Soft-sensor technique is often used to estimate key variables in industrial manufacturing, of which the commonly used approaches as the mechanism modeling and data-driven modeling both have their limitations. To take full advantage of the modeling methods and overcome the problems of nonlinearity, unmodeled dynamics and unlabeled data in industrial manufacturing, a hybrid modeling method combining the mechanism with the semi-supervised learning is developed in this paper. In the framework of this hybrid model, the model can be divided into mechanism view and data view. In the mechanism view, the unmodeled dynamics in the mechanism model are obtained by an improved data-driven semi-supervised weighted probability partial least squares regression (SWPPLSR). In the data view, the present SPPLSR can solve the problem of the noise disturbance and output absent. On this basis, the locally weighted is adopted to handle the nonlinearity. Moreover, aiming at the imperfection of similarity measurement, varying working conditions and model redundancy, ensemble just-in-time learning and moving window techniques are combined to obtain an improved SWPPLSR. Finally, the real-world data in the roller hearth kiln of ternary cathode material manufacturing is applied for simulation to verify the validity of the model. The results have practical guiding significance.

软传感器技术通常用于估算工业制造中的关键变量，其中机制建模和数据驱动建模等常用方法都有其局限性。为了充分利用建模方法，克服工业制造中的非线性，动力学未建模和数据未标注等问题，本文提出了一种将机理与半监督学习相结合的混合建模方法。在此混合模型的框架中，该模型可以分为机制视图和数据视图。在机构视图中，机构模型中未建模的动力学是通过改进的数据驱动的半监督加权概率偏最小二乘回归（SWPPLSR）获得的。在数据视图中，目前的SPPLSR可以解决噪声干扰和输出不存在的问题。在此基础上，采用局部加权处理非线性。此外，针对相似性测量的不完善，变化的工作条件和模型冗余性，将集成的实时学习和移动窗口技术相结合以获得改进的SWPPLSR。最后，将三元阴极材料制造的辊式炉窑中的真实数据用于仿真，以验证该模型的有效性。结果具有实际指导意义。集成的即时学习和移动窗口技术相结合以获得改进的SWPPLSR。最后，将三元阴极材料制造的辊式炉窑中的真实数据用于仿真，以验证该模型的有效性。结果具有实际指导意义。集成的即时学习和移动窗口技术相结合以获得改进的SWPPLSR。最后，将三元阴极材料制造的辊式炉窑中的真实数据用于仿真，以验证该模型的有效性。结果具有实际指导意义。