The present study is related to the field of imaging of aeroacoustic noise sources. Traditional techniques include the use of phased microphone arrays and acoustic beamforming of the signals signals using algorithms such as the Delay-And-Sum (DAS). Over the last years, there has been an increasing interest in methods in which some of the sensors traverse in prescribed paths and motion. Some of the challenges of this approach include the treatment of the non-stationarity of the signal due to the motion of the microphone(s).

An objective of this work is to review the methodology presented by D. Papamoschou, P. Shah and myself in the AIAA Journal "Inverse Acoustic Methodology for Continuous-Scan Phased Arrays" since it provides the building grounds for the thesis. The methodology accounts for the direct estimation of the spatio-spectral distribution of an acoustic source from microphone measurements that include fixed and continuously scanning sensors. The non-stationarity of the signal is addressed by means of the Wigner-Ville spectrum. Suppression of the non-stationary effects involves the division of the signal into blocks and the application of a frequency-dependent window within each block. The direct estimation approach involves the inversion of an integral that relates the modeled pressure field, the measured pressure field and the response of the array. A Bayesian-estimation that allows for efficient inversion of the integrals and performs similarly to the conjugate gradient method is reviewed.

The coherence-based noise source distribution is studied in this work and the influence of the signal segmentation on its spatial resolution is analyzed. This thesis provides specific guidelines related to the signal processing. The signal is divided into blocks meeting a desired mathematical condition. A minimum and maximum size for the resulting blocks is proposed in this work, as well as a minimum and maximum block overlap. A safe region for the signal segmentation is presented as well.

This work presents a methodology to synchronize the signals from the microphones (scanning or not) with the position of the scanning sensor. It also shows the methods to check the accuracy of the position scanning sensor.

The methodology is applied to acoustic fields emitted by impinging jets approximating a point source and an overexpanded supersonic jet. Noise source maps that included the scanning sensor and a dense block distribution have increased spatial resolution and reduced sidelobes. The ability of the continuous scan paradigm to provide high-definition noise source maps with a lower sensor count is confirmed in this work as well. The effect of the proposed signal segmentation on sparse arrays is discussed.

This work aims at improving the current state-of-the-art in noise source localization techniques and phased array technologies by extending and adapting distinct traditional beamforming and deconvolution techniques to microphone phased arrays that contain continuously-scanning sensors. The continuous-scan approach is capable to attain a high-resolution noise source localization, which is of utmost importance when analyzing certain aeroacoustic sources. Care must be taken when handling the microphone signals from continuously-scanning sensors as these are non-stationary due to the traversing of a spatially-varying acoustic field. Quasi-stationarity is sought by dividing the signals into smaller, quasi-stationary blocks and by applying a frequency-dependent window within each block. The motion of the sensors also requires modification of the steering vectors used in beamforming to include a Doppler-shifted frequency. Optimal block schedules versus frequency are proposed and demonstrated to exploit the benefits of the continuous-scan paradigm by enhancing the spatial resolution of the images while containing the computational cost. Beamforming is carried out using three distinct approaches: application of the classical delay-and-sum technique to the cross-spectral matrix obtained for each blocks, followed by assembly of non-repeated elements of each block; a cross-spectral matrix completion process; and a partial fields decomposition method. The last two approaches result in a unified cross-spectral matrix that enables deconvolution of the array output and the use of advanced beamforming approaches such as orthogonal or functional beamforming. This work features three deconvolution approaches: DAMAS, Clean-SC, and the Richardson-Lucy method. All the beamforming and deconvolution methods are applied in conjunction with the proposed signal processing to the acoustic fields emitted by an impinging-jets source, a subsonic turbulent jet in isolation and integrated with a shielding plate, and a supersonic jet in isolation and with upstream reflector surfaces. Introduction of a single scanning sensor to a far-field array improves dramatically the fidelity of beamforming. The deconvolved images further improve the spatial resolution. The point spread function and the impinging jets source are used to assess the performance of all the techniques. The source distributions obtained with the continuous-scan approaches are compared to those obtained utilizing an array containing fixed sensors only. The techniques are then used to predict the effect of a shielding plate on the subsonic turbulent jet, and discern the location of the peak noise source as a function of frequency. The methods are also applied to the imaging of the supersonic flow issuing from a convergent nozzle that presented the screech phenomenon. The jet oscillated in well-known mode B (lateral). The continuous-scan paradigm is capable of obtaining the location of the screech sources and determination of the fine shock-cell structure of the supersonic jet flow from far-field microphone measurements only, underscoring its potential. Addition of conical reflector surfaces to the supersonic jet gave rise to a new mode E, with tonal components that do not fall into any known category (mode A1, A2, B or C). The source distribution of mode E and mode B is analyzed.