An overview of reconstructing acoustic pressure fields using the HELS method

Abstract

The acoustic pressures radiated from complex vibrating structures are reconstructed by using the Helmholtz equation least-squares (HELS) method [Wang and Wu, J. Acoust. Soc. Am. 102, 2020–2032 (1997); Wu and Yu, ibid. 104, 2054–2060 (1998)]. Specific examples include an engine block and the interior space of a passenger vehicle. These structures are of arbitrary shapes and geometry, containing sharp edges and corners, and abrupt changes in surface contour. To test the robustness of the HELS method, measurements of field acoustic pressures are taken over a planar surface at a certain distance away from the structure. The reconstructed acoustic pressures, however, extend over the entire (nonplanar) surface of the structure. Note that the input data in these cases are not error free due either to measurement uncertainties or to the loss of the near-field effect. On the other hand, reconstructed acoustic pressures consist of predominantly the near-field effect. Hence the problem becomes mathematically ill-posed. To overcome this ill-posedness difficulty, an optimization scheme is developed which enables one to obtain satisfactory reconstruction results with a relatively few number of measurements in the field. The HELS method is shown to be effective in the low- to mid-frequency range, and can become a robust noise diagnostic tool for analyzing structure-borne sounds. [Work supported by NSF.]