Uncertainty Quantification

Background

The aviation industry has experienced significant growth over the past several decades and is projected to continue growing in the following decades to come. To insure a sustainable growth for the aviation industry, policy-makers and stake-holders need to be well informed on the environmental and economic impacts of their decision. To support this endeavor the Laboratory for Aviation and the Environment, along with the Federal Aviation Administration’s Office for Energy and the Environment, are developing a set of comprehensive models to assess the environmental impacts of the aviation industry.

Uncertainty quantification assists in supporting this endeavor by providing a rigorous procedure to represent, characterize, and analyze the uncertainties in models of how aviation impacts the environment. Uncertainty quantification of these comprehensive models is critical because it quantifies the uncertainties of the modules with respect to their inputs. It is important to comprehend this relationship between input uncertainty and output uncertainty because it properly facilitates the transfer of policy-relevant information from the model developers to the policy-makers and other stake-holders.

 

Examples of uncertain variables and their uncertainty distributions used in assessing the climate impacts of aviation.

 

Uncertainty quantification at the Laboratory for Aviation and the Environment

The application of numerical simulations such as set of comprehensive models for policy-making decisions raises such questions as:  “What confidence can one have in the model results?” and “What can be done to improve this confidence?” The objective of uncertainty quantification is to answer these questions, and more specifically, to:

  • Relate variability in model inputs to the variability in model outputs
  • Rank model inputs based on their contribution to output variability
  • Identify limitations in model functionality that may hinder the model’s applicability
  • Identify sources of uncertainty which may be reduced through further research and validation

Uncertainty quantification investigates the impacts of the inputs on the final output, by performing an uncertainty analysis and a global sensitivity analysis. An uncertainty analysis aims to answer the question, “How do uncertainties in model factors propagate to uncertainties in model outputs?”. Uncertainties in model outputs refers to statistics of interest, such as model output means, variances, and the probability of an event occurring. These quantitative representations of variability in model outputs provide a means of comparing various policy scenarios and quantitatively evaluating the performance of the model relative to fidelity requirements.

Global sensitivity analysis aims to determine how each model input contributes to variability in the outputs. The outcome is used to identify the inputs on which future research should be directed so as to reduce input uncertainty and thereby output variability.

Outcomes and applications

Our uncertainty quantification research is used to properly inform the policy-makers and stakeholders on the environmental and economic impacts of their decisions. More specifically, we are interested in quantifying uncertainty at a system-level, which is the integration of the set of computational tools (e.g., aircraft design, aircraft operation, and aviation impacts). System-level uncertainty quantification is particularly important because it enables the policy-makers and stakeholders to identify the significant factors (e.g., aircraft components, aircraft routes) which affect the outputs of interest (e.g., environmental impacts, economic impacts).