Application of the LMS algorithm to identify the surface velocity responsible for the radiated sound pressure

A time domain approach based on the least mean square (LMS) algorithm is applied to reconstruct the source amplitude and source distribution on a plate. For this a numerical experiment is established. A boundary element model is used to calculate the required impulse response functions describing the pressure in near- and far-field for a given volume flow at individual patches on the plate. Three different cases are considered. Firstly, a volume flow is given to a single patch. The LMS algorithm is used to reconstruct the source signal by means of receiving positions in the far-field. Secondly, the approach is used to identify the vibration pattern and source signal on a line of patches. Thirdly, a vibration pattern was given to the plate as the whole. For the reconstruction an assumption was made about the underlying vibration patterns (e.g. expansion in vibrational modes). Such an approach proved to be very time efficient and powerful. It also showed the need to place the receiving positions in the near-field to be able to obtain correct results over the whole frequency range. However, this is not a problem of the approach based on the LMS algorithm, but just due to the underlying physics. It is not possible to deduce the near-field from far-field observations, and therefore the vibrations mainly leading to a near-field are simply not visible in the far-field