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Published in: Structural and Multidisciplinary Optimization 4/2018

05-10-2017 | RESEARCH PAPER

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

Authors: Chong Wang, Hermann G. Matthies, Zhiping Qiu

Published in: Structural and Multidisciplinary Optimization | Issue 4/2018

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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.

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Appendix
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Literature
go back to reference Abonyi J (2003) Fuzzy Model Identification for Control. Springer Science Business Media, New YorkCrossRefMATH Abonyi J (2003) Fuzzy Model Identification for Control. Springer Science Business Media, New YorkCrossRefMATH
go back to reference Agarwal H, Mozumder CK, Renaud JE, Watson LT (2007) An inverse-measure-based unilevel architecture for reliability-based design optimization. Struct Multidiscip O 33(3):217–227CrossRef Agarwal H, Mozumder CK, Renaud JE, Watson LT (2007) An inverse-measure-based unilevel architecture for reliability-based design optimization. Struct Multidiscip O 33(3):217–227CrossRef
go back to reference Akkaram S, Beeson D, Agarwal H, Wiggs G (2007) Inverse modeling technology for parameter estimation. Struct Multidiscip O 34(2):151–164CrossRef Akkaram S, Beeson D, Agarwal H, Wiggs G (2007) Inverse modeling technology for parameter estimation. Struct Multidiscip O 34(2):151–164CrossRef
go back to reference Ben-Haim Y, Elishakoff I (2013) Convex Models of Uncertainty in Applied Mechanics. Elsevier Science, AmsterdamMATH Ben-Haim Y, Elishakoff I (2013) Convex Models of Uncertainty in Applied Mechanics. Elsevier Science, AmsterdamMATH
go back to reference Bilal M, Hussain A, Jaffar MA, Choi T, Mirza AM (2014) Estimation and optimization based ill-posed inverse restoration using fuzzy logic. Multimed Tools Appl 69(3):1067–1087CrossRef Bilal M, Hussain A, Jaffar MA, Choi T, Mirza AM (2014) Estimation and optimization based ill-posed inverse restoration using fuzzy logic. Multimed Tools Appl 69(3):1067–1087CrossRef
go back to reference Blackwell B, Beck JV (2010) A technique for uncertainty analysis for inverse heat conduction problems. Int J Heat Mass Tran 53(4):753–759CrossRefMATH Blackwell B, Beck JV (2010) A technique for uncertainty analysis for inverse heat conduction problems. Int J Heat Mass Tran 53(4):753–759CrossRefMATH
go back to reference Capasso V, Engl HW, Kindermann S (2008) Parameter identification in a random environment exemplified by a multiscale model for crystal growth. Multiscale Model Sim 7(2):814–841MathSciNetCrossRefMATH Capasso V, Engl HW, Kindermann S (2008) Parameter identification in a random environment exemplified by a multiscale model for crystal growth. Multiscale Model Sim 7(2):814–841MathSciNetCrossRefMATH
go back to reference Carrera J, Alcolea A, Medina A, Hidalgo J, Slooten LJ (2005) Inverse problem in hydrogeology. Hydrogeol J 13(1):206–222CrossRef Carrera J, Alcolea A, Medina A, Hidalgo J, Slooten LJ (2005) Inverse problem in hydrogeology. Hydrogeol J 13(1):206–222CrossRef
go back to reference Choi CK, Yoo HH (2016) Stochastic inverse method to identify parameter random fields in a structure. Struct Multidiscip O 54(6):1557–1571MathSciNetCrossRef Choi CK, Yoo HH (2016) Stochastic inverse method to identify parameter random fields in a structure. Struct Multidiscip O 54(6):1557–1571MathSciNetCrossRef
go back to reference Fletcher R (2013) Practical Methods of Optimization. John Wiley & Sons, New YorkMATH Fletcher R (2013) Practical Methods of Optimization. John Wiley & Sons, New YorkMATH
go back to reference Fujimoto RM (2000) Parallel and Distributed Simulation Systems. John Wiley & Sons, New York Fujimoto RM (2000) Parallel and Distributed Simulation Systems. John Wiley & Sons, New York
go back to reference Jiang C, Liu G, Han X (2008) A novel method for uncertainty inverse problems and application to material characterization of composites. Exp Mech 48(4):539–548CrossRef Jiang C, Liu G, Han X (2008) A novel method for uncertainty inverse problems and application to material characterization of composites. Exp Mech 48(4):539–548CrossRef
go back to reference Klimke A (2006) Uncertainty Modeling Using Fuzzy Arithmetic and Sparse Grids. Ph.D. Thesis, Universität Stuttgart, Shaker Verlag, Aachen Klimke A (2006) Uncertainty Modeling Using Fuzzy Arithmetic and Sparse Grids. Ph.D. Thesis, Universität Stuttgart, Shaker Verlag, Aachen
go back to reference Korycki R (2001) Two-dimensional shape identification for the unsteady conduction problem. Struct Multidiscip O 21(3):229–238CrossRef Korycki R (2001) Two-dimensional shape identification for the unsteady conduction problem. Struct Multidiscip O 21(3):229–238CrossRef
go back to reference Ku CJ, Cermak JE, Chou LS (2007) Random decrement based method for modal parameter identification of a dynamic system using acceleration responses. J Wind Eng Ind Aerod 95(6):389–410CrossRef Ku CJ, Cermak JE, Chou LS (2007) Random decrement based method for modal parameter identification of a dynamic system using acceleration responses. J Wind Eng Ind Aerod 95(6):389–410CrossRef
go back to reference Lai Y, Jiang X, Fang L (2012) Isight Optimization Theory and Examples. Beihang University Press, Beijing Lai Y, Jiang X, Fang L (2012) Isight Optimization Theory and Examples. Beihang University Press, Beijing
go back to reference Li S (2015) Engineering Fuzzy Mathematics with Applications. Harbin Institute of Technology Press, Harbin Li S (2015) Engineering Fuzzy Mathematics with Applications. Harbin Institute of Technology Press, Harbin
go back to reference Liu J, Sun X, Han X, Jiang C, Yu D (2015a) Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method. Mech Syst Signal Pr 56:35–54CrossRef Liu J, Sun X, Han X, Jiang C, Yu D (2015a) Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method. Mech Syst Signal Pr 56:35–54CrossRef
go back to reference Liu J, Sun X, Li K, Jiang C, Han X (2015b) A probability density function discretization and approximation method for the dynamic load identification of stochastic structures. J Sound Vib 357:74–94CrossRef Liu J, Sun X, Li K, Jiang C, Han X (2015b) A probability density function discretization and approximation method for the dynamic load identification of stochastic structures. J Sound Vib 357:74–94CrossRef
go back to reference Moens D, Hanss M (2011) Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics recent advances. Finite Elem Anal Des 47(1):4–16CrossRef Moens D, Hanss M (2011) Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics recent advances. Finite Elem Anal Des 47(1):4–16CrossRef
go back to reference Nayak S, Chakraverty S (2013) Non-probabilistic approach to investigate uncertain conjugate heat transfer in an imprecisely defined plate. Int J Heat Mass Tran 67:445–454CrossRef Nayak S, Chakraverty S (2013) Non-probabilistic approach to investigate uncertain conjugate heat transfer in an imprecisely defined plate. Int J Heat Mass Tran 67:445–454CrossRef
go back to reference Nicolai BM, Egea JA, Scheerlinck N, Banga JR, Datta AK (2011) Fuzzy finite element analysis of heat conduction problems with uncertain parameters. J Food Eng 103:38–46CrossRef Nicolai BM, Egea JA, Scheerlinck N, Banga JR, Datta AK (2011) Fuzzy finite element analysis of heat conduction problems with uncertain parameters. J Food Eng 103:38–46CrossRef
go back to reference Rice JA (1995) Mathematical Statistics and Data Analysis. Duxbury Press, BelmontMATH Rice JA (1995) Mathematical Statistics and Data Analysis. Duxbury Press, BelmontMATH
go back to reference Selimefendigil F, Öztop HF (2012) Fuzzy-based estimation of mixed convection heat transfer in a square cavity in the presence of an adiabatic inclined fin. Int Commun Heat Mass 39(10):1639–1646CrossRef Selimefendigil F, Öztop HF (2012) Fuzzy-based estimation of mixed convection heat transfer in a square cavity in the presence of an adiabatic inclined fin. Int Commun Heat Mass 39(10):1639–1646CrossRef
go back to reference Sepahvand K, Marburg S (2015) Non-sampling inverse stochastic numerical-experimental identification of random elastic material parameters in composite plates. Mech Syst Signal Pr 54:172–181CrossRef Sepahvand K, Marburg S (2015) Non-sampling inverse stochastic numerical-experimental identification of random elastic material parameters in composite plates. Mech Syst Signal Pr 54:172–181CrossRef
go back to reference Stavroulakis GE (2013) Inverse and Crack Identification Problems in Engineering Mechanics. Springer, Berlin Stavroulakis GE (2013) Inverse and Crack Identification Problems in Engineering Mechanics. Springer, Berlin
go back to reference Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132CrossRefMATH Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132CrossRefMATH
go back to reference Tao W (2001) Numerical Heat Transfer. Xi’an Jiaotong University Press, Xi’an Tao W (2001) Numerical Heat Transfer. Xi’an Jiaotong University Press, Xi’an
go back to reference Theodoridis D, Boutalis Y, Christodoulou M (2012) Dynamical recurrent neuro-fuzzy identification schemes employing switching parameter hopping. Int J Neural Syst 22(2):1250004CrossRef Theodoridis D, Boutalis Y, Christodoulou M (2012) Dynamical recurrent neuro-fuzzy identification schemes employing switching parameter hopping. Int J Neural Syst 22(2):1250004CrossRef
go back to reference Wang C, Qiu Z (2015a) Interval analysis of steady-state heat convection–diffusion problem with uncertain-but-bounded parameters. Int J Heat Mass Tran 91:355–362CrossRef Wang C, Qiu Z (2015a) Interval analysis of steady-state heat convection–diffusion problem with uncertain-but-bounded parameters. Int J Heat Mass Tran 91:355–362CrossRef
go back to reference Wang C, Qiu Z (2015b) Hybrid uncertain analysis for temperature field prediction with random, fuzzy and interval parameters. Int J Therm Sci 98:124–134CrossRef Wang C, Qiu Z (2015b) Hybrid uncertain analysis for temperature field prediction with random, fuzzy and interval parameters. Int J Therm Sci 98:124–134CrossRef
go back to reference Wang C, Qiu Z (2015c) Improved numerical prediction and reliability-based optimization of transient heat conduction problem with interval parameters. Struct Multidiscip Optim 51(1):113–123CrossRef Wang C, Qiu Z (2015c) Improved numerical prediction and reliability-based optimization of transient heat conduction problem with interval parameters. Struct Multidiscip Optim 51(1):113–123CrossRef
go back to reference Wang X, Yang C, Wang L, Yang H (2013) Membership-set identification method for structural damage based on measured natural frequencies and static displacements. Struct Health Monit 12(1):23–34CrossRef Wang X, Yang C, Wang L, Yang H (2013) Membership-set identification method for structural damage based on measured natural frequencies and static displacements. Struct Health Monit 12(1):23–34CrossRef
go back to reference Wang X, Xia Y, Zhou X, Yang C (2014) Structural damage measure index based on non-probabilistic reliability model. J Sound Vib 333(5):1344–1355CrossRef Wang X, Xia Y, Zhou X, Yang C (2014) Structural damage measure index based on non-probabilistic reliability model. J Sound Vib 333(5):1344–1355CrossRef
go back to reference Wang C, Qiu Z, Yang Y (2016a) Uncertainty propagation of heat conduction problem with multiple random inputs. Int J Heat Mass Tran 99:95–101CrossRef Wang C, Qiu Z, Yang Y (2016a) Uncertainty propagation of heat conduction problem with multiple random inputs. Int J Heat Mass Tran 99:95–101CrossRef
go back to reference Wang C, Qiu Z, Yang Y (2016b) Collocation methods for uncertain heat convection-diffusion problem with interval input parameters. Int J Therm Sci 107:230–236CrossRef Wang C, Qiu Z, Yang Y (2016b) Collocation methods for uncertain heat convection-diffusion problem with interval input parameters. Int J Therm Sci 107:230–236CrossRef
go back to reference Wang C, Qiu Z, Xu M (2017) Collocation methods for fuzzy uncertainty propagation in heat conduction problem. Int J Heat Mass Tran 107:631–639CrossRef Wang C, Qiu Z, Xu M (2017) Collocation methods for fuzzy uncertainty propagation in heat conduction problem. Int J Heat Mass Tran 107:631–639CrossRef
go back to reference Wendlandt WW (1974) Thermal Methods of Analysis. Wiley Interscience, New York Wendlandt WW (1974) Thermal Methods of Analysis. Wiley Interscience, New York
go back to reference Xia B, Yu D, Liu J (2013) Interval and subinterval perturbation methods for a structural-acoustic system with interval parameters. J Fluid Struct 38:146–163CrossRef Xia B, Yu D, Liu J (2013) Interval and subinterval perturbation methods for a structural-acoustic system with interval parameters. J Fluid Struct 38:146–163CrossRef
go back to reference Xue Y, Yang H (2013a) Interval estimation of convection-diffusion heat transfer problems. Numer Heat Tr B-Fund 64(3):263–273CrossRef Xue Y, Yang H (2013a) Interval estimation of convection-diffusion heat transfer problems. Numer Heat Tr B-Fund 64(3):263–273CrossRef
go back to reference Xue Y, Yang H (2013b) Interval identification of thermal parameters for convection-diffusion heat transfer problems. Asia-Pacific Congress for Computational Mechanics, Singapore Xue Y, Yang H (2013b) Interval identification of thermal parameters for convection-diffusion heat transfer problems. Asia-Pacific Congress for Computational Mechanics, Singapore
go back to reference Yilmaz S, Oysal Y (2010) Fuzzy wavelet neural network models for prediction and identification of dynamical systems. IEEE T Neural Network 21(10):1599–1609CrossRef Yilmaz S, Oysal Y (2010) Fuzzy wavelet neural network models for prediction and identification of dynamical systems. IEEE T Neural Network 21(10):1599–1609CrossRef
go back to reference Zhang W, Liu J, Cho C, Han X (2015) A hybrid parameter identification method based on Bayesian approach and interval analysis for uncertain structures. Mech Syst Signal Pr 60:853–865CrossRef Zhang W, Liu J, Cho C, Han X (2015) A hybrid parameter identification method based on Bayesian approach and interval analysis for uncertain structures. Mech Syst Signal Pr 60:853–865CrossRef
Metadata
Title
Optimization-based inverse analysis for membership function identification in fuzzy steady-state heat transfer problem
Authors
Chong Wang
Hermann G. Matthies
Zhiping Qiu
Publication date
05-10-2017
Publisher
Springer Berlin Heidelberg
Published in
Structural and Multidisciplinary Optimization / Issue 4/2018
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-017-1821-2

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