An efficient uncertainty propagation analysis method for problems involving non-parameterized probability-boxes

As a kind of imprecise probabilistic model, probability-box (P-box) model can deal with both aleatory and epistemic uncertainties in parameters effectively. The P-box can generally be categorized into two classes, namely, parameterized P-box and non-parameterized P-box. Currently, the researches involving P-boxes mainly aim at the parameterized P-boxes while the works handling the non-parameterized P-boxes are relatively inadequate. This paper proposes an efficient uncertainty propagation analysis method based on cumulative distribution function discretization (CDFD) for problems with non-parameterized P-boxes, through which the bounds of statistical moments and the cumulative distribution function (CDF) of a response function with non-parameterized P-box variables can be obtained. Firstly, a series of linear programming models are established for acquiring the lower and upper bounds of the first four origin moments of the response function. Secondly, based on the bounds of the origin moments, the CDF bounds for the response function can be obtained using Johnson distributions fitting and an optimization approach based on percentiles. Finally, the accuracy and efficiency of the proposed method are verified by investigating two numerical examples.

Time Series Clustering and Classification for Uncertainty Analysis by MAAP5 Code

The MAAP5.04 code uncertainty analysis was carried out for the Power Burst Facility Severe Fuel Damage Test 1-4. Comparisons between experimental data and analysis results were focused on hydrogen generation. The uncertainty propagation analysis was conducted through random variations of input uncertainty parameters of phenomenological models whose ranges were determined by the MAAP5 Zion parameter file. The time series clustering technique using the mean-shift algorithm was applied to the data set generated by the uncertainty propagation analysis. It was confirmed that the code predicted well the hydrogen mass generated and the uncertainty bounds of the analysis included the measured hydrogen generation history. The time series clustering technique demonstrated that the key model parameters could be identified for classifying the uncertainty analysis results using a decision tree classifier. Furthermore, the regression models were constructed which predict the uncertainty of the hydrogen generation from the model uncertainty parameters by using the support vector regressions. The hold-out method of cross validation was applied to the regression models of the hydrogen generation to investigate the training error and the test error for the uncertainty prediction of the hydrogen generation.