Near-field acoustic holography (NAH) has become an effective tool for acoustic source identification. It usually requires many microphones near the source surface to catch sufficient evanescent waves for good spatial resolution. Besides, such a measurement is time-consuming and uneconomical in practice; standard measurements using densely and uniformly populated sensors are sometimes impossible when dealing with massive sources. Eventually, the compressive sensing (CS) technique has been suggested for NAH, which employs a sparse number of sensors. Most existing works in NAH based on compressive sensing theory have focused on developing acoustic models and algorithms; In contrast, less attention has been paid to the best practice of sensor placement. The present study aims to propose and validate the methods for the optimal selection of sparse measuring points using the compression technique for NAH. Due to the small number of measuring sensors, the transfer matrix between source and hologram points becomes underdetermined. Under such a data condition, even though every piece of data would be felt precious for the reconstruction, the information from some sensors should be discarded further because not all data provide meaningfully independent information. To this end, effective independence and singular-value monitoring methods are used to test the selection of the optimal sensor position from a set of candidate positions. The former chooses non-redundant measurement data, whereas the latter keeps the low condition number of the transfer matrix. Simulation results with vibrating plates show that optimized sensor positions could effectively facilitate the optimality of the approximate solution for CS theory compared to uniformly or randomly distributed measurements. It is because the established transfer matrix has the lowest condition number due to being sparser and more independent sensor positions. Experimental results exhibit a better reconstruction error (10–40%) at 200–2,000 Hz when the sensor positions are optimized than the uniform or random selection approaches.

In practical conditions, near-field acoustic holography (NAH) requires the measurement environment to be a free sound field. If vibrating objects are located above the reflective ground, the sound field becomes non-free in the presence of a reflecting surface, and conventional NAH may not identify the sound source. In this work, two types of half-space NAH techniques based on the Helmholtz equation least-squares (HELS) method are developed to reconstruct the sound field above a reflecting plane. The techniques are devised by introducing the concept of equivalent source in HELS-method-based NAH. Two equivalent sources are tested. In one technique, spherical waves are used as the equivalent source, and the sound reflected from the reflecting surface is regarded as a linear superposition of orthogonal spherical wave functions of different orders located below the reflecting surface. In the other technique, some monopoles are considered equivalent sources, and the reflected sound is considered a series of sounds generated by simple sources distributed under the reflecting surface. The sound field is reconstructed by matching the pressure measured on the holographic surface with the orthogonal spherical wave source in the vibrating object and replacing the reflected sound with an equivalent source. Therefore, neither technique is related to the surface impedance of the reflected plane. Compared with the HELS method, both methods show higher reconstruction accuracy for a half-space sound field and are expected to broaden the application range of HELS-method-based NAH techniques.

Source identification and sound field reconstruction using near-field acoustical holography (NAH) is particularly challenging when the measurement data are relatively fewer than the sources to reconstruct. Fast wideband acoustical holography (WBH) is an inverse solution method based on the compressed sensing theory, which enables the NAH with such sparse measurement and extends its applicable frequency range. WBH usually works well at high frequencies, but it is often unsatisfactory when dealing with low-frequency coherent sources. This work proposes a modified WBH method to improve low-frequency and high-frequency performance substantially. It is developed by combining the conventional WBH and the steepest descent methods in computing the initial source strength values. It contrasts the WBH method using specific initial values for the equivalent sources. The iteration is repeated to ensure that these source strengths are not involved in the threshold filtering process during the iteration process. The simulation and experiment show that the proposed modified WBH substantially improves the reconstruction accuracy of coherent sound sources at low frequencies without degrading the reconstruction performance at mid to high-frequencies.

The number of hologram points in near-field acoustical holography (NAH) for a vibro-acoustic system plays a vital role in conditioning the transfer function between the source and measuring points. The requirement for many overdetermined hologram points for extended sources to obtain high accuracy poses a problem for the practical applications of NAH. Furthermore, overdetermination does not generally ensure enhanced accuracy, stability, and convergence, owing to the problem of rank deficiency. To achieve satisfactory reconstruction accuracy with underdetermined hologram data, the best practice for choosing hologram points and regularization methods is determined by comparing cross-linked sets of data-sorting and regularization methods. Three typical data selection and treatment methods are compared: iterative discarding of the most dependent data, monitoring singular value changes during the data reduction process, and zero padding in the patch holography technique. To test the regularization method for inverse conditioning, which is used together with the data selection method, the Tikhonov method, Bayesian regularization, and the data compression method are compared. The inverse equivalent source method is chosen as the holography method, and a numerical test is conducted with a point-excited thin plate. The simulation results show that selecting hologram points using the effective independence method, combined with regularization via compressed sensing, significantly reduces the reconstruction error and enhances the modal assurance criterion value. The experimental results also support the proposed best practice for inverting underdetermined hologram data by integrating the NAH data selection and regularization techniques.