Assume a design space of N physical variables (e.g. flow rate, particle size, thermal properties, etc.) that can be reduced to M < N dimensionless variables by applying dimensional analysis.
The region of the N-dimensional hyperspace which is experimentally accessible is assumed to be known. The set of dimensionless variables Qi defines M families of curves in sub-parts of the space, e.g. if Q1 = x1*y1 then y1 = Q1/x1 where x1, y1 are physical variables and Q1 a dimensionless variable that becomes as a parameter in this family of curves.
The question is now how to find "extreme conditions" (points) along the edges of the permissible physical (hyper)region that maximize the differences in values of the dimensionless variables?
For the simplest case of N = 2 and M = 1, this could be done graphically by taking intersections of the family of curves obtained by varying Q1 with the 2-dimensional region (e.g. rectangle) given by the physically accessible variable space.
For N = 3 this already seems more challenging and for N > 3 no direct visualisation seems possible.
Can anyone point me towards suitable algorithms or texts addressing this problem? The end goal is an experimental design in Q space yielding e.g. a regression function for a dimensionless target variable.
Dear Jan,
I am not sure if I understand your question... but typically I take "physical limits" for the variables to set the boundaries of the DoE and then to efficiently populate the space I use a flavor of the Latin Hyper-cube algorithm (see attached document).
Kind regards,
Julian
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