Buku Pedoman Adiwiyata 2012

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 9, SEPTEMBER 2010 2315

Active Noise Cancellation Without SecondaryPath Identification by Using an

Adaptive Genetic AlgorithmCheng-Yuan Chang and Deng-Rui Chen

Abstract—This paper presents an adaptive genetic algorithm(AGA) for an active noise control (ANC) system. The conventionalANC system often implements the filtered extended least meansquare (FXLMS) algorithm to update the coefficients of the linearfinite-impulse response (FIR) and nonlinear Volterra filters, owingto its simplicity; meanwhile, the FXLMS algorithm may convergeto local minima. In this paper, the FXLMS algorithm is replacedwith an AGA to prevent the local minima problem. Additionally,the proposed AGA method does not require identifying the sec-ondary path for the ANC, explaining why no plant measurementis necessary when designing an AGA-based ANC system. Simu-lation results demonstrate that the effectiveness of the proposedAGA method can suppress the nonlinear noise interference underseveral situations without clearly identifying the secondary path.

Index Terms—Active noise control (ANC), adaptive genetic algo-rithm (AGA), local minima, plant measurement, secondary path.

I. INTRODUCTION

G IVEN its ability to utilize artificial noise interference tocancel out the undesired noise interference, active noise

control (ANC) has attracted considerable attention for its use indeveloping a high-speed digital signal processor. This schemegenerates an antinoise signal with the same magnitude and a180◦ phase shift to the undesired noise interference to disrupt it.ANC systems are generally efficient in reducing low-frequencynoise [1]. Additionally, by using sound-absorbing materials,passive noise control is only effective in canceling out high-frequency noise interference. However, most industrial noisehas its main power in a low frequency, explaining why the ANCsystem has extensively been studied.

Many investigators have implemented the filtered extendedleast mean square (FXLMS) algorithm to design the ANCsystem, owing to its simplicity. Despite its effectiveness in at-tenuating low-frequency noise, FXLMS has several limitations.For instance, while it may converge to local minima duringthe adaptive process, FXLMS may also require identifying thesecondary path before adaptation. To overcome such limita-tions, investigators have adopted intelligent control strategies

Manuscript received May 17, 2009; revised July 28, 2009; acceptedSeptember 27, 2009. Date of publication June 28, 2010; date of current versionAugust 11, 2010. This work was supported by the National Science Councilof the Republic of China, Taiwan, under Contract NSC-96-2221-E-033-074-MY2. The Associate Editor coordinating the review process for this paper wasDr. John Sheppard.

The authors are with the Department of Electrical Engineering, Chung YuanChristian University, Jhongli 320, Taiwan (e-mail: [email protected]).

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.2009.2036410

such as fuzzy and neural network strategies [2], [3]. However,these methods cannot cope with nonlinear effects in practicalsituations, such as the nonlinear behavior of a noise sourceor acoustic plant. While nonlinear methods, including Volterrafilters with Volterra FXLMS (VFXLMS), have been utilizedto diminish undesired noise [4], [5], such methods must stillidentify the secondary path in advance.

As universal searching schemes that use a so-called fitnessfunction, genetic algorithms (GAs) are classified as a globalsearching method to derive the exact or approximate opti-mal solution to searching problems [6]–[8]. GAs also belongto evolutionary computations that adopt schemes inspired byevolutionary biology. Among the several operations of a typ-ical GA include encoding, evaluation of the fitness function,reproduction, crossover, mutation, and replacement [6]–[12].Its major features include parallel computation, robustness,multiple objectives, multimodality, number representation, andconstraints. GA applications in signal processing problemshave been studied. Beligiannis et al. developed a nonlinear-model-structure-based identification method that incorporatescomplex biomedical data by using a GA [13]. Previous studieshave also examined adaptive system modeling and data min-ing [14]. Moreover, Russo and Sicuranza presented a geneticoptimization scheme for several nonlinear systems [15]. Theaforementioned successful signal processing applications havefurther spurred the interest of GA researchers.

This paper presents a linear finite-impulse-response (FIR)filter using an adaptive genetic algorithm (FAGA) and a nonlin-ear Volterra filter using an adaptive genetic algorithm (VAGA)to mitigate undesired noise interference in ANC systems.Importantly, in addition to not requiring the secondary pathto be identified, the adaptive genetic algorithm (AGA)-basedANC helps to prevent local minima. The ability of an AGAto search for the global solution to automatically update thefilter coefficients explains why measuring the plant informationof the secondary path in the correction term is unnecessary.Therefore, an AGA-based ANC system can be designed with-out any plant information measurements. However, the GAperformance depends on the accurate choices of probabilitiesof crossover and mutation. Both of the important parametersin a GA determine the enhancement and performance of ANC.Therefore, in this paper, an adaptive organism is designed toadjust the probabilities of crossover and mutation. Thus, thefitness function can automatically be determined by the mostappropriate crossover rate and mutation rate, thus enhancing theperformance of the AGA-based ANC.

0018-9456/$26.00 © 2009 IEEE

2316 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 9, SEPTEMBER 2010

Fig. 1. (a) ANC headset. (b) Block diagram.

The rest of this paper is organized as follows. Section IIintroduces the concepts of the proposed AGA-based ANCsystem, along with a description of how to update the coef-ficients of FAGA and VAGA. Section III then describes theperformance of FAGA and VAGA systems. Various types ofundesired noise interference and primary and secondary pathsare presented to demonstrate the effectiveness of the proposedAGA. Conclusions are finally drawn in Section IV, along withrecommendations for future research.

II. AGA-BASED ANC IN A HEADSET

An ANC headset is considered as an example, in whicha microphone (Mic) is placed in the ear cup to determineunwanted noise interference. After the processes of ANC, aspeaker transmits artificial noise to cancel out the unwantednoise in the ear cup. This application helps protect humanhearing in a noisy environment, as shown in Fig. 1(a), and theblock diagram is shown in Fig. 1(b). Assume that x(n) denotesthe unwanted noise interference, d(n) denotes the measurednoise by the microphone in the ear cup, y(n) denotes the outputsignal of ANC, and y′(n) represents the output of the speakerto cancel the measured noise. Additionally, P (z) refers to theprimary path, which denotes the transfer function from thelocation of unwanted noise interference to the microphone, andS(z) is the secondary path, which runs from the speaker to themicrophone. The ANC, which is an FIR or Volterra filter, isdenoted as W (z). Here, the conventional FXLMS or VFXLMSalgorithm is replaced with an AGA to update the coefficients ofANC for canceling out the measured noise in the ear cup.

In practice, an ANC system must consider its secondarypath when utilizing either the FXLMS or VFXLMS algorithmto search for the right correction term to obtain the optimalsolution of weighting parameters. However, an AGA is a global

searching and optimization procedure modeled from naturalgenetics, exploring the search space by incorporating a set ofcandidate solutions in parallel. Doing so allows the searchingresults of the AGA to directly replace the correction terms, thussaving the computing effort of identifying the secondary path.Additionally, crossover and mutation probabilities are adoptedby using the fitness function to enhance the performance ofANC. The probabilities of crossover and mutation are generallyfixed in a typical GA, efficiently preventing the predefinedcrossover and mutation rates from canceling out the unwantednoise.

The evolution of GA from one generation to the next onelargely involves fitness evaluation, selection, and reproduction.First, the current population is evaluated using the fitnessevaluation function and then ranked based on their fitnessvalues. Second, GAs stochastically select “parents” from thecurrent population with a bias in which better chromosomesare more likely to be selected, as achieved by using a selectionprobability determined by either the fitness value or the rankingof a chromosome. Third, the GA reproduces “children” fromselected “parents” using crossover and mutation operations.This cycle of evaluation, selection, and reproduction terminateswhen either an acceptable solution is obtained or a predeter-mined limit on the number of iterations is reached [6]–[8].

Moreover, the flowchart of the proposed AGA-based ANCfilters (Fig. 2) consists of the following steps.

Step 1) Set the parameters. The population size is set top, and the order of the FIR and Volterra filters isL − 1 in this paper. Each chromosome of the GApopulation has L × 10 bits. The maximum numberof learning generations of the AGA is set to g.

Step 2) Undertake the filtering of noise. In the FIR fil-ter, p groups of the antinoise signal y′

j(n) canbe generated after decoding the p groups ofpopulation into the real coefficients Wj(n) =[wj(0, n), wj(1, n), . . . , wj(L−1, n)], j =1, . . . , p,defined as

⎡⎢⎢⎣

y1(n)y2(n)

...yp(n)

⎤⎥⎥⎦ =

⎡⎢⎢⎣

w1(0, n) w1(1, n) · · · w1(L − 1, n)w2(0, n) w2(1, n) · · · w2(L − 1, n)

......

......

wp(0, n) wp(1, n) · · · wp(L − 1, n)

⎤⎥⎥⎦

·

⎡⎢⎢⎣

x(n)x(n − 1)

...x(n − L + 1)

⎤⎥⎥⎦ (1)

⎡⎢⎢⎣

y′1(n)

y′2(n)

...y′

p(n)

⎤⎥⎥⎦ =

⎡⎢⎢⎣

y1(n) y1(n − 1) y1(n − L1 + 1)y2(n) y2(n − 1) y2(n − L1 + 1)

...... · · · ...

yp(n) yp(n − 1) yp(n − L1 + 1)

⎤⎥⎥⎦

·

⎡⎢⎢⎣

s1

s2...

sL1

⎤⎥⎥⎦ (2)

CHANG AND CHEN: ACTIVE NOISE CANCELLATION WITHOUT SECONDARY PATH IDENTIFICATION 2317

Fig. 2. Flowchart of an AGA.

where [s1, s2, . . . , sL1 ] denote the impulse responseof the secondary path S(z), and Wj(n) denotes thecoefficient vector of the jth population of FIR filterW (z) at time n, with length L1. However, whenusing a Volterra filter instead of an FIR filter in theANC system, (1) becomes

⎡⎢⎢⎣

y1(n)y2(n)

...yp(n)

⎤⎥⎥⎦ =

⎡⎢⎢⎣

w1(0, n) w1(1, n) · · · w1(L − 1, n)w2(0, n) w2(1, n) · · · w2(L − 1, n)

......

......

wp(0, n) wp(1, n) · · · wp(L − 1, n)

⎤⎥⎥⎦

·

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

x(n)x(n − 1)

...x

(n − L

2 + 1)

x2(n)x2(n − 1)

...x2

(n − L

2 + 1)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

. (3)

Step 3) Perform the fitness function. The residual noise func-tion is designed as

ej(n) = d(n) − y′j(n), j = 1, . . . , p (4)

and⎡⎢⎢⎣

O1(n)O2(n)

...Op(n)

⎤⎥⎥⎦

=

⎡⎢⎢⎣

max (|e1(n)| , |e1(n − 1)| , . . . , |e1(n − L + 1)|)max (|e2(n)| , |e2(n − 1)| , . . . , |e2(n − L + 1)|)

...max (|ep(n)| , |ep(n − 1)| , . . . , |ep(n − L + 1)|)

⎤⎥⎥⎦. (5)

The residual noise of the ANC system can beminimized by defining the fitness functions of ppopulations as

fj =1

Oj, j = 1, . . . , p. (6)

Thus, the performance of each individual in p popu-lations can be evaluated using the fitness function.

Step 4) Reproduce the population. Using roulette wheel se-lection involves the following procedures.1) Normalized fitness functions Rj , j = 1, . . . , p,

are estimated

Rj =fj

p∑j=1

fj

. (7)

The accumulated of normalized fitness functionsshould obviously be 1

p∑j=1

Rj = 1. (8)

2) The p random number rj , j = 1, . . . , p, is gener-ated between 0 and 1.

3) The selected individual is determined by randomnumber rj , 0 ≤ rj ≤ 1, j = 1, . . . , p.

For instance, if the selected number r1 is smallerthan R1 (r1 < R1), then the individual W1 is re-produced, and if the number r2 satisfies R1 < r2 <R1 + R2, then the individual W2 is reproduced.Thus, the new p populations after reproduction pro-cedures are obtained. The strings with the best per-formance indices have a higher likelihood of beingreproduced.

Step 5) Perform crossover operations. The crossover rateis an important parameter in a GA. The crossoverrate is generally selected based on engineering ex-perience. In this paper, the probabilities of thecrossover rate are adopted using the fitness functionto enhance the GA-based ANC because the correctcrossover rate is difficult to obtain. An adaptivemeans of determining the crossover rate accelerates

2318 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 9, SEPTEMBER 2010

the GA operation to search for the global minimum,leading to

pc ={

k1(fmax − f ′)/(fmax − favg), f ′ > favg

k3, f ′ ≤ favg(9)

where

favg =

(p∑

i=1

fi

)

pfmax = max(f1, f2, . . . , fp) (10)

where fmax and favg represent the maximum andaverage fitness functions in the current population,f ′ refers to the larger fitness function of the twochromosomes to be crossed, and k1 and k3 areweighting parameters [10]. The adaptive number pc

is applied to be the crossover probability. As a ge-netic operator used to vary the programming of chro-mosomes from one generation to the next, crossoveroperations are normally divided into two classes:“one-point”- and ”two-point”-type crossovers. Theparents are randomly selected based on step 4.Additionally, a randomly generated crossover pointis selected. Two chromosomes beyond this pointare swapped to form the offspring in the one-point-type crossover. Moreover, the two-point-typecrossover resembles the one-point crossover in thattwo crossover points are randomly generated for twochromosomes, and then, the contents of two pointsare swapped to form the offspring. The two-point-type crossover is performed in the proposed method.

Step 6) Implement the mutation operation. This steppresents the mutation processing in the AGA. Themutation rate is also an important parameter in aGA. Although a larger mutation rate transformsthe GA into a purely random search algorithm, thetypical mutation rate only uses the fixed value within0.005–0.05. This paper adapts the mutation rate ac-cording to the fitness function. The adaptive methodcan help identify the appropriate mutation rate ofeach generation when conducting the mutation op-eration. The adaptive mutation rate is expressed as

pm ={

k2(fmax − f)/(fmax − favg), f > favg

k4, f ≤ favg(11)

where f represents the fitness function of the mu-tated chromosome, fmax and favg are the same asthose in step 5, and k2 and k4 denote the weightingparameters [10].

The premature convergence of the AGA is pre-vented by undertaking the mutation operation. Theclassic example of a mutation operator involves aprobability that an arbitrary bit in a genetic sequencechanges from its original state.

Step 7) Conduct the new population. After a new populationis generated, the new chromosomes that representthe p group of the new filter coefficients are[wnewj

(0, n), wnewj(1, n), . . . , wnewj

(L − 1, n)],j = 1, . . . , p.

Step 8) Perform filtering operations. After the new coeffi-cients of the filter are used, the following signal isobtained:

⎡⎢⎢⎣

ynew1(n)ynew2(n)

...ynewp

(n)

⎤⎥⎥⎦

=

⎡⎢⎢⎣

wnew1(0, n) wnew1(1, n) · · · wnew1(L − 1, n)wnew2(0, n) wnew2(1, n) · · · wnew2(L − 1, n)

......

......

wnewp(0, n) wnewp

(1, n) · · · wnewp(L − 1, n)

⎤⎥⎥⎦

·

⎡⎢⎢⎣

x(n)x(n − 1)

...x(n − L + 1)

⎤⎥⎥⎦ (12)

for the FIR filter and

⎡⎢⎢⎣

ynew1(n)ynew2(n)

...ynewp

(n)

⎤⎥⎥⎦

=

⎡⎢⎢⎣

wnew1(0, n) wnew1(1, n) · · · wnew1(L − 1, n)wnew2(0, n) wnew2(1, n) · · · wnew2(L − 1, n)

......

......

wnewp(0, n) wnewp

(1, n) · · · wnewp(L − 1, n)

⎤⎥⎥⎦

·

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

x(n)x(n − 1)

...x

(n − L

2 + 1)

x2(n)x2(n − 1)

...x2

(n − L

2 + 1)

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(13)

for the Volterra filter. Thus, the p groups of the newantinoise signal are defined as

⎡⎢⎢⎢⎣

y′new1

(n)y′new2

(n)...

y′newp

(n)

⎤⎥⎥⎥⎦

=

⎡⎢⎢⎣

ynew1(n) ynew1(n − 1) ynew1(n − L1 + 1)ynew2(n) ynew2(n − 1) ynew2(n − L1 + 1)

...... · · · ...

ynewp(n) ynewp

(n − 1) ynewp(n − L1 + 1)

⎤⎥⎥⎦

·

⎡⎢⎢⎣

s1

s2...

sL1

⎤⎥⎥⎦ . (14)

CHANG AND CHEN: ACTIVE NOISE CANCELLATION WITHOUT SECONDARY PATH IDENTIFICATION 2319

Step 9) Perform the new fitness function. After p popula-tions of antinoise signal y′

newj(n), j = 1, . . . , p, are

generated, the new fitness function is evaluated todecide the optimum one, similar to that in step 3.

Step 10) Perform replacement operations. The population ofthe AGA is updated by applying the generational-replacement method. The new fitness function repli-cates two best fitness functions of chromosomesfrom the old population to replace two worst fitnessfunctions of chromosomes in the offspring.

Step 11) Perform iterative operations. Following the replace-ment in step 10, steps 4–10 are repeated to locatethe largest fitness function and realize the antinoisesignal to cancel out the unwanted noise interference.

III. SIMULATIONS RESULTS

The effectiveness of the proposed AGA-based ANC isdemonstrated by considering the following conditions. The ef-fectiveness of ANC is verified using different kinds of primarypath P (z) and secondary path S(z). Additionally, the enhance-ment is confirmed by comparing the performance of FAGAand VAGA with that of conventional FXLMS and VFXLMSalgorithms. The coefficient length of a FIR or Volterra filteris L = 20, and the step size is µ = 0.01 for conventionalFXLMS and VFXLMS algorithms. The initial population sizep is 600, and the number of generations g is 500 in FAGAand VAGA [15]. The adaptive parameters k1 = k3 = 1 andk2 = k4 = 0.01 are defined. Analytical results are implementedby a personal computer with dual 1.6-GHz central processingunits and 2-GB dynamic random access memory in Matlab.

Four adaptive controllers are used. The first and second con-trollers are the conventional twentieth-order FIR filter and thenonlinear Volterra filter with a memory size of 10 and an orderof power 2 using the FXLMS algorithm. This paper describestwo GA-based controllers to enhance the performance of ANCmeasurement. The third one is a twentieth-order FAGA. Thefourth one is a nonlinear Volterra filter that is also with amemory size of 10 and an order of power 2 using AGA(VAGA), which is to be the contrast.

Additionally, the noise reduction performance with eachcontroller is evaluated using both linear and nonlinear transferfunctions of primary and secondary paths. The linear transferfunctions of the primary path and secondary path are FIR filterssuch as [4], [15]

Plinear(z) = z−5 − 0.3z−6 + 0.2z−7 (15)

Slinear(z) = z−2 + 1.5z−3 − z−4. (16)

Moreover, the nonlinear functions of primary and secondarypaths are described as follows. The primary noise d(n) at thecanceling point is assumed here to be generated based on thethird-order polynomial model

t(n) = x(n − 3) − 0.3x(n − 4) + 0.2x(n − 5) (17)

d(n) = t(n − 2) + 0.08 [t(n − 2)]2 − 0.04 [t(n − 2)]3 . (18)

Furthermore, the antinoise signal y′(n) at the canceling point isassumed here to be generated by the nonlinear secondary path[4], [15]

r(n) = 0.66 tanh (1.5y(n)) (19)

y′(n) = r(n − 2) + 1.5r(n − 3) − r(n − 4). (20)

The first experiment assesses the performance with a linearprimary path and a nonlinear secondary path. The unwantednoise measurement is assumed to be a 200-Hz pure-sine-wavenoise. Fig. 3(a)–(d) summarizes those results, indicating thatthe results of FAGA and VAGA methods are better than those ofthe conventional FXLMS and VFXLMS filters because the cor-rection term of adaptive filters with a nonlinear secondary pathis difficult to obtain based on FXLMS and VFXLMS methods.Although the global searching ability of the AGA enhances theperformance of ANC, the fitness function in Fig. 3(e) representsthe performance of FAGA and VAGA. VAGA is also betterthan FAGA.

Fig. 4 summarizes the performance of canceling out narrow-band noise interference with a nonlinear primary path and alinear secondary path. Moreover, Fig. 5 displays the results ofhaving both nonlinear primary and secondary paths. Those re-sults resemble those in Fig. 3. AGA-based methods outperformthe conventional FXLMS-based methods, particularly when thetransfer function of the secondary path is a nonlinear function.Both of the fitness functions in Figs. 4(e) and 5(e) also indicatethat VAGA is more appropriate to cancel out the noise in thenonlinear plant.

Exactly when the unwanted noise measurement becomesrandom noise is examined next. The noise power is increasedhigher than those in the previous experiments. Figs. 6–8summarize the results of reducing random noise within200–300 Hz. Different kinds of primary and secondary pathsare also presented to verify the performance of noise cancel-lation. Fig. 6 compares the results obtained from the linearprimary and nonlinear secondary paths. According to this fig-ure, the FXLMS and VFXLMS methods cannot effectivelysuppress the broadband noise, as shown in Fig. 6(a) and (b).However, the AGA-based filters still satisfactorily perform, asshown in Fig. 6(c) and (d). Fig. 6(e) shows the fitness functionsof FAGA and VAGA. This figure reveals that, when applyingthe nonlinear secondary path, the nonlinear VAGA performsbetter than the FAGA filter.

Fig. 7 summarizes the results with a nonlinear primary pathand a linear secondary path. Additionally, Fig. 8 presents theresults of having both nonlinear primary and secondary paths.According to these figures, the FXLMS and VFXLMS meth-ods cannot also adequately cancel out the noise interference.However, FAGA and VAGA still provide an effective meansof efficiently canceling out the noise. Figs. 7(e) and 8(e) alsodisplay the respective fitness functions of FAGA and VAGA,indicating that both of fitness functions of VAGA in Figs. 7(e)and 8(e) are better than those of FAGA.

The enhancement of the proposed adaptive algorithm isdemonstrated as follows. The unwanted noise measurement is

2320 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 9, SEPTEMBER 2010

Fig. 3. 200-Hz noise with a linear primary path and a nonlinear secondary path. (a) FXLMS. (b) VFXLMS. (c) FAGA. (d) VAGA. (e) Fitness function.

a complex random noise ranging from 200 to 300 and 400to 600 Hz. The performance of FIR and Volterra filters usingGA (FGA and VGA), FAGA, and VAGA is evaluated usingnonlinear plant information. The mutation and crossover ratesof FGA and AGA are 0.01 and 0.8, respectively. According toFig. 9(a) and (b), the noise canceling performance is around15–25 dB for FGA and VGA. However, FAGA and VAGA canstill cancel out the complex random noise interference at about

20–30 dB, as shown in Fig. 9(c) and (d). The fitness functions ofFGA, VGA, FAGA, and VAGA also illustrate the improvementof the proposed adaptive method, as shown in Fig. 9(e).

Table I lists the average performance matrices of eachmethod. The aforementioned results suggest that the FXLMS-and VFXLMS-based ANC systems can effectively suppressthe 200-Hz random noise signal with the nonlinear transferfunctions of primary and secondary paths. Moreover, VAGA

CHANG AND CHEN: ACTIVE NOISE CANCELLATION WITHOUT SECONDARY PATH IDENTIFICATION 2321

Fig. 4. 200-Hz noise with a nonlinear primary path and a linear secondary path. (a) FXLMS. (b) VFXLMS. (c) FAGA. (d) VAGA. (e) Fitness function.

is more effective than the FAGA method in solving ANCproblems with the nonlinear plant model.

/tablegraphic_alt> In addition, most industrial noise hasits main frequency range within 200–300 and 400–600 Hz;therefore, the authors choose the random noise with the specificfrequency range to do the implementation.

Remark 1: As is well known, a GA has a low convergentspeed. The convergent speed of an AGA is approximately a

hundred times higher than that of FXLMS. However, in ourANC headset design, the global optimal coefficients of FIR orVolterra filters can be searched for in advance by using an AGA.After the optimal values are derived, these values for ANC canbe replicated to achieve real-time control. The plant informationis stationary when one wears the headphone because the ANCheadset cancels out the measured noise interference within theear cup, thus achieving real-time control. The authors also

2322 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 9, SEPTEMBER 2010

Fig. 5. 200-Hz noise with nonlinear primary and secondary paths. (a) FXLMS. (b) VFXLMS. (c) FAGA. (d) VAGA. (e) Fitness function.

discuss and analyze the performance of different acoustic plantsand noise types to verify the effectiveness of variations in theenvironment/measured signal.

Remark 2: Among the several parameters set in this paperinclude the population, the generation of a GA, and the filterlength of ANC. Although a higher GA population can more ef-ficiently search for the optimal value, higher computing effortsare incurred. The stop criterion of a GA is normally determined

by the limit of the remaining error or the number of generations.The filter length also determines the filter performance. Thispaper selects a population size of 600, a number of generationsof 500, and a filter length of 20, which are the same as in anotherstudy [15] to compare the performance of noise cancellation.Moreover, a complex or dynamic measurement environmentimplies a high filter length. Based on the fitness functions, inthis paper, the mutation and crossover rates are determined

CHANG AND CHEN: ACTIVE NOISE CANCELLATION WITHOUT SECONDARY PATH IDENTIFICATION 2323

Fig. 6. 200–300-Hz random noise with a linear primary path and a nonlinear secondary path. (a) FXLMS. (b) VFXLMS. (c) FAGA. (d) VAGA.(e) Fitness function.

using k1–k4. A binary GA mainly relies on the crossover opera-tion to produce new points in the searching space. The mutationoperation plays a secondary role in a binary GA by introducingstochastic randomness to the reproduction process. Therefore,the crossover probability is often substantially higher than the

mutation probability [6]–[8]. Additionally, a higher value of thecrossover rate implies a quicker speed in which new solutionsare introduced into the population. Large values of the mutationrate transform the GA into a purely random search algorithm,while some mutations must prevent the premature convergence

2324 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 9, SEPTEMBER 2010

Fig. 7. 200–300 Hz random noise with a nonlinear primary path and a linear secondary path. (a) FXLMS. (b) VFXLMS. (c) FAGA. (d) VAGA.(e) Fitness function.

of the GA to suboptimal solutions. Therefore, in this paper,higher crossover and mutation rates are used when the fitnessfunction is low; in addition, lower values of the crossover andmutation rates are used when the fitness function exceeds theaverage in the current population.

Remark 3: Both of the proposed ANC methods, i.e.,FAGA and VAGA, are based on linear FIR and nonlinearVolterra filters, respectively. Simulation results indicated thatthe nonlinear-based ANC performs better than the linear-basedANC, particularly in terms of canceling out the noise with a

CHANG AND CHEN: ACTIVE NOISE CANCELLATION WITHOUT SECONDARY PATH IDENTIFICATION 2325

Fig. 8. 200–300 Hz random noise with nonlinear primary and secondary paths. (a) FXLMS. (b) VFXLMS. (c) FAGA. (d) VAGA. (e) Fitness function.

nonlinear primary or secondary path. Specifically, linear ANCsystems can efficiently reduce low-frequency noise. However,under some circumstances, the noise interference originatingfrom a dynamic system may be nonlinear and deterministicnoise rather than stochastic, white, or tonal noise; in addi-

tion, the primary noise at the canceling point may exhibitnonlinear distortion. If such circumstances persist, the linearANC system degrades in performance [4], explaining why theproposed VAGA, which is based on a multichannel structure,outperforms FAGA.

2326 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 9, SEPTEMBER 2010

Fig. 9. Complex random noise with nonlinear primary and secondary paths. (a) FGA. (b) VGA. (c) FAGA. (d) VAGA. (e) Fitness function.

IV. CONCLUSION

This paper has presented AGA-based methods for ANCsystems. The proposed methods do not require evaluating thesecondary path when implementing ANC systems. The globalsearching property of GAs also facilitates efforts to preventlocal minima. Additionally, the proposed method has been

implemented in a real-time application. Different measurednoise signals and linear and nonlinear paths confirm that theproposed methods yield satisfactory results. In addition toits simplicity and effectiveness, the proposed AGA methodis versatile with respect to the other potential applicationsof ANC measurement, such as electronic mufflers, silencers,headboards, and infant incubators.

CHANG AND CHEN: ACTIVE NOISE CANCELLATION WITHOUT SECONDARY PATH IDENTIFICATION 2327

TABLE INOISE CANCELING PERFORMANCE OF ANC FILTERS

ACKNOWLEDGMENT

The author would like to thank T. Knoy for his editorialassistance.

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Cheng-Yuan Chang was born in Taiwan in 1968.He received the B.S. and M.S. degrees in control en-gineering from the National Chiao Tung University,Hsinchu, Taiwan, in 1990 and 1994, respectively,and the Ph.D. degree in electrical engineering fromthe National Central University, Taoyuan, Taiwan, in2000.

From 1994 to 2007, he was with the Departmentof Electronic Engineering, Ching Yun University,Taoyuan. Since August 2007, he has been with theDepartment of Electrical Engineering, Chung Yuan

Christian University, Jhongli, Taiwan, where he is currently an AssociateProfessor. His research interests are in the area of fuzzy neural controller design,GA algorithm, active noise control applications and nonlinear crane trackingcontroller design.

Deng-Rui Chen was born in Taiwan, in 1984. Hereceived the B.S. degree in electrical engineeringfrom St. John’s University, Taipei, Taiwan, in 2007and the M.S. degree in electrical engineering fromChung Yuan Christian University, Jhongli, Taiwan,in 2009.

He is currently with the Department of ElectricalEngineering, Chung Yuan Christian University. Hiscurrent research interests are in the area of intelligentcontrol applications and active noise control system.