Abstract

In this paper, an improved automatic step-size procedure in forward-difference approximation for reliability analysis and optimization design is proposed. Traditionally, the step-size is pre-selected and does not change during optimization / reliability design process. This fixed step-size procedure may provide “poor” derivative approximations for highly nonlinear problems or the problems having insufficient digits of the outputs. The proposed method computes the optimum step size for each design variable by minimizing the truncation and condition errors. The condition error is focused on the error caused by insufficient digits of the outputs in this paper. Several numerical problems are tested to demonstrate the proposed procedure. The results comparison shows that the proposed procedure provides more accurate gradients for optimization and reliability design.

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