For the various engineering structures with non-probabilistic uncertain parameters, the ellipsoid modeling is a momentous analysis method considering parameter cross-dependency. To efficiently procure a more precise analysis results based on ellipsoid model, this paper proposes a novel data-driven strategy for uncertainty quantification and propagation. Firstly, a similarity distribution-based identification method is presented to eliminate the data deviation caused by outliers. For the problem with dispersed samples, a fuzzy equivalence relation-based clustering method is subsequently introduced, where the number of clusters is adaptively determined by the prior similarity levels. On the basis of the above data preprocessing procedure, a more precise multi-ellipsoid modeling framework is constructed, in which the statistical information of existing samples is utilized to derive the explicit expression of ellipsoid models. Meanwhile, to improve the computational efficiency of uncertainty propagation analysis under the multi-ellipsoid model, the back propagation artificial neural network (BPANN) is constructed as the surrogate model of the original time-consuming simulation model. Eventually, two numerical examples are provided to investigate the effectiveness of the proposed methods.