We propose a general methodology of sequential locally optimal design of experiments for explicit or implicit nonlinear models, as they abound in chemical engineering and, in particular, in vapor-liquid equilibrium modeling. As a sequential design method, our method iteratively alternates between performing experiments, updating parameter estimates, and computing new experiments. Specifically, our sequential design method computes a whole batch of new experiments in each iteration and this batch of new experiments is designed in a two-stage locally optimal manner. In essence, this means that in every iteration the combined information content of the newly proposed experiments and of the already performed experiments is maximized. In order to solve these two-stage locally optimal design problems, a recent and efficient adaptive discretization algorithm is used. We demonstrate the benefits of the proposed methodology on the example of the parameter estimation for the non-random two-liquid model for narrow azeotropic vapor-liquid equilibria. As it turns out, our sequential optimal design method requires substantially fewer experiments than traditional factorial design to achieve the same model precision and prediction quality. Consequently, our method can contribute to a substantially reduced experimental effort in vapor-liquid equilibrium modeling and beyond.

中文翻译：

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汽液平衡建模的序贯优化实验设计


我们提出了一种用于显式或隐式非线性模型的连续局部最优实验设计的通用方法，因为它们在化学工程中，特别是在气液平衡建模中大量存在。作为一种顺序设计方法，我们的方法在执行实验、更新参数估计和计算新实验之间迭代交替。具体来说，我们的顺序设计方法在每次迭代中计算一整批新实验，并且这批新实验是以两阶段局部最优方式设计的。本质上，这意味着在每次迭代中，新提出的实验和已经执行的实验的组合信息内容被最大化。为了解决这些两阶段局部最优设计问题，使用了一种最新且高效的自适应离散化算法。我们以窄共沸汽液平衡的非随机二液模型的参数估计为例，证明了所提出方法的优点。事实证明，我们的序贯优化设计方法比传统的因子设计需要更少的实验才能达到相同的模型精度和预测质量。因此，我们的方法可以大大减少汽液平衡建模及其他方面的实验工作。