Please wait a minute...
浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (11): 2254-2265    DOI: 10.3785/j.issn.1008-973X.2023.11.013
    
Seismic fragility study of high arch dam based on balanced spectral clustering algorithm
Yang SU1,2(),Cheng ZHANG3,4,En-liang HU1,2,*()
1. College of Mathematics, Yunnan Normal University, Kunming 650500, China
2. Yunnan Key Laboratory of Modern Analytical Mathematics and Applications, Kunming 650500, China
3. Changjiang River Scientific Research Institute of Changjiang Water Resources Commission, Wuhan 430010, China
4. Key Laboratory of Basin Water Resource and Eco-Environmental Science in Hubei Province, Wuhan 430010, China
Download: HTML     PDF(3822KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

A seismic fragility analysis method integrating unsupervised clustering was proposed, which was a balanced spectral clustering algorithm that combined approximate orthogonal restrictions of the membership matrix with spectral clustering. A representative subset of samples was selected from the provided seismic waves based on the re-representation of the Laplacian matrix, which alleviated the "curse of dimensionality" generated by too many selected ground motion intensity measures. The problem of "uniform effect" resulting from the use of the traditional spectral clustering algorithm was solved by incorporating the approximate orthogonal restrictions of the membership matrix. As a practical case, the seismic fragility of a "arch dam-foundation structure" as a whole system was studied. The seismic fragility model with 15 samples of the normative response spectrum and 109 overall samples as the reference was established to evaluate the effect of clustering model. Results showed that the seismic fragility findings from clustered samples were similar to those of the overall samples. Under the performance indicators of the damage volume ratio, dam crest displacement, and the maximum joint opening, the maximum errors of their fragility probability were 4.39%, 3.84%, and 6.64%, respectively, and the minimum probabilities of the errors not exceeding 5% were 92.24%, 99.19%, and 81.75%, respectively, which illustrating the effectiveness of the algorithm in selecting typical seismic waves.

Key words： high arch dam      seismic fragility      multiple stripe analysis (MSA)      spectral clustering      clustering membership matrix      orthogonal constraint     
Received: 19 September 2022      Published: 11 December 2023
CLC:  TU 312  
Fund:  国家自然科学基金资助项目(62266055)
Corresponding Authors: En-liang HU     E-mail: 18261786736@163.com;el.hu@ynnu.edu.cn
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Yang SU
Cheng ZHANG
En-liang HU
Cite this article:

Yang SU,Cheng ZHANG,En-liang HU. Seismic fragility study of high arch dam based on balanced spectral clustering algorithm. Journal of ZheJiang University (Engineering Science), 2023, 57(11): 2254-2265.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.11.013     OR     https://www.zjujournals.com/eng/Y2023/V57/I11/2254


基于平衡化谱聚类算法的高拱坝结构地震易损性研究

提出融入无监督聚类的地震易损性分析方法?将隶属度矩阵的近似正交约束与谱聚类相结合的平衡化谱聚类算法. 该算法基于图Laplacian矩阵的重表示矩阵，从给定的所有地震记录中筛选出具有代表性的样本子集，缓解由所选地震动强度指标过多引起的“维数灾难”问题；并通过隶属度矩阵的近似正交约束，解决应用传统谱聚类算法筛选地震波时产生的“均匀效应”问题. 以实际工程为例，开展以“拱坝-地基结构”为整体体系的地震易损性研究，分别建立以15条规范反应谱样本、109条整体样本为参照基准的地震易损性模型进行聚类算法效果验证. 结果表明，聚类算法筛选的样本与整体样本的地震易损性结果接近，在损伤体积比、坝顶位移、横缝最大开度性能指标下，两者易损性概率最大误差分别为4.39%、3.84%、6.64%，误差不超过5%的最小概率分别为92.24%、99.19%、81.75%，表明该算法在筛选典型地震样本方面的有效性.


关键词： 高拱坝,  地震易损性,  多样条带分析法(MSA),  谱聚类,  聚类隶属度矩阵,  正交约束 
Fig.1 Response spectrum curves of ground motion samples
IM 定义
1）注： $ {t_{{\rm{tot}}}} $为地震持时指标，PGA为峰值加速度指标，均为基本说明指标.
地震持时、有效持时、重要持时、主导周期、平均周期 ${t_{ {\text{tot} } } } ^{1)}$、 ${t_{ {\text{ed} } } } = {t_{ {\text{IA} } = 0.125\;{\rm{m}}/{\rm{s}}} } - {t_{ {\text{IA} } = 0.01\;{\rm{m}}/{\rm{s}}} }$、 $ {t_{{\text{sd}}(5 - 95)}} = {t_{0.95{\text{IA}}}} - {t_{0.05{\text{IA}}}} $、 $ {T_{\text{P}}} $、 $ {T_{\text{M}}} $
震级、震源距、震中距、土体类型、峰值加速度、速度、位移 $ M $、 $ {R_{{\text{hypo}}}} $、 $ {R_{{\text{epi}}}} $、 $ {\text{VS}} $、 $ {\text{PGA}} $、 $ {\text{PGV}} $、 $ {\text{PGD}} $
谱加速度、速度、位移、峰值谱加速度、速度、位移 ${ {{S} }_a}(T,\zeta )$、 $ {S_v}(T,\zeta ) $、 $ {{\text{S}}_d}(T,\zeta ) $、 $ {\text{P}}{{\text{S}}_a} $、 $ {\text{P}}{{\text{S}}_v} $、 $ {\text{P}}{{\text{S}}_d} $
A95加速度、有效设计加速度、持续最大加速度、速度 ${\text{A} }95 、 {\text{EDA} }、{\text{SMA} }、{\text{SMV} }$
Arias强度、特征强度、 ${\rm{C}} {\text{-} } {\rm{M}}$强度 ${\text{IA} } = \dfrac{{\text{π} } }{ {2g} }\displaystyle \int_0^{ {t_{ {\text{tot} } } }} {\mathop {\left[ {\ddot u(t)} \right]}\nolimits^2 } {\text{d} }t$、 $ {\text{IC}} = {\left( {{A_{{\text{rms}}}}} \right)^{3/2}}{\left( {{t_{{\text{sd}}}}} \right)^{1/2}} $、 ${\text{ID} } = \dfrac{ {2g} }{{\text{π} } }{\text{IA} }{\left( { {\text{PGA} } } \right)^{ - 1} }{\left( { {\text{PGV} } } \right)^{ - 1} }$
有效峰值加速度、速度、位移 $ {\text{EPA}} = \dfrac{1}{{2.5}}\left( {\left. {{\text{S}}{{\text{a}}_{{\text{avg}}}}\left( {{T_i},\zeta } \right)} \right|_{{T_{{\text{down}}}} = 0.1}^{{T_{{\text{up}}}} = 0.5}} \right) $、 $ {\text{EPV}} = \dfrac{1}{{2.5}}\left( {\left. {{\text{S}}{{\text{v}}_{{\text{avg}}}}\left( {{T_i},\zeta } \right)} \right|_{{T_{{\text{down}}}} = 0.8}^{{T_{{\text{up}}}} = 2.0}} \right) $、

$ {\text{EPD}} = \dfrac{1}{{2.5}}\left( {\left. {{\text{S}}{{\text{d}}_{{\text{avg}}}}\left( {{T_i},\zeta } \right)} \right|_{{T_{{\text{down}}}} = 2.5}^{{T_{{\text{up}}}} = 4.0}} \right) $
均方加速度、速度、位移 ${ {{P} }_a} = \dfrac{1}{ { {t_{ {\text{tot} } } } } }\displaystyle \int_0^{ {t_{ {\text{tot} } } }} {\mathop {\left[ {\ddot u(t)} \right]}\nolimits^2 } {\text{d} }t$、 ${ {{P} }_v} = \dfrac{1}{ { {t_{ {\text{tot} } } } } }\displaystyle \int_0^{ {t_{ {\text{tot} } } }} {\mathop {\left[ {\dot u(t)} \right]}\nolimits^2 } {\text{d} }t$、 ${ {{P} }_d} = \dfrac{1}{ { {t_{ {\text{tot} } } } } }\displaystyle \int_0^{ {t_{ {\text{tot} } } }} {\mathop {\left[ {\dot u(t)} \right]}\nolimits^2 } {\text{d} }t$
均方根加速度、速度、位移 $ {A_{{\text{rms}}}} = {\left( {\dfrac{1}{{{t_{{\text{tot}}}}}}\displaystyle \int_0^{{t_{{\text{tot}}}}} {\mathop {\left[ {\ddot u(t)} \right]}\nolimits^2 } {\text{d}}t} \right)^{1/2}} $、 $ {V_{{\text{rms}}}} = {\left( {\dfrac{1}{{{t_{{\text{tot}}}}}}\displaystyle \int_0^{{t_{{\text{tot}}}}} {\mathop {\left[ {\dot u(t)} \right]}\nolimits^2 } {\text{d}}t} \right)^{1/2}} $、

$ {D_{{\text{rms}}}} = {\left( {\dfrac{1}{{{t_{{\text{tot}}}}}}\displaystyle \int_0^{{t_{{\text{tot}}}}} {\mathop {\left[ {u(t)} \right]}\nolimits^2 } {\text{d}}t} \right)^{1/2}} $
平方加速度、速度、位移 ${ {{E} }_a} = \displaystyle \int_0^{ {t_{ {\text{tot} } } }} {\mathop {\left[ {\ddot u(t)} \right]}\nolimits^2 } {\text{d} }t$、 ${ {{E} }_v} = \displaystyle \int_0^{ {t_{ {\text{tot} } } }} {\mathop {\left[ {\dot u(t)} \right]}\nolimits^2 } {\text{d} }t$、 ${ {{E} }_d} = \displaystyle \int_0^{ {t_{ {\text{tot} } } }} {\mathop {\left[ {u(t)} \right]}\nolimits^2 } {\text{d} }t$
平方根加速度、速度、位移 $ {A_{{\text{rs}}}} = {\left( {\displaystyle \int_0^{{t_{{\text{tot}}}}} {\mathop {\left[ {\ddot u(t)} \right]}\nolimits^2 } {\text{d}}t} \right)^{1/2}} $ 、 $ {V_{{\text{rs}}}} = {\left( {\displaystyle \int_0^{{t_{{\text{tot}}}}} {\mathop {\left[ {\dot u(t)} \right]}\nolimits^2 } {\text{d}}t} \right)^{1/2}} $ $ {D_{{\text{rs}}}} = {\left( {\displaystyle \int_0^{{t_{{\text{tot}}}}} {\mathop {\left[ {u(t)} \right]}\nolimits^2 } {\text{d}}t} \right)^{1/2}} $
伪谱加速度、速度 ${P_{ {\text{seu} } } }{S_a} = \dfrac{ {2{\text{π} } } }{T}{S_v}(T,\zeta ) = \dfrac{ {4{ {\text{π} } ^2} } }{ { {T^2} } }{S_d}(T,\zeta )$、 ${P_{ {\text{seu} } } }{S_v} = \dfrac{ {2{\text{π} } } }{T}{S_d}(T,\zeta )$
速度强度、加速度谱强度、速度 ${ {{I} }_v} = { { {E} }_v}{\left( { {\text{PGV} } } \right)^{ - 1} }$、 $ {\text{ASI}} = \displaystyle \int_{0.1}^{0.5} {{S_a}} (T,\zeta ){\text{d}}t $、 $ {\text{VSI}} = \displaystyle \int_{0.1}^{2.5} {{S_v}} (T,\zeta ){\text{d}}t $
累积绝对速度、Fajfar强度、复合强度 $ {\text{CAV}} = \displaystyle \int_0^{{t_{{\text{tot}}}}} {\left| {\ddot u(t)} \right|} {\text{d}}t $、 ${ {\text{I} }_{\rm{F}}} = {\text{PGV} }{\left( { {t_{ {\text{sd} } } }} \right)^{1/4} }$、 $ {I_v} = {\left( {{\text{PGV}}} \right)^{2/3}}{\left( {{t_{{\text{sd}}}}} \right)^{1/3}} $、 $ {I_d} = {\text{PGD}}{\left( {{t_{{\text{sd}}}}} \right)^{1/3}} $
频率比 $ {I_{v/a}} = {\text{PGV}}{\left( {{\text{PGA}}} \right)^{ - 1}} $、 $ {I_{{v^2}/a}} = {\left( {{\text{PGA}}} \right)^{ - 1}}{\left( {{\text{PGV}}} \right)^2} $、 $ {I_{d/v}} = {\text{PGD}}{\left( {{\text{PGV}}} \right)^{ - 1}} $
Tab.1 Ground motion measures and definitions
Fig.2 Clustering number and algorithm convergence
Fig.3 Spatial distribution of seismic waves of all types
材料 E/GPa ρ/（kg·m?3） ν
坝体 31.2 2400 0.167
基础 26.0 2800 0.240
钢筋 260.0 7800 0.300
Tab.2 Various material parameters of arch dam
Fig.4 Finite element model of arch dam and modal shape
损伤描述 判别准则 样本类别 DVR/% DT/m $ C $/m
坝踵与坝肩均无明显宏观开裂，拱坝下游表面出现
损坏或损坏较小仅存在细微开裂 		基本完好
No Damage
（ND） 		整体样本 <0.031 <0.072 <0.050
反应谱样本 <0.032 <0.076 <0.057
聚类样本 <0.030 <0.066 <0.051
坝踵与坝肩开裂，下游面中部与上部开始发生宏观裂缝，
上游面暂未发生宏观开裂 		轻微破坏
Slight Damage（SD） 		整体样本 0.031~0.099 0.072~0.106 0.050~0.080
反应谱样本 0.032~0.109 0.076~0.111 0.057~0.089
聚类样本 0.030~0.107 0.066~0.096 0.051~0.079
坝体下游产生大面积宏观开裂，
并且延伸至上游发生宏观开裂 		中等破坏
Moderate Damage（MD） 		整体样本 0.099~0.236 0.106~0.154 0.080~0.123
反应谱样本 0.109~0.229 0.111~0.167 0.089~0.132
聚类样本 0.107~0.245 0.096~0.146 0.079~0.123
坝体下游中上部开裂延伸至上游直至贯穿，
上游也已开始产生大面积宏观开裂 		严重破坏
Extensive Damage（ED） 		整体样本 >0.236 >0.154 >0.123
反应谱样本 >0.229 >0.167 >0.132
聚类样本 >0.245 >0.146 >0.123
Tab.3 Grade of performance level of high arch dam
Fig.5 Statistical results of finite element calculation points of all types
Fig.6 Statistical chart of coefficient of variation of all types
Fig.7 Seismic fragility curves of all types
Fig.8 Error analysis of seismic fragility curves of all types
[1]   EKANAYAKE J, SHRIDEEP P, GEOFFREY F. Mapreduce for data intensive scientific analyses [C]// 2008 IEEE 4th International Conference on eScience. Washington: IEEE Computer Society, 2008: 277-284.
[2]   ZAïANE O R, FOSS A, LEE C H, et al. On data clustering analysis: scalability, constraints, and validation[C]// Pacific-Asia Conference on Knowledge Discovery and Data Mining. [s.l.]: PAKDD , 2002: 28-39.
[3]   STOJADINOVIĆ Z, KOVAČEVIĆ M, MARINKOVIĆ D, et al Rapid earthquake loss assessment based on machine learning and representative sampling[J]. Earthquake Spectra, 2022, 38 (1): 152- 177
doi: 10.1177/87552930211042393
[4]   MARINIELLO G, PASTORE T, BILOTTA A, et al Seismic pre-dimensioning of irregular concrete frame structures: mathematical formulation and implementation of a learn-heuristic algorithm[J]. Journal of Building Engineering, 2022, 46: 103733
doi: 10.1016/j.jobe.2021.103733
[5]   JALAYER F. Direct probabilistic seismic analysis: implementing non-linear dynamic assessments[M]. Palo Alto: Stanford University, 2003.
[6]   NAZRI F M. Seismic fragility assessment for buildings due to earthquake excitation[M]. Penang Malaysia: School of Civil Engineering Universiti Sains Malaysia, 2018
[7]   HARIRI-ARDEBILI M A, SAOUMA V E, PORTER K A Quantification of seismic potential failure modes in concrete dams[J]. Earthquake Engineering and Structural Dynamics, 2016, 45 (6): 979- 997
doi: 10.1002/eqe.2697
[8]   中华人民共和国住房和城乡建设部. 建筑抗震设计规范: GB 50011-2010 [S]. 北京: 中国建筑工业出版社, 2010.
[9]   COUNCIL A T. Quantification of building seismic performance factors [M]. Washington: US Department of Homeland Security, FEMA, 2009.
[10]   JAYARAM N, LIN T, BAKER J W A computationally efficient ground-motion selection algorithm for matching a target response spectrum mean and variance[J]. Earthquake Spectra, 2011, 27 (3): 797- 815
doi: 10.1193/1.3608002
[11]   BAKER J W, LEE C An improved algorithm for selecting ground motions to match a conditional spectrum[J]. Journal of Earthquake Engineering, 2018, 22 (4): 708- 723
doi: 10.1080/13632469.2016.1264334
[12]   BIAN X, XIE Q Fragility analysis of substation equipment based on ground motion clustering[J]. Proceedings of the CSEE, 2021, 41 (8): 2671- 2682
[13]   VON LUXBURG U A tutorial on spectral clustering[J]. Statistics and Computing, 2007, 17 (4): 395- 416
doi: 10.1007/s11222-007-9033-z
[14]   DING C, HE X, SIMON H D. On the equivalence of nonnegative matrix factorization and spectral clustering [C]// Proceedings of the 2005 SIAM International Conference on Data Mining, 2005.
[15]   WEN Z, YANG C, LIU X, et al Trace-penalty minimization for large-scale eigenspace computation[J]. Journal of Scientific Computing, 2016, 66 (3): 1175- 1203
doi: 10.1007/s10915-015-0061-0
[16]   WEDDERBURN R W Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method[J]. Biometrika, 1974, 61 (3): 439- 447
[17]   范书立, 田硕, 陈健云 基于向量地震动强度指标的拱坝地震易损性分析[J]. 水利学报, 2019, 50 (3): 335- 345
FAN Shu-li, TIAN Shuo, CHEN Jian-yun Seismic fragility analysis of arch dam based on vector-valued intensity measure[J]. Journal of Hydraulic Engineering, 2019, 50 (3): 335- 345
[18]   于晓辉. 钢筋混凝土框架结构的概率地震易损性与风险分析[D]. 哈尔滨: 哈尔滨工业大学, 2012.
YU Xiao-hui. Probabilistic seimic fragility and risk analysis of reinforced concrete frame structures[D]. Harbin: Harbin Institute of Technology, 2012.
[19]   KODINARIYA T M, MAKWANA P R Review on determining number of Cluster in K-Means Clustering[J]. International Journal of Advance Research in Computer Science and Management Studies, 2013, 1 (6): 90- 95
[20]   LUCO N, CORNELL C A Effects of connection fractures on SMRF seismic drift demands[J]. Journal of Structural Engineering, 2000, 126 (1): 127- 136
doi: 10.1061/(ASCE)0733-9445(2000)126:1(127)
[21]   PANG R, XU B, KONG X, et al Seismic fragility for high CFRDs based on deformation and damage index through incremental dynamic analysis[J]. Soil Dynamics and Earthquake Engineering, 2018, 104: 432- 436
doi: 10.1016/j.soildyn.2017.11.017
[22]   李琳. 强震动记录选取中目标谱的研究及应用[D]. 哈尔滨: 中国地震局工程力学研究所, 2015.
LI Lin. Research and application of the target spectrum in strong motion records selection[D]. Harbin: Institute of Engineering Mechanics, China Earthquake Administration, 2015.
[23]   靳聪聪, 迟世春 高心墙堆石坝弹塑性动力反应分析及地震易损性研究[J]. 浙江大学学报: 工学版, 2020, 54 (7): 1390- 1400
JIN Cong-cong, CHI Shi-chun Elasto-plastic dynamic response analysis and seismic fragility research of high core earth-rockfill dam[J]. Journal of Zhejiang University: Engineering Science, 2020, 54 (7): 1390- 1400
[24]   孙宝成. 基于 ABAQUS 的混凝土高拱坝三维有限元静动力分析[D]. 郑州: 郑州大学, 2016.
SUN Bao-cheng. Static and dynamic analysis of high concrete arch dam was studied using the 3D finite element method on ABAQUS[D]. Zhengzhou: Zhengzhou University, 2016.
[25]   田硕. 混凝土高拱坝地震易损性分析[D]. 大连: 大连理工大学, 2019.
TIAN Shuo. Seismic fragility analysis of high concrete arch dam [D]. Dalian: Dalian University of Technology, 2019.
[26]   QIU Y X, WANG J T, JIN A Y, et al Simple models for simulating shear key arrangement in nonlinear seismic analysis of arch dams[J]. Soil Dynamics and Earthquake Engineering, 2021, 151: 107006
doi: 10.1016/j.soildyn.2021.107006
[27]   WANG J T, JIN A Y, DU X L, et al Scatter of dynamic response and damage of an arch dam subjected to artificial earthquake accelerograms[J]. Soil Dynamics and Earthquake Engineering, 2016, 87: 93- 100
doi: 10.1016/j.soildyn.2016.05.003
[28]   LEE J, FENVES G L A plastic-damage concrete model for earthquake analysis of dams[J]. Earthquake Engineering and Structural Dynamics, 1998, 27 (9): 937- 956
doi: 10.1002/(SICI)1096-9845(199809)27:9<937::AID-EQE764>3.0.CO;2-5
[29]   张建伟, 刘鹏飞, 王涛, 等 基于混凝土塑性损伤本构的高拱坝损伤开裂分析[J]. 中国农村水利水电, 2020, (4): 158- 165
ZHANG Jian-wei, LIU Peng-fei, WANG Tao, et al Damage cracking analysis of high arch dam based on plastic damage constitutive model of concrete[J]. China Rural Water and Hydropower, 2020, (4): 158- 165
doi: 10.3969/j.issn.1007-2284.2020.04.029
[30]   徐强, 张天然, 陈健云, 等 基于ETA模型的配筋措施对于高拱坝变形损伤指标的影响[J]. 工程科学与技术, 2021, 53 (3): 77- 88
XU Qiang, ZHANG Tian-ran, CHEN Jian-yun, et al Influence of reinforcement measures on deformation damage index of high-arch dam based on endurance time analysis model[J]. Advanced Engineering Sciences, 2021, 53 (3): 77- 88
[31]   CHEN H Seismic safety of high concrete dams[J]. Earthquake Engineering and Engineering Vibration, 2014, 13 (1): 1- 16
doi: 10.1007/s11803-014-0207-3
[32]   曹翔宇. 高拱坝动力监测的传感器优化布置与基于深度学习的地震损伤识别方法研究[D]. 大连: 大连理工大学, 2021.
CAO Xiang-yu. Study on optimal sensor placement for dynamic monitoring and seismic damage identification method based on deep learning for high arch dams [D]. Dalian: Dalian University of Technology, 2021.
[33]   姚霄雯. 基于性能的高拱坝地震易损性分析与抗震安全评估[D]. 杭州: 浙江大学, 2013.
YAO Xiao-wen. Performance-based seismic fragility analysis and safety assessment of high arch dams[D]. Hangzhou: Zhejiang University, 2013.
[34]   WANG J, ZHANG M, JIN A, et al Seismic fragility of arch dams based on damage analysis[J]. Soil Dynamics and Earthquake Engineering, 2018, 109: 58- 68
doi: 10.1016/j.soildyn.2018.01.018
[35]   李静, 陈健云, 徐强, 等 高拱坝抗震性能评价指标研究[J]. 水利学报, 2015, 46 (1): 118- 124
LI Jing, CHEN Jian-yun, XU Qiang, et al Study on index of seismic performance evaluation of arch dam[J]. Journal of Hydraulic Engineering, 2015, 46 (1): 118- 124
doi: 10.13243/j.cnki.slxb.2015.01.016
[36]   XU Q, ZHANG T, CHEN J, et al The influence of reinforcement strengthening on seismic response and index correlation for high arch dams by endurance time analysis method[J]. Structures, 2021, 32: 355- 379
doi: 10.1016/j.istruc.2021.03.007
[1] Wen-tao SHI,Hong-yan LI,Jian-guo CUI,Yi-yang MA,Chong ZHANG,Ying-hong DONG. DMA partition method of urban water distribution network under extreme small depressurization space[J]. Journal of ZheJiang University (Engineering Science), 2022, 56(8): 1533-1541.
[2] Bo HUANG,Kai-long LIAO,Yu ZHAO,Jian-qun JIANG. Seismic fragility analysis of multi-storey frame structure considering effect of valley terrain[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(4): 692-701.
[3] YAO Xiao-wen, JIANG Jian-qun. Correlation between ground motion intensity measures and seismic response of high arch dam[J]. Journal of ZheJiang University (Engineering Science), 2014, 48(2): 254-261.
[4] ZHAO Wei-ming, WANG Dian-hai, ZHU Wen-tao, DAI Mei-wei. Optimization of time-of-day breakpoints based on improved NJW algorithm[J]. Journal of ZheJiang University (Engineering Science), 2014, 48(12): 2259-2265.
[5] WANG Tong, WANG Yan, XIE Xu, ZHANG He. Seimic fragility of steel damper bearings in isolated railway bridges with different-height piers[J]. Journal of ZheJiang University (Engineering Science), 2014, 48(11): 1909-1916.
[6] CHEN Wei, ZHANG Cheng, WANG Can, BU Jia-jun, CHEN Chun, CHEN Hong. Online event detection in news stream[J]. Journal of ZheJiang University (Engineering Science), 2011, 45(6): 1006-1012.