Incubator-based active noise control device: comparison to ear covers and noise reduction zone quantification.

BACKGROUND: Noise exposure in the neonatal intensive care unit (NICU) is consistently higher than current recommendations. This may adversely affect neonatal sleep, weight gain, and overall health. We sought to evaluate the effect of a novel active noise control (ANC) system. METHODS: An ANC device's noise reduction performance was compared to that of adhesively affixed foam ear covers in response to alarm and voice sounds in a simulated NICU environment. The zone of noise reduction of the ANC device was quantified with the same set of alarm and voice sounds. RESULTS: The ANC device provided greater noise reduction than the ear covers in seven of the eight sound sequences tested in which a noise reduction greater than the just noticeable difference was achieved. For noise in the 500 Hz octave band, the ANC device exhibited consistent noise reduction throughout expected patient positions. It provided better performance for noise below 1000 Hz than above 1000 Hz. CONCLUSIONS: The ANC device provided generally superior noise reduction to the ear covers and provided a zone of noise reduction throughout the range where an infant would be placed within an incubator. Implications for patient sleep and weight gain are discussed. IMPACT: Active noise control device can effectively reduce noise inside an infant incubator due to bedside device alarms. This is the first analysis of an incubator-based active noise control device and comparison to adhesively affixed silicone ear covers. A non-contact noise reduction device may be an appropriate means of reducing noise exposure of the hospitalized preterm infant.

Improved efficiency of vibration-based sound power computation through multi-layered radiation resistance matrix symmetry.

Computing sound power using complex-valued surface velocities involves using a geometry-dependent acoustic radiation resistance matrix multiplied by a velocity vector to compute sound power for a given frequency range. Using a laser scan grid with constant spacing and a scalar radiator area approximation, a multi-layered Toeplitz symmetry exists in the radiation resistance matrix. An innovative approach was developed to exploit this Toeplitz symmetry. This approach preserved accuracy and resulted in a maximum of ∼1300% computation time reduction for curved plate calculations and a ∼9600% computation time reduction for cylindrical shell sound power calculations.

A coherence-based phase and amplitude gradient estimator method for calculating active acoustic intensity.

The phase and amplitude gradient estimator (PAGE) method [Thomas, Christensen, and Gee, J. Acoust. Soc. Am. 137, 3366-3376 (2015)] has been developed as an alternative to the traditional p-p method for calculating energy-based acoustic measures such as active acoustic intensity. While this method shows many marked improvements over the traditional method, such as a wider valid frequency bandwidth for broadband sources, contaminating noise can lead to inaccurate results. Contaminating noise degrades performance for both the traditional and PAGE methods and causes probe microphone pairs to exhibit low coherence. When coherence is low, better estimates of the pressure magnitude and gradient can be obtained by using a coherence-based approach, which yields a more accurate intensity estimate. This coherence-based approach to the PAGE method, known as the CPAGE method, employs two main coherence-based adjustments. The pressure magnitude adjustment mitigates the negative impact of uncorrelated contaminating noise and improves intensity magnitude calculation. The phase gradient adjustment uses coherence as a weighting to calculate the phase gradient for the probe and improves primarily the calculation of intensity direction. Though requiring a greater computation time than the PAGE method, the CPAGE method is shown to improve intensity calculations, both in magnitude and direction.

Vibration-based sound power measurements of arbitrarily curved panels.

Vibration-based sound power (VBSP) measurement methods are appealing because of their potential versatility in application compared to sound pressure and intensity-based methods. It has been understood that VBSP methods have been reliant on the acoustic radiation resistance matrix specific to the surface shape. Expressions for these matrices have been developed and presented in the literature for flat plates, simple-curved plates (constant radius of curvature in one direction), and cylindrical- and spherical-shells. This paper shows that the VBSP method is relatively insensitive to the exact form of the radiation resistance matrix and that computationally efficient forms of the radiation resistance matrix can be used to accurately approximate the sound power radiated from arbitrarily curved panels. Experimental sound power measurements using the VBSP method with the simple-curved plate radiation resistance matrix and the ISO 3741 standard method are compared for two arbitrarily curved panels and are shown to have good agreement. The VBSP method based on the simple-curved plate form of the radiation resistance matrix is also shown to have excellent agreement with numerical results from a boundary element model, which inherently uses the appropriate form of the radiation resistance matrix.

Solving one-dimensional acoustic systems using the impedance translation theorem and equivalent circuits: A graduate level homework assignment.

The natural frequency resonances and sound radiation from one-dimensional acoustic systems are of great interest in the study of musical instruments, human vocal tract effects on speech, automotive exhaust pipes, duct systems for temperature control in buildings, and more. The impedance translation theorem is an approach that may be used to solve for the input impedance and therefore the resonance frequencies of one-dimensional systems. Equivalent circuits offer another approach to solving one-dimensional systems, though with equivalent circuits you can also solve for the response at any location in the system, including the radiated sound pressure. At Brigham Young University, there are two graduate level courses that teach these two techniques. One of the most challenging and memorable homework assignments from these courses is based on using one of these techniques to analyze a particular acoustic system and compare its response with the real thing. This paper discusses the basics of these two techniques and applies them to an analysis of phonemes produced by altering the human vocal tract. Details about the homework assignments are also given.

Sound power of vibrating cylinders using the radiation resistance matrix and a laser vibrometer.

Research has shown that using acoustic radiation modes combined with surface velocity measurements provide an accurate method of measuring the radiated sound power from vibrating plates. This paper investigates the extension of this method to acoustically radiating cylindrical structures. The mathematical formulations of the radiation resistance matrix and the accompanying acoustic radiation modes of a baffled cylinder are developed. Computational sound power calculations using the vibration-based radiation mode (VBRM) method and the boundary element method are then compared and shown to have good agreement. Experimental surface velocity measurements of a cylinder are taken using a scanning laser Doppler vibrometer and the VBRM method is used to calculate sound power. The results are compared to sound power measurements taken using ISO 3741.

Bandwidth extension of intensity-based sound power estimates.

The traditional method for intensity-based sound power estimates often used in engineering applications is limited in bandwidth by microphone phase mismatch at low frequencies and by microphone spacing at high frequencies. To overcome these limitations, the Phase and Amplitude Gradient Estimator (PAGE) method [Gee, Neilsen, Sommerfeldt, Akamine, and Okamoto, J. Acoust. Soc. Am. 141(4), EL357-EL362 (2017)] is applied to sound power for a reference sound source, a blender, and a vacuum cleaner. Sound power measurements taken according to ISO 3741:2010 (2010) are compared against traditional- and PAGE-processed intensity-based sound power estimates measured according to ANSI S12.12-1992 (R2017). While the traditional method underestimates the sound power at the spatial Nyquist frequency by 7-10 dB, the PAGE-based sound power is accurate up to the spatial Nyquist frequency, and above when phase unwrapping is successful.

Bandwidth extension of narrowband-signal intensity calculation using additive, low-level broadband noise.

Calculation of acoustic intensity using the phase and amplitude gradient estimator (PAGE) method has been shown to increase the effective upper frequency limit beyond the traditional p-p method when the source of interest is broadband in frequency [Torrie, Whiting, Gee, Neilsen, and Sommerfeldt, Proc. Mtgs. Acoust. 23, 030005 (2015)]. PAGE processing calculates intensity for narrowband sources without bias error up to the spatial Nyquist frequency [Succo, Sommerfeldt, Gee, and Neilsen, Proc. Mtgs. Acoust. 30, 030015 (2018)]. The present work demonstrates that for narrowband sources with frequency content above the spatial Nyquist frequency, additive low-level broadband noise can improve intensity calculations. To be effective, the angular separation between the source and additive noise source should be less than 30°, while using phase unwrapping with a smaller angular separation will increase the usable bandwidth. The upper frequency limit for the bandwidth extension depends on angular separation, sound speed, and probe microphone spacing. Assuming the signal-to-additive-noise ratio (SNRa) is larger than 10 dB, the maximum level and angular bias errors incurred by the additive broadband noise beneath the frequency limit-or up until probe scattering effects must be taken into account-are less than 0.5 dB and 2.5°, respectively. Smaller angular separation yields smaller bias errors.

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.

Highly directional pressure sensing using the phase gradient.

Many methods of two-microphone directional sensing have limited bandwidth. For active intensity, finite-difference error can be removed by using the phase and amplitude gradient estimator method. Using similar principles, a directional pressure sensor based on the phase gradient is developed that is accurate up to the spatial Nyquist frequency, and beyond if phase unwrapping is applied. A highly directional frequency-independent array response of arbitrary order can be achieved with two microphones. The method is compared against beamforming and traditional gradient sensing for single and multiple sources and is found to have improved localization capabilities and increased bandwidth.

Three-microphone probe bias errors for acoustic intensity and specific acoustic impedance.

In acoustic intensity estimation, adding a microphone at the probe center removes errors associated with pressure averaging. Analytical bias errors are presented for a one-dimensional, three-microphone probe for active intensity, reactive intensity, and specific acoustic impedance in a monopole field. Traditional estimation is compared with the Phase and Amplitude Gradient Estimator (PAGE) method; the PAGE method shows an increased bandwidth for all three quantities. The two- and three-microphone methods are compared experimentally, showing reduced bias errors with three-microphone PAGE for active and reactive intensity, whereas using two microphones is preferred for specific acoustic impedance.

Active control of simply supported cylindrical shells using the weighted sum of spatial gradients control metric.

It is often desired to reduce sound radiated from cylindrical shells. Active structural acoustic control (ASAC) provides a means of controlling the structural vibration in a manner to efficiently reduce the radiated sound. Previous work has often required a large number of error sensors to reduce the radiated sound power, and the control performance has been sensitive to the location of error sensors. The ultimate objective is to provide global sound power reduction using a minimal number of local error measurements, while also minimizing any dependence on error sensor locations. Recently, a control metric referred to as weighted sum of spatial gradients (WSSG) was developed for ASAC. Specific features associated with WSSG make this method robust under a variety of conditions. In this work, the WSSG control metric is extended to curved structures, specifically a simply supported cylindrical shell. It is shown that global attenuation of the radiated sound power is possible using only one local error measurement. It is shown that the WSSG control metric provides a solution approximating the optimal solution of attenuating the radiated sound power, with minimal dependence on the error sensor location. Numerical and experimental results are presented to demonstrate the effectiveness of the method.

Bias error analysis for phase and amplitude gradient estimation of acoustic intensity and specific acoustic impedance.

Sound intensity measurements using two microphones have traditionally been processed using a cross-spectral method with inherent error in the finite-sum and finite-difference formulas. The phase and amplitude gradient estimator method (PAGE) has been seen experimentally to extend the bandwidth of broadband active intensity estimates by an order of magnitude. To provide an analytical foundation for the method, bias errors in active intensity and specific acoustic impedance are presented and compared to those of the traditional method. Bias errors are reported for a plane-wave field and sound radiated from a monopole and a dipole. Additionally, bias errors are reported for reactive intensity, the estimation of which is unchanged by the PAGE method for the two-microphone case.

Experimental validation of acoustic intensity bandwidth extension by phase unwrapping.

The phase and amplitude gradient estimator (PAGE) method for active acoustic intensity uses pairwise microphone transfer functions to obtain the phase gradient, which improves the calculation bandwidth over the traditional weighted quadspectral method. Additionally, for broadband sources, the PAGE theory indicates that the transfer function phase can be unwrapped to further extend the usable frequency range to beyond the spatial Nyquist frequency. Here, two experiments demonstrate intensity bandwidth extension by more than an order of magnitude using phase unwrapping. First, plane-wave tube results show accurate one-dimensional intensity calculations with the microphones separated by five wavelengths, 30 times the traditional limit. Second, two-dimensional measurements of a laboratory-scale jet with a four-microphone probe yield physically reasonable calculations at frequencies 15 times the traditional limit.

An analysis of control using the weighted sum of spatial gradients in active structural acoustic control for flat panels.

Active structural acoustic control uses a control metric that when minimized reduces the radiated sound. Previous research has identified the weighted sum of spatial gradients (WSSG) control metric and has shown that it is effective in attenuating the radiated sound power from a plate. The WSSG control metric is computed using weighted measurements of the structural response from four closely spaced accelerometers. In this work, it is shown that the weights used to compute WSSG directly impact the control performance and further understanding into choosing appropriate weights is presented. Weights optimized for single frequencies are investigated and shown to achieve nearly the same performance as minimizing sound power. A set of parameter-based weights for broadband frequency control is also proposed and analyzed. These parameter-based weights are inversely proportional to the square of the flexural wavenumber and can be computed using the ratio of the flexural rigidity to the mass per unit area. Both numerical and experimental results are presented using parameter-based weights for simply supported and clamped plates. The results show that the WSSG control using parameter-based weights is easy to implement and works more effectively than previous methods.

Experimental active structural acoustic control of simply supported plates using a weighted sum of spatial gradients.

A limitation currently facing active structural acoustic control (ASAC) researchers is that an ideal minimization quantity for use in the control algorithms has not been developed. A novel parameter termed the "weighted sum of spatial gradients" (WSSG) was recently developed for use in ASAC and shown to effectively attenuate acoustic radiation from a vibrating flat simply supported plate in computer simulations. This paper extends this research from computer simulations and provides experimental test results. The results presented show that WSSG is a viable control quantity and provides better results than the volume velocity approach. The paper also investigates several of the challenges presented by the use of WSSG. These include determining a method to measure WSSG experimentally, an analysis of the influence of noise on WSSG control results and complications presented when degenerate modes exist. Results are shown and discussed for several experimental configurations.

Generalized acoustic energy density based active noise control in single frequency diffuse sound fields.

In a diffuse sound field, prior research has established that a secondary source can theoretically achieve perfect cancellation at an error microphone in the far field of the secondary source. However, the sound pressure level is generally only reduced in a small zone around the error sensor, and at a distance half of a wavelength away from the error sensor, the averaged sound pressure level will be increased by more than 10 dB. Recently an acoustic energy quantity, referred to as the generalized acoustic energy density (GED), has been introduced. The GED is obtained by using a weighting factor in the formulation of total acoustic energy density. Different values of the weighting factor can be chosen for different applications. When minimizing the GED at the error sensor, one can adjust the weighting factor to increase the spatial extent of the "quiet zone" and to achieve a desired balance between the degree of attenuation in the quiet zone and the total energy added into the sound field.

Comparison of multimicrophone probe design and processing methods in measuring acoustic intensity.

Three multimicrophone probe arrangements used to measure acoustic intensity are the four-microphone regular tetrahedral, the four-microphone orthogonal, and the six-microphone designs. Finite-sum and finite-difference processing methods can be used with such probes to estimate pressure and particle velocity, respectively. A numerical analysis is performed to investigate the bias inherent in each combination of probe design and processing method. Probes consisting of matched point sensor microphones both embedded and not embedded on the surface of a rigid sphere are considered. Results are given for plane wave fields in terms of root-mean-square average bias and maximum bias as a function of angle of incidence. An experimental verification of the analysis model is described. Of the combinations considered and under the stated conditions, the orthogonal probe using the origin microphone for the pressure estimate is shown to have the lowest amount of intensity magnitude bias. Lowest intensity direction bias comes from the six-microphone probe using an average of the 15 intensity components calculated using all microphone pairs. Also discussed are how multimicrophone probes can advantageously use correction factors calculated from a numerical analysis and how the results of such an analysis depend on the chosen definition of the dimensionless frequency.

Development of a pseudo-uniform structural quantity for use in active structural acoustic control of simply supported plates: an analytical comparison.

Active structural acoustic control has been an area of research and development for over two decades with an interest in searching for an "optimal" error quantity. Current error quantities typically require the use of either a large number of transducers distributed across the entire structure, or a distributed shaped sensor, such as polyvinylidene difluoride. The purpose of this paper is to investigate a control objective function for flat, simply-supported plates that is based on transverse and angular velocity components combined into a single composite structural velocity quantity, termed V(comp). Although multiple transducers are used, they are concentrated at a single location to eliminate the need for transducers spanning most or all of the structure. When used as the objective function in an active control situation, squared V(comp) attenuates the acoustic radiation over a large range of frequencies. The control of squared V(comp) is compared to other objective functions including squared velocity, volume velocity, and acoustic energy density. The analysis presented indicates that benefits of this objective function include control of radiation from numerous structural modes, control largely independent of sensor location, and need to measure V(comp) at a single location and not distributed measurements across the entire structure.

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.