Uncertainty-aware power consumption prediction in customized stainless-steel manufacturing: A comparative study of hierarchical Bayesian and deep neural models

Energy-efficient and data-driven decision-making has become a critical priority in modern manufacturing, particularly in customized or make-to-order (MTO) production where product variability causes large fluctuations in power consumption. Existing prediction models in this domain are often deterministic, lacking the ability to quantify uncertainty and capture hierarchical data dependencies, which limits their reliability for operational use. This study addresses this gap by developing a hierarchical Bayesian learning framework for power consumption prediction in customized stainless-steel manufacturing. The objective is to design models that not only achieve high predictive accuracy but also provide calibrated uncertainty estimates to support risk-aware production decisions. Four models, i.e., Hierarchical Bayesian Linear Regression (HBLR), Hierarchical Bayesian Neural Network (HBNN), Fully Connected Neural Network (FCN), and One-Dimensional Convolutional Neural Network (1D-CNN), were implemented and benchmarked using three inference algorithms: No-U-Turn Sampler (NUTS), Automatic Differentiation Variational Inference (ADVI), and Stein Variational Gradient Descent (SVGD). The innovation lies in systematically quantifying uncertainty using coverage probability, sharpness, and calibration error, and in establishing a unified comparison between probabilistic and deterministic models. Results show that the HBLR–NUTS model achieves the best trade-off between accuracy (RMSE = 11.85) and calibration quality (coverage ≈ 0.98), while ADVI offers near-equivalent performance with significantly lower computation time. These uncertainty-aware predictions can be directly integrated into Manufacturing Execution System (MES) and Enterprise Resource Planning (ERP) environments for energy-optimized scheduling and cost-aware planning. The proposed framework provides a scalable, interpretable, and statistically reliable foundation for advancing sustainable, data-driven manufacturing analytics. • Predict power consumption from product specifications in customized stainless-steel manufacturing. • Develop and compare Hierarchical Bayesian models and deep neural networks. • Incorporate NUTS, ADVI, and SVGD inference methods to evaluate uncertainty quantification. • Demonstrate the value of uncertainty-aware predictions for energy-aware and risk-informed decision-making.