With the flourishment of sensing technology, a huge mass of functional data can be acquired to describe the manufacturing process and predict the product quality. But these data simultaneously bring in modeling challenges of multi-type data, high-dimensional variables, data irregularity, and complex correlations. To address these challenges, this work proposes the Functional Kernel Partial Least Squares (FKPLS) methodology, which is a function-on-function regression. The FKPLS method first smooths the discrete sequences to continuous functions via functional data analysis (FDA) to retain the dynamic characteristics of variables, and then relies on basis function expansion to estimate the regression coefficient functions in order to avoid the ill-posed problem in directly estimating the functional eigenequation. An artificial dataset and a real-world steelmaking process are used to validate the effectiveness of the FKPLS method. The results demonstrate lower mean relative prediction error of the FKPLS method than the traditional methods, which is no more than 0.36% on simulation data and no more than 14.88% on industrial data. As the regression coefficients are functions, the FKPLS method is also effective in predicting dynamic mapping between predictors and responses.

随着传感技术的蓬勃发展，可以获取大量的功能数据来描述制造过程并预测产品质量。但这些数据同时带来了多类型数据、高维变量、数据不规则性和复杂相关性的建模挑战。为了应对这些挑战，这项工作提出了函数核偏最小二乘法 (FKPLS) 方法，这是一种函数对函数的回归。FKPLS方法首先通过泛函数据分析（FDA）将离散序列平滑为连续函数，以保留变量的动态特性，然后依靠基函数展开来估计回归系数函数，以避免直接出现不适定问题。估计功能特征方程。人工数据集和真实炼钢过程用于验证 FKPLS 方法的有效性。结果表明，FKPLS方法的平均相对预测误差低于传统方法，在模拟数据上不超过0.36%，在工业数据上不超过14.88%。由于回归系数是函数，因此 FKPLS 方法在预测预测变量和响应之间的动态映射方面也很有效。