A filter-based approach for global sensitivity analysis of models with functional inputs. (July 2019) - Roux, Sébastien; Loisel, Patrice; Buis, Samuel
Highlights: A new method for GSA of models with functional inputs is introduced. Filtering operators are used to perturb the functional inputs. The response on model outputs is studied with Sobol Indices of boolean variables. Relationships between Sobol Indices and error due to filtering are established. The approach is generic and can improve model understanding or input acquisition. Abstract: We design a method called filter-based global sensitivity analysis (filter-based GSA) to analyze computer models with functional inputs. Understanding the impact of functional inputs is central in many applications like building energy or environmental studies. The present work is a step further in the analysis of the impact of functional inputs signal components onto model responses of interest. To perform filter-based GSA, the functional inputs are modified with filters in order to either enhance or suppress some components in the signal. The influence of filters on the model response is assessed by computing the Sobol' indices of Boolean factors that trigger the filters application. Two relationships between these indices and the error resulting from the filters application are established. The method is illustrated with smoothing filters applied on the climatic inputs of a toy model simulating crop yield. We show that the high frequencies for three out of the four climatic inputs are not important in the tested configuration. The present method does not require any hypotheses on the model or the type of filters used. It seems promising for model understanding, validation or simplification.