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本帖最后由 hillside 于 2013-12-24 19:25 编辑
集对分析（Set Pair Analysis(SPA) ，发明人：赵克勤教授）作为一种数学方法，在水文学等多个领域已有不少应用，在气象领域的应用也有增加。
比如下面的文献所示： 不确定性理论——集对分析在MOS概率天气预报中的应用 王国强
《浙江气象科技》 1999年01期
【摘要】：概率天气预报的关键问题之一是天气预报的不确定性,而集对分析(SPA)为研究天气预报的不确定性问题提供了新的思路和途径。本文针对概率天气预报的特点,应用SPA中联系度的概念,对数值预报产品的预报因子设立中相关概率区间,进行同异反分析,建立了基于SPA的MOS概率天气预报模型。试验表明,联系度概念的引进增强了概率天气预报模型结构的合理性,提高了用数值预报产品制作概率天气预报的准确率。
【作者单位】： 浙江省绍兴市气象台
【关键词】： 概率天气预报 不确定性 集时分析 联系度
天气预报多元回归模型中模糊因子的集对分析
王国强 赵克勤 郑选军
《科技通报》 2004年02期
【摘要】：天气预报模型中的预报因子一般都有较好的预报能力,因为它们是根据预报对象的特点、预报因子的物理意义和预报经验,使用一定的技术方法而精心筛选的.但是预报因子在每次天气预报中的性能表现有清晰和模糊之分.从集合预报和近邻估计两种方法的基本思路出发,定义了描述因子模糊性的统计量———变异系数,并用此来识别多元回归模型中的模糊因子;从集对分析的基本理论出发,推导了适合于多元回归分析的联系度公式,并借此来处理模糊因子.在此基础上建立基于集对分析的天气预报多元回归模型,比传统模型明显地提高了天气预报准确率.
【作者单位】： 浙江省绍兴市气象台 浙江省诸暨市联系数学研究所 浙江省绍兴市气象台
【关键词】： 大气科学 天气预报 多元回归 模糊因子 集对分析
秩次集对分析（Rank-Set Pair analysis）是集对分析的一种改进之一，下面附录一位网友自编的计算秩次的程序。
A small matlab program
http://hesiweide.blog.163.com/bl ... 738201162093053263/
2011-07-20 21:47:20| 分类： Technique | 标签：matlab rank-set pair analys rank
Yesterday, I encountered a problem, rank-set pair analysis, a method was used to predict future. The principle of this method is very simple; the main problem in implementing is the calculated amount. Because there is no formed source code to use, I have to write it myself. Unfortunately, I have little experience in programming, so the program below cost a day time. To my delight, it is work.
This program is used to make a rank transform, which is a part of Rank sum test, also knowing as Wilcoxon and Wallis test in statistics.
b=[1 1 1 8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 1]; % the array you want to test!
[rank_b,index]=sort(b);
rank=1:length(b);
k=0;
i=2;
while i<=length(b)
if(rank_b(i)~=rank_b(i-1))
i=i+1;
else
k=length(find(rank_b==rank_b(i)));
sum=0;
if i+k-2<=length(b)
for n=i-1:i+k-2
sum=sum+rank(n);
end
ave=sum/k;
end
if i+k-2<=length(b)
for n=i-1:i+k-2
rank(n)=ave;
end
disp(k)
i=i+k-1;
disp(i)
end
end
end
disp(rank_b)
disp(rank) % the rank we obtain
经测试，以上程序的运行结果为（已将上述计算秩次的程序存为MATLAB文档，见附件）： 4
5
8
13
8
21
Columns 1 through 12
1 1 1 1 8 8 8 8 8 8 8 8
Columns 13 through 20
10 10 10 10 10 10 10 10
Columns 1 through 7
2.5000 2.5000 2.5000 2.5000 8.5000 8.5000 8.5000
Columns 8 through 14
8.5000 8.5000 8.5000 8.5000 8.5000 16.5000 16.5000
Columns 15 through 20
16.5000 16.5000 16.5000 16.5000 16.5000 16.5000
附1：一篇关于秩次集的论文（ 从网址名称看，应系作者南卓铜 ，下面的“Download the paper”链接由原作者提供 ） http://nanzt.info/tag/hydrology
[1] He S, Nan Z. Application of Rank Set Pair Analysis Method to Predicting Groundwater Dynamics[J]. 2013, 45(S2): 55—60.[何思为，南卓铜. 使用秩次集对方法预测地下水位动态变化[J]. 四川大学学报(工程科学版). 2013, 45(S2): 55—60.]
附2：来自网络的一篇使用秩次集对分析的论文
《基于秩次集对分析的年径流预测模型》
摘要： 简要介绍了集对分析原理,提出了秩次集对预测模型.以岷江紫坪铺站多年径流资料对秩次集对模型的预测效果进行了验证,并与自回归模型和BP模型的预测结果进行了对比.比较结果表明:以相对误差e≤20%合格为标准,秩次集对模型的预测合格率为100%,而自回归模型和BP模型的预测合格率为93.3%.此外,秩次集对模型原理清晰,计算简单,预测精度较高.
附3：一篇用集对分析法研究极端气温的论文
http://www.hindawi.com/journals/mpe/2013/516150/（该网页提供全文下载。附件为已下载的论文）
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 516150, 7 pages
http://dx.doi.org/10.1155/2013/516150Research Article
Set Pair Analysis Based on Phase Space Reconstruction Model and Its Application in Forecasting Extreme TemperatureYin Zhang,1 Xiao-hua Yang,2 Ling Zhang,3 Wan-ying Ma,1 and Ling-xia Qiao1
1School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
2State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875, China
3Department of Mathematics and Statistics, Auburn University, Auburn, AL 36832, USA Received 3 June 2013; Revised 16 July 2013; Accepted 19 July 2013 Academic Editor: Ming Li Copyright © 2013 Yin Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
AbstractIn order to improve the precision of forecasting a time series, set pair analysis based on phase space reconstruction (SPA-PSR) model is established. In the new model, by using chaos analysis, we reconstruct the phase space with delay time and embedding dimension. Based on it, we rebuilt history sets and current sets in the SPA-PSR model. Two cases of forecasting extreme temperature in Mount Wutai and Datong are taken to examine the performance of SPA-PSR model. The results indicate that the mean relative error (MRE) of SPA-PSR model has decreased by 65.97%, 59.32%, and 7.79% in the case of Mount Wutai and 29.11%, 32.82%, and 9.03% in the case of Datong, respectively, compared with autoregression (AR) model, rank set pair analysis (R-SPA) model, and Back-Propagation (BP) neural network model. It gives a theoretical support for set pair analysis and improves precision of numerical forecasting.
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发表于 2013-12-24 13:29:39
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