Active Sound and Vibration Control: theory and applications Volume 25/3 || ANC for road noise attenuation

Chapter 14

Active noise .control for £oadbooming noise attenuation

Y. Park, H. S. Kim and S.H. OhDepartment of Mechanical EngineeringKorea Advanced Institute of Science and TechnologyScience Town, Taejon, Enail: [email protected]

This chapter presents an application of active noise control techniques for pas-senger comfort in cars. At the analysis stage nonstationary vibrations of thefront and rear wheels are generated by nonuniform road profiles and change ofvehicle speed. These propagate through the tyre and the complicated suspen-sion system and finally generate structure-borne noise, impulsive noise, andother low-frequency noise in the interior of the passenger vehicle. These noisesproduce acoustical resonance in the interior of the passenger car and such res-onant noise is called uroad booming noise". Cancellation of this noise is thetopic of this chapter.

14.1 Introdution

There axe several characteristics of road booming noise. Independent vibra-tions of the four wheels generate it, so it can hardly be reduced by ANC withjust one or two reference sensors. Second, the properties of road boomingnoise change as vehicle speed or road profile varies. And the system from thewheel vibration to road booming noise is not linear because of the complexityof the suspension system, nonlinear interaction between the structural vibra-tion and the interior acoustics etc. We want to compensate for road booming

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346 Active Sound and Vibration Control

noise, which has a strong correlation with the vibration signals measured atthe suspension system. Active noise control of road booming noise is ratherdifficult to achieve because of its nonstationary characteristics. We developeda multi-input multi-output constraint filtered-x least-mean-square algorithmusing an IIR-based filter. The proposed algorithm can track nonstationaryprocesses and concentrate the control efforts on the desired control frequencyrange which can be selected arbitrarily by the designers.

In a feedforward-type active noise control approach, a number of secondarysources (usually loudspeakers) are controlled to cancel the noise of the desiredspace. The physical principle of this approach is destructive interference ofacoustic waves. For active control of road booming noise, a set of referencesignals presumed to be the cause of the booming in the car interior is measuredfrom the car suspension system. This is natural, because the road inputsmust pass through the suspension system before they produce noise insidethe vehicle. Controller W(z) is inserted between these reference inputs andsecondary sources. Denoting the number of reference signals as N and thenumber of secondary sources as K, the controller W(z) is characterised by aiV-input if-output filter. If one locates M microphones in the desired quietzone to monitor the performance, the auxiliary system between the secondarysources and the measuring microphones can be represented as a K-input M-output secondary path H{z). If we let X(k) be the Nbyl reference vector, anddenoting the system from the reference to the error microphone as iV-input M-output plant P(z), the control problem becomes to find optimal W(z) whichminimises the M by 1 error vector E(k) = [P(z) + H(z)W(z)]X(k). If wechoose the cost function as E(k)TE(k) (the squared sum of the error signalfrom the M microphones) and construct W(z) as an FIR-based adaptive filter,we can get an MFX (multiple filtered-z) LMS algorithm [82]. The MFX LMSalgorithm has been a basic feedforward control algorithm in the active controlof road booming noise applications [93, 128, 208, 281, 282, 283].

There are some problems in applying the MFX LMS algorithm to the roadbooming noise attenuation application. The delay in the secondary path de-creases the upper limit of the convergence speed in this algorithm, and this maydegrade the performance considerably for nonstationary reference input cases,such as in road booming noise applications. In order to recover the convergencebound of the MFX LMS algorithm, a CMFX (constraint multiple filtered-:*:)LMS algorithm can be used [281]. The frequency band of road booming isusually fixed and is not greater than a few tens of hertz and is independentof driving speed. However, the FIR-filter-based MFX LMS algorithm tries tooptimise W(z) with equivalent weighting for all frequency ranges resulting in awaste of control effort. In this chapter, to overcome the aforementioned draw-


ANC for road noise attenuation 347

backs, a novel active noise control algorithm is proposed. Every SISO channelof W(z) is organised as a linear combination of the IIR base filters which aresecond-order narrow bandpass filters. The centre frequency of each IIR filtercovers the road booming frequency ranges. Also the error signals used for up-dating weights in W(z) are reconstructed to maximise the convergence speedas originally introduced in the CMFX LMS algorithm. To demonstrate theeffectiveness of the proposed algorithm to the road booming noise attenuationapplication, experiments are performed for a rough asphalt road profile.

14.2 Constraint multiple filtered-x LMS algorithm

When the noise to be attenuated is caused by several independent inputs suchas with road booming noise inside a car, it is necessary to deal with multiplereference signals to actively control the undesired noise. Each of the fourwheel vibrations due to irregular road surface excitation can be considered asan independent noise source. We can place multiple control sources and errormicrophones to enlarge the quiet zone or increase the noise reduction level.For this purpose the CFX LMS algorithm should be extended to a multi-inputmulti-output system. In CMFX LMS, the mth error em(k) and the constrainterror e'm{k) are:

em(k) = dm{k) + E E E E W»**(* - i)xn{k - i - j) (14.1)

e'm(k) = dm{k) + E E E E KkjWkrtiftxnVt -i-j) (14.2)n=l k=l j=0 i=0

where dm{k) is the undesired noise signal at the mth microphone, xn(k)is the nth reference and wkni is the ith coefficient of FIR-type adaptive filter

Wkn(z), i.e. Wkn(z) = £ Wkni(k)z~l the input of which is the nth referencei=0

and the output of which goes to the A;th control speaker. hmkj is the jthcoefficient of the secondary path Hmk(z), i.e. Hmk(z) = which is locatedbetween the A;th control speaker and the mth error microphone. The constrainterror ef

m(k) expressed in eqn. (14.2) cannot be measured directly, but can becalculated by modifying em(k) by eliminating dm(k) from eqns (14.1) and(14.2). Weights of CMFX LMS are updated by the steepest descent method.Derivation of the CMFX LMS algorithm which tries to minimise the costfunction e'l(k) 4- e'Kfy + * * * + 6 'M(^) *S straightforward and the results areshown in Table 14.1. The signal fxmkn(k) is a filtered signal of xn(k) through



Table 14.1 Constraint multiple filtered-x LMS algorithm

given xn{k), em(fc), n = 1,2, - •, AT, m = 1,2, - -, M at fc step

fxmkn(k) = £ hmkjxn(k - j)tf Lfc JV IT Z,

- £ £ hrnkjUkik - j ) + £ £ £ Wfcni(fc)/£mjfcn(fc - 0fc=lj=O n=lfc=li=O

= ^fcm(^) - 2fi £ e^(fc)/xmfcn(fc - z)m = l

AT Lyk\'") ~~ 2LJ 2LJ Wkfiiyfo)Jjiiyrv t/j

n=l t=0

the error path model Hmk(z). The CMFX LMS algorithm is different fromthe MFX LMS algorithm only in that it uses e'm(fc) instead of em(k).

14.3 Constrained multiple filtered-x LMS algorithm usingan IIR-based filter

We consider an adaptive filter W(z) consisting of a linear combination of stableIIR filter bases the impulse responses of which are exponentially developedsinusoidal functions. Let us define Bi(z) as one of these filter bases. Toconsider L frequency components in an IIR-based filter, there must be 2L IIRfilter bases of B{(z). Each IIR base can be expressed in the discrete timedomain as follows:

where

cos u)

Denoting ynk(k) as the control output to the fcth secondary source due to thenth reference input, the control output to the fcth secondary source denotedas yk(k) can be obtained as the summation of ynk(k) for n = 1,2, • • •, N asfollows:



Table 14,2 IIR-based constraint multiple filtered-x IMS algorithm

Uni(k) = Bi(z)Xn(k)

fxmkn{k) = £ hmkjXn(k-j)j=0

= B i ( z ) f x m k n ( k )

e'm(k) = e m (fc) - E E h m k j y k ( k - j ) + E E E wTkni(k)fumkni{k)

fel j 0 n = l f t l « OM

jU E e'm(k)fumkni(k)m=l

= E E wL(*)«»(*)n=l t=0

»*(*) = E ynk(k) (14.5)n=l

where

ynk(k) = Ewlni(k)uni(k) (14.6)

ft(^B(*) (14.7)

Scalar controller coefficients wkni(k) are adaptive weights of uni(k) which is theith IIR filter output of xn(k). The proposed IIR-based filter has an infiniteimpulse response, but it does not have any nonlinearity or instability problemson updating filter weights unlike the conventional adaptive IIR filters. So,it is easy to model a lightly damped system with an IIR-based filter. TheIIR-based CMFX LMS algorithm is summarised in Table 14.2, and its blockdiagram representation is shown in Figure 14.1.

14.4 Experimental results

To carry out an experiment, four acceleration signals (y and z directions oftwo front wheels) and acoustic pressure signals from two microphones nearthe headrest of the two front seats were used as the reference signals and theerror signals, respectively. We developed an ANC system of four references,two secondary speakers and two error microphones. The test car was a Sonata



Figure 14.1 Block diagram of CMFX LMS algorithm using IIR base B(z)



II from Hyundai with a 2000 cc engine. ANC was performed while drivingon a rough asphalt road with 60 km/h speed. Four reference signals werelowpass filtered with a cut-off frequency of 500 Hz and then A/D convertedalong with two microphone signals which are considered as undesired noiseD(k). The sampling frequency was 1000 Hz, and four secondary paths wereidentified using two secondary speakers located behind the front seats. ADSP board equipped with a TMS320c40 chip was used. After several drivingtests on various road profiles, changing the vehicle speed from 40 up to 80km/h, it was found that road booming frequency in our test vehicle is about250 Hz with a 15 Hz bandwidth. FIR adaptive filter lengths and the FIRmodel for the secondary path were 130 and 50, respectively. 18 IIR bases withcentre frequencies of 230, 235, 240, 245, 250, 255, 260, 265 and 270 Hz anddamping coefficient of <7j =25 were selected. The length of the FIR filter couldnot be increased to more than 130 because of the calculation power limit ofDSP hardware, although the filter length for one secondary source and oneerror microphone configuration could be increased up to 300. The overallexperimental setup is given in Figure 14.2.

The attenuation of the overall level of the A-weighted spectrums is plottedin Figure 14.3. The spectrum of e(k) before ANC, after ANC using con-ventional CMFX and using an IIR-based one are represented with a dottedline, solid line, and thick solid line, respectively. No remarkable reduction isachieved by using the conventional CMFX LMS algorithm, and even an in-crement of the noise level is observed. This is because the signal power of theroad booming component in the error microphone signal before A-weightingis significantly smaller than that of the noise component under 200 Hz. Thereason for the poor performance of the CMFX LMS is thought to be due to theshort weight length used; another important reason is that the FIR filter triesto treat all frequency ranges with more weighting for higher power componentsin the error signal in the least-squares sense. The power under 200 Hz is dom-inant from the microphone signal in the car interior and adaptive filters willtry to attenuate these components first. Since there is low coherence betweenreferences and error signals in this frequency range, weights of the adaptivefilter fluctuate rapidly consuming a lot of the control effort. The effort to at-tenuate road booming near 250 Hz is comparatively very small despite highercoherence than in other frequency ranges. These make the performance ofCMFX LMS worse in this application. 5-7 dB reduction was achieved at roadbooming frequency region (around 250 Hz) when the IIR-based filter was used.There is no considerable change of noise level out of the booming frequencyrange where IIR bases are not located. Because of the road booming noisecharacteristics, the CMFX LMS algorithm using an FIR filter tries to reduce



Four references

(left front y, z, right front y,z)

Low pass and A/D D/A, Low pass and Amp.

Figure 14.2 Experimental setup



the low-frequency range and little sound attenuation is achieved, whereas theIIR-based filter reduced noise effectively in the range of the road boomingfrequency.

14.5 Conclusions

Road booming noise of a vehicle is a naturally time varying signal due to thechange of vehicle speed and road profile and it appears in a certain frequencyrange which is not wideband. The conventional CMFX LMS algorithm becauseof its characteristics achieves little sound attenuation of nonstationary roadbooming noise. So, an IIR-based filter incorporating a stable and narrowbandpass IIR filter is proposed to effectively reduce the road booming noisein a passenger vehicle. With the IIR-based filter, it is possible to controlundesired noise only in a selected frequency range and enhance the controlefficiency in road booming noise control. To compare the performance of thealgorithm using the IIR-based and the conventional FIR filter, an experimentwas performed. Driving the rough asphalt with constant 60 km/h speed, weattenuated the noise in the headrest areas of the two front seats with two errormicrophone, two control speakers and four references which are accelerationsignals near the suspension system. In the experiment, it is difficult to achievenoise reduction with the FIR adaptive filter, however, 5-7 dB reduction ofnoise in booming frequency range was achieved with the IIR-based filter. Ifthe desired control frequency range is not wideband such as in the case of roadbooming noise, the IIR-based filter is more effective than FIR filter and thisis verified by the experiment.

14.6 Acknowledgments

The authors would like to express appreciation to Hyundai motor companyand KATECH for their financial support.



-80'

-90'

Asphalt road (error rhic. #1)'Befor controlAfter control(CMFX LMS)After control(CMFX LMS with MR based filter)

100 200Hz

300 400

-90"

Asphalt road (error rhic. #2)Befor control

• After c6ntrol(CMFX LMS)-After control(CMFX LMS with MR based filter)

100 200Hz

I

300 400

Figure 14.3 Experimental results for rough asphalt road at (a) right-handfront seat and (b) left-hand front seat with two different adaptivefilters


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Active Sound and Vibration Control: theory and applications Volume 25/3 || ANC for road noise attenuation