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Joint probabilistic modeling of cement strength

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In cement manufacturing, ensuring simultaneous compliance with compressive (CCS) and flexural strength (FS) requirements is challenging due to their divergent responses to shared inputs. Industrial variability (e.g., fluctuations in C3S content, grinding heterogeneity, and curing conditions) exacerbates this challenge, leading to high batch rejection (15–20%) and excessive clinker overdesign that contributes 7% of global CO2 emissions. Traditional single-property models fail by treating CCS and FS in isolation, producing deterministic predictions that ignore uncertainty, and conflating material-driven (aleatoric) with model-induced (epistemic) uncertainty—precluding risk-aware decisions. To overcome these limitations, this study introduces the Multi-Property Cement Strength Estimator (MPCSE)—the first joint probabilistic framework to model CCS and FS as full distributions via multi-head Gaussian Mixture Models with shared latent representations. MPCSE delivers four innovations: (1) joint probabilistic modeling that captures cross-property dependencies (7.8% lower MAE for CCS and 9.3% for FS versus single-property baselines); (2) explicit uncertainty decomposition enabling targeted process control (e.g., tighter grinding for 36–52 μm particles reduces FS variability by 15%) and strategic data collection (e.g., low-C3A regimes, < 4%); (3) a novel dual-strength compliance probability metric, P(CCS ≥ cmin ∩ FS ≥ fmin), revealing a near-total collapse to 0.38% at 50 MPa CCS / 9 MPa FS in industrial settings (versus 11.2% under controlled laboratory conditions) and quantifying the previously unmeasured risk of simultaneous failure; (4) context-dependent mechanistic interpretability via SHAP analysis, showing granulometry (uniformity index, SHAP = 0.032) dominates industrial variability while stoichiometry (C3S, SHAP = 0.058) governs laboratory performance—explaining the CCS–FS correlation gap (lab r = 0.945 vs. industry r = 0.101). MPCSE achieves > 95% confidence-interval coverage on industrial data and enables 12–15% clinker reduction with approximately 25% fewer batch rejections through risk-aware rerouting of borderline batches, advancing sustainable cement production.

Descrição

Islam, M., Li, C., Yang, B., & Liu, C. (2026). Joint probabilistic modeling of cement strength: Dual-strength compliance and uncertainty decomposition for risk-aware and sustainable quality control. Materials Today Communications, 52, Article 115030. https://doi.org/10.1016/j.mtcomm.2026.115030

Palavras-chave

Building materials Cement strength Joint modeling Uncertainty decomposition Dual-strength compliance Sustainable manufacturing General Materials Science Mechanics of Materials Materials Chemistry SDG 9 - Industry, Innovation, and Infrastructure

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