Abstract
Ordinary differential equations can describe many dynamic systems. When physics is well understood, the time-dependent responses are easily obtained numerically. The particular numerical method used for integration depends on the application. Unfortunately, when physics is not fully understood, the discrepancies between predictions and observed responses can be large and unacceptable. In this thesis, we show how to directly implement integration of ordinary differential equations through recurrent neural networks using Python. We leveraged modern machine learning frameworks, such as TensorFlow and Keras. Besides offering basic models capabilities (such as multilayer perceptrons and recurrent neural networks) and optimization methods, these frameworks offer powerful automatic differentiation. With that, our approach's main advantage is that one can implement hybrid models combining physics-informed and data-driven kernels, where data-driven kernels are used to reduce the gap between predictions and observations. In order to illustrate our approach, we used two case studies. The first one consisted of performing fatigue crack growth integration through Euler's forward method using a hybrid model combining a data-driven stress intensity range model with a physics-based crack length increment model. The second case study consisted of performing model parameter identification of a dynamic two-degree-of-freedom system through Runge-Kutta integration. Additionally, we performed a numerical experiment for fleet prognosis with hybrid models. The problem consists of predicting fatigue crack length for a fleet of aircraft. The hybrid models are trained using full input observations (far-field loads) and very limited output observations (crack length data for only a portion of the fleet). The results demonstrate that our proposed physics-informed recurrent neural network can model fatigue crack growth even when the observed distribution of crack length does not match the fleet distribution.
Notes
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Graduation Date
2020
Semester
Fall
Advisor
Viana, Felipe
Degree
Master of Science in Aerospace Engineering (M.S.A.E.)
College
College of Engineering and Computer Science
Department
Mechanical and Aerospace Engineering
Degree Program
Aerospace Engineering; Space System Design and Engineering
Format
application/pdf
Identifier
CFE0008328; DP0023765
URL
https://purls.library.ucf.edu/go/DP0023765
Language
English
Release Date
December 2020
Length of Campus-only Access
None
Access Status
Masters Thesis (Open Access)
STARS Citation
Giorgiani do Nascimento, Renato, "Hybrid Physics-informed Neural Networks for Dynamical Systems" (2020). Electronic Theses and Dissertations, 2020-2023. 357.
https://stars.library.ucf.edu/etd2020/357