Data-driven Methods for Signal Analysis and Nonlinear System Identification

Authors

Cristian Felipe López Ruano, University of Nebraska-LincolnFollow

First Advisor

Keegan J. Moore

Committee Members

Florin Bobaru, Joseph Turner, Jian Wang, Richard Wood

Date of this Version

7-2025

Document Type

Dissertation

Citation

A dissertation presented to the faculty of the Graduate College at the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Mechanical Engineering and Applied Mechanics

Under the supervision of Professor Keegan J. Moore

Lincoln, Nebraska, July 202

CHAPTER 2 has been published as: López C., Moore K.J. “Enhanced Adaptive Linear Chirplet Transform for Crossing Frequency Trajectories”, Journal of Sound and Vibration, 578:118358, 2024. doi: 10.1016/j.jsv.2024.118358

CHAPTER 3 has been published as: López C., Singh A., Naranjo Á., Moore K.J. “A Data-Driven, Energy-based Approach for Identifying Governing Dynamics in Vibrating Structures Directly from Measurements”. Mechanical Systems and Signal Processing. 225:112341, 2025. doi: 10.1016/j.ymssp.2025.112341

CHAPTER 4 has been published as: López C., Moore K.J. “Energy-based dual-phase dynamics identification of clearance-types nonlinearities”. Nonlinear Dynamics. doi: 10.1007/s11071-025-11098-z

CHAPTER 5 is a manuscript: López C., Naranjo Á., Salazar D., Moore K.J. “Weak-form modified sparse identification of nonlinear dynamics”. https://arxiv.org/abs/2410.17838, under review in the Journal of Computational Physics

CHAPTER 6 is a manuscript: López C., Moore K.J. “Structural System Identification via Validation and Adaptation”, submitted to Nonlinear Dynamics. https://arxiv.org/abs/2506.20799

Comments

Copyright 2025, Cristian Felipe López Ruano. Used by permission

Abstract

In recent years, data-driven modeling has gained considerable attention in nonlinear system identification, offering a powerful alternative to traditional physics-based methods. This has been possible by advances in machine learning, sparse regression, and differential equations in a weak form, which allow the accurate capture of complex nonlinear dynamics, even when the measurements are in strong background noise. Moreover, integrating these models with physical knowledge further enhances their reliability and interpretability, making them suitable for a wide range of science and engineering applications.

In this dissertation, we investigate algorithms for data-driven nonlinear system identification to obtain ordinary differential equations that govern the system dynamics. This task requires data from dynamical systems, theoretical techniques such as Lagrangian mechanics, conservation of mechanical energy, the weak form of differential equations, and computational approaches such as automatic differentiation, sparse regression, and neural networks.

We start with a signal decomposition method that deals with when the signal components have crossover frequencies. We then move to a structural system identification method that novelly leverages the system’s energy to achieve its aim for the case of smooth nonlinearities. Then, we extend this method to a more complex scenario where clearance nonlinearities are present. We then combine two system identification methods to create a robust approach to obtain governing equations of motion for different dynamical systems when the data is under strong noise. Finally, we introduce an approach that simultaneously performs parametric system identification, validation, and uncertainty quantification.

Advisor: Keegan J. Moore