Hardware Reference
In-Depth Information
Fig. 4.4 Fill distance h and
separation distance q
q
h
quality and numerical stability, one should maximize the ratio max( q/h ). Clearly this
objective is achieved for a well distributed, almost uniform, set of training points. But
in general, for scattered data, one deals with q h . In case of uniform distribution
of data, there is no way for further improving both objectives: there is a trade-off
situation between min h and max q . This fact explains the choice of Sect. 4.2.2 :
Random DoE (i.e., a uniform Monte Carlo) is a good algorithm for generating points
to be used as training database by RSM, since it maximizes the ratio max( q/h ). In
general any space filler DoE can be used.
Some enhanced techniques could be implemented in case a even more accurate
uniformity is necessary. E.g., Incremental Space Filler , for augmenting an existing
database in order to fill the space in a uniform way (filling the gaps), or Uniform
Latin Hypercube that uses Latin Hypercube - an advanced Monte Carlo which maps
better the marginal probability distribution of each single variable—for generating
random numbers conforming to a uniform distribution.
In case of discrete variables, the separation distance q has a lower bound, strictly
related to the variables resolution (number of levels). In general numerical stability
is not a pressing problem. On the contrary, in order to achieve approximation quality,
it is important to fill as uniformly as possible the gaps in the regular grid formed by
the set of all the combinations of admissible discrete variables values. Usually space
filling techniques, even though conceived for continuous design space, are able to
manage correctly also discrete variables. So in general neither approximation quality
is an insurmountable problem, given that the seek for uniformity in a discrete design
space is properly considered.
 
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