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<p>In the task of multi-indicator interval prediction of steel properties, complex nonlinear relationships, strong variable coupling, and data uncertainty pose significant challenges in industrial production. To address these issues, this paper proposes a multi-objective evolutionary learning framework for the interval prediction of multiple mechanical properties in the continuous annealing process (CAP). In the first stage, a deep principal component analysis approach is employed to extract hierarchical and informative features from multiple relevant factors affecting steel properties. This approach effectively identifies new hierarchical variables, by coupling the principal components across multiple feature layers. In the second stage, a multi-indicator interval prediction model based on Gaussian process is constructed, and probabilistic prediction with confidence intervals is achieved through the design of a kernel function incorporating prior knowledge. Furthermore, a multi-objective differential evolutionary algorithm with a knee-point solution strategy is introduced to jointly optimize the model structure and parameters. The proposed method is validated using industrial production data from a cold-rolled carbon steel continuous annealing line, containing 65,288 samples with 27 features, including process parameters and chemical composition variables. After data pre-processing, 63,137 samples are randomly selected to construct subsets, and each subset is divided into 80 pct training data and 20 pct testing data. Experimental results show that the proposed model achieves high prediction accuracy with RMSE values of 23.40, 32.51, and 3.83 for tensile strength (TS), yield strength (YS), and elongation (EL), respectively. In addition, the constructed prediction intervals provide reliable uncertainty estimation, with average coverage fractions of 0.96, 0.92, and 0.82 for TS, YS, and EL, respectively. Compared with several machine learning and deep learning models, the proposed method achieves lower prediction errors and more stable interval estimation, thereby improving the reliability of mechanical-property prediction and supporting more effective quality control and process optimization in the CAP.</p>

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An Efficient Multi-objective Evolutionary Learning Framework for Multi-Indicator Interval Prediction of Steel Properties in Continuous Annealing Process

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Chang Liu,
  • Zherui Tao,
  • Yuxuan Chai

摘要

In the task of multi-indicator interval prediction of steel properties, complex nonlinear relationships, strong variable coupling, and data uncertainty pose significant challenges in industrial production. To address these issues, this paper proposes a multi-objective evolutionary learning framework for the interval prediction of multiple mechanical properties in the continuous annealing process (CAP). In the first stage, a deep principal component analysis approach is employed to extract hierarchical and informative features from multiple relevant factors affecting steel properties. This approach effectively identifies new hierarchical variables, by coupling the principal components across multiple feature layers. In the second stage, a multi-indicator interval prediction model based on Gaussian process is constructed, and probabilistic prediction with confidence intervals is achieved through the design of a kernel function incorporating prior knowledge. Furthermore, a multi-objective differential evolutionary algorithm with a knee-point solution strategy is introduced to jointly optimize the model structure and parameters. The proposed method is validated using industrial production data from a cold-rolled carbon steel continuous annealing line, containing 65,288 samples with 27 features, including process parameters and chemical composition variables. After data pre-processing, 63,137 samples are randomly selected to construct subsets, and each subset is divided into 80 pct training data and 20 pct testing data. Experimental results show that the proposed model achieves high prediction accuracy with RMSE values of 23.40, 32.51, and 3.83 for tensile strength (TS), yield strength (YS), and elongation (EL), respectively. In addition, the constructed prediction intervals provide reliable uncertainty estimation, with average coverage fractions of 0.96, 0.92, and 0.82 for TS, YS, and EL, respectively. Compared with several machine learning and deep learning models, the proposed method achieves lower prediction errors and more stable interval estimation, thereby improving the reliability of mechanical-property prediction and supporting more effective quality control and process optimization in the CAP.