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Structural and Multidisciplinary Optimization

, Volume 57, Issue 4, pp 1495–1505 | Cite as

Optimization-based inverse analysis for membership function identification in fuzzy steady-state heat transfer problem

  • Chong Wang
  • Hermann G. Matthies
  • Zhiping Qiu
RESEARCH PAPER

Abstract

Based on the optimization design technology and fuzzy uncertainty theory, this paper proposes a novel inverse analysis method for membership function identification in steady-state heat transfer problem with fuzzy modeling parameters. The system subjective uncertainties associated with expert opinions are quantified as fuzzy parameters, which can be converted into interval variables by level-cut strategy. By means of the errors between measured and calculated temperature data, the parameter identification process is executed as a nested-loop optimization model. To avoid the considerable computational cost caused by nested-loop, an interval vertex method is presented to replace the inner-loop for predicting the temperature response bounds. The eventual membership functions of input fuzzy parameters are constructed by using the fuzzy decomposition theorem. Comparing results with traditional Monte Carlo method, a numerical example about 3D air cooling system is provided to verify the feasibility of proposed method for fuzzy parameter identification in engineering.

Keywords

Membership function identification Steady-state heat transfer problem Fuzzy uncertain parameters Nested-loop optimization model Interval vertex method 

Notes

Acknowledgements

This work was supported by the Alexander von Humboldt Foundation, 111 Project (No. B07009), and National Natural Science Foundation of PR China (No.11432002).

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of Scientific ComputingTechnische Universität BraunschweigBraunschweigGermany
  2. 2.Institute of Solid MechanicsBeihang UniversityBeijingPeople’s Republic of China

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