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.
- Design Engineering Division and Computers in Engineering Division
Conservative Prediction via Safety Margin: Design Through Cross-Validation and Benefits of Multiple Surrogates
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Viana, FAC, Picheny, V, & Haftka, RT. "Conservative Prediction via Safety Margin: Design Through Cross-Validation and Benefits of Multiple Surrogates." Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 35th Design Automation Conference, Parts A and B. San Diego, California, USA. August 30–September 2, 2009. pp. 741-750. ASME. https://doi.org/10.1115/DETC2009-87053
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