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G. Filippi and M. Vasile
when sizing the solar arrays on a spacecraft. The value of the quantity of interest
at system level, after margins are applied, is often called the Maximum Expected
value (ME). The difference between the ME and the Maximum Possible value (MP)
is generally considered to be a further margin that accounts for the unexpected
variation of all uncertain components [1–3]. These traditional methods, however,
lack an appropriate quantification of uncertainty. As a consequence, there can be an
overestimation or an underestimation of the effect of uncertainty which can lead to
either an increase in costs and development time or to the occurrence of undesirable
events. As it was recognised during the Columbia Accident Investigation Board
(CAIB) [4], the classic pattern that brings to failure, common to many other tragic
accidents [5], is the combination of production pressure, that pushes to reduce
the safety margins, and a fragmented problem solving that lacks a system level
understanding. Hence one can argue that there is the need to incorporate a proper
quantification of uncertainty within any systems engineering approach [6, 7].
In this direction, the research field based on the synergy of optimisation
algorithms and uncertainty quantification theories that is known as Optimisation
Under uncertainty (OUU) [8], Uncertainty-Based Design (UBD) [9], etc. is of
increasing importance and interest. In particular, it is used to quantify and optimise
different uncertainty measures: robustness, reliability and in the last years also
resilience. They have brought, respectively, to the approaches of Robust Design
Optimisation (RDO) [10], Reliability Based Design Optimisation (RBDO) [11] and
Resilience Based Design Optimisation (ReBDO) [12, 13]. Moreover, due to the
complexity of engineered systems [14, 15], a further important step is given by
the application of holistic system-level view and multidisciplinary principles within
UBD. Uncertainty-Based Multidisciplinary Design Optimisation (UMDO) theory
[16] covers for this research direction.
If one looks at the different types of uncertainty that a system can be subject
to, two macro-categories can be identified: aleatory uncertainty and epistemic
uncertainty [17]. Aleatory uncertainty is natural randomness which cannot be
reduced. Epistemic uncertainty is due to the lack of information or incomplete data.
This type of uncertainty is reducible by acquiring more knowledge on the problem.
This chapter introduces a methodology to account for epistemic uncertainty in
the design for robustness of complex engineering systems. The concept proposed
in this chapter is called Evidence-Based Robust Optimisation (EBRO). In EBRO,
epistemic uncertainty is modelled with Dempster–Shafer Theory of Evidence (DST)
[18, 19]. DST offers a natural way to assign degrees of belief to the expected
performance of a system and to rigorously quantify the impact of epistemic
uncertainty on the associated quantities of interest. In EBRO the system design is
then optimised to maximise performance under epistemic uncertainty.
As generally recognised [16] most of the effort in UMDO community should
be spent in developing complexity-reduction methods to be applied within the
optimisation strategies. This is particularly true when non-probabilistic uncertainty
theories, for example, DST, are adopted. Some approaches for the reduction of
computational complexity of UQ with DST can be found in [20–22]. Recent
approaches of UMDO with the use of DST have been proposed in [23–25]. In
G. Filippi and M. Vasile
when sizing the solar arrays on a spacecraft. The value of the quantity of interest
at system level, after margins are applied, is often called the Maximum Expected
value (ME). The difference between the ME and the Maximum Possible value (MP)
is generally considered to be a further margin that accounts for the unexpected
variation of all uncertain components [1–3]. These traditional methods, however,
lack an appropriate quantification of uncertainty. As a consequence, there can be an
overestimation or an underestimation of the effect of uncertainty which can lead to
either an increase in costs and development time or to the occurrence of undesirable
events. As it was recognised during the Columbia Accident Investigation Board
(CAIB) [4], the classic pattern that brings to failure, common to many other tragic
accidents [5], is the combination of production pressure, that pushes to reduce
the safety margins, and a fragmented problem solving that lacks a system level
understanding. Hence one can argue that there is the need to incorporate a proper
quantification of uncertainty within any systems engineering approach [6, 7].
In this direction, the research field based on the synergy of optimisation
algorithms and uncertainty quantification theories that is known as Optimisation
Under uncertainty (OUU) [8], Uncertainty-Based Design (UBD) [9], etc. is of
increasing importance and interest. In particular, it is used to quantify and optimise
different uncertainty measures: robustness, reliability and in the last years also
resilience. They have brought, respectively, to the approaches of Robust Design
Optimisation (RDO) [10], Reliability Based Design Optimisation (RBDO) [11] and
Resilience Based Design Optimisation (ReBDO) [12, 13]. Moreover, due to the
complexity of engineered systems [14, 15], a further important step is given by
the application of holistic system-level view and multidisciplinary principles within
UBD. Uncertainty-Based Multidisciplinary Design Optimisation (UMDO) theory
[16] covers for this research direction.
If one looks at the different types of uncertainty that a system can be subject
to, two macro-categories can be identified: aleatory uncertainty and epistemic
uncertainty [17]. Aleatory uncertainty is natural randomness which cannot be
reduced. Epistemic uncertainty is due to the lack of information or incomplete data.
This type of uncertainty is reducible by acquiring more knowledge on the problem.
This chapter introduces a methodology to account for epistemic uncertainty in
the design for robustness of complex engineering systems. The concept proposed
in this chapter is called Evidence-Based Robust Optimisation (EBRO). In EBRO,
epistemic uncertainty is modelled with Dempster–Shafer Theory of Evidence (DST)
[18, 19]. DST offers a natural way to assign degrees of belief to the expected
performance of a system and to rigorously quantify the impact of epistemic
uncertainty on the associated quantities of interest. In EBRO the system design is
then optimised to maximise performance under epistemic uncertainty.
As generally recognised [16] most of the effort in UMDO community should
be spent in developing complexity-reduction methods to be applied within the
optimisation strategies. This is particularly true when non-probabilistic uncertainty
theories, for example, DST, are adopted. Some approaches for the reduction of
computational complexity of UQ with DST can be found in [20–22]. Recent
approaches of UMDO with the use of DST have been proposed in [23–25]. In