The aim of this work is to extend the usual optimal experimental design paradigm to experiments where the settings of one or more factors are functions. Such factors are known as profile factors, or as dynamic factors. For these new experiments, a design consists of combinations of functions for each run of the experiment. After briefly introducing the class of profile factors, basis functions are described with primary focus given on the B-spline basis system, due to its computational efficiency and useful properties. Basis function expansions are applied to a functional linear model consisting of profile factors, reducing the problem to an optimisation of basis coefficients. The methodology developed comprises special cases, including combinations of profile and non-functional factors, interactions, and polynomial effects. The method is finally applied to an experimental design problem in a Biopharmaceutical study that is performed using the Ambr250 modular bioreactor.

翻译：本研究旨在将传统最优实验设计范式扩展至一个或多个因子设定为函数的实验场景。此类因子被称为轮廓因子或动态因子。针对这类新型实验，每个实验运行的设计由函数组合构成。在简要介绍轮廓因子类别后，本文重点描述了基函数系统，其中因计算效率和实用特性而着重关注B样条基函数系统。通过将基函数展开应用于包含轮廓因子的函数线性模型，可将问题转化为基系数优化。所建立的方法论包含多种特殊情形，包括轮廓因子与非函数因子的组合、交互作用及多项式效应。最终，本方法被应用于一项采用Ambr250模块化生物反应器的生物制药研究中的实验设计问题。