Orthogonal contributor number for the measurement of sound power

Orthogonal contributors to a global error represent a very efficient design method in terms of both sensing and control of noise radiation. In practice the price of a sensing system will be determined by the number of errors it must resolve. Therefore predicting the most efficient way of measuring radiation power is an important problem. Recently work has compared sensing the number of vibration modes to the number of orthogonal contributors to radiated power. The required number of vibration modes was based on the proximity of the structural mode resonance frequency and the excitation frequency. While ultimately this technique will result in a valid estimate of radiated power, it is shown here that the number of structural modes can be minimized by first considering orthogonal radiators based on structural mode amplitudes. Two disturbance cases are considered: a point force and an even disturbance coupling to each structural mode. Also, under these conditions the practicality of estimating the number of orthogonal radiators when it is assumed that each contributor is equal in amplitude is examined. Finally in an attempt to optimism the number of signals to be sensed, a variable error margin for the estimate of power, based on the ratio of the sound power at each frequency to the maximum peak in the considered frequency range is proposed and analyzed.