Probabilistic assessment of dynamic system performance

Accurate prediction of dynamic system failure behavior can be important for the reliability and risk analyses of nuclear power plants, as well as for their backfitting to satisfy given constraints on overall system reliability, or optimization of system performance. Global analysis of dynamic systems through investigating the variations in the structure of the attractors of the system and the domains of attraction of these attractors as a function of the system parameters is also important for nuclear technology in order to understand the fault-tolerance as well as the safety margins of the system under consideration and to insure a safe operation of nuclear reactors. Such a global analysis would be particularly relevant to future reactors with inherent or passive safety features that are expected to rely on natural phenomena rather than active components to achieve and maintain safe shutdown. Conventionally, failure and global analysis of dynamic systems necessitate the utilization of different methodologies which have computational limitations on the system size that can be handled. Using a Chapman-Kolmogorov interpretation of system dynamics, a theoretical basis is developed that unifies these methodologies as special cases and which can be used for a 2 comprehensive safety and reliability analysis of dynamic systems. It is shown that the theoretical basis leads to generic (i.e. system independent) algorithms which reduce the computational limitations in applications. The practicality of these algorithms in nuclear engineering is demonstrated with example nonlinear systems from reactor dynamics. The results of these applications show that, for dynamic systems, the new algorithms can speed up: (a) interval reliability analysis by a factor of 6 and reduce the storage requirements by a factor of 20, (b) global analysis by a factor 20 and reduce the storage requirement by a factor of 2.5, and, (c) sensitivity analysis by a factor proportional to the number of different probability density functions (pdf) that may need to be considered if a unique pdf cannot be identified to represent the stochasticity in the system parameters. The computational advantages of these algorithms increase their range of applicability to include larger systems.