Enhancement of Capability in Probabilistic Risk Analysis by Genetic Algorithms

Abstract

Probabilistic Risk Analysis (PRA) has been widely recognized for its crucial role in various disciplines. The investigation and assessment of system failure or system malfunction is a main interest in PRA. A system is considered in a failure status when the system cannot satisfy a set of prescribed performance criteria. The prescribed performance criteria are referred to as the performance functions. The performance functions are explicitly or implicitly defined in terms of random variables that characterize the problems of interest. The performance functions also divide the high dimension space of random variables into a failure domain and a safe domain. The failure domain is the subspace of random variables that result in the failure of system. The complementary subspace is the safe domain. The essential information that is particularly desired from PRA includes Point of Maximum Likelihood (PML) in failure domain and the failure probability. PML represents the combination of variable magnitudes that most likely contribute to the failure and to the corresponding failure probability. In practice, systems under consideration can be highly non-linear and large. It is also possible that the performance functions of systems are implicit, non-linear, non-differentiable, noisy, and can only be characterized in terms of numerical values. Computation of failure probabilities under such situations of complex systems and complicated failure domains thus generally demands considerable computational efforts and resources in order to obtain results with high confidence levels, especially in case of rare-event analysis. The objective here is to show how Genetic Algorithms (GAs) can enhance the capability in PRA for numerous key aspects of risk-based information. Fundamental problems in PRA will be first addressed. GAs in context of PRA is next described. The demonstration of capability enhancement then follows. The demonstration starts from the application of GAs to the determination of PML. A generic problem in which it is not possible to visualize the failure domain due to its dimensionality and non-linearity characteristics is considered. The capability in PRA is significantly enhanced by GAs in such a way that the PRA can be accomplished without the requirement of a priori knowledge about the geometry of failure domain. The enhancement of the capability in PRA of rare events is subsequently illustrated. A numerical technique which utilizes the GAs-determined PML is introduced. The technique is referred to as an Importance Sampling around PML (ISPML). ISPML computes the failure probabilities of rare events with a considerably less computational effort and resource than Monte Carlo Simulation (MCS). In this regards, GAs enhance the capability in O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg