The interval PHI2 analysis method for time-dependent reliability
Abstract
The uncertainty modeling and time-dependent reliability analysis for time-dependent structures with a large number of inherently uncertain parameters is very important in engineering. When evaluating the reliability of structures under stochastic loadings through traditional methods, the distribution parameters of random variables, such as strength, stiffness and damping, are usually determined, but the accurate value of distribution parameters can hardly be known in practical engineering. In this paper an interval PHI2 (I-PHI2) method is proposed to solve the time-dependent reliability for random problems with the interval distribution parameters. I-PHI2 method can provide the reliability interval for assessing design reliability over the whole lifecycle of uncertain structures. Firstly, the time-dependent reliability analysis model is built for uncertain problem of interval distribution parameters. Secondly, the interval distribution parameters of random variables and stochastic processes are determined by use of the interval analysis method and then transferred into the standard coordinate space. Thirdly, the analytical expression of out-crossing rate in which there are many interval parameters are derived and the corresponding upper and lower bounds of out-crossing rate can be obtained. Finally, based on the traditional time-independent reliability tools such as FORM, an efficient algorithm for time-dependent structure is developed to obtain the upper and lower bounds of time-dependent reliability index and failure probability. Two numerical examples are presented for verification of the validity of I-PHI2 method.
