Robust Optimization of a Thermal Anti-Ice Protection System in Uncertain Cloud Conditions

This paper presents a framework for the robust optimization of the heat flux distribution for an anti-ice electrothermal ice protection system under uncertain conditions. The considered uncertainty regards a lack of knowledge concerning the characteristics of the cloud, i.e., the liquid water content and the median volume diameter of water droplets, and the accuracy of measuring devices, i.e., the static temperature probe. Uncertain parameters are modeled as random variables, and two sets of bounds are investigated. A forward uncertainty propagation analysis is carried out using a Monte Carlo approach exploiting a surrogate models. The optimization framework relies on a gradient-free algorithm (mesh adaptive direct search), and two different objective functions are considered, namely, the 95 quantile of the freezing mass rate and the statistical frequency of the fully evaporative operating regime. The framework is applied to a reference test case, revealing a potential to improve the heat flux distribution of the baseline design. A new heat flux distribution is proposed, and it presents a more efficient use of the thermal power, increasing flight safety even at nonnominal environmental conditions.