基于线性矩的特征波高区域频率分析
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摘要
在处理海岸工程的一系列问题如岸滩掩护、冲刷、基础和海岸结构物的设计时,都需要考虑当地多年一遇的设计波高状况,多年一遇设计波高的取值决定结构的安全性和经济性。
本文首先将一种广泛应用于陆地水文学且能够很好概括水文资料统计性质的统计方法-线性矩理论引入到海洋水文分析领域。使用Monte-Carlo模拟对线性矩方法在参数估计方面的表现与经典的三种估计方法进行了对比,讨论了四种方法在参数估计中的不确定性。模拟认为线性矩方法在小样本的参数估计方面有良好的无偏性和样本变异性,并且在估计多参数模型时的计算量方面远小于传统的矩方法和极大似然估计方法。
本文第二部分从数理统计的角度讨论了极值波高推算的方法和各种模型的理论基础,应用特点及适用范围。使用线性矩方法分别结合两种常用的随机波浪长期统计方法(过阈极值法和年度极大值法)分析美国沿岸站点的实测数据和我国秦皇岛历史波浪数据,并对线性矩方法估计得到的结果同传统的经验适线方法的结果进行了对比。认为线性矩方法可以应用在对应重现期特征波高的计算。
推求多年一遇的设计波高时需要大量的实测数据作为统计分析工作的基础,而在实际工程中某些站点缺少充分的信息,以至于不足以确定罕遇事件的频率。基于线性矩的区域频率分析方法的基本思想是利用不同站点的水文信息,以空间替代时间,来弥补单站记录的短缺。本文的第三部分通过对北美洲加利福尼亚海域的实际观测数据进行近岸波浪区域频率分析。具体内容包括:数据甄别、区域一致性检验、统计模型选取与拟和、各站区域频率分位数推求。将区域分析结果与单测站估计结果进行了对比。研究认为,经过检验满足数据一致性的区域可以使用该方法弥补数据的稀缺。
The determination of the significant wave heights should be considered while the engineers deal with some coastal engineering problems such as erosion control, scour protection, foundation, environmental and marine structures. The extreme wave heights play an important role in the design of the marine structures in both safety and economics. The uncertainty analysis is conducted in the process of designing the extreme wave height by different stochastic analysis model and parameter estimation method. An regional frequency analysis based on L-moments is introduced to estimate the extreme wave height.
L-moments are linear combinations of order statistics, which are robust to outliers and virtually unbiased for small samples, making them suitable for frequency analysis, including identification of distribution and parameter estimation. It is introduced to the coastal engineering field. A Monte-Carlo simulation is conducted to analyze and compare the parameter estimation performance of four estimation methods. L–moments is unbiased and has the smallest variations in small sample among the four methods.
The theoretical background and scope of various common stochastic models are discussed in the second chapter. L-moments is applied to estimate the extreme wave heights using the data of California coastline from NDBC and historical field measure data from Qinghuangdao port. The difference between two models (Peak over threshold and Annual Maximum) are discussed.
Enough historical information is of vital importance to the accuracy of the extreme wave height design. However, in practice, the record length is not long enough to give assuring estimation. Regional frequency is a way using the nearby information to add the record length of the interest site. Significant wave height data of 7 California coastline stations are used to perform the regional frequency analysis, including discordancy measure, heterogeneity measure, goodness-of-fit measure and regional quantile estimation. The study shows regional frequency can be used to give reliable quantile estimation using available scrutinized neighborhood historical data
本文首先将一种广泛应用于陆地水文学且能够很好概括水文资料统计性质的统计方法-线性矩理论引入到海洋水文分析领域。使用Monte-Carlo模拟对线性矩方法在参数估计方面的表现与经典的三种估计方法进行了对比,讨论了四种方法在参数估计中的不确定性。模拟认为线性矩方法在小样本的参数估计方面有良好的无偏性和样本变异性,并且在估计多参数模型时的计算量方面远小于传统的矩方法和极大似然估计方法。
本文第二部分从数理统计的角度讨论了极值波高推算的方法和各种模型的理论基础,应用特点及适用范围。使用线性矩方法分别结合两种常用的随机波浪长期统计方法(过阈极值法和年度极大值法)分析美国沿岸站点的实测数据和我国秦皇岛历史波浪数据,并对线性矩方法估计得到的结果同传统的经验适线方法的结果进行了对比。认为线性矩方法可以应用在对应重现期特征波高的计算。
推求多年一遇的设计波高时需要大量的实测数据作为统计分析工作的基础,而在实际工程中某些站点缺少充分的信息,以至于不足以确定罕遇事件的频率。基于线性矩的区域频率分析方法的基本思想是利用不同站点的水文信息,以空间替代时间,来弥补单站记录的短缺。本文的第三部分通过对北美洲加利福尼亚海域的实际观测数据进行近岸波浪区域频率分析。具体内容包括:数据甄别、区域一致性检验、统计模型选取与拟和、各站区域频率分位数推求。将区域分析结果与单测站估计结果进行了对比。研究认为,经过检验满足数据一致性的区域可以使用该方法弥补数据的稀缺。
The determination of the significant wave heights should be considered while the engineers deal with some coastal engineering problems such as erosion control, scour protection, foundation, environmental and marine structures. The extreme wave heights play an important role in the design of the marine structures in both safety and economics. The uncertainty analysis is conducted in the process of designing the extreme wave height by different stochastic analysis model and parameter estimation method. An regional frequency analysis based on L-moments is introduced to estimate the extreme wave height.
L-moments are linear combinations of order statistics, which are robust to outliers and virtually unbiased for small samples, making them suitable for frequency analysis, including identification of distribution and parameter estimation. It is introduced to the coastal engineering field. A Monte-Carlo simulation is conducted to analyze and compare the parameter estimation performance of four estimation methods. L–moments is unbiased and has the smallest variations in small sample among the four methods.
The theoretical background and scope of various common stochastic models are discussed in the second chapter. L-moments is applied to estimate the extreme wave heights using the data of California coastline from NDBC and historical field measure data from Qinghuangdao port. The difference between two models (Peak over threshold and Annual Maximum) are discussed.
Enough historical information is of vital importance to the accuracy of the extreme wave height design. However, in practice, the record length is not long enough to give assuring estimation. Regional frequency is a way using the nearby information to add the record length of the interest site. Significant wave height data of 7 California coastline stations are used to perform the regional frequency analysis, including discordancy measure, heterogeneity measure, goodness-of-fit measure and regional quantile estimation. The study shows regional frequency can be used to give reliable quantile estimation using available scrutinized neighborhood historical data
引文
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[2] Graham,C.g., 1982, Problem with the design statistical approach in extreme value analysis of directional wind and wave data, Wave and wind directionality apply. To the sdesign of structures, pp 379-401
[3] Hald, A., 1952. Statistical Theory with Engineering Applications, John Wiley and Sons, Inc., New York.
[4] Benjamin, J.R., and Cornell, C.A., 1970. Probability, Statistics and Decision for Civil Engineers,McGraw-Hill, Inc.
[5] Ang, A.H.S., and Tang, W.H., 1990. Probability concepts in engineering, planning and design, Volume II, Decision, risk and reliability.
[6] Bernier, J., 1987. Elements of Bayesian analysis of uncertainty in hydrological reliability and risk models, Engineering reliability and risk in water resources, Ed. Duckstein, L., and Plate, E.J.,NATO ASI series, No. 124, p.405-423.
[7] Bernier, J., 1993. Estimation of uncertainties for design extreme values of waves and sea level,Reliability and Uncertainty Analyses in Hydraulic Design, p.179-189.
[8] Goda, Y., 1988. On the methodology of selecting design wave height, Coastal Engineering, pp.899-913.
[9] Goda, Y., 1992. Uncertainty of design parameters from viewpoint of extreme statistics, Journal of Offshore-Mechanics-and-Arctic-Engineering, v 114 n 2 May 1992, p 76-82.
[10] Andrew, M.E., and Hemsley, J.M., 1990. Resampling approach to extreme wave-height analysis, Journal of Waterway, Port, Coastal and Ocean Engineering, Vol. 116, No. 4, July-August 1990, pp. 444-458.
[11] De Groot, M.B., Luger, H.J., and Voortman, H.G., 1996. Description of failure modes, DelftGeotechnics, Delft University of Technology, Technical Report, MAST-III/PROVERBS, Delft.
[12] Vrouwenvelder, A.C.W.M., 1997. Project Onzekerheidsanalyse Mechanisme Overslag/ Overloop (Project Uncertainty-analysis (in Dutch). Delft: TNO 97-CON-R0935.
[13] Slijkhuis, K.A.H., Van Gelder, P.H.A.J.M., Vrijling, J.K., and Vrouwenvelder, A.C.W.M., 1999. On the lack of information in hydraulic engineering models, In: Safety and Reliability, Vol. 1, pp.713-718.
[14] P.H.A.J.M. Van Gelder PhD Dissertation. TU Delft, Faculty of Civil Engineering.
[15] Guedes Soares, C., and Henriques, A.C., 1996.Statistical uncertainty in long-term distributions ofsignificant wave height, Journal of Offshore Mechanics and Arctic Engineering, Vol. 118, pp.284-291, November 1996.
[16] Guedes Soares C. and M. Scotto. Modelling uncertainty in long-term predictionsof significant wave height, Ocean Engineering 28 (2001) 329 - 342
[17] Le Mehaute, B., and Wang, S., 1985. Wave statistical uncertainties and design of breakwater, WaterResources Research, sept.1985.
[18] 王超,刘德辅,设计波浪中的不确定性研究 海洋学报,1999.11,13(6).874-881
[19] Longuet-Higgens, M.S., 1952. On the statistical distribution of the heights of sea waves. Journal ofMarine Research, Vol. XI, No. 3, p.245.
[20] Van Gelder, P.H.A.J.M., and Vrijling, J.K., 1999. On the distribution function of the maximum wave height in front of reflecting structures,Coastal Structures, Santander, June 7-10,1999.
[21] Rodriguez, G., Guedes Soares, C., and Machado, U., 1999. Uncertainty of the sea state parameters resulting from the methods of spectral estimation. Ocean Engineering, 26, pp. 991-1002.
[22] 俞聿修. 随机海浪及其工程应用. 大连:大连理工大学出版社. 2000
[23] Jurjen A. Battjes and Heiko W. Groenendijk. Wave height distributions on shallow foreshores Coastal Engineering 40 2000 161–182 (2000)
[24] Green, M.O., 1994. Wave-height distribution in storm sea: effect of wave breaking. Journal of Waterway, Port, Coastal and Ocean Engineering. Vol. 120, No. 3,May/June 1994.
[25] Battjes, J.A., 1970. Long-term wave height distributions at seven stations around the British isles, NIO Report No. 44, National Institute of Oceanography, UK.
[26] Teng, C.-C., Timpe, G.L., Palao, I.M., and Brown, D.A., 1993. Design waves and wave spectra for engineering applications, WAVES '93, pp. 993-1007.
[27] Teng, C.-C., and Palao, I.M., 1996. Wave height and period distributions from long-term wave measurement, Coastal Engineering, pp.368-379.
[28] Goda, Y., and Kobune, K., 1990. Distribution Function Fitting for Storm Wave Data, Proceedings of the International Conference on Coastal Engineering, Delft, The Netherlands.
[29] Rossouw, J., 1988. Design waves and their probability density functions, Coastal Engineering, pp.822-834.
[30] Van Vledder, G., Goda, Y., Hawkes, P., Mansard, E., Martin, M.J., Mathiesen, M., Peltier, E., and Thompson, E., 1993. Case studies of extreme wave analysis: a comparitive analysis. In:WAVES'93, pp. 978-992.
[31] Burcharth, H.F., and Liu, Z., 1994. On the extreme wave height analysis, In Port and Harbour Research Institute, Ministry of Transport, editor, International Conference on Hydro-Technical Engineering for Port and Harbor Construction (Hydro-Port), Yokosuka, Japan, 1994, pages 123-142, Yokosuka: Coastal development Institute of Technology.
[32] Mathiesen, M., Goda, Y., Hawkes, P.J., Mansard, E., Martin, M.J., Peltier, E., Thompson, E.F., and Van Vledder, G., 1994. Recommended practice for extreme wave analysis, Journal of Hydraulic Research, Vol. 32, No. 6, pp.803-814.
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