A steady-state detection (SSD) algorithm to detect non-stationary drifts in processes

• Published in: Journal of process control Vol. 23; no. 3; pp. 326 - 331
• Main Authors: Kelly, Jeffrey D., Hedengren, John D.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2013
• Subjects: Hypothesis testing; Random walk with drift; Stationarity; Steady-state; Student's t; White-noise; Hypothesis testing; Student's t; Stationarity; Steady-state; White-noise; Random walk with drift
• ISSN: 0959-1524; 1873-2771
• DOI: 10.1016/j.jprocont.2012.12.001

► A new SSD algorithm is described which accounts for non-stationary drifts in process signals. ► Simple calculations to estimate the drift's slope and the mean and standard deviation of the process signal. ► Multivariate systems are addressed using the Sidak inequality correction. ► Two examples are provided which demonstrate the effectiveness of the algorithm. 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.