Heterogeneous recurrence T² charts for monitoring and control of nonlinear dynamic processes

Many real-world systems are evolving over time and exhibit dynamical behaviors. Real-time sensing brings the proliferation of big data (i.e., dynamic, nonlinear, nonstationary, high dimensional) that contains rich information on nonlinear dynamic processes. Nonetheless, limited work on studying nonlinear dynamics underlying sensing data for quality control has been reported. This paper presents a new approach of heterogeneous recurrence T² control chart for online monitoring and anomaly detection in nonlinear dynamic processes. A partition scheme, named Q-tree indexing, is firstly introduced to delineate local recurrence regions in the multidimensional continuous state space. Further, we designed a new fractal representation of state transitions, among recurrence regions, and then develop new measures to quantify heterogeneous recurrence patterns. Finally, we developed a multivariate Hotelling T² Chart 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 an effective online control charts to monitor and detect dynamical transitions in the underlying nonlinear process.