A k-nearest neighbours framework with Trajectory-Embedded Decay for cycle-time forecasting in temperature swing adsorption

In many cyclic process operations a phase switch is triggered when a measured signal crosses a plant-defined threshold, and anticipating that crossing rather than reacting to it can yield significant energy and product-quality gains. The decision therefore reduces to forecasting the time-to-threshold (TTT), the time remaining until a cyclic signal crosses the threshold, from a partially observed cycle. We present a Multi-Feature k-Nearest Neighbours (MF-kNN) framework with Trajectory-Embedded Decay (TED) for real-time TTT forecasting in such operations. The framework performs direct, one-shot TTT prediction by matching the partially observed current trajectory to historical cycle segments across multiple process variables and reusing their future continuations, thereby avoiding recursive rollouts and model retraining. Its central component, TED, adapts the forecast online by reweighting and pruning neighbours according to exponentially decayed rolling prediction errors, giving segment-aware adaptation without per-segment retuning. To ensure methodological rigour and commercial deployability, the framework further incorporates boundary-safe cycle segmentation, cycle-consistent windowed neighbour search, moving-window embeddings, and clustering-guided mode-aware memory restriction. Applied to 52 industrial regeneration cycles under a cycle-blocked evaluation protocol, MF-kNN outperformed univariate k-NN and a panel of statistical, neural, and lightweight machine-learning baselines (ARMA, Theta, LSTM, ridge-regularised autoregression, and gradient-boosted trees). Relative to univariate k-NN, the multivariate formulation reduced the mean TTT error by approximately 20 % and the trajectory error by approximately 12 %, while producing markedly more stable forecasts across cycles; relative to the strongest trained baseline (LSTM) it reduced TTT error by approximately 79 % (nearly fivefold). Windowed search delivered a 4.9 × per-forecast speedup with no measurable loss of accuracy, and TED further reduced the mean TTT error by approximately 48 % relative to baseline MF-kNN. These results show that the proposed framework provides a transparent, efficient, and practically deployable solution for long-horizon cycle-time forecasting in cyclic adsorption processes.