Virtual Sensing Network for Statistical Process Monitoring

Physical sensing is increasingly implemented in modern industries to improve information visibility, which brings real-time signals that are spatially distributed and temporally varying. These signals are often nonlinear and nonstationary in the high-dimensional space, which pose significant challenges to monitoring and control of complex systems. Therefore, this paper presents a new “virtual sensing” approach that places imaginary sensors at different locations in signaling trajectories to monitor evolving dynamics within the signal space. First, we propose self-organizing principles to investigate distributional and topological features of nonlinear signals for optimal placement of imaginary sensors. Second, we design and develop the network model to represent real-time flux dynamics among these virtual sensors, in which each node represents a virtual sensor, while edges signify signal flux among sensors. Third, the establishment of a network model as well as the notion of transition uncertainty enable a fine-grained view into system dynamics and then extend a new Flux Rank (FR) algorithm for process monitoring. Nonetheless, FR is compositional where constituent elements sum to one and thereby calls upon the design and development of new monitoring schemas with the isometric log-ratio (ilr) transform. Further, this study investigates and benchmarks the performance of three network FR control charts, namely , Hotelling , and Generalized Likelihood Ratio (GLR), with case studies on both a nonlinear dynamical system (i.e., Lorenz) and physiological signals. Experimental results show that network FR methods not only delineate real-time flux patterns in nonlinear signals, but also effectively monitor spatiotemporal changes in the dynamics of nonlinear dynamical systems. The proposed virtual sensing approach shows strong potential as a sensor-based statistical process control method to handle multidimensional nonlinear signals observed from complex systems.