Energy quantities, which are calculated from pressure and particle velocity, yield a great deal of information about acoustic fields. Errors in pressure or particle velocity estimation lead to bias errors the estimation of energy quantities. The bias errors arise from different probe configurations and processing methods. Two processing methods are examined: the traditional method and the recently developed Phase and Amplitude Gradient Estimation (PAGE) method. These two methods are compared to investigate how each estimates pressure and particle velocity and the subsequent bias errors in a plane wave, standing wave, and spherical spreading wave field. Analytical expressions are derived for the energy quantity estimation using ideal one-dimensional probes. A simulation of the field from a baffled circular piston and measurements using ideal two-dimensional probes is computed. Compared to the traditional method, the PAGE method significantly extends the range of frequencies for which the results are accurate. It is found that a probe with a center microphone significantly reduces the estimation error and extends the usable range of frequencies. The PAGE method with unwrapping, perfectly matches the analytical results for plane waves, while the traditional method is only good at wavelengths that are large compared to the probe size. Furthermore, the PAGE method has a constant bias error in spherical wave fields due to the 1/r decrease in pressure. The traditional method has a frequency dependent bias error that is much worse at higher frequencies. Lastly, the PAGE method has the same or worse error for the standing wave. As an application of energy quantities, acoustic intensity is used to develop an equivalent source model for jet noise from an F-22 at military and afterburner engine conditions. An optimization is used to find the best-matching wavepacket model for measured intensity vectors. The results are compared to another intensity method of estimating the source region and source directivity, and the two methods have good agreement.

An alternative pressure-sensor based method for estimating the acoustic intensity, the phase and amplitude gradient estimation (PAGE) method, is presented. This method is similar to the finite-difference p-p (FD) method, in which the intensity is estimated from pressure measurements made using an array of closely spaced microphones. The PAGE method uses the same hardware as the FD method, but does not suffer from the frequency-dependent bias inherent to the FD method. Detailed derivations of the new method and the traditional FD method are presented. Both methods are then compared using two acoustic fields: a plane wave and a three monopole system. The ability to unwrap the phase component of the PAGE method is discussed, which leads to accurate intensity estimates above previous frequency limits. The uncertainties associated with both methods of estimation are presented. It is shown that the PAGE method provides more accurate intensity estimates over a larger frequency bandwidth. The possibility of using a higher-order least-squares estimation with both methods is briefly demonstrated. A laboratory experiment designed to validate the PAGE method was conducted. The preliminary results from this experiment are presented and compared to analytical predictions. Finally, the application of the PAGE method to a static rocket test firing is presented. The PAGE method is shown to provide accurate intensity estimates at frequencies that are higher than possible with just the FD method.

Energy-based acoustic quantities provide vital information about acoustic fields and the characterization of acoustic sources. Recently, the phase and amplitude gradient estimator (PAGE) method has been developed to reduce error and extend bandwidth of energy-based quantity estimates. To inform uses and applications of the method, analytical and experimental characterizations of the method are presented. Analytical PAGE method bias errors are compared with those of traditional estimation for two- and three-microphone one-dimensional probes. For a monopole field when phase unwrapping is possible, zero bias error is achieved for active intensity using three-microphone PAGE and for specific acoustic impedance using two-microphone PAGE. A method for higher-order estimation in reactive fields is developed, and it is shown that a higher-order traditional method outperforms higher-order PAGE for reactive intensity in a standing wave field. Extending the applications of PAGE, the unwrapped phase gradient is used to develop a method for directional sensing with improved bandwidth and arbitrary array response.

This Master´s thesis deals with principles of determination of the sound power level. At the very beginning there is an explanation of important concepts. Afterwards there is an overview of standards that deal with the sound power level determination, including the ČSN EN ISO 9614-1 standard which is used for the experiment. Last but not least, there is described the experiment, consisting of several measurements of the same object, but every time with different configuration of measuring and sound reflective surfaces.

Coherence, which gives the similarity of signals received at two microphone locations, can be a powerful tool for calculating acoustic quantities, particularly active acoustic intensity. To calculate active acoustic intensity, a multi-microphone probe is often used, and therefore coherence between all microphone pairs on the probe can be obtained. The phase and amplitude gradient estimator (PAGE) method can be used to calculate intensity, and is well suited for many situations. There are limitations to this method—such as multiple sources or contaminating noise in the sound field—which can cause significant error. When there are multiple sources or contaminating noise present, the coherence between microphone pairs will be reduced. A coherence-based approach to the PAGE method, called the CPAGE method, is advantageous.Coherence is useful in phase unwrapping. For the PAGE method to be used at frequencies where the probe microphone spacing is larger than half a wavelength (above the spatial Nyquist frequency), the phase of transfer functions between microphone pairs must be unwrapped. Phase differences are limited to a 2π radian interval, so unwrapping—adding integer multiples of 2π radians to create a continuous phase relation across frequency—is necessary to allow computation of phase gradients. Using coherence in phase unwrapping can improve phase gradient calculation, which in turn leads to improved intensity calculation.Because phase unwrapping is necessary above the spatial Nyquist frequency, the PAGE method is best suited to dealing with broadband signals. For narrowband signals, which lack coherent phase information at many frequencies, the PAGE method can give erroneous intensity results. One way to improve calculation is with low-level additive broadband noise, which provides coherent phase information that can improve phase unwrapping, and thereby improve intensity calculation. There are limitations to this approach, as additive noise can have a negative impact on intensity calculation with the PAGE method. The CPAGE method, fortunately, can account for contaminating noise in some situations. A magnitude adjustment—which arises naturally from investigation of the bias errors of the PAGE method—can account for the additional pressure amplitude caused by the contaminating noise, improving pressure magnitude calculations. A phase gradient adjustment—using a coherence-weighted least squares algorithm—can likewise improve phase gradient calculations. Both adjustments depend upon probe microphone coherence values. Though not immune to contaminating noise, this method can better account for contaminating noise. Further experimental work can verify the effectiveness of the CPAGE method.

The phase and amplitude gradient estimator (PAGE) method has proven successful in improving the accuracy of measured energy quantities over the p-p method, which has traditionally been used, in several applications. One advantage of the PAGE method is the use of phase unwrapping, which allows for increased measurement bandwidth above the spatial Nyquist frequency. However, phase unwrapping works best for broadband sources in free-field environments with high coherence. Narrowband sources often do not have coherent phase information over a sufficient bandwidth for a phase unwrapping algorithm to unwrap properly. In fact, phase unwrapping processing can cause significant error when there is no coherent signal near and above the spatial Nyquist frequency. However, for signals at any frequencies up to the spatial Nyquist frequency, the PAGE method provides correct intensity measurements regardless of the bandwidth of the signal. This is an improved bandwidth over the traditional method. For narrowband sources above the spatial Nyquist frequency, additional information is necessary for the PAGE method to provide accurate acoustic intensity. With sufficient bandwidth and a coherence of at least 0.1 at the spatial Nyquist frequency, a relatively narrowband source above the spatial Nyquist frequency can be unwrapped accurately. One way of using extra information, called the extrapolated PAGE method, uses the phase of a tone below the spatial Nyquist frequency and an assumption of a propagating field, and therefore linear phase, to extrapolate the phase above the spatial Nyquist frequency. Also, within certain angular and amplitude constraints, low-level broadband noise can be added to the field near a source emitting a narrowband signal above the spatial Nyquist frequency. The low-level additive broadband noise can then provide enough phase information for the phase to be correct at the frequencies of the narrowband signal. All of these methods have been shown to work in a free-field environment.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Neste trabalho é apresentado um estudo para a determinação do tamanho ótimo da malha de elementos, utilizando redes neurais artificiais, para o cálculo da intensidade útil. A ideia principal é treinar as redes de modo a possibilitar a aprendizagem e o reconhecimento do melhor tamanho para diversas áreas superficiais em fontes sonoras com geometria plana. A vantagem de se utilizar redes neurais artificiais deve-se ao fato de apresentarem um único tamanho para a obtenção da intensidade útil, consequentemente, uma redução significativa de tempo computacional quando comparado com o tempo de cálculo de uma malha bem refinada. Ensaios numéricos com placas planas - geometria separável que permite uma solução analítica - são utilizados para se realizar comparações. É apresentado um estudo comparativo entre o tempo computacional gasto para a obtenção da intensidade útil e o mesmo com a malha otimizada via redes neurais artificiais. Também é apresentada uma comparação do nível de potência sonora mediante solução numérica, a fim de validar os resultados apresentados pelas redes neurais. / In this paper, a study to determine the optimal size of the mesh elements, using artificial neural networks, to calculate useful intensity is presented. The main idea is training the neural networks, enabling them learning and recognizing the best size for the various superficial areas in sound sources with at geometry. The advantage of using artificial neural networks is due to the fact that they present a single size for obtaining the useful intensity, thereby significantly reducing computation time compared with the calculation time for a too fine mesh. Numerical tests with at plates - separable geometry that enables an analytical solution - are used to make comparisons. A comparative study of the computational time spent to obtain the useful intensity and the computational time spent to obtain the useful intensity using the mesh optimized via artificial neural networks is presented. A comparison of the sound power level obtained by the numerical solution in order to validate the results using neural networks is also presented.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Neste trabalho é apresentado um estudo para a determinação do tamanho ótimo da malha de elementos, utilizando redes neurais artificiais, para o cálculo da intensidade útil. A ideia principal é treinar as redes de modo a possibilitar a aprendizagem e o reconhecimento do melhor tamanho para diversas áreas superficiais em fontes sonoras com geometria plana. A vantagem de se utilizar redes neurais artificiais deve-se ao fato de apresentarem um único tamanho para a obtenção da intensidade útil, consequentemente, uma redução significativa de tempo computacional quando comparado com o tempo de cálculo de uma malha bem refinada. Ensaios numéricos com placas planas - geometria separável que permite uma solução analítica - são utilizados para se realizar comparações. É apresentado um estudo comparativo entre o tempo computacional gasto para a obtenção da intensidade útil e o mesmo com a malha otimizada via redes neurais artificiais. Também é apresentada uma comparação do nível de potência sonora mediante solução numérica, a fim de validar os resultados apresentados pelas redes neurais. / In this paper, a study to determine the optimal size of the mesh elements, using artificial neural networks, to calculate useful intensity is presented. The main idea is training the neural networks, enabling them learning and recognizing the best size for the various superficial areas in sound sources with at geometry. The advantage of using artificial neural networks is due to the fact that they present a single size for obtaining the useful intensity, thereby significantly reducing computation time compared with the calculation time for a too fine mesh. Numerical tests with at plates - separable geometry that enables an analytical solution - are used to make comparisons. A comparative study of the computational time spent to obtain the useful intensity and the computational time spent to obtain the useful intensity using the mesh optimized via artificial neural networks is presented. A comparison of the sound power level obtained by the numerical solution in order to validate the results using neural networks is also presented.

Orientador: Jose Maria Campos dos Santos / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-08T16:32:33Z (GMT). No. of bitstreams: 1 Moraes_ElsonCesar_M.pdf: 10024919 bytes, checksum: 5229531ae57fbedd477ddafcf581d5b2 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho apresenta-se uma implementação e avaliação experimental da grandeza acustica denominada de Intensidade Acustica Supersonica (IAS), a qual permite determinar a parcela da intensidade acustica de uma fonte sonora que sera radiada para o campo distante. Tal grandeza permite quantificar de forma mais precisa a eficiencia de radiação ou não de radiadores acusticos na solução dos problemas de vibroacustica. A IAS origina-se da Holografia Acustica de Campo Proximo (Nearfield Acoustic Holography - NAH) e tem por objetivo identificar as regiões de uma fonte de ru?do que contribuem para a potencia sonora radiada para o campo distante (supersonica) filtrando, consequentemente, a parcela referente as ondas sonoras recirculantes e evanescentes (subsonicas). O trabalho apresenta uma breve revisão teorica dos fundamentos da holografia acustica plana usando a transformada de Fourier e sua extensão para obtenção da Intensidade Acustica Supersonica. Com base no NAH para sistemas em coordenadas Cartesiano (holografia plana) implementou-se em linguagem MatLab um algoritmo do calculo da IAS e simulações em estrutura plana do tipo placa foram realizadas. Os resultados simulados foram verificados atraves de medições experimentais em uma placa real com as mesmas propriedades, dimensões, condições iniciais e de contorno. Os resultados obtidos são analisados e discutidos / Abstract: This work presents an experimental implementation and evaluation of the acoustic parameter named Supersonic Acoustic Intensity (SAI) which permits determining the part of the acoustic intensity of sound source that will be radiate to farfield. This parameter permits quantify precisely the radiation efficiency or acoustic radiator to solve the vibroacoustic problems. SAI had origin from Nearfield Acoustic Holography (NAH) it has as objective identify the regions of the sound source that contribute to the sound power radiated to the far field (supersonic) filtered out as a result the part of the sound recirculating and evanescence waves (subsonic). The work presents a brief theoretical review of the planar acoustic holography fundaments using the Fourier Transformed and its extension to obtain the supersonic acoustic intensity. With base in the NAH for coordinates systems (planar holography) it was implemented in MatLab language an algorithm from the SAI calculus and simulation in planar structure type plate were achieved. The simulated results were verified through experimental measurements in a realistic plate with the same properties, dimension, initial conditions and boundaries. The results obtained are analyzed and discussed. / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

This thesis describes the phase and amplitude correction of 12.7 mm diameter, Type-1 microphones for three frequency bands, including within the infrasound regime, and its application to acoustic measurements. Previous data stem from acoustic intensity measurements using two-dimensional, four-microphone probes, which emphasized the requirement of having the acoustic phase and amplitude difference be much greater than the interchannel mismatch. Although correcting the amplitude/phase is well-known, obtaining the necessary transfer functions in the infrasound regime is challenging because (1) signal-to-noise ratios are often poor, (2) long measurement times are required for averaging, and (3) microphone responses vary significantly across these low frequencies. In this paper, a convenient infrasound source previously studied for infrasound adverse effects on humans is intended for performing a relative calibration. This work also seeks to elaborate recommendations for probe spacing, averages or length recordings, and instrument mismatch. The last two chapters show the PAGE method application in infrasonic sources. Those chapters have the intensity measurements using free-field microphones with larger separation distances than commercial intensity probes but compact compared to state of the art in infrasonic arrays.