Bayesian optimal design of experiments (BODE) has been successful in acquiring information about a quantity of interest (QoI) which depends on a black-box function. BODE is characterized by sequentially querying the function at specific designs selected by an infill-sampling criterion. However, most current BODE methods operate in specific contexts like optimization, or learning a universal representation of the black-box function. The objective of this paper is to design a BODE for estimating the statistical expectation of a physical response surface. This QoI is omnipresent in uncertainty propagation and design under uncertainty problems. Our hypothesis is that an optimal BODE should be maximizing the expected information gain in the QoI. We represent the information gain from a hypothetical experiment as the Kullback-Liebler (KL) divergence between the prior and the posterior probability distributions of the QoI. The prior distribution of the QoI is conditioned on the observed data and the posterior distribution of the QoI is conditioned on the observed data and a hypothetical experiment. The main contribution of this paper is the derivation of a semi-analytic mathematical formula for the expected information gain about the statistical expectation of a physical response. The developed BODE is validated on synthetic functions with varying number of input-dimensions. We demonstrate the performance of the methodology on a steel wire manufacturing problem.
翻译:Bayesian 最佳实验设计( BODE) 成功地获得了关于一定数量利益( QoI) 的信息,这种利益取决于黑盒功能。 BODE的特点是,在通过填充抽样标准选择的特定设计中,按顺序询问功能。然而,目前大多数 BODE 方法在特定情况下运作,如优化,或学习黑盒功能的普遍分布。本文件的目的是设计一个 BODE,以估计对实际反应表面的统计预期值为条件。 QoI 在不确定性问题的传播和设计中无处不在。 我们的假设是,最佳的BODE应该最大限度地增加QoI的预期信息收益。我们代表从假设实验中获得的信息收益,如Kullback-Liebler(KL)在前一和后一概率分布上的差异。 QOI 先前的分布取决于观察到的数据和QoI 的后一发行问题。 我们的假设是观察到的数据和假设的假设性实验。 本文的主要贡献是,一个假设性能的数学模型的模型,是对数字的预测。