Statistical approximations for characteristic-mode-based power flow analysis

Abstract

This paper presents a general statistical treatment for power flow analysis in a complex structure. The nominal power flow is computed using the characteristic constraint (CC) modes of the component structures. These CC modes are built from component mode synthesis (CMS) of finite element models, and they form a highly-reduced order basis for capturing the motion of the interface between components — and thus the power flow. The power flow statistics are then calculated over an ensemble of systems due to the variation of structural system parameters. Each modal response is expanded in a basis of quadrature polynomials or locally linear interpolation (LLI) functions in these uncertain parameters. The system equations for the reduced order CMS model with uncertainties are derived using Galerkin's method. These equations have the same form as the nominal power flow equations, but the number of equations is increased by a factor equal to the order of the polynomials (when using quadrature polynomials) or the number of nodes in the parameter space (when using LLI functions). Thus, the ensemble-averaged power flow can be calculated by solving this new set of equations, instead of using Monte Carlo simulations. A cantilever plate and a L-shaped plate are used as example structures for the demonstration of these statistical approximations. In general, this statistical treatment provides efficient and accurate modeling of parameter uncertainties, which is critical for mid-frequency vibration analysis.