Grouping detection of uncertain structural process by means of cluster analysis

Structural analysis under consideration of the uncertainty of input parameters, such as loads, material, and geometry leads to uncertain time-dependent results. Such uncertain structural process shows for the uncertain input parameters all possible behaviours of a structure. Modelling of uncertainty in input parameters when only incomplete or expert knowledge based information is available requires the introduction of the uncertainty model fuzziness. A fuzzy process is a fuzzy set of real valued processes, whereas each of them possesses an assigned membership value indicating the degree of possibility. In order to obtain an engineering interpretation of a fuzzy process some representative crisp processes have to be chosen from numerous realisations of this uncertain function. In this paper a cluster analysis based approach for grouping similar and detecting different time-dependent structure behaviours is introduced. The similarity of processes within one cluster is assessed with similarity metrics: neighbouring location, affinity, and correlation. The uncertain assignment of real valued realizations of fuzzy process to clusters is executed with the Fuzzy-c-Means cluster algorithm. The capability of this approach is demonstrated within the controlled collapse simulation of a reinforced concrete framework structure carried out in LS-DYNA. In this example an analysis of a fuzzy process is performed by means of cluster methods and "-level discretization in order to select collapse sequences, significantly differing from each other and having other degrees of possibility.