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


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.


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



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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