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Applying inverse mapping across coupled and feedback loop processes

Posted on 15/06/2017

Which uncertain inputs contribute most to uncertain output?

Using inverse mapping to reduce aircraft noise and emissions.

By Matt Butchers

This article is part of our series on High value manufacturing: dealing with the unknown

Certain sectors operate within very stringent performance and regulatory limits, so determining feasible design options at the early stages of development is key.

Crucially, at this early stage, design engineers must be able to identify the uncertainties in the inputs that contribute the most to uncertainties in the output, in this way forming a strategy for robust design decision-making and managing those which are driving performance and regulatory metrics, and thus need the most careful control.

A case in point: aerospace

24-hour operation aircraft operate under strict regulations, including noise curfews and emission levels. Design approaches are needed that explore a large number of permutations of aircraft configurations with respect to their climb-out noise levels, their cruise performance and their emission levels, all under uncertainty.

The process

The basic concept is to generate data for a set of representative aircraft configurations, combining a range of airframes with a range of engines. Specific noise measurement criteria need to be deduced. Then, using coupled analyses ‘plug-ins’, performance models need to be derived that enable exploration of the sensitivities among three exemplar measures of aptness.

These measures of aptness are (in this case): noise levels (target = low) and noise level margins (target = high); cruise fuel consumptions (target = low); emissions (target = low) and emission margins (target = high). This provides a multi-dimensional challenge for determining, visualising and acting on the uncertainties through the analyses.

The objective is to narrow the set of possible aircraft configurations to a feasible list, using uncertain, multi-dimensional decision criteria. The process is then repeated, using analyses models closer to the laws of nature, to narrow the set of feasible configurations to a set that provides competitive advantages.

Uncertainty Quantification and Management considerations

The UQ&M analyses is used to make robust designs that narrow the set of possible configurations; discover the parameters that contribute to the variations in the measures of aptness; and manage key parameters to drive reliably towards the desired properties and behaviours.

The approach

In SIG-funded study groups, various approaches were trialled, including:

History matching: a framework to identify regions of the input space that comply with prescribed requirements
Global sensitivity analysis: to identify the inputs that contribute the most to the variability of the output
Constrained optimisation: exploring the input space
How to meet the distributional requirements for the Figures of Merit and provide guidance for potential answers
Set-based design and UQ&M concepts: applied to achieve the objectives of the study

The benefits

The benefit is improved decision making based on a robust understanding of which uncertainties in the inputs contribute most strongly to uncertainties in the output performance and regulatory metrics, and thus need the most careful control. Ultimately, these approaches lead to faster design cycles which are compliant with an increasingly stringent regulatory environment.

Read more use cases in this series

Developing early stage designs for compliance with flight performance requirements

Visualisation of uncertainty to aid the decision making process

Integration of multi-fidelity and multi-source analyses and data

More information about upcoming UQ&M SIG group activities can be found here.