Optimal Sensor Positioning for the Sparse Measurement in the Acoustic Reconstruction of a Large Source

Abstract

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.