An advanced solution design for Heat Conduction Equation

Adaptive fuzzy approach

Yung-Yu Chen, Shyang Jye Chang

Research output: Contribution to journalArticle

Abstract

A new technique using an adaptive fuzzy algorithm to obtain the solution of "Heat Conduction Equation" (HCE) is presented. The design objective is to find one fuzzy solution to satisfy precisely the "Heat Conduction Equation" encountered in practical application and the initial/boundary conditions. According to the concept of fuzzy logic systems, a rough fuzzy solution with adjustable parameters for the "Heat Conduction Equation" is first described. Then, a set of adaptive laws for tuning the free parameters in the consequent part is derived from minimizing an appropriate error function. In addition, an elegant approximated error bound between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors has also been proven. Furthermore, the error equations in mesh points are also proven to converge to zero for the "Heat Conduction Equation" with one sufficient condition. As the above mentions, our design objective is to treat the solution finding problem of the "Heat Conduction Equation" with a really new fuzzy approach concept.

Original languageEnglish
Pages (from-to)863-867
Number of pages5
JournalAdvanced Science Letters
Volume8
DOIs
Publication statusPublished - 2012 Aug 2

Fingerprint

Heat Conduction Equation
Heat conduction
heat
Hot Temperature
Fuzzy Logic System
Fuzzy Logic
Fuzzy Algorithm
Error function
logic
Fuzzy Rules
Adaptive Algorithm
Error Bounds
fuzzy mathematics
Rough
Fuzzy rules
Tuning
Exact Solution
Fuzzy logic
Design
Mesh

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Health(social science)
  • Mathematics(all)
  • Education
  • Environmental Science(all)
  • Engineering(all)
  • Energy(all)

Cite this

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abstract = "A new technique using an adaptive fuzzy algorithm to obtain the solution of {"}Heat Conduction Equation{"} (HCE) is presented. The design objective is to find one fuzzy solution to satisfy precisely the {"}Heat Conduction Equation{"} encountered in practical application and the initial/boundary conditions. According to the concept of fuzzy logic systems, a rough fuzzy solution with adjustable parameters for the {"}Heat Conduction Equation{"} is first described. Then, a set of adaptive laws for tuning the free parameters in the consequent part is derived from minimizing an appropriate error function. In addition, an elegant approximated error bound between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors has also been proven. Furthermore, the error equations in mesh points are also proven to converge to zero for the {"}Heat Conduction Equation{"} with one sufficient condition. As the above mentions, our design objective is to treat the solution finding problem of the {"}Heat Conduction Equation{"} with a really new fuzzy approach concept.",
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An advanced solution design for Heat Conduction Equation : Adaptive fuzzy approach. / Chen, Yung-Yu; Chang, Shyang Jye.

In: Advanced Science Letters, Vol. 8, 02.08.2012, p. 863-867.

Research output: Contribution to journalArticle

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