Conservative Prediction via Safety Margin: Design through Cross Validation and Benefits of Multiple Surrogates

[Felipe A. C. Viana]

Dear all,

Here it is a reference on conservative surrogates:

F. A. C. Viana, V. Picheny, and R.T. Haftka, "Conservative Prediction
via Safety Margin: Design through Cross Validation and Benefits of
Multiple Surrogates," in: Proceedings of the ASME 2009 International
Design Engineering Technical Conferences & Computers and Information
in Engineering Conference: IDETC/CIE 2009, San Diego, USA, August 30 -
September 2, 2009, DETC2009-87053.

The use of surrogates for facilitating optimization and statistical
analysis of computationally expensive simulations has become
commonplace. Usually, surrogate models are fit to be unbiased (i.e.,
the error expectation is zero). However, in certain applications, it
might be interesting to safely estimate the response (e.g., in
structural analysis, the maximum stress must not be underestimated in
order to avoid failure). In this work we use safety margins to
conservatively compensate for fitting errors associated with
surrogates. We propose the use of cross-validation for estimating the
required safety margin for a given desired level of conservativeness
(percentage of safe predictions). We also check how well we can
minimize the losses in accuracy associated with conservative predictor
by selecting between alternate surrogates. The approach was tested on
two algebraic examples for ten basic surrogates including different
instances of kriging, polynomial response surface, radial basis neural
networks and support vector regression surrogates. For these examples
we found that cross validation (i) is effective for selecting the
safety margin; and (ii) allows us to select a surrogate with the best
compromise between conservativeness and loss of accuracy. We then
applied the approach to the probabilistic design optimization of a
cryogenic tank. This design under uncertainty example showed that the
approach can be successfully used in real world applications.

You can find more about it online:
http://fchegury.googlepages.com

All the best,
Felipe A.C. Viana