A procedure for generating vectors of time domain signals that are partially coherent in a prescribed manner is described. The procedure starts with the spectral density matrix,[Gxx(f)], that relates pairs of elements of the vector random process{X(t)},−∞<t<∞. The spectral density matrix is decomposed into the form[Gxx(f)]=[U(f)][S(f)][U(f)]'where[U(f)]is a matrix of complex frequency response functions, and[S(f)]is a diagonal matrix of real functions that can vary with frequency. The factors of the spectral density matrix,[U(f)]and[S(f)], are then used to generate a frame of random data in the frequency domain. The data is transformed into the time domain using an inverse FFT to generate a frame of data in the time domain. Successive frames of data are then windowed, overlapped, and added to form a vector of normal stationary sampled time histories,{X(t)}, of arbitrary length.

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Epistemic uncertainty, characterizing lack-of-knowledge, is often prevalent in engineering applications. However, the methods we have for analyzing and propagating epistemic uncertainty are not as nearly widely used or well-understood as methods to propagate aleatory uncertainty (e.g. inherent variability characterized by probability distributions). In this paper, we examine three methods used in propagating epistemic uncertainties: interval analysis, Dempster-Shafer evidence theory, and second-order probability. We demonstrate examples of their use on a problem in structural dynamics, specifically in the assessment of margins. In terms of new approaches, we examine the use of surrogate methods in epistemic analysis, both surrogate-based optimization in interval analysis and use of polynomial chaos expansions to provide upper and lower bounding approximations. Although there are pitfalls associated with surrogates, they can be powerful and efficient in the quantification of epistemic uncertainty.

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