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| Chaos control of performance measure approach for evaluation of probabilistic constraints |
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| DOI：10.7511/jslx20085123 |
| KeyWord:probabilistic design,performance measure approach,AMV iterative procedure,convergent failure,chaotic dynamics,stability transformation method |
| YANG Di-xiong YI Ping |
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| Abstract: |
| Performance measure approach(PMA) is a recently proposed method for evaluation of probabilistic constraints in reliability based design optimization.The advanced mean-value(AMV) method is well suitable for PMA due to its simplicity and efficiency.However,when the AMV iterative scheme is applied to search for the minimum performance target point for some nonlinear performance functions,the iterative sequences could fall into the periodic oscillation and even chaotic state.The convergence control of AMV procedure of PMA is implemented by the stability transformation method of chaos feedback control in the present paper.Firstly,it is illustrated that using the AMV iterative scheme the iterative solution generates the phenomenon of periodic oscillation and chaos for some performance functions.And the chaotic dynamics analysis on this iterative procedure is performed.Then,the stability transformation method is employed for the chaos control of solution in the parameter interval in which the iterative scheme of AMV fails.The numerical results demonstrate that the control of periodic oscillation,bifurcation and chaos for AMV iterative procedure is achieved,and the expected stable convergent solutions are obtained. |
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