Model-based design of experiments based on local model networks for nonlinear processes with low noise levels
Model-based design of experiments based on local model networks for nonlinear processes with low noise levels
复制标题
基于局部模型网络的低噪声非线性过程实验设计
DOI：
10.1109/acc.2011.5990833
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
O. Nelles
中科院分区：
文献类型：
--
作者：
Benjamin Hartmann;Tobias Ebert;O. Nelles
最常见的实验设计方法是经典设计、几何设计和优化设计。这两类方法都没有将有关过程行为的具体信息纳入实验设计中。在优化设计的情况下，通常选择底层模型结构作为低阶多项式，其灵活性受到很大限制，如果用于高维问题，则会导致问题。此外，这些方法的重点在于方差误差的最小化。然而，在许多应用中，与通常导致较大偏置误差的高度非线性行为相比，过程噪声可以忽略不计。因此，本文提出了新算法 HilomotDoE，这是一种主动学习算法，旨在最小化模型的偏差误差。这是通过局部模型网络的迭代细化并同时添加一定数量的测量点来实现的。演示示例以及与常见 D 最优设计的理论比较显示了 HilomotDoE 对于上述问题类别的有用性。
Most common methods for experiment design are classical, geometric designs and optimal designs. Both categories of methods don't incorporate specific information about the process behavior into the design of experiments. In the case of optimal design often the underlying model structure is chosen as low order polynomial which is very restricted in its flexibility and causes problems, if used for higher-dimensional problems. Furthermore, the focus of these approaches lies on the minimization of the variance error. However, in many applications the process noise is negligible in comparison to the highly nonlinear behavior which usually causes a large bias error. Therefore, this paper presents the new algorithm HilomotDoE which is an active learning algorithm that aims to minimize the bias error of the model. This is achieved by an iterative refinement of a local model network and simultaneously the addition of a certain amount of measurement points. Demonstration examples and theoretical comparisons with the common D-optimal design show the usefulness of HilomotDoE for the mentioned problem class.