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G. Filippi and M. Vasile
Furthermore, a lack of measurements is in itself an epistemic uncertainty. When
this uncertainty is aleatory, it is probably the easiest to understand and model, if
enough data are available on the exact repeatability of measurements.
• Geometric uncertainty is a form of aleatory uncertainty on the exact repeatability
of the manufacturing of parts and systems.
• Parameter uncertainty can be either aleatory or epistemic and refers to the
variability of model parameters and boundary conditions.
• Numerical (or algorithmic) uncertainty, also known as numerical errors, refers
to different types of uncertainty related to each particular numerical scheme, and
to the machine precision (including clock drifts).
• Human uncertainty is difficult to capture as it has both aleatory and epistemic
elements and is dependent on our conscious and unconscious decisions and
reactions. It includes the possible variability of goals and requirements due to
human decisions.
Uncertainty can be associated to the purpose for which the system is created
(uncertainty in the requirements and objectives), in its operations and functionalities, in the phase of its development or in its temporal evolution. Finally, it is
important to distinguish between uncertainty affecting functional and physical constraints, and thus defining the feasibility or reliability of a system, and uncertainty
affecting the cost or objective function that quantifies the performance of a system.
This latter uncertainty defines the robustness of a system. In the following we will
consider more specifically epistemic uncertainty in cost function and constraints.
17.1.2 From Design by Analysis to Robust Design Optimisation
In the classical approach to engineering design, Design by Formula, the active
work of engineers was required throughout the whole design process. In the more
recent Design by Analysis [26] approach, the development of software analysis
tools (numerical methods) shortened the design process and enabled a better
understanding of the problem without the use of expensive experimental analyses.
The design and associated decision-making process were still performed by engineers, but the analysis of different configurations was automatised by numerical
procedures. A further advancement was introduced with Design by Optimisation
[27], where numerical optimisation tools were coupled with numerical simulations
to automatically identify globally, or locally, optimal design solutions. Finally, in
the last two decades an increasing attention has been devoted to tackle optimisation
under uncertainty. Design for Reliability and Robustness [10, 11, 28–31] is radically
changing systems engineering, making designers and decision makers able to handle
higher degrees of complexity.
Design for robustness means to look for a solution for which the value of the
objective function/s (or performance index/es) is optimal under uncertainty while
design for reliability means to look for a solution that increases the probability of
G. Filippi and M. Vasile
Furthermore, a lack of measurements is in itself an epistemic uncertainty. When
this uncertainty is aleatory, it is probably the easiest to understand and model, if
enough data are available on the exact repeatability of measurements.
• Geometric uncertainty is a form of aleatory uncertainty on the exact repeatability
of the manufacturing of parts and systems.
• Parameter uncertainty can be either aleatory or epistemic and refers to the
variability of model parameters and boundary conditions.
• Numerical (or algorithmic) uncertainty, also known as numerical errors, refers
to different types of uncertainty related to each particular numerical scheme, and
to the machine precision (including clock drifts).
• Human uncertainty is difficult to capture as it has both aleatory and epistemic
elements and is dependent on our conscious and unconscious decisions and
reactions. It includes the possible variability of goals and requirements due to
human decisions.
Uncertainty can be associated to the purpose for which the system is created
(uncertainty in the requirements and objectives), in its operations and functionalities, in the phase of its development or in its temporal evolution. Finally, it is
important to distinguish between uncertainty affecting functional and physical constraints, and thus defining the feasibility or reliability of a system, and uncertainty
affecting the cost or objective function that quantifies the performance of a system.
This latter uncertainty defines the robustness of a system. In the following we will
consider more specifically epistemic uncertainty in cost function and constraints.
17.1.2 From Design by Analysis to Robust Design Optimisation
In the classical approach to engineering design, Design by Formula, the active
work of engineers was required throughout the whole design process. In the more
recent Design by Analysis [26] approach, the development of software analysis
tools (numerical methods) shortened the design process and enabled a better
understanding of the problem without the use of expensive experimental analyses.
The design and associated decision-making process were still performed by engineers, but the analysis of different configurations was automatised by numerical
procedures. A further advancement was introduced with Design by Optimisation
[27], where numerical optimisation tools were coupled with numerical simulations
to automatically identify globally, or locally, optimal design solutions. Finally, in
the last two decades an increasing attention has been devoted to tackle optimisation
under uncertainty. Design for Reliability and Robustness [10, 11, 28–31] is radically
changing systems engineering, making designers and decision makers able to handle
higher degrees of complexity.
Design for robustness means to look for a solution for which the value of the
objective function/s (or performance index/es) is optimal under uncertainty while
design for reliability means to look for a solution that increases the probability of