First-passage probability analysis of Wiener process using different methods and its applications in the evaluation of structural durability degradation

Abstract

The first-passage probabilities in stochastic processes are important for the evaluation of structural reliability. In this work, Wiener process’s first-passage probability was analysed using different methods. First, the Poisson process method was used to analyse the first-passage probability of the Wiener process, and it was found this method cannot calculate the first-passage probability of the Wiener process. Then, the symmetry and Markov property of the Wiener process were used to derive equations for calculating the first-passage probability of a Wiener process. The results indicate analytical expressions for the first-passage time probability distribution function of the Wiener process can be derived either through the symmetry or Markov property of the process. Neither of the analytical expressions requires the use of assumptions in their derivations. The analytical method based on the symmetry of the Wiener process yields fully exact solution, whereas the analytical method based on the Markov property of the Wiener process produces highly accurate solution. Finally, the Wiener process is used to represent the time-varying amount of structural degradation at any point in time, leading to a non-stationary stochastic model for the degradation process, which will provide a basis for an estimation of the durability and reliability of concrete structures.

Keywords:

• Wiener process
• first-passage probability
• Poisson process method
• accurate analytical methods
• Markov property
• durability degradation

Additional information

Funding

This work was jointly supported by the National Key Basic Research Program of China (973 Progam) (grant no. 2015CB057706), the National Natural Science Foundation of China (grant no. 51108044), the Natural Science Foundation of Hunan Province (grant no. 2018JJ2443), and the Innovative Project of Key Disciplinary of Civil Engineering of CSUST (18ZDXK07).