### Optimising Spacecraft Design for A World-leading Space Agency

**Submitting Institution**

University of Southampton**Unit of Assessment**

Mathematical Sciences**Summary Impact Type**

Technological**Research Subject Area(s)**

Mathematical Sciences: Applied Mathematics, Numerical and Computational Mathematics

Information and Computing Sciences: Computation Theory and Mathematics

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PDF**Summary of the impact**

Through close collaboration with scientists at the European Space Agency (ESA), research at the University of Southampton has developed new algorithms and an associated software tool that have contributed to more efficient spacecraft design. Now a standard component of the ESA's design technology, the tools have doubled the speed in which crucial design processes can be completed, resulting in increased efficiency over the REF period of 20 person-years — equivalent to €1 million in monetary terms — and maintaining the ESA's manufacturing competitiveness. The success of this work led to a €480,000 EU grant to adapt the tools for the avionics industry as part of efforts to meet ambitious environmental targets under the EU Clean Sky Initiative.

**Underpinning research**

Spacecraft are used for a variety of purposes: communications, meteorology, navigation, exploration and transportation. Designing spacecraft is an incredibly complex process; a vast number of parameters, including component geometry and material properties, must be taken into account. Rather than looking to optimise a single objective, engineers simultaneously weigh up several competing criteria such as cost, weight and durability in a process known as multi-objective optimisation. The design of heat pumps in spacecraft is a case in point; the cost and weight of the pumps need to be minimised, while their mechanical efficiency must be maximised. Engineers rely on mathematical algorithms to solve these multi-objective problems as efficiently as possible.

Standard techniques for multi-objective optimisation — for example
weighting objectives and adding
them up — involve the transformation of the given problem into an infinite
family of parameterised
standard optimisation problems. Solving *all* such problems for *all*
possible parameters amounts to
solving the original problem, but requires the solution of an infinite
number of sub-problems. Thus
in the real world one usually resorts to solving a finite number of these
problems to obtain an
approximate answer to the original question. This approach leaves various
important numerical
questions unanswered that need to be considered before practical
algorithms can be designed, in
particular:

- What are the numerical properties of transformations from a multi-objective problem to a family of parameterised single-objective problems?
- Is there an efficient way to discretise the parameter space of such a family of parameterised single-objective problems?
- Is it possible to use information from one parameterised problem to draw conclusions about the solutions of another parameterised problem?

The University of Southampton's Joerg Fliege (Professor, 2007-present) is
an expert in
mathematical and multi-objective optimisation and has contributed to a
greater understanding of all
aspects of these problems, from the underpinning mathematics to the design
of efficient
algorithms. He showed that a certain class of transformations have
favourable numerical properties
that can be exploited to reduce computation times **[3.1]**. Together
with colleagues in Brazil, he
developed, for the first time, a highly efficient algorithmic scheme for
discretizing parameter spaces
in an efficient manner **[3.2]** and designed a sensitivity analysis
that found it was indeed possible to
provide a solution to the third question outlined above.

This highly efficient numerical scheme makes use of recent algorithm
developments, notably an
adaptive scheme for the parameter space of a multi-objective programming
problem. From 2008-2010,
a team comprising Fliege, Gerdts (University of the Federal Armed Forces
Munich), Vicente
(University of Coimbra) and scientists at the European Space Agency (ESA)
employed these ideas
to develop new algorithms and produce a computational toolbox to solve
multi-objective problems
in spacecraft design **[3.3]**.

The multi-objective optimisation algorithm was implemented and
incorporated into the toolbox in a
follow-up project **[3.4]**. The Nonlinear Programme Solver code that
was developed included a
Graphical User Interface that allows an efficient exploration of the
design space for a given multi-objective
problem and consideration of trade-offs between the different objectives.
ESA engineers
were then able to explore the full parameter space in an efficient way to
significantly improve the
design process and enhance the quality of the final product.

**References to the research**

**Publications:**

**3.1** **(*)** Fliege, J. (2007): The
effects of adding objectives to an optimisation problem on the solution
set. *Operations Research Letters*, 35, (6), 782-790.

**3.2** **(*)** Fliege, Drummond, M.G. and Svaiter, B.F. (2009):
Newton's method for multicriteria
optimisation. *SIAM Journal on Optimisation*, 20, (2), 602-626.

**3.3** Gerdts, Fliege, Vicente, L.N. (2009): FGS Toolbox Software
Manual. European Space
Agency Study Contract Report 22170/08/NL/ST WP3000. September 2009.

**3.4** Fliege, J. and Xu H. (2011): Stochastic Multiobjective
Optimisation: Sample Average
Approximation and Applications. *Journal of Optimisation Theory and
Applications*, 151 (2). 135-162.

**(*)** These references best indicate the quality of the underpinning
research.

**Grants:**

**3.G1** European Space Agency Study Contract Report 22170/08/NL/ST
`Versatility of Filtering
Techniques in Non-Linear Programming Optimisation'. Awarded to the
Universities of
Birmingham, Southampton, and Coimbra. November 2008 — January 2010, EURO
180,000.

**3.G2** European Space Agency Contract t 5001003472, FGS-ECM-RfQ-1001
`MCO Add-On for
FGS Toolbox'. Awarded to the University of Southampton. December 2010 —
April 2011,
EURO 20,000.

**3.G3** Fliege, J. EU FP7 CLEANSKY Programme, call ID
SP1-JTI-CS-2012-03, `AWACS —
Adaption of WORHP to Avionics Constraints'. Awarded to the University of
Southampton, April
2013 — April 2015, EURO 474,000. http://www.cleansky.eu/

**Details of the impact**

Europe is one of the world's leading players in space engineering,
competing in the commercial
markets for telecommunications and launchers and forming a key partner for
the United States,
Russia and other countries. The ESA employs more than 2,000 people and has
an annual budget
of €4 billion. The European Space Research and Technology Centre (ESTEC)
which makes use of
the Southampton research is ESA's technical heart with a workforce of
around 2,700 and an
annual budget of €2.4 billion **[5.C1]**. ESTEC guarantees investors a
return rate of 96%; thus, the
annual value it adds to the European economy exceeds €2 billion, excluding
spin-off companies.

Each year, well over 100 payloads worth $100 billion are launched into
space **[5.C2]**. Arianespace,
the ESA's major launch provider and Europe's foremost commercial space
transportation company
with an annual revenue of €1 billion, accounts for about half the
commercial market. Each of their
satellites contains at least one antenna system, several heat pumps and
various other items whose
efficiency and cost require careful optimisation. Currently, the ESA has
20 spacecraft and missions
in the planning and design phases with launch dates between 2013 and 2022
and costs for each
mission ranging from several hundred million to one billion euros. Each
contains various
subsystems with conflicting design objectives. With costs of up to $40,000
to bring just one
kilogramme of payload into orbit, the design of efficient but lightweight
system components plays a
key role in spacecraft engineering.

Southampton's research has led to the development of a software tool
capable of efficiently solving
multi-objective optimisation problems that occur in space engineering and
spacecraft design. The
toolbox has, since April 2011, been a standard part of the ESA's design
technology. It has been
applied to the thermal design of spacecraft subsystems and in optimising
the shape of antenna
systems. The use of these tools has halved the computational time for
optimising the thermal
design of spacecraft sub-systems and the shape of antennae systems,
leading to an increased
efficiency equivalent to savings of 20 person-years (approximately €1
million). As the Head of the
ESA Guidance Navigation and Control Section will confirm, Southampton's
research has
significantly lowered the hurdles to new spacecraft designs and allowed
the ESA to maintain a
competitive edge in the manufacture of these products **[5.1]**.

As a specific example, in the design of a heat pipe an engineer needs to
vary the design
parameters that specify the basic geometry and the properties of the
materials used in construction
to maximise the heat throughput, while minimising the weight and the cost.
These criteria are
combined to produce a trade-off curve, which reveals the optimum
performance. Previously this
involved a large number of one-off calculations and there was no certainty
that the optimum
scenario was indeed achieved, often resulting in a large waste of
computational effort and
preventing a comprehensive exploration of the design space. The new
process developed by
Southampton automatically generates the design curve along with the
associated parameters and
cost. This enables designers to explore the parameter space in an
efficient and user-friendly way,
while the GUI interface allows them to develop an intuitive insight into
the problem. In particular,
the toolbox has enabled designers to find previously undiscovered regions
of the design space and
rapidly find the limits to a particular design, which aids the development
of new and innovative
solutions to the problem **[5.C3]**.

According to the official report of Dr G Ortega Head of the ESA Guidance,
Navigation, and Control
Section and responsible for evaluating the project `*ESA has concluded
with high success the
development of a Nonlinear Programming Solver (NLP) for numerical
optimization. The
Development Team has been deeming to be classified as fully outstanding.
The newly developed
NLP solver increases capacity and capability of European industry in the
area of numerical
optimization for applications such as launcher design optimization and
material optimization*.' In a
measure of the value the ESA places on our research, it gave €200,000 in
funding in 2010 to
enable the German software company Astos Solutions to develop the
Southampton co-designed
software tool further **[5.2]**, as part of the ESA's own General
Support Technology Programme
(GSTP). These GSTP activities, now in their fifth five-year cycle, are
designed `to ensure the right
technologies at the right maturity are available at the right time' **[5.C4]**
and to convert the best
concepts into mature products.

The success of the software tool inspired €480,000 in EU funding to
Southampton to adapt the tool
to meet design challenges in the avionics industry under the EUP FP7
project *AWACS — Adaption
of WORHP to Avionics Constraints*, coordinated by Thales, the world's
third-largest avionics
service provider **[3.G3]**. AWACS is funded under the EU Clean Sky
Initiative, which aims to
develop technologies that will achieve a 75% reduction in CO_{2}
emissions per passenger kilometre,
a 90% reduction in nitrogen oxide emissions and a 65% reduction in
perceived aircraft noise.
These targets pose significant challenges for aircraft trajectory
optimisation and AWACs is one of
the first projects to attempt to develop a corresponding software solution
to optimise aircraft
trajectory.

**Sources to corroborate the impact **

**Contextual References:**

**5.C1** http://www.esa.int/About_Us/ESTEC/ESTEC
European Space Research and Technology
Centre

**5.C2** Governmental budgets for space activities in *The Space
Economy at a Glance* 2011,
OECD Publishing (2011)

**5.C3** The design features of the toolbox and GUI interface are
described in detail in ESA Study
Contract Report, 5001003472, `MCO-FGS Software Toolbox Manual'; ESA Study
Contract
Report, 5001003472, `MCO-FGS Architectural Design Document' and `ESA Study
Contract
Report, 5001003472, `Multicriteria Optimisation'.

**5.C4** http://www.esa.int/Our
Activities/Technology/About the General Support Technology Programme GST

**Sources to corroborate the impact:**

**5.1** Head of the Guidance, Navigation and Control Section, European
Space Agency (ESA) **[He
can confirm the increased efficiency saving resulting from the use of
the computational
toolbox]**

**5.2** http://www.worhp.de/content/history.
[**This specifically mentions University of
Southampton's involvement in the WORHP development].**