Forecasting Univariate Root-Mean-Square Vibration Sequences: A Benchmark of Statistical, Deep Learning, and Foundation Models on Two Rotating-Machinery Datasets.

Forecasting vibration-derived health indicators is distinct from fault diagnosis and remaining-useful-life estimation, yet controlled comparisons that preserve temporal order, physical scale, and dependence among forecast errors remain limited. This study presents a systematic empirical benchmark for point forecasting univariate root-mean-square (RMS) vibration sequences from two public rotating-machinery datasets with different experimental meanings: "Vibration, Acoustic, Temperature, and Motor Current Dataset of Rotating Machine Under Varying Load Conditions for Fault Diagnosis" (DB1), which provides separately recorded operating and fault conditions, and the "Intelligent Maintenance Systems (IMS) Bearings" record (DB2), from which one run-to-failure recording is used. Twelve methods span naive, statistical, supervised deep-learning, and zero-shot foundation-model families. Every method receives the same 128-step observed context and is evaluated at horizons of 1, 8, and 32 steps on common forecast origins after chronological point-level splitting and training-only scaling. Original-scale errors, per-lead behavior, paired skill, circular moving-block-bootstrap intervals, conditioned cross-regime tests, controlled corruptions, and a desktop central processing unit (CPU) reference workload provide complementary evidence. On DB1 0 Nm Normal, the lowest observed mean absolute error (MAE) is 0.0202 g at the one-step horizon (long short-term memory (LSTM)), 0.0283 g at the eight-step horizon (TimeMixer), and 0.0290 g at the 32-step horizon (inverted Transformer (iTransformer)), although the leading supervised intervals overlap. On DB2 2nd_test, persistence is lowest at the one- and eight-step horizons (0.00788 and 0.01491 dataset acceleration units), while drift is lowest at the 32-step horizon (0.02948); several statistical and zero-shot intervals overlap these leaders. The benchmark combines an explicitly specified waveform-to-target construction, a leakage-safe common-origin design across four model families, dependence-aware inference, and matched robustness and efficiency analyses. The findings show that model value is dataset- and horizon-dependent and that sophisticated forecasters should be judged against strong local baselines under the intended operating context.