In recent years, data-driven approaches (e.g., latent variable model) have excited the development of new products and the control of product quality. To derive an input space within which raw material properties or initial operating conditions can yield the required product quality, previous researchers developed a linear latent variable model and derived the solution of inputs through PLS model inversion. In this research, a novel method based on kernel partial least squares (KPLS) model inversion is proposed for product design of nonlinear processes and an input domain is derived. Constraints on the model inputs or outputs and on the KPLS model are discussed, and solutions are provided based on an optimization framework and the Monte Carlo sampling method. The effectiveness of the method is demonstrated by numerical simulation and a beer fermentation experiment, and the KPLS model inversion method outperforms the PLS model inversion method in terms of the precision.

近年来，数据驱动的方法（例如，潜变量模型）激发了新产品的开发和产品质量的控制。为了推导出原材料属性或初始操作条件可以产生所需产品质量的输入空间，以前的研究人员开发了一个线性潜变量模型，并通过 PLS 模型反演推导出了输入的解决方案。在这项研究中，提出了一种基于核偏最小二乘 (KPLS) 模型反演的新方法，用于非线性过程的产品设计，并推导出输入域。讨论了对模型输入或输出以及 KPLS 模型的约束，并基于优化框架和蒙特卡罗采样方法提供了解决方案。