ALBERT

Description: The FXLMS algorithm, used extensively in active noise control (ANC), exhibits frequency-dependent convergence behavior. This leads to degraded performance for time-varying tonal noise and noise with multiple stationary tones. Previous work by the authors proposed the eigenvalue equalization filtered-x least mean squares (EE-FXLMS) algorithm. For that algorithm, magnitude coefficients of the secondary path transfer function are modified to decrease variation in the eigenvalues of the filtered-x autocorrelation matrix, while preserving the phase, giving faster convergence and increasing overall attenuation. This paper revisits the EE-FXLMS algorithm, using a genetic algorithm to find magnitude coefficients that give the least variation in eigenvalues. This method overcomes some of the problems with implementing the EE-FXLMS algorithm arising from finite resolution of sampled systems. Experimental control results using the original secondary path model, and a modified secondary path model for both the previous implementation of EE-FXLMS and the genetic algorithm implementation are compared.

Description: The weighted sum of spatial gradients (WSSG) control minimization parameter is developed for use in active structural acoustic control (ASAC) on a clamped flat rectangular plate. The WSSG minimization parameter is measured using four accelerometers grouped closely together on the test structure. In previous work, WSSG was developed on a simply supported flat rectangular plate and showed promise as a control metric. The displacement on the clamped plate has been modeled using an approximate analytical solution assuming shape functions corresponding to clamped-clamped beams. From the analytical formulation, weights, which were found to be the reciprocal of the wave number squared, have been derived to produce a uniform WSSG field across the plate. In active control simulations, this quantity has been shown to provide better global control of acoustic radiation than volume velocity. Analysis is presented which shows that comparable control, regardless of the sensor location, can be achieved using WSSG. Experimental results are presented which demonstrate that WSSG works effectively in practice, with results similar to the simulations. The results show that minimization of WSSG can be used as an effective control objective on clamped rectangular plates to achieve attenuation of acoustic radiation.

Description: The objective of this research project is to further investigate and develop a novel approach for actively controlling the sound field in enclosures. Typically the acoustic field in an enclosure has been controlled by minimizing the sum of the squared pressures from several microphones distributed throughout the enclosure. The approach being investigated in this project involves minimizing the acoustic energy density at the sensor locations, rather than the squared pressure. Previous research in a simple one-dimensional enclosure showed that improved global attenuation of the acoustic field is often obtained by minimizing the energy density, rather than the pressure. The current project builds on the previous research by extending the method of controlling the acoustic energy density to three-dimensional enclosures. The results will establish if improved control can still be expected in a more general enclosure. Pending successful results, the method could be applied to control problems such as attenuating the acoustic noise in an aircraft fuselage, an automobile cabin, or other general enclosures. The research project was set up as a two-year project designed to achieve both numerical and experimental results. The primary focus of the first year of research (now being completed) was on the analytical/numerical modeling of the method of controlling the acoustic energy density. During the second year, the research focuses on experimental verification of the approach and extending our understanding of the method.

Description: An acoustic energy-based probe has been developed that incorporates multiple acoustic sensing elements in order to obtain the acoustic pressure and three-dimensional acoustic particle velocity. With these quantities, the user can obtain various energy-based quantities, including acoustic energy density, acoustic intensity, and acoustic impedance. In this specific development, the probe has been designed to operate in an environment characterized by high temperatures and high pressures as is found in the close vicinity of rocket plumes. Given these capabilities, the probe is designed to be used to investigate the acoustic conditions within the plume of a rocket engine or jet engine to facilitate greater understanding of the noise generation mechanisms in those plumes. The probe features sensors mounted inside a solid sphere. The associated electronics for the probe are contained within the sphere and the associated handle for the probe. More importantly, the design of the probe has desirable properties that reduce the bias errors associated with determining the acoustic pressure and velocity using finite sum and difference techniques. The diameter of the probe dictates the lower and upper operating frequencies for the probe, where accurate measurements can be acquired. The current probe design implements a sphere diameter of 1 in. (2.5 cm), which limits the upper operating frequency to about 4.5 kHz. The sensors are operational up to much higher frequencies, and could be used to acquire pressure data at higher frequencies, but the energy-based measurements are limited to that upper frequency. Larger or smaller spherical probes could be designed to go to lower or higher frequency range

Description: A calibrator, referred to as the spider design, can be used to calibrate probes incorporating multiple acoustic sensing elements. The application is an acoustic energy density probe, although the calibrator can be used for other types of acoustic probes. The calibrator relies on the use of acoustic waveguide technology to produce the same acoustic field at each of the sensing elements. As a result, the sensing elements can be separated from each other, but still calibrated through use of the acoustic waveguides. Standard calibration techniques involve placement of an individual microphone into a small cavity with a known, uniform pressure to perform the calibration. If a cavity is manufactured with sufficient size to insert the energy density probe, it has been found that a uniform pressure field can only be created at very low frequencies, due to the size of the probe. The size of the energy density probe prevents one from having the same pressure at each microphone in a cavity, due to the wave effects. The "spider" design probe is effective in calibrating multiple microphones separated from each other. The spider design ensures that the same wave effects exist for each microphone, each with an indivdual sound path. The calibrator s speaker is mounted at one end of a 14-cm-long and 4.1-cm diameter small plane-wave tube. This length was chosen so that the first evanescent cross mode of the plane-wave tube would be attenuated by about 90 dB, thus leaving just the plane wave at the termination plane of the tube. The tube terminates with a small, acrylic plate with five holes placed symmetrically about the axis of the speaker. Four ports are included for the four microphones on the probe. The fifth port is included for the pre-calibrated reference microphone. The ports in the acrylic plate are in turn connected to the probe sensing elements via flexible PVC tubes. These five tubes are the same length, so the acoustic wave effects are the same in each tube. The flexible nature of the tubes allows them to be positioned so that each tube terminates at one of the microphones of the energy density probe, which is mounted in the acrylic structure, or the calibrated reference microphone. Tests performed verify that the pressure did not vary due to bends in the tubes. The results of these tests indicate that the average sound pressure level in the tubes varied by only 0.03 dB as the tubes were bent to various angles. The current calibrator design is effective up to a frequency of approximately 4.5 kHz. This upper design frequency is largely due to the diameter of the plane-wave tubes.

Description: The objective of this study was to further investigate and develop a novel approach for actively controlling the sound field in enclosures that is based on the acoustic energy density. Typically the acoustic field in an enclosure has been controlled by minimizing the sum of the squared pressures from several microphones distributed throughout the enclosure. The approach investigated in this study involved minimizing the acoustic energy density at the sensor locations, rather than the squared pressure. Research previous to this study in a simple one-dimensional enclosure showed that improved global attenuation of the acoustic field is often obtained by minimizing the energy density, rather than the pressure. The current study built on the previous research by extending the method of controlling the acoustic energy density to three-dimensional enclosures. The study was intended to help establish if improved control can still be expected in a more general enclosure. The study was designed to be both analytical/numerical and experimental in nature.