Efficient Methods for Uncertainty Propagation in Computational-Fluid-Dynamics-Based Fire PRA, 20-R8271
Inclusive Dates: 11/14/11 – 12/16/13
Background — U.S. Nuclear Power Plants (NPPs) have recently been allowed to transition from a deterministic fire protection licensing basis to a risk-informed performance-based program. The transition requires a full Fire Probabilistic Risk Assessment (FPRA) to quantify the effect of fire incidents on core damage frequency and large early release frequency. Realistic FPRA involves an accurate evaluation of the performance of critical components for a range of design fires (heat release rates). Ideally, this process heavily relies on the use of computational fluid dynamics (CFD) codes [i.e., Fire Dynamics Simulator (FDS)]. Because CFD codes are computationally intensive (a single run may take days or even weeks), fire modeling is currently limited to point estimates, which do not explicitly account for uncertainties in input parameters and forces the analyst to make conservative assumptions in lieu of full quantification of uncertainty. The traditional Monte Carlo approach for propagating uncertainty requires a large number of CFD simulations (several hundred), which makes uncertainty quantification intractable. There is a strong need for developing an uncertainty quantification method that can propagate uncertainty without sacrificing computational accuracy in FPRA.
Approach — The approach adopted in this project is to propagate input uncertainties in FPRA using a small number of Monte Carlo realizations (a few tens to hundreds as opposed to thousands), which would improve computation time by at least an order of magnitude compared to a pure Monte Carlo method. The methods explored are reliability-based methods that minimize the need for a large number of Monte Carlo realizations to construct a cumulative distribution function (CDF) from the model outputs. The approach involves constructing an approximate CDF from a few Monte Carlo realizations by applying mean value and advanced mean value methods and refining the approximate CDF to the desired level of accuracy by applying an importance-sampling approach. The method involves careful selection of a number of estimation points on the approximate CDF, constructing a CDF through these points, and then repeating the process until the CDF is obtained with the desired level of accuracy for various statistical moments. The results from this method are compared against the regular Monte Carlo method using the stratified sampling method to gauge improvement in computational efficiency. The methods are then tested using a variety of realistic fire scenario examples.
Accomplishments — A Monte Carlo (and stratified sampling) FDS model has been developed for benchmarking that will be used once the reliability-based methods are developed. The Monte Carlo FDS code is capable of running the FDS code repeatedly after sampling from input parameter distribution functions (i.e., probability density functions or PDFs), correlating parameters if needed, and propagating one "vector" of input values to a processor on the parallel computer cluster, and collecting FDS code outputs for constructing the model output CDF. An example study of NPP control room abandonment in response to Switchgear Room electric-cable cabinet fire scenario has been explored. Parameters for which uncertainties are to be represented in these test problems and performance function output uncertainties of interest have been identified. Uncertainty is represented via PDFs and propagated through the model for 18 parameters. For a computationally intensive model such as FDS, this is considered to be a relatively large set. Special considerations have been given to time-dependent parameters, such as the heat-release rate curves. Because developing the reliability and Monte Carlo methods requires a large number of trial runs during the model development phase, a faster Monte Carlo CFAST code has been developed to serve as a surrogate for the time-consuming Monte Carlo FDS code. Figure 1 shows a spectrum of temperature evolution curves from which the probability of failure of cables is determined based on a temperature threshold criterion. Reliability-based calculations have been effectively used to extend the failure time prediction to four standard deviations around the mean.