Comparison of two metamodeling approaches for sensitivity analysis of a geological disposal model

Probabilistic methods of higher order sensitivity analysis provide a possibility for identifying parameter interactions by means of sensitivity indices. Better understanding of parameter interactions may help to better quantify uncertainties of repository models, which can behave in a highly nonlinear, non-monotonic or even discontinuous manner. Sensitivity indices can efficiently be estimated by the Random-Sampling High Dimensional Model Representation (RS-HDMR) metamodeling approach. This approach is based on truncating the ANOVA-HDMR expansions up to the second order, while the truncated terms are then approximated by orthonormal polynomials. By design, the sensitivity index of total order (SIT) in this method is approximated as the sum of the indices of first order (SI1’s) plus all corresponding indices of second order (SI2’s) for a considered parameter. RS-HDMR belongs to a wider class of methods known as polynomial chaos expansion (PCE). PCE methods are based on Wiener’s homogeneous chaos theory published in 1938. It is a widely used approach in metamodeling. Usually only a few terms are relevant in the PCE structure. The Bayesian Sparse PCE method (BSPCE) makes use of sparse PCE. Using BSPCE, SI1 and SIT can be estimated. In this work we used the SobolGSA software [1] which contains both the RS-HDMR and BSPCE methods.

We have analysed the sensitivities of a model for a generic LILW repository in a salt mine using both the RS-HDMR and the BSPCE approach. The model includes a barrier in the near field which is chemically dissolved (corroded) over time by magnesium-containing brine, resulting in a sudden significant change of the model behaviour and usually a rise of the radiation exposure. We investigated the model with two sets of input parameters: one with 6 parameters and one with 5 additional ones (LILW6 and LILW11 models, respectively). For the time-dependent analysis, 31 time points were used.

The SI1 indices calculated with both approaches agree well with those obtained from the well-established and reliable first-order algorithm EASI [2] in most investigations. The SIT indices obtained from the BSPCE method seem to increase with the number of simulations used to build the metamodel. The SIT time curves obtained from the RS-HDMR approach with optimal choice of the polynomial coefficients agree well with the ones from the BSPCE approach only for relatively low numbers of simulations. As, in contrast to RS-HDMR, the BSPCE approach takes account of all orders of interaction, this may be a hint for the existence of third- or higher-order effects.

Acknowledgements

The work was financed by the German Federal Ministry for Economic Affairs and Energy (BMWi). We would also like to thank Dirk-A. Becker for his constructive feedback.

References

[1]         S. M. Spiessl, S. Kucherenko, D.-A. Becker, O. Zaccheus, Higher-order sensitivity analysis of a final repository model with discontinuous behaviour. Reliability Engineering and System Safety, doi: https://doi.org/10.1016/j.ress.2018.12.004, (2018).

[2]          E. Plischke, An effective algorithm for computing global sensitivity indices (EASI). Reliability Engineering and System Safety, 95: 354–360, (2010).