Non-elastic time series fuzzy clustering for efficient analysis of industrial data sets

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In line with the green transition and digitalization trends, there is an increasing need for effective performance and health monitoring of production machines. Machine operation footprints resonate in quantities such as supply current and pneumatic line pressure, providing valuable insights when analyzed. Examining these low-level signals allows for monitoring and identification of changes in machine operation over time. A critical step in analyzing machine data is clustering, requiring an effective method for calculating time series cluster centroids. This paper introduces Error in Aligned series (ERAL), a novel method that generates a time series centroid that distills the fundamental shape of the underlying datasets. ERAL employs a fuzzy clustering-inspired iterative process for temporal alignment and averaging, avoiding the pathological artifacts often introduced by popular time-warping methods. Our analysis shows that existing methods can create artificial spikes and plateaus, which ERAL mitigates; it remains faithful to the original data shape. Additionally, ERAL offers improvements in computational efficiency and prototype quality. We evaluate the method against Dynamic Time Warping (DTW)-based methods across various datasets, and apply it to a time series clustering task using a real-world industrial dataset. In combination with a fuzzy clustering algorithm, ERAL generates visually convincing clusters. By leveraging fuzzy membership concepts, it achieves robust and adaptable clustering outcomes that reflect real-world data complexity and ambiguity.