Theorical and experimental research on the HELS method in the cyclostationary acoustic field

Abstract

Helmholtz equation least square method (HELS) is based on the assumption that the acoustic field can be approximated by the superposition of a series of spherical waves. According to the principle of least square error between the reconstruction and measurement, the expansion number of the spherical wave equation and the related coefficients can be determined by the least-square method. The HELS method is applied in the practice due to its efficient computing and less measurements comparing with other acoustical holography algorithms. HELS and other near-field acoustic holography methods are all based on the stationary acoustic field. As a special example of the non-stationary acoustic field, the cyclostationary acoustic field is usually analyzed by dealing with signals in a single channel and its nth order statistics are often utilized to detect mechanical faults. In the present paper, HELS method is modified to analyze the cyclostationary acoustic field with the variance of cyclic spectrum density. The reconstruction in the appropriate cyclic frequency will supply visible acoustic field information, especially that hidden under the cyclostationary condition. A numerical simulation is done to verify the validity of the modified HELS, in which the effects of the ways of measurement are discussed. At last, a spherical sound box driven by cyclostationary signal is set in a semi-anechoic chamber and the acoustic field is reconstructed by modified HELS method.