Automated symbolic model identification for nonlinear dynamical systems from time-series data with limited sampling frequency and precision

Zhou, Long

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https://hdl.handle.net/2142/117539 Copy

Description

Title

Automated symbolic model identification for nonlinear dynamical systems from time-series data with limited sampling frequency and precision

Author(s)

Zhou, Long

Issue Date

2022-10-28

Director of Research (if dissertation) or Advisor (if thesis)

Zhang, Yang

Doctoral Committee Chair(s)

Zhang, Yang

Committee Member(s)

• Huff, Kathryn D.
• Bretl, Timothy Wolfe
• Uddin, Rizwan

Department of Study

Nuclear, Plasma, & Rad Engr

Discipline

Nuclear, Plasma, Radiolgc Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• System identification
• Black-box modeling
• Nonlinear systems

Abstract

The advancement in data science has influenced many fields in science and engineering. One revolutionizing application is the use of data-driven modeling methods to extract the governing equations of unknown systems from measurement data. Such modeling approaches require little a priori knowledge and have the potential to automate the scientific discovery process. Different from the traditional black-box modeling in system identification, these methods seek concise mathematical expressions to describe the system, which provide better explainability of the underlying process. One of the implementations of data-driven model discovery in the engineering field is the Sparse Identification of Nonlinear Dynamics (SINDy) method. This method utilizes sparse regression and compressed sensing techniques to find models that are linear in the parameters. We studied the behavior of the SINDy method under nonideal data, where both the sampling frequency and the measurement precision are limited, and proposed two improvements to make the method more robust in real-world applications. Under low sampling frequencies, the derivative approximated by numerical methods suffers from large systematic error. We solved this problem using neural-network-based system identification, utilizing adjacent samples in the phase space to improve the derivative estimation for time-invariant systems. Low measurement precision under low sampling frequencies makes noise hard to filter. We mitigated this problem by designing a sparse regression method with high noise tolerance, using random dropout and adaptive thresholding on ridge coefficient (DATRidge). The DATRidge method can find multiple candidate models of different sparsity and fitness. We use a Pareto front to present the results for making trade-offs. We tested our method on four model systems: the Van der Pol oscillator, the Lorenz system, the boiling water reactor (BWR) model by March-Leuba et al., and the glycolytic oscillator in bioengineering. Our method successfully recovered all the nonlinear polynomial equations in these systems, using data with limited sampling frequency and precision. In all the tests, our method shows a much higher tolerance to imperfect data than the SINDy method. As an extension, we studied the possibility of estimating variable relevance by applying layer-wise relevance propagation (LRP) on the neural network model. Since a dependent variable may not be affected by all other variables, excluding the irrelevant variable helps reduce the dimension of the search space. We show that due to the curse of dimensionality, the data required for making such estimations grows exponentially with the number of variables in the system. Since the trajectory of a dynamical system usually does not provide dense coverage of the phase space, the relevance estimation is generally not reliable.

Graduation Semester

2022-12

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Long Zhou

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