1. An explicit compound Poisson process-based shock deterioration model for reliability assessment of aging structures
- Author
-
Cao Wang
- Subjects
050210 logistics & transportation ,Exponential distribution ,05 social sciences ,0211 other engineering and technologies ,Transportation ,02 engineering and technology ,Poisson distribution ,Standard deviation ,Shock (mechanics) ,symbols.namesake ,021105 building & construction ,0502 economics and business ,Compound Poisson process ,symbols ,Gamma distribution ,Applied mathematics ,Random variable ,Reliability (statistics) ,Civil and Structural Engineering ,Mathematics - Abstract
Existing structures may suffer from resistance deterioration due to repeated attacks. The modeling of resistance deterioration is a critical ingredient in the reliability assessment and service life prediction of these degraded structures. In this paper, an explicit compound Poisson process-based model is developed to describe the shock deterioration of structural resistance, where the magnitude of each shock deterioration increment is modeled by a Gamma-distributed random variable. The moments (mean value and variance) and the distribution function of the cumulative shock deterioration are derived in a closed form, based on a proposed W-function. A method for the efficient calculation of the W-function is presented, which reduces to the Bessel type I function if the shock deterioration increment is exponentially distributed (a special case of Gamma distribution). The proposed shock deterioration model is applicable to either a stationary or a nonstationary Poisson process of random jumps. Subsequently, the overall resistance deterioration is modeled as the linear combination of gradual and shock deteriorations, based on which the proposed model can be used in the time-dependent reliability assessment of aging structures efficiently. A numerical example is presented to demonstrate the applicability of the proposed deterioration model by estimating the time-dependent reliability of an aging bridge. It is found that a smaller threshold for the degraded resistance leads to greater mean value and standard deviation of the time to failure, and this effect is enhanced by a smaller occurrence rate of the shock deterioration.
- Published
- 2022