基于改进合成少数类过采样技术的非概率可靠性指标解
Solution to non-probabilistic reliability indices based on improved synthetic minority oversampling technique
张梦 1陈旭勇 1彭元林 1李书雅1
作者信息
- 1. 武汉工程大学土木工程与建筑学院,湖北 武汉 430074
- 折叠
摘要
当结构的功能函数呈现高度非线性、极限状态曲面为多区域的情形时,现有算法无法有效求解非概率可靠性指标,为解决此类问题,将合成少数类过采样技术(SMOTE)进行改进,提出了基于改进SMOTE算法的非概率可靠性指标解法.首先基于非概率可靠性指标的几何意义,将样本分类策略、超球限制策略与标准SMOTE算法相结合,提出了改进SMOTE算法来进一步提升算法在极限状态曲面附近的采样效率;然后结合改进SMOTE算法在标准化空间中高精度的拟合局部极限状态曲面,进而搜索得到非概率可靠性指标;最后给出了基于改进SMOTE算法的非概率可靠性指标解的主要流程.数值算例表明,当极限状态曲面呈现局部闭合、多区域的特点时,改进后的SMOTE算法可以高效地获取位于极限状态曲面附近的样本点,进而高精度地拟合极限状态曲面.将本文方法的计算结果与解析解对比,相对误差远远小于工程中的最大误差限值5%,说明改进SMOTE算法能够较好地处理高度非线性功能函数,验证了所提算法的有效性和实用性.
Abstract
The existing algorithm cannot solve the non-probabilistic reliability indices(NPRIs)effectively when the functional function of the structure presents a high degree of nonlinearity and the limit state surface is multi-regional.To solve such problems,a synthetic minority oversampling technique(SMOTE)was improved and the NPRIs solution method was proposed.Firstly,based on the geometric meaning of NPRIs,an improved SMOTE algorithm was proposed to further improve the sampling efficiency of the algorithm near the critical surface by combining the sample classification strategy,hypersphere restriction strategy and the standard SMOTE algorithm.Then the improved SMOTE algorithm was combined to fit the local limit state surface in the normalized space with high accuracy,and the NPRIs were searched.Finally,the main flow of the NPRIs solution based on the improved SMOTE algorithm was given.The numerical example shows that when the limit state surface presents the characteristics of local closure and multiple regions,the improved SMOTE algorithm can efficiently produce the sample points located near the limit state surface,and then fits the limit state surface with high accuracy.Comparing the calculation results with that of the analytical solution,the relative errors are less than the maximum error limit of 5%in engineering,which indicates that the improved SMOTE algorithm can better handle the highly nonlinear functional functions and verifies the effectiveness and practicality of the proposed algorithm.
关键词
非概率可靠性指标/合成少数类过采样技术/样本分类策略/超球限制策略/极限状态曲面Key words
non-probabilistic reliability indices/synthetic minority oversampling technology/sample classification strategy/super ball restriction strategy/limit state surface引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
维普
万方数据