Frequency-Domain Analysis for Nonlinear Systems With Time-Domain Model Parameter Uncertainty

Abstract

Frequency-domain analysis of dynamic systems is important across many areas of engineering. However, whilst there are many analysis methods for linear systems, the problem is much less widely studied for nonlinear systems. Frequencydomain analysis of nonlinear systems using frequency response functions (FRFs) is particularly important to reveal resonances, super/sub-harmonics and energy transfer across frequencies. In this paper the novel contribution is a time-domain model-based approach to describing the uncertainty of nonlinear systems in the frequency-domain. The method takes a nonlinear inputoutput model that has normally distributed parameters, and propagates that uncertainty into the frequency-domain using analytic expressions based on FRFs. We demonstrate the approach on both synthetic examples of nonlinear systems and a real-world nonlinear system identified from experimental data. We benchmark the proposed approach against a brute-force technique based on Monte Carlo sampling and show that there is good agreement between the methods.

AC-BioSD : A biomolecular signal differentiator module with enhanced performance (extended version)

“…Performance characteristics of the output response that merit attention include deterministic features such as settling time, rising time, and overshoot as well as estimation of the variance or higher moments in the stochastic setting. Finally, our understanding of the non-local behavior of the BioSD modules would be enhanced by adopting more sophisticated mathematical approaches based, for example, on frequencydomain analysis methods for nonlinear systems [31], [32]. (18).…”

Interpretable Deep Learning for Nonlinear System Identification Using Frequency Response Functions With Ensemble Uncertainty Quantification

“…Additionally, it would be of interest to investigate how modern variational inference methods in deep learning for NSID [35], [36] could be linked to more efficient methods of uncertainty quantification in the frequency-domain. This has been done for NARX models [45], resulting in significant improvements in computational efficiency, and so highlights a future research gap to address for deep learning models.…”

“…Methods exist for propagating uncertainty in NARX models into the frequency-domain using Monte Carlo sampling [44] and analytic methods [45] but this has not yet been done for deep learning models. This is an important research gap to address because it will extend the use of NOFRF analysis with uncertainty quantification to models identified by deep learning identification methods, which are now becoming more popular.…”