Efficient Solution for Calculation of Upcrossing Rate of Nonstationary Gaussian Process
- 1 April 2018
- journal article
- research article
- Published by American Society of Civil Engineers (ASCE) in Journal of Engineering Mechanics
Abstract
Almost all engineering systems are not only uncertain, but also time-variant. As such, it is most appropriate to use a time-dependent reliability method, e.g.,first passage probability, in the prediction of their failures. Mathematically, this problem can be modeled as an upcrossing (or outcrossing) of a stochastic process from a safe domain. A thorough examination of published literature suggests that there are very limited analytical solutions for the calculation of the upcrossing rate. This paper attempts to derive an efficient analytical solution for calculation of upcrossing of a nonstationary Gaussian process. The merit of the derived solution is that the upcrossing rate for nonstationary Gaussian processes can be calculated in a simple and computationally efficient procedure. The application of the derived solution is demonstrated with an example of a cast-iron pipe in which internal pressure is modeled as a nonstationary Gaussian load process. It is found that smaller values of correlation length, i.e.,higher cycle rate of the process, would increase the upcrossing rate. The paper concludes that the derived new solution performs very well in calculation of upcrossing of a nonstationary Gaussian process in terms of accuracy and efficiency.Keywords
This publication has 20 references indexed in Scilit:
- Closed-Form Solution to First Passage Probability for Nonstationary Lognormal ProcessesJournal of Engineering Mechanics, 2016
- Risk based service life prediction of underground cast iron pipes subjected to corrosionReliability Engineering & System Safety, 2013
- Barrier failure dominance in time variant reliability analysisProbabilistic Engineering Mechanics, 2004
- The PHI2 method: a way to compute time-variant reliabilityReliability Engineering & System Safety, 2004
- Optimal Discretization of Random FieldsJournal of Engineering Mechanics, 1993
- Vector Process Out‐Crossing as Parallel System Sensitivity MeasureJournal of Engineering Mechanics, 1991
- Asymptotic crossing rates for stationary Gaussian vector processesStochastic Processes and their Applications, 1988
- Structural response to non‐stationary non‐white stochastic ground motionsEarthquake Engineering & Structural Dynamics, 1986
- Gaussian Outcrossings from Safe Convex PolyhedronsJournal of Engineering Mechanics, 1983
- On the Number of Exits Across the Boundary of a Region by a Vector Stochastic ProcessTheory of Probability and Its Applications, 1968