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首页> 外文期刊>Mathematical Problems in Engineering >On the Relation between NARX Clusters and Even/Odd Nonlinearities through Frequency-Domain Analysis
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On the Relation between NARX Clusters and Even/Odd Nonlinearities through Frequency-Domain Analysis

机译：通过频域分析研究NARX簇与偶/奇非线性之间的关系

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摘要

Although polynomial NARX models have been intensively used in nonlinear system identification, few papers discussed how to relate the inner nonlinearities to specific types of clusters and regressors. The objective of this paper is to discuss this relationship for a class of systems that contain even or odd nonlinearities. This class covers block-structured models (Hammerstein, Wiener, and others) and systems with dynamic nonlinearities. To achieve the paper's aim, a deep frequency-domain analysis is performed. For each type of nonlinearity, all the NARX clusters are investigated and the results show that each regressor type provides specific nonlinear contribution. The investigation is based on an output power spectra analysis when a specific multisinusoidal excitation is applied. According to the spectral contributions in some of the frequency lines, the nonlinearity classification is possible. By applying the same procedure to the clusters, one interprets how these clusters can (or not) contribute to explain the system nonlinearity. The paper findings have two major impacts: (i) one gains deep knowledge on how the nonlinearities are coded by the clusters, and (ii) this information can be used, for instance, to aid a structure selection procedure (ERR, term clustering, etc.) during the discarding of the clusters which are not able to explain the system nonlinear behavior. Some practical and experimental aspects are discussed, while numerical examples are presented to show the validity of the theoretical analysis.
机译：尽管多项式NARX模型已广泛用于非线性系统识别中，但很少有论文讨论如何将内部非线性与特定类型的簇和回归变量相关联。本文的目的是针对一类包含偶数或奇数非线性的系统讨论这种关系。该课程涵盖具有动态非线性的块结构模型（Hammerstein，Wiener等）和系统。为了达到本文的目的，进行了深入的频域分析。对于每种类型的非线性，都对所有NARX簇进行了研究，结果表明，每种回归类型都提供了特定的非线性贡献。该研究基于施加特定多正弦激励时的输出功率谱分析。根据某些频率线中的频谱贡献，可以进行非线性分类。通过对群集应用相同的过程，可以解释这些群集如何（或不可以）有助于解释系统非线性。论文的发现有两个主要影响：（i）深入了解群集如何对非线性进行编码；（ii）此信息可用于例如帮助进行结构选择程序（ERR，术语群集，等等）丢弃无法解释系统非线性行为的群集。讨论了一些实践和实验方面的问题，并通过数值例子说明了理论分析的有效性。

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