Nuclear Science and Engineering / Volume 184 / Number 3 / November 2016 / Pages 400-429
Technical Paper / dx.doi.org/10.13182/NSE16-37
Appropriate model assessment requires proper understanding of the impact of variations of model parameters and their interactions on results. However, in many thermal-hydraulic (TH) simulations, the code often predicts time-dependent output where the impact of model parameter variations on the overall transient is not easily discernible from quantities of interest (QoIs) based on the maximum, minimum, or average over space and/or time. This work proposes a methodology to analyze transient code output in a more comprehensive manner and coupled with established global sensitivity analysis (SA) methods.
This paper first describes how the particularities of transient output variations can be characterized through application of functional data analysis (FDA) techniques. The convoluted amplitude and phase variations in the output are separated first by using a registration technique. The high-dimensional transient output is then projected in reduced dimension by using principal component analysis. Based on this, innovative QoIs that capture the variation over the whole course of the transient are finally derived.
The subsequent global SA is a two-step process. First, the noninfluential parameters are identified using the efficient Morris screening method. The exclusion of these parameters reduces the size of the problem and decreases the cost of the downstream analysis. Second, the sensitivity of the influential model parameters with respect to a selected QoI is computed using the Sobol’ method. The method gives a set of sensitivity indices quantifying the contributions of input variations to the QoI variation considering possible interactions among the parameters.
The applicability of the proposed methodology is demonstrated by analyzing a 26-parameter reflood experiment simulation model with the TRAC/RELAP Computational Engine (TRACE) TH system code. The FDA-derived QoI on the time-dependent cladding temperature was able to give a deeper insight on particular modes of variations exhibited by the model over the whole course of the reflood transient. That is, the variations in the cladding temperature transient could be simply divided into two modes: the reversal phase (from heatup until shortly after the temperature turnaround) and the descent phase (onward until quenching). The applied SA method was then able to attribute the variation of these two modes to the variation of the model parameters. It was found that the model was additive during the temperature reversal phase with dispersed flow film boiling–related parameters contributing to most of the model output variation, consistent with the adopted phenomenological model. Yet, the variation during the temperature descent could only be explained through parameter interactions indicating a more complex input/output relationship.
Through study of this particular case, it is shown that if different QoIs based on the same time-dependent output variable are used—thus inspecting functional aspects of the output—the model might behave differently, being additive with respect to one QoI and interacting with respect to another, thus revealing more information on the model behavior, which might be overlooked in a SA based on extreme or time-averaged QoIs.