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The gradient projection algorithm with adaptive mutation step length for non-probabilistic reliability index

机译：非概率可靠性指标的自适应变异步长梯度投影算法

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摘要

Aiming at the problems of selection parameter step-size and premature convergence that occurred when searching the local area in the optimal design of adaptive gradient projection algorithm in this paper, adaptive variable step-size mechanism strategy and adaptive variable step-size mechanism were established. They were introduced into the gradient projection algorithm, and were used to control iteration step length. Through the examples of non-probabilistic reliability index, it can be showed that the method could quickly and accurately calculate the reliability index when the model had multiple variables and complex limit state function. To compare and contrast this algorithm with the simple gradient projection algorithm, this algorithm is not sensitive to the initial point position. And it not only takes into account both local performance and global search ability, but also has fast convergence speed and high precision. So it is an efficient and practical optimization algorithm.
机译：针对本文在自适应梯度投影算法的优化设计中寻找局部区域时选择参数步长和收敛过早的问题，建立了自适应变量步长机制策略和自适应变量步长机制。将它们引入梯度投影算法中，并用于控制迭代步长。通过非概率可靠性指标的实例可以看出，当模型具有多个变量和复杂的极限状态函数时，该方法可以快速，准确地计算出可靠性指标。为了将该算法与简单的梯度投影算法进行比较和对比，该算法对初始点位置不敏感。它不仅兼顾了局部性能和全局搜索能力，而且收敛速度快，精度高。因此，它是一种高效实用的优化算法。

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