Determination of bounds on failure probability in the presence of hybrid uncertainties

Abstract

A fundamental component of safety assessment is the appropriate representation and incorporation of uncertainty. A procedure for handling hybrid uncertainties in stochastic mechanics problems is presented. The procedure can be used for determining the bounds on failure probability for cases where failure probability is a monotonic function of the fuzzy variables. The procedure is illustrated through an example problem of safety assessment of a nuclear power plant piping component against stress corrosion cracking, considering the stochastic evolution of stress corrosion cracks with time. It is found that the bounds obtained enclose the values of failure probability obtained from probabilistic analyses.

Literature review of methods for representing uncertainty

“…The (nested) α-cuts of μ F ,Y (figure 6.1, bottom) constitute the focal elements of the corresponding possibilistic body of evidence, whose possibility and necessity measures and basic probability assignments are reported in table 6.1. As a further example, consider the following [Anoop et Rao 2008;Baraldi et Zio 2008]. We consider an uncertain parameter y; based on its definition we know that the parameter can take values in the range [4,6] and the most likely value is 5: to represent this information a triangular possibility distribution on the interval [4,6] is used, with maximum value at 5; cf.…”

A Refined Methodology for Durability‐Based Service Life Estimation of Reinforced Concrete Structural Elements Considering Fuzzy and Random Uncertainties

“…In this connection, Guyonnet et al (2003) proposed an approach (termed a hybrid approach) which combines Monte Carlo random sampling of probability distribution functions with fuzzy calculus for assessment of risk due to human exposure to Cadmium. Anoop et al (2005, 2008) used a hybrid approach combining vertex method with Monte Carlo simulation (MCS) method for computing the fuzzy failure probabilities of a piping component against stress corrosion cracking with time. Sadeghi et al (2010) proposed a fuzzy MCS framework for risk analysis in construction project management considering both fuzzy and random inputs.…”

“…Sadeghi et al (2010) proposed a fuzzy MCS framework for risk analysis in construction project management considering both fuzzy and random inputs. Anoop and Balaji Rao (2008) proposed a procedure based on possibility theory for determining the bounds on failure probability compatible with the available data, considering both probabilistic and fuzzy uncertainties. Such approaches are found to be useful for safety assessment of engineering components considering hybrid uncertainties.…”