Bayesian Monte Carlo method for monotonic models applying the Generalized Beta distribution

A novel Bayesian Monte Carlo method for monotonic models (BMCM) is described in this paper. The BMCM method enjoys the advantages of the recently developed method of Dynamic Bounds [1] for the reliability assessment of monotonic models, and incorporates weighted logical dependence between neighboring points of the limit state equation (LSE) as prior information for improving computational speed. The BMCM benefits from the global uncertainty concept that links global and local uncertainties. This integrated approach is superior to other techniques used in safety assessment of monotonic models as it substantially increases the efficiency of Monte Carlo method. The formulation of BMCM is provided in this paper with an example showing its ability to dramatically improve efficiency of simulations. This is achieved by employing prior information obtained from monotonic models and outcomes of the preceding simulations. The theory and numerical algorithms of the BMCM method for multi-dimensional problems, and integration with a probabilistic finite element model, are discussed in this paper. These coupled models are applied to the 17th Street Flood Wall in New Orleans to assess reliability of a flood defence system.