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.

翻译：我们提出了一种基于在线控制动态模态分解（ODMDwC）的新型变点检测方法。该方法利用ODMDwC在纳入控制效应的同时发现并跟踪非线性系统线性近似的能力，动态适应因老化和季节性导致的系统行为变化。此方法能够检测空间、时间和频谱模式的变化，提供了一种鲁棒的解决方案，保持了评分与系统动力学变化程度之间的对应关系。我们构建了ODMDwC的截断版本，并利用高阶时滞嵌入来抑制噪声并提取宽带特征。我们的方法解决了工业环境中面临的挑战，其中安全关键系统产生非均匀数据流，同时需要及时准确的变点检测以保护利润和生命安全。结果表明，与基于奇异值分解的方法相比，该方法产生了更直观且改进的检测结果。我们使用合成数据和真实数据验证了该方法，展示了其在复杂系统基准数据集上与其他方法的竞争力。所提供的超参数选择指南增强了我们方法的实际适用性。