Construction and multivariate influence pattern analysis of Mass Energy Coupling Coefficient (MEC) for steel rolling reheating furnaces

• Propose dual scale MEC indicators, complementary to SEC, for billet level screening and line level benchmarking. • Use an SEC controlled ROC protocol to assess the practical separability of MEC from SEC. • Support indicator comparisons with paired uncertainty estimation and correlated ROC curve testing. • Use multivariate models with interaction terms to report empirical influence patterns of key factors on MEC. Operational energy-efficiency evaluation of Steel Rolling Reheating Furnaces (SRRFs) is challenging under mixed-specification production and rhythm-dependent losses. The conventional Specific Energy Consumption (SEC) metric remains convenient for reporting, but it neglects billet-mass heterogeneity and the time cost of heating, limiting consistent cross-line benchmarking and single-billet deviation screening. This study proposes an energy-accounting-motivated, unit-consistent composite indicator Mass–Energy Coupling Coefficient (MEC) framework comprising a macro-level benchmarking index (MEC mac ) and a micro-level screening index (MEC mic ), explicitly coupling mass, energy, residence time, and the heating duty (Δ T ). Using 1,000 industrial billet records, a dual screening protocol combining hard plausibility constraints with 3 σ quality-control flagging and plausibility validation yielded 782 effective records for analysis. Multivariate influence was examined using Spearman rank correlation and standardized regression with statistical inference and interaction testing. Under an SEC-controlled discriminability protocol, poor heating effectiveness was defined by the lowest 20% of the heating-rate proxy Δ T /t. Within the nominal SEC band (0.920–1.491 GJ/t; N SEC = 500), receiver operating characteristic (ROC) analysis shows that MEC mic and MEC mac achieve higher area under the ROC curve (AUC) than SEC (0.813/0.801 vs 0.608) and higher recall at a fixed false positive rate (FPR) of 0.05 (0.29/0.31 vs 0.08), indicating improved screening separability under comparable SEC levels: MEC mac supports standardized benchmarking across mixed billet masses, while MEC mic enables single-billet screening for potential process deviations, forming a practical macro–micro toolkit for SRRF energy management.