Deterministic and Probabilistic Approaches to Model and Update Dynamic Systems

Abstract

Updating simulation models, based on flight test or other data, or creating a model using only experimental data is a necessary process that can be costly and laborious. Simulation updates are necessary for high-fidelity simulations used in analysis, control development, handling qualities prediction, fleet training, etc. This paper presents methods to update aircraft models based on deterministic and probabilistic approaches. The deterministic approach is based on a collection of signal processing, statistical analysis, and maximum likelihood estimators embodied in the Algorithms to Update Simulation Parameters with Experimental Data tool. Mathematically sound and statistically rigorous techniques are used to calculate updates of current model parameters and suggest new terms capturing unmodeled dynamics, thereby improving correlation with observed vehicle response. The probabilistic approach is based on generalized polynomial chaos theory included in the Algorithms for Uncertainty Representation and Analysis (AURA) tool. The AURA tool allows the user to update probabilistic models based on experimental data, formulated as a Bayesian inference problem. This paper will present the methodology for both deterministic and probabilistic approaches and provide examples of their application to different aircraft designs, including tilt-rotor and rotary-wing unmanned air system vehicles. The results for both deterministic and probabilistic modeling approaches demonstrate excellent results. The probabilistic approach is novel in its expressive power to propagate and update probabilistic models and provides users with an intuitive and powerful modeling approach.