EXTREME VALUES OF FIRST- AND SECOND-ORDER WAVE-INDUCED VESSEL MOTIONS

A recently developed expansion for the joint probability density function of two variables has been used to develop a means of determining the mean up-crossing rate of a combined first- and second-order random process. The first term in the series corresponds to the assumption that the response displacement and velocity processes are statistically independent, and further terms depend upon the joint displacement-velocity cumulants. The extreme statistics are then determined using the Poisson assumption of up-crossings. The accuracy of the method is examined by comparing the results with time domain simulation, and it is found that the displacement and velocity are, to a good approximation, statistically independent for the examples studied.

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