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基于HLRF法与修正对称秩1方法的改进可靠度方法

范文亮 刘丞 李正良

范文亮, 刘丞, 李正良. 基于HLRF法与修正对称秩1方法的改进可靠度方法[J]. 工程力学, 2022, 39(9): 1-9. doi: 10.6052/j.issn.1000-4750.2021.05.0379
引用本文: 范文亮, 刘丞, 李正良. 基于HLRF法与修正对称秩1方法的改进可靠度方法[J]. 工程力学, 2022, 39(9): 1-9. doi: 10.6052/j.issn.1000-4750.2021.05.0379
FAN Wen-liang, LIU Cheng, LI Zheng-liang. IMPROVED RELIABILITY METHOD BASED ON HLRF AND MODIFIED SYMMETRIC RANK 1 METHOD[J]. Engineering Mechanics, 2022, 39(9): 1-9. doi: 10.6052/j.issn.1000-4750.2021.05.0379
Citation: FAN Wen-liang, LIU Cheng, LI Zheng-liang. IMPROVED RELIABILITY METHOD BASED ON HLRF AND MODIFIED SYMMETRIC RANK 1 METHOD[J]. Engineering Mechanics, 2022, 39(9): 1-9. doi: 10.6052/j.issn.1000-4750.2021.05.0379

基于HLRF法与修正对称秩1方法的改进可靠度方法

doi: 10.6052/j.issn.1000-4750.2021.05.0379
基金项目: 中能建规划设计集团科技项目(GSKJ2-T05-2020);国家自然科学基金项目(51678092)
详细信息
    作者简介:

    刘 丞(1995−),男,重庆石柱人,博士生,主要从事可靠度分析研究 (E-mail: liucheng19950330@163.com)

    李正良(1963−),男,江苏江阴人,教授,博士,博导,主要从事结构工程和结构抗风方面研究(E-mail: lizhengl@hotmail.com)

    通讯作者:

    范文亮(1979−),男,江西九江人,教授,博士,博导,主要从事结构工程、随机系统分析和可靠度分析方面的研究(E-mail: davidfwl@126.com)

  • 中图分类号: TB114.3;TU318+.1

IMPROVED RELIABILITY METHOD BASED ON HLRF AND MODIFIED SYMMETRIC RANK 1 METHOD

  • 摘要: 一次可靠度方法简单、高效,但在处理强非线性功能函数时存在较大误差;已有的二次可靠度方法在提高精度的同时往往降低了效率。为此,该文中在发展改进一次可靠度方法的同时提出了更好地兼顾精度与效率的改进二次可靠度方法。将修正对称秩1方法与HLRF法的步长确定策略相结合,提出了具有较好收敛性的改进一次可靠度方法,且在基本不增加计算量的前提下获得了功能函数的近似Hessian矩阵;结合坐标旋转、单变量降维近似和非中心卡方分布,提出了与改进一次可靠度方法同效率但具有更高精度的改进二次可靠度方法;通过数值算例和工程算例验证了建议方法的广泛适用性以及精度或效率上的优势。
  • 图  1  悬臂管

    Figure  1.  Cantilever tube

    表  1  常用分布的mi

    Table  1.   mi for common distribution

    分布类型mi
    正态分布1
    极值I型分布4
    对数正态分布$\max \{ 2,floor[2 + 20({\sigma _{\ln }} - 0.1)/3]\} $
    注:floor$ \left(A\right) $函数指小于$ A $的最大整数值。
    下载: 导出CSV

    表  2  算例1中随机变量的统计特征

    Table  2.   Statistical characteristics of the random variables in Example 1

    变量概率分布均值变异系数
    $ {X}_{1} $ 对数正态分布 1.0 0.1600
    $ {X}_{2} $ 极值I型分布 20.0 0.1000
    $ {X}_{3} $ 韦布尔分布 48.0 0.0625
    下载: 导出CSV

    表  3  算例1中可靠度计算结果

    Table  3.   computed reliability results of Example 1

    方法分析次数可靠指标失效概率/
    (×10−2)
    误差/(%)
    MCS 1×108 2.9040 0.1842
    HLRF 21 3.0855 0.1016 44.84
    HLRF-BFGS 13 3.0855 0.1016 44.84
    Breitung 21+6 2.8972 0.1882 2.19
    拟牛顿近似 13 2.8967 0.1886 2.36
    建议方法1 11 3.0855 0.1016 44.84
    建议方法2-1 11 2.8956 0.1892 2.71
    建议方法2-2 11 2.8956 0.1892 2.71
    下载: 导出CSV

    表  4  算例2中可靠度计算结果

    Table  4.   computed reliability results of Example 2

    方法分析次数可靠指标失效概率/(×10−2)误差/(%)
    MCS 1×108 2.1890 1.4301
    HLRF 8 2.0457 2.0392 42.59
    HLRF-BFGS 8 2.0457 2.0392 42.59
    Breitung 8+10 2.1644 1.5217 6.42
    拟牛顿近似 8 2.1644 1.5217 6.42
    建议方法1 8 2.0457 2.0392 42.59
    建议方法2-1 8 2.2125 1.3466 5.82
    下载: 导出CSV

    表  5  确定性参数

    Table  5.   deterministic parameters

    基础确定性参数数值
    宽度B/m 30
    长度L/m 40
    嵌入深度D/m 3
    地层厚度H/m 10
    角数m 4
    影响因素I1 0.073
    影响因素I2 0.089
    影响因素IF 0.950
    下载: 导出CSV

    表  6  算例3中随机变量的统计特征

    Table  6.   Statistical characteristics of the random variables in Example 3

    变量概率分布均值标准差
    均布荷载$ {q}_{0} $/kPa 对数正态分布 280.00 40.00
    泊松比$ \nu $ 对数正态分布 0.25 0.08
    弹性模量${E}_{{\rm{s}}}$/MPa 正态分布 70.00 2.50
    下载: 导出CSV

    表  7  算例3中可靠度计算结果

    Table  7.   computed reliability results of Example 3

    方法分析次数可靠指标失效概率/
    (×10−2)
    误差/(%)
    MCS 1×108 3.0697 0.1071
    HLRF 52 3.0259 0.1239 15.69
    HLRF-BFGS 20 3.0259 0.1239 15.69
    Breitung 52+6 3.0668 0.1082 0.98
    拟牛顿近似 20 3.0390 0.1187 10.78
    建议方法1 20 3.0259 0.1239 15.69
    建议方法2-1 20 3.0741 0.1056 1.46
    下载: 导出CSV

    表  8  算例4中随机变量的统计特征

    Table  8.   Statistical characteristics of the random variables in Example 4

    随机变量均值标准差分布类型
    壁厚t/mm 4.0 0.04 正态分布
    直径d/mm 40.0 0.40 正态分布
    长度L1/mm 120.0 6.00 正态分布
    长度L2/mm 60.0 3.00 正态分布
    外力F1/kN 3.0 0.30 正态分布
    外力F2/kN 3.0 0.30 正态分布
    外力P/kN 12.0 1.20 正态分布
    扭转T/Nm 90.0 9.00 正态分布
    屈服强度Sy/MPa 350.0 50.00 正态分布
    下载: 导出CSV

    表  9  算例4中可靠度计算结果

    Table  9.   computed reliability results of Example 4

    方法分析次数可靠指标失效概率/
    (×10−2)
    误差/(%)
    MCS1×1083.40270.033 36
    HLRF403.40420.033 180.539
    HLRF-BFGS503.40420.033 180.539
    Breitung40+453.40330.033 290.209
    拟牛顿近似503.40150.033 510.449
    建议方法1403.40420.033 180.539
    建议方法2-1403.40250.033 380.059
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-05-21
  • 录用日期:  2021-11-16
  • 修回日期:  2021-11-01
  • 网络出版日期:  2021-11-16
  • 刊出日期:  2022-09-01

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