Abductive learning-guided uncertainty modeling for time series anomaly detection

Time series anomaly detection is essential for enhancing the reliability of complex equipment. With the continuous advancements in digitalization, digital twin technology has emerged as a promising approach for addressing this challenge. Nevertheless, as production processes are dynamically optimized or equipment undergoes adjustments, the behavior of digital twin systems evolves correspondingly. This evolution introduces inherent uncertainties into the time-series data, thereby compromising the effectiveness and accuracy of conventional anomaly detection methods. To address this challenge, this research proposes a knowledge-driven uncertainty-modeling framework for time-series anomaly detection. The framework utilizes both numerical time-series data and textual domain knowledge, integrating them into a unified symbolic representation space. Specifically, the proposed framework involves two key steps: (1) discretizing the continuous time-series data into symbolic sequences and (2) employing a logical reasoning agent to transform domain-specific textual rules into anomalous symbols, thereby constructing a symbolic anomaly library. Subsequently, the anomalous symbols are applied as a sliding window to the symbolized time series data, locating anomalous segments and producing labelled data. For the noise and periodicity inherent in time-series data, the framework employs Gaussian processes (GP) augmented with Fourier transforms to effectively capture stochastic noise and recurring patterns. Finally, a TimesNet network enhanced with Gaussian processes is trained for supervised anomaly detection. Comprehensive experimental evaluations demonstrate the superiority of the proposed approach. Compared to the baseline TimesNet model, the framework achieves an 8.4% improvement in F1-score and a 10.36% increase in recall, showcasing its effectiveness in enhancing anomaly detection performance under uncertain and dynamic conditions.