Probabilistic Torsional Vibration Analysis of a Marine Diesel Engine Shafting System: An Alternative Approach to the Level Crossing Problem

Abstract

The level crossing problem is treated and the first excursion probability is presented for the case of a cyclostationary random process. A new method is then introduced, where the cyclostationary process is replaced with an equivalent stationary random process. The latter is defined to either (1) render exactly the same upcrossing rate at a given threshold as the time averaged upcrossing rate of the cyclostationary process, or (2) have an envelope process with the same upcrossing rate as the envelope of the cyclostationary process. Both these processes are assumed to have the same probability of upcrossing a specific threshold. An analytical expression is derived for this upcrossing probability for a certain form of a cyclostationary process and compared with existing results. The agreement between this approach and the "exact" but time-consuming "Markov approach" presented in earlier work of the authors is found to be excellent.