Reliability based optimisation of engineering structures under imprecise information

In many engineering applications, probability theory has been employed in a multidisciplinary design optimisation procedure to address uncertainty in a structural system. However, in a general situation where some uncertain variables are not random or where complete information about their randomness is unavailable, probability theory may be inappropriate to describe the propagation of uncertainty. In this work, the Dempster-Shafer (DS) theory, also called the evidence theory, is proposed to handle this general situation as an alternative to the classical probability theory for the mathematical representation of uncertainty. Evidence theory allows us to express partial beliefs when it is impossible or impractical to assess the complete probability distribution confidently. DS theory is applied to a reliability-based optimisation problem in a general situation with imprecise information for an aircraft wing preliminary design example.