Geometric-Temporal Potential Warping for Multidimensional Dynamic Trajectory Alignment in Industrial Processes

Trajectories in complex industrial processes contain critical spatiotemporal information, including dynamic behaviors and structural patterns. Due to inconsistencies in data acquisition processes, trajectory alignment is required to enable understanding of system behaviors across varying conditions. However, existing methods have difficulty separating local geometric changes from temporal dynamics, resulting in misalignment of key event features in complex data sets. To address these challenges, this paper proposes a new framework called Geometric-Temporal Potential Warping (GTPW), which integrates geometric and temporal potentials into a unified cost field. By modeling trajectories as multimodal feature fields that capture both local geometric structures and dynamic temporal dependencies, GTPW adaptively aligns key features, preserves spatiotemporal consistency, and handles trajectory changes across different industrial scenarios. We validate GTPW on a numerical simulation data set and two complex industrial process data sets. Quantitative results show that GTPW achieves superior performance in spatiotemporal consistency, with an average score of 0.9259, compared to DTW (0.9028), ADTW (0.9154), and ESDTW (0.9023).