A dynamical design space for the batch milling process of a hazelnut-and-cocoa-based paste in a stirred ball mill was obtained through functional data analysis (FDA) combined with design of experiments (DOE). A face-centred central composited design with two functional responses, fineness and energy, and three factors (rotational speed, mass of balls and ball diameter) was used. The functional responses were pre-processed, smoothed through B-spline approximation and subjected to functional principal component analysis (FPCA). The scores of the FPCA were modelled as a function of the experimental factors through response surface models and used to build a final model for the functional responses including only one principal component for energy and two for fineness. The developed models were able to predict with good accuracy the functional responses as a function of the experimental factors and time and allowed to build a dynamical design space. FDA combined with DOE appears to be an efficient and easy-to-use tool to model batch processes and obtain their dynamical design space.

通过功能数据分析（FDA）与实验设计（DOE）相结合，获得了搅拌球磨机中基于榛子和可可糊的批处理过程的动态设计空间。使用具有两个功能响应，细度和能量以及三个因素（转速，球的质量和球的直径）的面心中央复合设计。对功能响应进行预处理，通过B样条逼近进行平滑处理，然后进行功能主成分分析（FPCA）。通过响应面模型将FPCA的分数建模为实验因子的函数，并用于构建功能响应的最终模型，其中仅包含一个能量主成分和两个主成分。所开发的模型能够根据实验因素和时间准确地预测功能响应，并建立动态设计空间。FDA与DOE相结合似乎是一种用于建模批处理过程并获得其动态设计空间的高效且易于使用的工具。