A parameter tree approach to estimating system sensitivities to parameter sets

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) i s available. The objective of our technique is to analyze the input vectors and the corresponding output vectors (that is, post-process the results) t o estimate the relative sensitivity of the output to input parameters (take n 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 p arameter space is not required before the simulation. A tree structure (whi ch looks similar to an event tree) is developed to better explain the techn ique. Each limb of the tree represents a particular combination of paramete rs or a combination of system components. For convenience and to distinguis h 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 parame ter value is greater than or less than a specified branching criterion (e.g ., mean, median, percentile of the population). The corresponding system ou tputs are also segregated into similar bins. Partitioning the first paramet er into a "+" or a "-" bin creates the first level of the tree containing t wo branches. At the next level, realizations associated with each first-lev el branch are further partitioned into two bins using the branching criteri a on the second parameter and so on until the tree is fully populated. Rela tive 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 pr eliminary simulations of the proposed high-level radioactive waste reposito ry at Yucca Mountain, NV. Using a Total System Performance Assessment Code called TPA, realizations are obtained and analyzed. In the examples present ed, groups of five important parameters, one for each level of the tree, ar e used to identify branches of the tree and construct the bins. In the firs t example, the five important parameters are selected by more traditional s ensitivity analysis techniques. This example shows that relatively few bran ches of the tree dominate system performance. In another example, the same realizations are used but the most important five-parameter set is determin ed in a stepwise manner (using the parameter tree technique) and it is foun d that these five parameters do not match the five of the first example. Th is important result shows that sensitivities based on individual parameters (i.e. one parameter at a time) may differ from sensitivities estimated bas ed 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 th e 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. (C) 2000 Elsevier Science Ltd. All rights rese rved.