Polymorphic uncertain nonlinear programming model and algorithm for maximizing the fatigue life of V-belt drive

Shaojun Zhang; Zhong Wan

doi:10.3934/jimo.2012.8.493

Article Contents

2012, Volume 8, Issue 2: 493-505. Doi: 10.3934/jimo.2012.8.493

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Polymorphic uncertain nonlinear programming model and algorithm for maximizing the fatigue life of V-belt drive

Shaojun Zhang^1, and
Zhong Wan^2,

1.
School of Mathematical Sciences and Computing Technology, Central South University, Hunan Changsha, 410083
2.
School of Mathematics Sciences and Computing Technology, Central South University, Hunan Changsha, 410083

Received: January 31, 2011

Revised: November 30, 2011

Published: March 2012

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Abstract

In this paper, a polymorphic uncertain nonlinear programming (PUNP) model is constructed to formulate the problem of maximizing the V-belt's fatigue life according to the practical engineering design conditions. The model is converted into an equivalent interval programming only involved with interval parameters for any given degree of membership and confidence level. Then, a deterministic equivalent formulation (DEF) for the original model is obtained based on the concept of possibility degree for the order of two interval numbers. An algorithm, called sampling based algorithm, is developed to find a robust optimal design scheme for maximizing the fatigue life of the V-belt. Case study is employed to demonstrate the validity and the practicability of the constructed model and the algorithm.

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Mathematics Subject Classification: Primary: 90B50, 90C15; Secondary: 60K10.

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