A new method for reliability assessment of structural dynamic systems with random parameters

• Direct reliability assessment of structural dynamic systems based on the equivalent extreme value distribution.
• An estimator–corrector theme to obtain the accurate distribution promptly.
• A comparative study to keep the tradeoff of accuracy and efficiency.
• Validation of the proposed method through two examples.

The reliability of structural dynamic systems involving random parameters can be assessed based on the equivalent extreme value distribution of response. To derive such probability density function, a new method is proposed in the present paper, in which an iterative scheme is involved. In each iterative step, an estimated solution is easily obtained firstly by solving a linear system of equations and the more accurate result is then searched around the estimated solution with high efficiency. The derivation is based on the principle of maximum entropy, in which an un-constrained optimization problem with fractional moments is involved. Three different methods for numerical integration of fractional moments are compared, which indicates that the bivariate dimension reduction method ensures the accuracy and efficiency simultaneously. Two examples, of which one deals with a linear random structure subjected to seismic excitation, the other deals with a nonlinear structure with random parameters subjected to random ground motions, are illustrated to validate the proposed method. The investigations show that the proposed method is of satisfactory accuracy and applicable to the reliability assessment of practical structural dynamic systems.