Page 303 - Practical Design Ships and Floating Structures

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Corresponding to the wave spectrum Ss (w) of the seaway the response spectrum S, (0) represents
the energy distribution of the output signal. Utilizing the response amplitude operator H,", wave and
rcsponse spectra are related by

A significant double amplitude of system response (2s,), , comparable to the significant wave height
H, , follows from the response spectrum:

These significant double amplitudes characterize the behaviour of floating systems in stationary short-
term sea states. Comparing systems by means of significant double amplitudes allows to select the
most suitable design for a specific location and task, e.g. a lifting operation.
Development of new designs usually requires consideration of performance during longer time spans.
In this case long-term wave statistics are applied. If operational requirements limit the significant
double amplitude of response, e.g. acceleration, to (2i0)v , expected downtime due to exceeding
this limit can be evaluated. Applying the appropriate response amplitude operator Eqs. (1) and (2) are
evaluated for all classes of zero-up-crossing periods Tfff in the wave scatter diagram. This yields the
highest acceptable significant wave height as a function of zero-up- crossing periods T,Jf:

The values H,,l,,,, (ToJ) are transferred into the wave scatter diagram and sea states are assigned to a
feasible (H% < H,.,,!",,(TaJ)) and an infeasible (H, > Hs.,,,,,,,(TaJ)) region. The summation of all
occurrences of the infeasible region, krk,, related to the total number of observations ra,
yields the expected probability of downtime P

The index k ranges over all H, -classes where H,(Taf) exceeds H,,l,m,,(T,,)

To account for the non-uniform distribution of wave directions the computed values of expected
downtime pd8 are multiplied by the probability of occurrence q8. Summing up yields the averaged
downtime considering all wave directions

Before we apply this rational design criteria to optimize a semisubmersible a short review of the
optimization framework is given.