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.

The propagator for the reduced scalar Helmholtz equation plays a significant role in both analytical and computational studies of acoustic direct wave propagation. Path (functional) integrals are taken to provide the principal representation of the propagator and are computed directly. The path integral is the primary tool in extending the classical Fourier methods, so appropriate for wave propagation in homogeneous media, to inhomogeneous media. For transversely inhomogeneous environments, the n-dimensional Helmholtz equation can be exactly factored into separate forward and backward one-way wave equations. A parabolicbased (one-way) phase space path integral construction provides the generalization of the Tappert/Hardin split-step FFT algorithm to the full one-way (factored Helmholtz) wave equation. These extended marching algorithms can readily accommodate density profiles and range updating, and further, in conjunction with imbedding methods, provide the basis for incorporating backscatter effects. In a complementary manner, for general range-dependent environments, elliptic-based (two-way) path integral constructions lead to an approximate representation of the propagator (Feynman/Garrod) and a natural statistical (Monte Carlo) means of evaluation. Taken together, the path integrals provide the basis for a global analysis in addition to providing a unifying framework for dynamical approximations, resolution of the square root operator, and the concept of an underlying stochastic process. The one-way marching algorithms are applied to ocean acoustic environments, seismological environments, and extreme model environments designed to establish their range of validity and manner of breakdown.

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Public reporting burden for tsis collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of infotnnadon, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Sukie 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY)2 SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR / MONITOR'S ACRONYM(S)Office of Naval Research One Liberty Center 875 North Randolph Street 11. SPONSOR / MONITOR'S REPORT Arlington, VA 22217-1995 NUMBER(S) DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release; distribution is unlimited.13. SUPPLEMENTARY NOTES *Hughes Associates, Inc., Baltimore, MD **Nova Research, Inc., Alexandria, VA ABSTRACTThe Volume Sensor Prototype (VSP) system has been designed to detect, flame, smoldering fires, water releases (e.g., pipe ruptures), gas leaks, and hot objects and to discriminate nuisance sources, such as hot work. The tests presented in this report were conducted on the ex-USS Shadwvell from July 25 to August 5, 2005, to evaluate the VSP systems operating in six test compartments. The VSP performance was compared to the performance of state-of-the-art spot-type smoke detection systems. The VSP systems demonstrated the ability to function in multiple compartments, specifically discriminating between multiple types of events in multiple compartments. The VSP systems demonstrated the ability to discriminate between source types by detecting flaming and smoldering fire sources, water releases, and gas releases while rejecting nuisance sources. The VSP systems generally performed better than Video Image Detectors and spot-type smoke detection systems relative to range of detection capabilities, ability to detect fires, ability to reject nuisance sources, and speed of response.

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