Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Correlation among aleatory uncertain variables
Alias: none
Argument(s): REALLIST
Default: identity matrix (uncorrelated)
Aleatory uncertain variables may have correlations specified through use of an uncertain_correlation_matrix
specification. This specification is generalized in the sense that its specific meaning depends on the nondeterministic method in use.
When the method is a nondeterministic sampling method (i.e., sampling), then the correlation matrix specifies rank correlations [51].
When the method is a reliability (i.e., local_reliability
or global_reliability
) or stochastic expansion (i.e., polynomial_chaos
or stoch_collocation
) method, then the correlation matrix specifies correlation coefficients (normalized covariance)[41].
In either of these cases, specifying the identity matrix results in uncorrelated uncertain variables (the default). The matrix input should be symmetric and have all entries where n is the total number of aleatory uncertain variables.
Ordering of the aleatory uncertain variables is:
When additional variable types are activated, they assume uniform distributions, and the ordering is as listed on variables.
Consider the following random variables, distributions and correlations:
uncertain_correlation_matrix # ordering normal, exponential, weibull # \f$X_1\f$ \f$X_2\f$ \f$X_5\f$ \f$X_4$\f \f$X_3\f$ 1.00 0.00 0.00 0.00 0.00 0.00 1.00 0.50 0.24 0.78 0.00 0.50 1.00 0.00 0.20 0.00 0.24 0.00 1.00 0.49 0.00 0.78 0.20 0.49 1.0