We study approaches to the robust model-based design of experiments in the context of maximum-likelihood estimation. These approaches provide robustification of model-based methodologies for the design of optimal experiments by accounting for the effect of the parametric uncertainty. We study the problem of robust optimal design of experiments in the framework of nonlinear least-squares parameter estimation using linearized confidence regions. We investigate several well-known robustification frameworks in this respect and propose a novel methodology based on multi-stage robust optimization. The proposed methodology aims at problems, where the experiments are designed sequentially with a possibility of re-estimation in-between the experiments. The multi-stage formalism aids in identifying experiments that are better conducted in the early phase of experimentation, where parameter knowledge is poor. We demonstrate the findings and effectiveness of the proposed methodology using four case studies of varying complexity.

我们在最大似然估计的背景下研究基于稳健模型的实验设计方法。这些方法通过考虑参数不确定性的影响，为优化实验的设计提供了基于模型的方法论的稳健性。我们在使用线性化置信区域的非线性最小二乘参数估计框架中研究了稳健的优化实验设计问题。我们在这方面研究了几个著名的鲁棒化框架，并提出了一种基于多阶段鲁棒优化的新方法。所提出的方法旨在解决一些问题，其中实验是按顺序设计的，并且有可能在实验之间进行重新估计。多阶段形式主义有助于识别在实验的早期阶段进行的更好的实验，在那里参数知识很差。我们使用四个不同复杂性的案例研究证明了所提出方法的发现和有效性。