Second Order Statistics and Discrete-Time Detection Modeling for Partially Saturated Processes

The basic problem in underwater detection is formulated under the general assumptions of partially saturated propagation of narrow‐band and acoustic signals. Expressions for the joint probability density function (PDF) of ρ, the short‐time average root‐mean‐square pressure at the receiver are obtained. This joint PDF is a general result reducing to the PDF’s for the fully saturated and the unsaturated cases for limiting values of the appropriate variables. Subsequently, defining detection as occurring whenever ρ exceeds a specified threshold level ρ0 and, using the above results, the upcrossing and downcrossing statistics of the envelope process are studied. Closed form expressions for the probability mass functions (PMF’s) of the interarrival time (time between two successive detections) and holding time (time between an upcrossing and the first subsequent downcrossing) are obtained. Results using our partially saturated detection model reduce, in limiting cases, to results already obtained in the literature for fully saturated and unsaturated propagation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86233/1/Perakis15.pd

Discrete-time Detection Modeling for Unsaturated Ocean Acoustic Propagation

The basic problem in ocean acoustic detection is formulated under the assumption of unsaturated sound propagation. The latter essentially amounts to a constant signal plus Gaussian noise. Detection is defined as occurring whenever ρ, the root mean square pressure at the receiver, exceeds a specified threshold level ρ0. A two‐state, discrete‐time Markov model is derived, and closed‐form expressions for the probability mass functions of the number of time steps separating two successive detections (interarrival time) or one detection and the first subsequent ‘‘downcrossing’’ (holding time) are presented. Expressions for the joint probability density function of ρ at two different points in time are obtained and used to determine the relevant one‐step transition probabilities of the Markov model. Sample results using the model are finally presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86235/1/Perakis17.pd

A Sequential Hypothesis Testing, Optimal Stopping Problem in Underwater Acoustic Detection

A sequential hypothesis testing, optimal stopping problem in underwater acoustic detection is formulated and solved using dynamic programming. The problem calls for deciding whether acoustic signals being received over long ranges in the ocean are due to a source or to ambient noise alone, so as to minimize the expected value of a specified cost function over a given time horizon. The cost function incorporates a constant cost per observation as well as terminal costs for false acceptance of either hypothesis. According to previous work by the authors, and without loss of generality, modeling the acoustic signals assumes a two‐state discrete‐time Markov process for each of the two hypotheses, the state of the process depending on whether the intensity of the signal at the receiver is above a specified threshold or not. The decision process presented is based on observations of the signal’s ‘‘interarrival times,’’ that is, the time intervals between two successive detection events. The algorithm is then extended into more than two alternative hypotheses (several ‘‘false’’ targets) and results using both simulated and experimental acoustic data for the two and three hypotheses cases are presented. Computational issues in implementing the algorithms as well as possible extensions of this work are finally discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86234/1/Perakis16.pd

A Basic Problem of Resource Allocation in Target Tracking

Stochastic dynamic programming techniques are used to formulate and solve the problem of tracking two independent and stationary targets with one sensor in order to maximize a certain measure of performance. At any point in time, the sensor, usually a passive sonar array, can be allocated to only one of the two targets. Assuming the fluctuation process in the ocean to be governed by a phase‐random multipath law, the sensor ’’holds’’ the target when ρ, the root‐mean‐square pressure at the receiver, is above a user‐specified threshold. Using discrete time models for the ocean acoustic detection process formulated in earlier papers, we solve the problem for a finite horizon of observations using several alternative objective and reward/penalty functions. Delays of user‐specified magnitude in ’’switching’’ from one target to the other are also incorporated in our algorithms. Examples using both real and simulated data are presented and discussed. Finally, future research directions are suggested.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86218/1/Perakis18.pd

Statistical Methods for Planning Diesel Engine Overhauls in the U. S. Coast Guard

The United States Coast Guard has recently investigated new strategies to maintain cutter propulsion diesel engines. Reliability centered maintenance with statistical methods may allow the time between costly scheduled overhauls to be increased. One indicator of engine aging is the number of failures experienced with increasing operating hours. The purpose of this paper is to investigate the failure-time relationship of the ALCO 251 marine diesel propulsion engine operated on Reliance class cutters. This analysis used exponential, Weibull, and three-part composite Weibull failure density functions to model engine casualty data dating back to 1978. The data does not indicate the source of the engine failure, but every failure had a significant operational impact. Results indicate an increasing failure rate as the engine ages to the 24,000 hour overhaul time. The evidence indicates a constant failure useful life region, but the increasing failure rate from the Weibull models suggests that the periodic over-hauls do not prevent wearout failures. As a result, the Coast Guard should consider refining diesel engine overhaul policy in order to prevent increasing age-related failures.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86221/1/Perakis3.pd

Closed-form Approximations and Series Representations for Partially Saturated Ocean Acoustic Processes

An approximate, closed‐form expression for the value of the integral encountered in the calculation of the probability density function (PDF) of the envelope of a partially saturated ocean acoustic process is obtained. Furthermore, an expression of this PDF as a series of modified Bessel functions is presented. The results may also be directly applied to the evaluation of the PDF encountered in the structural reliability analysis of rotating machinery components. Numerical applications show that the closed‐form expression is always within 1%2% of the exact result. The required computational effort is substantially lower than that required by direct numerical integration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86232/1/Perakis14.pd

New Models on the Ocean Acoustic Detection Process

The basic problem of the ocean acoustic detection process is formulated analytically under the assumption of fully developed saturated phase random multipath acoustic fluctuations. Detection is defined as occurring whenever ρ, the root‐mean‐square pressure at the receiver, exceeds a specified threshold level ρ0. Two models, one exact and one approximate, are developed for obtaining the probability density functions of the time between two successive detections and of the time ρ is above ρ0 (holding time). The two models are compared with one another and with the extensively used (λ, σ) model. One of the reasons that the latter model has a limited success in practice is the inability to estimate the appropriate value for λ, a parameter which is determined empirically. In this paper we have derived an appropriate value for λ, in terms of ν (the single path root‐mean‐square phase rate), σ21 (half the long time average mean‐square pressure at the receiver) and ρ0 (the threshold level). Using this equivalent value for λ, we observe that our exact and approximate detection models exhibit similar long‐term behavior but markedly different short‐term characteristics as compared with the (λ,σ) model. This is due to the memory of the process, a property that cannot be accounted for in the (λ,σ) model. A comparison of these models with data obtained from various field experiments demonstrates, in most cases, an improved capability over the (λ,σ) model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86219/1/Perakis19.pd

Seaborne Petrochemical Spill Analysis Within the United States, 1992–1999

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42404/1/30310532.pd

Problems in Optimal Fleet Deployment

The problem of minimum-cost operation of a fleet of ships that has to carry a specific amount of cargo between two ports in a given time period for a specific, fixed contract price is studied. Detailed and realistic operating cost functions are developed. Sensitivity analyses are performed to study the effects of small or large changes of one or more cost components on the total cost. A realistic model for the annual transport capacity as a function of speed is also used, in contrast to the linear relation used in the literature.http://deepblue.lib.umich.edu/bitstream/2027.42/91683/1/Publication_No_295.pd

Multi-Attribute Decision Analysis of Mandatory Ballast Water Treatment Measures in the US Great Lakes

Mandatory ballast water management, resulting in an increase of required freight rates on the St. Lawrence Seaway, could induce a modal shift away from marine transportation. Such a shift may cause such side effects as increased air pollution and lower transportation safety. A multinomial logit model is built to predict the changes in market shares of competing transportation modes. Two wheat transportation scenarios are studied. The results show that only a small shift, if at any, will accompany mandatory measures for ballast water treatment. To evaluate the trade-offs between the side effects brought by any modal shifts and the NIS invasion effects, the analytic hierarchy process is used to analyze the preferences of federal and state decision-makers. Analysis of questionnaires shows that among the three alternatives, ballast water exchange, filtration/UV, and heat, ballast water exchange proved to be the favored method.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86222/1/Perakis4.pd