Interval Uncertainty Analysis Using CANDECOMP/PARAFAC Decomposition
A new interval uncertain analysis method is proposed based on CANDECOMP/PARAFAC (CP) decomposition. In interval uncertain analysis of structural dynamics, we need to evaluate the lower and upper bounds of uncertain responses. To avoid the overestimation of the lower and upper bounds caused by the wrapping effect, the CP decomposition is used to approximate the interval functions. In CP decomposition, the interval functions are represented with only a few terms, and the energy of each term usually decays fast. In this way, we can achieve shaper and tighter bounds of the interval functions. CP decomposition can be obtained using different methods. Some numerical examples are demonstrated to compare the method with other methods and illustrate the effectiveness of this method.
KeywordsInterval uncertainty quantification Dynamical response CANDECOMP/PARAFAC decomposition Tensor decomposition Low-rank decomposition
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