Another approach, as followed herein, has for its basis the 

 categorization of the various model characteristics. This approach 

 is systematic and therefore, more instructive and illuminating. 

 However, it suffers from the disadvantage of requiring some know- 

 ledge of the general nature of the problem and of the pertinent 

 ship-motion literature. But, this is a meaningful requirement for 

 a seminar such as this. Therefore, it is appropriate to categorize 

 the various model characteristics in terms of a hierarchy, as shown 

 in Figure 1, and to discuss the representative mathematical models 

 in terms of these characteristics. 



Deterministic versus Stochastic Models 



It seems natural to consider that the most important division 

 of mooring dynamic model characteristics is the division between 

 deterministic and stochastic models, as shown in Figure 1. A few 

 comments are in order. We know that if the input is deterministic, 

 then the output is deterministic. We also know that if the input 

 is stochastic, then the output should be stochastic. But, the 

 problem that emerges is - How is it (i.e., the output) computed? 

 Is it com.puted directly or indirectly? How many simulation runs 

 are needed? How long should each run be? What will it cost? and 

 so on . 



An example of a direct computation stochastic model is one 

 for which the non-linear terms appearing in the governing system 

 of equations have undergone "equivalent statistical linearization." 

 That is to say, that the process of linearizing the non-linear 

 terms is one in which the errors (associated with the linearized 

 terms) are minimized. 



This is in contrast to equivalent linearization in the 

 deterministic sense wherein the energy (or some other variable) 

 is averaged over one "cycle". 



Of course, another example of a direct stochastic model is 

 one wherein the system is linear. In this case, the output 

 statistics are obtained directly. Since there are all kinds of 



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