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A Dual-Scheme Cointegration Framework for Condition Monitoring and Fault Detection Using Non-Joint and Mixed-Order Time Series

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Abstract:

Recent years have seen growing faith in data-driven tools for condition monitoring and fault detection, a trend accelerated further by advances in artificial intelligence. In many industrial systems typical examples like chemical plants and wind-energy installations—the underlying process variables do not behave in a stable or predictable manner. Their statistical features shift over time, and conventional monitoring methods which assume an essentially stationary assumption, often struggle to handle high-dimensional signals. Much of the difficulty stems from the fact that several variables move together over long periods but differ in their degree of non-stationarity. To deal with this challenge, two monitoring strategies are designed to react reliably to deviations even when the data show complicated stochastic behaviour. The framework consists of two cointegration-based schemes. Scheme 1 treats all series jointly (i.e., mixed order), regardless of their integration order, while Scheme 2, first separates them into 𝐼(0), 𝐼(1), and 𝐼(2) groups using the augmented DickeyFuller (ADF) test and then each group fed to cointegration model individually. In both cases, the residuals serve as indicators. Monitoring statistics are estimated based on the Mahalanobis Distance (MD), utilizing residuals from testing set; the control limit (CL) is computed based on the Kernel Density Estimation (KDE) utilizing residuals from training set. Any deviation of monitoring statistics crossing the CL highlights the abnormal conditions in the system. Numerical case studies demonstrate the efficacy of non-joint cointegration-based monitoring (Scheme 2), which provides a flexible and computationally efficient method for monitoring non-stationary processes. In comparison to traditional PCA and CA-based Schemes, the Scheme 2 framework has better performance with a lower false alarm.

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Periodical:

Advances in Science and Technology (Volume 181)

Pages:

269-278

DOI:

https://doi.org/10.4028/p-J3Wqgx

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Online since:

August 2026

Authors:

Nasir Hussain Razvi Syed*, Debela Alema Teklemariyem, Wieslaw Jerzy Staszewski, Phong B. Dao

Keywords:

Augmented Dickey Fuller (ADF) Test, Cointegration Analysis (CA), Condition Monitoring, Fault Detection, Mixed-Order Time Series, Non-Joint Time Series

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© 2026 Trans Tech Publications Ltd. All Rights Reserved

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* - Corresponding Author

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