Generating extreme ship responses using non-uniform phase distributions

Modified Gaussian phase distributions are used to generate short time series containing a specific extreme value of a ship response. The corresponding incident wave train is calculated via linear systems theory. Sample response and wave time series are compared to the expected time series as calculated by probabilistic analysis. The average of the sample response time series compares favorably to the expected time series, but the average of the sample wave trains does not, in general, match the expected wave train. These comparisons show the danger in estimating extreme ship responses considering only extreme waves. A sample analysis for a Great Lakes bulk carrier is included for illustration.