基于BP神经网络-Monte Carlo法的结构可靠性分析

  目的  船舶结构极限承载能力不足会导致海损事故，为此提出改进AK-MCS法，用于船舶结构极限强度可靠性研究。  方法  通过引入信息熵中的学习函数H对样本点进行二次寻优，以提高最佳样本点的质量，从而提高Kriging模型的精度和更新效率；采用K折交叉验证替代AK-MCS法的迭代停止准则，解决原本迭代停止准则过于保守的问题，以有效避免发生过学习和欠学习状态，从而以较少的样本点训练Kriging模型，实现对极限状态函数的高度拟合。使用非线性振荡器数学模型进行验证，并将改进AK-MCS法应用于船舶板架的极限强度可靠性研究。  结果  仿真结果表明，改进AK-MCS法调用有限元模型的次数比原方法减少了38%，验证了改进AK-MCS法的求解效率和精度。应用结果表明，该方法的计算精度最高，且调用有限元仿真次数比原方法减少32%，验证了改进AK-MCS法在船舶板架极限强度可靠性研究中的适用性和高效性。  结论  使用改进AK-MCS法研究船舶板架极限强度的可靠性，可评估船舶实际航行中局部结构尤其局部较危险结构的失效概率。

A new efficient simulation method to approximate the probability of failure and most probable point

  Objectives  In view of the frequent occurrence of marine accidents caused by low ultimate bearing capacity of ships. To this end, the improved AK-MCS method is proposed for the research of the ultimate strength reliability of ship structures.  Methods  The information entropy function H was introduced to perform secondary optimization on the sample points to improve the quality of the best sample points, so as to improve the accuracy and update efficiency of the Kriging model; and then the iterative stop criterion of AK-MCS was replaced by K-fold cross validation, so as to avoid over-learning and under-learning situation, thus the Kriging model is trained with fewer sample points to achieve a high degree of fitness to the limit state function. The nonlinear oscillator mathematical model is used to verify the results. The improved AK-MCS method is applied to the ultimate strength reliability study of shipboard frame.  Results  The results show that the number of calls to the finite element calculation in the improved AK-MCS method is reduced by 38% compared with the original method, and the efficiency and accuracy of the improved AK-MCS method are verified. The application results show that The calculation accuracy of this method is the highest, and the number of calls to finite element calculation is reduced by 32% compared with the original method. This verifies the applicability and efficiency of the improved AK-MCS method in the study of the ultimate strength reliability of ship plates.  Conclusions  The improved AK-MCS method is used to research the ultimate strength reliability of ship plates and evaluate the failure probability of local structures, especially dangerous structures during actual navigation.