Modeling Temporal Pattern and Event Detection using Hidden Markov Model with Application to a Sludge Bulking Data

This paper discusses a method of modeling temporal pattern and event detection based on Hidden Markov Model (HMM) for a continuous time series data. We also provide methods for checking model adequacy and predicting future events. These methods are applied to a real example of sludge bulking data for detecting sludge bulking for a water plant in Chicago

Prediction of Filamentous Sludge Bulking using a State-based Gaussian Processes Regression Model.

Activated sludge process has been widely adopted to remove pollutants in wastewater treatment plants (WWTPs). However, stable operation of activated sludge process is often compromised by the occurrence of filamentous bulking. The aim of this study is to build a proper model for timely diagnosis and prediction of filamentous sludge bulking in an activated sludge process. This study developed a state-based Gaussian Process Regression (GPR) model to monitor the filamentous sludge bulking related parameter, sludge volume index (SVI), in such a way that the evolution of SVI can be predicted over multi-step ahead. This methodology was validated with SVI data collected from one full-scale WWTP. Online diagnosis and prediction of filamentous bulking sludge with real-time SVI prediction was tested through a simulation study. The results showed that the proposed methodology was capable of predicting future SVIs with good accuracy, thus providing sufficient time for predicting and controlling filamentous sludge bulking

Predictive Pattern Discovery in Dynamic Data Systems

This dissertation presents novel methods for analyzing nonlinear time series in dynamic systems. The purpose of the newly developed methods is to address the event prediction problem through modeling of predictive patterns. Firstly, a novel categorization mechanism is introduced to characterize different underlying states in the system. A new hybrid method was developed utilizing both generative and discriminative models to address the event prediction problem through optimization in multivariate systems. Secondly, in addition to modeling temporal dynamics, a Bayesian approach is employed to model the first-order Markov behavior in the multivariate data sequences. Experimental evaluations demonstrated superior performance over conventional methods, especially when the underlying system is chaotic and has heterogeneous patterns during state transitions. Finally, the concept of adaptive parametric phase space is introduced. The equivalence between time-domain phase space and associated parametric space is theoretically analyzed

Applying an Improved MRPS-GMM Method to Detect Temporal Patterns in Dynamic Data System

The purpose of this thesis is to introduce an improved approach for the temporal pattern detection, which is based on the Multivariate Reconstructed Phase Space (MRPS) and the Gaussian Mixture Model (GMM), to overcome the disadvantage caused by the diversity of shapes among different temporal patterns in multiple nonlinear time series. Moreover, this thesis presents an applicable software program developed with MATLAB for users to utilize this approach. A major study involving dynamic data systems is to understand the correspondence between events of interest and predictive temporal patterns in the output observations, which can be used to develop a mechanism to predict the occurrence of events. The approach introduced in this thesis employs Expectation-Maximization (EM) algorithm to fit a more precise distribution for the data points embedded in the MRPS. Furthermore, it proposes an improved algorithm for the pattern classification process. As a result, the computational complexity will be reduced. A recently developed software program, MATPAD, is presented as a deliverable application of this approach. The GUI of this program contains specific functionalities so that users can directly implement the procedure of MRPS embedding and fit data distribution with GMM. Moreover, it allows users to customize the related parameters for specific problems so that users will be able to test their own data