Transient near-field acoustical holography (NAH) formulation is derived from the Helmholtz equation least squares (HELS) method to reconstruct acoustic radiation from a spherical surface subject to transient excitations in a free field. To facilitate derivations of temporal solutions, we make use of the Laplace transform and expansion in terms of the spherical Hankel functions and spherical harmonics, with their coefficients settled by solving a system of equations obtained by matching an assumed-form solution to the measured acoustic pressure. To derive a general form of solution for a temporal kernel, we replace the spherical Hankel functions and their derivatives by polynomials, recast infinite integrals in the inverse Laplace transform as contour integrals in a complex s-plane, and evaluate it via the residue theorem. The transient acoustic quantities anywhere including the source surface are then obtained by convoluting the temporal kernels with respect to the measured acoustic pressure. Numerical examples of reconstructing transient acoustic fields from explosively expanding, impulsively accelerating, and partially accelerating spheres, and that from a sphere subject to an arbitrarily time-dependent excitation are depicted. To illustrate the effectiveness of HELS-based transient NAH formulations, all input data are collected along an arbitrarily selected line segment and used to reconstruct transient acoustic quantities everywhere.
Vibrating structures are often mounted on or located near a passive plane surface with finite acoustic impedance, and hence the acoustic pressures measured in a half-space bounded by the surface consist of both the direct radiation from the structure and the reflection from the boundary surface. In order to visualize the direct radiation from the source into free space, a reconstruction method based on expansion in half-space spherical wave functions is proposed. First, the series of half-space spherical wave functions is derived based on the analytical solution of the sound field due to a multipole source located near an impedance plane. Then the sound field in the half-space is approximated by the superposition of a finite number of half-space expansion terms. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching this assumed solution to the total acoustic pressures in the half-space. The free-space radiation can finally be reconstructed via multiplying the free-space spherical wave functions by the corresponding coefficients. Numerical simulation examples of a vibrating sphere and a vibrating baffled plate are demonstrated. The effects of specific acoustic impedance of the boundary and the locations of the measurement points on the accuracy of reconstruction are examined.
A thorough theory of detection problem using active time reversal has been investigated in several recent papers. Although active time reversal method is theoretically superior to the others, its practical implementation for target detection is far more difficult. This paper investigates the detection problem using passive decomposition of the time reversal operator (DORT) method. Provided that the signal components can be modeled as a linear combination of basis vectors with an unknown signal subspace, the generalized likelihood ratio test (GLRT) is derived based on Neyman-Person lemma with the unknown signal subspace replaced by its maximum likelihood estimation. The test statistics is one of the dominant eigenvalues of the time reversal operator for a point-like scatterer. Finally, the performance of the DORT detector is investigated with acoustic data collected from a waveguide tank. The experimental results show that the DORT detector can provide, respectively, 1.4 dB, 1.1 dB, and 0.8 dB performance gains over the energy detector given false alarms rate of 0.0001, 0.001, and 0.01.
A non-projection fringe vision measurement system suitable for vibration monitoring was proposed by using the concept of a 2D optical coherence vibration tomography (2D-OCVT) technique. An artificial quasi-interferogram fringe pattern (QIFP), similar to the interferogram of the 2D-OCVT system, was pasted onto the surface of a vibrating structure as a sensor. Image sequences of the QIFP were captured by a high-speed CMOS camera that worked as a detector. It was possible to obtain both the in-plane and out-of-plane vibration simultaneously. The in-plane vibration was obtained by tracking the center of the imaged QIFP using an image cross-correlation method, whilst the out-of-plane vibration was obtained from the changes in period density of the imaged QIFP. The influence of the noise sources from the CMOS image sensor, together with the effect of the imaging distance, the period density of the QIFP and also the key parameters of the fringe density enhanced by the spectrum correction method on the accuracy of the displacement measurement, were investigated by numerical simulations and experiments. Compared with the results from a conventional accelerometer-based measurement system, the proposed method was demonstrated to be an effective and accurate technique for measuring structural vibration without introducing any extra mass from the accelerometer. The significant advantages of this method include its simple installation and real-time dynamic response measurement capability, making the measurement system ideal for the low- and high-frequency vibration monitoring of engineering structures.
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