An ensemble source spectra model for merchant ship-radiated noise

This paper presents an evaluation of the classical model for determining an ensemble of the broadband source spectra of the sound generated by individual ships and proposes an alternate model to overcome the deficiencies in the classical model. The classical model, proposed by Ross [Mechanics of Underwater Noise (Pergamon, New York, 1976)] postulates that the source spectrum for an individual ship is proportional to a baseline spectrum with the constant of proportionality determined by a power-law relationship on the ship speed and length. The model evaluation, conducted on an ensemble of 54 source spectra over a 30-1200-Hz to 1200-Hz frequency band, shows that this assumption yields large rms errors in the broadband source level for the individual ships and significantly overestimates the variability in the source level across the ensemble of source spectra. These deficiencies are a consequence of the negligible correlation between the source level and the ship speed and the source level and the ship length. The alternate model proposed here represents the individual ship spectra by a modified rational spectrum where the poles and zeros are restricted to the real axis and the exponents of the terms are not restricted to integer values. An evaluation of this model on the source spectra ensemble indicates that the rms errors are significantly less than those obtained with any model where the frequency dependence is represented by a single baseline spectrum. Furthermore, at high frequencies (400 to 1200 Hz), a single-term rational spectrum model is sufficient to describe the frequency dependence and, at the low frequencies (30 to 400 Hz), there is only a modest reduction in the rms error for a higher order model. Finally, a joint probability density on the two parameters of the single term model based on the measured histograms of these parameters is proposed. This probability density provides a mechanism for generating an ensemble of ship spectra.