Prior Knowledge for System Identification with Linear and Nonlinear FIR Models

该项目将研究一种新的线性和非线性系统辨识方法。它融合了经典方法和现代基于核的机器学习思想。本项目的目标是开发一类新的线性和非线性有限脉冲响应模型的系统辨识方法。这些是非常灵活、内在稳定的输出误差模型，它们的参数是线性的。关键的挑战是尽管名义参数/维度的数量巨大，但如何自动控制偏差/方差权衡。尤其是，应广泛探索通过正则化惩罚项(或贝叶斯解释中的先验知识)合并关于脉冲响应形状的先验知识的各种可能性。这将允许灰箱建模方法在从黑到白的不同透明度之间平滑过渡，而不是Ljung为各种流行的模型结构提出的经典离散分类。次级目标1：改进线性正则化有限脉冲响应模型的性能和可解释性。次目标2：通过本地模型网络将许多特征从次目标1转移到非线性世界。在尝试将线性FIR模型天真地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特性来解决：将有效性函数和局部模型的输入空间分开。

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.