EQUALIZED ALGORITHM FOR A TRUCK CABIN ACTIVE NOISE CONTROL SYSTEM

EQUALIZED ALGORITHM FOR A TRUCK CABIN ACTIVE NOISE CONTROL SYSTEM Guangrong Zou, Maro Antila, Antti Lanila and Jari Kataja Sart Machines, VTT Technical Research Centre of Finland P.O. Box 00, FI-0 Tapere, Finland guangrong.zou@vtt.fi, aro.antila@vtt.fi INTRODUCTION The noise inside a truc cabin is caused by various sources such as the engine, transission, wheel vibrations, wind, and soe other external sources. In general, the interior noise of vehicles is coposed of two coponents: one is synchronized with the engine rotation or other periodic noise, while the other is caused by stochastic sources []. For ost idsized trucs with an in-line four-cylinder engine, periodic noise is the doinant part of the internal noise. Such periodic noise is a cobination of the haronic noise coponents, also nown as noise orders. Furtherore, the order frequency range is relatively low, typically below 500 Hz. That aes Active Noise Control (ANC) effective in attenuating the order-related noise. The ost coonly used strategy is narrowband feedforward ANC with a Filtered-x Least Mean Squares (FXLMS) algorith []. The FXLMS algorith, first derived by Widrow in 98, has been used successfully for any applications, such as broadband noise in an enclosure [2], single frequency noise in a duct [], ultiple frequency noise in a helicopter [4], and tievarying noise in a tractor [5]. As the speed of truc engine changes, the order frequencies change continuously during operation. That coproises the overall perforance of the ANC syste because the FXLMS approach exhibits the frequency-dependent convergence behavior. Although several variations to the FXLMS algorith have been developed in an effort to overcoe the perforance degradation, their drawbac is that they either increase the coputational burden of the algorith or add the algorith s coplexity. Recently, a new approach nown as the Eigenvalue Equalization Filtered-x Least Mean Squares (EE-FXLMS) algorith has been developed by Thoas et al. [6], and already been proven effective to overcoe the frequency dependent perforance, and to iprove the overall perforance in the desired frequency range [6], [7], [8]. More iportantly, the ipleentation of the equalized algorith is straightforward and only inor odifications are needed to the existing FXLMS algoriths. In this paper, a narrowband feedforward ANC syste for a truc cabin is presented. A noral FXLMS algorith and an equalized FXLMS algorith based on the forer case are ipleented, and the perforance of the approaches is copared experientally. 2 THE ACTIVE NOISE CONTROL SYSTEM Based on a real truc cabin provided by Dongfeng Motor Copany (DFL) fro China, the recordings of the noise data at all relevant driving speeds are easured and analyzed [9]. According to the results, at each gear, the ost doinant periodic coponent throughout the range is the 2nd order, the firing frequency of the engine. There are also other two orders which are clearly detectable orders in the spectra, the 4th and the 6th orders. As suggested [8], the orders 2, 4 and 6 are attenuated consequently as uch as possible in the practical ANC

syste. For the periodic noise caused by an engine, narrowband feedforward techniques are effective in reducing repetitive noise. Instead of using an acoustic reference sensor, a tachoeter is eployed to provide inforation about the engine speed. Thus, the reference signal will not be affected by the outputs of the secondary sources. This is useful for the practical attenuation in a real vehicle cabin since ANC will not be affected by vehicle warnings, radio or speech. Furtherore, in order to achieve an adequate attenuation of the noise in both the driver s and co-driver s positions, a ulti-channel ANC syste is needed. In principle, the nuber of secondary sources needed to obtain perfect sound cancellation in the enclosure is the sae as the nuber of acoustic odes being excited []. As shown in Figure, a -channel narrowband feedforward ANC syste with the tachoeter input is constructed [9]. The realization of the ANC syste is done with loudspeaers and icrophones, with an additional subwoofer to handle the low frequency coponents. The control algoriths developed with Siulin are ipleented on a Texas Instruents TMS20C67 DSP processor. The control unit in use has been specially developed for an Active Noise Profiling (ANP) syste [0]. Measureent equipent Measureent signal Error sensors () onitor icrophone loudspeaers () Subwoofer Recorded signal tachoeter signal priary excitation (loudspeaer) control syste Figure. The siplified diagra of the ANC syste inside the truc cabin [9]. PRINCIPLE OF THE FXLMS ALGORITHM A -channel narrowband feedforward ANC syste was constructed to attenuate the noise inside the truc cabin. As for the narrowband ipleentation all order references are generated fro a tachoeter signal x(n), the ANC syste has references, secondary sources, and error sensors. Fro the control point of view, the syste is a xx Multi- Reference Multiple Input Multiple Output (MR-MIMO) syste. A siplified bloc diagra of this MR-MIMO ANC syste is illustrated in Figure 2. The variable t is used as a discrete tie index and the variable z is used as a discrete frequency doain index. A single-reference signal x(t) is used for all the three adaptive filters. Vector e(t) 2

represents the outputs of the error icrophones and y(t) is the actual output of the filters driven by the reference input signal. The atrix is fored by the estiates of the secondary paths fro the secondary loudspeaers to the error icrophones and x (t) is the filtered reference signal. x(t) P d(t) w(z) y(t) S y (t) e(t) + LMS x (t) 9 Figure 2. Siplified bloc diagra of the -channel ANC syste. The control filter updated equation for the vector w can be expressed as ( t + ) = w( t) µ X ( t) e( t) w () This equation can also be partitioned into equations as ( t ) = w ( t) + x () te () t, =,2, w + µ (2) = where µ is the step size of the th filter, vectors e (t) and w (t) are defined as T ( t) = [ e ( t), e ( t ),, e ( t L + ) ] e L w T ( t) [ w w, L w ] = 0,, ( L ) and L is the length of the adaptive filters. The filtered reference signal vectors of the reference atrix X (t) are defined as () (4) () t = sˆ () t x() t = sˆ ( t) x( t i),,,2, x L i=, i = (5) 4 EQUALIZED ALGORITHM As the periodic noise is tie-varying, to achieve a reasonable reduction of the noise inside the truc cabin, a fast algorith to adapt the adaptive filter coefficients is essential to provide a cancelling signal that tracs under rapidly changing conditions. One of the ain treatents to get the optial convergence speed is to adjust the step sizes of the filters. But, because of the frequency-dependent convergence behavior of the FXLMS algorith, it is difficult to get a fast convergence speed in the overall frequency range without the syste becoing unstable. This can be understood better with the autocorrelation atrix of the filter-x signal, which is largely a function of the estiate of secondary paths. The autocorrelation atrixes of the filtered-x signal of different filters are defined as

R T [ x ( t) x ( t) ],, =,2, = E (6) As already entioned in Reference [], the range of the chosen step sizes of the control syste is liited by the following equation 2 0 < µ <, =,2, (7) λ ax and the Mean Square Errors (MSE) tie constant of the adaptive process can be bounded as where λ ax and in λax τ se T (8) λin λ are the axiu and iniu eigenvalues of the autocorrelation atrix for the filtered-x signal in the overall target frequency range. Thus, the convergence speed of the FXLMS algorith is dependent on the axiu eigenvalue and the eigenvalue spread (the ratio of the axiu to iniu eigenvalues) of the autocorrelation atrix R. Since it is difficult to get a precise estiate of the secondary paths, the eigenvalues λ ax and λ in are also difficult to calculate. In order to reduce the spread of eigenvalues, soe equalization process needs to be done to the filtered reference signals. In Reference [6], the equalized FXLMS algorith reoves the variance in the eigenvalue by changing the agnitude coefficients while preserving the phase of (z). Another approach uses genetic algorith to find the agnitude coefficients that give the least variation in eigenvalues of the autocorrelation atrix [8]. As a straightforward way, the equalized FXLMS algorith was used to flatten the agnitude coefficients. After an offline syste identification process, the equalization is also done offline before the real-tie ANC operation. For ulti-channel systes, the process is repeated for each estiate of the secondary paths. The plots in Figure show the agnitudes and phases of the original and odified secondary path estiates. The pea agnitude is reduced to /5 of the original and the overall agnitude has been considerably flattened, while the phase reains alost the sae. This decreases the axiu eigenvalue and also the eigenvalue spread. As a result, the step sizes of adaptive filters ay be increased and the robustness and stability of the ANC syste is iproved. Furtherore, as an offline process, it adds no coputational burden to the standard algorith when the ANC syste is running. Figure. Original and odified coefficients of the secondary path estiate. 4

5 EXPERIMENTAL RESULTS Based on the constructed -channel ANC Syste, the experients with both algoriths with the noise recorded inside the real truc cabin were carried out. The recordings were ade at several engine rotational speeds, fro 600 RPM to 000 RPM. Control syste was set to attenuate the doinant orders 2, 4 and 6. Table shows the optial step sizes for the equalized FXLMS algorith can be even 20 ties larger than for noral FXLMS algorith. With the larger step sizes the faster convergence speed can be achieved, which is iportant while attenuating the tie-varying noise in practice. Table. The noralized optial step size of the algoriths in different RPM. Step sizerpm Algorith 600 90 560 920 2400 000 Noral Algorith EE Algorith 8 8 20 7 6 5 Figure 4 shows the easured SPLs with a onitor icrophone at driver s position at 560 RPM. The green curve represents the noise without the ANC treatent. The purple and blue curves represent the treated noise with the noral FXLMS algorith and the equalized algorith, respectively. 00.000 dbv 90.000 ANC_OFF_Original_Noise ANC_ON_NB_Algorith ANC _ON_EE_Algorith NB_FXLMS Attenuation =.2 db EE_FXLMS Attenuation = 4. db 80.000 70.000 SPL (db) 60.000 50.000 40.000 0.000 20.000 0.00 Hz 0.00 Hz 50.00 Hz 70.00 Hz 90.00 Hz 0.00 Hz 0.00 Hz 50.00 Hz 70.00 Hz 90.00 Hz 20.00 Hz Frequency (Hz) Figure 4. The attenuations of different algoriths for the ANC syste at 560 RPM. As shown in Figure 4, the frequencies of the 2nd, 4th and 6th orders are at 52 Hz, 04 Hz and 56 Hz, respectively. Both algoriths have achieved large attenuations at these frequencies. Especially at 52 Hz, the attenuations are ore than 20 db. At the overall frequency range 5

fro 0 Hz to 20 Hz, the achieved attenuation by the noral FXLMS algorith is.2 db, and the attenuation of the equalized FXLMS algorith reaches 4. db. On average, the equalized FXLMS algorith perfored. db better than the noral one. 6 CONCLUSIONS Based on the constructed -channel ANC syste for a truc cabin, the optial perforances of two different FXLMS algoriths are evaluated with the recorded noises. In coparison to the noral FXLMS algorith, the equalized algorith has the faster convergence speed and iproved noise attenuation. Especially, the equalized algorith has achieved 5-ties faster convergence speed and db better perforance than the noral FXLMS algorith. Moreover, the equalized algorith did not increase the online coputational load. Because of the iproved perforance, the equalized FXLMS algorith is ore effective than the noral FXLMS algorith for the practical use in truc cabins. ACKNOWLEDGEMENT The results presented in this paper are based on the wor carried out in European FP 6 MCAproject Sart Structures (MRTN-CT-2006-05559) and the VTT-DFL joint research project, which are gratefully acnowledged. REFERENCES. KUO S M & MORGEN D R, Active noise control systes: algoriths and DSP ipleentations. John Wiley and Sons, Inc, 996. 2. PARK Y C & SOMMERFELDT S D, Global attenuation of broadband noise fields using energy density control. J Acoust Soc A 0, 997, 50 59.. BURGESS J C, Active adaptive noise control in a duct: A coputer siulation. J Acoust Soc A 70, 98, 75 726. 4. BOUCHER C C, ELLIOTT S J & BAEK K H, Active control of helicopter rotor tones. Proceedings of the INTER-NOISE 96, 996, 79 82. 5. FABER B & SOMMERFELDT S D, Global control in a oc trac cabin using energy density. Proceedings of the ACTIVE 04, 994. 6. THOMAS J K, LOVSTEDT S P, et al., Eigenvalue equalization filtered-x (EE-FXLMS) algorith applied to the active iniization of tractor noise in a oc cabin. Noise Control Eng. J. 56 (), 2008, 25 4. 7. THOMAS J K, LOVSTEDT S P, et al., Eigenvalue equalization filtered-x algorith for the ulti-channel active noise control of stationary and non-stationary signals. J Acoust Soc A 2 (6), 2008, 428 4249. 8. LOVSTEDT S P, et al., Genetic algorith applied to the Eigenvalue Equalization Filteredx LMS algorith (EE-FXLMS). Advanced in Acoustics and Vibration, 2008, 2. 9. ANTILA Maro, HAO Y, et al., Possibilities and benefits of Active Noise Control (ANC) in truc cabins. Proceedings of the INTER-NOISE 2008, 2008. 0. ANTILA Maro, LANKILA Antti, Application-oriented developent of an Active Noise Profiling control syste. Proceedings of the INTER-NOISE 2008, 2008. 6