Keywords

Steady-state, Stationarity, Random walk with drift, White-noise, Hypothesis testing, Student's t

Abstract

Detecting windows or intervals of when a continuous process is operating in a state of steadiness is useful especially when steady-state models are being used to optimize the process or plant on-line or in real-time. The term steady-state implies that the process is operating around some stable point or within some stationary region where it must be assumed that the accumulation or rate-of-change of material, energy and momentum is statistically insignificant or negligible. This new approach is to assume the null-hypothesis that the process is stationary about its mean subject to independent and identically distributed random error or shocks (white-noise) with the alternative-hypothesis that it is non-stationary with a detectable and deterministic slope, trend, bias or drift. The drift profile would be typical of a time-varying inventory or holdup of material with imbalanced flows or even an unexpected leak indicating that the process signal is not steady. A probability of being steady or at least stationary over the window is computed by performing a residual Student t test using the estimated mean of the process signal without any drift and the estimated standard-deviation of the underlying white-noise driving force. There are essentially two settings or options for the method which are the window-length and the Student t critical value and can be easily tuned for each process signal that are included in the multivariate detection strategy.

Original Publication Citation

http://www.sciencedirect.com/science/article/pii/S0959152412002661