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ACTIVE NOISE CANCELLATION IN A LABORATORY DUCT USING FUZZY LOGIC AND NEURAL NETWORK

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The main goal of this paper is to present a simulation scheme to simulate an adaptive filter using LMS (Least mean square) adaptive algorithm for noise cancellation. The main objective of the noise cancellation is to estimate the noise signal and to subtract it from original input signal plus noise signal and hence to obtain the noise free signal. There is an alternative method called adaptive noise cancellation for estimating a speech signal corrupted by an additive noise or interference. This method uses a primary input signal that contains the speech signal and a reference input containing noise. The reference input is adaptively filtered and subtracted from the primary input signal to obtain the estimated signal. In this method the desired signal corrupted by an additive noise can be recovered by an adaptive noise canceller using LMS (least mean square) algorithm. This adaptive noise canceller is useful to improve the S/N ratio. Here we estimate the adaptive filter using Labview /MATLAB/SIMULINK environment . For achieving the goal we also use modern algorithms like ANFIS, FIS and Neural Network and compare the PSD of all the algorithms.

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ACTIVE NOISE CANCELLATION IN A LABORATORY DUCT USING FUZZY LOGIC AND NEURAL NETWORK

  1. 1. 1 PROJECT REPORT ON “ACTIVE NOISE CANCELLATION IN A LABORATORY DUCT USING FUZZY LOGIC AND NEURAL NETWORK ” Submitted by- Rishikesh 11-1-6-002 Jigmi Basumatary 11-1-6-018 Abdul Khaliq 11-1-6-029 Under the guidance of Mr. Sudarsan Sahoo Asst. Professor. Electronics and Instrumentation Department. DEPARTMENT OF ELECTRONICS AND INSTRUMENTATION NATIONAL INSTITUTE OF TECHNOLOGY SILCHAR, ASSAM 780010 SESSION: JAN.- MAY., 2015.
  2. 2. 2 CERTIFICATE OF APPROVAL This is to certify that the exposition titled “ACTIVE NOISE CANCELLATION IN LABORATORYDUCT DUCT USING FUZZY LOGIC AND NEURAL NETORK” carried out by following 8th semester students- i) Rishikesh ii) Jigmi Basumatary iii) Abdul Khaliq of Department of Electronics and instrumentation, National Institute of Technology, Slichar, is a valid work carried out by them during the academic Jan-May 2015 under my supervision and guidance. (Mr. Sudarsan Sahoo) Asst. Professor Electronics and Instrumentation Department.
  3. 3. 3 DECLARATION We hereby declare that the work project on “Active Noise Cancellation in a LABORATORY DUCT ” is a real work carried out by us under the guidance of Mr. Sudarsan Sahoo, during academy session Jan.- May 2015 and this work has not been submitted for similar purpose anywhere else except to department of Electronics and Instrumentation, National Institute of Technology, Silchar. Date: 5th May 2015 Rishikesh Place: Silchar Jigmi Basumatary Abdul Khaliq
  4. 4. 4 CONTENTS 1 Introduction 1.1 Overview of the Project 1.2 Scope of this project 1.3 Division of Project 11 2 Literature Review 2.1 Literature Survey 13 3 Adaptive Filtering 3.1 Introduction 3.2 Adaptive Filtering System Configuration 3.3 Approach for Active Noise Control 16 4 Adaptive Algorithm 4.1 Introduction 4.2 Adaptive Algorithm 23 5 Hardware and Software Description 5.1 Hardware Description 5.2 LabVIEW 5.3 MATLab 30 6 Result and Discussion 6.1 Active Noise Cancellation System Design in LabVIEW 6.2 Low frequency noise cancellation simulation in MatLab 6.3 Active Noise Cancellation System Design in FIS 6.4 Active Noise Cancellation System Design in NN 6.5 Active Noise Cancellation System Design using ANFIS 33 7 Summary and Conclusion 43 8 References 44
  5. 5. 5 ABSTRACT The main goal of this paper is to present a simulation scheme to simulate an adaptive filter using LMS (Least mean square) adaptive algorithm for noise cancellation. The main objective of the noise cancellation is to estimate the noise signal and to subtract it from original input signal plus noise signal and hence to obtain the noise free signal. There is an alternative method called adaptive noise cancellation for estimating a speech signal corrupted by an additive noise or interference. This method uses a primary input signal that contains the speech signal and a reference input containing noise. The reference input is adaptively filtered and subtracted from the primary input signal to obtain the estimated signal. In this method the desired signal corrupted by an additive noise can be recovered by an adaptive noise canceller using LMS (least mean square) algorithm. This adaptive noise canceller is useful to improve the S/N ratio. Here we estimate the adaptive filter using Labview /MATLAB/SIMULINK environment . For achieving the goal we also use modern algorithms like ANFIS, FIS and Neural Network and compare the PSD of all the algorithms.
  6. 6. 6 ACKNOWLEDGEMENT Words often fail to pay one’s gratitude oneself, still we would like to convey our sincere thanks to Mr. Sudarsan Sahoo, supervisor at every stage of completion of our project and providing us with valuable material and guidance whenever we felt the need. Also we would like to thank everybody who directly or indirectly helped us in successfully completion of our project. Our special thanks to Mr. L.S.Lashkar, HOD (i/c), department of Electronics and Instrumentation for helping us in the completion of project work and its report submission. Rishikesh (11-1-6-002) Jigmi Basumatary (11-1-6-018) Abdul khaliq (11-1-6-029)
  7. 7. 7 LIST OF FIGURES NO TITLE PAGE NO 1.1 Noise Control Classification 12 2.1 Timeline ofNoise Cancellation Techniques 13 3.1 Adaptive System Identification Configuration 16 3.2 Adaptive Noise Cancellation Configuration 17 3.3 Linear Prediction Configuration 18 3.4 Adaptive Inverse Configuration 18 3.5 Feed Forward Arrangement 19 3.6 Feedback connection 19 3.7 Block diagram ANC of duct system 20 3.8 Feedforward Experimental Setup of duct system 20 3.9 Feed Forward Path estimation arrangement 21 3.10 Feed Back Path Arrangement 21 3.11 Single Channel feed-forward ANC 22 4.1 Logic Flow Diagram 24 4.2 Filtered-X arrangement 25 4.3 Input Membership Function 26 4.4 Rule Base 26 4.5 Schematic Diagram of Noise Cancellation ANFIS 28 4.6 Structure of Fuzzy Neuro Network 29 5.1 NI PXI 30 5.2 NI cRIO 31 6.1 LabVIEW Fx-LMS Arrangement 33 6.2 Noise Residue and Control Signal 33 6.3 Noise Residue and Control Signal in Frequency Domain 34 6.4 Identification Error and Estimated Coefficient of Secondary path 34 6.5 PSD Before FxLMS 34 6.6 PSD After FxLMS 35 6.7 Reference Signal and Noise residue from FIS 35
  8. 8. 8 6.8 PSD Before Applying Fuzzy Filter 36 6.9 PSD After Applying a Fuzzy Filter 36 6.10 Input and Noise Signal 37 6.11 Input and Estimated Signal 37 6.12 PSD Before Neural Filter 38 6.13 PSD After Neural Filter 38 6.14 Desire Signal 39 6.15 Noise Signal 39 6.16 MeasuredSignal 40 6.17 Inference Signal 40 6.18 Noise Residue in ANFIS 43 6.19 PSD Before ANFIS 43 6.20 PSD After ANFIS 42
  9. 9. 9 LIST OF TABLES NO TITLE PAGE NO 2.1 Literature survey on Noise Cancellation techniques using Adaptive Control 13
  10. 10. 10 List of Acronyms : 1. ANC Adaptive Noise Control 2. FIS Fuzzy Inference System 3. NN Neural Network 4. PSD PowerSpectralDensity 5. ANFIS Adaptive Neurro Fuzzy Inference System 6. LMS LeastMean Square 7. FxLMS Filtered LeastMeanSquare 8. PXI PCI Extensible for Instrumentation 9. ADC Analog to Digital Convertor 10. cRIO CompactRealtime Input Output 11. DAC Digital to Analog Converter 12. DSP Digital SignalProcessing 13. LabVIEW Laboratory Virtual Instrumentation Engineering WorkBench
  11. 11. 11 CHAPTER-1 INTRODUCTION 1.1 Overview of project This Project involves the principles of Adaptive Noise Control (ANC) and its implementation in a Laboratory duct system. The principle of adaptive noise cancellation is to obtain an estimate of the noise signal and subtract it from the corrupted signal. Adaptive noise Cancellation is an alternative technique of estimating signals corrupted by additive noise or interference. Acoustic noise problems become more and more evident as increased numbers of industrial equipment such as engines, blowers, fans, transformers, and compressors are in use. The traditional approach to acoustic noise control uses passive techniques such as enclosures, barriers, and silencers to attenuate the undesired noise. These passive silencers are valued for their high attenuation over a broad frequency range; however, they are relatively large, costly, and ineffective at low frequencies. Mechanical vibration is another related type of noise that commonly creates problems in all areas of transportation and manufacturing, as well as with many household appliances. The ANC system efficiently attenuates low-frequency noise. ANC using signal processing is an emerging technology that offers the unique ability to control spectral shape, to allow flexible system operation, and to provide low lifetime cost. The main purpose of the active sound control is to provide higher noise reduction at low frequencies. Adaptive noise Cancellation is an alternative technique of estimating signals corrupted by additive noise or interference. Its advantage lies in that, with no a priori estimates of signal or noise, levels of noise rejection are attainable that would be difficult or impossible to achieve by other signal processing methods of removing noise .ANC is developing rapidly because it permits improvements in noise control, often with potential benefits in size, weight, volume, and cost. Adaptive filters adjust their coefficients to minimize an error signal and can be realized as (transversal) finite impulse response (FIR), (recursive) infinite impulse response (IIR) and transform-domain filters. The most common form of adaptive filter is the transversal filter using the LMS algorithm. Although ANC has been around for quite some time, the technology is still under development and looking for widespread practical applications .There are some modern technique of noise cancellation i.e. noise cancellation using ANFIS, Fuzzy Inference System and Neural Network also perform under this project.
  12. 12. 12 1.2 Scope of thesis project The scope of the thesis is to develop a Noise Control in Laboratory Duct that enable students to perform noise control in laboratory duct experiments such as system identification, active control of noise from a remote computer, etc. This includes measurement and analysis of noise and configuring the hardware for estimation and noise control in laboratory duct experiments. 1.3 Division of project The development for Noise Control in Laboratory Duct involves the study of duct system and noise setup. Fig 1.1 Noise Control Classification Noise control Active noise control Adaptive Non-Adaptive Passive noise control
  13. 13. 13 CHAPTER-2 LITERATURE REVIEW In the early 1960’s first system for noise cancellation used a simple delay and invert approach but the variability of the real world components limited their effectiveness. In the mid 1970’s a major step forward took place with the applications of adaptive filters to generate anti-noise. This greatly enhanced the effectiveness of the systems. A second breakthrough in the mid 1970’s was the recognition that many noise sources particularly those made my man-made machines exhibit periodic or tonal noise. Practical applications of this active noise control (ANC) still has to wait as the electrical technology availability at that time was not sufficient for implementing in the systems. Now digital computer technology has evolved to the point where cost effective DSP microprocessors can perform the complex calculations involved in Active noise control. Since its beginning, considerable effort has been devoted to the theoretical and practical development of ANC systems with the major developments coming in the past twenty years Fig 2.1 Timeline of Noise Cancellation Techniques Table 2.1 Literature survey on Noise Cancellation techniques using Adaptive Control Sl.No Author/Title/Paper Objective of study Major findings
  14. 14. 14 1. Lifu Wua, Xiaojun Qiu, YecaiGuo, “A simplified adaptive feedback active noise control system” Applied Acoustics 81 (2014) 40–46 1. Purpose a simplified adaptive feedback active noise control system which adopts the error signal directly as the reference signal in an adaptive feedforward control system and utilizes the leaky filtered-x LMS algorithm to update the controller. 2. The convergence properties of the proposal system are investigated. 1. It is advantageous in computational load and ease of implementation because of the elimination of the convolution operation required in the conventional IMC based system. 2. Tabatabaeiardekani, W.H Abdulla, “On the convergence of real-time active noise control systems” Signal Processing 91 (2011) 1262–1274 To conduct a new convergence analysis for Fx-LMS based active noise control systems with band-limited white noise and moving average secondary paths The adaptation size leading to the fastest convergence rate is derived . 3. Guilhermede Souza Papini, “Active noise control for small diameter exhaustion system” ABCM Symposium Series in Mechatronics - Vol. 3 - pp.148-156 Considering a feedforward ANC system for active noise control for a small diameter exhaust system using FXLMS algorithm. In this work, the first steps of an active noise control are developed for an exhaustion system. The FXLMS algorithm canhelp an ANCsystem to have a high level of noise attenuation regardless of the single-tone noise source. 4. Ho.-Wuk Kim, Hong-sug Park,Sang-kwon Lee,”Modefied –filtered-u LMS algo for ANC & its application to a short acoustic duct” Mechanical ssytems and signal processing25(2011)475484 To develop a new adaptive algorithm for active noise control (ANC) that can be effectively applicable to a short acoustic duct, where the stability and fast convergence of ANC system is particularly important. The new algorithm, called the modified-filtered-u LMS algorithm (MFU-LMS), is developed based on the recursive filtered-u LMS algorithm (FU-LMS) incorporating the simple hyper- stable adaptive recursive filter (SHARF) to ensure the control stability and the variable step size to enhance the convergence rate. 5. Masaki Kobayashi, yasaku tanaka,” Active noise control using SSFC adaptive algorithm” Electronics and Communications in Japan, Vol. 97, No. 5, 2014, 1328–1333 A comparison of the required degree of the adaptive filter to the conventional system using the Filtered-x adaptive algorithm is presented Purposed a pre-inversed ANC system that does not use a replica of secondary path causing unstability. The inverse function of the secondary path is estimated by SSFC (Square sum of correlation function) adaptive algorithm which is robust to disturbances.
  15. 15. 15 6. S.Hu, R.Rajamani, ”Directional cancellation of acoustic noise for home window applications” Applied Acoustics 74 (2013) 467–477 To design a new system which can be able to accurately preserve desired internal sound while cancelling uncorrelated external noise using feedforward algorithms. This paper proposed to integrate the FXLMS feedforward ANC system with a wave separation algorithm, which separates externalsound from other sound in the environment. The resulting new ANC system used the separated external sound from the wave separation for reference and error signals instead of direct microphone measurements. 7. ZhenyuYang. Active noise control for a 1-D acoustic duct usingfeedback control techniques; Modellingandsimulation. WEAS Transactionson Systems, 3(1):46-54, Jan. 2004. Derive the state-space models as well as the transfer function based on physical principles. To simulate tests using a simple lag compensator and show a bright potential of using feedback control techniques in the ANC design The ANC design can be formulated into a set of standard feedback control design problems. A simple lag compensator is developed for the considered system, and simulation tests under different situations show the bright potential of using feedback control in the ANC design1.
  16. 16. 16 CHAPTER-3 Adaptive Filtering 3.1 Introduction Digital signal processing (DSP) has been a major player in the current technical advancements such as noise filtering, system identification, and voice prediction. Standard DSP techniques, however, are not enough to solve these problems quickly and obtain acceptable results. Adaptive filtering techniques must be implemented to promote accurate solutions and a timely convergence to that solution. 3.2 Adaptive Filtering System Configurations There are four major types of adaptive filtering configurations; adaptive system identification, adaptive noise cancellation, adaptive linear prediction, and adaptive inverse system. All of the above systems are similar in the implementation of the algorithm, but different in system configuration. All 4 systems have the same general parts; an input x(n), a desired result d(n), an output y(n), an adaptive transfer function w(n), and an error signal e(n) which is the difference between the desired output u(n) and the actual output y(n). In addition to these parts, the system identification and the inverse system configurations have an unknown linear system u(n) that can receive an input and give a linear output to the given input. 3.2.1Adaptive System Identification Configuration The adaptive system identification is primarily responsible for determining a discrete estimation of the transfer function for an unknown digital or analog system. The same input x(n) is applied to both the adaptive filter and the unknown system from which the outputs are compared (see figure 1). The output of the adaptive filter y(n) is subtracted from the output of the unknown system resulting in a desired signal d(n). The resulting difference is an error signal e(n) used to manipulate the filtercoefficientsof the adaptive system trending towards an error signal of zero.
  17. 17. 17 After a number of iterations of this process are performed, and if the system is designed correctly, the adaptive filter’s transfer function will converge to, or near to, the unknown system’s transfer function. For this configuration, the error signal does not have to go to zero, although convergence to zero is the ideal situation, to closely approximate the given system. There will, however, be a difference between adaptive filter transfer function and the unknown system transfer function if the error is nonzero and the magnitude of that difference will be directly related to the magnitude of the error signal. Additionally the order of the adaptive system will affect the smallest error that the system can obtain. If there are insufficient coefficients in the adaptive system to model the unknown system, it is said to be under specified. This condition may cause the error to converge to a nonzero constant instead of zero. In contrast, if the adaptive filter is over specified, meaning that there is more coefficients needed to modelled a unknown system, the error will converge to zero, but it will increase the time it take to converge the filter. 3.2.2 Adaptive Noise Cancellation Configuration The second configuration is the adaptive noise cancellation configuration as shown in figure 2. In this configuration the input x(n), a noise source N1(n), is compared with a desired signal d(n), which consists of a signal s(n) corrupted by another noise N0(n). The adaptive filter coefficients adapt to cause the error signal to be a noiseless version of the signal s(n).
  18. 18. 18 Both of the noise signals for this configuration need to be uncorrelated to the signal s(n). In addition, the noise sources must be correlated to each other in some way, preferably equal, to get the best results. Do to the nature of the error signal, the error signal will never become zero. The error signal should converge to the signal s(n), but not converge to the exact signal. In other words, the difference between the signal s(n) and the error signal e(n) will always be greater than zero. The only option is to minimize the difference between those two signals. 3.2.3 Adaptive Linear Prediction Configuration Adaptive linear prediction is the third type of adaptive configuration (see figure 3). This configuration essentially performs two operations. The first operation, if the output is taken from the error signal e(n), is linear prediction. The adaptive filter coefficients are being trained to predict, from the statistics of the input signal x(n), what the next input signal will be. The second operation, if the output is taken from y(n), is a noise filter similar to the adaptive noise cancellation outlined in the previous section. As in the previous section, neither the linear prediction output nor the noise cancellation output will converge to an error of zero. This is true for the linear prediction output because if the error signal did converge to zero, this would mean that the input signal x(n) is entirely deterministic, in which case we would not need to transmit any information at all. In the case of the noise filtering output, as outlined in the previous section, y(n) will converge to the noiseless version of the input signal. 3.2.4 Adaptive Inverse System Configuration The final filter configuration is the adaptive inverse system configuration as shown in figure 4. The goal of the adaptive filter here is to model the inverse of the unknown system u(n). This is particularly useful in adaptive equalization where the goal of the filter is to eliminate any spectral changes that are caused by a prior system or transmission line. The way this filter works is as follows. The input x(n) is sent through the unknown filter u(n) and then through the adaptive filter resulting in an output y(n). The input is also sent through a delay to attain d(n). As the error signal is
  19. 19. 19 converging to zero, the adaptive filter coefficients w(n) are converging to the inverse of the unknown system u(n). For this configuration, as for the system identification configuration, the error can theoretically go to zero. This will only be true, however, if the unknown system consists only of a finite number of poles or the adaptive filter is an IIR filter. If neither of these conditions are true, the system will converge only to a constant due to the limited number of zeroes available in an FIR system. 3.3 Approaches of ANC The following are the connection schemes of noise controlling using adaptive filter Fig 3.5 Feed Forward Arrangement 3.3.1 Feed forward As shown in the figure adove it uses reference noise and error are applied to the controller. This system is mostly used over feedback because of inherent stability 3.3.2 Feed back
  20. 20. 20 In this system only one output and single input Error is fed to the controlle Fig.3.6 Feedback connection Fig 3.7 Block diagram ANC of duct system Fig 3.8 Feedforward Experimental Setup of duct system
  21. 21. 21 3.3.3 Forward path estimation The control signal path from the DAC, low pass filter, amplifier, anti-noise speaker, acoustic path, error microphone, low pass filter, amplifier and ADC form the forward path of the ANC system. To estimate the forward path an identification signal, i.e. band limited random noise may be used to excite the physical forward path. The signal x(n) shown in the Figure 6.2 is the identification signal and signal d(n) sensed by the error microphone is the desired signa fed to the DSP. System identification based on the LMS algorithm may be utilized in the DSP. Here the error signal e(n) is difference between the adaptive filter’s output signal y(n) and the desired signal d(n). Fig 3.9 Feed Forward Path estimation arrangement
  22. 22. 22 3.3.4 Feedback path estimation Fig 3.10 Feed Back Path Arrangement In the single channel feed forward ANC system a reference microphone which is used to sense the reference signal ideally will also sense anti-noise generated by anti-noise speaker, known as acoustic feedback. This feedback path from DAC, low pass filter, amplifier, anti-noise speaker, acoustic path, reference microphone, low pass filter, amplifier, ADC may be estimated similar to forward path estimation. In this system identification problem signal from reference microphone is used as desired signal d(n) as shown in Figure . 3.3.5 Single channel feed-forward ANC In the current laboratory setup the user can perform ANC experiments with or without reference microphone. In this section steps involved in performing single channel feed forward ANC experiments using the remote laboratory are discussed. A block diagram of single channel feedforward ANC system is shown in Figure
  23. 23. 23 Fig 3.11 Single Channel feed-forward ANC In Figure F| is the forward path estimate while B| is the feedback path estimate as discussed in Section 6.3.1 and Section 6.3.2 respectively. The signal filtered by F| and B| are XF|(n) and XB|(n) respectively. Reference signal sensed by the reference microphone, error signal sensed by error microphone and the control signal fed to the control speaker are x(n), e(n) and y(n) in the Figure 6.8. In this section reference microphone 2 is used as a reference microphone. If the user carry out ANC experiments without using any reference microphone then feedback path will not be estimated.
  24. 24. 24 CHAPTER-4 ADAPTIVE FILTER ALGORITHM 4.1 Introduction Adaptive noise Cancellation is an alternative technique of estimating signals corrupted by additive noise or interference. Its advantage lies in that, with no appropriate estimates of signal or noise, levels of noise rejection are attainable that would be difficult or impossible to achieve by other signal processing methods of removing noise. Its cost, inevitably, is that it needs two inputs a primary input containing the corrupted signal and a reference input containing noise correlated in some unknown way with the primary noise. The reference input is adaptively filtered and subtracted from the primary input to obtain the signal estimate. Adaptive filtering before subtraction allows the treatment of inputs that are deterministic or stochastic, stationary or time- variable. The effect of uncorrelated noises in primary and reference inputs, and presence of signal components in the reference input on the ANC performance is investigated. It is shown that in the absence of uncorrelated noises and when the reference is free of signal; noise in the primary input can be essentially eliminated without signal distortion. A configuration of the adaptive noise canceller that does not require a reference input and is very useful many applications is also presented. The usual method of estimating a signal corrupted by additive noise is to pass it through a filter that tends to suppress the noise while leaving the signal relatively unchanged i.e. direct filtering. The design of such filters is the domain of optimal filtering, which originated with the pioneering work of Wiener and was extended and enhanced by Kalman, Bucy and others. Filters used for direct filtering can be either Fixed or Adaptive. 4.2 Adaptive Algorithms 4.2.1 Least MeanSquare Algorithms (LMS) To make exact measurements of the gradient vector ▼J(n) at each iteration n, and if the step-size parameter µ is suitably chosen then the tap-weight vector computed by using the steepest descent algorithm would converge to the optimum wiener solution. The exact measurements of the gradient vector are not possible and since that would require prior knowledge of both the autocorrelation matrix R of the tap inputs and the cross correlation vector p between the tap inputs and the desired response, the optimum wiener solution could not be reached. Consequently, the gradient vector must be estimated from the available data when we operate in an unknown environment. After estimating the gradient vector we get a relation by which we can update the tap weight vector recursively as: w(n+1)=w(n)+ µu(n)[d*(n)-uH(n)w(n)] Where, µ= step size parameter uH(n)= Hermit of a matrix u
  25. 25. 25 d*(n)= Complex conjugate of d(n) Fig 4.1 Logic Flow Diagram We may write the result in the form of three basic relations as follows: Filter output: (y)=wH(n)u(n) Estimation error or error signal: e(n)=d(n)-y(n) Tap weight adaptation: w(n+1)=w(n)+ µu(n)e*(n) Equations (2) and (3) define the estimation error e(n), the computation of which is based on the current estimate of the tap weight vector(n) . Note that the second term u(n)e*(n), on the right hand side of equation (4) represents the adjustments that are applied to the current estimate of the tap weight vector (w) . The iterative procedure is started with an initial guess w(0) .The algorithm described by equations (2) and (3) is the complex form of the adaptive least mean square (LMS) algorithm. At each iteration or time update, this algorithm requires knowledge of the most recent values u(n), d(n) and w(n) The LMS algorithm is a member of the family of stochastic gradient algorithms. In particular, when the LMS algorithm operates on stochastic inputs, the allowed set of directions along which we “step” from one iteration to the next is quite random and therefore cannot be thought of as consisting of true gradient directions. 4.2.2 Fuzzy Adaptive Filtered X-Algorithm
  26. 26. 26 The usual ANC system, which utilises the filtered-X algorithm, is shown in Fig. 1. In the plant model, Hp(z) represents the primary speaker and P(z) denotes the mathematical transfer function of the acoustic duct, the input signal xk represents the kth undesired noise sample, and the residual noise ek is measured by an error microphone. The output signal of the filtered-X algorithm uk drives an anti-noise speaker with transfer function Hs(z), in an attempt to cancel the undesired noise in the duct. The acoustic transfer function from the location of the anti-noise speaker to the error microphone Mp(z) is referred to as the error path and is represented by He(z). The (N+1)th order adaptive active noise controller with weighting parameters. Fig 4.2 Filtered-X arrangement 4.2.2.1 Fuzzy Sets and Membership Function Generally speaking, the output of a (N+1)th order FIR filter is composed of the moving averages of the past (N+1) input noise samples. Hence, one uses the past (N+1) noise samples to design the fuzzy filter. For a (N+1)th order fuzzy ANC system, one can define M fuzzy sets F for each input noise sample xk_i with Gaussian membership functions where l=1,2, M, i=0,1,2,.., N and k and denotes the time samples. In (7),_xx l i are the centres and sl xi are standard deviations of the Gaussian functions, respectively. In this study, we set M¼7, N¼20 and the initial standard deviations equal to 0.2. Hence, each input sample xk_i, has seven linguistic terms which initially are equally distributed in the input signal range [-1 1]; NB (negative big), NM(negative medium), NS (negative small), AZ (almost zero),PS (positive
  27. 27. 27 small), PM (positive medium) and PB (positive big). Figure 4 shows the results of this step in constructing a twenty-first order fuzzy FIR filter. Fig4.3 Input Membership Function Fig 4.4 Rule Base In a fuzzy inference engine, fuzzy logic principles combine fuzzy rules into a mapping from an input fuzzy set to an output fuzzy set. 4.2.2.2 Linguistic Variables and Rule Bases
  28. 28. 28 Linguistic variables are values defined by fuzzy sets. A linguistic variable such as ‘Negative More ’ for example could consist of numbers that are equal to or between -1 and -0.1. The conditional statements that make up the rules that govern fuzzy logic behaviour use these linguistic variables and have an if-then syntax. These if-then rules are what make up fuzzy rule bases. A sample if-then rule where A and B represent linguistic variables could be: if x is A then y is B The statement is understood to have both a premise, if ‘x is A’, and a conclusion, then ‘y is B’. The premise also known as the antecedent returns a single number between 0 and 1 whereas the conclusion also known as the consequent assigns the fuzzy set B to the output variable y. Another way of writing this rule using the symbols of assignment ‘=’ and equivalence ‘==’ is: if x == A then y = B An if-then rule can contain multiple premises or antecedents. For example, if velocity is high and road is wet and brakes are poor then Similarly, the consequent of a rule may contain multiple parts. if temperature is very hot then fan is on and throughput is reduced 4.2.2.3 Defuzzifier The proposed filter, using a minimum the inference engine and centroid defuzzifier, is obtained by combining the M rules defined in the previous step. The filter is represented as To minimise the power of residual noise, the fuzzy filtered-X LMS algorithm uses the following:
  29. 29. 29 Type equation here. where λ is a small positive constant. 4.2.3 ANFIS ANFIS uses a hybrid learning algorithm to identify the membership function parameters of single- output, fuzzy inference systems (FIS). Fuzzy systems lack the ability of learning. Relying on IF- THEN rules and logical inference, it explains its reasoning. Combination of fuzzy with neural network controller can assist a fuzzy controller and the controller could save the time to achieve the optimal solution. The basic idea of combining fuzzy systems and neural networks is to design an architecture that uses a expert knowledge of fuzzy system in addition to possessing the learning ability of a neural network. ANFIS cancels out the interference signal and gives better performance even if the complexity of the signal is very high.
  30. 30. 30 The basic idea of an adaptive noise cancellation purposed here is to pass the inference signal generated by anfis. To estimate the interference signal d(k), we need to pick up a clean version of the noise signal n(k) that is independent of the required signal. ANFIS is used to estimate the unknown interference 𝑑 ̂( 𝑘). When 𝑑 ̂( 𝑘) and d(k) are close to each other, these two get cancelled and we get the estimated output signal 𝑥 ̂( 𝑘)which is close to the required signal. The passage f represents the passage dynamics that the noise signal n(k) goes through. The adaptive neuro-fuzzy inference system (anfis) is the main architecture of the controller in adaptive noise control(ANC). In this study the Mamdani-type of IF-THEN rule is used to construct human knowledge. The jth fuzzy rule has the following form Rule: IF 𝑥1 is 𝐴1𝑗 and 𝑥2is 𝐴2𝑗 and…𝑥 𝑖is 𝐴𝑖𝑗 THEN 𝑦1is 𝐶1 and 𝑦2 is 𝐶2 and … 𝑦𝑗 is 𝐶𝑗 Where 𝑥 𝑖 and 𝑦𝑗 are the input and output variables of the system, 𝐴𝑖𝑗 are the membership functions of the antecedent part, and 𝐶𝑗 ′ 𝑠 are the real no. which simply cut the consequent mf at the level of antecedent truth. In figure 2, Layer 1 is the input layer. Each node in this layer transmits external crisp signals 𝑥_𝑖 directly to the next layer. Layer 2 is the fuzzification layer, which maps input 𝑥_𝑖 into the fuzzy set 𝐴_𝑖𝑗. Layer 3 is a fuzzy reasoning layer, which performs IF-condition reasoning by a min or product operation and generates the firing strength 𝑦_𝑗^((3)) Layer4 and layer 5 performs the approximation centre of gravity (COG) defuzzification method to generate a crisp output regarded as the final output of the control system. The basic steps used in the computation of ANFIS in matlab are given below:
  31. 31. 31 Generate an initial conditions Sugeno-type FIS system using the matlab command genfis1 for anfis training. i) Give the parameters like number of MF, step size. ii) genfis1 is used to fuzzify the training data matrix. Start learning process using the command anfis and stop when goal is achieved or the epoch is completed. Anfis uses a back-propagation algorithm to identify the membership function parameters of single- output, Sugeno type fuzzy inference systems to emulate a training data. The final step is to evaluate the fuzzy inference system using the command “evalfis” to perform fuzzy inference calculations.This function use to get the estimated interference signal by using the training data and the fuzzification of the output. CHAPTER-5 HARDWARE AND SOFTWARE DESCRIPTION 5.1 Hardware description Hardware used in traditional laboratories for ANC experiments have to meet the specific re-quirements of ANC system. However when duct laboratory for ANC system is designed hardware should be capable of handling requirements from both ends i.e. from ANC system and duct system.Following sections describe the requirement and implementation of each hardware module used in the duct laboratory. 5.1.1 PXI
  32. 32. 32 PXI is a rugged PC-based platform for measurement and automation systems. PXI combines PCI electrical-bus features with the modular, Eurocard packaging of CompactPCI and then adds specialized synchronization buses and key software features. PXI is both a high- performance and low-cost deployment platform for applications such as manufacturing test, military and aerospace, machine monitoring, automotive, and industrial test. Developed in 1997 and launched in 1998, PXI is an open industry standard governed by the PXI Systems Alliance (PXISA), a group of more than 70 companies chartered to promote the PXI standard, ensure interoperability, and maintains the PXI specification. Fig 5.1 NI PXI Since inventing the standard in 1997 and founding the PXI Systems Alliance industry consortium in 1998, National Instruments has been at the forefront of delivering the benefits of PXI to engineers and scientists worldwide. With the largest selection of chassis, controllers, and timing and synchronization and more than 600 modules, you can address virtually any engineering challenge. 5.1.2 CRIO CompactRIO is a reconfigurable embedded control and acquisition system. The CompactRIO system’s rugged hardware architecture includes I/O modules, a reconfigurable FPGA chassis, and an embedded controller. Additionally, CompactRIO is programmed with NI LabVIEW graphical programming tools and can be used in a variety of embedded control and monitoring applications.
  33. 33. 33 Fig 5.2 NI cRIO With the introduction of CompactRIO in 2004, National Instruments redefined the embedded market by offering a reconfigurable solution that combines the flexibility of custom design with the short time to market of an off-the-shelf product. CompactRIO paired with the NI LabVIEW graphical development environment gives you the ability to create embedded control and monitoring systems with unparalleled productivity. 5.1.3 Duct, Microphone and Speaker The ventilation duct used in the experiment should be of length such that the lower order acoustic modes are observable. The broadband noise used to excite the duct may be in the range [50Hz-400Hz] so that the upper limit is well within the planar wave region of the duct. Limiting the sound waves within the planar wave region of the duct enables the microphones to be installed at various position of the duct for measurements. Thus a circular duct of 4m in length and 315mm inner diameter is chosen which meets above mentioned requirements. The microphones and speakers used in the ANC system should have at frequency response in the control band width [50Hz-400Hz]. The microphones selected are battery powered Integrated Electronics Piezo Electric (IEPE) microphones. These microphones have at frequency response from 20Hz to 16000Hz. In the ventilation duct _ve microphones, reference microphones and error microphone, are installed at di_erent positions and two Fostex 6301B3 loudspeakers (primary noise source and anti-noise source) are installed, one at respective duct end. 5.2 LabVIEW LabVIEW from National Instruments is a visual programming language which supports interaction with di_erent software and hardware. Programming in LabVIEW is done by Virtual Instruments (VI's). VIs are composed of front panel and block diagrams. Front panel shows
  34. 34. 34 the graphical view of the VI which will be visible to the end user while actual programming is done in block diagram. LabVIEW provides facility to interact with the Code Composer Studio automation tool using the DSP Test Integration toolkit. This toolkit provides di_erent VIs to interact with the Code Composer Studio such as opening Code Composer Studio, compiling the project, memory read write operations etc. Further functions can be added using LabVIEW programming.Above discussion concerns the development environment but in order to make this development environment remotely accessible LabVIEW provides di_erent options which are discussed below. 5.3 Matlab MATLAB® is a high-level language and interactive environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java™. You can use MATLAB for a range of applications, including signal processing and communications, image and video processing, control systems, test and measurement, computational finance, and computational biology. More than a million engineers and scientists in industry and academia use MATLAB, the language of technical computing. CHAPTER-6 RESULT AND DISCUSSION 6.1 Active Noise Cancellation System Designin LabVIEW Successfully implemented the design of Active Noise Cancellation in LabVIEW
  35. 35. 35 Fig 6.1 LabVIEW Fx-LMS Arrangement 6.2 Low frequency noise cancellation simulation in MatLab After going through a series of process and experiments to get appropriate value for step size and filter length we get our desired result at Step size(mu)=0.9. Here in this process I have collected a noise from my Laptop cooling fan and the recorded noise was minimized by applying FxLMS algorithm in Matlab.. Fig 6.2 Noise Residue and Control Signal In frequency Domain:
  36. 36. 36 Fig 6.3 Noise Residue and Control Signal in Frequency Domain Identification Error and Estimated Coefficient of Secondary path: Fig 6.4 Identification Error and Estimated Coefficient of Secondary path Power spectrum of noise: Initially the level of noise i.e before ANC was -10dB but was attenuated to -20dB after ANC using FX-LMS Algorithm. A total noise reduction of 10 dB. Fig 6.5 PSD Before FxLMS
  37. 37. 37 Fig 6.6 PSD After FxLMS 6.3 Active Noise Cancellation System Designin Fuzzy Logic using Mamdani Input Reference Signal to Fuzzy System Fig 6.7 Reference Signal and Noise residue from FIS
  38. 38. 38 Compare the Power Spectrum of Before and After applying Fuzzy Filter Fig 6.8 PSD Before Applying Fuzzy Filter Fig 6.9 PSD After Applying a Fuzzy Filter
  39. 39. 39 6.4 Active Noise Cancellation System Designin Neural Network Using single Layer Neural Network with learning constant 0.05 u(t)=blue d(t)=Green Fig 6.10 Input and Noise Signal u(t)=blue uh(t)=Green Fig 6.11 Input and Estimated Signal
  40. 40. 40 Fig 6.12 PSD Before Neural Filter Fig 6.13 PSD After Neural Filter
  41. 41. 41 6.5 Active Noise Cancellation System Designusing ANFIS Fig 6.14 Desire Signal
  42. 42. 42 Fig 6.15 Noise Signal Fig 6.16 Measured Signal Fig 6.17 Inference Signal
  43. 43. 43 Fig 6.18 Noise Residue in ANFIS Fig 6.19 PSD Before ANFIS
  44. 44. 44 Fig 6.20 PSD After ANFIS
  45. 45. 45 CHAPTER-6 SUMMARY AND CONCLUSION A Laborartory Duct ANC in which we are performed all the necessary steps required for ANC experiment and at the end we designed and successfully perform simulation.We are successfully implemented ANC in both artificial as well as real world noise using modern FxLMS algorithm. We simulate our code several time by changing some of the filter parameters like step size , filter length etc to get best result .We need to keep it in mind that it works for noise frequency ranging from 100 to 800 Hz. We also implement the ANC using fuzzy and neural based algorithms. And getting better result than FxLMS.ANFIS(Adaptive Neuro Fuzzy Inference System) gives best result for Adaptive Noise Cancellation
  46. 46. 46 CHAPTER-7 REFERENCES 1. Guilhermede Souza Papini, “Active noise control for small diameter exhaustion system” ABCM Symposium Series in Mechatronics - Vol. 3 - pp.148-156 2. S.Hu, R.Rajamani, ”Directional cancellation of acoustic noise for home window applications” Applied Acoustics 74 (2013) 467–477 3. Lifu Wua, Xiaojun Qiu, Yecai Guo, “A simplified adaptive feedback active noise control system” Applied Acoustics 81 (2014) 40–46 4. Ho.-Wuk Kim, Hong-sug Park, Sang-kwon Lee,”Modefied –filtered-u LMS algo for ANC & its application to a short acoustic duct” Mechanical sytems and signal processing 25 (2011) 475-484 5. Zhenyu Yang. Active noise control for a 1-D acoustic duct using feedback control techniques; Modelling and simulation. WEAS Transactions on Systems, 3(1):46-54, Jan. 2004. 6. H.R pota and A.G Kelkar “modeling and control of acoustic ducts” journal of Vibration and acoustics, Transactions of the ASME , Vol. 123, Jan 2001. 7. Zhenyu Yang and Steffen Podlech ,theoretical modeling issue in ANC for a one-dimensional acoustic duct system Proceedings of the 2008 IEEE International Conference on Robotics and Biomimetics Bangkok, Thailand, February 21 - 26, 2009 8. Fuller, C. R., and von Flotow, A. H., 1995, ‘‘Active control of sound and vibration,’’ IEEE Control Syst. Mag., 16, No. 6, pp. 9–19, December. 9. Wikipedia.org (http://en.wikipedia.org/wiki/Active_noise_control).

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