非充分模拟模型的随机克立格法
Stochastic Kriging for Inadequate Simulation Models
摘要：
随机克里格法是一种流行的元建模技术，用于表示仿真模型的未知响应面。然而，仿真模型可能是不充分的，在这个意义上，它与感兴趣的真实系统之间可能存在不可忽略的差异。不考虑模型的差异可能会导致对真实系统性能的错误预测，并误导决策过程。本文提出了一个元模型，扩展随机克里金法，将模型的差异。模拟输出和真实数据都被用来表征模型的差异。所提出的元模型可以增强对实际系统性能的预测。我们得出的实验设计和分析的一般结果，并证明了所提出的元模型相对于竞争方法的优势。最后，我们研究了公共随机数（CRN）的影响。众所周知，CRN的使用通常不利于随机克里金法的预测精度。相比之下，我们表明，CRN在新的背景下的效果是相当复杂的。CRN的使用可能是有害的，也可能是有益的，这取决于观测误差的大小与其他相关参数之间的相互作用。
英文摘要：
Stochastic kriging is a popular metamodeling technique for representing the unknown response surface of a simulation model. However, the simulation model may be inadequate in the sense that there may be a non-negligible discrepancy between it and the real system of interest. Failing to account for the model discrepancy may conceivably result in erroneous prediction of the real system's performance and mislead the decision-making process. This paper proposes a metamodel that extends stochastic kriging to incorporate the model discrepancy. Both the simulation outputs and the real data are used to characterize the model discrepancy. The proposed metamodel can provably enhance the prediction of the real system's performance. We derive general results for experiment design and analysis, and demonstrate the advantage of the proposed metamodel relative to competing methods. Finally, we study the effect of Common Random Numbers (CRN). The use of CRN is well known to be detrimental to the prediction accuracy of stochastic kriging in general. By contrast, we show that the effect of CRN in the new context is substantially more complex. The use of CRN can be either detrimental or beneficial depending on the interplay between the magnitude of the observation errors and other parameters involved.
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