Shapley Effects as a Global Sensitivity Metric for Robust Design and Control

This paper introduces a novel robust design approach aimed at reducing the sensitivity of a target metric to parameter uncertainties. Using Shapley effects from game theory as a global sensitivity proxy, we analyze a clamped-free Euler-Bernoulli beam with two uncertain mass positions. The first case study reduces sensitivity of the second mode frequency to mass location uncertainty and is validated experimentally on a gantry-suspended beam. In the second case, a robust controller minimizes the Shapley effect of residual energy on mass location uncertainty. Our approach significantly reduces average residual energy compared to traditional Zero Vibration Derivative Input Shapers, as confirmed by experiments.