利用局部灵敏度分析方法和Morris全局灵敏度分析方法,分析了二维瞬时投源河流水质模型方程解析解输入参数的误差对计算结果的影响程度,分别对模型方程输入参数的灵敏度进行计算并比较,讨论了单参数及多个参数相互作用下的系统扰动对污染物浓度计算结果的影响;绘制了局部灵敏度分析法下各参数的灵敏度变化曲线。灵敏度分析结果显示:二维河流水质模型方程解析解对不同参数的敏感程度不同,其中河流的平均流速最为灵敏,而污水排放点的位置坐标的灵敏性最弱;各参数间存在着相互作用,各参数灵敏度大小顺序为|Su|>|SDy|>|Sy0|>|Sx0|,但定量地分析各参数的灵敏度值却是不同的,Morris全局灵敏度分析方法综合考虑了多个参数间的相互作用,故其结果较局部灵敏度法更为可靠,更能反映实际情况。
Abstract
The influences of input parameter errors on the calculation result of 2-D river water quality model were analyzed using local sensitivity analysis and Morris global sensitivity analysis respectively. The sensitivity of analytical solution to input parameters were calculated and compared; the influence of system disturbance on calculated results of pollutant concentration under the action of single parameter or multiple parameters was analyzed. Furthermore, curves of sensitivity obtained from local sensitivity analysis method were given. The results reveal that the sensitivities to parameters were different: the average flow velocity of river is the most influential, whereas the location of pollutant discharge has the weakest influence on pollutant concentration. The sensitivity of calculation result to parameters follows the order of |Su|>|SDy|>|Sy0|>|Sx0|. Besides, the sensitivity calculated by local analysis under the changes of single parameter is different from that by Morris global analysis. Morris global analysis considers the interaction among multiple parameters, therefore is more reliable than local analysis and better reflects the real situation.
关键词
局部灵敏度分析 /
全局灵敏度分析 /
二维河流水质模型 /
解析解 /
相对误差 /
灵敏度
Key words
local sensitivity analysis /
global sensitivity analysis /
2-D model of river water quality /
analytical solution /
relative error /
sensitivity
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参考文献
[1] 金士博,杨汝均,侯然杰.水环境数学模型[M].北京:中国建筑工业出版社,1987.
[2] 项彦勇.地下水力学概论[M].北京:科学出版社,2011:231-232.
[3] SRIVASTAVA K, SERRANO S E. Uncertainty Analysis of Linear and Nonlinear Groundwater Flow in a Heterogeneous Aquifer[J]. Journal of Hydrologic Engineering, 2007, 12(3): 306-318.
[4] LIU Y, SUN A Y, NELSON K, et al. Could Computing for Integrated Stochastic Groundwater Uncertainty Analysis[J]. International Journal of Digital Earth, 2013, 6(4): 313-337.
[5] 郭建青,李云峰,钱 会.一维河流水质方程解析解性态的初步分析[J].水文,1999,8(6):30-33.
[6] 封建湖,车刚明,聂玉峰.数值分析原理[M].北京:科学出版社, 2001.
[7] 束龙仓,王茂枚,刘瑞国,等.地下水数值模拟中的参数灵敏度分析[J].河海大学学报(自然科学版),2007,35(5):491-495.
[8] 束龙仓,朱元生.地下水资源评价中的不确定因素分析[J].水文地质工程地质,2000, 27(6): 6-8.
[9] 徐爱兰,姚 琪,王 鹏,等.基于太湖数字流域系统的水质模型参数灵敏度分析[J].水利科技与经济,2007,13(1):17-19.
[10]SALTELLI A, CHAN K, SCOTT M,et al. Sensitivity Analysis, Probability and Statistic Series[M]. New York: John Wiley & Sons, 2000: 41-47.
[11]CROSETTO M, TARANTOLA S. Uncertainty and Sensitivity Analysis: Tools for GIS-Based Model Implementation[J]. International Journal of Geographical Information Science, 2001, 15(5): 415-437.
[12]孟宪萌,田富强.越流区承压含水层特殊脆弱性评价模型的参数灵敏度分析[J].水利发电学报,2011,30(4):49-55.
[13]HAMBY D M. A Comparison of Sensitivity Analysis Techniques[J]. Health Physics, 1995, 68(2): 195-204.
[14]MCKAY M D, BECKMAN R J, CONOVER W J. A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code[J]. Technometrics, 1979, 21(4): 239-245.
[15]MORRIS M D. Factorial Sampling Plans for Preliminary Computational Experiments[J]. Technometrics, 1991, 33(2):161-174.
[16]SOBOL I M. Sensitivity Estimates for Nonlinear Mathematical Models[J]. Mathematical Modeling Computational Experiments,1993,1(4): 407-414.
[17]郭建青,李 彦,王洪胜,等.分析二维河流水质试验数据的相关系数极值法[J].水利发电学报,2010,29(4):102-106.
[18]张红菲.基于小生境蚁群算法的水质模型参数反演研究[D].哈尔滨:哈尔滨工业大学,2012.
[19]魏亚妮.第一类越流系统井流非理性条件的影响研究[D].西安:长安大学,2012.
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