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Generating Comprehensible Equations from Unknown Discrete Dynamical Systems Using Neural Networks

Maroli, John Michael
http://orcid.org/0000-0001-7844-6107
http://rave.ohiolink.edu/etdc/view?acc_num=osu1574760744876635

Abstract Details

2019, Doctor of Philosophy, Ohio State University, Electrical and Computer Engineering.
This research presents a novel framework for generating system equations from the input-output data of unknown discrete dynamical systems. The two-step process consists of system identification followed by a black box input-output analysis in the likes of Monte Carlo sample-based global sensitivity analysis. System identification is performed using temporal convolutional networks trained with only input-output data. A structured approach to network design and training is detailed for yielding accurate identification models and a benchmark is performed using a publicly available dataset known as the Silverbox. The trained identification model serves as a system emulator that can be excited at low computational cost, allowing for detailed sample-based sensitivity analysis. The key to the analysis is an imagined decomposition of the the model into a sum of less complex constituent functions of all input combinations. A method for sampling the constituent functions is presented to not only determine relevant constituents, but to estimate them as well. The sum of relevant constituent functions is equal to the original model, which parallels the source system of the original input-output data. The imagined decomposition of the identification model allows for a potentially complex estimation problem to be broken down into many smaller and less complex problems. The analysis resultant is a human comprehensible mathematical model for the discrete dynamical system, where comprehensibility implies that the equation gives insight into system operation. The presented framework helps to shed light on black box identification models, and the system equation extracted from the identification model can be used as a transparent replacement for the original model. This aids in a myriad of practical applications such as control, stability analysis, and software verification. The framework is fully implemented and made publicly available. A number of synthetic examples are presented along with data-driven analysis of the Silverbox dataset, vehicle dynamics data, and simulated motor cooling data.
Ümit Özgüner (Advisor)
Keith Redmill (Advisor)
Yingbin Liang (Committee Member)
141 p.
Computer Engineering; Computer Science; Electrical Engineering
system identification; sensitivity analysis; discrete dynamical systems; temporal convolutional networks

Recommended Citations

Citations

  • Maroli, J. M. (2019). Generating Comprehensible Equations from Unknown Discrete Dynamical Systems Using Neural Networks [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1574760744876635

    APA Style (7th edition)

  • Maroli, John. Generating Comprehensible Equations from Unknown Discrete Dynamical Systems Using Neural Networks. 2019. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1574760744876635.

    MLA Style (8th edition)

  • Maroli, John. "Generating Comprehensible Equations from Unknown Discrete Dynamical Systems Using Neural Networks." Doctoral dissertation, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1574760744876635

    Chicago Manual of Style (17th edition)

osu1574760744876635
196
© 2019, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.