HELS法在循环平稳声场全息重建中的理论与实验研究

Helmholtz 方程最小二乘法利用一组球面波基函数拟合声源产生的声场，根据重建和实际声压的误差最小原则，利用最小二乘法确定基函数展开的项数以及对应的权重系数，该方法具有计算效率高和需要测点少的优点，在实际工程中有很大的实用性.Helmholtz 方程最小二乘法和其他近场声全息方法一样都是针对平稳声场，对非平稳声场的分析很少.对于实际工程中经常遇到的一类特殊非平稳声场——循环平稳声场，现有的技术多以单通道信号分析为主，其高阶统计量在故障诊断领域应用较广.分析了循环平稳声场中Helmholtz方程最小二乘 关键词： 声全息 循环平稳 Helmholtz 方程 球面波

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

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.