Functional outlier detection by means of h-mode depth and dynamic time warping

This paper deals with the problem of finding outliers, i.e. data that differ distinctly from other elements of the considered dataset, when they belong to functional infinite-dimensional vector spaces. Functional data are widely present in the industry and may originate from physical measurements or numerical simulations. The automatic identification of outliers can help to ensure the quality of a dataset (trimming), to validate the results of industrial simulation codes, or to detect specific phenomena or anomalies. This paper focuses on data originated from expensive simulation codes, such as nuclear thermal-hydraulic simulators, in order to take into account the realistic case where only a limited quantity of information about the studied process is available. A detection methodology based on different features, e.g. the h-mode depth or the Dynamic Time Warping, is proposed in order to evaluate the outlyingness both in the magnitude and shape senses. Theoretical examples are also used in order to identify pertinent feature combinations and showcase the quality of the detection method with respect to state-of-the-art methodologies of detection. Finally, we show the practical interest of the methodology in an industrial context thanks to a nuclear thermal-hydraulic use-case and how it can serve as a tool to perform sensitivity analysis on functional data.