Explicit Uncertainty Quantification for Probabilistic Handling Qualities Assessment

Abstract

Modern flight vehicle development typically involves significant uncertainty in aerodynamic loads and vehicle control responses. In many cases, it may be necessary to consider this uncertainty in preliminary evaluations of stability, handling qualities (HQ), and performance. This paper introduces a novel methodology for computing these quantities in a probabilistic framework using the Koopman operator. The algorithm discretizes the uncertainty space and uses relevant transformations or simulations to map each point to the handling qualities evaluation domain, resulting in a stability, HQ, and/or performance assessment for each discretized point. The expected value of the stability, HQ, and/or performance requirement is then computed through an expected value integral with the initial joint probability density function, yielding a probabilistic assessment with respect to relevant specifications. The methodology is used to evaluate handling qualities of a quadrotor Unmanned Aerial System (UAS), for which a multi-loop Dynamic Inversion (DI) flight control law is developed. The UAS example is evaluated with respect to quantitative handling qualities specifications based on scaled Mission Task Elements (MTEs). The proposed explicit UQ approach is shown to provide a convenient framework for the propagation of parametric uncertainty to stability, HQ, and performance specifications with unique advantages over Monte Carlo techniques.