Monitoring Nonstationary Processes Using Stationary Subspace Analysis and Fractional Integration Order Estimation

Abstract

This article introduces a framework to monitor complex dynamic and mildly nonstationary processes that are driven by a set of latent factors that can have different integration orders. The framework (i) relies on a novel deflation-based stationary subspace analysis that extracts latent source variables from recorded data sets in an iterative manner and (ii) utilizes the exact local Whittle estimator to calculate the fractional integration orders of the extracted source variables. The framework is embedded within a multivariate time-series structure to model the dynamic characteristics of the latent factors and to remove serial correlation in order to construct univariate monitoring statistics. A numerical and an industrial case study show that this framework is capable of modeling dynamic and mildly nonstationary variable inter-relationships that can have different integration orders.

Monitoring nonstationary processes based on recursive cointegration analysis and elastic weight consolidation

“…V. MONITORING ALGORITHM State-of-the-art approaches explore the nonstationary processes for a single mode [14], [22], [23], [26], where the stationary variables and the long-term static equilibrium fluctuate within a certain range. When the operating mode changes, the data distribution may vary accordingly and the original cointegration relationship is broken.…”

“…However, the monitoring consequences are affected by the length of data block and it is intractable to determine the optimal value. Only the dynamic information that reflected the control performance was extracted and the remaining information was neglected, thus causing insensitivity to detecting the faults that are orthogonal to cointegration space [26].…”

A Fault Diagnosis Methodology Based on Non-Stationary Monitoring Signals by Extracting Features With Unknown Probability Distribution

“…Generally, almost all monitored stationary signals are regarded as weak stationary. And non-stationary monitoring signals are considered as that the signals do not meet the statistical characteristics of equations ( 1) and ( 2) [3].…”

“…In particular, modern industrial systems are increasingly moving toward quite large scale due to the widespread usage of Distributed Control System (DCS), precision instrumentation systems, and industrial Internet [1], [3]- [5]. In order to avoid the occurrence of safety accidents, more and more measurement nodes are installed for each equipment to monitor the states of modern industrial systems.…”

“…Furthermore, with the advancement of sensor technology, the sampling frequency is getting higher and higher. And from the beginning of its service to the end of its life, data collection time has been getting longer and longer, and this makes the volume of monitoring data has become larger and larger [3]- [11].…”