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arXiv 2502.19307cs.LGcs.AI

复杂动态系统中的异常检测:基于嵌入理论与物理启发一致性的系统框架

Anomaly Detection in Complex Dynamical Systems: A Systematic Framework Using Embedding Theory and Physics-Inspired Consistency

JOANNEUM RESEARCH Forschungsgesellschaft mbH(JOANNEUM RESEARCH 研究所);TU Graz(格拉茨技术大学)

Michael Somma, Thomas Gallien, Branka Stojanovic

AI总结:

提出基于嵌入理论与物理一致性原理的系统框架,引入TDC-AE模型,在C-MAPSS数据集上达到与LSTM相当且优于Transformer的性能,并实现近100倍计算量缩减,适用于边缘计算。

摘要:

复杂动态系统中的异常检测对于确保工业和网络物理基础设施的可靠性、安全性和效率至关重要。预测性维护有助于防止代价高昂的故障,而随着数字化系统面临日益增长的威胁,网络安全监控也变得至关重要。许多此类系统表现出振荡行为和有界运动,这要求异常检测方法能够捕获结构化的时间依赖性,同时遵循物理一致性原则。在这项工作中,我们提出了一种基于系统理论的异常检测方法,该方法以经典嵌入理论和物理启发的一致性原理为基础。我们基于分形惠特尼嵌入普适定理(Fractal Whitney Embedding Prevalence Theorem),该定理将传统嵌入技术扩展到复杂系统动力学。此外,我们引入了状态-导数对作为嵌入策略,以捕获系统演化。为了强制时间一致性,我们开发了时间微分一致性自编码器(TDC-AE),其中包含TDC损失,该损失将潜在变量的近似导数与其动态表示对齐。我们在C-MAPSS数据集(涡轮风扇发动机退化的基准数据集)的两个子集(FD001、FD003)上评估了我们的方法。TDC-AE与LSTM性能相当,并优于Transformer,同时实现了近100倍的MAC操作减少,使其特别适用于轻量级边缘计算。我们的研究结果支持了异常会破坏稳定系统动力学的假设,为异常检测提供了稳健的信号。

英文摘要:

Anomaly detection in complex dynamical systems is essential for ensuring reliability, safety, and efficiency in industrial and cyber-physical infrastructures. Predictive maintenance helps prevent costly failures, while cybersecurity monitoring has become critical as digitized systems face growing threats. Many of these systems exhibit oscillatory behaviors and bounded motion, requiring anomaly detection methods that capture structured temporal dependencies while adhering to physical consistency principles. In this work, we propose a system-theoretic approach to anomaly detection, grounded in classical embedding theory and physics-inspired consistency principles. We build upon the Fractal Whitney Embedding Prevalence Theorem that extends traditional embedding techniques to complex system dynamics. Additionally, we introduce state-derivative pairs as an embedding strategy to capture system evolution. To enforce temporal coherence, we develop a Temporal Differential Consistency Autoencoder (TDC-AE), incorporating a TDC-Loss that aligns the approximated derivatives of latent variables with their dynamic representations. We evaluate our method on two subsets (FD001, FD003) of the C-MAPSS dataset, a benchmark for turbofan engine degradation. TDC-AE machtes LSTMs and outperforms Transformers while achieving a nearly 100x reduction in MAC operations, making it particularly suited for lightweight edge computing. Our findings support the hypothesis that anomalies disrupt stable system dynamics, providing a robust signal for anomaly detection.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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