Stochastic Dynamic Load Identification on an Uncertain Structure With Correlated System Parameters

Abstract

A stochastic dynamic load identification algorithm is proposed for an uncertain dynamic system with correlated random system parameters. The stochastic Green's function is adopted to establish the relationship between the Gaussian excitation and the response. The Green's function is approximated by the second-order perturbation method, and orthogonal polynomial chaos bases are adopted to replace the corresponding bases in the Tayler series. The stochastic system responses and the stochastic forces are then represented by the polynomial chaos expansion (PCE) and the Karhunen–Loève expansion (KLE), respectively. A unified probabilistic framework for the stochastic dynamic problem is formulated based on the PCE. The stochastic load identification problem of an uncertain dynamic system is then transformed into a stochastic load identification problem of an equivalent deterministic system with the orthogonality of the PCE. Numerical simulations and experimental studies with a cantilever beam under a concentrate stochastic force are conducted to estimate the statistical characteristics of the stochastic load from the stochastic structural response samples. Results show that the proposed method has good accuracy in the identification of force's statistics when the level of uncertainty in the system parameters is not small. Large errors in the identified statistics may occur when the correlation in the random system parameters is neglected. Different correlation lengths for the random system parameters are investigated to show the effectiveness and accuracy of the proposed method.