Energy-Efficiency-Constrained Diffusion Model for High-Energy-Consumption Anomaly Diagnosis in Slab Reheating Furnaces

Slab reheating furnaces are among the most energy-intensive units in hot-rolling production lines, and their operating states directly affect fuel consumption, temperature uniformity, and production cost. High energy consumption conditions often arise from coupled changes in reheating time, furnace-temperature regulation, combustion status, and production rhythm, making them difficult to identify using fixed energy thresholds or manual experience alone. This study proposes an energy-efficiency-constrained DDPM-ConvTransformer method for data-driven high-energy-consumption anomaly diagnosis in slab reheating furnaces. Continuous industrial records are converted into fixed-length production windows, and a denoising diffusion probabilistic model is used to learn the multivariate temporal distribution of normal operating conditions. A convolutional module and a Transformer encoder are embedded in the denoising network to capture local thermal-process fluctuations and long-range temporal dependencies. During training, a specific-energy auxiliary constraint guides the shared representation toward operating patterns associated with energy efficiency. During inference, window-level anomaly scores are obtained from diffusion denoising errors, and the decision threshold is determined from validation-set score quantiles. Using 7476 industrial production records for model development and evaluation, the test-set results show that the detected abnormal windows have 47.83% higher specific energy consumption and 62.17% higher total energy consumption than normal windows, with Cohen’s d values of 1.27 and 1.60, respectively. Compared with PCA, Isolation Forest, autoencoder-based models, an energy-constrained Transformer autoencoder, and diffusion-based baselines, the proposed method produces stronger post hoc energy-consumption differences, while computational cost analysis further clarifies its practical trade-off for offline diagnosis and periodic screening. Group analysis, typical-window diagnosis, and perturbation validation further support its applicability for energy-efficiency diagnosis and high-consumption operating-condition screening in slab reheating furnaces.