A new variance-based global sensitivity analysis technique Original Research Article

A new set of variance-based sensitivity indices, called image-indices, is proposed. Similar to the Sobol’s indices, both main and total effect indices are defined. The image-main effect indices measure the average reduction of model output variance when the ranges of a set of inputs are reduced, and the total effect indices quantify the average residual variance when the ranges of the remaining inputs are reduced. Geometrical interpretations show that the image-indices gather the full information of the variance ratio function, whereas, Sobol’s indices only reflect the marginal information. Then the double-loop-repeated-set Monte Carlo (MC) (denoted as DLRS MC) procedure, the double-loop-single-set MC (denoted as DLSS MC) procedure and the model emulation procedure are introduced for estimating the image-indices. It is shown that the DLRS MC procedure is suitable for computing all the image-indices despite its highly computational cost. The DLSS MC procedure is computationally efficient, however, it is only applicable for computing low order indices. The model emulation is able to estimate all the image-indices with low computational cost as long as the model behavior is correctly captured by the emulator. The Ishigami function, a modified Sobol’s function and two engineering models are utilized for comparing the image- and Sobol’s indices and verifying the efficiency and convergence of the three numerical methods. Results show that, for even an additive model, the image-total effect index of one input may be significantly larger than its image-main effect index. This indicates that there may exist interaction effects among the inputs of an additive model when their distribution ranges are reduced.