Identification and quantification of spatial interval uncertainty in numerical models

This paper presents a novel methodology for the identification and quantification of spatial uncertainty, modelled as an interval field. In order to make a realistic assessment of the spatial uncertainty on the model parameters, the dimensionality of the interval field as well as its constituting base functions and interval scalars have to be identified. For this purpose, this work introduces an identification method based on objective measurement data. The specific challenge in this context lies in the fact that a continuous spatial input parameter has to be identified on a high-resolution discretised model of the structure under consideration, based on possibly high-dimensional measurement data set, obtained in the result domain of the analysed model. In the presented method, the field dimensionality is quantified based on the concept of effective dimension of the measurement data. The base functions of the interval field are identified by minimising the difference between the gradients of the halfspaces respectively bounding the measurement data and the realisations of the interval field. The method is illustrated using two case studies: an dynamic model of a cantilever beam and a quasi-static model of a cast pressure vessel. It is shown that the presented methods are capable of accurately identifying the interval field uncertainty that is present on the model parameters, and that this identification is robust against the size of the measurement data set.