Uncertainty analysis methodology for internally coupled systems with many random variables

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An approach for performing uncertainty analysis of internally coupled systems is presented. An internally coupled system is defined as an assemblage of calculational modules that are linked together in order to compute a global response. In the general case, each module accepts as input one or more independent problem variables and one or more output responses from other modules in the system. In many cases, these problems also involve a large number of random variables. Because efficient uncertainty analysis methods require calculation of global response sensitivities with respect to problem input parameters, the time required to compute sensitivities for internally coupled systems by finite differencing the entire system can quickly become prohibitive, especially if one or more of the modules requires an expensive calculation, or if the number of random variables is large. Moreover, accuracy problems associated with finite differencing are exacerbated for internally coupled systems. The paper presents an approach for dealing with these issues using a method that computes global response sensitivities from local module sensitivities. Several simple examples are presented to illustrate the method. A more complex example that emulates a complex code for performing nuclear waste repository assessment is presented to illustrate the efficiency of the method on a problem of significant size.