Influence of measurement data metrics on the identification of Interval Fields for the representation of spatial variability in finite element models

Due to the exponential growth in computing power, numerical modelling techniques method have gained an increasing amount of interest for engineering and design applications. Nowadays, the deterministic finite element (FE) method, an efficient tool to accurately solve the Partial Differential Equations (PDE) that govern most real-world problems, has become an indispensable tool for an engineer in various design stages. A more recent trend herein is to use the ever increasing computing power incorporate uncertainty and variability, which is omnipresent is all real-live applications, into these FE models. Several advanced techniques for incorporating either variability between nominally identical parts or spatial variability within one part into the FE models, have been introduced in this context. For the representation of spatial variability on the parameters of an FE model in a possibilistic context, the theory of Interval Fields (IF) was proven to show promising results. Following this approach, variability in the input FE model is introduced as the superposition of base vectors, depicting the spatial ‘patterns’, which are scaled by interval factors, which represent the actual variability. Application of this concept, however, requires identification of the governing parameters of these interval fields, i. e. the base vectors and interval scalars. Recent work of the authors therefore was focussed on finding a solution to the inverse problem, where the spatial uncertainty on the output side of the model is known from measurement data, but the spatial variability on the input parameters is unknown. Based on an a priori knowledge on the constituting base vectors of the interval field, the simulated output of the IFFEM computation is compared to measured data, and the input parameters are iteratively adjusted in order to minimize the discrepancy between the variability in simulation and measurement data. This discrepancy is defined based on geometric properties of the convex sets of both measurement and simulation data. However, the robustness of this methodology with respect to the size of the measurement data set that is used for the identification, as yet remains unclear. This paper therefore is focussed on the investigation of this robustness, by performing the identification on different measurement sets, depicting the same variability in the dynamic response of a simple FE model, which contain a decreasing amount of measurement replica. It was found that accurate identification remains feasible, even under a limited amount of measurement replica, which is highly relevant in the context of a non-probabilistic representation of variability in the FE model parameters. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)