首页 >

基于 RBF 和主动学习的非概率可靠度求解方法

姜峰1,李华聪2,符江锋1,洪林雄1   

  1. 1. 西北工业大学
    2. 西北工业大学动力与能源学院
  • 收稿日期:2021-11-16 修回日期:2022-01-21 出版日期:2022-01-26 发布日期:2022-01-26
  • 通讯作者: 李华聪
  • 基金资助:
    国家科技重大专项;国家科技重大专项

A combined radial basis function and active learning method for structural non-probabilistic reliability analysis

  • Received:2021-11-16 Revised:2022-01-21 Online:2022-01-26 Published:2022-01-26
  • Contact: Huacong 无LI
  • Supported by:
    National Science and Technology Major Project;National Science and Technology Major Project

摘要: 进行结构非概率可靠性分析时,对于失效域与超椭球不确定域发生干涉的情况,非概率可靠度相较于非概率可 靠度指标更具有适用性。为了提高超椭球模型下结构非概率可靠度的求解效率,本文提出一种求解非概率可靠度问题的 高效主动学习方法。首先,结合交叉验证和jackknifing方法推导了RBF模型在未知点处的jackknifing方差以评估模型预测 的不确定性,并根据该方差基于RBF的主动学习函数对非概率可靠度进行求解。其次,提出有效收敛准则来终止非概率 可靠性分析的主动学习过程。最后,三个算例表明该方法能够在较少功能函数调用次数下得到精确的非概率可靠度估计 值,具有良好的工程应用价值。

关键词: 非概率可靠性分析, 超椭球模型, RBF模型, 交叉验证, 主动学习

Abstract: In the non-probabilistic reliability analysis, for the case when the failure domain and hyper-ellipsoid uncertainty domain interfere with each other, the non-probabilistic reliability is more suitable than the non-probabilistic reliability index. In order to improve the efficiency of solving non-probabilistic reliability under the hyper-ellipsoid model, this paper proposes an efficient active learning method for solving non-probabilistic reliability problems. The jackknifing variance of the RBF model is derived by the combined cross-validation and jackknifing methods, to estimate the uncertainty of the predicted values. To solve the non-probabilistic reliability, the active learning function of RBF is employed which is based on the variance. An effective convergence criterion is then proposed to terminate the process of active learning. Three numerical examples reveal that this method can estimate the exact non-probabilistic reliability value under the condition of less calculation of the limit state function, and has strong applicability in the structural non-probabilistic reliability analysis

Key words: Non-probabilistic reliability, Hyper-ellipsoidal model, Radial basis function, Active learning, Cross validation method

中图分类号: