adaptive active noise suppression using multiple model...

Research ArticleAdaptive Active Noise Suppression Using MultipleModel Switching Strategy

Quanzhen Huang1 Suxia Chen2 Mingming Huang1 and Zhuangzhi Guo1

1School of Electrical Information Engineering Henan Institute of Engineering Zhengzhou 451191 China2School of Computer Henan Institute of Engineering Zhengzhou 451191 China

Correspondence should be addressed to Zhuangzhi Guo guozhuangzhi2012126com

Received 21 September 2016 Revised 26 November 2016 Accepted 19 December 2016 Published 29 January 2017

Academic Editor Jeong-Hoi Koo

Copyright copy 2017 Quanzhen Huang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Active noise suppression for applications where the system response varies with time is a difficult problemThe computation burdenfor the existing control algorithms with online identification is heavy and easy to cause control system instability A new activenoise control algorithm is proposed in this paper by employing multiple model switching strategy for secondary path varyingThe computation is significantly reduced Firstly a noise control system modeling method is proposed for duct-like applicationsThen a multiple model adaptive control algorithm is proposed with a new multiple model switching strategy based on filter-uleast mean square (FULMS) algorithm Finally the proposed algorithm was implemented on Texas Instruments digital signalprocessor (DSP) TMS320F28335 and real time experiments were done to test the proposed algorithm and FULMS algorithm withonline identification Experimental verification tests show that the proposed algorithm is effective with good noise suppressionperformance

1 Introduction

Nowadays noise cancellation becomesmore andmore impor-tant for industrial applications such as engines blowers fanstransformers and compressors [1ndash6] The traditional passivenoise cancellation techniques using sound absorbent mate-rials can suppress high-frequency acoustic noises effectivelyusually higher than 500Hz [7] But they are ineffective ortend to be bulky for low frequency cases Meanwhile thepassive noise control equipment is relatively large and expen-sive In contrast with the passive noise suppression methodsactive noise control techniques have excellent low frequencycharacteristic with potential benefits in size weight and cost[8]

The idea of active noise control using a microphoneand loudspeaker was first proposed in a 1936 patent byLueg In the 1980s the development of solid state elec-tronics and digital signal processing technologies enabledlow-cost implementation of powerful adaptive algorithmsand encouraged widespread development and application

of active noise control systems While the characteristicsof the noise source and the acoustic environment are timevarying an active noise control system is required to trackthese changes and uncertainties In particular the secondarypath between the loudspeakers and error sensors is timevarying as the temperature and noise propagation conditionwould vary even though the noise source does not changeSo in most actual applications simultaneous secondary pathidentification should be done

Various algorithms can be used for this purpose depend-ing on the problem setting and the allowed computationalcomplexity The most famous one is Filtered-x Least MeanSquares (FxLMS) algorithms which is proposed by differentresearchers independently Several theoretical developmentsand successful applications are documented in the related lit-erature [3 9ndash13] FxLMS is used to adapt FIR filter coefficientsof a controller however the IIR adaptive filter is preferred incase the optimal controller has one or more poles close to theunit circle whichmay yield a very lone FIR optimal controllerIn case the plant to be controlled contains intrinsic acoustical

HindawiShock and VibrationVolume 2017 Article ID 7289076 6 pageshttpsdoiorg10115520177289076

2 Shock and Vibration

Noise source Secondary sourceError sensor

l0 l3l2l1

R1 R2

Figure 1 Schematic diagram for a duct-like application

feedback especially and the optimal controller might containunstable poles it is even impossible to use an FIR adaptivefilter to do optimal control without reducing the bandwidthof the controller Many adaptive online identification meth-ods are reported [14ndash18] A functional-link-artificial-neural-network- (FLANN-) based multichannel nonlinear activenoise control (ANC) system trained using a particle swarmoptimization (PSO) algorithm suitable for nonlinear noiseprocesses is proposed in [19] A novel online secondarypath modeling scheme based on the Generalized LevinsonDurbin (GLD) algorithm is proposed in [20] A new adaptivestrategy based on fractional signal processing is proposedusing multidirectional step size fractional least mean squarealgorithm for online secondary path modeling in [21] Asimplified subband ANC algorithm without secondary pathmodeling is proposed in [22]

But most of them could not be applied to the cases whilesecondary path varies rapidly and not suited for multipleinput multiple output applications with too many unknownparameters

To solve these problems a new adaptive multiple modelswitching control algorithm is proposed The paper is orga-nized as follows Section 2 introduces the active noise controlsystemmodelingmethod for duct-like applications Section 3introduces the FULMS algorithm Section 4 proposes a mul-tiple model switching strategy Section 5 gives the real timetest results Section 6 comes the conclusion

2 Active Noise Control System Modeling forDuct-Like Applications

Schematic diagram of active noise control system for a duct-like application is shown in Figure 1The sound incident fromthe left noise source is picked up by the microphone and aftersome processing by the active noise controller this signal

is fed to the secondary sources (loudspeaker) such that tothe right side the primary signal and the additional signalcancel each other The noise source is located at 1198970 from oneend of the duct and an error sensor is located at 1198973 fromthe other end of the duct The secondary source is located at1198971 form the noise source The pressure reflection coefficientsin two ends are 1198771 and 1198772 respectively The primary pathbetween the noise source and the secondary source is 119875the secondary path between the secondary source and errorsensor is 119878

According the steady state travelling wave theory thefrequency response for secondary path and the primary pathcan be obtained as follows

119878 (119895119908)

=119867119904119867119890119890minus1198961198972 [1 + 1198631198901198772119890minus21198961198973] [1 + 1198631199041198771119890minus2119896(1198970+1198971)]

1 minus 11987711198772119890minus2119896119897

119875 (119895119908)

=119867119890119867119901119890minus119896(1198971+1198972) [1 minus 1198631198901198772119890minus21198961198973] [1 + 1198631199011198771119890minus21198961198970]

1 minus 11987711198772119890minus2119896119897

(1)

Here 119867119901 is the electroacoustic transfer function of thenoise source 119867119904 is the electroacoustic transfer function ofthe secondary source and 119867119890 is the electroacoustic transferfunction of the error sensor 119863119901 is the directivity factor ofthe noise source 119863119904 is the directivity factor of the secondarysource and 119863119890 is the directivity factor of the error source119896 = 119895120596119888 in which 120596 is angular frequency and 119888 is soundspeed For 119911-transform

119878 (119911) =119911minus1198992 [1 + 1198772119911minus21198993] [1 + 1198771119911minus2(1198990+1198991)]

1 minus 11987711198772119911minus119873

119875 (119911) =119911minus(1198991+1198992) [1 + 1198772119911minus21198993] [1 + 1198771119911minus21198990]

1 minus 11987711198772119911minus119873

(2)

Here 119899119894 is the integer near to 119897119894119891119904119888 here 119891119904 is samplingfrequency of the control system 119888 is the sound speed 119873 =2(1198990 +1198991 +1198992 +1198993) while the sound speed changes with timethe whole system becomes time varying

Unfolding (2)

119878 (119911) =119911minus1198992 + 1198771119911minus2(1198990+1198991+051198992) + 1198772119911minus2(051198992+1198993) + 11987711198772119911minus2(1198990+1198991+051198992+1198993)

1 minus 11987711198772119911minus119873

119875 (119911) =119911minus(1198991+1198992) + 1198771119911minus2(1198990+051198991+051198992) + 1198772119911minus2(051198991+051198992+1198993) + 11987711198772119911minus2(1198990+051198991+051198992+1198993)

1 minus 11987711198772119911minus119873

(3)

3 FULMS Algorithm

A block diagram of an adaptive IIR ANC system usingFULMS algorithm is illustrated in Figure 2The output signal

of the IIR filter 119910(119899) is computed as

119910 (119899) = a119879 (119899) 119909 (119899) + b119879 (119899) 119910 (119899 minus 1) (4)

Shock and Vibration 3

x(n)P(z)

A(z) S(z)

d(n)

y(n) s(n) e(n)

+

LMS

LMS

B(z)

+

+minus

S(z)

S(z)

x998400(n)

y998400(n)


x(n)P(z)

W(z)

d(n)

e(n)+

FULMS

+

y(n)

Randomnoise

S(z)

+

FULMSf(n)

v(n)S(z)

S(z)

x998400(n)

998400(n)

y998400(n) + 998400(n)

minus

minus minus

Figure 3 FULMS algorithm with online identification

Here a(119899) = [1198860(119899) 1198861(119899) sdot sdot sdot 119886119871minus1(119899)]119879 is the weight

vector of 119860(119911) and b(119899) = [1198871(119899) 1198872(119899) sdot sdot sdot 119887119872(119899)]119879 is the

weight vector of 119861(119911) And FULMS algorithm can be adoptedto find the optimal set of these coefficients

a (119899 + 1) = 119886 (119899) + 1205831199091015840 (119899) 119890 (119899)

b (119899 + 1) = 119887 (119899) + 1205831015840 (119899 minus 1) 119890 (119899) (5)

Here 1015840(119899 minus 1) = (119899) lowast 119910(119899 minus 1)Most of current researches are involved in online iden-

tification A schematic diagram of FULMS algorithm withonline identification is shown in Figure 3

Zero-meanwhite noise V(119899) is used to drive the secondarysource Estimated (119911) is used in parallel with the secondarypath but only with a white noise input The adaptive filtersare updated using FULMS algorithm After algorithm con-vergence the residual noise will perturb the coefficients (119911)and result in a misalignment

1205902 equiv lim119899rarrinfin

119864119872minus1

sum119898=0

[119898 (119899) minus 119904119898 (119899)]2 asymp

12058321198721205902119906 (6)

Here 119898(119899) 119904119898(119899) 119898 = 0 1 119872 minus 1 are theimpulse response of (119911) 119878(119911) respectively Here 119864 meansmathematical expectation 120590 means variance 120583 is adaptivestep size

4 Multiple Model Switching Strategy

Multiple model adaptive control is a control strategy that canidentify and adapt system changing characteristics Multiplemodel strategy has an advantage over single model schemesbecause it selects the most suitable model among finite set ofpossible models The computational burden does not muchincrease even though the number of channels increases Theblock diagram of the proposed multiple model switchingstrategy is shown in Figure 4

The residual error for 119894-th model is

120576119894 (119899) = 119890 (119899) minus 119904119894 (119899) (7)

The power of the 119894-th error can be used to select the (119911)

119869119894 (119905) =119905

sum119895=0

119890minus120582(119905minus119895)1205762119894 (119895) (8)

Here 120582 is forgetting factor 119905 is time index Model bankcontains a fixed model bank for estimation of 119878(119911) Theidentified model is fed to the block of (119911) which is used tofilter 119909(119899) LMS algorithm is employed to adjust the weightsof filter A and filter B

The model which has the minimum residual power isselected as current (119911) The algorithm procedure can beshown as follows

(1) Constructing a model bank with m fixed models(2) Calculating 119869119894 for each model(3) Selecting (119911)which has theminimumresidual power(4) Employing the selected (119911) into the FULMS algo-

rithm to generate the filtered reference signals Thecomputation burden of the proposed multiple modelstrategy is significantly reduced as no adaptive modelidentification is carried out

5 Experimental Tests and Results

To test the proposed algorithm a test experimental platformis constructed using a 10-meter duct with two loudspeak-ers two microphones and an acoustic rate sensor Oneloudspeaker is used to generate noise while canceling noisechanneled through the other speaker A microphone isplaced in cancellation zone to pick up the resultant noisesignal The control paradigm is implemented on a TexasInstrument TMS320F28335 Digital Signal Processing chipThe experimental platform schematic diagram is shown inFigure 5 The sampling frequency is 10000Hz 120583 = 0001 andthe length of adaptive filters is 24

At first sound speed is measured for various condi-tions using the acoustic rate sensor and minimum value is325msec and the maximum value is 355msec Six fixedmodels are used to construct the model bank and one modelcalculated using the current measured acoustic rate is usedas the reference model to value the model switching perfor-mance To accelerate the experiment rather than waiting forcondition change an air conditioner is employed


S(z)

x(n)P(z)

A(z)

B(z)

d(n)

y(n)e(n)s(n)

+

LMS

LMS

+

+

Model bank

Whiteprocessv(n)

+

++

+

+

S(z)

S(z)

S(z)

x998400(n)

y998400(n)

S2(z)

S1(z)

Sm(z)sm(n)

s2(n)

s1(n)

1205762(n)

1205761(n)

120576m(n)

minus

minus

minus

minus

select

Figure 4 Block diagram of the proposed multiple model switching control system


Acoustic rate sensor

Amplifier

e(n)

TMS320F28335

DAArbitraryfunctiongenerator

Amplifier

Reference sensor

DA DA

l0 l3l2l1

R1R2

Figure 5 Experimental platform setup

Table 1 Duct parameter value

Duct parameter Symbol ValueReflection coefficients 1198771 1198772 065 065Duct length 1198970 1198971 1198972 1198973 22m 92m 52m 18m

The duct parameters are shown in Table 1Two paradigms are tested on the experimental platform

The first one is the FULMS with online identification algo-rithm while the model change rate is not so fast (the airconditioner changes slowly) The control performance isshown in Figure 6 It is clear that while the model changerate is slow the control performance of FULMS algorithmwith online identification is still acceptable While the airconditioner changes fast the control performance can beshown in Figure 7 The FULMS with online identificationcannot assure the satisfactory control performance anymore

To test the performance of the proposed multiple modelswitching control algorithm several experiments were done

minus25minus2

minus15minus1

minus050

051

152

25

e (v)

1 2 3 4 5 6 7 8 9 100t (s)

Figure 6 Control performance with slow model change

The first experiment is designed to find a suitable memorylength three cases are listed in Figure 8 the memory lengthin Figure 8(a) is 100 the memory length in Figure 8(b) is1000 and the memory length in Figure 8(c) is 5000 Thesolid line is the model calculated using the current measured


minus8minus6minus4minus2

02468

e (v)

1 2 3 4 5 6 7 8 9 100t (s)

Figure 7 Control performance with fast model change

1 2 3 4 5 60t (s)

123456

Mod

el

(a) Memory length is 100

1 2 3 4 5 60t (s)

123456

Mod

el

(b) Memory length is 1000

1 2 3 4 5 60t (s)

1

2

3

4

5

6

Mod

el

(c) Memory length is 5000Figure 8 Model switching with different memory length

acoustic rate and it is rounded to the six fixed models Asshown in Figure 8 while the memory length is too shortthe model switching is too fast and will cause instabilityWhile the memory length is too long the switching is tooslow and the model change rate is larger it would also causeinstability The final control performance of our multiplemodel switching FULMS algorithm is shown in Figure 9Theproposed algorithm could guarantee a satisfactory suppres-sion performance while the secondary path changes

6 Conclusion

A novel active noise control algorithm is proposed in thispaper by employing multiple model switching strategy for

10 20 30 40 50 600t (s)

minus3minus2minus1

0123

e (v)

Figure 9 Control performance of the proposed method

secondary path with noise control system modeling methodfor duct-like applications Real time experiments were doneThe experimental results show that the proposed algorithmhas good noise suppression performance while the secondarypath changesThe transient process ofmultiplemodel switch-ing needs to be analyzed for nonlinear applications

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is supported by the National Nature ScienceFoundation of China (no 61403123 no 61305106) Techno-logical Innovation Talents Projects ofHenanUniversities (no17HASTIT020) Henan Province Science and TechnologyProject (no 162102210099 no 162102310081) and HenanProvince Youth Backbone Teachers Scheme in 2016 year

References

[1] N V George and G Panda ldquoAdvances in active noise controla survey with emphasis on recent nonlinear techniquesrdquo SignalProcessing vol 93 no 2 pp 363ndash377 2013

[2] Y Li X Wang and D Zhang ldquoControl strategies for aircraftairframe noise reductionrdquo Chinese Journal of Aeronautics vol26 no 2 pp 249ndash260 2013

[3] Z Bo J Yang C Sun and S Jiang ldquoA filtered-x weighted accu-mulated LMS algorithm stochastic analysis and simulations fornarrowband active noise control systemrdquo Signal Processing vol104 pp 296ndash310 2014

[4] I-H Yang J-E Jeong U-C Jeong J-S Kim and J-E OhldquoImprovement of noise reduction performance for a high-speedelevator using modified active noise controlrdquo Applied Acousticsvol 79 pp 58ndash68 2014

[5] G Nelson R Rajamani and A Erdman ldquoNoise controlchallenges for auscultation on medical evacuation helicoptersrdquoApplied Acoustics vol 80 pp 68ndash78 2014

[6] Y Kajikawa W-S Gan and S M Kuo ldquoRecent applicationsand challenges on active noise controlrdquo in Proceedings of the8th International Symposiumon Image and Signal Processing andAnalysis (ISPA rsquo13) Trieste Italy September 2013

[7] S Bianchi A Corsini and A G Sheard ldquoA critical review ofpassive noise control techniques in industrial fansrdquo Journal ofEngineering for Gas Turbines and Power vol 136 no 4 ArticleID 044001 2013


[8] D Moreau Active Control of Noise and Vibration CRC PressSecond edition 2012

[9] G Sun T Feng M Li and T C Lim ldquoConvergence analysisof FxLMS-based active noise control for repetitive impulsesrdquoApplied Acoustics vol 89 pp 178ndash187 2015

[10] B Krstajic Z Zecevic and Z Uskokovic ldquoIncreasing conver-gence speed of FxLMS algorithm in white noise environmentrdquoAEU - International Journal of Electronics and Communicationsvol 67 no 10 pp 848ndash853 2013

[11] T Wang and W-S Gan ldquoStochastic analysis of FXLMS-basedinternal model control feedback active noise control systemsrdquoSignal Processing vol 101 pp 121ndash133 2014

[12] I T Ardekani and W H Abdulla ldquoTheoretical convergenceanalysis of FxLMS algorithmrdquo Signal Processing vol 90 no 12pp 3046ndash3055 2010

[13] I T Ardekani and W H Abdulla ldquoFiltered weight FxLMSadaptation algorithm analysis design and implementationrdquoInternational Journal of Adaptive Control and Signal Processingvol 25 no 11 pp 1023ndash1037 2011

[14] P Davari and H Hassanpour ldquoDesigning a new robust on-line secondary path modeling technique for feedforward activenoise control systemsrdquo Signal Processing vol 89 no 6 pp 1195ndash1204 2009

[15] H Hassanpour and P Davari ldquoAn efficient online secondarypath estimation for feedback active noise control systemsrdquoDigital Signal Processing vol 19 no 2 pp 241ndash249 2009

[16] M T Akhtar M Abe M Kawamata and A Nishihara ldquoOnlinesecondary path modeling in multichannel active noise controlsystems using variable step sizerdquo Signal Processing vol 88 no8 pp 2019ndash2029 2008

[17] Q Huang J Luo Z Gao X Zhu andH Li ldquoAn improved filter-u least mean square vibration control algorithm for aircraftframeworkrdquo Review of Scientific Instruments vol 85 no 9Article ID 095003 2014

[18] G-Y Jin T-J Yang Y-H Xiao and Z-G Liu ldquoA simultaneousequation method-based online secondary path modeling algo-rithm for active noise controlrdquo Journal of Sound and Vibrationvol 303 no 3ndash5 pp 455ndash474 2007

[19] N V George and G Panda ldquoA particle-swarm-optimization-based decentralized nonlinear active noise control systemrdquoIEEETransactions on Instrumentation andMeasurement vol 61no 12 pp 3378ndash3386 2012

[20] S Tyagi V Katre and N V George ldquoOnline estimation ofsecondary path in active noise control systems using Gener-alized Levinson Durbin algorithmrdquo in Proceedings of the 19thInternational Conference on Digital Signal Processing (DSP rsquo14)pp 552ndash555 IEEE Hong Kong August 2014

[21] M S Aslam and M A Z Raja ldquoA new adaptive strategy toimprove online secondary pathmodeling in active noise controlsystems using fractional signal processing approachrdquo SignalProcessing vol 107 pp 433ndash443 2015

[22] MGao J Lu andXQiu ldquoA simplified subbandANCalgorithmwithout secondary path modelingrdquo IEEEACM Transactions onAudio Speech and Language Processing vol 24 no 7 pp 1164ndash1174 2016

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks




l0 l3l2l1

R1 R2


feedback especially and the optimal controller might containunstable poles it is even impossible to use an FIR adaptivefilter to do optimal control without reducing the bandwidthof the controller Many adaptive online identification meth-ods are reported [14ndash18] A functional-link-artificial-neural-network- (FLANN-) based multichannel nonlinear activenoise control (ANC) system trained using a particle swarmoptimization (PSO) algorithm suitable for nonlinear noiseprocesses is proposed in [19] A novel online secondarypath modeling scheme based on the Generalized LevinsonDurbin (GLD) algorithm is proposed in [20] A new adaptivestrategy based on fractional signal processing is proposedusing multidirectional step size fractional least mean squarealgorithm for online secondary path modeling in [21] Asimplified subband ANC algorithm without secondary pathmodeling is proposed in [22]

But most of them could not be applied to the cases whilesecondary path varies rapidly and not suited for multipleinput multiple output applications with too many unknownparameters

To solve these problems a new adaptive multiple modelswitching control algorithm is proposed The paper is orga-nized as follows Section 2 introduces the active noise controlsystemmodelingmethod for duct-like applications Section 3introduces the FULMS algorithm Section 4 proposes a mul-tiple model switching strategy Section 5 gives the real timetest results Section 6 comes the conclusion

2 Active Noise Control System Modeling forDuct-Like Applications

Schematic diagram of active noise control system for a duct-like application is shown in Figure 1The sound incident fromthe left noise source is picked up by the microphone and aftersome processing by the active noise controller this signal

is fed to the secondary sources (loudspeaker) such that tothe right side the primary signal and the additional signalcancel each other The noise source is located at 1198970 from oneend of the duct and an error sensor is located at 1198973 fromthe other end of the duct The secondary source is located at1198971 form the noise source The pressure reflection coefficientsin two ends are 1198771 and 1198772 respectively The primary pathbetween the noise source and the secondary source is 119875the secondary path between the secondary source and errorsensor is 119878

According the steady state travelling wave theory thefrequency response for secondary path and the primary pathcan be obtained as follows

119878 (119895119908)

=119867119904119867119890119890minus1198961198972 [1 + 1198631198901198772119890minus21198961198973] [1 + 1198631199041198771119890minus2119896(1198970+1198971)]

1 minus 11987711198772119890minus2119896119897

119875 (119895119908)

=119867119890119867119901119890minus119896(1198971+1198972) [1 minus 1198631198901198772119890minus21198961198973] [1 + 1198631199011198771119890minus21198961198970]

1 minus 11987711198772119890minus2119896119897

(1)

Here 119867119901 is the electroacoustic transfer function of thenoise source 119867119904 is the electroacoustic transfer function ofthe secondary source and 119867119890 is the electroacoustic transferfunction of the error sensor 119863119901 is the directivity factor ofthe noise source 119863119904 is the directivity factor of the secondarysource and 119863119890 is the directivity factor of the error source119896 = 119895120596119888 in which 120596 is angular frequency and 119888 is soundspeed For 119911-transform

119878 (119911) =119911minus1198992 [1 + 1198772119911minus21198993] [1 + 1198771119911minus2(1198990+1198991)]

1 minus 11987711198772119911minus119873

119875 (119911) =119911minus(1198991+1198992) [1 + 1198772119911minus21198993] [1 + 1198771119911minus21198990]

1 minus 11987711198772119911minus119873

(2)

Here 119899119894 is the integer near to 119897119894119891119904119888 here 119891119904 is samplingfrequency of the control system 119888 is the sound speed 119873 =2(1198990 +1198991 +1198992 +1198993) while the sound speed changes with timethe whole system becomes time varying

Unfolding (2)

119878 (119911) =119911minus1198992 + 1198771119911minus2(1198990+1198991+051198992) + 1198772119911minus2(051198992+1198993) + 11987711198772119911minus2(1198990+1198991+051198992+1198993)

1 minus 11987711198772119911minus119873

119875 (119911) =119911minus(1198991+1198992) + 1198771119911minus2(1198990+051198991+051198992) + 1198772119911minus2(051198991+051198992+1198993) + 11987711198772119911minus2(1198990+051198991+051198992+1198993)

1 minus 11987711198772119911minus119873

(3)

3 FULMS Algorithm

A block diagram of an adaptive IIR ANC system usingFULMS algorithm is illustrated in Figure 2The output signal

of the IIR filter 119910(119899) is computed as

119910 (119899) = a119879 (119899) 119909 (119899) + b119879 (119899) 119910 (119899 minus 1) (4)


x(n)P(z)

A(z) S(z)

d(n)

y(n) s(n) e(n)

+

LMS

LMS

B(z)

+

+minus

S(z)

S(z)

x998400(n)

y998400(n)


x(n)P(z)

W(z)

d(n)

e(n)+

FULMS

+

y(n)

Randomnoise

S(z)

+

FULMSf(n)

v(n)S(z)

S(z)

x998400(n)

998400(n)

y998400(n) + 998400(n)

minus

minus minus





a (119899 + 1) = 119886 (119899) + 1205831199091015840 (119899) 119890 (119899)

b (119899 + 1) = 119887 (119899) + 1205831015840 (119899 minus 1) 119890 (119899) (5)





119864119872minus1

sum119898=0

[119898 (119899) minus 119904119898 (119899)]2 asymp

12058321198721205902119906 (6)





120576119894 (119899) = 119890 (119899) minus 119904119894 (119899) (7)


119869119894 (119905) =119905

sum119895=0

119890minus120582(119905minus119895)1205762119894 (119895) (8)









S(z)

x(n)P(z)

A(z)

B(z)

d(n)

y(n)e(n)s(n)

+

LMS

LMS

+

+

Model bank

Whiteprocessv(n)

+

++

+

+

S(z)

S(z)

S(z)

x998400(n)

y998400(n)

S2(z)

S1(z)

Sm(z)sm(n)

s2(n)

s1(n)

1205762(n)

1205761(n)

120576m(n)

minus

minus

minus

minus

select




Amplifier

e(n)

TMS320F28335


Amplifier

Reference sensor

DA DA

l0 l3l2l1

R1R2







minus25minus2

minus15minus1

minus050

051

152

25

e (v)

1 2 3 4 5 6 7 8 9 100t (s)





02468

e (v)

1 2 3 4 5 6 7 8 9 100t (s)


1 2 3 4 5 60t (s)

123456

Mod

el


1 2 3 4 5 60t (s)

123456

Mod

el


1 2 3 4 5 60t (s)

1

2

3

4

5

6

Mod

el



6 Conclusion


10 20 30 40 50 600t (s)

minus3minus2minus1

0123

e (v)



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










x(n)P(z)

A(z) S(z)

d(n)

y(n) s(n) e(n)

+

LMS

LMS

B(z)

+

+minus

S(z)

S(z)

x998400(n)

y998400(n)


x(n)P(z)

W(z)

d(n)

e(n)+

FULMS

+

y(n)

Randomnoise

S(z)

+

FULMSf(n)

v(n)S(z)

S(z)

x998400(n)

998400(n)

y998400(n) + 998400(n)

minus

minus minus





a (119899 + 1) = 119886 (119899) + 1205831199091015840 (119899) 119890 (119899)

b (119899 + 1) = 119887 (119899) + 1205831015840 (119899 minus 1) 119890 (119899) (5)





119864119872minus1

sum119898=0

[119898 (119899) minus 119904119898 (119899)]2 asymp

12058321198721205902119906 (6)





120576119894 (119899) = 119890 (119899) minus 119904119894 (119899) (7)


119869119894 (119905) =119905

sum119895=0

119890minus120582(119905minus119895)1205762119894 (119895) (8)









S(z)

x(n)P(z)

A(z)

B(z)

d(n)

y(n)e(n)s(n)

+

LMS

LMS

+

+

Model bank

Whiteprocessv(n)

+

++

+

+

S(z)

S(z)

S(z)

x998400(n)

y998400(n)

S2(z)

S1(z)

Sm(z)sm(n)

s2(n)

s1(n)

1205762(n)

1205761(n)

120576m(n)

minus

minus

minus

minus

select




Amplifier

e(n)

TMS320F28335


Amplifier

Reference sensor

DA DA

l0 l3l2l1

R1R2







minus25minus2

minus15minus1

minus050

051

152

25

e (v)

1 2 3 4 5 6 7 8 9 100t (s)





02468

e (v)

1 2 3 4 5 6 7 8 9 100t (s)


1 2 3 4 5 60t (s)

123456

Mod

el


1 2 3 4 5 60t (s)

123456

Mod

el


1 2 3 4 5 60t (s)

1

2

3

4

5

6

Mod

el



6 Conclusion


10 20 30 40 50 600t (s)

minus3minus2minus1

0123

e (v)



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










S(z)

x(n)P(z)

A(z)

B(z)

d(n)

y(n)e(n)s(n)

+

LMS

LMS

+

+

Model bank

Whiteprocessv(n)

+

++

+

+

S(z)

S(z)

S(z)

x998400(n)

y998400(n)

S2(z)

S1(z)

Sm(z)sm(n)

s2(n)

s1(n)

1205762(n)

1205761(n)

120576m(n)

minus

minus

minus

minus

select




Amplifier

e(n)

TMS320F28335


Amplifier

Reference sensor

DA DA

l0 l3l2l1

R1R2







minus25minus2

minus15minus1

minus050

051

152

25

e (v)

1 2 3 4 5 6 7 8 9 100t (s)





02468

e (v)

1 2 3 4 5 6 7 8 9 100t (s)


1 2 3 4 5 60t (s)

123456

Mod

el


1 2 3 4 5 60t (s)

123456

Mod

el


1 2 3 4 5 60t (s)

1

2

3

4

5

6

Mod

el



6 Conclusion


10 20 30 40 50 600t (s)

minus3minus2minus1

0123

e (v)



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











02468

e (v)

1 2 3 4 5 6 7 8 9 100t (s)


1 2 3 4 5 60t (s)

123456

Mod

el


1 2 3 4 5 60t (s)

123456

Mod

el


1 2 3 4 5 60t (s)

1

2

3

4

5

6

Mod

el



6 Conclusion


10 20 30 40 50 600t (s)

minus3minus2minus1

0123

e (v)



Competing Interests


Acknowledgments


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









adaptive active noise suppression using multiple model...

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