Variance Decomposition
Sensitivity evaluation of numerical models establishes how much each input parameter contributes to the variability of the final result. Within this statistical domain, sobol sensitivity analysis decomposes the total variance of the model output into fractions that can be attributed to single inputs or to interactions between them. This method provides a rigorous quantitative measure of parameter importance across the entire input space.
Index Computation
The technique computes first-order sensitivity indices to measure the individual effect of each parameter. When executing sobol sensitivity analysis, total-effect indices are also calculated to capture all the interaction effects between the parameters. These indices sum to one in additive models but can exceed that value when interactions are present.
Computational Method
Evaluating these indices requires a large number of model evaluations, typically generated via quasi-Monte Carlo sampling. Engineers use low-discrepancy sequences to distribute the sampling points evenly across the multi-dimensional parameter space. High computational costs can arise for models with long execution times.
To address this, designers often train a surrogate model on a small dataset before running sobol sensitivity analysis on the fast approximation.
Design Optimization
Results from these sensitivity indices guide developers in simplifying complex simulation models by fixing non-influential parameters to default values. This parameter reduction focuses the calibration effort on the most critical variables. This improves both the speed and the reliability of the optimization process.
