554 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 2, FEBRUARY 2012

Particle Swarm Optimization Based Active NoiseControl Algorithm Without Secondary

Path IdentificationNirmal Kumar Rout, Debi Prasad Das, Member, IEEE, and Ganapati Panda, Senior Member, IEEE

Abstract—In this paper, particle swarm optimization (PSO)algorithm, which is a nongradient but simple evolutionarycomputing-type algorithm, is proposed for developing an efficientactive noise control (ANC) system. The ANC is conventionally usedto control low-frequency acoustic noise by employing a gradient-optimization-based filtered-X least mean square (FXLMS) algo-rithm. Hence, there is a possibility that the performance of theANC may be trapped by local minima problem. In addition,the conventional FXLMS algorithm needs prior identification ofthe secondary path. The proposed PSO-based ANC algorithmdoes not require the estimation of secondary path transfer func-tion unlike FXLMS algorithm and, hence, is immune to time-varying nature of the secondary path. In this investigation, a smallmodification is incorporated in the conventional PSO algorithmto develop a conditional reinitialized PSO algorithm to suit tothe time-varying plants of the ANC system. Systematic computersimulation studies are carried out to evaluate the performance ofthe new PSO-based ANC algorithm.

Index Terms—Active noise control (ANC), adaptive filtering,conditional reinitialized PSO (CRPSO), optimization, particleswarm optimization (PSO).

I. INTRODUCTION

THE PROBLEMS associated with acoustic noise in indus-try are increasing day by day, and hence, their control has

been an important topic of the present-day research. The noisesources may be due to automobiles, engines, compressors, orelectric drives. Excessive noise induces hearing loss, aggravateshealth issue, degrades occupational performance, and, aboveall, interferes in communication. There are two approachesto control acoustic noise: passive and active. The traditionalapproach to control acoustic noise employs passive techniques,such as enclosures, barriers, and silencers. These methods

Manuscript received January 26, 2011; revised July 7, 2011; acceptedAugust 17, 2011. Date of publication October 26, 2011; date of current versionJanuary 5, 2012. The Associate Editor coordinating the review process for thispaper was Dr. John Sheppard.

N. K. Rout is with the School of Electronics Engineering, Kalinga Insti-tute of Industrial Technology University, Bhubaneswar 751024, India (e-mail:routnirmal@rediffmail.com).

D. P. Das is with the Process Engineering and Instrumentation Cell, CSIR-Institute of Minerals and Materials Technology, Council of Scientific andIndustrial Research, Bhubaneswar 751013, India (e-mail: debi_das_debi@yahoo.com; dpdas@immt.res.in).

G. Panda is with the School of Electrical Sciences, Indian Institute of Tech-nology Bhubaneswar, Bhubaneswar 751013, India (e-mail: ganapati.panda@gmail.com; gpanda@iitbbs.ac.in).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIM.2011.2169180

are very costly for achieving high attenuation over a widefrequency range and also ineffective at low frequencies. Activenoise control (ANC) has been an alternative to this, particularlyfor low-frequency noise control. The ANC is an electroacousticor electromechanical system which cancels an acoustic noisebased on the principle of destructive interference with anothernoise produced by the controller generating the same amplitudeand frequency as that of original noise but opposite in phase. Aschematic diagram of a single-channel ANC system is shownin Fig. 1(a). In an ANC system, a reference microphone isused to feed the reference noise signal to the controller of theANC system, which is usually an adaptive filter. The output ofthe adaptive filter is used to generate the antinoise through aloudspeaker system. An error microphone is used to sense theresidual noise which, in turn, is used to tune the ANC controller.The acoustical path from the noise source to the point ofnoise cancellation is called the primary path, and the pathfrom the output of the adaptive filter through the loudspeakersystem and the acoustical path between the loudspeaker andthe error microphone up to the received signal through themicrophone system is named the secondary path. Fig. 1(b)shows the block diagram of a commonly used filtered-X leastmean square (FXLMS) algorithm-based ANC system [1]. TheFXLMS algorithm uses the offline estimate of the secondarypath. The reference signal x(n), which acoustically propagatestoward the cancellation point through the primary path [denotedas P (z) in Fig. 1(b)], transformed to d(n). The x(n) is receivedby the reference microphone and fed to the ANC filter W (z).The output of the ANC algorithm travels through a secondarypath. The secondary path is an electroacoustic path consistingof a digital-to-analog converter, reconstruction filter, poweramplifier, loudspeaker, acoustic path between the cancelingloudspeaker and the error microphone, preamplifier, antialias-ing filter, and analog-to-digital converter [1]. The secondarypath is required to be estimated prior to running the FXLMS-based ANC algorithm. From the derivation of the FXLMSalgorithm presented in [1], it can be found that the weights ofthe ANC filter W (z) are updated using the error microphonesignal e(n) and a filtered reference signal x′(n). The filteredreference signal is the reference signal x(n) filtered throughthe estimated secondary path S(z). The estimated secondarypath S(z) is a mathematical model (often represented by adigital filter) of the actual secondary path S(z) shown inFig. 1(a) and (b). The FXLMS algorithm assumes that S(z)is equal to S(z). Error in the estimate of the secondary path

0018-9456/$26.00 © 2011 IEEE

ROUT et al.: PSO BASED ANC ALGORITHM WITHOUT SECONDARY PATH IDENTIFICATION 555

Fig. 1. Single-channel ANC system. (a) Schematic diagram. (b) Block diagram using FXLMS algorithm as the ANC algorithm.

leads to degraded performance of the ANC algorithm. Differentvariants of FXLMS algorithms have been proposed to cir-cumvent different issues linked with the ANC. In [2], thecomputational issue is addressed, and a fast version of FXLMSalgorithm is proposed. The FXLMS algorithm is modifiedby using nonlinear adaptive filters in [3], [4] to address thenonlinear noise processes. All these algorithms employ thepre-estimated secondary path transfer function and may leadto divergence of the algorithm due to estimation error. Fur-thermore, in practical situations, it is often observed that thesecondary path behaves as a time-varying system. In additionto this, the FXLMS algorithm may also lead to local minimaproblem as it uses gradient method to update the coefficient ofthe adaptive filter of the ANC. The genetic algorithms (GAs) [5]have been used as an alternative learning algorithm to developan ANC without the use of secondary path estimation. The GA-based ANC using IIR filter [6] and nonlinear Volterra filters[7]–[9] is proposed for ANC applications. The authors haveshown that the GA-based approach is superior to the FXLMSalgorithm as the former does not use secondary path estimatefor its adaptation. Recently, particle swarm optimization (PSO)has been proposed as a useful alternative to GA and has beenapplied to many practical problems. The PSO is originallyproposed by Kennedy et al. in [10]–[12] as an optimizationtool. The same is modified and applied as adaptive filter algo-rithms by Krusienski and Jenkins in [13]–[16]. Adaptive noisecanceler based on PSO algorithm is proposed in [17]. A PSO-based adaptation of the weights of multilayer neural networkas a nonlinear ANC algorithm has been proposed in [18]. Theperformance of the PSO-based adaptation in a linear ANCsystem is presented in [19] where the algorithm uses the modelsof primary path and secondary path to generate the ANC con-troller. The comprehensive learning PSO, an improved versionof the PSO algorithm, has been proposed recently for a systemidentification [20].

In this paper, we develop a systematic algorithm for PSO-based ANC system. The PSO and other evolutionary computa-tion algorithms are often used as offline optimization tools asthe fitness value of these algorithms depends on a number ofinput samples instead of a single sample. This is because theaverage of errors over certain time duration (set of samples)is a better performance criterion for evolutionary algorithms

compared to a single error that is generated in every sampleof input signal. However, the conventional ANC parameters areupdated on a sample-by-sample basis. In this paper, a schemefor using the PSO algorithm to run on a sample-by-samplemanner is proposed for the design of ANC. Through simulationexperiments, it is shown that the basic PSO algorithm fails toadapt properly for time-varying primary and secondary paths.Therefore, a new scheme is proposed to reinitialize the particlevectors of the PSO algorithm, when it tends to be trapped in lo-cal minima situation. The proposed scheme has been shown tooutperform the basic PSO-based algorithm for the ANC whiletrying to combat noise with abruptly time-varying primary andsecondary paths.

This paper is organized as follows. Section II describes theproposed scheme of using the basic PSO-based algorithm forthe ANC system and the new particle reinitialization schemefor time-varying primary and secondary paths. Section IIIpresents the results obtained from computer simulations. Fi-nally, in Section IV, the conclusion of the investigation ispresented.

II. PROPOSED PSO-BASED ANC SYSTEM

In the ANC system, the electrical control signal is generatedin a sample-by-sample basis and is converted to acoustic signal(antinoise) using a loudspeaker system. The control signal isgenerated by passing the reference microphone signal throughthe ANC system. A linear ANC system consists of a finiteimpulse response (FIR) filter. The objective of the tuning algo-rithm in an ANC system is to optimize the FIR filter coefficientsof the ANC system such that the received signal in the errormicrophone is minimized [refer to Fig. 1(a)]. The evolutionaryalgorithm like the GA or the PSO cannot be directly used in theANC system as the performance of the algorithm depends ona set of error samples (the error microphone signal samples fora certain duration of time) and not on the instantaneous value(single sample value) of the error microphone. In addition, inthe conventional PSO- or GA-based optimization, the samedata set is used to update the particles or the chromosomes,respectively, in every generation. However, in a practical ANCsystem, there is no scope for providing the same set of noise

556 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 2, FEBRUARY 2012

samples to the adaptive algorithm, as noise is generated from acontinuous dynamical system.

A. Proposed Scheme of Online ANC Adaptation

It is often felt that the GA-based [7]–[9] or PSO-based[18], [19] ANC algorithms are used to detect global minimumvalues, without the prior knowledge of the secondary paths,and they are more robust than traditional algorithms. However,their real-time adaptability is questionable in a large number ofapplications. It is to be noted here that the GA- or PSO-basedalgorithm uses P -sets of adaptive filter as opposed to the one inthe case of the FXLMS algorithm. In real-time algorithm, onlyone of the P adaptive filters should be used at a time. As theANC algorithm trains its control parameters using a real noisesource, we do not have control over sending the same noisesource to all the adaptive filters to find out their fitness values.Therefore, the proposed implementation scheme is dedicatedtoward real-time adaptability of the PSO algorithm which relieson a continuously generating noise source. Like conventionalANC, the noise source propagates through the primary pathon a real-time basis. The noise so generated is captured by thereference microphone and is sent to one of the P adaptive filtersvia a demultiplexer (DMUX). The select signal input of themultiplexer (MUX) and DMUX (in Fig. 2) allows one of the Padaptive filters to get the input signal and generate the output,which is then fed to the loudspeaker system to generate theantinoise. The noise and antinoise superimpose in the acousticenvironment generating residual noise signal that is captured bythe PSO processor by the error microphone. The select signalis used to provide equal numbers of noise samples to eachadaptive filter in each generation. The PSO processor controlsthe repeated production of the select signal, acquisition of theresidual noise signal, and the updating of the filter weights inevery generation.

The original noise generated by the noise source acousticallytraveling through the primary path to the point of cancellation,denoted here as d(n), acoustically superimposes with the anti-noise d(n) to produce the residual noise and is captured bythe error microphone as e(n). In this process, a set of errorsignal samples is stored in the PSO processor for one adaptivefilter. The process is repeated by changing the select signalso that the noise passes through each adaptive filter one byone. It is to be noted that the same set of noise samples neednot be sent to other adaptive filters. Hence, running the noisesource and selecting P adaptive filters would store P -meansquare errors in the PSO processor. These P -mean square errorsare used to update the weights of the adaptive filters usingthe PSO-based algorithm as presented in the next section. Ina GA- or a PSO-based algorithm, a generation is defined asa time where the populations carry out genetic or swarmingoperations, respectively, to go to the next generation. In here, atevery generation, all the P adaptive filters are used to generateantinoise and update themselves using a PSO algorithm. Sinceit is an online adaptive algorithm, the weight adaptation processcontinues until the ANC is in operation unlike the conventionalGA-based algorithm where there is a stopping criterion atwhich the adaptation of weights is suspended but the ANC keep

producing the antinoise with its fixed weights. Advantage ofcontinuous adaptation is to match the ANC filter to any changethat occurs in the primary and secondary paths. Hence, thereis no stopping criterion as in the conventional GA and PSOapplications.

B. PSO-Based ANC Algorithm

The objective of the aforementioned scheme of the onlineANC algorithm is to minimize the mean square error that issensed by the error microphone. To apply the PSO algorithm tosuch an optimization problem, let us consider a coefficient vec-tor of P adaptive filters as population which is represented as aset of particles in the PSO terminology. The PSO algorithm isan evolutionary computation technique developed by Kennedyand Eberhart [10], which is inspired by social behavior ofswarms. The PSO is initialized with a population of randomsolutions like other evolutionary algorithms. In this case, thecoefficient vectors of the P adaptive filters are used as the initialrandom solutions. Let this set be represented as

W =

w11 w2

1 · · · wP1

w12 w2

2 · · · wP2

...... · · ·

...w1

N w2N · · · wP

N

. (1)

Each column of the W in (1) is a potential initial solution andis called a particle. Referring to the block diagram in Fig. 2,each column of W in (1) represents the coefficient vector ofone of the P adaptive filters. The noise signal received bythe reference microphone is fed to each of these filters whichproduce y1(n), y2(n), . . . , yP (n) as output at different timeframes. The P outputs act as the control signal in the ANC,which pass through the loudspeaker system to generate theantinoise signal set represented as {d1(n), d2(n), . . . , dP (n)}.It is clarified here that the set {y1(n), y2(n), . . . , yP (n)} con-sists of electrical signals whereas {d1(n), d2(n), . . . , dP (n)}represents the acoustical signal. A set of residual error signals{e1(n), e2(n), . . . , eP (n)} is received by the error microphone.These error signal set is a result of the acoustical superposi-tion of {d1(n), d2(n), . . . , dP (n)} with the noise signal at thecanceling point, i.e., d(n), at different time intervals. Thus, theerror signals generated are given by

ep(n) = d(n) + dp(n) (2)

where p = 1, 2, 3, . . . , P, n denotes the sample index of theinput signal which ranges from 1 to M and M is the totalnumber of samples used in each generation. The mean squareerror of each of these P errors, which represents the fitness ofeach particle (adaptive filter), is stored in the PSO processor.In the PSO terminologies, the particle is flown through theproblem space with a velocity which is dynamically updatedby using an update equation. The update equation is derivedusing the flying experiences of its own and that of the othermembers of its generation. The position of the ith particle andits velocity in the kth iteration (generation) are denoted byWi(k) and Vi(k), respectively. The position of the ith particle

ROUT et al.: PSO BASED ANC ALGORITHM WITHOUT SECONDARY PATH IDENTIFICATION 557

Fig. 2. Block diagram of PSO-based training of an ANC system for scheme-II.

with smallest mean square error in the previous position isrecorded and represented by the symbol pbesti (personal best),and its position is represented as Wpbesti

. The best among allthe particles is represented by the symbol gbest (global best),and its position is represented as Wgbest. The PSO algorithmupdates the velocity and the position of each particle towardits Wpbest and Wgbest positions at each step according to thefollowing update equations:

Vi(k) =Vi(k − 1) + r1 [Wpbesti− Wi(k)]

+ r2 [Wgbest − Wi(k)] (3)

Wi(k) =Wi(k − 1) + Vi(k) (4)

where r1 and r2 are two random numbers that are generated in-dependently in the range [0, 1]. In [21], the basic PSO algorithmuses two random vectors for r1 and r2; however, we use r1and r2 as random numbers instead, due to reduced complexity.Equation (3) calculates a new velocity for each particle (po-tential solution) based on its previous velocity Vi(k − 1), theparticle’s position at which the best fitness has been achievedWpbesti

, and the best positions of each particle achieved sofar among the neighbors Wgbest. Equation (4) updates eachparticle’s position in the solution hyperspace. This process iscontinued on a real-time basis.

C. Modified PSO-Based ANC Algorithm for Time-VaryingPrimary and Secondary Paths

Dynamic environment might be either a slow or an abruptchange in environment. The PSO algorithm fails to achieveglobal optimization when adapting a dynamic environmentand is suitably modified to cope with the slow change in theenvironment by utilizing the experience of the particles of theold environment in the new situation [21]–[23]. However, dy-namic environment in ANC system refers to an abrupt changein the primary and/or secondary paths with respect to time.

They are also referred as time-varying primary and secondarypaths. Primary path can change due to the change in acousticenvironment. The secondary path can change due to the changein both acoustic and electric components. Since these changesare abrupt in nature, the PSO algorithms proposed in [21]–[23] are not suitable. It is shown through simulation study (inSection III) that the basic PSO-based ANC algorithm mini-mizes the error for fixed primary- and secondary-path cases.The performance criterion, i.e., the squared error, is minimizedto its achievable minimum value. If the primary or secondarypath is changed after all the particles stabilize to their optimumvalues, they cannot adapt to the change and remain in theirlocal minima (see the dotted curve in Fig. 6). The reason forthis is the randomness of the particle initialization that gets lostafter it is fully optimized. At optimized stage, all the particlesconverge to the same value, and hence, there is a need for areinitialization of the particles once this change in primary orsecondary path is detected. It is seen (in Figs. 6 and 9) thatthe square error value of the gbest particle gives an indicationof the change in the primary or secondary path. This squareerror value E2

gbest shows a sudden change if the primary orthe secondary path is abruptly changed (see the dotted curve inFig. 6). The E2

gbest value remains almost constant if it is fullyoptimized. The following piece of the conditional algorithmwas inserted with the conventional PSO algorithm to reinitializethe particles to make them suitable to adapt to any change inprimary or secondary path

If∣∣E2

gbest(n − 1) − E2gbest(n − 2)

∣∣ ≤ k1

&∣∣E2

gbest(n) − E2gbest(n − 1)

∣∣ ≥ k2 then

Reinitialize V and W (5)

where k1 < k2, k1 is a very small quantity close to zero, and k2

can be found by experiment using a trial-and-error method. Itshows that the particle and the velocity vectors are required to

558 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 2, FEBRUARY 2012

be reinitialized (randomized), if the errors in previous genera-tions are negligible and the errors in the present generation aresignificantly high.

D. Comparison of PSO- and FXLMS-Based ANC Systems

In the FXLMS algorithm, the ANC filter coefficients are up-dated at every sample, whereas in PSO-based algorithm, theseare updated after each generation. Each generation consists ofM × P samples, where P is the population count and M is thenumber of samples used for evaluating the performance crite-rion. Since FXLMS algorithm is a gradient-based algorithm, itis highly susceptible to initialization of the parameter. A wronginitialization may lead to local minima. In addition to this,the FXLMS algorithm employs the pre-estimated secondarypath transfer function to update the ANC filter coefficients.The FXLMS fails miserably if the secondary path changessignificantly from its estimated value [1]. However, the PSO-based algorithm, being an evolutionary algorithm, has got lesschance of falling into local minima if it is randomly initialized.In addition to this, the proposed modified PSO algorithm hasa high likelihood of achieving global optimization as it in-corporates the reinitialization of weights at appropriate time.The high likelihoodness is tested with random trials in thesimulation section. The proposed algorithm does not require theestimation of secondary path transfer function, and hence, it isimmune to the change in the secondary path.

E. Comparison of PSO- and GA-Based ANC Systems

The works reported in [8] and [9] propose a GA and an adap-tive GA-based nonlinear ANC system without employing sec-ondary path estimate. However, no specific scheme for weightupdate, like the one given in this paper, has been outlined. Fur-thermore, these papers do not consider the time-varying natureof the primary and the secondary paths. The GA-based ANCused in those papers uses a binary-coded string for each weightof the adaptive filter. The GA also involves slow convergence,and it requires many operations in a generation as shown later inthe simulation section (Fig. 12). The slow convergence is dueto the fact that, in the GA, the binary-coded filter coefficientsare kept in a string format and are termed as chromosome. Thechromosomes undergo single-point crossover and mutation,generation by generation. Due to single-point crossover, manyweight parameters remain untouched, and it takes a lot ofgeneration to be updated. In contrast, in the proposed PSO-based ANC system, all filter coefficients are updated using asystematic and simple update equations presented in (3) and(4). Hence, the PSO is expected to achieve faster convergencecompared to its GA counterpart. In addition to this, PSO doesnot require any binary coding and decoding which also reducescomputational complexity. However, the scheme presented hereto implement PSO algorithm for ANC system can also beused to implement other evolutionary computational algorithm-based ANC systems.

III. SIMULATION EXPERIMENTS

To evaluate the performance of the proposed PSO-basedANC algorithm, a number of simulation experiments are con-ducted. In all these experiments, the transfer functions ofprimary path and the secondary path are chosen as P (z) =z−5 + 0.2z−6 + 0.5z−7 − 0.9z−8 and S(z) = z−1 + 1.5z−2 −z−3, respectively, unless otherwise stated in the specific exper-iment. The primary noise signal is considered to be a uniformwhite noise signal with a zero mean.

A. Experiment 1: Effect of Order of ANC Filter

The order of the ANC filter refers to the length of the FIRfilter of the ANC. At the outset, the order of the ANC filter isnot known. Simulation experiments are conducted by varyingthe length of the adaptive filter N from 5 to 40. The PSO-based ANC filters are updated by using 20 error sample points.A population size of P = 200 is considered. The convergenceof the square error of the gbest particle is plotted in Fig. 3. Itis observed that, if the length of the adaptive filter is increasedbeyond N = 10, the convergence performance degrades. Therecould be two reasons for this. First, there is a model mismatch ifthe ANC filter length increases beyond ten. Second, the higherlength of the ANC filter demands more number of parameters tobe optimized which, in turn, demands a higher population sizeP . It is also studied by reducing the length from N = 10. Ifthe length is reduced from N = 10, the E2

gbest converges fasteruntil N = 8, but the steady-state error stabilizes with highervalues as seen in the zoomed portion in Fig. 3. Therefore, anANC with N = 10 is chosen for the rest of the experiments.

B. Experiment 2: Effect of the Number of Error Sample PointsRequired for Evaluating the Cost Function

The cost function or the fitness function that represents theperformance criteria is very important in every evolutionarycomputing algorithm. In this algorithm, the average of thesquare error value over a number of sample points is chosenas the cost function. The number of sample point is a vari-able which can be set depending on the performance. Highernumber of sample points to find the average would give betterperformance over the lower number of sample values. However,a higher number would pose higher computational complexity.To find the optimum value of such a number, a series of experi-ments is conducted by varying M from 10 to 60. The populationsize P = 200 and the ANC order N = 10 are chosen in all thesimulation runs. The convergence plots are shown in Fig. 4. Itis seen that the convergence with M = 20 onward is almostidentical with respect to convergence speed and the steady-stateerror. However, for M = 10, the convergence speed and thesteady-state error performance are degraded. Therefore, in therest of the experiments, M is set as equal to 20. It is also feltthat the number of sample points should be at least double ofthe filter length.

ROUT et al.: PSO BASED ANC ALGORITHM WITHOUT SECONDARY PATH IDENTIFICATION 559

Fig. 3. Convergence characteristic of online PSO-based ANC for different ANC orders N . P = 200 and M = 20.

Fig. 4. Convergence characteristic of online PSO-based ANC for different M ’s with P = 200 and N = 10.

C. Experiment 3: Effect of the Population Size

To study the effect of population size on the optimization ofthe ANC controller, the length of the ANC adaptive filter isfixed at N = 10. Twenty sample points are used to evaluate theperformance criteria. The algorithm is run for 100 generations,and the E2

gbest for each generation is plotted to see the conver-gence characteristic for different population sizes. Populationsize is referred here as the number of particles present in thepopulation and represented as P . The P is varied from 10 to200. It is found from Fig. 5 that the increase in population sizeguarantees faster convergence and a lower steady-state value ofE2

gbest. It is found that, for this ANC setup, P = 200 is ideal,and hence, for the rest of the experiments, this value is fixed.

D. Experiment 4: Time-Varying Primary Path

The conventional basic PSO algorithm is tested for a time-varying primary path. In a practical application, if the ANCis in operation inside a room or a vehicle cabin and the door

Fig. 5. Effect of population size for M = 20 and N = 10.

is suddenly opened or closed, the acoustic environment ischanged. This leads to an abrupt change in the primary and/orthe secondary path. In this experiment, such an abrupt change

560 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 2, FEBRUARY 2012

Fig. 6. PSO performance with time-varying primary path: In the reinitializedPSO, the W and V are reset to random values knowingly at generation count200.

in the primary path is chosen. The primary path is chosenas P (z) = z−5 + 0.2z−6 + 0.5z−7 − 0.9z−8 up to 200 gener-ations, and after that, the primary path is abruptly changed toP (z) = z−5 + 0.2z−6 − 0.5z−7 − 0.9z−8. The secondary pathremains constant throughout this experiment. The populationsize P = 200, order of ANC N = 10, and the number ofsample points used in each generation M = 20 are set for thisexperiment. Fig. 6 shows the convergence plot, which clearlydepicts that the conventional PSO-based ANC is not able toconverge to its global minima after 200th generation. It canbe seen that, since all the particles in the PSO are stabilizedby adapting to particular primary- and secondary-path cases, itneeds a randomization or reinitialization of the particles in thepopulation set to cope with this dynamic environment. To testthis, all the particles are reinitialized at generation count 200when the primary path is changed. It is found in Fig. 6 that thereinitialized PSO is capable of converging to its global optimumvalue.

To automatically identify such abrupt change in primaryor secondary paths and reinitialize the velocity and the po-sition vector of each particle in the population, the modi-fied PSO algorithm proposed in this paper was used. Fig. 7shows the performance of the proposed conditional reinitial-ized PSO (CRPSO) algorithm compared to the conventionalPSO algorithm. To further evaluate the convergence perfor-mance of the CRPSO algorithm, the primary path transferfunction is changed at generation count 200 and again madeit back to the original transfer function at generation count300. The convergence characteristic shown in Fig. 8 shows theeffectiveness of the CRPSO algorithm over the conventionalPSO algorithm.

E. Experiment 5: Time-Varying Secondary Path

Similar to the study of the time-varying primary path, thetime-varying secondary path is studied independently in thisexperiment. In this experiment, the secondary path is chosen asS(z) = z−1 + 1.5z−2 − z−3 up to 200 generations, and afterthat, the same is abruptly changed to S(z) = z−1 + 0.5z−2.The primary path remains intact throughout this experiment

Fig. 7. Performance of CRPSO with time-varying primary path: Primary pathchanges at generation count 200.

Fig. 8. Performance of the proposed CRPSO with time-varying primary path:The primary path is changed at generation count 200 and returned to original atgeneration count 300.

as P (z) = z−5 + 0.2z−6 + 0.5z−7 − 0.9z−8. The PSO param-eters were fixed as used in Experiment 4. The convergencecharacteristic of the E2

gbest with respect to the generation isplotted in Fig. 9. The proposed CRPSO is shown to outperformthe conventional PSO in terms of achieving global minimaeven after the abrupt change in the secondary path. At thispoint, it may be noted that the FXLMS would have failed evenmiserably if the secondary path and its estimates are differ-ent which happens in the case of the time-varying secondarypath [1].

F. Experiment 6: Performance Guarantee of the CRPSOAlgorithm Under Time-Varying Primary and Secondary Paths

It is well known that the performance of the PSO-basedalgorithms, namely, conventional and the proposed CRPSO,depends on the particle initialization. Since the particles arerandomly initialized, they show different performances at dif-ferent run times. To evaluate the performance guarantee of theproposed CRPSO with respect to the conventional PSO-basedANC algorithms with a time-varying primary path as used inExperiment 4, E2

gbest of ten independent runs is plotted inFig. 10 with the same random input signal using the randomseed equal to “zero.” The conventional PSO did not achieve the

ROUT et al.: PSO BASED ANC ALGORITHM WITHOUT SECONDARY PATH IDENTIFICATION 561

Fig. 9. Performance of CRPSO with time-varying secondary path.

Fig. 10. Performance of CRPSO with time-varying primary path for tenindependent runs with random seed equal to zero.

global minimum in most of the cases after the abrupt change inthe primary path at generation count 200, whereas the proposedCRPSO achieves the global minimum steady-state square errorfor every case.

Similarly, the secondary path is abruptly varied as in Experi-ment 5, and E2

gbest for ten independent runs is plotted in Fig. 11.This experiment also confirms the convergence performance ofthe CRPSO to achieve the minimum steady-state square errorunder abrupt change in the secondary path.

G. Experiment 7: Comparison of the GA- and theCRPSO-Based ANC Algorithms

Since the GA and PSO are the same class of algorithmsapplied to the ANC application, comparison of the convergenceperformance and the optimum weight vector obtained in boththese algorithms is conducted. The type of GA used in [8] waschosen for comparison. The population size of GA was chosenas either 600 or 100; however, the population size of the PSOwas chosen as 100. The GA used 8-b binary conversion asused in [8]. The ANC filter uses ten coefficients in both GAand PSO algorithms. The convergence of the square error ofthe best chromosome in each generation of the GA is plottedwith the square error of the gbest of the CRPSO algorithm

Fig. 11. Performance of CRPSO with time-varying secondary path for tenindependent runs with random seed equal to zero.

Fig. 12. Comparison of convergence performances of the GA- and CRPSO-based ANC algorithms.

Fig. 13. Comparison of optimized weight vectors of ANC filter using theFXLMS, GA-based, and CRPSO-based ANC algorithms.

for comparison in Fig. 12. From Fig. 12, it can be confirmedthat the PSO converges faster than the GA. The GA with apopulation size of 600 [8] converges faster than the GA with a

562 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 2, FEBRUARY 2012

population size of 100. Higher population size incurs additionalcomputational load. To further compare the performances ofthe GA and the PSO algorithms (with a population size of100), the optimum weight vector of the ANC adaptive filter(obtained after 200 generations) is plotted with respect to theweight vector obtained using FXLMS algorithm (with exactestimation of secondary path) in Fig. 13. It can be seen inFig. 13 that the PSO-optimized ANC filter coefficients exactlymatch with the weights obtained in FXLMS algorithm, but theweights obtained with the GA-based optimization do not match.It may be noted here that the FXLMS algorithm when usingthe exact estimated secondary path can converge to a minimumsolution, and hence, comparison of the proposed algorithm ismade with this. However, if there is a secondary path estimationerror, the FXLMS shows very poor performance [1], but theproposed algorithm converges to the minimum without the useof secondary path estimate.

IV. CONCLUSION

This paper has presented a new online ANC algorithm usingPSO-based training. The conventional PSO-based algorithm isshown to be ineffective to regain convergence in the case ofoccurrence of an abrupt change in primary and/or secondarypaths. To cope with the abrupt change in the primary and thesecondary paths, the conventional PSO algorithm is modifiedto introduce a new CRPSO algorithm. A number of computersimulation experiments are carried out to show the usefulness ofthe proposed new PSO algorithm. Analytical discussion is madefor the effectiveness of the proposed algorithm over the FXLMSand GA-based ANC algorithms. The proposed algorithm doesnot use secondary path identification and, hence, is immuneto the change in secondary path. The algorithm is also simpleto implement unlike binary-coded GA-algorithm-based ANC.A new online implementation scheme of the PSO-based ANCalgorithm is proposed in this paper.

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewers fortheir constructive comments which have improved the qualityof this paper.

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Nirmal Kumar Rout received the B.E. degree inelectronics and telecommunication engineering fromthe University College of Engineering (presentlyknown as Veer Surendra Sai University of Technol-ogy), Sambalpur University, Burla, India, in 1991and the M.Tech. degree in computer science fromthe Utkal University, Bhubaneshwar, India, in 2001.He is currently working toward the Ph.D. degree atthe Kalinga Institute of Industrial Technology (KIIT)University, Bhubaneshwar.

From 1993 to 2002, he was a Lecturer with the De-partment of Electronics and Communication Engineering, Orissa EngineeringCollege, Bhubaneswar. He also served as a Faculty Member of the Institute ofChartered Financial Analysts of India (ICFAI) Institute of Science Technology(ICFAITech), Hyderabad, India, from 2002 to 2007. He is currently an Asso-ciate Professor with the School of Electronics Engineering, KIIT University. Hehas published four research papers in various refereed international conferencesand Indian journals. His current research interests include active noise control,adaptive signal processing, soft computing, and evolutionary computing.

ROUT et al.: PSO BASED ANC ALGORITHM WITHOUT SECONDARY PATH IDENTIFICATION 563

Debi Prasad Das (M’10) received the B.Sc.(Hons.) degree in physics from Utkal University,Bhubaneswar, India, in 1996, the M.Sc. degree inelectronics from Sambalpur University, Burla, India,in 1998, and the Ph.D. degree in electronics andinstrumentation engineering from the National Insti-tute of Technology, Rourkela, India, in 2004.

From 2003 to 2004, he was an Assistant Profes-sor and the Head of the Department of Electronics,Silicon Institute of Technology, Bhubaneswar. From2004 to 2005, he was a Postdoctoral Research As-

sociate with the Indian Institute of Technology Kharagpur, Kharagpur, India.From April 2005 to May 2008, he was a Scientist with the Central ElectronicsEngineering Research Institute, Council of Scientific and Industrial Research(CSIR), Pilani, India. Since May 2008, he has been a Scientist with theProcess Engineering and Instrumentation Cell, CSIR-Institute of Mineralsand Materials Technology, Bhubaneswar. During 2010–2011, he visited theUniversity of Adelaide, Adelaide, Australia, for postdoctoral research in thearea of active noise control. His current research interests include active noisecontrol, adaptive signal processing, computationally efficient and hardware-suitable algorithms, microcontroller-based system development, and imageprocessing for the mineral industry.

Dr. Das was a recipient of the Orissa Young Scientists Award in 2004 by theGovernment of Orissa, India; CSIR Young Scientist Award in 2009 by CSIR,India; and Better Opportunities for Young Scientists in Chosen Areas of Scienceand Technology Fellowship from 2009 to 2010 by Department of Science andTechnology, Government of India.

Ganapati Panda (M’94–SM’97) received the B.Sc.degree in electrical engineering and the M.Sc. Eng.degree in communication systems from SambalpurUniversity, Burla, India, in 1971 and 1977, respec-tively, and the Ph.D. degree in electronics and com-munication engineering from the Indian Instituteof Technology (IIT) Kharagpur, Kharagpur, India,in 1981.

From 1984 to 1986, he was a PostdoctoralResearcher with The University of Edinburgh,Edinburgh, U.K. He was the Founder Head of the

School of Electrical Sciences, IIT Bhubaneswar, Bhubaneswar, India, as well asthe Founder Head of the Electronics and Communication Engineering Depart-ment, National Institute of Technology (NIT), Rourkela, India. He also actedas a Coordinator for World Bank Project with NIT, Rourkela. He has served38 years in teaching and research in leading technical institutions of India.He also served as the Director of the NIT, Jamshedpur, India. He is currentlya Deputy Director and Professor with the School of Electrical Sciences, IITBhubaneswar. Prior to this, he was the Dean (Academic Affairs) with IITBhubaneswar and the Dean (Administration) with the NIT, Rourkela. He hasalready guided 21 Ph.D. students in the field of signal processing, communica-tion, and soft computing and has published more than 300 research papers invarious refereed international and Indian journals and conferences. Most of hisresearch papers are extensively cited. He has successfully completed a numberof research projects from All India Council for Technical Education, Ministry ofHuman Resource Development, Indian Space Research Organization, DefenceResearch and Development Organization, Department of Science and Technol-ogy, and British Council, U.K. He has also edited two books in the area of DSP.His research interests are digital signal processing, digital communication, softcomputing, intelligent instrumentation, evolutionary computing, computationalfinance, sensor networks, and distributed signal processing.

Prof. Panda is a Fellow of the National Academy of Engineering, India, in2000, and a Fellow of The National Academy of Sciences, India, in 2003, for hissignificant research contribution to signal processing and telecommunication.He is a Fellow of the Institution of Electronics and Telecommunication Engi-neers, Fellow of the Institution of Engineers, life member of Computer Societyof India, life member of Indian Society for Technical Education, and life mem-ber of System Society. He is a regular Reviewer of many international journalsincluding IEEE, Institution of Engineering and Technology, and Elsevier. Hehas chaired and delivered keynote addresses in many international conferencesin India and abroad. He was a recipient of the Samanta Chandra Sekhar Awardin 1993 from the Department of Science and Technology, Government ofOrissa, for his high-quality research work in the field of engineering.