Initialization Strategies in Simulation-Based SFE Eigenvalue Analysis

Abstract

Abstract: The efficiency of many eigensolution strategies is affected by the selection of the starting vector. Poor initializations often result in slow convergence, and in certain instances may lead to an incorrect or irrelevant answer. The problem of selecting an appropriate starting vector becomes even more complicated when the structure involved is characterized by properties that are random in nature. Here, a good initialization for one sample could be poor for another sample. Thus, the proper eigenvector initialization for uncertainty analysis involving Monte Carlo simulations is essential for efficient random eigenvalue analysis. Most simulation procedures to date have been sequential in nature, that is, a random vector to describe the structural system is simulated, a FE analysis is conducted, the response quantities are identified by post-processing, and the process is repeated until the standard error in the response of interest is within desired limits. A different approach is to generate all the sample (random) structures prior to performing any FE analysis, sequentially rank order them according to some appropriate measure of distance between the realizations, and perform the FE analyses in similar rank order, using the results from the previous analysis as the initialization for the current analysis. The sample structures may also be ordered into a tree-type data structure, where each node represents a random sample, the traverse of the tree starts from the root of the tree until every node in the tree is visited exactly once. This approach differs from the sequential ordering approach in that it uses the solution of the “closest” node to initialize the iterative solver. The computational efficiencies that result from such orderings (at a modest expense of additional data storage) are demonstrated through a stability analysis of a system with closely spaced buckling loads and the modal analysis of a simply supported beam.

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