Chandra Mouli, Department of Mechanical Engineering, Narasaraopeta Engineering College, Narasaraopeta, Andhra Pradesh, India Ch. Ratnam, Department of Mechanical Engineering, Andhara University, Vasakhapatnam, Andhra Pradesh, India
ABSTRACT In this paper, an efficient normalization based adaptive algorithm is used for active noise control in mechanical systems in order to reject extensive disturbances. The proposed implementations are suitable in applications like various motors, generators, aircrafts, battle field and elevators, etc where noise reduction is very important. In the experiments, the authors used several variants of the familiar Filtered X Least Mean Square (FXLMS) algorithm. In FXLMS the vector of past inputs is first filtered by the secondary path transfer function, hence it is named as filtered X LMS. These modified results normalized FXLMS (NFXLMS) and normalized clipped FXLMS (NCFXLMS) algorithms, leads to fast convergence, better noise rejection capability. The NCFXLMS algorithm requires only half of the multiplications requires than NFXLMS. This type of low complexity strategy is not used in active noise control application in mechatronic systems. Simulation results prove that the proposed active noise cancellers provide better performance in terms of signal to noise ratio than the conventional FXLMS. Keywords:
Active Noise Control, Convergence, Filtered X Least Mean Square (FXLMS) Algorithm, Mechanical Noises, Mechatronics, Normalized Clipped Adaptive Algorithm
1. INTRODUCTION Extraction of high resolution information signals is important in all practical applications. In our modern mechanized world, research on noise control has become increasingly important. The need to cancel or filter noise is not only a matter of human comfort, but will also reduce the stress imposed by vibrations
on mechanical structures. Generally, filtering techniques are classified as non-adaptive and adaptive. In the case of non-adaptive filtering, filter characteristics are fixed or constant irrespective of input noise, i.e., treatment is similar for any type of noise. These types of filters are acceptable if a noise signal is stationery. In practical cases, the noises generated by various types of machinery are not stationery, and their
DOI: 10.4018/ijmmme.2013070105 Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
International Journal of Manufacturing, Materials, and Mechanical Engineering, 3(3), 76-88, July-September 2013 77
magnitude, frequency, phase and intensity vary instantaneously. In such cases, non-adaptive filters, whose coefficients are constant, are unable to control noise; therefore, adaptive filters should be utilized. These filters are capable of changing their filter coefficients; perform filtering depending up on the input signal (hence the designation adaptive). The concept of noise reduction in mechanical machinery is known as active noise control (ANC), and adaptive filter plays a key role. ANC use the phenomenon of wave interference; when two waves with the same amplitude and frequency, but phase-reversed, travel in the same direction, they neutralize each other to destructive interference. The resulting sound is null as, the sound energy is transformed into heat. In typical ANC, a reference signal is generated and the adaptive filter adjusts the amplitude and phase of the reference signal to minimize the noise signal. The Least Mean Square (LMS) algorithm is a basic adaptive algorithm that has been extensively used in many applications due to its simplicity and robustness. Adaptive filters are normally defined for problems such as electrical noise cancelling where the filter output is an estimate of a desired signal. In control applications, however, the adaptive filter works as a regulator, controlling a dynamic system containing actuators, amplifiers etc. The estimate (anti-vibrations or anti-sound) in this case can thus be seen as the output signal from a dynamic system, i.e. a forward path. Since there is a dynamic system between the filter output and the estimate, the selection of adaptive filter algorithms must be made with care. A conventional adaptive algorithm such as the LMS algorithm is likely to be unstable in this application due to the phase shift (delay) introduced by the forward path. The well-known filtered-x LMS (FXLMS) algorithm is, however, an adaptive filter algorithm that is suitable for active noise control applications. It is developed from the LMS algorithm, where a model of the dynamic system between the filter output and the estimate, i.e. the forward path is introduced between the input signal and the algorithm for
the adaptation of the coefficient vector. Because of this feature, the FXLMS algorithm is extensively used in active noise control. Several noise control techniques has presented in literature to control noise component occurred in mechanical systems (Barrault et al., 2007; Ming et al., 2008). In this type of analysis the role of signal processing is very important and that leads the new era of mechatronics in noise control applications. Several mechatronics techniques are reported in the contest of active noise control (Li Tan et al., 2001; Sethares et al., 1992). In Barrault et al. (2007) derived a new model of active noise control based on stochastic differential equation, this model is based on FXLMS algorithm. A variant of LMS algorithm is presented in (Sun et al., 2006) based on weighted time average as cost function. Similarly variants of LMS and FXLMS algorithms are used for active noise control in mechanical systems (Ming et al., 2008; Chenyuan et al., 2009). The reference inputs to the FXLMS algorithm are deterministic functions and are de-fined by a periodically extended, truncated set of orthonormal basis functions. In such a case, the FXLMS algorithm operates on an instantaneous basis such that the weight vector is updated for every new sample within the occurrence based on an instantaneous gradient estimate. However, a steady-state convergence analysis for the FXLMS algorithm with deterministic reference inputs showed that the steady-state weight vector is biased and thus the adaptive estimate does not approach the Wiener solution. To handle this drawback, another strategy was considered for estimating the coefficients of the linear expansion, namely, the block FXLMS (BFXLMS) algorithm (Vikram Kumar et al., 2010), in which the coefficient vector is updated only once for every occurrence based on a block gradient estimation. The BFXLMS algorithm has been proposed in the case of random reference in-puts and when the input is stationary, the steady-state misadjustment and convergence speed is the same as the FXLMS algorithm. A major advantage of the block or the transform domain FXLMS algorithm is that the input signals are approximately uncorrelated.
Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
11 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the publisher's webpage: www.igi-global.com/article/a-novel-approach-to-active-noisecontrol-using-normalized-clipped-adaptive-algorithm/84148
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A Novel Approach to Active Noise Control using Normalized Clipped Adaptive Algorithm A. Chandra Mouli, Department of Mechanical Engineering, Narasaraopeta Engineering College, Narasaraopeta, Andhra Pradesh, India Ch. Ratnam, Department of Mechanical Engineering, Andhara University, Vasakhapatnam, Andhra Pradesh, India
ABSTRACT In this paper, an efficient normalization based adaptive algorithm is used for active noise control in mechanical systems in order to reject extensive disturbances. The proposed implementations are suitable in applications like various motors, generators, aircrafts, battle field and elevators, etc where noise reduction is very important. In the experiments, the authors used several variants of the familiar Filtered X Least Mean Square (FXLMS) algorithm. In FXLMS the vector of past inputs is first filtered by the secondary path transfer function, hence it is named as filtered X LMS. These modified results normalized FXLMS (NFXLMS) and normalized clipped FXLMS (NCFXLMS) algorithms, leads to fast convergence, better noise rejection capability. The NCFXLMS algorithm requires only half of the multiplications requires than NFXLMS. This type of low complexity strategy is not used in active noise control application in mechatronic systems. Simulation results prove that the proposed active noise cancellers provide better performance in terms of signal to noise ratio than the conventional FXLMS. Keywords:
Active Noise Control, Convergence, Filtered X Least Mean Square (FXLMS) Algorithm, Mechanical Noises, Mechatronics, Normalized Clipped Adaptive Algorithm
1. INTRODUCTION Extraction of high resolution information signals is important in all practical applications. In our modern mechanized world, research on noise control has become increasingly important. The need to cancel or filter noise is not only a matter of human comfort, but will also reduce the stress imposed by vibrations
on mechanical structures. Generally, filtering techniques are classified as non-adaptive and adaptive. In the case of non-adaptive filtering, filter characteristics are fixed or constant irrespective of input noise, i.e., treatment is similar for any type of noise. These types of filters are acceptable if a noise signal is stationery. In practical cases, the noises generated by various types of machinery are not stationery, and their
DOI: 10.4018/ijmmme.2013070105 Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
International Journal of Manufacturing, Materials, and Mechanical Engineering, 3(3), 76-88, July-September 2013 77
magnitude, frequency, phase and intensity vary instantaneously. In such cases, non-adaptive filters, whose coefficients are constant, are unable to control noise; therefore, adaptive filters should be utilized. These filters are capable of changing their filter coefficients; perform filtering depending up on the input signal (hence the designation adaptive). The concept of noise reduction in mechanical machinery is known as active noise control (ANC), and adaptive filter plays a key role. ANC use the phenomenon of wave interference; when two waves with the same amplitude and frequency, but phase-reversed, travel in the same direction, they neutralize each other to destructive interference. The resulting sound is null as, the sound energy is transformed into heat. In typical ANC, a reference signal is generated and the adaptive filter adjusts the amplitude and phase of the reference signal to minimize the noise signal. The Least Mean Square (LMS) algorithm is a basic adaptive algorithm that has been extensively used in many applications due to its simplicity and robustness. Adaptive filters are normally defined for problems such as electrical noise cancelling where the filter output is an estimate of a desired signal. In control applications, however, the adaptive filter works as a regulator, controlling a dynamic system containing actuators, amplifiers etc. The estimate (anti-vibrations or anti-sound) in this case can thus be seen as the output signal from a dynamic system, i.e. a forward path. Since there is a dynamic system between the filter output and the estimate, the selection of adaptive filter algorithms must be made with care. A conventional adaptive algorithm such as the LMS algorithm is likely to be unstable in this application due to the phase shift (delay) introduced by the forward path. The well-known filtered-x LMS (FXLMS) algorithm is, however, an adaptive filter algorithm that is suitable for active noise control applications. It is developed from the LMS algorithm, where a model of the dynamic system between the filter output and the estimate, i.e. the forward path is introduced between the input signal and the algorithm for
the adaptation of the coefficient vector. Because of this feature, the FXLMS algorithm is extensively used in active noise control. Several noise control techniques has presented in literature to control noise component occurred in mechanical systems (Barrault et al., 2007; Ming et al., 2008). In this type of analysis the role of signal processing is very important and that leads the new era of mechatronics in noise control applications. Several mechatronics techniques are reported in the contest of active noise control (Li Tan et al., 2001; Sethares et al., 1992). In Barrault et al. (2007) derived a new model of active noise control based on stochastic differential equation, this model is based on FXLMS algorithm. A variant of LMS algorithm is presented in (Sun et al., 2006) based on weighted time average as cost function. Similarly variants of LMS and FXLMS algorithms are used for active noise control in mechanical systems (Ming et al., 2008; Chenyuan et al., 2009). The reference inputs to the FXLMS algorithm are deterministic functions and are de-fined by a periodically extended, truncated set of orthonormal basis functions. In such a case, the FXLMS algorithm operates on an instantaneous basis such that the weight vector is updated for every new sample within the occurrence based on an instantaneous gradient estimate. However, a steady-state convergence analysis for the FXLMS algorithm with deterministic reference inputs showed that the steady-state weight vector is biased and thus the adaptive estimate does not approach the Wiener solution. To handle this drawback, another strategy was considered for estimating the coefficients of the linear expansion, namely, the block FXLMS (BFXLMS) algorithm (Vikram Kumar et al., 2010), in which the coefficient vector is updated only once for every occurrence based on a block gradient estimation. The BFXLMS algorithm has been proposed in the case of random reference in-puts and when the input is stationary, the steady-state misadjustment and convergence speed is the same as the FXLMS algorithm. A major advantage of the block or the transform domain FXLMS algorithm is that the input signals are approximately uncorrelated.
Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
11 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the publisher's webpage: www.igi-global.com/article/a-novel-approach-to-active-noisecontrol-using-normalized-clipped-adaptive-algorithm/84148
Related Content Optimization of Natural Gas Liquefaction Process Mohd Shariq Khan and Moonyong Lee (2015). Handbook of Research on Advances and Applications in Refrigeration Systems and Technologies (pp. 854-880).
www.irma-international.org/chapter/optimization-of-natural-gas-liquefactionprocess/136767/ Generic Models of Electric Machine Applications in Hybrid Electric Vehicles Power Train Simulations (2013). Hybrid Electric Power Train Engineering and Technology: Modeling, Control, and Simulation (pp. 95-150).
www.irma-international.org/chapter/generic-models-electric-machineapplications/76583/ An Experimental Investigation during Micro Machining of E-Glass-FibreEpoxy Composite on Developed Electrochemical Spark Machining Setup Alakesh Manna and Vivek Narang (2012). International Journal of Manufacturing, Materials, and Mechanical Engineering (pp. 46-60).
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www.irma-international.org/chapter/feature-recognition-datum-extractionsetup/67777/
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