Eur. Phys. J. B (2016) 89: 155
https://doi.org/10.1140/epjb/e2016-60850-y

Regular Article

Heterogeneous recurrence representation and quantification of dynamic transitions in continuous nonlinear processes

Complex Systems Monitoring, Modeling and Control Laboratory, The Pennsylvania State University, 310 Leonhard Building, University Park, PA 16802, USA

^a e-mail: huy25@psu.edu

Received: 27 October 2015
Received in final form: 22 January 2016
Published online: 20 June 2016

Abstract

Many real-world systems are evolving over time and exhibit dynamical behaviors. In order to cope with system complexity, sensing devices are commonly deployed to monitor system dynamics. Online sensing brings the proliferation of big data that are nonlinear and nonstationary. Although there is rich information on nonlinear dynamics, significant challenges remain in realizing the full potential of sensing data for system control. This paper presents a new approach of heterogeneous recurrence analysis for online monitoring and anomaly detection in nonlinear dynamic processes. A partition scheme, named as Q-tree indexing, is firstly introduced to delineate local recurrence regions in the multi-dimensional continuous state space. Further, we design a new fractal representation of state transitions among recurrence regions, and then develop new measures to quantify heterogeneous recurrence patterns. Finally, we develop a multivariate detection method for on-line monitoring and predictive control of process recurrences. Case studies show that the proposed approach not only captures heterogeneous recurrence patterns in the transformed space, but also provides effective online control charts to monitor and detect dynamical transitions in the underlying nonlinear processes.