A parameter tree approach to estimating system sensitivities to parameter sets

Abstract A post-processing technique for determining relative system sensitivity to groups of parameters and system components is presented. It is assumed that an appropriate parametric model is used to simulate system behavior using Monte Carlo techniques and that a set of realizations of system output(s) is available. The objective of our technique is to analyze the input vectors and the corresponding output vectors (that is, post-process the results) to estimate the relative sensitivity of the output to input parameters (taken singly and as a group) and thereby rank them. This technique is different from the design of experimental techniques in that a partitioning of the parameter space is not required before the simulation. A tree structure (which looks similar to an event tree) is developed to better explain the technique. Each limb of the tree represents a particular combination of parameters or a combination of system components. For convenience and to distinguish it from the event tree, we call it the parameter tree. To construct the parameter tree, the samples of input parameter values are treated as either a “+” or a “−” based on whether or not the sampled parameter value is greater than or less than a specified branching criterion (e.g., mean, median, percentile of the population). The corresponding system outputs are also segregated into similar bins. Partitioning the first parameter into a “+” or a “−” bin creates the first level of the tree containing two branches. At the next level, realizations associated with each first-level branch are further partitioned into two bins using the branching criteria on the second parameter and so on until the tree is fully populated. Relative sensitivities are then inferred from the number of samples associated with each branch of the tree. The parameter tree approach is illustrated by applying it to a number of preliminary simulations of the proposed high-level radioactive waste repository at Yucca Mountain, NV. Using a Total System Performance Assessment Code called TPA, realizations are obtained and analyzed. In the examples presented, groups of five important parameters, one for each level of the tree, are used to identify branches of the tree and construct the bins. In the first example, the five important parameters are selected by more traditional sensitivity analysis techniques. This example shows that relatively few branches of the tree dominate system performance. In another example, the same realizations are used but the most important five-parameter set is determined in a stepwise manner (using the parameter tree technique) and it is found that these five parameters do not match the five of the first example. This important result shows that sensitivities based on individual parameters (i.e. one parameter at a time) may differ from sensitivities estimated based on joint sets of parameters (i.e. two or more parameters at a time). The technique is extended using subsystem outputs to define the branches of the tree. The subsystem outputs used in this example are the total cumulative radionuclide release (TCR) from the engineered barriers, unsaturated zone, and saturated zone over 10,000 yr. The technique is found to be successful in estimating the relative influence of each of these three subsystems on the overall system behavior.