改进随机森林−蒙特卡罗法在A型液舱支座结构可靠性分析中的应用

李雪剑; 秦斌; 肖艺峰; 付泽坤

doi:10.19693/j.issn.1673-3185.02181

改进随机森林−蒙特卡罗法在A型液舱支座结构可靠性分析中的应用

doi: 10.19693/j.issn.1673-3185.02181

江南造船(集团)有限责任公司江南研究院，上海201913

详细信息

作者简介:
李雪剑，男，1992年生，硕士，工程师

秦斌，男，1989年生，工程师

肖艺峰，男，1995年生，助理工程师

付泽坤，男，1993年生，助理工程师

通信作者:
李雪剑

中图分类号: U661.42
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出版历程
- 收稿日期: 2020-11-13
- 修回日期: 2021-01-15
- 网络出版日期: 2022-01-28
- 刊出日期: 2022-03-02

An improved random forest-Monte Carlo method and application for structural reliability analysis of A-type independent liquid tank support structure

Jiangnan Institute of Technology, Jiangnan Shipyard (Group) Co., Ltd., Shanghai 201913, China

改进随机森林−蒙特卡罗法在A型液舱支座结构可靠性分析中的应用由李雪剑，等创作，采用知识共享署名4.0国际许可协议进行许可。

摘要

摘要: 目的随着液化天然气（LNG）船舶结构研究和设计深度的提高，需要有能够快速和准确地评估不确定性因素的可靠性分析方法。为此，提出基于改进随机森林−蒙特卡罗（RF-MC）法来解决A型独立液舱支座结构失效概率的计算问题。方法首先，根据不确定性因素的概率分布，使用MC法生成样本集；然后，以局部离群因子为准则，筛选出失效面附近的样本点，再对筛选出的样本点进行有限元计算后添加至训练集，通过重复训练随机森林近似模型，直至满足精度要求；最后，使用近似模型判别样本点是否失效，结合MC法计算结构的失效概率。结果综合考虑算法的准确率、复杂度和效率并结合算例1和2，可以发现在分析可靠性问题时改进RF-MC法比MC和BP-MC等方法具有更大优势。算例3的应用结果表明了改进RF-MC法在A型独立液舱支座结构可靠性分析中的适用性。结论研究结果可为LNG船舶的优化设计提供可行的技术方案。
- 结构可靠性 /
- 局部离群因子 /
- 随机森林
Abstract: Objectives In response to the increasing depth of research and design on liquefied natural gas (LNG) ship structures, higher requirements are put forward for a reliability analysis method that can quickly and accurately evaluate uncertain factors. This paper proposes a method based on an improved random forest-Monte Carlo method (RF-MC) to solve the calculation of the failure probability of A-type independent liquid tank support structures. Methods First, the MC method is used to generate a sample set according to the probability distribution of uncertain factors, then take the local outlier factor (LOF) as the criterion for filtering out sample points near the failure surface. After selecting the sample points, they are calculated using finite element software and added to the training set to train the random forest (RF) model. The generation, filtering and training process is repeated until the approximate model meets the accuracy requirements. Finally, the approximate model is used to determine whether the sample points are invalid, then combined with the MC method to calculate the failure probability of the structure. Results Considering the accuracy, complexity and efficiency of the algorithm, and combined with Cases 1 and 2, it is found that the improved RF-MC method has better advantages than MC or biased probability (BP)-MC in analyzing reliability problems. The results of Case 3 show applicability of the method in reliability analysis of an A-type independent liquid tank support structure. Conclusions This study provides a feasible technical solution for future optimization design of liquefied gas carriers.
- structural reliability /
- local outlier factor /
- random forest

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图 1 随机森林模型原理

Figure 1. Principle of RF model

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图 2 改进RF-MC方法流程

Figure 2. Workflow of improved RF-MC method

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图 3 离群点数量随$k$值变化曲线

Figure 3. The number of outliers varying with k-value

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图 4 十杆形桁架结构

Figure 4. Crossbar truss structure

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图 5 MC法计算结果

Figure 5. Calculation result of MC method

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图 6 有限元计算模型

Figure 6. Finite element model

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表 1 算例1计算结果

Table 1. Calculation results of Case 1

方法	失效概率$ {P}_{\mathrm{f}} $	相对误差$/\text{%}$	样本数量
MC	$ \text{2.85}\times {10}^{-5} $	−	$ \text{5}\times {10}^{7} $
BP-MC	$ \text{3.22}\times {10}^{-5} $	$ 12.98 $	$ 124 $
改进RF-MC	$ \text{3.1}\text{5}\times {10}^{-5} $	$ 4.91 $	$ 124 $

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表 2 基本随机变量统计特征值

Table 2. Statistical characteristic values of basic random variable

随机变量$ /{\mathrm{c}\mathrm{m}}^{2} $	均值$ \mu $	标准差$ \sigma $	分布类型
$ {A}_{1} $	83.87	8.387	正态
$ {A}_{2} $	12.90	1.290	正态
$ {A}_{3} $	58.06	5.806	正态

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表 3 算例2计算结果

Table 3. Calculation results of Case 2

方法	失效概率$ {P}_{\mathrm{f}} $	相对误差$ /\text{%} $	样本数量
MC	$\text{0.176}\;\text{40}$	−	$ {10}^{5} $
改进RF-MC	$\text{0.179}\;\text{85}$	$ 1.96 $	$ 200 $

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表 4 A型液舱支座结构的设计变量分布

Table 4. Design variables distribution of A-type liquid tank support

类别	编号	变量	参数1	参数2	分布类型
支座结构支反力	$ {X}_{1} $	$ f_1/\mathrm{N} $	$ 5.24\times {10}^{6} $	$ 5.31\times {10}^{6} $	均匀分布
	$ {X}_{2} $	$ f_1/\mathrm{N} $	$ 4.72\times {10}^{6} $	$ 4.86\times {10}^{6} $	均匀分布
	$ {X}_{3} $	$ f_2/\mathrm{N} $	$ 2.57\times {10}^{6} $	$ 2.59\times {10}^{6} $	均匀分布
	$ {X}_{4} $	$ f_2/\mathrm{N} $	$ 2.74\times {10}^{6} $	$ 2.76\times {10}^{6} $	均匀分布
	$ {X}_{5} $	$ f_2/\mathrm{N} $	$ 1.94\times {10}^{6} $	$ 2.02\times {10}^{6} $	均匀分布
	$ {X}_{6} $	$ f_3/\mathrm{N} $	$ 2.09\times {10}^{6} $	$ 2.13\times {10}^{6} $	均匀分布
	$ {X}_{7} $	$ f_3/\mathrm{N} $	$ 1.98\times {10}^{6} $	$ 2.07\times {10}^{6} $	均匀分布
	$ {X}_{8} $	$ f_3/\mathrm{N} $	$ 2.36\times {10}^{6} $	$ 2.43\times {10}^{6} $	均匀分布
	$ {X}_{9} $	$ f_3/\mathrm{N} $	$ 2.81\times {10}^{6} $	$ 2.83\times {10}^{6} $	均匀分布
	$ {X}_{10} $	$ f_3/\mathrm{N} $	$ 3.97\times {10}^{6} $	$ 3.99\times {10}^{6} $	均匀分布
	$ {X}_{11} $	$ f_3/\mathrm{N} $	$ 4.87\times {10}^{6} $	$ 4.91\times {10}^{6} $	均匀分布
板材厚度	$ {X}_{12} $	$ d_1/\mathrm{m}\mathrm{m} $	14	1.4	正态分布
	$ {X}_{13} $	$ d_1/\mathrm{m}\mathrm{m} $	12	1.2	正态分布
	$ {X}_{14} $	$ d_2/\mathrm{m}\mathrm{m} $	18	1.8	正态分布
	$ {X}_{15} $	$ d_3/\mathrm{m}\mathrm{m} $	18	1.8	正态分布
	$ {X}_{16} $	$ d_4/\mathrm{m}\mathrm{m} $	11	1.1	正态分布
	$ {X}_{17} $	$ d_4/\mathrm{m}\mathrm{m} $	11	1.1	正态分布
	$ {X}_{18} $	$ d_5/\mathrm{m}\mathrm{m} $	18	1.8	正态分布
	$ {X}_{19} $	$ d_6/\mathrm{m}\mathrm{m} $	14	1.4	正态分布
纵骨尺寸	$ {X}_{20} $	$ d_7/\mathrm{m}\mathrm{m} $	12	1.2	正态分布
纵骨尺寸	$ {X}_{21} $	$ d_8/\mathrm{m}\mathrm{m} $	12	1.2	正态分布

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表 5 算例3计算结果

Table 5. Calculation results of Case 3

方法	失效概率$ {P}_{\mathrm{f}} $	相对误差$ /\text{%} $	样本数量
MC	$ {2.53\times 10}^{-2} $	−	$ {10}^{5} $
改进RF-MC	$ \text{2.46}{\times 10}^{-2} $	$ 2.77 $	$ 250 $

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