The representation of uncertainties that give rise to a spatially distributed influence is still a topic of research in the non-probabilistic approach. The authors have developed an interval field framework to deal with multiple dependent uncertainties. Recently, the interval field method was developed to deal with random field expansions with an uncertain correlation length. The base vectors of this interval field come from a number of exact expansions of the random field in the correlation length space (e.g., Karhunen-Loe`ve expansion). The scaling interval factors are essentially a function of the correlation length. The present paper studies for the first time the convergence of an uncertain FE output (i.e. the interval on the FE output) with respect to the dimension of the base vector space, which is determined by the number of eigenvectors retained in one exact random field expansion and the number of exact random field expansions used to build the interval field representation.

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