Topological Data Analysis for High-Dimensional Dynamic Process Monitoring

Modern industrial processes generate massive, high-dimensional datasets that are often highly coupled and nonlinear, making traditional fault detection difficult. The authors address the challenge of monitoring these systems by moving beyond standard vector-based representations. They propose a framework that treats multivariate time-series data as 2D manifolds. By applying topological data analysis (TDA)—specifically, computing Euler characteristic (EC) curves through sublevel-set filtration—the authors summarize the system's structural shape. They then train a neural ordinary differential equation (NODE) to learn the continuous-time evolution of these topological descriptors. An event is flagged when the system exhibits a significant deviation in the time derivative of these descriptors, indicating a shift in the underlying dynamical structure.

The authors compare their TDA-NODE framework against three established methods: Principal Component Analysis (PCA) and Autoencoders (AE), which are reconstruction-based, and Koopman Autoencoders (KAE), which are trajectory-based. While reconstruction-based methods detect events by measuring errors relative to a nominal state, the TDA-NODE approach focuses on the temporal directionality of the system's topology. Using real-world data from an industrial olefins plant, the authors demonstrate that their topological approach provides a robust and interpretable signature for detecting both major disturbances and subtle, dynamically evolving instabilities that other methods might miss.

This work bridges the gap between topological data analysis and dynamic machine learning for industrial applications. By representing complex process data as manifolds, the framework gains robustness to noise and invariance to certain perturbations, such as scaling or rotation. Because TDA does not require extensive training procedures for the initial feature extraction, the method is computationally efficient and scalable. This provides engineers with a powerful, interpretable tool for real-time monitoring that can detect the onset of faults before they manifest as large-scale reconstruction errors.