Change-Point Detection in Industrial Data Streams based on Online Dynamic Mode Decomposition with Control

TL;DR

The paper tackles change-point detection in safety-critical industrial data streams that are non-stationary and non-uniformly sampled. It introduces a truncated online DMD with control (ODMDwC) framework for online CPD, leveraging time-delay embeddings to capture broadband dynamics and control effects. Key contributions include a runtime CPD-DMD algorithm, learning and detection procedures, and practical guidelines for hyperparameter selection, demonstrated on synthetic and real datasets where it competitively outperforms SVD-based CPD approaches. The approach enables real-time, interpretable monitoring by linking CPD statistics to dissimilarities in system dynamics across time, space, and spectrum, with clear implications for robust industrial operation and safety.

Abstract

We propose a novel change-point detection method based on online Dynamic Mode Decomposition with control (ODMDwC). Leveraging ODMDwC's ability to find and track linear approximation of a non-linear system while incorporating control effects, the proposed method dynamically adapts to its changing behavior due to aging and seasonality. This approach enables the detection of changes in spatial, temporal, and spectral patterns, providing a robust solution that preserves correspondence between the score and the extent of change in the system dynamics. We formulate a truncated version of ODMDwC and utilize higher-order time-delay embeddings to mitigate noise and extract broad-band features. Our method addresses the challenges faced in industrial settings where safety-critical systems generate non-uniform data streams while requiring timely and accurate change-point detection to protect profit and life. Our results demonstrate that this method yields intuitive and improved detection results compared to the Singular-Value-Decomposition-based method. We validate our approach using synthetic and real-world data, showing its competitiveness to other approaches on complex systems' benchmark datasets. Provided guidelines for hyperparameters selection enhance our method's practical applicability.

Figures (8)

• Figure 1: Increasing value of all the hyperparameters at once increases robustness to noise and delays peak of CPD statistics.
• Figure 2: The influence of changing hyperparameter (denoted in the title of each column) values on CPD in synthetic unit step dataset. Increasing value of base size stabilizes the score without significantly delaying the peak of CPD. Increasing test size and number of time-delays in embedding increases robustness to noise more prominently while delaying the peak of CPD.
• Figure 3: Steps detection in artificial data (1). Change score is evaluated for the proposed method as presented in Section \ref{['sec:method']} (2), the proposed method evaluating score as the difference of errors (3), and the reference method using online SVD (4). Our method is capable of detecting minor CPs that are missed by the reference method.
• Figure 4: NPRS43: Sleep stage transition detection based on respiration data (1). Change score is evaluated for the proposed method as presented in Section \ref{['sec:method']} (2), the proposed method evaluating score as the difference of errors (3), and the reference method using online SVD (4). While both methods detect the first CP, our method detects the second CP as well, albeit with a longer delay due to the proximity of the CPs.
• Figure 5: NPRS434: Sleep stage transition detection based on respiration data (1). Change score is evaluated for the proposed method as presented in Section \ref{['sec:method']} (2), the proposed method evaluating score as the difference of errors (3), and the reference method using online SVD (4). While both methods detect CPs, our method detects the first one with a score three times higher than the peaks unrelated to tracked events, while OSVD only doubles the score.