Stage-wise thermal regime diagnosis of an industrial black-box billet reheating process using low-rank decomposition and change-point analysis

Full-process instrumented-billet trials provide rare in situ evidence of how thermal gradients and spatial non-uniformity evolve during industrial reheating, but these multichannel records are often interpreted only through prescribed furnace zones or individual temperature traces. This study combines singular value decomposition (SVD) with Pruned Exact Linear Time (PELT) change-point analysis for one complete trial in an industrial regenerative walking-beam furnace. Nine synchronized billet-temperature channels were recorded at 20 s intervals, yielding 856 observations without missing values. Rank 6 was selected as the smallest non-full rank satisfying both a cumulative explained-energy threshold of 99.99% and a root-mean-square error (RMSE) threshold of 2°C for full-record reconstruction. The retained representation captured 99.9980% of the centered-data energy with an overall RMSE of 1.593°C. PELT identified 13 candidate boundaries; resampling-based consolidation retained eight primary boundaries and defined nine thermal regimes. The regime sequence progressed from gradual surface-to-center separation to rapid gradient escalation, center-temperature catch-up, and partial through-thickness homogenization. The mean absolute surface-to-center difference reached 130.52°C in Stage 7, whereas the maximum linewise surface-to-center difference reached 209.77°C in Stage 8. During the final stage, the center temperature increased by 124.39°C while the surface increased by 26.19°C, reducing the terminal difference to 16.61°C. Leave-one-thermocouple-out analysis preserved subspace similarities of 0.91–0.99, and the transitions near 212.7 and 240.0 min showed the greatest overall persistence across the combined robustness analyses. The framework provides an interpretable offline diagnostic for locating when through-thickness and lateral non-uniformity intensify and for guiding targeted furnace-operation review.