Prior Knowledge for System Identification with Linear and Nonlinear FIR Models

使用线性和非线性 FIR 模型进行系统辨识的先验知识

• 批准号: 439767479
• 负责人: Professor Dr.-Ing. Oliver Nelles
• 金额: --
• 依托单位: Arbeitsgruppe Mess- und Regelungstechnik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/439767479?language=en
• 关键词: Prior; Knowledge; System; Identification; Linear

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.

本项目将研究线性和非线性系统辨识的新方法。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系统识别方法，用于线性和非线性有限脉冲响应模型。这些是非常灵活的，固有稳定的，输出误差模型，它们的参数是线性的。关键的挑战是自动控制偏差/方差权衡，尽管有大量的名义参数/维度。特别是，通过正则化惩罚项（或贝叶斯解释中的先验）将脉冲响应形状的先验知识纳入的各种可能性将得到广泛的研究。这将允许灰盒建模方法在从黑色到白色的不同透明度之间平滑过渡，这与Ljung为各种流行的模型结构提出的经典离散分类形成对比。子目标1：改进线性正则化有限脉冲响应模型的性能和可解释性。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。这个问题是通过局部模型网络的一个特殊特性来解决的：有效性函数和局部模型的输入空间分离。