Thesis Title: Modeling, monitoring, and diagnosis of complex systems with high-dimensional streaming data 

Advisor: 

Dr. Kamran Paynabar, School of Industrial and Systems Engineering, Georgia Tech 

Committee Members: 

Dr. Jianjun Shi, School of Industrial and Systems Engineering, Georgia Tech  

Dr. Yajun Mei, School of Industrial and Systems Engineering, Georgia Tech  

Dr. Brani Vidakovic, Department of Statistics, Texas A & M University 

Dr. Babak Mahmoudi, Department of Biomedical Informatics, Emory University 

Date and Time: Wednesday, July 14, 2021, @ 10:00 am (EDT) 

Meeting URL (BlueJeans): https://bluejeans.com/664184357 

Meeting ID (BlueJeans): 664 184 357 

Abstract: 

With the development of technology, sensing systems became ubiquitous. As a result, a wide variety of complex systems are continuously monitored by hundreds of sensors collecting large volumes of rich data. Learning the structure of complex systems, from sensing data, provides unique opportunities for real-time process monitoring and for accurate fault diagnosis in a wide range of applications. This dissertation presents new methodologies to analyze the high-dimensional data collected by sensors to learn the interactions between different entities in complex systems for system monitoring and diagnosis. Chapter 1 presents the research background, motivation, and challenges, and briefly introduces the methodologies developed. 

Chapters 2 and 3 aim at representing complex systems as probabilistic graphical models to capture the relationships between the variables in the system. Chapter 2 presents a methodology to learn directed graphical models when the sensing data has a functional form. The goal is to use the direction of the edges in the graph to identify the root-causes behind system failures. Learning a directed graphical model from data includes parameter learning and structure learning. When the structure of the graph is known, function-to-function linear regression is used to estimate the parameters of the graph. When the goal is to learn the structure, a penalized least square loss function is defined. The cyclic coordinate accelerated proximal gradient descent algorithm is employed to minimize the loss function and learn the structure of the directed graph. To illustrate the advantages of the proposed methodology, multivariate sensor data from an internal combustion engine is used. 

Chapter 3 aims at monitoring the structural evolution of complex systems by sequentially estimating undirected graphical models from high-dimensional streaming data. The main idea is to exploit the spectral information contained in the data to learn the system's structure over time. For this purpose, the streaming data is divided into windows, and the graphical LASSO for time series data is used to learn the conditional independence relationships of the system's variables. The structural change between windows is allowed but regularized to allow for change-point detection. The proposed monitoring strategy is efficiently implemented by applying the Alternating Direction Method of Multipliers and can be used for real-time monitoring. The effectiveness of the methodology is demonstrated in two case studies. First, we track human motion, and later we monitor for changes in the brain's functional connectivity. 

Chapter 4 leaves aside probabilistic graphical models to deal with a challenge commonly encountered when analyzing high-dimensional sensing data: incomplete information. In many applications, the sensing system that collects online data can only provide partial information from the process under study due to resource constraints. In such cases, an adaptive sampling strategy is needed to decide where to collect data while maximizing the change detection capability. This chapter proposes an adaptive sampling strategy for online monitoring and diagnosis with partially observed data. The proposed methodology integrates two novel ideas: (i) the recursive projection of the high-dimensional streaming data onto a low-dimensional subspace to capture the spatio-temporal structure of the data while performing missing data imputation; and (ii) the development of an adaptive sampling scheme, balancing exploration and exploitation, to decide where to collect data at each acquisition time. Through simulations and two case studies, the proposed framework's performance is evaluated and compared with benchmark methods.