Safety assessment of infrastructures using a new Bayesian Monte Carlo method

Abstract

A recently developed Bayesian Monte Carlo (BMC) method and its application to safety assessment of structures are described in this paper. We use a one-dimensional BMC method that was proposed in 2009 by Rajabalinejad in order to develop a weighted logical dependence between successive Monte Carlo simulations. Our main objective in this research is to show that the extended BMC can dramatically improve simulation efficiency by using prior information from modelling and outcomes of preceding simulations. We provide theory and numerical algorithms for an extended BMC method for multi-dimensional problems, integrate it with a probabilistic finite element model and apply these coupled models to assessment of reliability of a flood defence for the 17th Street Flood Wall system in New Orleans. This is the first successful demonstration of the BMC method to a complex system. We provide a comparison of the numerical efficiency for the BMC, Monte Carlo (MC) and Dynamic Bounds methods that are used in reliability assessment of complex infrastructures.

Keywords:

• reliability
• simulation
• Bayesian Monte Carlo
• Dynamic Bounds
• flood defence
• Bayesian methods
• coastal structures
• dikes
• reliability analysis

Notes

1. It is an uninformative prior, see Rajabalinejad et al. (2010b).

2. An efficient criterion is essential to rank variables for the Improved Dynamic Bounds (IDB) method.

3. The rank correlation shows that variables 3, 8 and 4 are the most influential variables and this sequence may change when the structure's response becomes nonlinear at the high WL, WL=+8 ft (2.4 m).

4. The variations of soil parameters were assumed to estimate the reliability of this structure; this assumption affects the calculated probability of failure.