Estimation of ARX models with time varying time delays

• Author / Creator

  Zhao,Yujia

• Processes in industry usually encounter time varying time delays as well as outliers in measurement data. These make identification of the process a challenging problem. Thus, a reliable estimation of the time delay and a correct estimation of the noise to include outliers are essential to efficient process identification. In this thesis, time-varying delay is modeled by a Markov chain in order to reflect the correlation between any consecutive delay values. To deal with this problem, two approaches are considered: off-line parameter estimation (batch estimation) and on-line adaptive parameter estimation (recursive estimation). Two statistical frameworks, i.e., the expectation-maximization (EM) algorithm and a full-Bayesian estimation method named as variational Bayesian (VB), are investigated to model the time delay processes. Normally distributed measurement noise is modeled by the Gaussian distribution in the proposed method, while in the presence of large random noises, the robustness of the proposed algorithms is enhanced by modeling the noise as t-distributions. During the iterative estimation procedure, outlying observations are down-weighted by a latent variable of the t-distribution automatically, and hence, minimizing their adverse influence on identification. The proposed algorithms are verified by simulations and experiments. Finally, models based on the proposed algorithms are identified to effectively predict the production rate for the time-delay extraction process used in the oil sands industry.

• Subjects / Keywords

  • Markov chains
  • T-distribution
  • Time delay

• Graduation date

  Spring 2016

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3XW4821D

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.