Probability Statistical Model for Measured Ground Motion Based on Generalized Extreme Value Distribution

doi:10.16183/j.cnki.jsjtu.2023.558

Abstract

Abstract:

To develop a probability distribution model of peak ground acceleration, 255365 ground motion recordings are collected from 500 stations to create initial statistical samples of peak ground acceleration. First, the generalized extreme value distribution is employed as the probability model for peak ground acceleration. The effectiveness of the maximum likelihood estimation method and the linear moment estimation method, commonly used for estimating parameters of the extreme value distribution model, is assessed using the proposed generalized extreme value distribution model. Then, a method is proposed to determine the minimum required sample length when establishing a generalized extreme value distribution model based on the asymptotic normality of the maximum likelihood estimation. The analysis indicates that the data sample size should not be less than 120 when constructing the generalized extreme value distribution model for peak ground acceleration in seismic events. Statistical analysis is conducted on seismic peak ground acceleration data samples which meet the sample size requirement. It is observed that the model parameters converge to a relatively narrow range as the sample size increases. Ultimately, probability statistical models for measured peak ground acceleration and seismic hazard calculation formulas for different types of sites are established.

Key words: generalized extreme value distribution, maximum likelihood estimation, minimum sample length, earthquake action probability distribution, seismic hazard

CLC Number:

TU312

FENG Pengfei, ZHOU Mi, LI Zhixuan, ZHU Guoqiang. Probability Statistical Model for Measured Ground Motion Based on Generalized Extreme Value Distribution[J]. Journal of Shanghai Jiao Tong University, 2025, 59(8): 1133-1144.

Figures/Tables 13

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References 35

[1]	KARATZETZOU A, STEFANIDIS S, STEFANIDOU S, et al. Unified hazard models for risk assessment of transportation networks in a multi-hazard environment[J]. International Journal of Disaster Risk Reduction, 2022, 75: 102960.
[2]	BIAZAR S, KAMESHWAR S, BALOMENOS G P. Multi-hazard fragility modeling framework for bridges with shallow foundations subjected to earthquake, scour, and vehicular loading[J]. Soil Dynamics & Earthquake Engineering, 2024, 178: 108482.
[3]	JIN Z B, LIU W Z. Fragility analysis for vehicle derailment on railway bridges under earthquakes[J]. Railway Engineering Science, 2022, 30(4): 494-511.
[4]	KWAG S, GUPTA A, BAUGH J, et al. Significance of multi-hazard risk in design of buildings under earthquake and wind loads[J]. Engineering Structures, 2021, 243: 112623.
[5]	ROY T, MATSAGAR V. Multi-hazard analysis and design of structures: Status and research trends[J]. Structure & Infrastructure Engineering, 2023, 19(6): 845-874.
[6]	ZHANG Z L, DE RISI R, SEXTOS A. Multi-hazard fragility assessment of monopile offshore wind turbines under earthquake, wind and wave loads[J]. Earthquake Engineering & Structural Dynamics, 2023, 52(9): 2658-2681.
[7]	AASHTO. LRFD Bridge Design Specifications[S]. 9th ed. Washington: AASHTO, 2020.
[8]	吕大刚, 贾明明. 钢框架结构基于变形可靠度的全概率抗震设计[J]. 工程力学, 2011, 28(5): 117-123.
	LU Dagang, JIA Mingming. Full probability aseismic design of steel frame structures based on deformation reliability[J]. Engineering Mechanics, 2011, 28(5): 117-123.
[9]	李杰. 论第三代结构设计理论[J]. 同济大学学报(自然科学版), 2017, 45(5): 617-624.
	LI Jie. On the third generation of structural design theory[J]. Journal of Tongji University (Natural Science), 2017, 45(5): 617-624.
[10]	CORNELL C A. Engineering seismic risk analysis[J]. Bulletin of the Seismological Society of America, 1968, 58(5): 1583-1606.
[11]	高小旺, 鲍霭斌. 地震作用的概率模型及其统计参数[J]. 地震工程与工程振动, 1985, 5(1): 13-22.
	GAO Xiaowang, BAO Aibin. Probabilistic model and its statistical parameters for seismic load[J]. Earthquake Engineering & Engineering Vibration, 1985, 5(1): 13-22.
[12]	LILLO C, LEIVA V, NICOLIS O, et al. L-moments of the Birnbaum-Saunders distribution and its extreme value version: Estimation, goodness of fit and application to earthquake data[J]. Journal of Applied Statistics, 2018, 45(2): 187-209.
[13]	THOMPSON E M, BAISE L G, VOGEL R M. A global index earthquake approach to probabilistic assessment of extremes[J]. Journal of Geophysical Research: Solid Earth, 2007, 112(B6): 1-12.
[14]	周敉, 赵威, 石雄伟, 等. 高烈度软土场地桥梁地震与冲刷联合作用效应研究[J]. 振动与冲击, 2020, 39(8): 88-98.
	ZHOU Mi, ZHAO Wei, SHI Xiongwei, et al. A study on combined effect of earthquake and scour of bridge in high earthquake-intensity and soft soil site[J]. Journal of Vibration & Shock, 2020, 39(8): 88-98.
[15]	周敉, 赵威, 刘阳, 等. 公路桥梁地震设计状况荷载组合分项系数研究[J]. 中国公路学报, 2021, 34(2): 317-330. doi: 10.19721/j.cnki.1001-7372.2021.02.020
	ZHOU Mi, ZHAO Wei, LIU Yang, et al. Partial coefficient of load combination in seismic design of highway bridge[J]. China Journal of Highway & Transport, 2021, 34(2): 317-330.
[16]	REN J Z, SONG J Y, ELLINGWOOD B R. Reliability assessment framework of deteriorating reinforced concrete bridges subjected to earthquake and pier scour[J]. Engineering Structures, 2021, 239: 112363.
[17]	LI H N, ZHENG X W, LI C. Copula-based joint distribution analysis of wind speed and direction[J]. Journal of Engineering Mechanics, 2019, 145(5): 04019024.
[18]	李宏男, 郑晓伟, 李超. 高性能结构抗多次多种灾害全寿命性能分析与设计理论研究进展[J]. 建筑结构学报, 2019, 40(2): 56-69.
	LI Hongnan, ZHENG Xiaowei, LI Chao. Research progress on life-cycle multihazard-based design theory for high-performance structures[J]. Journal of Building Structures, 2019, 40(2): 56-69.
[19]	ZHENG X W, LI H N. Life-cycle failure probability analysis of deteriorated RC bridges under multiple hazards of earthquakes and strong winds[J]. Earthquake Engineering & Engineering Vibration, 2022, 21(3): 811-823.
[20]	KAMESHWAR S, PADGETT J E. Multi-hazard risk assessment of highway bridges subjected to earthquake and hurricane hazards[J]. Engineering Structures, 2014, 78: 154-166.
[21]	KHOSRAVIKIA F, CLAYTON P. Updated evaluation metrics for optimal intensity measure selection in probabilistic seismic demand models[J]. Engineering Structures, 2020, 202: 109899.
[22]	史道济. 实用极值统计方法[M]. 天津: 天津科学技术出版社, 2006.
	SHI Daoji. Practical extreme value statistical method[M]. Tianjin: Tianjin Scientific & Technical Publishers, 2006.
[23]	ARIF M, KHAN F, AHMED S, et al. Extreme wind load analysis using non-stationary risk-based approach[J]. Safety in Extreme Environments, 2022, 4(3): 247-255.
[24]	郭健, 钟陈杰, 王仁贵, 等. 跨海桥梁受台风影响的风速概率模型分析[J]. 工程力学, 2022, 39 (Sup.1): 180-186.
	GUO Jian, ZHONG Chenjie, WANG Rengui, et al. Analysis of wind speed probability model of sea-crossing bridge affected by typhoons[J]. Engineering Mechanics, 2022, 39(S1): 180-186.
[25]	ASADI P, ENGELKE S, DAVISON A C. Optimal regionalization of extreme value distributions for flood estimation[J]. Journal of Hydrology, 2018, 556: 182-193.
[26]	KHASTAGIR A, HOSSAIN I, AKTAR N. Evaluation of different parameter estimation techniques in extreme bushfire modelling for Victoria, Australia[J]. Urban Climate, 2021, 37: 100862.
[27]	RAI S, HOFFMAN A, LAHIRI S, et al. Fast parameter estimation of generalized extreme value distribution using neural networks[J]. Environmetrics, 2024, 35(3): e2845.
[28]	BHASKARAN S, VERMA A S, GOUPEE A J, et al. Comparison of extreme wind and waves using different statistical methods in 40 offshore wind energy lease areas worldwide[J]. Energies, 2023, 16(19): 6935.
[29]	AKBAR M H, ALI S, SHAH I, et al. Sample size determination for time-to-event endpoints in randomized selection trials with generalized exponential distribution[J]. Heliyon, 2024, 10(5): e27013.
[30]	MCCLUSKEY C J, GUERS M J, CONLON S C. Minimum sample size for extreme value statistics of flow-induced response[J]. Marine Structures, 2021, 79: 103048.
[31]	SOUKISSIAN T H, TSALIS C. Effects of parameter estimation method and sample size in metocean design conditions[J]. Ocean Engineering, 2018, 169: 19-37.
[32]	戈立婷, 宋松柏. 基于统计推断的GEV分布水文频率计算充分样本长度研究[J]. 水利学报, 2022, 53(8): 1004-1016.
	GE Liting, SONG Songbai. Research on sufficient sample length for calculation of hydrological frequency of GEV distribution based on statistical inference[J]. Journal of Hydraulic Engineering, 2022, 53(8): 1004-1016.
[33]	茆诗松, 程依明, 濮晓龙. 概率论与数理统计教程[M]. 第3版. 北京: 高等教育出版社, 2019.
	MAO Shisong, CHENG Yiming, PU Xiaolong. Course of probability theory and mathematical statistics[M]. 3rd ed. Beijing: Higher Education Press, 2019.
[34]	中华人民共和国国家市场监督管理总局, 中华人民共和国国家标准化管理委员会. 中国地震烈度表: GB/T 17742—2020[S]. 北京: 中国标准出版社, 2020.
	General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, Standardization Administration of the People’s Republic of China. The Chinese seismic intensity scale: GB/T 17742—2020[S]. Beijing: Standards Press of China, 2020.
[35]	吕红山. 基于地震动参数的灾害风险分析[D]. 北京: 中国地震局地球物理研究所, 2005.
	LÜ Hongshan. Disaster risk analysis based on ground motion parameters[D]. Beijing: Institute of Geophysics China Earthquake Administation, 2005.

场地	k	σ	μ
I	0.891	1.974	2.863
II	0.842	2.069	3.124
III	0.848	2.179	3.325
IV	0.825	2.120	3.027