Static system reliability analysis of cable-stayed bridge based on improved BP neural network
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摘要: 为提高斜拉桥静力体系可靠度计算效率，基于改进的反向传播(BP)神经网络构建了体系可靠度计算模型，引入了遗传算法(GA)优化BP神经网络，实现斜拉桥关键构件功能函数的高效重构和验算点的快速捕捉，建立了构件可靠指标的GA-BP-GA-Monte Carlo(GBGMC)算法；应用修正的β约界法识别失效历程中的候选失效单元，采用GBGMC计算随结构拓扑模型改变而更新变化的构件可靠指标，搜寻结构主要失效模式，建立了结构失效树；在确定各失效模式等效线性功能函数和相关系数的基础上，利用微分等价递归算法实现了结构体系可靠度计算；通过3个数值算例的可靠度分析，验证了GBGMC的正确性和有效性；以主跨448 m的斜拉桥为例，采用提出的体系可靠度计算模型分析了失效历程各阶段斜拉桥关键构件可靠指标的演化规律，创建了斜拉桥结构体系失效树，实现了结构体系可靠指标的高效计算和控制体系安全性的重要构件识别。研究结果表明: GBGMC的计算误差在0.3%以内, 优于其他传统方法; 正常使用极限状态下, 斜拉桥主跨跨中挠度可靠指标最小, 为2.7, 承载能力极限状态下, 主跨跨中斜拉索、索塔处主梁和索塔拉索锚固区下部可靠指标相对较小，分别为3.1、3.6和3.9, 为失效历程第一阶段候选单元，失效风险大; 搜寻19个获得承载能力极限状态的主要失效模式, 计算该斜拉桥体系可靠指标为3.8, 可为斜拉桥设计优化和维养决策体系安全性管控提供量化分析依据。Abstract: In order to enhance the efficiency of static system reliability calculation for cable-stayed bridges, a system reliability analysis model was developed based on an improved back propagation (BP) neural network. By introducing the genetic algorithm (GA) into the BP neural network, the limit state functions of key cable-stayed bridge components could be efficiently reconstructed, the design points could be captured rapidly, and the algorithm of GA-BP-GA-Monte Carlo (GBGMC) for component reliability index calculation was established. The rectified β-unzipping method was used to select candidate failure components, and the structure was modified by assuming in turn failure in the potential failure elements. The primary failure modes of the cable-stayed bridge were identified, upon which the fault tree was subsequently constructed. Based on the equivalent linear functions of the failure modes and correlation coefficients, the differential equivalent recursion algorithm was employed to calculate the reliability of the structural system. The effectiveness and accuracy of GBGMC were verified through a reliability study of three numerical examples. The proposed system reliability analysis method was used to evaluate the structural failure history of a cable-stayed bridge with a main span of 448 m. The component reliability indexes in each failure stage were calculated, and the structural system failure tree of the cable-stayed bridge was created. The structural system reliability index was efficiently calculated, and important components controlling the system safety were identified. Research results show that the computational error of GBGMC is within 0.3%, which is better than other traditional methods.The deflection reliability index at the main span center of the cable-stayed bridge is the lowest for the normal utilization limit state, which is 2.7. In terms of the ultimate limit state, the reliability indexes of the cables in the center of the main span, the main girder at the tower, and the lower section of the tower's cable anchorage area all pose a high risk of failure. Their respective reliability indexes are 3.1, 3.6, and 3.9, respectively. Nineteen main failure modes for the cable-stayed bridge at ultimate limit state are obtained, and the system reliability index is 3.8. Research results provide a theoretical basis of system safety control for the design optimization and maintenance decision of cable-stayed bridges.
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Key words:
- bridge engineering /
- cable-stayed bridge /
- system reliability /
- BP neural network /
- genetic algorithm /
- failure mode
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图 4 期望输出和BP神经网络预测输出曲线
Figure 4. Curves of desired output and BP neural network predicted output
图 18 失效第一阶段主梁位移可靠指标
Figure 18. Reliability indexes of girder displacement in first failure stage
表 1 算例1计算结果对比
Table 1. Comparison of calculation results in example 1
方法 验算点 可靠指标 失效概率 FORM (1 118.546 5, 165.464 7) 2.331 9.88×10-3 RSM (1 125.711 5, 165.816 4) 2.331 9.87×10-3 MCS 2.336 9.74×10-3 BP神经网络 2.361 9.12×10-3 GBGMC (1 125.257 0, 165.986 3) 2.334 9.82×10-3 
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表 2 算例2计算结果对比
Table 2. Comparison of calculation results in example 2
方法 验算点 可靠指标 失效概率 FORM (-2.539 7, 0.945 3) 2.710 3.40×10－3 RSM (-2.458 6, 1.159 5) 2.718 3.30×10－3 MCS 2.688 3.60×10－3 BP神经网络 2.702 3.40×10－3 GBGMC (-2.627 0, 0.827 6) 2.688 3.60×10－3
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表 3 算例3计算结果对比
Table 3. Comparison of calculation results in example 3
可靠度计算方法 可靠指标 失效概率 MCS 2.835 2.30×10－3 BP神经网络(隐节点20个，抽样10万次) 2.819 2.40×10－3 GBGMC(隐节点10个，抽样1万次) 2.831 2.30×10－3
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表 4 迭代索力与设计索力对比
Table 4. Comparison of iterated and designed cable force
编号 设计索力/kN 计算索力/kN 误差率/ % 编号 计算索力/kN 误差率/ % C1 25.03 24.79 0.99 C15 24.47 0.85 C2 21.12 70.78 1.67 C16 20.74 1.30 C3 23.64 23.26 1.64 C17 22.59 1.16 C4 28.05 27.62 1.54 C18 25.78 0.95 C5 29.74 29.40 1.14 C19 26.69 0.53 C6 31.37 31.15 0.69 C20 29.35 0.12 C7 33.96 33.87 0.26 C21 30.84 0.28 C8 35.29 35.34 0.13 C22 34.47 0.58 C9 38.79 38.98 0.49 C23 38.04 0.75 C10 39.79 40.08 0.74 C24 41.42 0.95 C11 40.36 40.77 0.91 C25 39.65 1.01 C12 40.89 41.30 1.00 C26 42.69 0.95 C13 41.47 41.90 1.02 C27 45.49 0.87 C14 42.05 42.47 0.99 C28 46.59 0.79
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表 5 随机变量统计
Table 5. Statistical random variables
随机变量名称 变量分类 变量分布类型 均值 标准差 弹性模量/GPa 主梁 正态 200 20.0 索塔 正态 36 3.6 斜拉索 正态 205 20.5 截面面积/m2 主梁 对数正态 1.76 0.18 索塔下部 对数正态 27.50 1.37 索塔中部 对数正态 17.80 0.89 索塔上部 对数正态 63.90 3.20 109型斜拉索 对数正态 7.85×10－3 7.85×10－5 139型斜拉索 对数正态 9.50×10－3 9.50×10－5 151型斜拉索 对数正态 1.04×10－2 1.04×10－4 163型斜拉索 对数正态 1.13×10－2 1.13×10－4 187型斜拉索 对数正态 1.23×10－2 1.23×10－4 199型斜拉索 对数正态 1.54×10－2 1.54×10－4 惯性矩/m4 主梁 对数正态 3.83 0.19 索塔下部 对数正态 166.00 8.28 索塔中部 对数正态 60.90 3.04 索塔上部 对数正态 225.00 11.30 材料容重/(kg·m－3) 主梁 正态 7.70×103 770.00 索塔 正态 2.60×103 160.00 拉索 正态 7.85×103 785.00 荷载集度/(kN·m－1) 活载 正态 63.00 6.30
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