Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mechanical Engineering

Committee Chair/Advisor

Huang, Yong

Committee Member

Gowdy , John

Committee Member

Jalili , Nader

Committee Member

Vahidi , Ardalan


Recurrent neural networks (RNN) have been rapidly developed in recent years. Applications of RNN can be found in system identification, optimization, image processing, pattern reorganization, classification, clustering, memory association, etc.
In this study, an optimized RNN is proposed to model nonlinear dynamical systems. A fully connected RNN is developed first which is modified from a fully forward connected neural network (FFCNN) by accommodating recurrent connections among its hidden neurons. In addition, a destructive structure optimization algorithm is applied and the extended Kalman filter (EKF) is adopted as a network's training algorithm. These two algorithms can seamlessly work together to generate the optimized RNN. The enhancement of the modeling performance of the optimized network comes from three parts: 1) its prototype - the FFCNN has advantages over multilayer perceptron network (MLP), the most widely used network, in terms of modeling accuracy and generalization ability; 2) the recurrency in RNN network make it more capable of modeling non-linear dynamical systems; and 3) the structure optimization algorithm further improves RNN's modeling performance in generalization ability and robustness.
Performance studies of the proposed network are highlighted in training convergence and robustness. For the training convergence study, the Lyapunov method is used to adapt some training parameters to guarantee the training convergence, while the maximum likelihood method is used to estimate some other parameters to accelerate the training process. In addition, robustness analysis is conducted to develop a robustness measure considering uncertainties propagation through RNN via unscented transform.
Two case studies, the modeling of a benchmark non-linear dynamical system and a tool wear progression in hard turning, are carried out to testify the development in this dissertation.
The work detailed in this dissertation focuses on the creation of: (1) a new method to prove/guarantee the training convergence of RNN, and (2) a new method to quantify the robustness of RNN using uncertainty propagation analysis. With the proposed study, RNN and related algorithms are developed to model nonlinear dynamical system which can benefit modeling applications such as the condition monitoring studies in terms of robustness and accuracy in the future.



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