Linear System Identification in a Nonlinear Setting - Nonparametric analysis of the nonlinear distortions and their impact on the best linear approximation

TL;DR

This paper investigates the detection and analysis of nonlinearities in system identification, assessing the reliability of linear models amidst nonlinear distortions, and providing tools to evaluate potential gains from nonlinear modeling.

Contribution

It introduces nonparametric methods to detect nonlinearities early, studies the validity of linear identification under nonlinear distortions, and offers tools to quantify benefits of nonlinear models.

Findings

Nonlinearities can be detected without extensive data increase.

Linear models remain reliable under certain nonlinear distortions.

Tools are provided to evaluate when nonlinear modeling offers significant advantages.

Abstract

This article addresses the following problems: 1) First, a nonlinearity analysis is made looking for the presence of nonlinearities in an early phase of the identification process. The level and the nature of the nonlinearities should be retrieved without a significant increase in the amount of measured data. 2) Next it is studied if it is safe to use a linear system identification approach, even if the presence of nonlinear distortions is detected. The properties of the linear system identification approach under these conditions are studied, and the reliability of the uncertainty bounds is checked. 3) Eventually, tools are provided to check how much can be gained if a nonlinear model were identified instead of a linear model. Addressing these three questions forms the outline of this article. The possibilities and pitfalls of using a linear identification framework in the presence of nonlinear distortions will be discussed and illustrated on lab-scale and industrial examples. In this article, the focus is on nonparametric and parametric black box identification methods, however the results might also be useful for physical modeling methods. Knowing the actual nonlinear distortion level can help to choose the required level of detail that is needed in the physical model. This will strongly influence the modeling effort. Also, in this case, significant time can be saved if it is known from experiments that the system behaves almost linearly. The converse is also true. If the experiments show that some (sub-)systems are highly nonlinear, it helps to focus the physical modeling effort on these critical elements.