Applying the Hopfield Neural Network to the Solution of the Temperature Distribution Field in Heat Conduction Problems

REFERENCES

• M. N. Özisik and H. R. B. Orlande , Inverse Heat Transfer, , 2nd ed. , pp. 1 – 59 , Taylor & Francis , New York , 2000 .
   Google Scholar
• J. V. Beck , B. Blackwell , and C. R. St. Clair , Inverse Heat Conduction Ill-posed Problems , pp. 1 – 3 , Wiley , New York , 1985 .
   Google Scholar
• M. M. Gupta , L. Jin , and N. Homma , Static and Dynamic Neural Networks , pp. 345 – 354 , Wiley , New York , 2003 .
   Google Scholar
• J. J. Hopfield , Neurons with Graded Response have Collective Computational Properties Like Those of Two-State Neurons , Proc. Natl. Acad. Science USA , vol. 81 , pp. 3088 – 3092 , 1984 . [CSA]
   PubMed Web of Science ®Google Scholar
• J. J. Hopfield and D. W. Tank , Computing with Neural Circuits: A Model , Science , vol. 233 , pp. 625 – 633 , 1986 . [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• T. Uchiyama and N. Sonehara , Solving Inverse Problems in Nonlinear PDEs by Recurrent Neural Networks , Neural Networks, IEEE Int. Conf. , vol. 1 , pp. 99 – 102 , 1993 . [CSA]
   Google Scholar
• H. Yamashita , N. Kowata , V. Cingoski , and K. Kaneda , Direct Solution Method for Finite Element Analysis Using Hopfield Neural Network , Magnetics, IEEE Trans. , vol. 31 , pp. 1964 – 1967 , 1995 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• G. Fei , Z. Peng , W. Fang , M. Xikni , and Q. Guanyuan , Finite Element Analysis Based Hopfield Neural Network Model for Solving Nonlinear Electromagnetic Field Problems , Neural Networks, Int. Joint Conf. , vol. 6 , pp. 4399 – 4403 , 1999 . [CSA]
   Google Scholar
• P. C. Tuan , C. C. Ji , L.W. Fong , and W. T. Huang , Application of Kalman Filtering with Input Estimation Technique to On-line Cylindrical Inverse Heat Conduction Problems, Int. J. Jpn. Soc. Mech. Eng. Ser. B , vol. 40, pp. 126–133, 1997. [CSA]
   Google Scholar
• P. C. Tuan , C. C. Ji , L.W. Fong , and W. T. Huang , An Input Estimation Approach to On-line Two-Dimensional Inverse Heat Conduction Problems , Numer. Heat Transfer B , vol. 29 , pp. 345 – 363 , 1996 . [CSA]
   Web of Science ®Google Scholar
• E. Kreyszig , Advanced Engineering Mathematics, , 7th ed. , pp. 648 – 649 , Wiley , New York , 1993 .
   Google Scholar
• J. V. Beck , B. Blackwell , and C. R. St. Clair , Inverse Heat Conduction Ill-posed Problems , pp. 169 – 171 , Wiley , New York , 1985 .
   Google Scholar
• H. S. Carslaw and J. C. Jaeger , Conduction of Heat in Solids, , 2nd ed. , pp. 203 , 328 – 329 , Oxford University Press , New York , 1959 .
   Google Scholar
• J. V. Beck , B. Blackwell , and C. R. St. Clair , Inverse Heat Conduction Ill-posed Problems , pp. 17 – 18 , Wiley , New York , 1985 .
   Google Scholar
• J. B. Gao , J. Z. Zhang , and M. Q. Xu , Measuring One Dimensional Temperature Field of Rotor Using Hopfield Neural Network , Thermal Turbine , vol. 32 , pp. 78 – 81 , 2003 . [CSA]
   Google Scholar