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隐变量模型如部分最小二乘已经被广泛用于建立低维子空间,并以此建立回归模型用于质量预测。然而,它们都是基于工业过程的静态假设,一般实际的工业过程都是动态的。本文提出一种非线性慢特征回归模型,用作动态软测量模型。首先,对线性慢特征分析进行非线性扩展,然后非线性的慢特征作为隐变量通过扩展后的慢特征分析从过程数据中被提取出来。不同于传统的隐变量模型,慢特征分析假设隐变量具有缓慢变化的动态特性。由于工业过程明显的动态变化,慢特性可以被看作有效的先验知识加以利用。最后,利用提取的慢特征建立回归模型并用于产品质量的预测。实验结果表明,基于非线性慢特征的软测量模型要比传统的软测量模型预测精度高。
Latent variable models, such as partial least squares, have been widely used to establish low-dimensional subspaces and to build regression models for quality prediction. However, they are all based on the static assumption of industrial processes. Generally, the actual industrial processes are dynamic. This paper presents a nonlinear regression model of slow features, used as a dynamic soft-sensing model. First, the linear slow feature analysis is non-linearly extended, and then the nonlinear slow feature is extracted from the process data as an implicit variable through the extended slow feature analysis. Different from the traditional latent variable model, the slow characteristic analysis assumes that the latent variable has slowly changing dynamic characteristics. Due to the obvious dynamic changes in industrial processes, slow features can be used as effective prior knowledge. Finally, a regression model is built using the extracted slow features and used for product quality prediction. Experimental results show that the soft-sensing model based on the nonlinear slow feature has higher prediction accuracy than the traditional soft-sensing model.