Biology-Inspired Acoustic Sensors for Sound Source Localization

Biology-Inspired Acoustic Sensors for Sound Source Localization Haijun Liu, Zhong Chen, and Miao Yu Department of Mechanical Engineering, University of Maryland, College Park, MD, 20742

ABSTRACT In this article, the design of a biology-inspired miniature directional microphone is presented. This microphone consists of two clamped circular diaphragms, which are mechanically coupled by a connecting bridge that is pivoted at its center. A theoretical model is constructed to determine the microphone response to sound incident from an arbitrary direction. Both the simulation and preliminary experimental results show that the proposed microphone provides a remarkable amplification of the time delay associated with the sound induced diaphragm responses. This study should be relevant to various sound source localization applications. Keywords: biology-inspired sensor, directional microphone, sound source localization

1. INTRODUCTION Sound source localization is important for many applications, including hearing aid devices, robot navigation, and underwater sensor networks [1-2]. To enhance the signal-to-noise ratio, arrays of two or more microphones are usually used to exploit the coherence of the sound field and create a directional response pattern [1]. A directional microphone can be constructed from two or three microphones, which exhibits a high sensitivity along the direction of the sound source. Currently, a time delay estimation based locator is widely used to calculate the sound-source azimuth angle relative to the directional microphone or the microphone array [3]. In order for a microphone pair to detect the time delay of arrival in some discernible manner, the two microphones need to be placed so that their separation is greater than a critical distance (depending on the microphone’s resolution). This poses a fundamental challenge to the miniaturization of directional microphones. However, in some small insects, the auditory receptors are forcibly set close to each other. Such ears can be found in the parasitoid fly Ormia Ochracea, which shows a remarkable ability to locate a sound source [4-8]. For hearing animals, directional hearing relies on acoustic cues such as the interaural intensity difference (IID) and interaural time difference (ITD). Such differences are mainly determined by the spatial separation between the ears and their position relative to the sound source. With a separation of only 520 µm between the ears, which renders a maximum ITD of 1.45 µs and IID of less than 1 dB, the fly can detect extremely small changes (less than 2°) in the incident sound direction [8]. The small auditory systems of the fly Ormia can inspire one to solve the technological challenge of miniaturizing directional microphones. In recent years, extensive studies have been performed on the fly’s auditory organ. It has been found that the interaural difference in the fly ear response is greatly amplified due to the mechanical coupling between the ears’ motions. This coupling is provided by a cuticular structure that joins the two membranes and pivots about its center, as shown in Figure 1. Miles et al.[9] proposed a two-degree-of-freedom (two-DOF) mechanical model to illustrate the mechanism that is used by the fly ears to amplify interaural differences. In this model, the two ears are modeled as two spring-mass systems coupled by another torsion spring, and the motions of the fly ears are described as a combination of a rocking mode and a bending mode. Based on this model, some miniature biology-inspired directional microphones have been designed and studied [10-12]. However, none of these studies show how to design the mechanical structure of the sensor to fully realize the fly’s hearing capabilities. Although the two-DOF model can provide an explanation for the exceptional directional hearing ability of the fly Ormia, it is not sufficient for designing a biology-inspired directional microphone. Noting that the auditory organs of the fly include two diaphragms (tympanal membranes) connected by an intertympanal bridge, it is necessary to use a distributed-parameter model to obtain a more complete understanding of the vibratory motions of the diaphragm-bridgediaphragm system. This is supported by experiments carried out with the actual fly ears, which point to the presence of Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2008, edited by Masayoshi Tomizuka, Proc. of SPIE Vol. 6932, 69322Y, (2008) 0277-786X/08/$18 · doi: 10.1117/12.776519 Proc. of SPIE Vol. 6932 69322Y-1 2008 SPIE Digital Library -- Subscriber Archive Copy

diaphragm vibratory modes [13]. Hence, to fully understand the physics of the fly ear structure and realize the potential of its directional hearing mechanisms, an enhanced model that can capture the essential dynamics of the mechanical structure (two mechanically coupled diaphragms) is needed.

Tympanal bridge

θl

Bridge Diaphragm

θr

rl rr

520µm

Tympanal membranes

(a)

(b)

Figure 1: (a) Fly ear structure; (b) structure of the biology-inspired directional microphone.

2. MODEL DEVELOPMENT In this effort [14-16], a continuum mechanics model is developed to guide the design of the biology-inspired directional microphone shown in Figure. 1. This microphone consists of two clamped circular diaphragms connected by a coupling bridge that pivots about its center and connects the two diaphragm centers. For simplification, the mass of the connecting bridge is neglected and it is modeled as having a spring-damping force effect on each diaphragm center. The associated spring stiffness and the viscous damping coefficient are labeled as k and ca, respectively. After choosing a polar coordinates system, locating the origins at the respective diaphragm centers, and considering the diaphragm as a plate, the equations governing the open domains of the left and right diaphragms can be written as ⋅

⋅

kδ ( rl ) wl ( 0,θ , t ) + wr ( 0,θ , t ) caδ ( rl ) wl ( 0,θ , t ) + wr ( 0,θ , t ) , D∇ wl + γ wl + ρ h wl = fl − − π a2 π a2 2 2 ⋅

4

⋅⋅

(1)

and ⋅

⋅

kδ ( rr ) wl ( 0,θ , t ) + wr ( 0,θ , t ) caδ ( rl ) wl ( 0,θ , t ) + wr ( 0,θ , t ) , D∇ wr + γ wr + ρ h wr = f r − − π a2 π a2 2 2 4

⋅

⋅⋅

(2)

where wl(rl,θl,t) and wr(rr,θr,t) denote the displacement fields of the left and right diaphragms. Furthermore, D=Eh3/12(1ν2), and E, ν, γ, ρ, and h denote the diaphragm’s Young’s modulus, Poisson’s ratio, damping coefficient, density, and thickness, respectively. The forces fl and fr correspond to the pressure fields applied on the left and right diaphragms, respectively. k and ca are the stiffness and damping ratio of the coupling bridge, respectively. δ(rl) and δ(rr) mean the coupling force is applied at the centers of two diaphragms. In terms of boundary conditions, the left and right diaphragms are assumed to be clamped along their respective edges; that is, at rl=a, where a is the diaphragm radius, wl=0 & ∂wl/∂rl=0; and at rr=a, wr=0 & ∂wr/∂rr=0. Suppose the sound source is at the far field. For an acoustic sensor mimicking the fly’s ears, the direction of the sound can be obtained through two means: i) mechanical response amplitude (intensity) difference between the two diaphragms (defined as mIID) and ii) mechanical response time difference between the two diaphragms (defined as mITD). The mIID can be simply obtained as

Proc. of SPIE Vol. 6932 69322Y-2

⎛W mIID = 20 log10 ⎜ l ⎝ Wr

⎞, ⎟ ⎠

(5)

where Wl and Wr are the displacement responses at the center of left and right diaphragms, respectively. The mITD can be calculated by finding the time corresponding to the maximum value of the cross-correlation of the displacement responses of two single microphone diaphragms at center; that is mITD = arg corr ( Wl , Wr )

(6)

3. PARAMETRIC STUDY Simulations were conducted to study the biology-inspired directional microphone illustrated in Figure 1 with the following design parameters: i) polyimide diaphragm (E=7.5 GPa, ν=0.35, and ρ=1200 kg/m3) with a radius of 0.3 mm and a thickness of 1µm, ii) diaphragm stiffness of 0.388N/m, and iii) separation of 0.8 mm between the two diaphragm centers. Five plate modes were used to model the displacement field of each diaphragm.. Unlike the two-DOF model proposed by Miles et al.[9], which only predicts a rocking mode and a bending mode of the fly ear structure, the system considered here has an infinite number of vibration modes. In Figure 2(a)-(d), the first two rocking modes and two bending modes are shown. Similar to the two-DOF model, the first natural frequency is found to be only related to the diaphragm. Considering all these rocking modes and bending modes is expected to help better understand the fly ear hearing mechanism and obtain a more accurate sensor performance prediction.

(a) f1=13.8 kHz

(b) f2 = 28.2 kHz

(c) =54.2 kHz

(d) f4 =73.1 kHz

Figure 2: Vibration modes of the biology-inspired diaphragm with a coupling bridge stiffness of 2.4 N/m. As seen from Eqs. (1) and (2), the strength of coupling between the motions of the two clamped diaphragms is determined by the bridge stiffness k and the damping coefficient ca. For the chosen diaphragm stiffness value, the coupling bridge can be characterized as a “soft” bridge for k=0.2 N/m, a “medium” bridge for k=2.4 N/m, and a “stiff” bridge for k=40 N/m in the simulations. For different bridge stiffness values, the mITD and mIID are studied as a function of the sound incident direction for an 8 kHz planar sound field. This excitation frequency is below the directional microphone’s first rocking frequency. The damping factor used in the simulation is 0.8. As shown in Figure 3(a), for a “rigid” bridge, although a large amplification of ITD can be achieved, the mITD quickly saturates at large sound incident angles (>50°); that is, the gradient of mITD is too small to differentiate the sound incident angle. For a “soft” bridge, the coupling becomes too weak to render sufficient magnification of the mITD. Therefore, a “medium” bridge is more desirable to obtain a good magnification of the mITD and differentiable mITDs for different incident angles, which is also found to be characteristic of the fly ear structure. The results obtained also show that in addition to


the benefit to the mITD, a “medium” bridge also provides a superior mIID (best amplification and differentiation) compared to the “soft” and “rigid” bridges, as shown in Figure 3(b). In addition to the bridge stiffness, damping is another important parameter that affects the mITD and the mIID. The frequency responses of the IID and ITD for different damping factors ( ζ = c / 2 k / m ) are shown in Figure 4. To generate a

the results shown in this figure, a “medium” bridge (k =2.4 N/m) has been chosen and the sound incident angle is assumed to be 30°. As shown in Figure 4(a), when the damping is small, the maximum of mITD is achieved at the first rocking natural frequency (f1=13.8 kHz). The sign of mITD changes at this frequency because the sign of corresponding phase delay (180°) changes. Introducing damping will reduce the mITD but it can help obtain a constant mITD sensitivity-frequency response, which is important for unambiguously determining the sound emanating from a broadband source. However, too large a damping will result in significant degradation of the mITD in the high frequency range. As can be seen in Figure 4(b), for a small damping factor (ζ=0.1), the mIID curve peaks at a frequency between the first rocking frequency and first bending frequency. As the damping is increased, the peak level mIID reduces. Moreover, when the sound frequency is far below the first rocking natural frequency, the mIID actually benefits from a large damping. However, as can be seen from Figure 5, increasing damping factor cannot increase mIID and mITD simultaneously, indicating the presence of design tradeoffs in this aspect. 6

x 10

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14 Rigid bridge Medium bridge Soft bridge Uncoupled

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Rigid bridge Medium bridge Soft bridge Uncoupled

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(a)

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Figure 3: Variations with respect to sound incident angle for different coupling bridge stiffness values: (a) mITD and (b) mIID. 6

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5 4 3

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(a) (b) Figure 4: Variations with respect to excitation frequency for different damping factors ζ: (a) mITD and (b) mIID.


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(a) (b) Figure 5: Variations with respect to incident angle for different damping factors ζ: (a) mITD and (b) mIID. For a fly’s auditory organ, the observed ratio of the bridge stiffness to the diaphragm stiffness and the damping factor are 10 and 1.2, respectively [9]. These values correspond to the “medium” coupling bridge and large damping factor case of the above analysis. Hence, to achieve the desired performance of a biology-inspired directional microphone and fully realize the fly’s sound localization capablity, in terms of high mITD and high mIID (signal-to-noise ratio), better differentiation of mITD and mIID (sensitivity and resolution) to the sound incident direction, care should be taken to choose the apropriate values of stiffness k and damping ratio ca.

4. EXPERIMENTAL STUDY OF THE FABRY-PEROT SENSOR FOR INTRADISCAL PRESSURE MEASUREMENTS To investigate the performance of the proposed biology-inspired directional microphone, a large scale proof-of-concept system has been developed as shown in Figure 6(a). The diaphragm is made from Mylar (E=3.45 GPa, ν=0.41, and ρ=1390 kg/m3), and has a radius of 3.5 mm and a thickness of 22 µm. A bridge is constructed to couple the centers of two diaphragms by glue connection and is supported at its center (pivot), see Figure 6 (a). A speaker (ALTEC LANSING ACS340) was placed in the far field to produce sound signals of different frequencies. The sound incidence angle was changed by moving the speaker.

Bridge

Diaphragm

(a) Diaphragms and bridge

(b) System setup

Figure 6: Large-scale proof-of-concept directional microphone.


A fiber optic system based on low coherence Fabry-Perot interferometer [16] is used to detect the deflection of diaphragms induced by sound pressure. The schematic of the system is shown in Fig. 7. Light from a low coherence light source (superluminescent diode (SLD), Model OELED-100 from O/E Land Inc) with a coherence length Lc is first sent to a tunable Fabry-Perot interferometer, and then via a 1×2 coupler to other couplers. At the output of each coupler, the light beam (Ein1 or Ein2) is sent to the two Fabry-Perot sensors (sensing interferometers). The surface of the reflective diaphragm serves as one partial mirror of the Fabry-Perot cavity, while the fiber tip serves as the other, as shown in Fig. 7. The returned light waves from the diaphragm surface (Eout12) and the fiber tip (Eout11) have an optical path difference (OPD) Ls that induces a phase difference φs=k0Ls, where k0 =2π/λ is the free-space wave number and λ is the wavelength. The acoustic pressure induced diaphragm deflection produces a phase difference change ∆φ in φs. The reflected light from the Fabry-Perot sensor is then sent to a photodetector via the coupler. The tunable Fabry-Perot interferometer has an initial optical path difference (Lr) (or phase difference φr=k0Lr), acting as a reference interferometer. When it is path-matched to the Fabry-Perot sensors (Lr ≅Ls) and the coherence length Lc is much shorter than Lr and Ls , the output intensity received by the detector is [17]

I det ect ≈ A + B cos k0 ( Ls − Lr ) = A + B cos(φs − φr ) = A + B cos( ∆φ ) ,

(1) where A and B are the constants related to the mirror properties of the Fabry-Perot interferometer, and ∆φ is the differential phase change between the sensing interferometer and reference interferometer. Note that ∆φ is the only parameter related to the center displacement (X) of the diaphragm and ∆φ=2k0X. Therefore, the pressure sensitivity (displacement/pressure) of the diaphragm can be amplified by a factor of 2k0 (107 times at λ=1300 nm). In addition, owing to the differentiation of the phase signal between the two interferometers, this technique has immunity to wavelength and power fluctuation induced noise, permits a short effective sensing cavity (several µm), and yields a high resolution and a large dynamic range.

Tunable FebryPerot Filter

Multiplexed Microphones Ein2

SLD

OPD: Lr

Coupler

Ein1

Directional Microphone

Fabry-Perot Sensor E out12 Optical EEout12 E out11 out11 Fiber EEin1in1 Detector arrays OPD: Ls

Diaphragm

Figure 7: Low coherence Fabry-Perot interferometer based optical detection system. Two types of materials, steel and brass, are used for the coupling bridge. The steel bridge is 25.4 mm long, 1.2 mm wide and 0.1 mm thick. The equivalent stiffness is determined to be 17 N/m. As shown in Figure 8, when the steel beam is used, the time difference can only be amplified by two times compared with that obtained from two uncoupled microphones for a 90 degree sound incident angle. Based on the discussion in Section 3, this beam renders a “soft” bridge that cannot provide enough amplification of the time delay. When the beam thickness is increased from 0.1 mm to 0.2 mm, and the material is changed from steel to brass, the corresponding equivalent stiffness increases to 69 N/m. In this case, the mITD obtained from the bio-inspired microphone is about five times larger than that obtained from two uncoupled microphones. The model predictions obtained for a damping factor of 1.2 are found to match well with the experimental data for both cases. The preliminary experimental results have verified the prediction of the continuum mechanics model and laid the foundation for future fabrication of miniature MEMS directional microphones.


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Figure 8: Comparison of the mITD obtained from the bio-inspired microphone, model prediction, and uncoupled two microphones with a separation of 25.4mm.

5. CONCLUDING REMARKS In summary, the design of a biology-inspired miniature directional microphone has been presented along with a continuum mechanics model that can be used to predict the behavior of the directional microphone. Based on the model, simulations have been carried out to study the influence of two key parameters (stiffness of the coupling bridge and damping) on the performance of the microphone. The results indicate that only when these parameters are chosen appropriately, the microphone can perform like the fly’s ear. Preliminary experimental results show that the biologyinspired directional microphone can effectively amplify the time delay response, which is also validated by the model prediction. The analyses and results are expected to be valuable for carrying out the design of miniature directional microphones for various applications.

6. ACKNOWLEDGEMENTS This research is partially supported by the U.S. National Science Foundation (NSF) under the grant No. 0644914 and Air Force Office of Scientific Research (AFOSR) under the grant No. 070718-8611.

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