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I have a finite element model of a geometric structure which is computationally expensive to solve. The model is parameterized with 3 parameters. Each configuration is solved for an increasing load between 0 and load_max at n discrete loads. So the output (a specific property of the geometric structure) per configuration is a series of n values. I evaluated 3^3=27 combinations of these parameters.

Given the input combinations and the 27 output value series, how can I perform a sensitivity analysis to quantify the influence of each parameter on the output value and to determine which parameter combination can minimize the output value?

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    $\begingroup$ I'm not sure if this is properly described as "sensitivity-analysis". It seems more like standard experimental design issues in engineering. Are you assuming / worried about the possibility of interactions? If not, fractional-factorial designs are worth exploring. $\endgroup$ Commented Apr 4, 2015 at 15:56
  • $\begingroup$ Yes, I assume that there are interactions between the parameters. $\endgroup$ Commented Apr 4, 2015 at 16:01

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With only 27 data points (and you haven't said how precise these values are), you should be concerned about overfitting the data. I'd start by fitting a simple quadratic response surface model and see whether the predictions look reasonable.

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