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机械结构可靠性分析时,常常会采用代理模型拟合隐式功能函数来解决计算量大的问题,但由于试验设计方案需要同时考虑代理模型的拟合精度和可靠度计算精度的问题。因此,为了能够充分使用较少的样本信息,最大化可靠度计算精度,本文充分发挥Kriging预测的随机特性,提出一种主动学习可靠度计算方法。首先,类似于优化问题中改善函数的选点方式,提出一种基于Kriging预测的学习函数,基于Monte Carlo法生成大量的候选样本点,找出学习函数最小值对应的样本点作为最佳取样点。其次,推导和提出了一种学习停止的条件,保证了Monte Carlo样本点预测符号的正确性且学习次数明显减小。最后,通过2个数值算例分析结果表明,该算法相比其他方法需要更少的样本数量,得到的可靠度计算精度更高,验证了本文算法的正确性和高效性。
In the reliability analysis of mechanical structure, the proxy model fitting implicit function is often used to solve the problem of large amount of calculation. However, the experimental design needs to consider both the fitting accuracy of the proxy model and the accuracy of reliability calculation. Therefore, in order to make full use of less sample information and to maximize the accuracy of reliability calculation, this paper gives full play to the random characteristics of Kriging prediction and proposes a method of active learning reliability calculation. First of all, similar to the method of selecting points for improving function in optimization, a learning function based on Kriging prediction is proposed. Based on Monte Carlo method, a large number of candidate samples are generated, and the sample points corresponding to the minimum of learning function are selected as the best sampling points . Secondly, a condition of learning stop is deduced and put forward, which guarantees the correctness of the prediction symbols of Monte Carlo sample points and the obvious decrease of learning times. Finally, the results of two numerical examples show that the proposed algorithm requires fewer samples than other methods, and the obtained reliability is more accurate, which verifies the correctness and efficiency of the proposed algorithm.