Prior Knowledge for System Identification with Linear and Nonlinear FIR Models

本计画将探讨线性与非线性系统辨识之新方法。它融合了经典方法和现代基于内核的机器学习思想。本计画的目标是针对线性与非线性有限冲激响应模型，发展一类新颖的系统辨识方法。这些都是非常灵活的，固有的稳定，输出误差模型，其参数是线性的。关键的挑战是自动控制的偏差/方差的权衡，尽管大量的标称参数/dimensions.In特别是，各种可能性，通过正则化惩罚项（或先验的贝叶斯解释）的脉冲响应的形状纳入先验知识应广泛追求。这将允许灰箱建模方法与不同程度的透明度之间的平滑过渡，从黑色到白色，在不同流行的模型结构的Ljung提出的经典离散分类。子目标2：通过局部模型网络将子目标1的许多特征转移到非线性世界。在试图天真地将线性FIR模型转换为非线性模型时，一个关键的见解是，大量的参数变成了大量的维度。这个问题通过局部模型网络的一个特殊功能来解决：有效性函数和局部模型的输入空间的分离。

This project shall investigate a new approach to linear and nonlinear system identification. It fuses classical methods with modern kernel-based machine learning ideas. The goal of this project is the development of a class of novel system identification methods for linear and nonlinear finite impulse response models. These are extremely flexible, inherently stable, output error models which are linear in their parameters. The key challenge is to automatically control the bias/variance tradeoff in spite of the huge number of nominal parameters/dimensions.In particular, various possibilities to incorporate prior knowledge on the shape of the impulse response via the regularization penalty term (or prior in terms of the Bayesian interpretation) shall be pursued extensively. This shall allow for gray-box modeling approaches with a smooth transition between different degrees of transparency from black to white, in contrast to the classical discrete classification proposed by Ljung for various popular model structures.Subgoal 1: Improvement of the performance and interpretability of linear regularized finite impulse response models. Subgoal 2: Transfer of many features from subgoal 1 to the nonlinear world via local model networks. A key insight while trying to transfer linear FIR models to nonlinear ones naively is, that the huge number of parameters becomes a huge number of dimensions. This issue is solved via a special feature of local model networks: the separation of input spaces for the validity functions and for the local models.