Abstract
The application of dimensionality reduction method on the reliability and reliability sensitivity analysis of vibration systems was examined. The dimensionality of a vibration reliability problem was reduced to only two independent dimensions by the means of polar transformation. As the safe and failure classes of samples are clearly distinguishable and occupy a standard position in a two-dimensional plot in the case that the important direction exists, the relevant samples are selected visually. The reliability and reliability sensitivity problems were solved using the position of the relevant samples. Before the reliability and reliability sensitivity estimation, an essential visualization analysis is conducted to examine the capacity of the method in terms of the existence of the important direction which is used to reduce the dimensionality of the reliability problem. In order to calculate the design point correctly, the improved Hasofer-Lind-Rackwitz-Fiessler method was extended with a procedure for determining the perturbation in the calculation of the gradient vector by finite differences according to the numerical precision of the limit state function. The dimensionality reduction method saves the numbers of calling limit state function a lot and has the same accuracy as Monte Carlo method. Examples involving single and multiple degree-of-freedom nonlinear vibration systems were used to demonstrate the approach.