Abstract
Sensitivity analysis is a commonly used method in engineering applications to identify the input variables whose variance has the largest impact on the variance of a model output. Two major difficulties are often encountered. First, many computationally intensive model evaluations are required to obtain sensitivity indices with high statistical confidence. Second, input variables are often correlated, which cannot be handled unambiguously by most sensitivity analysis methods.
Shapley values are a promising sensitivity measure for problems with correlations between input variables, as interaction effects are distributed evenly among the respective input parameters. However, Shapley values are affected by spurious correlations with input variables that have no functional influence. In this case, the Shapley value is dispersed and its significance is reduced. Therefore, a sensitivity measure that detects input variables without functional influence is desirable.
This paper analyzes the behavior of different sensitivity measures with respect to correlated input variables. It is shown that first-order and total-effect Sobol sensitivity indices, and Shapley values alone do not fully detect input variables without functional influence. Therefore, the modified coefficient of importance is introduced to detect such input variables.
In the final part of this paper, a sensitivity analysis for a compressor blade subject to manufacturing variability and wear is performed using the aforementioned sensitivity measures. The blade variation is described by profile parameters. First, the sensitivity analysis is performed, which allows to identify profile parameters that have no functional influence on the isentropic efficiency. Then, the sensitivity analysis is repeated with appropriately grouped profile parameters. It is found that the profile parameters describing the blade thickness have the greatest influence on the variance of the efficiency. With the proposed approach, it is therefore possible to identify the most important profile parameters, even if they are correlated.
