一种改进投影寻踪风险评估函数模型
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摘要
针对投影寻踪模型存在的一些不足之处,改进发展了一种基于信息熵理论的投影寻踪风险评估模型.首先基于极差正规化方法对指标进行预处理以消除指标的量纲效应,保持指标的同趋势化.其次采用投影值的信息熵表示投影指标函数,基于最大熵原理估计最佳投影方向对指标进行降维处理,克服了传统投影指标函数在某些情形下无法准确刻画序列的变异程度.最后建立了S型风险评估函数模型,该函数具备单调性、有界性、变化的连续平稳性等性质.借助洪灾风险和联合作战海洋环境风险的评估实验得到的研究结果如下:与投影寻踪模型相比,改进投影寻踪模型对洪灾风险等级评估的改进幅度为7.0%～8.8%,对海洋环境风险评估的改进效果更加明显,改进幅度为27.1%～53.9%.
A model of project pursuit risk assessment is developed based on information entropy theory for dealing with the weakness of current project pursuit model. First, range normalization is performed to remove dimensional effect and keep the same trend for indicators. Second, the entropy of the projection value, which cannot describe sequence variations under some situations quantitatively, is applied to express the projection index function,and the optimal projection direction is estimated by the maximum entropy principle for dimension reduction. Finally, an S type risk assessment model is built and it characterized from the aspects of monotonicity, boundness, and continuous and smooth change. Two experiments about flood risk and marine environmental risk have been made. The results show that our model can improve the result of the project pursuit by between 7.0% and8.8% for the flood risk, and have an evident improvement by between 27.1% and 53.9% for the marine environmental risk.
A model of project pursuit risk assessment is developed based on information entropy theory for dealing with the weakness of current project pursuit model. First, range normalization is performed to remove dimensional effect and keep the same trend for indicators. Second, the entropy of the projection value, which cannot describe sequence variations under some situations quantitatively, is applied to express the projection index function,and the optimal projection direction is estimated by the maximum entropy principle for dimension reduction. Finally, an S type risk assessment model is built and it characterized from the aspects of monotonicity, boundness, and continuous and smooth change. Two experiments about flood risk and marine environmental risk have been made. The results show that our model can improve the result of the project pursuit by between 7.0% and8.8% for the flood risk, and have an evident improvement by between 27.1% and 53.9% for the marine environmental risk.
引文
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[15]钱龙霞,王红瑞,蒋国荣,俞淞.基于Logistic回归和NFCA的水资源供需风险分析模型及其应用[J].自然资源学报,2011, 26(12):2039-2049.Qian L X, Wang H R, Jiang G R, Yu S. Model for risk analysis between supply and demand of water resources based on logistic regression and NFCA and its application[J]. Journal of Natural Resources, 2011, 26(12):2039-2049.(in Chinese)
[16]金菊良,张欣莉,丁晶.评估洪水灾情等级的投影寻踪模型[J].系统工程理论与实践,2002, 22(2):140-144.Jin J L, Zhang X L, Ding J. Projection pursuit model for evaluating grade of flood disaster loss[J]. Systems Engineering-Theory&Practice, 2002, 22(2):140-144.(in Chinese)
[17]张明,金菊良,张礼兵.流域可持续评价的最大熵原理——投影寻踪偶尔模型[J].地理科学,2007,27(2):177-181.Zhang M, Jin J L, Zhang L B. Pursuit projection evaluation model based on principle of maximum entropy for river basin sustainability evaluation[J]. Scientia Geographic Sinica, 2007,27(2):177-181.(in Chinese)
[18]任若恩,王惠文.多元统计数据分析——理论、方法、实例[M].北京:国防工业出版社,1998:109-113, 149-163.
[19]李炳军,朱春阳,周杰.原始数据无量纲化处理对灰色关联排序的影响[J].河南农业大学学报,2002,32:199-202.Li B J, Zhu C Y, Zhou J. Effects of non-dimensional quantities of the original data on grey incidence order[J]. Journal of Henan Agricultural University, 2002, 32:199-202.(in Chinese)
[20] Friedman J H, Tukey J W. A projection pursuit algorithm for exploratory data analysis[J].IEEE Transactions on Computer, 1974, 23(9):881-890.
[21]吴乃龙,袁素云.最大熵方法[M].长沙:湖南科学技术出版社,1991.
[22]李安贵,张志宏,孟艳,顾春.模糊数学及其应用[M].北京:冶金工业出版社,1991.
[23]蒋金才,季新菊.河南省1950—1990年水旱灾害分析[J].灾害学,1996, 11(4):69-73.Jiang J C, Ji X J. Analysis on the flood and drought disaster from 1950 to 1990 in Henan Province[J]. Journal of Catastrophology, 1996, 11(4):69-73.(in Chinese)
[2] Wu W Y, Yin S Y, Liu H L. Groundwater vulnerability assessment and feasibility mapping under reclaimed water irrigation by a modified drastic model[J]. Water Resources Management,2014, 28(5):1219-1234.
[3] Xie Y L, Xia D H, Huang G H, Li W, Xu Y. A multistage stochastic robust optimization model with fuzzy probability distribution for water supply management under uncertainty[J].Stochastic Environmental Research and Risk Assessment, 2017, 31(1):125-143.
[4]刘思峰,蔡华,杨英杰,曹颖.灰色关联分析模型研究进展[J].系统工程理论与实践,2013, 33(8):2041-2046.Liu S F, Cai H, Yang Y J, Cao Y. Advance in grey incidence analysis modelling[J]. Systems Engineering-Theory&Practice 2013, 33(8):2041-2046.(in Chinese)
[5] Qian L X, Wang H R, Zhang K N. Evaluation criteria and model for risk between water supply and water demand and its application in Beijing[J]. Water Resources Management, 2014, 28(13):4433-4447.
[6] Qian L X, Zhang R, Hong M, Wang H R, Yang L Z. A new multiple integral model for water shortage risk assessment and its application in Beijing, China[J]. Nat Hazards, 2016, 80(1):43-67.
[7]张晓慧,冯英浚.一种非线性模糊综合评价模型[J].系统工程理论与实践,2005, 25(10):54-59.Zhang X H, Feng Y J. A nonlinear fuzzy comprehensive assessment model[J]. Systems Engineering-Theory&Practice, 2005, 25(10):54-59.(in Chinese)
[8]张晓慧,冯英浚,白莽.一种反映突出影响因素的评价模型[J].哈尔滨工业大学学报,2003, 35(10):1168-1170.Zhang X H, Feng Y J, Bai M. Evaluation model for reflection of dominant influencing factors[J]. Journal of Harbin Institute of Technology, 2003, 35(10):1168-1170.(in Chinese)
[9]侯定丕,王战军.非线性评估的理论探索与应用[M].合肥:中国科学技术大学出版社,2001.
[10]钱龙霞,张韧,王红瑞,洪梅.基于MEP和DEA的水资源短缺风险损失模型及其应用[J].水利学报,2015, 46(10):1199-1206.Qian L X, Zhang R, Wang H R, Hong M. A model for water shortage risk loss based on MEP and DEA and its application[J]. Journal of Hydraulic Engineering, 2015, 46(10):1199-1206.(in Chinese)
[11]黄明聪,解建仓,阮本清,汪雅梅.基于支持向量机的水资源短缺风险评价模型及其应用[J].水利学报,2007, 38(3):255-259.Huang M C, Xie J C, Ruan B Q, Wang Y M. Model for assessing water shortage risk based on support vector machine[J]. Journal of Hydraulic Engineering, 2007, 38(3):255-259.(in Chinese)
[12]张韧,徐志升,洪梅,黄志松.基于不完备数据样本的联合作战大气——海洋环境风险决策[J].军事运筹与系统工程,2009, 23(1):48-52.Zhang R, Xu Z S, Hong M, Huang Z S. Atmospheric marine environmental risk decision—making of joint operations based on incomplete data[J]. Military Operations Research and Systems Engineering, 2009, 23(1):48-52.(in Chinese)
[13]王红瑞,钱龙霞,许新宜,王岩.基于模糊概率的水资源短缺风险评价模型及其应用[J].水利学报,2009, 40(7):813-821.Wang H R, Qian L X, Xu X Y, Wang Y. Model for evaluating water shortage risk based on fuzzy probability and its application[J]. Journal of Hydraulic Engineering, 2009, 40(7):813-821.(in Chinese)
[14]邹君,杨玉蓉,谢小立.地表水资源脆弱性:概念、内涵及定量评价[J].水土保持通报,2007, 27(2):132-135.Zou J, Yang Y R, Xie X L. Concepts of vulnerability of surface water resources and its quantitative assessment[J]. Bulletin of Soil and Water Conservation, 2007, 27(2):132-135.(in Chinese)
[15]钱龙霞,王红瑞,蒋国荣,俞淞.基于Logistic回归和NFCA的水资源供需风险分析模型及其应用[J].自然资源学报,2011, 26(12):2039-2049.Qian L X, Wang H R, Jiang G R, Yu S. Model for risk analysis between supply and demand of water resources based on logistic regression and NFCA and its application[J]. Journal of Natural Resources, 2011, 26(12):2039-2049.(in Chinese)
[16]金菊良,张欣莉,丁晶.评估洪水灾情等级的投影寻踪模型[J].系统工程理论与实践,2002, 22(2):140-144.Jin J L, Zhang X L, Ding J. Projection pursuit model for evaluating grade of flood disaster loss[J]. Systems Engineering-Theory&Practice, 2002, 22(2):140-144.(in Chinese)
[17]张明,金菊良,张礼兵.流域可持续评价的最大熵原理——投影寻踪偶尔模型[J].地理科学,2007,27(2):177-181.Zhang M, Jin J L, Zhang L B. Pursuit projection evaluation model based on principle of maximum entropy for river basin sustainability evaluation[J]. Scientia Geographic Sinica, 2007,27(2):177-181.(in Chinese)
[18]任若恩,王惠文.多元统计数据分析——理论、方法、实例[M].北京:国防工业出版社,1998:109-113, 149-163.
[19]李炳军,朱春阳,周杰.原始数据无量纲化处理对灰色关联排序的影响[J].河南农业大学学报,2002,32:199-202.Li B J, Zhu C Y, Zhou J. Effects of non-dimensional quantities of the original data on grey incidence order[J]. Journal of Henan Agricultural University, 2002, 32:199-202.(in Chinese)
[20] Friedman J H, Tukey J W. A projection pursuit algorithm for exploratory data analysis[J].IEEE Transactions on Computer, 1974, 23(9):881-890.
[21]吴乃龙,袁素云.最大熵方法[M].长沙:湖南科学技术出版社,1991.
[22]李安贵,张志宏,孟艳,顾春.模糊数学及其应用[M].北京:冶金工业出版社,1991.
[23]蒋金才,季新菊.河南省1950—1990年水旱灾害分析[J].灾害学,1996, 11(4):69-73.Jiang J C, Ji X J. Analysis on the flood and drought disaster from 1950 to 1990 in Henan Province[J]. Journal of Catastrophology, 1996, 11(4):69-73.(in Chinese)