tailieunhanh - Lifetime-Oriented Structural Design Concepts- P21

Lifetime-Oriented Structural Design Concepts- P21: At the beginning of 1996, the Cooperative Research Center SFB 398 financially supported by the German Science Foundation (DFG) was started at Ruhr-University Bochum (RUB). A scientists group representing the fields of structural engineering, structural mechanics, soil mechanics, material science, and numerical mathematics introduced a research program on “lifetimeoriented design concepts on the basis of damage and deterioration aspects”. | 558 4 Methodological Implementation 1 XPc J3X P Rdj Q j 1 Correspondingly the recombination pattern has to be repeatedly used on all q parent vectors until the set Sg containing the individuals XaC a 1 2 3 . q is determined. The mutation mechanisms in the y o. A -ES is the heart of the strategy and the most vigorous optimization force. At this a specific strength is the property that besides the original optimization design variables also the step lengthes during the iteration of the optimization are becoming part of the continuous adjustment and adaptation of variables towards optimal quantities. In the most general case the population-based model allows for an adaptive adjustment of the step lengthes of each corresponding optimization design variable called anisotropic mutative step length control . This necessitates to expand the original optimization vector x by the step lengths or strategy parameters concentrated in the vector A leading to the new vector X A X X1 X2 . . . Xn 1 2 . . . Sn where the components 5 i 1 2 3 . n are the step lengths associated to the variables x i 1 2 3 . n. The mutation schema to create new child vectors from parent vectors takes the following form if the i-th optimization variable of all A child vectors in the set Sg are contemplated exclusively Xgc1 Xîp r1 Sip Ri 1 t N 0 1 xgc2 XP R2 . N 0 1 . . . XioA XiP RA R. --x N 0 1 Of course these instructions of generations have to be carried out for all indices i i 1 2 3 . . . n. The following explanations clarify the effects of the equations above. Parent variables are the originators of the generation where at the parent individuals are again randomly drawn from the set Sp according to Optimization and Design 559 Rj random_of 1 2 3 . a j 1 2 3 . X X . The increments added to the parent components are also random quantities. According to the nature of a mutation they are mainly driven by Gauss-distributed values large changes are rare small changes are more .

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