TY - JOUR

T1 - Efficient and user-friendly α-level optimisation for application-orientated fuzzy structural analyses

AU - Hübler, Clemens

AU - Hofmeister, Benedikt

N1 - Funding Information: We gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SFB-1463 – 434502799 and ENERGIZE – 436547100.

PY - 2021/11/15

Y1 - 2021/11/15

N2 - Inputs to many real-world engineering problems feature epistemic uncertainty. This type of uncertainty is frequently modelled by fuzzy values. Although fuzzy structural analyses have generally been state of the art for more than ten years, in many application-orientated research fields and in industry, they are less frequently conducted compared to deterministic or probabilistic analyses. There are at least two reasons for this fact. First, if fuzzy values are discretised by more than just a few α-levels, the corresponding fuzzy structural analyses can become computationally quite demanding. For each α-level, two optimisations have to be conducted. If the objective spaces of these optimisations are non-linear with several local extreme values, global optimisation methods are required for α-level optimisations. A second reason is the limited user friendliness. In most cases, global optimisation methods require comprehensive expert knowledge, for example, to set various optimisation parameters. Hence, in this work, a new efficient and user-friendly optimisation approach explicitly designed for α-level optimisations is proposed — the “Global Pattern Search for α-level optimisations” (αGPS). Its deterministic sample generation, which allows a reuse of many samples within the various α-level optimisations, makes the approach highly efficient. Moreover, information gained within an α-level optimisation can be used for all subsequent optimisations. Furthermore, αGPS has only a single parameter that controls the sample generation. This makes αGPS not only simple to apply, but also quite robust. αGPS is tested for a mathematical test function and engineering examples. It outperforms state-of-the-art algorithms with respect to efficiency and robustness. Therefore, it might motivate more researchers to consider fuzzy structural analyses in their application-orientated research fields.

AB - Inputs to many real-world engineering problems feature epistemic uncertainty. This type of uncertainty is frequently modelled by fuzzy values. Although fuzzy structural analyses have generally been state of the art for more than ten years, in many application-orientated research fields and in industry, they are less frequently conducted compared to deterministic or probabilistic analyses. There are at least two reasons for this fact. First, if fuzzy values are discretised by more than just a few α-levels, the corresponding fuzzy structural analyses can become computationally quite demanding. For each α-level, two optimisations have to be conducted. If the objective spaces of these optimisations are non-linear with several local extreme values, global optimisation methods are required for α-level optimisations. A second reason is the limited user friendliness. In most cases, global optimisation methods require comprehensive expert knowledge, for example, to set various optimisation parameters. Hence, in this work, a new efficient and user-friendly optimisation approach explicitly designed for α-level optimisations is proposed — the “Global Pattern Search for α-level optimisations” (αGPS). Its deterministic sample generation, which allows a reuse of many samples within the various α-level optimisations, makes the approach highly efficient. Moreover, information gained within an α-level optimisation can be used for all subsequent optimisations. Furthermore, αGPS has only a single parameter that controls the sample generation. This makes αGPS not only simple to apply, but also quite robust. αGPS is tested for a mathematical test function and engineering examples. It outperforms state-of-the-art algorithms with respect to efficiency and robustness. Therefore, it might motivate more researchers to consider fuzzy structural analyses in their application-orientated research fields.

KW - Fuzzy methods

KW - Fuzzy structural analysis

KW - Global optimisation

KW - Uncertainty

KW - Uncertainty quantification

KW - α-level optimisation

UR - http://www.scopus.com/inward/record.url?scp=85114952808&partnerID=8YFLogxK

U2 - 10.1016/j.engstruct.2021.113172

DO - 10.1016/j.engstruct.2021.113172

M3 - Article

VL - 247

JO - Engineering structures

JF - Engineering structures

SN - 0141-0296

M1 - 113172

ER -