Multimicrophone Probes Research Articles

Correcting microphone response mismatch for improved intensity measurements at infrasonic frequencies

Sound intensity measurements using multimicrophone probes at infrasonic frequencies are challenging mainly because the mismatch between microphone responses can be larger than the acoustic differences. Correcting microphone response mismatch via relative calibration requires an infrasound source that can provide good signal-to-noise ratios and sufficiently long averaging times. This paper describes the use of a moving vehicle as an infrasound source to obtain the necessary transfer functions between 12.7 mm diameter, type-1 microphones. The calibration approach is validated and an improved infrasound and low-audio range intensity measurement capability is demonstrated using hot-air balloon burners.

Initial characterization of infrasound sources using the phase and amplitude gradient estimator method for acoustic intensity

The phase and amplitude gradient estimator (PAGE) method for vector acoustic intensity [Thomas et al., J. Acoust. Soc. Am. 137, 3366–3376 (2015)] has been used previously to improve source characterization over broad frequency ranges. This paper describes initial applications of the PAGE method to the infrasound region for outdoor sources using multi-microphone probes. Measurement challenges include wind noise, which reduces signal-to-noise ratio and coherence, low-frequency phase and amplitude mismatch between microphones, and determining an appropriate microphone spacing to maximize bandwidth. Analysis challenges include phase unwrapping above the spatial Nyquist frequency, source statistical stationarity, and balancing frequency resolution with averaging across finite record lengths. This paper discusses how these challenges are being addressed for specific sources of infrasound, namely, wind turbines and large rocket motors. [Work supported by NSF.]

The effects of contaminating noise on the calculation of active acoustic intensity for pressure gradient methods.

Bias errors for two-dimensional active acoustic intensity using multi-microphone probes have been previously calculated for both the traditional cross-spectral and the Phase and Amplitude Gradient Estimator (PAGE) methods [Whiting, Lawrence, Gee, Neilsen, and Sommerfeldt, J. Acoust. Soc. Am. 142, 2208-2218 (2017)]. Here, these calculations are expanded to include errors due to contaminating noise, as well as probe orientation. The noise can either be uncorrelated at each microphone location or self-correlated; the self-correlated noise is modeled as a plane-wave with a varying angle of incidence. The intensity errors in both magnitude and direction are dependent on the signal-to-noise ratio (SNR), frequency, source properties, incidence angles, probe configuration, and processing method. The PAGE method is generally found to give more accurate results, especially in direction; however, uncorrelated noise with a low SNR (below 10-15 dB) and low frequency (wavelengths more than 1/4 the microphone spacing) can yield larger errors in magnitude than the traditional method-though a correction for this is possible. Additionally, contaminating noise does not necessarily impact the possibility of using the PAGE method for broadband signals beyond a probe's spatial Nyquist frequency.

Real-time source localization using phase and amplitude gradient estimator for acoustic intensity

Recent demonstrations of real-time source localization systems have used a variety of direction-finding methods. One such system uses a multi-microphone probe to estimate acoustic intensity [Inoue et al., Proc. Meetings Acoust. 29, 025001 (2016)], although the bandwidth of intensity estimates are traditionally limited by the microphone spacing. The Phase and Amplitude Gradient Estimator (PAGE) method [Thomas et al., J. Acoust. Soc. Am. 137, 3366–3376 (2015)] greatly extends the bandwidth of active intensity, providing an accurate method of source localization for a wide bandwidth. An initial system implemented in LabVIEW estimates active intensity using the PAGE method to identify the direction of the source location in real time. Using a paired webcam, the program then overlays the direction as a three-dimensional arrow onto a webcam image. A demonstration will be provided. Initial quantitative results show the accuracy of the system and limitations of the device. [Sponsored by the NSF REU program.]

Higher-order estimation of acoustic intensity

The phase and amplitude gradient estimator (PAGE) method [D. C. Thomas et al., J. Acoust. Soc. Am. 137, 3366-3376 (2015)] can be used to increase the bandwidth of complex acoustic intensity estimates obtained with multi-microphone probes. Despite the increased bandwidth, errors arise when using this method, which is based on linear least-squares gradients, in non-planar fields. Examples of non-planar fields include the acoustic near field of a radiating source or near a null in a standing-wave field. The PAGE method can be improved by using a Taylor expansion to obtain higher-order estimates of center pressure, pressure amplitude gradient, and phase gradient. With a sufficient number of microphones, the higher-order method is shown to improve the bandwidth of both the active and reactive intensity estimates. Additionally, this method can be used to estimate the spatial dependence of intensity across the extent of the probe. [Work supported by the National Science Foundation.]

Comparison of pressure-based intensity measurements for different probe designs and estimation methods

Acoustic intensity measurements have traditionally used cross spectral methods with multimicrophone probes to estimate the required pressure and particle velocity. The phase and gradient estimator (PAGE) method increases probe bandwidth without modifying microphone spacing as compared to the traditional cross spectral method [D. C. Thomas et al., J. Acoust. Soc. Am. 137, 3366–3376 (2015)]. In this study, high-frequency probe bandwidth obtained using both the PAGE method and the traditional method is compared across three different multimicrophone probe designs: a three-axis, six-microphone probe with variable solid spacer, a three-axis, four-microphone spherical probe, and a two-axis, four-microphone probe developed in-house for rocket measurements. Broadband, anechoic loudspeakermeasurements are used to examine the performance of each probe and estimation method. These include a single 7.6 cm diameter, enclosed loudspeaker driver, and two drivers of equal strength but opposite phase. Intensity measurements in a grid of 41 × 41 points inside a one square meter area are presented. Probe design robustness is determined by considering bias errors in calculation methods and probe scattering. [Work supported by NSF.]

Comparison of methods for processing acoustic intensity from orthogonal multimicrophone probes

One design for three-dimensional multimicrophone probes is the four-microphone orthogonal design consisting of one microphone at an origin position with the other three microphones equally spaced along the three coordinate axes. Several distinct processing methods have been suggested for the estimation of active acoustic intensity with the orthogonal probe; however, the relative merits of each method have not been thoroughly studied. This comparative study is an investigation of the errors associated with each method. Considered are orthogonal probes consisting of matched point sensor microphones both freely suspended and embedded on the surface of a rigid sphere. Results are given for propagating plane-wave fields for all angles of incidence. It is shown that the lowest error for intensity magnitude results from having the microphones in a sphere and using just one microphone for the pressure estimate. For intensity direction, the lowest error results from having the microphones in a sphere and using Taylor approximations to estimate the particle velocity and pressure.

Experimental analysis of multimicrophone probes for measurement of rocket noise.

Although the use of multimicrophone acoustic probes can be useful in characterizing rocket noise source regions, one challenge is that both high-bandwidth pressure and intensity data are desirable. The high-frequency bandwidth limitations arise from the microphone size, type, orientation, spacing, and the design of preamplifier holders. To explore their broadband responses, various tetrahedral four-microphone probes were placed in the far field of a loudspeaker and rotated in an anechoic chamber to determine their pressure magnitude and intensity magnitude/angle errors as a function of orientation and frequency. Results are presented comparing the advantages and limitations of each design, particularly as they apply to obtaining rocket noise data. One probe design considered consists of microphones flush-mounted on a hard sphere. Other designs consist of sets of microphones arranged in tetrahedral configurations with their preamplifiers set at different angles.

Analytical comparison of spherical multimicrophone probes.

Probes with microphones flush-mounted in hard spheres have been used to measure energy-based acoustic quantities by estimating the pressure gradient using finite-difference approximations. The number of microphones, their orientation in the sound field, and the frequency content of an incident acoustic wave affect the probe’s accuracy. This study analytically compares errors in measuring acoustic intensity and energy density of plane waves incident on ideal point microphones located on a rigid sphere. The difference between implementing such a probe as a series of three orthogonal 1-D probes or using a least-squares approximation using all microphones is considered. Estimation errors as a function of incidence angle and frequency have been calculated, thereby providing insight into the relative merits of each probe configuration.

Impact of spherical probe scattering on estimation of acoustic vector quantities.

Multimicrophone probes are often used to measure energy‐based acoustical quantities. In some cases, these probes consist of microphones mounted on the surface of a sphere, which, due to the high level of symmetry, permits scattering effects to be better characterized. Scattering of a plane wave incident on a rigid sphere has been modeled to observe how particle velocity and intensity calculations are affected by the presence of the sphere. These effects have been investigated for the traditional “finite‐difference” method and a recently developed “wave vector” estimation method. In the computer model, 3‐D surface plots were made showing the calculated error as a function of angle of the incident plane wave and frequency. It is shown that using the wave vector method and purposefully orienting the probe in the planar sound field generally results in the most accurate measurements. [Work supported by NASA Stennis Space Center and STI Technologies.]

Harsh environment windscreen analysis and design

This paper presents the analysis and design for a multimicrophone probe placed outdoors in relatively harsh environments including high temperature, high humidity, rain, wind, and soil particles. The windscreen was designed to minimize the insertion loss as well as maintain the phase relationship in a circular 5-probe microphone array. A numerical CFD model, which accounts for wind, soil particles, the windscreen material, and transient pressure fluctuations, will be presented. The parametric design using this numerical model will be presented and discussed, along with experimental results. The experimental testing consists of measuring the wind attenuation, the insertion loss, as well as any errors in the phase relationship. Testing is done in an anechoic chamber using two methods: a stationary microphone array, and attaching the microphone system to a rotating arm to simulate the wind. Measurement results which correlate the density and thickness of the foam with the insertion loss and the drop in wind noise level caused by the foam will be presented. Also, the insertion loss due to different weather-proof coverings is reported.