Proceedings of Meetings on Acoustics

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1 Proceedings of Meetings on Acoustics Volume 9, 23 ICA 23 Montreal Montreal, Canada 2-7 June 23 Signal Processing in Acoustics Session asp: Array Signal Processing for Three-Dimensional Audio Applications I asp8. Aircraft sound environment reproduction: Sound field reproduction inside a cabin mock-up using microphone and actuator arrays Philippe-Aubert Gauthier*, Cédric Camier, Olivier Gauthier, Yann Pasco and Alain Berry *Corresponding author's address: Mechanical engineering, Groupe d'acoustique de l'université de Sherbrooke, 25 boul. de l'université, Sherbrooke, JK 2R, Québec, Canada, philippe_aubert_gauthier@hotmail.com Sound environment reproduction of various flight conditions in aircraft cabin mock-ups is useful for the design, demonstration and jury testing of interior aircraft sound quality. To provide a faithfully perceived sound environment, time, frequency and spatial characteristics should be preserved. Physical sound field reproduction approaches for spatial sound reproduction are mandatory to immerse the listener in the proper sound field so that localization cues are recreated. A 8-channel microphone array was built and used to capture a 2-hour recording of in-flight sound environments within an actual Bombardier CRJ aircraft. An instrumented cabin mock-up was used to reproduce, in the least-meansquare sense, the recorded sound field using a 4-channel trim-panel actuator array. In this paper, experiments with multichannel equalization are reported. One of the practical difficulties was related to the use of the trim panels as sound sources. Windows and trim panels introduce audible squeaks and rattles if driven at low frequencies. Bass management was therefore implemented. Floor shakers and a subwoofer were used to recreate the low frequency content while the trim panels were only used for the high frequency range. The paper presents objective evaluations of reproduced sound fields. Results and practical compromises are reported. Published by the Acoustical Society of America through the American Institute of Physics 23 Acoustical Society of America [DOI:.2/ ] Received 2 Jan 23; published 2 Jun 23 Proceedings of Meetings on Acoustics, Vol. 9, 558 (23) Page

2 INTRODUCTION Sound quality and noise annoyance are sometimes oversimplistically described by sound pressure level or more complex psychoacoustic metrics that remain numbers only meaningful to specialists (Powell and Fields, 995). The possibility to conduct sound quality and noise annoyance studies in laboratory conditions represents an interesting avenue for vehicles manufacturers and researchers. Early work dedicated to sound reproduction or synthesis of vehicles for sound quality or annoyance studies seems to be the NASA ANOSS project (McCurdy and Grandle, 987). Recently, Janssens et al. (28) and Berckmans et al. (28) investigated analysis and synthesis algorithms for aircraft interior and exterior sounds. In these studies, the spatial character of sound reproduction is not a primary aim. However, it is known that spatial distribution of sound sources influences auditory masking and, therefore, the overall sound quality. In our case, we focus on spectral and spatial quality of the sound. The aim is the reproduction of an aircraft cabin sound field, namely, a target sound field, inside a full-scale mock-up of the cabin. In preliminary experiments (Gauthier et al., 22), both the target and reproduced sound fields were generated and measured in laboratory conditions: the target sound field was created using four loudspeakers outside the mock-up to simulate an external excitation. Reproduction was achieved using multichannel equalization based on pseudo-inversion and least-mean-square methods with Tikhonov regularization to drive trim-panel actuators. In this paper, we investigate similar types of algorithms but driven by real in-flight recordings. Effects of the regularization parameter and crossover frequency on the objective performance are reported. AIRCRAFT SOUNDS AND MULTICHANNEL EQUALIZATION Except for transitional stages such as taxi, take-off, landing, engine starts, flaps operations, most of the aircraft sounds as heard in passenger cabins are stationary, at least from frame and perceptive viewpoint (Verron et al., 2; Langlois et al., 2). For fixed flight conditions and aircraft configurations, the resulting sound environment is mostly made of emerging stationary tones and filtered noise with stationary spectral envelop (Ploner-Bernard et al., 25; Verron et al., 2). Tones result from rotating machinery while broadband noises are created by the turbulent boundary layer on the fuselage, engine jet noise and the air climate system (Mixson and Wilby, 995; Wilby, 996). In this paper, we investigate sound field reproduction of these stationary sounds measured in-flight. To illustrate these signal assumptions, a typical aircraft sound as recorded at a single position in a Bombardier CRJ9 is shown in Fig.. Note that absolute physical units are deliberately not presented in this paper. As shown in Fig., the sound pressure level is stationary. Figs. and (c) show the overall loudness (Zwicker and Fastl, 999) as function of time and the signal spectrogram. On the basis of the signal spectrogram, the aforementioned assumptions are verified. Although the sound field reproduction methods and multichannel signal processing presented in this paper do not rely on signal stationarity hypothesis, the fact that the investigated sound fields are stationary circumvents known issues encountered in single channel or multichannel equalization algorithms based on system inversion, i.e. audible artifacts such as pre- and post-echoes (Gauthier et al., 22) or ringing. However, for broadband and sufficiently stationary sounds considered from a frequency domain viewpoint, pre- and post-echoes as found in the equalization filter matrix are masked by the stationary nature of the sounds under test. Loudness, spectrogram and power spectal densities (PSD) were computed using a commercial software. The recorded microphone signal was filtered by high-pass filters with cut-off frequency at 2 Hz. Loudness versus time was computed using FFT according to standard ISO 532 B with: Hanning window, FFT size of 6384 samples, overlap of 75 %. The Proceedings of Meetings on Acoustics, Vol. 9, 558 (23) Page 2

3 FIGURE : Typical aircraft cabin sound. : Sound pressure level versus time, Loudness versus time, (c) Power spectral density versus time and (d) Average power spectral density from a 4-second sample. PSD and PSD versus time were computed on the basis of 6384-sample frames, Hanning window and 75 % overlap. SIGNAL PROCESSING: MULTICHANNEL SOUND FIELD REPRODUCTION The signal processing is represented in Fig. 2 as a block diagram in the frequency domain. A microphone array was used for the capture and evaluation of the target and reproduced sound fields, respectively. Reproduction sources inside the cabin are used for sound field reproduction. e jωδ ˆpe jωδ ˆp s r, ˆr + Ĝ # [k] G[k], L Ĝ[k] M ê M M E[k], Ê[k] FIGURE 2: Block diagram of the sound field reproduction system and signals. The plant including the reproduction sources, the vibroacoustic responses of the mock-up and the microphone array is described for each frequency bin k =,,..., N by a complex matrix G[k] C M L where M is the number of microphones, L the number of reproduction sources for the frequency bin k under consideration and N is the number of points in the frequency domain. The measurement of G will be denoted Ĝ (measured quantities are indicated by ˆ ). The multichannel equalization filter is denoted by a complex matrix Ĝ# [k] C L M. This filter transforms, by matrix multiplication, the M measured and digitized target signals in the frequency domain ˆp[k] C M into L digital transducer signals s[k] C L. This is written as follows s = Ĝ# ˆp. () Ideally, the combination of the equalization filter with the actual plant should lead to a white and decoupled system E[k] with a modeling delay of Δ samples E = GĜ# Ie jωδ, with ω 2π, the normalized angular frequency, and ω = 2πk/N. Matrix E C M M represents the Proceedings of Meetings on Acoustics, Vol. 9, 558 (23) Page 3

4 equalized system. The modeling delay is introduced to ensure that the equalization filters Ĝ# are causal. Any deviation of the equalized system E from the identity matrix with additional modeling delay e jωδ will lead to reproduction errors. The measured target sound field at the microphone array is denoted by ˆp C M and r[k] C M is the reproduced sound field at the microphone array with r = E ˆp = Gs and s = Ĝ# ˆp. The measurement of the reproduced sound field r in the cabin mock-up will be denoted ˆr. An ideal physical reconstruction of the sound field would lead to ˆr = r = ˆpe jωδ. A useful physical quantity is the reproduction error vector at the microphone array ê[k] C M = ˆpe jωδ ˆr. One way to circumvent the limitation of the brute-force inversion approach to the aforementioned problem (Ĝ# = Ĝ+ e jωδ, with + denoting pseudo-inversion) is to include a regularization of the solution norm in a least-mean-square reproduction error minimization. The solution is defined by (Gauthier et al., 22) s = argmin{ Ĝs e jωδ ˆp λ2 s 2 2 } (2) where the amount of regularization is controlled by the penalization parameter λ. Vector 2-norm is denoted by 2. We assume that λ is fixed for all frequencies. The solution of Eq. (2) is given by s = (ĜH Ĝ + λ 2 I) Ĝ H e jωδ ˆp, (3) and the equalization matrix is Ĝ # = (ĜH Ĝ + λ 2 I) Ĝ H e jωδ. (4) The penalization enhances the main diagonal of the denominator matrix, hence preventing the instability of the inversion and reducing the solution 2-norm s 2 2. EXPERIMENTAL SETUP: MICROPHONE AND TRANSDUCER ARRAYS The target sound fields have been recorded by a planar microphone array in single 2-hour flight aboard a CRJ9 jet aircraft in various conditions. This microphone array was described in an earlier paper (Gauthier et al., 22). The microphone array is made of 8 electret microphones and preamplifiers. The array installed in the aircraft cabin for the actual in-flight recording is shown in Fig. 3. The array configuration is based on a uniform rectangular grid array with additional variation over two layers along the vertical axis to distinguish propagating directions in the vertical direction. The approximate microphone-to-microphone distance is 2.5 cm so that spatial aliasing should be avoided up to.4 khz at the microphone array. FIGURE 3: In-flight recording with 8-channel microphone array (back), binaural manikin (right, front), 32-channel spherical microphone array (right, back), reference microphones (not shown) and accelerometers (not shown). The cabin mock-up is shown in Figs. 4 and 5. It models a Bombardier CRJ9 with 8 seats and 6 windows. Mock-up details are given in (Gauthier et al., 22). The main Proceedings of Meetings on Acoustics, Vol. 9, 558 (23) Page 4

5 reproduction transducers are 32-mm inertial actuators mounted on internal trim panels. Four of these actuators are mounted on each of the 9 trim panels. To induce vibration in the floor, 4 bass shakers are attached to the wood floor. A subwoofer is included. Actuators positions are shown in Fig. 4. The microphone array inside the cabin mock-up is shown in Figs. 5 and. The microphone array is identical to the one used for the in-flight recording (see Fig. 3). In the mock-up, the microphone array has two purposes: ) identification of the plant Ĝ and 2) measurements of the reproduced sound fields..5 x 3 [m].5 2 x [m] x 2 [m] FIGURE 4: Exterior view of the mock-up. In this paper, the external loudspeakers are not used. Geometrical arrangement of the trim-panel and floor actuators inside the mock-up. x 3 x 2 x FIGURE 5: Microphone array in the mock-up. Configuration of the 8-channel microphone array. The 328 (4 actuators 8 microphones) frequency response functions of the plant matrix Ĝ were measured with the logarithmic swept sine method using 2 averages for the trim panel actuators and 4 for the floor shakers and the subwoofer. The amplitudes of the swept sines were adjusted to avoid audible rattles or non-linear distortions caused by the trim panels. The resulting system was stored in matrices that include all these FRFs and IRs with zero-padding up to 24 samples (.5 seconds). The modeling delay Δ was set to 2 samples. The 4 floor shakers and subwoofer are in charge of reproducing the low frequency range of the target sound field at 4 of the microphones while the 36 trim-panel shakers must reproduce the remainder of the audio bandwidth over the 8 microphones. For most of our previous experiments, the crossover frequency was 22 Hz and was achieved using simple low-pass and high-pass 4th-order Butterworth filters (Gauthier et al., 22). We used forward and reverse filtering to ensure that the phases of the crossover filters are linear. This also gives a -6 db gain Proceedings of Meetings on Acoustics, Vol. 9, 558 (23) Page 5

6 at the cut-off frequency so that there is no amplification at the crossover frequency once the low-frequency and high-frequency range systems are combined. In this paper, we investigate a finer definition of an optimal crossover frequency that provides a better transition from the low to the high frequency ranges using similar high-pass 4th-order Butterworth filters. EXPERIMENTAL RESULTS: OBJECTIVE EVALUATION To quantify sound field reproduction at the microphone array in the frequency domain, several metrics are introduced. These metrics are defined in the discrete frequency domain k where signal spectra are represented by one-sided modified periodograms obtained using Welch s method and Hanning window. For the reported experiments, the modified Welch periodograms were evaluated with a Fourier transform size of 892 samples, an overlap of 5 % and a Hanning window. The averaged and normalized reproduction error is [k] = ê[k] 2, (5) ˆp[k] 2 it describes, on the average, how accurately the sound field is reproduced over the microphone array. = means a perfect reproduction. To quantify the reproduced sound environment with respect to timbre, the averaged magnitude spectrum error is defined in db ref / Hzby [k] = log ˆp[k] log ˆr[k] 2 /M, (6) it represents the reproduction error in terms of power density function of the measured ˆp[k] and reproduced ˆr[k] sound environments, i.e. it does not take into account the spatial distribution of the phase but only the spatial distribution of sound pressure amplitude. In Eq. (6), absolute value and log are elementwise. The source signal 2-norm is given by S LS [k] = s[k] 2. (7) In this paper, two parametric studies are reported: effect of regularization parameter λ and crossover frequency. As mentioned in (Gauthier et al., 22), the bass management was initially introduced to circumvent the presence of squeaks and rattles in the trim panels if driven by strong low frequency content. However, in this paper, the test sounds derived from real in-flight recording implied significant squeak and rattle noises in reproduction experiments. Therefore, for the parametric studies and objective evaluations of the signal architecture reported in this paper, the original microphone array signals were artificially reduced in amplitude to minimize any squeaks and rattles. This highlights the fact that sound field reproduction inside aircraft cabin mock-ups using vibration transducers should rely on high-quality materials and careful assembly of the trim panels. These considerations should be addressed at the design stage of the mock-up regrouping engineers and technicians in charge of mock-up fabrication. Results: Effect of regularization From theory and Eq. (2), it is expected that a smaller λ should give smaller reproduction errors. True in theory, it is not exactly true in practice: a small regularization parameter λ increases the reproduction source signals and may lead to a large reproduction error if the digital-to-analog converters saturate or if squeaks and rattles in the trim panels introduce non-linear distortions. Here we investigate the effect of λ on the objective performance of reproduced sound field at the microphone array. Results for the low-frequency system are shown in Fig. 6 while results for the high-frequency system are shown in Fig. 6. We conduct separate studies for the two frequency ranges since non-linear distortions in one frequency range might degrade the sound field reproduction in the other range. The best results, in terms Proceedings of Meetings on Acoustics, Vol. 9, 558 (23) Page 6

7 of and, are obtained with λ = and λ =. for the low and high frequencies, respectively. For the high-frequency range, it is interesting to note the sudden increase in and for the smallest regularization parameter (λ = ), this typically corresponds to emerging squeaks and rattles. From Fig. 6, one can also note that on the average the metric is below db/hz and is relatively flat for the broadband noise. Fig. 7 shows the corresponding power spectral densities. S LS [db ref / Hz] S LS..4.7 Frequency [Hz] S LS [db ref / Hz] S LS Frequency [Hz] FIGURE 6:, and S LS for various λ. The crossover frequency was set to 22 Hz and is shown as a thick dashed vertical line. : Low frequency range, : High frequency range. Welch Power Spectral Density Estimate at Mic #4, ygrid: Δ 2 db Welch Power Spectral Density Estimate at Mic #4, ygrid: Δ 2 db Power / Freq. [db ref / Hz]) Target..4.7 Freq. [Hz] Power / Freq. [db ref / Hz]) Target Freq. [Hz] FIGURE 7: Example of power spectral density of the target and reproduced sound fields for microphone #4. : Low frequency range, : High frequency range. Results: Effect of crossover frequency In this section, we look for a better crossover frequency to improve the transition from the low- to the high-frequency range, corresponding to a change of the plant dimension (from 5 Proceedings of Meetings on Acoustics, Vol. 9, 558 (23) Page 7

8 transducers and 4 microphones in the low-frequency range to 36 transducers and 8 microphones in the high-frequency range). Results obtained when changing the crossover frequency in the equalization matrix obtained with optimal λs as identified earlier are shown in Fig 8. The best crossover frequency is 4 Hz. Using this new crossover frequency and best regularization parameters, an example of power spectral density at a single microphone is shown in Fig. 9. Clearly, there is a good agreement between the target and reproduced sound. 4 Hz 6 Hz 8 Hz 2 Hz 22 Hz 24 Hz S LS [db ref / Hz] Hz 6 Hz 8 Hz 2 Hz 22 Hz 24 Hz (c) 4 Hz 6 Hz 8 Hz 2 Hz 5 22 Hz 24 Hz Frequency [Hz] FIGURE 8:, and S LS for various λ for varying crossover frequency (frequency axis is zoomed). Welch Power Spectral Density Estimate at Mic #4, ygrid: Δ 2 db Power / Freq. [db ref / Hz]) Target Reproduced 4 Freq. [Hz] FIGURE 9: Power spectral density of the target and reproduced sound fields for microphone #4 for the best reported case, λ =. for the low-frequency range, λ = for the high-frequency range and the crossover frequency is 4 Hz (thick dashed line). DISCUSSION AND CONCLUSION It was shown that sound field reproduction at a microphone array is possible for real in-flight sound recordings using standard multichannel leat-mean-square equalization. In all cases, the squeaks and rattles issue is not a limitation of the proposed signal processing but of our specific mock-up materials. Results are satisfactory if one takes into account several limitations and Proceedings of Meetings on Acoustics, Vol. 9, 558 (23) Page 8

9 compromises: ) the use of an overdetermined problem (M > L) and regularization to prevent excessively large reproduction signals that could lead to audible squeaks and rattles from the trim panels and 2) the need for a satisfactory global sound reproduction in the mock-up. Indeed, for the second issue, using a smaller microphone arrays with M = L could give very low reproduction error at the microphone array but with larger reproduction errors outside the microphone array, a consequence that is not acceptable. Current and future works are oriented towards to the adaptation of the improvement least-mean-square method. ACKNOWLEDGMENTS This work is part of a project involving: Consortium for Research and Innovation in Aerospace in Québec, Bombardier Aéronautique and CAE, supported by a Natural Sciences and Engineering Research Council of Canada grant. REFERENCES Berckmans, D., Janssens, K., der Auweraer, H. V., Sas, P., and Desmet, W. (28). Model-based synthesis of aircraft noise to quantify human perception of sound quality and annoyance, Journal of Sound and Vibration 3, Gauthier, P.-A., Camier, C., Lebel, F.-A., Pasco, Y., and Berry, A. (22). Experiments of sound field reproduction inside aircraft cabin mock-up, in Proceedings of the 33rd Audio Engineering Society Convention. Janssens, K., Vecchio, A., and der Auweraer, H. V. (28). Synthesis and sound quality evaluation of exterior and interior aircraft noise, Aerospace Science and Technology 2, Langlois, J., Verron, C., Gauthier, P.-A., and Guastavino, C. (2). Perceptual evaluation of interior aircraft sound models, in 2 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (IEEE). McCurdy, D. A. and Grandle, R. E. (987). Aircraft noise synthesis system, NASA technical memorandum 894. Mixson, J. S. and Wilby, J. F. (995). Interior noise, in Aeroacoustics of flight vehicles. Ploner-Bernard, H., Sontacchi, A., Lichtenegger, G., and Vössner, S. (25). Sound-system design for a professional full-flight simulator, in Proceedings of the 8th Int. Conference on Digital Audio Effects (DAFx5). Powell, C. A. and Fields, J. M. (995). Human response to aircraft noise, in Aeroacoustics of flight vehicles. Verron, C., Gauthier, P.-A., Langlois, J., and Guastavino, C. (2). Binaural analysis/synthesis of interior aircraft sounds, in 2 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (IEEE). Wilby, J. F. (996). Aircraft interior noise, Journal of Sound and Vibration 9, Zwicker, E. and Fastl, H. (999). Psycho-acoustics (Springer). Proceedings of Meetings on Acoustics, Vol. 9, 558 (23) Page 9