Reliability analysis of RC arch bridge during cantilever casting construction based on improved SO
Article Text (Baidu Translation)
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摘要: 为提高大跨钢筋混凝土(RC)拱桥悬臂浇筑施工期可靠度计算的精度和效率, 提出了一种基于改进蛇优化算法(SO)的可靠度分析方法；为提高标准SO的寻优性能, 引入了Tent混沌映射生成初始种群, 同时对迭代过程中的最优蛇个体进行高斯差分变异, 并采用了常用测试函数验证改进算法的有效性；基于试验实测数据和已有研究建立C80混凝土强度随时间发展模型, 采用了拉丁超立方法生成各随机变量的设计样本点, 基于有限元模型求解对应样本点处的目标响应值；在此基础上, 通过改进SO为支持向量机(SVM)参数寻优构建设计样本点与目标响应值之间的最优响应面, 利用该响应面结合蒙特卡洛法(MC)建立了悬臂浇筑RC拱桥施工期可靠度分析模型；采用提出的方法计算了某实桥施工期全过程的2种典型失效模式下的可靠度, 并进行了参数敏感性分析。分析结果表明：改进SO较对比算法具有明显优势, 将某实桥悬臂浇筑施工期主拱圈应力和扣索应力预测精度分别提升至0.994 5和0.986 2, 从而提高了悬臂浇筑RC拱桥施工期可靠度分析的精度；大跨RC拱桥悬臂浇筑施工过程中对主拱圈应力可靠度影响较大的随机变量为扣索初拉力、主拱圈弹性模量和重度, 扣塔、扣索的弹性模量和重度为不敏感因素。Abstract: To improve the reliability calculation accuracy and efficiency of long-span reinforced concrete (RC) arch bridges during cantilever casting construction, a reliability analysis method based on an improved snake optimizer (SO) was proposed. In order to improve the optimization performance of the standard SO, Tent chaotic mapping was introduced to generate the initial population. Gaussian difference variation was performed on the optimal snake individuals in the iterative process, and the effectiveness of the improved algorithm was verified by common test functions. A C80 concrete strength development model with time was established based on the experimental data and existing studies. The design sample points of each random variable were generated by the Latin hypervertical method, and the target response values at the corresponding sample points were solved based on the finite element model. On this basis, the optimal response surface between the design sample points and the target response values was constructed by using the improved SO to optimize the parameters of the support vector machine (SVM), and the reliability analysis model of the RC arch bridge during cantilever casting construction was established by combining the response surface with the Monte Carlo (MC) method. The reliability of two typical failure modes during the whole construction of a real bridge was calculated by using the method proposed in this paper, and the sensitivity of the parameters was analyzed. Analysis results show that the improved SO has obvious advantages over the comparison algorithm. In a case study of a certain actual bridge during cantilever casting construction, it has enhanced the prediction accuracy of the main arch ring stress to 0.994 5 and that of the stay cable stress to 0.986 2, thereby enhancing the precision of reliability analysis for cantilever-cast RC arch bridges during construction. In the cantilever casting construction of long-span RC arch bridges, the initial tension of temporary cables, elastic modulus, and unit weight of the main arch ring are identified as the most significant stochastic variables affecting stress reliability. In contrast, the elastic modulus and unit weight of the cable tower and temporary cables are insensitive factors.
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图 1 某悬臂浇筑RC拱桥扣锚系统布置立面
Figure 1. Elevation plan of anchorage system for a cantilever-cast RC arch bridge
图 4 立方体抗压强度拟合曲线与实测值对比
Figure 4. Comparison between fitting curve and measured value of compressive strength of cube
图 5 悬臂浇筑RC拱桥可靠度分析流程
Figure 5. Reliability analysis process of cantilever-cast RC arch bridge
图 6 左幅半跨RC拱桥施工体系有限元模型
Figure 6. Finite element model of construction system for left half span RC arch bridge
图 7 各施工阶段下主拱圈应力失效可靠度
Figure 7. Stress failure reliability of main arch ring under each construction stage
图 8 各施工阶段下扣索应力失效可靠度
Figure 8. Stress failure reliability of temporary cable under each construction stage
图 9 均值取不同α对主拱圈应力可靠度的影响
Figure 9. Influence of mean values with different α values on stress reliability of main arch ring
图 10 变异系数取不同α对主拱圈应力可靠度的影响
Figure 10. Influence of variation coefficient with different α values on stress reliability of main arch ring
表 1 测试函数
Table 1. Test function
函数名称 函数表达式 取值范围 F1 $\sum\limits_{i=1}^n x_i^2$ [-100, 100] F2 $\sum\limits_{i=1}^{n}\left|x_{i}\right|+\prod\limits_{i=1}^{n}\left|x_{i}\right|$ [-10, 10] F3 $\sum\limits_{i=1}^{n}\left(\sum\limits_{j=1}^{i} x_{j}\right)^{2}$ [-100, 100] F4 $\max _{i}\left\{\left|x_{i}\right|, 1 \leqslant i \leqslant n\right\}$ [-100, 100] F5 $\sum\limits_{i=1}^{n} i x_{i}^{4}+\operatorname{random}[0, 1]$ [-1.28, 1.28] 
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表 2 优化算法测试结果比较
Table 2. Comparison of test results of optimization algorithms
函数名称 优化算法 最小值 平均值 标准差 F1 TGSO 0 2.929 8×10-123 1.306 3×10-122 SO 3.754 5×10-100 6.547 7×10-95 3.487 7×10-94 WOA 5.460 3×10-95 9.814 6×10-85 3.614 0×10-84 GWO 6.856 4×10-35 3.927 3×10-33 5.055 9×10-33 PSO 1.960 4×10-7 6.849 6×10-6 8.517 8×10-6 F2 TGSO 0 3.049 8×10-67 1.118 8×10-66 SO 4.582 5×10-48 2.990 3×10-45 8.969 6×10-45 WOA 2.165 4×10-59 1.032 7×10-53 4.730 3×10-53 GWO 9.971 2×10-21 8.772 8×10-20 6.929 5×10-20 PSO 1.042 1×10-3 6.135 3×10-3 5.705 3×10-3 F3 TGSO 0 1.173 0×10-84 6.300 2×10-84 SO 4.319 8×10-70 1.221 1×10-60 3.552 8×10-60 WOA 2.744 7×103 2.575 3×104 1.042 9×104 GWO 8.957 7×10-11 4.930 1×10-8 9.917 8×10-8 PSO 1.969 7×101 4.393 6×101 1.534 1×101 F4 TGSO 0 1.188 2×10-57 5.974 0×10-57 SO 8.212 3×10-45 2.369 8×10-41 5.564 6×10-41 WOA 2.586 3×10-3 3.463 2×101 2.337 6×101 GWO 4.035 1×10-9 2.656 8×10-8 2.699 4×10-8 PSO 4.593 1×10-1 8.488 8×10-1 2.115 7×10-1 F5 TGSO 1.314 6×10-5 2.015 1×10-4 1.234 0×10-4 SO 2.943 3×10-5 2.155 9×104 1.520 1×10-4 WOA 3.547 1×10-5 1.946 7×10-3 3.073 4×10-3 GWO 3.348 8×10-4 1.129 0×10-3 5.565 8×10-4 PSO 3.853 0×10-2 1.103 9×10-1 3.908 9×10-2
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表 3 C80混凝土fcu曲线拟合结果
Table 3. fcu curves fitting results of C80 concrete
函数类型 函数表达式 a b c R2 和方差 指数函数 $f_{\text {cu }}=a \mathrm{e}^{b /\left(t^{\prime}+c\right)}$ 97.98 -1.159 0.367 4 0.971 0 6.852 2 幂函数 $f_{\mathrm{cu}}=a\left(t^{\prime}+b\right)^{c}$ 62.60 0.000 0.130 1 0.922 9 27.751 6 对数函数 $f_{\mathrm{cu}}=a+b \ln \left(t^{\prime}+c\right)$ 59.34 11.120 0.000 0 0.940 9 21.270 9
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表 4 施工阶段划分
Table 4. Division of construction stages
施工阶段 施工内容 1 激活拱圈1#、2#节段，张拉2#扣索和锚索 2 安装3#挂篮，激活拱圈3#节段 3 张拉3#扣索和锚索 4~35 4#~19#节段拱圈浇筑，对应扣索和锚索张拉 36 拆除2#扣索和锚索 37 挂篮前移，激活拱圈20#节段 38 张拉20#扣索和锚索 39 拆除3#扣索和锚索 40 挂篮前移，激活拱圈21#节段 41 张拉21#扣索和锚索 42 拆除4#、5#扣索和锚索 43 挂篮前移，激活拱圈22#节段 44 张拉22#扣索和锚索(拱圈合龙前最大悬臂状态)
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表 5 随机变量统计特征
Table 5. Statistical characteristics of random variables
变量类别 变量名称 对应构件 分布类型 均值 变异系数 弹性模量/GPa E1 主拱圈 正态分布 41.8 0.07 E2 扣塔 正态分布 206 0.05 E3 扣锚索 正态分布 195 0.05 重度/(kN·m-3) γ1 主拱圈 正态分布 26 0.05 γ2 扣塔 正态分布 78.5 0.05 γ3 扣锚索 正态分布 78.5 0.05 扣索初拉力/kN T2 2#扣索 正态分布 250 0.05 T3 3#扣索 正态分布 170 0.05 T4 4#扣索 正态分布 320 0.05 T5 5#扣索 正态分布 750 0.05 T6 6#扣索 正态分布 800 0.05 T7 7#扣索 正态分布 1 050 0.03 T8 8#扣索 正态分布 1 070 0.03 T9 9#扣索 正态分布 1 050 0.03 T10 10#扣索 正态分布 1 070 0.03 T11 11#扣索 正态分布 1 320 0.03 T12 12#扣索 正态分布 1 370 0.03 T13 13#扣索 正态分布 1 480 0.03 T14 14#扣索 正态分布 1 560 0.02 T15 15#扣索 正态分布 1 720 0.02 T16 16#扣索 正态分布 1 550 0.02 T17 17#扣索 正态分布 1 750 0.02 T18 18#扣索 正态分布 1 770 0.02 T19 19#扣索 正态分布 1 860 0.02 T20 20#扣索 正态分布 1 890 0.02 T21 21#扣索 正态分布 1 800 0.02 T22 22#扣索 正态分布 1 550 0.02
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表 6 各算法SVM的寻优结果R2
Table 6. R2 of SVM optimization results of various algorithms
失效模式 TGSO SO WOA GWO PSO 主拱圈应力失效 0.994 5 0.963 0 0.948 4 0.938 6 0.940 6 扣索应力失效 0.986 2 0.952 5 0.944 6 0.941 8 0.932 7
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