Topological Data Analysis for High-Dimensional Dynamic Process Monitoring

Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data. In this work, we present a new approach for process monitoring that combines tools of topological data analysis (TDA) and machine learning. In the proposed approach, we represent multivariate time-series data as manifolds and use topological descriptors to summarize the structure of such data; we then use a neural ordinary differential equation to learn the dynamic evolution of the topological structure of the system. Using real data from an industrial process, we show that this trajectory-based event detection approach is effective at detecting diverse types of events. We contrast this approach against reconstruction-based approaches such as principal component analysis and autoencoders and against a trajectory-based approach that uses Koopman autoencoders.

Video-Based Prediction of In-Flight Particle Characteristics in Atmospheric Plasma Spraying

Atmospheric plasma spraying (APS) is a widely used coating process in which in-flight particle temperature and velocity strongly influence coating quality. However, these particle characteristics are difficult to monitor continuously during operation, motivating the development of non-invasive data-driven diagnostic methods. In this work, we investigate the predictive potential of high-speed video observations of the plasma plume for estimating in-flight particle characteristics in APS. We introduce three different video-derived feature representations and evaluate them using Tabular Prior-Data Fitted Networks (TabPFN), convolutional neural networks (CNN), and classical regression baselines including Random Forest, Gradient Boosting, Support Vector Regression, and XGBoost. Experiments are conducted using grouped leave-one-out cross-validation on 126 labeled pre- and post-spray video recordings from 63 APS spray runs. Across the engineered feature experiments, TabPFN achieves the most consistent performance for temperature prediction, reaching R2 = 0.86 using the combined feature representation. CNN models particularly perform stronger for velocity prediction, achieving R2 of 0.81. In addition, we evaluate models operating directly on raw video frames using pretrained CNNs and find that the highest performance is achieved by a pretrained CNN with a regression head with R2 of 0.90 and 0.82 for temperature and velocity, respectively. The results demonstrate that video-derived plume information provides a promising and scalable foundation for non-invasive APS diagnostics and real-time process monitoring.