Interval K-L expansion of interval process model for dynamic uncertainty analysis

Abstract

The interval process model describes a time-variant or dynamic uncertain parameter by the upper and lower bounds rather than the precise probability distribution at each time point, providing an effective structural dynamic uncertainty quantification model with insufficient sample information. By reference to the Karhunen-Loève (K-L) expansion for stochastic process and random field models, a novel expansion method for the interval process model, namely, the interval K-L expansion is proposed in this work. The interval K-L expansion describes the continuous uncertainty of the interval process in time domain by superposition of infinite deterministic time-related functions with uncorrelated interval coefficients, which makes the interval process model much more convenient to use. By introducing a splicing technique, the interval K-L expansion method for multiple correlated interval processes is also presented. Based on the interval K-L expansion, the vibration of structures subject to interval process excitations is analyzed, where the analytic formulation of dynamic response bounds for linear elastic systems and continuum structures are derived. Finally, several numerical examples are investigated to demonstrate the effectiveness of the proposed method.