Tracking Nonlinear Correlation for Complex Dynamic Systems Using a Windowed Error Reduction Ratio Method

Studying complex dynamic systems is usually very challenging due to limited prior knowledge and high complexity of relationships between interconnected components. Current methods either are like a “black box” that is difficult to understand and relate back to the underlying system or have limited universality and applicability due to too many assumptions. This paper proposes a time-varying Nonlinear Finite Impulse Response model to estimate the multiple features of correlation among measurements including direction, strength, significance, latency, correlation type, and nonlinearity. The dynamic behaviours of correlation are tracked through a sliding window approach based on the Blackman window rather than the simple truncation by a Rectangular window. This method is particularly useful for a system that has very little prior knowledge and the interaction between measurements is nonlinear, time-varying, rapidly changing, or of short duration. Simulation results suggest that the proposed tracking approach significantly reduces the sensitivity of correlation estimation against the window size. Such a method will improve the applicability and robustness of correlation analysis for complex systems. A real application to environmental changing data demonstrates the potential of the proposed method by revealing and characterising hidden information contained within measurements, which is usually “invisible” for conventional methods.