Please wait a minute...
浙江大学学报(工学版)  2022, Vol. 56 Issue (1): 100-110    DOI: 10.3785/j.issn.1008-973X.2022.01.011
土木工程、水利工程     
基于改进量子遗传算法的模型交互修正方法
向胜涛1(),王达1,2,*()
1. 长沙理工大学 土木工程学院, 湖南 长沙 410114
2. 中南林业科技大学 土木工程学院, 湖南 长沙 410004
Model interactive modification method based on improved quantum genetic algorithm
Sheng-tao XIANG1(),Da WANG1,2,*()
1. School of Civil Engineering, Changsha University of Science and Technology, Changsha 410114, China
2. School of Civil Engineering, Central South University of Forestry and Technology, Changsha 410004, China
 全文: PDF(1146 KB)   HTML
摘要:

针对传统有限元模型修正方法低效率、高成本且易陷入局部极值的缺点,提出基于改进量子遗传算法的静力多尺度有限元模型交互修正方法. 依据量子计算理论,对量子比特矢量态进行实数编码,以改进量子旋转门实现旋转角自适应更新,引入量子全局干扰交叉、变异、灾变等遗传操作,设计改进量子遗传算法. 以某钢-混组合梁桥为工程背景建立多尺度有限元模型,建立目标函数,对待修正区域进行分块处理. 利用最大互信息系数对待修正参数进行筛选,给出目标函数权重,通过Python语言实现了基于改进量子遗传算法的静力多尺度有限元模型交互修正. 结果表明,改进量子遗传算法相较于传统遗传算法、量子遗传算法具有更高的性能与精度,自动交互修正方法的效率较高,对材料弹性模量、厚度、车辆荷载等参数的修正与工程实际测试的情况基本吻合,目标函数修正结果相较于有限元计算的初始值,挠度误差降低至1.4%~14.3%,混凝土底板应力误差降低至2.6%~18.8%,钢梁应力误差降低至0%~11.1%.

关键词: 桥梁工程钢-混组合梁改进量子遗传算法实桥试验模型交互修正    
Abstract:

A static multi-scale finite element model interactive modification method based on improved quantum genetic algorithm was proposed aiming at the disadvantages of traditional finite element model modification methods, which are low efficiency, high cost and easy to fall into local extremums. The quantum bit vector states were encoded by real numbers according to the quantum computing theory, and the rotation angle was adaptatively updated by improving the quantum revolving gate. The improved quantum genetic algorithm was designed by introducing the quantum global interference crossover, mutation, catastrophe and other genetic operations. A multi-scale finite element model was established with a steel-concrete composite girder bridge as the engineering background. The objective function was established, the correction region was partitioned, and the maximum mutual information coefficient was used to screen the parameters and obtain the weight of the objective function. The interactive modification of static multi-scale finite element model based on improved quantum genetic algorithm was realized by Python language. Results show that the improved quantum genetic algorithm has higher performance and accuracy than the traditional genetic algorithm and quantum genetic algorithm, and the automatic interactive modification method is more efficient. The modification of material elastic modulus, thickness, vehicle load and other parameters accorded with the actual engineering test. The deflection error was reduced to 1.4%-14.3%, the stress error of concrete floor was reduced to 2.6%-18.8%, and the stress error of steel beam was reduced to 0%-11.1% compared with the initial finite element calculation.

Key words: bridge engineering    steel-concrete composite girder bridge    improved quantum genetic algorithm    real bridge test    model interactive modification
收稿日期: 2021-06-12 出版日期: 2022-01-05
CLC:  U 441  
基金资助: 国家自然科学基金资助项目(51878072);湖南省研究生科研创新资助项目(CX20190661);湖南省科技创新计划资助项目(2020RC4049)
通讯作者: 王达     E-mail: 18390869644@163.com;yxwang2006@yeah.net
作者简介: 向胜涛(1994—), 男,博士生,从事钢-混组合结构大跨度桥梁施工控制的研究. orcid.org/0000-0002-3290-4050. E-mail: 18390869644@163.com
服务  
把本文推荐给朋友
加入引用管理器
E-mail Alert
作者相关文章  
向胜涛
王达

引用本文:

向胜涛,王达. 基于改进量子遗传算法的模型交互修正方法[J]. 浙江大学学报(工学版), 2022, 56(1): 100-110.

Sheng-tao XIANG,Da WANG. Model interactive modification method based on improved quantum genetic algorithm. Journal of ZheJiang University (Engineering Science), 2022, 56(1): 100-110.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.01.011        https://www.zjujournals.com/eng/CN/Y2022/V56/I1/100

图 1  全局干扰交叉的示意图
函数 算法 最优搜索值 均值 最优理论值
$ {f_1} $ GA 0.999 688 0.991 051 1
${f_1} $ QGA 0.999 754 0.992 084 1
${f_1} $ IQGA 0.999 991 0.999 112 1
$ {f_2} $ GA 0.240 051 0.239 887 0.240 035
${f_2} $ QGA 0.240 001 0.238 129 0.240 035
$ {f_2}$ IQGA 0.240 035 0.239 911 0.240 035
表 1  GA、QGA、IQGA算法的优化结果对比
图 2  GA、QGA、IQGA算法优化进程适应度函数值变化对比
图 3  FE模型修正的流程图
图 4  某高架桥的标准横断面图
车辆编号 Le/m W1/kN W2/kN W/kN
G1 4+1.4 80.5 322.1 402.6
G2 4+1.4 79.9 321.0 400.9
G3 4+1.4 78.6 319.0 397.6
G4 4+1.4 79.0 320.5 399.5
G5 4+1.4 78.9 321.0 399.9
G6 4+1.4 81.0 324.0 405.0
G7 4+1.4 40.5 160.1 200.6
G8 4+1.4 39.9 160.0 199.9
表 2  加载车轴重
图 5  多尺度有限元模型
材料 $\rho $/(kN·m?3) E/MPa ${E_{\rm{c}}}$/MPa $\upsilon $ 蠕变参数
A/10?11 n m R2
C50混凝土 24.2 34 500 0.2
Q345qd钢板 78.5 206 000 0.3
沥青混凝土 24.7 870 0.25 6.54 0.937 ?0.592 0.9326
表 3  有限元模型初始材料参数
图 6  有限元模型分块
工况 位置 边梁目标函数 中梁目标函数 权重
1 中跨跨中 竖向挠度B1 竖向挠度Z1 0.075
混凝土底板应力B2 混凝土底板应力Z2 0.04
钢梁底板应力B3 钢梁底板应力Z3 0.05
钢梁顶板应力B4 钢梁顶板应力Z4 0.05
2 墩顶 混凝土底板应力B5 混凝土底板应力Z5 0.01
钢梁底板应力B6 钢梁底板应力Z6 0.03
钢梁顶板应力B7 钢梁顶板应力Z7 0.03
3 边跨跨中 竖向挠度B8 竖向挠度Z8 0.075
混凝土底板应力B9 混凝土底板应力Z9 0.04
钢梁底板应力B10 钢梁底板应力Z10 0.05
钢梁顶板应力B11 钢梁顶板应力Z11 0.05
表 4  目标函数及权重
图 7  待修正参数与目标函数MIC矩阵热力图
Y
Xsum
Y
Xsum
Z1 0.050 5 B1 0.0461
Z2 0.045 8 B2 0.0451
Z3 0.041 7 B3 0.0451
Z4 0.043 7 B4 0.0514
Z5 0.040 7 B5 0.0457
Z6 0.045 7 B6 0.0429
Z7 0.046 1 B7 0.0445
Z8 0.043 0 B8 0.0432
Z9 0.047 0 B9 0.0477
Z10 0.045 9 B10 0.0467
Z11 0.043 8 B11 0.0477
表 5  目标函数各元素对应随机变量各元素MIC值之和
参数 块/编号 初始值 修正值 修正幅度/% 参数 块/编号 初始值 修正值 修正幅度/%
X5/mm A1 90 93 3.33 X3/mm C1 300 310 3.33
A2 90 92 2.22 C2 300 315 5.00
A3 90 95 5.56 C3 300 316 5.33
X2/MPa C1 34500 35900 4.06 C4 300 316 5.33
C2 34500 36151 4.79 C5 300 317 5.67
C3 34500 36151 4.79 C6 300 315 5.00
C4 34500 36991 7.22 C7 300 312 4.00
C5 34500 36991 7.22 C8 300 316 5.33
C6 34500 37100 7.54 C9 300 319 6.33
C7 34500 37890 9.83 C10 300 315 5.00
C8 34500 37100 7.54 C11 300 319 6.33
C9 34500 37201 7.83 C12 300 313 4.33
C10 34500 37333 8.21 C13 300 312 4.00
C11 34500 37332 8.21 C14 300 319 6.33
C12 34500 37332 8.21 C15 300 312 4.00
C13 34500 37333 8.21 C16 300 319 6.33
C14 34500 37199 7.82 C17 300 315 5.00
C15 34500 37101 7.54 C18 300 304 1.33
C16 34500 36001 4.35 C19 300 313 4.33
C17 34500 35100 1.74 C20 300 303 1.00
C18 34500 37155 7.70 C21 300 306 2.00
C19 34500 37161 7.71 X4/mm B1 1330 1320 ?0.75
C20 34500 36600 6.09 B2 1330 1329 ?0.08
C21 34500 37091 7.51 B3 1330 1328 ?0.15
X1/MPa D1 206000 209970 1.93 B10 1330 1330 0.00
D2 206000 209903 1.89 B11 1330 1327 ?0.23
D3 206000 209918 1.90 B12 1330 1329 ?0.08
D4 206000 209999 1.94 X1/MPa E1 206000 209800 1.84
D5 206000 212111 2.97 E2 206000 209953 1.92
D6 206000 211058 2.46 E3 206000 210471 2.17
D7 206000 210001 1.94 E4 206000 210513 2.19
D8 206000 210000 1.94 E5 206000 209699 1.80
D9 206000 210099 1.99 E6 206000 210987 2.42
D10 206000 212000 2.91 E7 206000 212100 2.96
D11 206000 211107 2.48 E8 206000 210117 2.00
D12 206000 210011 1.95 F1 206000 211098 2.47
D13 206000 212109 2.97 F2 206000 209987 1.94
D14 206000 210000 1.94 X6/kN G1 402.6 384 ?4.62
D15 206000 210100 1.99 G2 400.9 382.1 ?4.69
D16 206000 212010 2.92 G3 397.6 380.1 ?4.40
D17 206000 212087 2.95 G4 399.5 381.1 ?4.61
D18 206000 212033 2.93 G5 399.9 391.5 ?2.10
D19 206000 212011 2.92 G6 405 386.7 ?4.52
D20 206000 209410 1.66 G7 200.6 191.4 ?4.59
D21 206000 211099 2.48 G8 199.9 190.5 ?4.70
表 6  参数修正结果
函数值 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11
实测值 ?7.0 ?3.2 44.3 ?4.1 ?1.6 ?28.7 5.3 ?8.0 ?3.8 43.3 ?5.4
初始值 ?8.8 ?4.0 48.8 ?4.5 ?2.1 ?29.1 6.0 ?10.0 ?4.2 46.7 ?5.5
修正值 ?8.0 ?3.5 46.8 ?4.3 ?1.9 ?28.8 5.6 ?9.1 ?3.9 44.7 ?5.3
函数值 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11
实测值 ?12.0 ?2.1 30.6 ?2.7 ?1.1 ?19.4 3.0 ?14.0 ?2.5 30.6 ?3.7
初始值 ?12.9 ?2.5 33.6 ?3.2 ?1.5 ?21.1 3.4 ?14.8 ?2.7 32.6 ?4.0
修正值 ?12.3 ?2.2 32.0 ?3.0 ?1.3 ?19.6 3.1 ?14.2 ?2.7 30.8 ?3.7
表 7  目标函数计算结果与实测值的对比
图 8  修正前、后目标函数误差的对比
1 BENEDETTINI F, GENTILE C Operational modal testing and FE model tuning of a cable-stayed bridge[J]. Engineering Structures, 2011, 33 (6): 2063- 2073
doi: 10.1016/j.engstruct.2011.02.046
2 梁鹏, 李斌, 王秀兰, 等 基于桥梁健康监测的有限元模型修正研究现状与发展趋势[J]. 长安大学学报:自然科学版, 2014, 34 (4): 52- 61
LIANG Peng, LI Bin, WANG Xiu-lan, et al Present research status and development trend of finite element model updating based on bridge health monitoring[J]. Journal of Chang’an University: Natural Science Edition, 2014, 34 (4): 52- 61
doi: 10.3969/j.issn.1671-8879.2014.04.009
3 秦世强, 胡佳, 曹鸿猷, 等 基于试验数据的大跨度拱桥有限元模型修正[J]. 中国公路学报, 2019, 32 (7): 66- 76
QIN Shi-qiang, HU Jia, CAO Hong-you, et al Finite element model updating of large-span arch bridge based on experimental data[J]. China Journal of Highway and Transport, 2019, 32 (7): 66- 76
4 DENG L, CAI C S Bridge model updating using response surface method and genetic algorithm[J]. Journal of Bridge Engineering, 2010, 15 (5): 553- 564
doi: 10.1061/(ASCE)BE.1943-5592.0000092
5 方志, 唐盛华, 张国刚, 等 基于多状态下静动态测试数据的斜拉桥模型修正[J]. 中国公路学报, 2011, 24 (1): 34- 41
FANG Zhi, TANG Sheng-hua, ZHANG Guo-gang, et al Cable-stayed bridge model updating based on static and dynamic test data of multi-state[J]. China Journal of Highway and Transport, 2011, 24 (1): 34- 41
doi: 10.3969/j.issn.1001-7372.2011.01.006
6 JAISHI B, REN W X Structural finite element model updating using ambient vibration test results[J]. Journal of Structural Engineering, 2005, 131 (4): 617- 628
doi: 10.1061/(ASCE)0733-9445(2005)131:4(617)
7 REN W X, CHEN H B Finite element model updating in structural dynamics by using the response surface method[J]. Engineering Structures, 2010, 32 (8): 2455- 2465
doi: 10.1016/j.engstruct.2010.04.019
8 马印平, 刘永健, 刘江 基于响应面法的钢管混凝土组合桁梁桥多尺度有限元模型修正[J]. 中国公路学报, 2019, 32 (11): 51- 61
MA Yin-ping, LIU Yong-jian, LIU Jiang Multi-scale finite element model updating of CFST composite truss bridge based on response surface method[J]. China Journal of Highway and Transport, 2019, 32 (11): 51- 61
9 XING X, LIU Y, GARG A, et al An improved genetic algorithm for determining modified water-retention model for biochar-amended soil[J]. Catena, 2021, 200 (3): 105143
10 HAN J K Quantum-inspired evolutionary algorithms with a new termination criterion, H ε gate, and two-phase scheme[J]. IEEE Transactions on Evolutionary Computation, 2004, 8 (2): 156- 169
doi: 10.1109/TEVC.2004.823467
11 DAS A K, PRATIHAR D K Solving engineering optimization problems using an improved real-coded genetic algorithm (IRGA) with directional mutation and crossover[J]. Soft Computing, 2021, 25 (7): 5455- 5481
doi: 10.1007/s00500-020-05545-9
12 邢焕来, 潘炜, 邹喜华 一种解决组合优化问题的改进型量子遗传算法[J]. 电子学报, 2007, 35 (10): 1999- 2002
XING Huan-lai, PAN Wei, ZOU Xi-hua A novel improved quantum genetic algorithm for combinatorial optimization problems[J]. Acta Electronica Sinica, 2007, 35 (10): 1999- 2002
doi: 10.3321/j.issn:0372-2112.2007.10.034
13 熊焰, 陈欢欢, 苗付友, 等 一种解决组合优化问题的量子遗传算法QGA[J]. 电子学报, 2004, 32 (11): 1855- 1858
XIONG Yan, CHEN Huan-huan, MIAO Fu-you, et al A quantum genetic algorithm to solve combinatorial optimization problem[J]. Acta Electronica Sinica, 2004, 32 (11): 1855- 1858
doi: 10.3321/j.issn:0372-2112.2004.11.022
14 DIVINCENZO D P Two-bit gates are universal for quantum computation[J]. Physical Review A, 1995, 51 (2): 1015- 1022
doi: 10.1103/PhysRevA.51.1015
15 李士勇, 李盼池 基于实数编码和目标函数梯度的量子遗传算法[J]. 哈尔滨工业大学学报, 2006, 38 (8): 1216- 1218
LI Shi-yong, LI Pan-chi Quantum genetic algorithm based on real encoding and gradient information of object function[J]. Journal of Harbin Institute of Technology, 2006, 38 (8): 1216- 1218
doi: 10.3321/j.issn:0367-6234.2006.08.002
16 何新贵, 梁久祯 利用目标函数梯度的遗传算法[J]. 软件学报, 2001, 12 (7): 33- 38
HE Xin-gui, LIANG Jiu-zhen Genetic algorithms using gradients of object functions[J]. Journal of Software, 2001, 12 (7): 33- 38
17 祁正萍, 孙合明 一种改进的量子遗传算法[J]. 科学技术与工程, 2012, 12 (12): 2835- 2839
QI Zheng-ping, SUN He-ming An improved quantum genetic algorithm[J]. Science Technology and Engineering, 2012, 12 (12): 2835- 2839
doi: 10.3969/j.issn.1671-1815.2012.12.014
18 RESHEF D N, RESHEF Y A, FINUCANE H K, et al Detecting novel associations in large data sets[J]. Science, 2011, 334 (6062): 1518- 1524
doi: 10.1126/science.1205438
19 LI X F, NI Y Q, WONG K Y, et al Structural health rating (SHR)-oriented 3D multi-scale finite element modeling and analysis of Stonecutters Bridge[J]. Smart Structures and Systems, 2015, 15 (1): 99- 117
doi: 10.12989/sss.2015.15.1.099
[1] 马志元,刘江,刘永健,吕毅,张国靖. 钢-混组合梁桥有效温度取值的地域差异性[J]. 浙江大学学报(工学版), 2022, 56(5): 909-919.
[2] 冀伟,邵天彦. 多跨连续梁桥顶推施工双导梁的优化分析[J]. 浙江大学学报(工学版), 2021, 55(7): 1289-1298.
[3] 王立国,邵旭东,曹君辉,陈玉宝,何广,王洋. 基于超短栓钉的钢-超薄UHPC组合桥面性能[J]. 浙江大学学报(工学版), 2020, 54(10): 2027-2037.
[4] 戴显荣,王路,王昌将,王晓阳,沈锐利. 多塔悬索桥全竖向摩擦板式抗滑方案[J]. 浙江大学学报(工学版), 2019, 53(9): 1697-1703.
[5] 李明, 刘扬, 杨兴胜. 考虑轴重相关的随机车流荷载效应[J]. 浙江大学学报(工学版), 2019, 53(1): 78-88.
[6] 赵人达, 贾毅, 占玉林, 王永宝, 廖平, 李福海, 庞立果. 强震区多跨长联连续梁桥减隔震设计[J]. 浙江大学学报(工学版), 2018, 52(5): 886-895.
[7] 项贻强, 何超超, 邱政. 体外预应力钢-混组合梁长期滑移计算[J]. 浙江大学学报(工学版), 2017, 51(4): 739-744.
[8] 项贻强,刘成熹,唐国斌,陈雪奖,吴天真,罗晓峰. 计算独柱墩帽梁承载力的改进撑杆-系杆模型[J]. J4, 2012, 46(7): 1248-1254.
[9] 叶雨清 陈勇 孙炳楠 楼文娟 俞菊虎. 钱江四桥健康监测特征指标趋势分析[J]. J4, 2009, 43(2): 394-400.