Determination of Random Matrices Dispersion Parameters for Nonparametric Modeling of Stochastic Dynamic Systems with Experimental Verification

Abstract

Extraction of random behavior of dynamic systems under the influence of the uncertainty associated with modeling error is a major challenge. In the present study, Random Matrix Theory (RMT) is applied to simulate this type of uncertainty in rotor shafts of high-speed rotordynamic systems. For this purpose, simulation of a random matrix is carried out based on the nonparametric approach followed by the determination of the mean model and dispersion parameters. The mean model is determined by extracting the mechanical and dimensional parameters of 15 rotor shaft samples via exact dimensional measurements and Experimental Modal Analysis (EMA). In this study, presenting the Difference Measure (DM) value, the dispersion parameters of the mass and stiffness of the rotor shafts are exploited. In this research, by minimizing the DM value as an objective function, domain variations and probability density distribution of the uncertain response (rotor shaft natural frequencies in this paper) obtained from the EMA and RMT are coincided simultaneously. The simulation process of a random matrix is fulfilled using the direct Monte Carlo simulation and minimization of the DM parameter is performed using Bee’s Algorithm (BA). It is demonstrated that this swarm intelligence-based algorithm provides an approach to extract optimal and accurate dispersion parameters in RMT implementation. The results show that the calculated dispersion parameters are in good agreement with the experimental data and the BA-based method is effective.