Key responses of manufacturing processes are often represented by spatially or time‐ordered data known as functional data. In practice, these are usually treated by extracting one or few representative scalar features from them to be used in the following analysis, with the risk of discarding relevant information available in the whole profile and of drawing only partial conclusions. To avoid that, new and more sophisticated methods can be retrieved from the functional data analysis (FDA) literature. In this work, that represents a contribution in the direction of integrating FDA methods into the manufacturing field, the use of function‐on‐function linear regression modelling is proposed. The approach is based on a finite‐dimensional approximation of the regression coefficient function by means of two sets of basis functions, and two roughness penalties to control the degree of smoothness of the final estimator. The potential of the proposed method is demonstrated by applying it to a real‐life case study in powder bed fusion additive manufacturing for metals to predict the mechanical properties of an additively manufactured artefact, given the particle size distribution of the powder used for its production.

中文翻译：

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函数对函数回归用于评估工业制造中的生产质量

制造过程的关键响应通常由空间或时间顺序数据（称为功能数据）表示。在实践中，通常通过从它们中提取一个或几个代表性的标量特征进行处理，以用于以下分析，而这些风险可能会丢失整个配置文件中可用的相关信息，并且只会得出部分结论。为了避免这种情况，可以从功能数据分析（FDA）文献中检索新的和更复杂的方法。在这项工作中，这代表了将FDA方法整合到制造领域中的贡献，提出了使用功能对功能线性回归建模的方法。该方法基于借助两组基函数和两个粗糙度惩罚来控制最终估算器的平滑度的回归系数函数的有限维近似。