Showing 2 results for Random Eigenvalue Problem
Pooya Zakian, Pegah Zakian,
Volume 14, Issue 2 (2-2024)
Abstract
In this study, the support vector machine and Monte Carlo simulation are applied to predict natural frequencies of truss structures with uncertainties. Material and geometrical properties (e.g., elasticity modulus and cross-section area) of the structure are assumed to be random variables. Thus, the effects of multiple random variables on natural frequencies are investigated. Monte Carlo simulation is used for probabilistic eigenvalue analysis of the structure. In order to reduce the computational cost of Monte Carlo simulation, a support vector machine model is trained to predict the required natural frequencies of the structure computed in the simulations. The provided examples demonstrate the computational efficiency and accuracy of the proposed method compared to the direct Monte Carlo simulation in the computation of the natural frequencies for trusses with random parameters.
Pooya Zakian, Pegah Zakian,
Volume 15, Issue 4 (11-2025)
Abstract
This study employs Monte Carlo simulation together with a deep feedforward neural network to predict the natural frequencies of truss domes under uncertainty. Material and/or geometric properties of these structures are modeled as random variables, and their influence on the natural frequencies is examined. Monte Carlo simulation is applied to perform stochastic eigenvalue analyses of the finite element models. To reduce computational cost, a deep neural network is trained to predict natural frequencies in place of repeated eigenvalue solves, accelerating the overall simulation. Bayesian optimization is used to tune the network hyperparameters. Numerical examples show that the proposed approach substantially improves computational efficiency and predictive accuracy compared with direct Monte Carlo simulation for domes with random inputs.
