Metamodeling techniques are now being widely used by many industries to replace complex and expensive simulation models so that optimization and probabilistic design studies can be done in a more practical and affordable way. Due to the complexity of many engineering design systems and to the lack of a deep understanding of the metamodeling methods by engineers, many questions related to metamodeling accuracy, confidence, robustness, efficiency, etc. are now frequently asked. The need to establish comprehensive guidelines for engineers to correctly and efficiently apply metamodeling methods to their optimization and probabilistic design tasks is becoming more and more important. Based upon experiences and lessons learned at General Electric in recent years, this paper discusses important metamodeling mathematical details and addresses several common issues engineers are likely to encounter when applying metamodeling techniques to realistic engineering problems. The paper provides detailed guidelines on the best practices of metamodel creation and its application to the design process. Many results from benchmark examples and real applications are included to justify certain guidelines and rules of thumb.

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