Probabilistic Assessment of Resonant Instability N. Themelis, National Technical University of Athens K.J. Spyrou, National Technical University of Athens ABSTRACT Near regularity of excitation is conducive to large amplitude responses. Moreover, higher waves tend to appear in groups (Draper 1971). These observations are the drivers of our approach for the probabilistic assessment of intact stability. The intention is to maintain the rigour and breadth of the deterministic approach while taking fully into account the probabilistic character of the seaway. Critical wave groups are specified on the basis of deterministic analysis. A procedure is put forward for calculating the probability of encountering these wave groups. A Ro-Ro ships tendency for instability due to resonant behaviour in beam seas is used as the showcase for demonstrating the feasibility of the approach. Keywords: ship stability, wave group, probabilistic assessment 1. INTRODUCTION The mechanics that govern extreme ship behaviour and could host loss of intact stability have been studied for several years in a primarily deterministic context. This analysis has improved our understanding of the various types of ship instability, some times supplying also simple criteria to guide design. However, none could disregard that potentially destabilizing environmental excitations are of a probabilistic nature. A method to interface the deterministic analyses of ship dynamics with wind/wave models and statistics has been proposed recently, exploiting the groupiness characteristic of high waves and the idea that the probability of occurrence of a certain instability could be assumed as equal to the probability of encountering the critical (or worse) wave groups that generate the instability (Spyrou, 2005, Spyrou & Themelis, 2005). The method builds upon certain ideas that have been around in the field of ship stability for a number of years: Tikka & Paulling (1990) for example, discussed the calculation of the probability of encountering a high run of waves in astern seas and determined combinations of ships speed and heading that could favour such an encounter. DeKat (1994) pointed out the importance of considering wave groups and he referred to the use of joint distributions of wave length and steepness in order to determine such wave groups, given a significant wave height and period. Along the same lines, Myrhaug et al. (1999) investigated synchronous rolling using joint distributions of successive wave periods, targeting essentially the encounter of a wave group with critical period. In the current paper our objective is to demonstrate the feasibility of our method of stability assessment, through detailed application to a specific ship, of Ro-Ro ferry type. A popular route in the Mediterranean Sea is selected and probabilities of instability due to beam-sea resonance (in format of critical time as percentage of the duration of the voyage) are calculated. Two, conceptually different, cases of assessment are presented. 2. THE PROPOSED METHODOLOGY Given a ship, the methodology can be deployed for short or long-term