Kernel Methods for Confidence Regions in Optimal Experimental Design and Parameter Estimation

可靠的模型是虚拟工艺设计和工艺优化的前提。为此目的，根据测量数据校准模型，由于测量和模型中的不准确性而导致不确定性。可靠性的度量是模型参数空间中的置信区域和模型函数的预测误差。对于非线性模型，迄今为止，这些都是从导致椭圆置信区域和相应的预测误差的线性化中获得的。由于线性化，这些不足以代表真实的不确定性。因此，可能会对不确定性作出过于乐观或过于悲观的假设。在这个项目中，基于核的分类方法，核最小封闭球（KMEB），结合自适应贝叶斯数据生成，将被使用和进一步发展，以达到一个现实的量化的不确定性。核心技巧允许任意形状的置信区域，将它们映射到一个抽象的特征空间，在这个空间中再次假设椭圆形（甚至球形）。这些不确定性措施理想地拟合模型的非线性，参数估计和最优实验设计的方法应该是数值上更强大和有效的，更可靠的结果。以多相反应体系为例，说明了该方法在化工领域的可行性和实用性。这种系统是已知的强非线性与不连续和不可微的行为，参数估计和实验设计，他们相应的挑战。KMEB为基础的技术，最初在这里展示了简单的例子，开发和使用，以获得有前途的新方法参数估计和最优实验设计。模型中的数据是从自适应贝叶斯抽样策略中收集的;测量数据来自该项目中进行的实验。

Reliable models are the prerequisite for virtual process design and process optimization. For this purpose, models are calibrated on measurement data, resulting in uncertainties due to inaccuracies in the measurements and in the models. A measure of reliability are confidence regions in the space of the model parameters and prediction errors for the model functions. For nonlinear models, these have so far been obtained from linearizations leading to elliptical confidence regions and the corresponding prediction errors. Due to the linearization, these do not adequately represent the real uncertainties. As a result, overly optimistic or overly pessimistic assumptions about the uncertainties may be made. In this project, kernel-based classification methods, the Kernel Minimal Enclosing Balls (KMEB), combined with adaptive Bayes-like data generation, will be used and further developed to arrive at a realistic quantification of the uncertainties. The core trick allows arbitrarily shaped confidence regions by mapping them to an abstract feature space in which the elliptical shape (even spherical) is again assumed. With these resulting uncertainty measures ideally fitted to the model nonlinearities, methods for parameter estimation and optimal experimental design should be numerically much more robust and efficient, and more reliable in terms of results. The feasibility and usefulness of this method for chemical engineering is exemplified for a reactive multiphase system. Such systems are known for strong nonlinearities with discontinuous and non-differentiable behavior; parameter estimation and experimental design for them are correspondingly challenging. The KMEB-based technique, initially demonstrated here with simple examples, is developed and used to obtain promising new methods for parameter estimation and optimal experimental design. Data from the model are collected from adaptive Bayesian sampling strategies; measurement data come from experiments conducted in the project.