Conical Statistical Optimal Near-Field Acoustic Holography with Combined Regularization

Abstract

For the sound field reconstruction of large conical surfaces, current statistical optimal near-field acoustic holography (SONAH) methods have relatively poor applicability and low accuracy. To overcome this problem, conical SONAH based on cylindrical SONAH is proposed in this paper. Firstly, elementary cylindrical waves are transformed into those suitable for the radiated sound field of the conical surface through cylinder-cone coordinates transformation, which forms the matrix of characteristic elementary waves in the conical spatial domain. Secondly, the sound pressure is expressed as the superposition of those characteristic elementary waves, and the superposition coefficients are solved according to the principle of superposition of wave field. Finally, the reconstructed conical pressure is expressed as a linear superposition of the holographic conical pressure. Furthermore, to overcome ill-posed problems, a regularization method combining truncated singular value decomposition (TSVD) and Tikhonov regularization is proposed. Large singular values before the truncation point of TSVD are not processed and remaining small singular values representing high-frequency noise are modified by Tikhonov regularization. Numerical and experimental case studies are carried out to validate the effectiveness of the proposed conical SONAH and the combined regularization method, which can provide reliable evidence for noise monitoring and control of mechanical systems.

Conical near-field acoustic holography based on cylindrical wave function of variable radius and nonconformal plane measurement

“…In our previous work (Cheng et al, 2021), according to the changing radius of cone, the application of SOCNAH was extended from cylindrical to conical sources. On this basis, VR-SOCNAH is proposed in this paper and simulation is carried out under different parameters, which improves the accuracy of sound field reconstruction for conical sources.…”

MCML-BF: A Metal-Column Embedded Microstrip Line Transmission Structure with Bias Feeders for Beam-Scanning Leakage Antenna Design

“…The primary focus of holographic antenna design is to generate a holographic image that records the information of the target wave. The target wave can be restored by illuminating the holographic image with a reference wave source [ 56 , 57 ]. The reference wave equation, target wave equation, and interference wave equation for energy recording can respectively be expressed as follows: where represents the position information of the recording point on the holographic structure, represents the propagation constant of the reference wave, and represents the propagation constant of the object wave, which is the free-space propagation constant.…”

Sound Field Reconstruction Using Prolate Spheroidal Wave Functions and Sparse Regularization

“…Over the past four decades, numerous NAH algorithms with different sound field spatial bases and inverse methods have been proposed. Some notable methods include spatial discrete Fourier transform-based NAH (DFT-NAH) [2][3][4], the inverse boundary element method (IBEM) [5][6][7], statistically optimized near-field acoustic holography (SONAH) [8][9][10], Helmholtz equation least squares (HELS) [11][12][13] and the equivalent source method (ESM) [14][15][16]. In these algorithms, the sound field is approximated by a series of spatial bases, such as wave functions or simple sources, while the weighting coefficients are estimated by the measured data.…”

“…Consequently, Williams [4] employed the fast Fourier transform to solve a partial domain problem caused by the unbaffled cylinder with flat endcaps. Cheng [10] expressed the sound field of large conical surfaces as a superposition of characteristic elementary waves, which are constructed by cylindrical wave functions through cylinder-cone coordinates transformation. Overall, it is beneficial to carefully select or construct a spatial basis that aligns well with the elongated sources.…”