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Hans Journal of Data Mining 数据挖掘, 2013, 3, 1-5 doi:10.12677/hjdm.2013.31001 Published Online January 2013 (http://www.hanspub.org/journal/hjdm.html)

City Atmospheric Quality Optimal Assessment Based on Combined Model*
Li Xiao, Xianghong Hu, Guoquan Zhang
College of Science, South China Agricultural University, Guangzhou Email: scauxl@tom.com Received: Oct. 9th, 2012; revised: Oct. 30th, 2012; accepted: Nov. 7th, 2012

Abstract: This paper puts forward a new atmospheric quality assessment method that is, according to the combinatorial theories, using Goodness of Fit method to get weights to combine three models which are air pollution index method, cloud model and Projection Pursuit Grade method. The combined model is applied to the Hong Kong atmospheric quality assessment; the results show the method increases the evaluation performance, possesses more reliability and comprehension, and provides a new idea for the city atmospheric quality synthetically assessment. Keywords: Combined Model; Atmospheric Quality; Assessment

基于组合模型的城市空气质量评价优化法*
肖 莉,胡湘红,张国权

华南农业大学理学院,广州 Email: scauxl@tom.com 收稿日期:2012 年 10 月 9 日;修回日期:2012 年 10 月 30 日;录用日期:2012 年 11 月 7 日



要:本文提出一种新的空气质量评价方法,即应用组合原理,以拟合优度法确定权重组合三个模型(API 法,

云模型及粒子群投影寻踪法),并将之应用于香港空气质量评价中,实例表明该方法增加了评价性能,具有较强 的可靠性和全面性,为城市空气质量综合评价方法提供了一种新思路。 关键词:组合模型;空气质量;评价

1. 引言
我国正处于工业化和城市化发展的快速时期,而 环境质量仍在不断恶化,尤其是近年以来,由于经济 持续高速增长,使得环境压力明显增大,长期积累的 环境风险开始出现。在诸多环境问题中,空气污染造 成的损失尤其巨大,空气质量的控制成为各国环保机 构面临的一个重要课题,然而,要合理控制空气质量 的恶化,首先得对空气质量做出科学的评价,只有这 样才能有针对性的进行改善。目前国内外关于空气质 量评价方法的研究十分活跃,除了常用的方法如空气
*

污染指数法(Air Pollution Index,简称 API 法)、人工 神经元网格法、模糊聚类法、主成分分析法、灰色系 随着一些新学科的创立和计算技 统分析法[1-4]等之外, 术的发展,又有多种大气环境质量分析与评价的新方 法,如云模型法[5,6]、投影寻踪分析法[7,8]等。 然而由于大气环境系统是一个包括随机性、模糊 性、灰色性和不相容性等多种不确定性信息的系统, 因此,在实际应用中,仅采用上述单一的理论或分析 工具处理环境信息具有一定的局限性,此外,在选择 了某种方法后,不可避免的会丢失另外一些有用信 息,从而导致评价误差相对较大[9]。为了尽可能多地 利用有用信息,1969 年 J. N. Bates 和 C. W. J. Granger
1

基金项目:广东省自然科学基金项目(S2011010002371)。

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基于组合模型的城市空气质量评价优化法

在运筹学季刊中,提出了“组合预测”的思想。根据 组合定理,即使一个评价结果不理想的方法,如果它 含有系统的独立信息,当与另一个较好的评价方法进 因此, 行组合后, 同样可以增加系统的评价性能[10,11]。 组合评价能够更大化地利用有用信息,比单一评价方 法更为科学、有效。本文采用 API 指数、雷达图面积 –云模型评价和粒子群投影寻踪这 3 种方法分别对城 市空气质量进行评价,再运用组合原理,利用拟合优 度法确定权重,结合上述三种方法构建组合模型来综 合反映城市空气质量。

Ii 

Ci  Ci , j Ci , j 1  Ci , j

  I i , j 1  I i , j   I i , j

(1)

i  1, 2, , n; j  1, 2, , m
计算(1)式时, I i , j , I i , j 1 , Ci , j , Ci , j 1 等 4 个参 数值可通过查表 1 得到。 当 Ci  Ci , m 时,选择点  Ci , m 1 , I i , m 1  及点

C

i,m

, I i , m  来确定线性函数,其分指数为:

Ii 

Ci  Ci , m 1 Ci , m  Ci , m 1

  I i , m  I i , m 1   I i , m 1

(2)

2.1.2. 确定空气污染指数及首要污染物 当各种污染物的污染分指数计算出后,按下列公 式确定 API:

2. 研究方法
2.1. API 评价模型
空气污染指数(AIR POLLOTION INDEX,简称 API)是将环境保护署在每个空气质量监测站所录得 的空气污染物含量,如 SO2、可吸入悬浮粒子、NO2、 CO、O3,转化为一个简单易明的数字,其数值由 0 至 500 不等,并分级表征空气质量状况与空气污染的 程度,结果简明直观,使用方便,适用于表示城市的 空气质量状况和变化趋势。 2.1.1. 计算各污染物的污染分指数 各项污染物的分指数 I i ,由实测的污染物浓度值 j 个转折点  Ci , j , I i , j  的污染分指数和相应的浓度限值 见表 1。 当第 i 种污染物浓度 Ci , j  Ci  Ci , j 1 时,其分指 数为:
Table 1. Classification for Hong Kong air pollution index and its corresponding pollutant potencies limited value 表 1. 香港空气污染指数分级及对应的污染物浓度限值表
污染水 等级 平 轻微 中等 偏高 甚高 Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ 严重 Ⅵ Ⅶ 相应污染物浓度(微克/立方米) API 指数 可吸入 悬浮粒子 28 55 180 350 420 500 600 SO2 40 80 350 800 1600 2100 2620 NO2 40 80 150 280 565 750 940 CO 7500 15,000 30,000 60,000 90,000 O3 60 120 240 400 800

API  max  I1 , I 2 , I 3 , , I i , , I n 

(3)

即选污染物分指数最大者为该区域空气污染指 数 API ,并确定该污染物为首要污染物。当空气污染 指数 API  50 时,不报告首要污染物。

2.2. 基于雷达图面积的云模型评价
针对空气污染的特点,本文选取雷达图的面积作 为特征量,对多元数据进行融合从而降维,根据云模 型理论的基本特征,  Ex, En, He  三个数字特征来整 用 体表征一个具体概念,结合云模型定性与定量转换思 想进行转换,构造描述空气质量评价所用的语言值。 应用正向云进行空气质量的定量评价,应用逆向云进 行基础指标的定性分析,从而得到符合人类思维方式 的及模糊性与随机性为一体的定性和定量集成的空 气质量综合评价结果。图 1 是基于雷达图的云模型原 理图。

Ci ,按照分段线性方程计算,对于第 i 种污染物的第

25 50 100 200 300 400 500

120,000 1000 150,000 1200

Figure 1. Theory chart of cloud model based on radar chart 图 1. 基于雷达图的云模型原理图

2

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基于组合模型的城市空气质量评价优化法

2.3. 粒子群投影寻踪等级评价模型
投影寻踪(Projection Pursuit,PP)方法能充分利用 高维数据中的所有信息,它利用计算机把高维数据通 过某种组合,投影到低维子空间上,以达到研究和分 析高维数据的目的[12,13]。传统的投影寻踪算法常用遗 传算法寻找模型的最优值,但遗传算法实现过程复 杂,并且有多个参数需要调整,而粒子群算法简单、 易于实现,因此本文以粒子群优化算法替代遗传算 法,建立基于粒子群算法的投影寻踪等级评价模型

自身的数据特性寻求最优的投影方向,通过线性投影 计算反映评价样本综合特征信息的投影特征指标,根 据这一指标可以形象、直观地对样本进行分类或评 价,避免了诸如各评价因素权重确定的人为任意性。

API 法、雷达图云模型法、PSO-PPE 法分别考虑
了高值影响与平均影响,部分样本和全体的数据特 征,因此,将这 3 种方法应用组合模型方法进行分析 与评价,可以发挥各模型的优势,避免单一模型在因 素与函数关系方面的弊端,有利于提高评价的准确性 以及反应信息的全面性。 2.4.1. 组合评价模型 经过分析, 可 假设对某一问题有 M 种评价方法, 那么组合 以确定第 i 种方法的权重 wi  i  1, 2, , M  , 模型可表示为:
ˆ Yt   wi yti i 1 M

(PSO-PPE),PSO-PPE 模型建立的流程见图 2。

2.4. 组合评价模型及权重的确定
API 法计算方便,能够直观地显示首要空气污染
物的信息,有利于普通公众了解空气环境质量的优 劣,但该方法片面地重视单一样本数据的最大观测 值,没有考虑不同等级的多种污染物对分类的共同影 响。雷达图可将评价对象的各项指标映射到二维图形 中,直观形象,而云模型方法除能保留传统定性划分 的优点外,也更加符合实际的数据分布和人的思维方 式,雷达图和云模型的结合是一种有效的、可视化的 定性定量相结合的综合评价法,但该方法的缺点是计 算雷达图面积时会导致信息损失较大,确定云的三个 数字特征时主观性太强。粒子群投影寻踪法依据样本

(4)

ˆ 其中, Yt 为第 t 个样本的组合评价值; yti 为第 t 个样

本第 i 种评价模型的评价值,  wi  1 。 i 1

M

2.4.2. 权重的确定 组合模型常用等权组合和不等权组合两种形式, 但实验表明不等权的组合结果较为准确。由于本文三 种评价模型的结果较分散,采用拟合优度法确定权 重。该模型能予以预测标准误差最小的模型以最大的 权重, 使预测结果保证拟合优度, 权重公式定义如下:
M

wi 

 Sei  Sei i 1

 Sei i 1 n i 1

M

1 M 1

(5)

Sei 

  yti  yt  n 1

2

(6)

式中 yt 为第 t 个样本的实际值。

3. 研究结果与分析
3.1. 数据收集
选取 2011 年 1~12 月香港 14 个监测点每天 24 小 时的监测数据,数据来源于香港环保署网站
Figure 2. Flow chart of PSO-PPE model 图 2. PSO-PPE 模型流程图

(http://www.gov.hk/sc/residents/environment/air/api.htm)。
监测的污染物为:SO2、可吸入悬浮粒子、NO2、CO、
3

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基于组合模型的城市空气质量评价优化法
Table 2. Air quality evaluation results from four models for fourteen monitoring points in Hong Kong 表 2. 四个模型对香港 14 个监测点,2011 年 12 月份空气质量评价 结果
API 法 监测点 API 评价值 58 53 57 57 55 56 56 53 62 57 63 102 64 103 污染 等级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅲ级 Ⅱ级 Ⅲ级 云模型 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 PS0-PPE 模型 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅲ级 Ⅱ级 Ⅱ级 Ⅲ级 Ⅱ级 Ⅲ级 组合模型 组合 评价值 2.252 2.252 2.252 2.252 2.252 2.252 2.252 2.252 2.704 2.252 2.252 2.9544 2.7024 2.9544 污染 等级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅱ级 Ⅲ级 Ⅱ级 Ⅱ级 Ⅲ级 Ⅲ级 Ⅲ级

O3,香港空气质量评价标准参见表 1,图 3 是 14 个监
测点的分布图。

3.2. 评价结果
使用组合评价模型时,首先要确定各种方法的权 重,根据表 1,运用 SAS 统计软件随机模拟不同级别 的空气质量污染物浓度样本,以及 API 指数法,云模 型评价法, 粒子群投影寻踪法评价结果, 代入公式(5),
中西区 东区 大浦 葵涌 观塘 沙田 深水涉 塔门 东涌 荃湾 元朗 铜锣湾 旺角 中环站

0.2976, 0.4504)。 得到三个模型的权重分别为(0.2520,
表 2 是香港 2011 年 12 月份 14 个监测点的空气质量 评价结果,图 4 是香港 2011 年 12 月份空气质量监测 预警图。

3.3. 结果分析
从表 2 可知,香港 2011 年 12 月大部分地区空气 质量为Ⅱ级,处于中等水平。同时图 4 显示香港 2011 年 12 月的空气质量一般,污染程度较高,达到Ⅲ级。 结合图 3 和表 2 分析,从香港空气质量的路边检 测站点和香港主要道路交通情况来看,路边检测站有 中环、铜锣湾和旺角,是主要道路密集的地方,实际 污染程度大,而表 2 的结果显示,利用 API 法、云模 处 型和 PS0-PPE 模型评价出旺角的空气质量为Ⅱ级, 于中等水平,这与实际不符合,而组合模型对旺角空 气质量评价的结果为Ⅲ级,处于污染偏高水平,与客 观实际一致。 此外,靠近珠三角的东涌观测站空气质量为Ⅲ 级,污染处于偏高水平;利用 API 法可以分析主要污

Figure 4. Air quality monitoring and warning chart based on combination model in Hong Kong (data used in December, 2011) 图 4. 基于组合模型的香港 2011 年 12 月空气质量监测预警图

染物来源,路边监测点主要以 NO2 为主,其它监测点 主要为可悬浮颗粒。

4. 结论
1) 用拟合优度法确定 API、 雷达图云模型和 PSOPPE 组合模型的权重, 避免了主观确定权重的随意性,
Figure 3. The distribution chart for fourteen air quality monitoring points in Hong Kong 图 3. 香港 14 个空气质量监测点分布图

有效地解决了空气质量污染评价问题,且结果合理, 与实际符合,计算简便。

4

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基于组合模型的城市空气质量评价优化法 taminated soils. Chemosphere, 2008, 18(3): 344-352. 高俊枝, 程鹰. 安徽省宣州市大气环境质量的 API 评价[J]. 安徽师范大学学报(自然科学版), 2000, 23(2): 166-168. 付赟, 方德英. 雷达图法在综合评价中的应用研究[J]. 统计 与决策, 2007, 252(24): 176-178. 邸凯昌, 李德毅, 李德仁. 云理论及其在空间数据发掘和知 识发现中的应用[J]. 中国图像图形学报, 1999, 4(11): 930935. 王顺久, 李跃清. 基于投影寻踪原理的动态聚类模型及其在 气候区划中的应用[J]. 应用气象学报, 2007, 18(5): 722-725. J. H. Friedman, W. Stuetzle. Projection pursuit regression. Journal of the American Statistical Association, 1981, 76(376): 817823. 陈大伟, 李旭宏, 于世军, 朱彦东. 我国城市开发区客运交通 需求预测方法研究[J]. 交通运输系统工程与信息, 2004, 1: 80-83. 张世英, 张文泉, 王京芹. 技术经济预测与决策[M]. 天津: 天津大学出版社, 1996: 9. 刘思峰, 党耀国. 预测方法与技术[M]. 北京: 高等教育出版 社, 2005: 8. 王允良, 李为吉. 粒子群优化算法及其在结构优化设计中的 应用[J]. 机械科学与技术, 2005, 24(2): 248-252. 黄婉平. 自适应粒子群优化算法及其应用研究[D]. 浙江大学, 2006.

2) 应用组合定理, 充分利用已知信息, 提高多因
子综合评价精度,评价结果清楚,反映整体空气质量 的级别和优劣,可相互比较,具有一定的可行性和实 用性。

[4] [5] [6]

3) 本文的组合模型应用于空气质量评价是完全
可行的,不仅可以判定污染的等级,还便于在样本间 进行污染程度的比较,结果与其它方法基本一致,为 城市空气质量的判定提供了新的思路。
[9] [7] [8]

参考文献 (References)
[1] 袁秀娟, 毛显强. 用改进的灰色识别法评价大气环境质量—— 以北京市石景山区为例[J]. 环境科学与技术, 2006, 29(9): 7173. B. Fisher. Fuzzy environmental decision-making: Applications to air pollution. Atmospheric Environment, 2003, 37(14): 18651877. W. X. Li, X.-X. Zhang, B. Wu, et al. A comparative analysis of environmental quality assessment methods for heavy metal-con-

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[2]

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...From an early age I’ve always been deeply interested in computing. It was my dad, introducing me to the computer systems at his work place that first sparked this interest. I can always remember the feeling of wanting to know just how computers worked, why they worked and what else they could do. This interest never left me, only growing more profound and passionate with every new discovery I made. From communicating with an artificial intelligence to seeing the wonders of the Internet for the first time, computers have left me fascinated with just how much power yet mystery they hold. My studies have all helped me to develop my understanding of the subject. While Computing has given me a greater insight into the business aspects of the computer industry, 
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