Effects of limit state data on constructing accurate surrogate models for structural reliability analyses极限状态数据对构建结构可靠性分析准确代理模型的影响
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Doan NS, Dinh HB, 2024. Effects of limit state data on constructing accurate surrogate models for structural reliability analyses. Probabilistic Engineering Mechanics, 76: 103595.DOI: 10.1016/j.probengmech.2024.103595
摘要 | Abstract
工程问题主要以隐式过程定义，因此全概率分析，如蒙特卡罗模拟 (Monte Carlo simulation, MCS) 的实现成本高昂。实践中，解决这些问题的两种方法是减少模拟次数或为实际问题建立代理模型。后者不会减少蒙特卡罗模拟次数，且对概率计算的要求较低，因此大多数工程师更倾向于采用这种方法。本研究提出了一个高效框架，通过考虑极限状态 (limit state, LS) 边缘数据来开发有效且准确的代理模型。研究了在训练过程中包含极限状态数据的影响及所提元模型在处理与可靠性分析相关的大多数问题 (包括非线性性能函数、多失效模式和隐式定义问题) 时的表现。采用了两类机器学习算法，包括人工神经网络和 Gauss 过程，以验证所提方法的性能。研究结果表明，极限状态数据在建立可靠性分析准确代理模型中起着关键作用，将其纳入训练数据集有助于快速构建准确的元模型。这项工作为可靠性分析提供了一个实用框架，可以在不需要深入研究概率计算的情况下轻松检测到极限状态数据。关键词: 极限状态数据, 蒙特卡罗模拟, 代理模型, 机器学习技术, 数据驱动方法Engineering problems are mainly defined in implicit processes; hence, the fully probabilistic analyses, e.g., Monte Carlo simulations (MCS), are expensive to implement. In practice, two approaches to overcome the issues are either reducing the size of simulations or developing surrogate models for actual problems. The latter does not sacrifice the size of MCS and requires less insight into probabilistic calculation; hence, it is preferable to most engineers. This study proposes an efficient framework to develop reliable and accurate surrogate models by considering data at the limit state margins (LS data). Effects of involving LS data in the training process and performances of the proposed metamodels are investigated for most issues relating to reliability analyses, including nonlinear performance functions, multiple failure modes, and implicitly defined problems. Two machine learning algorithms, including artificial neural networks and the Gaussian process, are employed to prove the ability of the proposed method. Investigations reveal that the limit state data plays a vital role in developing accurate surrogate models for reliability analyses, and accumulating them into the training dataset helps quickly construct accurate metamodels. This work contributes a practical framework for reliability analyses because the LS data can be detected easily without insight into probabilistic calculations.Keywords: Limit state data; Monte Carlo simulation; Surrogate models; Machine learning techniques; Data-driven approach创新点 | Highlights
- 使用极限状态数据构建的主动学习元模型包括人工神经网络和 Gauss 过程
研究了非线性、多峰、高维和隐式问题
- A practical routine to detect data close to the limit margins is proposed (LS data)
- Active learning metamodels of ANN and Gaussian process constructed using LS data
- LS data can be easily combined with both stochastic and non-stochastic models
- Nonlinear, multimodal, high-dimensional, and implicit problems are examined
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图 1: 元模型的典型配置: (a) 人工神经网络; (b) Gauss 过程回归Fig. 1. Typical configuration of metamodels: (a) ANN; (b) GPR
图 2: 基于增强元模型的蒙特卡罗模拟流程图 (任意元模型)Fig. 2. Flowchart of iMM-based MCS (For any metamodel)
Fig. 3. Truss profile in Example 3
Fig. 4. Truss profile in Example 4
图 5: 增强人工神经网络的算例表现: (a) 输出训练数据的修正过程与直方图; (b) 元模型的最终表现Fig. 5. Performances of iANN for Example 1: (a) Improving process and histogram of output training data; (b) Performances of the final metamodel
图 6: 增强 Gauss 过程回归的算例表现: (a) 输出训练数据的修正过程与直方图; (b) 元模型的最终表现Fig. 6. Performances of iGPR for Example 1: (a) Improving process and histogram of output training data; (b) Performances of the final metamodel
图 7: 增强人工神经网络的算例表现: (a) 输出训练数据的修正过程与直方图; (b) 元模型的最终表现Fig. 7. Performances of iANN for Example 2: (a) Improving process and histogram of output training data; (b) Performances of the final metamodel
图 8: 增强 Gauss 过程回归的算例表现: (a) 输出训练数据的修正过程与直方图; (b) 元模型的最终表现Fig. 8. Performances of iGPR for Example 2: (a) Improving process and histogram of output training data; (b) Performances of the final metamodel
图 9: 算例收敛性: (a) 采用增强人工神经网络; (b) 采用增强 Gauss 过程回归Fig. 9. Convergences for Example 1: (a) Using iANN; (b) Using iGPR
图 10: 算例收敛性: (a) 采用增强人工神经网络; (b) 采用增强 Gauss 过程回归Fig. 10. Convergences for Example 2: (a) Using iANN; (b) Using iGPR
图 11: 采用 5 个初始数据点 2 个迭代极限状态数据点构建的增强 Gauss 过程回归算例表现: (a) 20 次修正迭代后的结果; (b) 50 次迭代的收敛性Fig. 11. Performance of iGPR5-2 for Example 2: (a) After 20 improving iterations; (b) Convergence at 50th iteration
图 12: 基于增强人工神经网络的蒙特卡罗模拟算例结果: (a) 预测失效概率与安全指标直方图; (b) 安全指标的经验概率分布函数Fig. 12. Results of iANNs-based MCS applied to Example 3: (a) Predicted failure probabilities and histogram of FSs; (b) Empirical cumulative distribution functions of FSs
图 13: 基于增强 Gauss 过程回归的蒙特卡罗模拟算例结果: (a) 预测失效概率与安全指标直方图; (b) 安全指标的经验概率分布函数Fig. 13. Results of iGPR-based MCS applied to Example 4: (a) Predicted failure probabilities and histogram of FSs; (b) Empirical cumulative distribution functions of FSs
作者信息 | Authors
越南海事大学 (Vietnam Maritime University) 土木工程学院
Huu-Ba Dinh, 通讯作者 (Corresp.) 越南范朗大学 (Van Lang University) 技术学院Email: ba.dinhhuu@vlu.edu.vn
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
