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.
S. Maleki, M. Ilchi Ghazaan, A. Ghafouri,
Volume 16, Issue 2 (4-2026)
Abstract
Reduced order models (ROMs) are widely used to approximate the dynamic response of large-scale structural systems while substantially reducing computational cost. Inherent uncertainties necessitate the assessment of ROMs within an uncertainty quantification (UQ) framework. Although the deterministic accuracy of reduction techniques has been extensively investigated, their capability for UQ remains insufficiently understood. This study presents a systematic UQ-based assessment of four condensation techniques: Guyan reduction, dynamic condensation, Improved Reduced System (IRS), and the System Equivalent Reduction Expansion Process (SEREP). A shear frame and a plane truss are used to evaluate the combined influence of the reduction technique, master degree of freedom (DOF) selection, and structural dynamic complexity on ROM predictive capability. Polynomial Chaos Expansion (PCE) is employed for UQ, and variance-based Sobol' indices are adopted for global sensitivity analysis (GSA). SEREP consistently provides the closest approximation to the full order model, whereas IRS also maintains high accuracy over most vibration modes. The accuracy of the Guyan and dynamic condensation methods decreases as higher-order dynamics become increasingly important.
