Probabilistic Torsional Vibration Analysis of a Marine Diesel Engine Shafting System: The Level Crossing Problem

Abstract

A probabilistic approach to the torsional vibration problem of a marine diesel engine shafting system has been developed. In this analysis, the shafting shear stress is found to be a Gaussian, harmonizable cyclostationary process with a harmonic series representation consisting of two complex conjugate components. In this paper, the level crossing problem for this stress process is studied. Two methods for estimating the probability that the stress exceeds a specified threshold at least once over a given time interval are presented. In the first method, a local maximum of the process is approximated by the value of the corresponding envelope at the time of occurrence of this maximum. A Markov-type condition is assumed to hold for the local maxima. The second method assumes that the maximum of the process over a reasonable number of cycles is approximately equal to that of the envelope process. The envelope crossings are assumed to constitute a Poisson process. The two methods are applied to estimate the upcrossing probability in various cases. The results of both approaches are found to be in good agreement with those from Monte Carlo simulation.