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Long Zhou - Final Exam

Event Type
Meeting
Sponsor
NPRE
Location
https://illinois.zoom.us/j/82171991860?pwd=Q1JnMDFPQmpwc2E2b0NhL2hNMzdhdz09. Meeting ID: 821 7199 1860 Password: 138534
Virtual
wifi event
Date
Dec 6, 2021   10:00 am - 12:00 pm  
Views
5
Originating Calendar
NPRE Events

 

Automated Symbolic Model Identification for Nonlinear Dynamic Systems from Time-series Data with Limited Sampling Frequency and Precision

ABSTRACT: The advancement in data science has influenced many areas of science and engineering.One revolutionizing application is using data-driven modeling methods to extract the governing equations and physical laws directly from the data collected from unknown systems. Such modeling approaches avoid the influence of human bias and have the potential to enable automated scientific discovery. The resulting models from the process are presented in human-understandable form, and the most efficient representation is the symbolic equations.

One of implementations of data-driven model discovery in the engineering field is he sparse identification on nonlinear dynamical systems (SINDy) method. This method utilizes sparse regression and compressed sensing techniques to find models in the form of the sum of nonlinear symbolic features. We studied the behavior of SINDy under imperfect data, where both the sampling frequency and data precision are limited, and purpose two improvements for making the method more robust in real-world applications.

Under low sampling frequency, the derivative approximation using numerical methods suffer from large error. We solve this problem using neural-network-based offline system identification, which utilizes all the adjacent samples in the phase space to predict the derivatives, rather than only the adjacent samples in the time domain. Low data precision upon low sampling frequency results in noises hard to filter, which have a negative impact on the sparse regression method. We mitigate this problem by designing a sparse regression method with high noise tolerance, using random dropout and adaptive thresholding on ridge coefficient (DATRidge). DATRidge results in a large variety of candidate models of different sparsity and fitness, we create a Pareto front to do the final trade-off.

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 from these systems,under limited sample frequency and limited data precision. In all the tests, the data quality required by our DATRidge method to recover the model is much lower than that required by the original SINDy method.

 

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