The sub-interval similarity: a general uncertainty quantification metric for both stochastic and interval model updating

One of the key challenges of uncertainty analysis in model updating is the lack of experimental data. The definition of an appropriate uncertainty quantification metric, which is capable of measuring as sufficient as possible information from the limited and sparse experimental data, is significant for the outcome of model updating. This work is dedicated to the definition and investigation of a general-purpose uncertainty quantification metric based on the sub-interval similarity. The discrepancy between the model prediction and the experimental observation is measured in the form of intervals, instead of the common probabilistic distributions which require elaborate experimental data. An exhaustive definition of the similarity between intervals under different overlapping cases is proposed in this work. A sub-interval strategy is developed to compare the similarity considering not only the range of the intervals, but more importantly, the distributed positions of the available observation samples within the intervals. This sub-interval similarity metric is developed to be capable of different model updating frameworks, e.g. the stochastic Bayesian updating and the interval model updating. A simulated example employing the widely known 3-dof mass-spring system is presented to perform both stochastic Bayesian updating and interval updating, to demonstrate the universality of the proposed sub-interval similarity metric. A practical experimental example is followed to demonstrate the feasibility of the proposed metric in practical application cases.