粒子群算法及神经网络在大气质量评价及预测中的应用
摘要
本文在计算大气污染损害率的普适公式的基础上，采用具有全局搜索功能的PSO算法对该公式中的参数进行优化，得到了对多种大气污染物均适用的具有更强普适性的大气污染损害率计算公式，从而得到了基于PSO的大气质量综合污染损害率评价模型和指数模型。通过实例评价的数值计算结果表明，该评价模型用于对城市大气质量评价具有一定的可行性、有效性，具有一定的实用价值。
1.1计算大气污染损害率的普适公式
第种大气污染物对大气质量的污染损害率可表示为：
（1）
在公式（1）中，ai、bi为与污染物特性有关的待定参数；ci为该污染物的实测浓度。李祚泳将ci用浓度的相对值xi替换，即：xi=ci / ci0，于是公式（1）可表示为：
（2）
其中ci0为设定的i污染物的某一确定值，通常取为其天然本底浓度值，采用相对值后的大气污染损害率计算公式中的参数ai、bi可认为与该污染物的特性无关。因此公式（2）是对于多种污染物均适用的具有普适性的大气污染损害率计算公式。
为了提出一种具有更强的普适性方法，文献[18]又在文献[17]方法的基础上，在公式（2）中引入一个与污染物特性无关的待确定的普适参数c，修正为：
（3）
1.2 PSO算法对参数a、b、c的优化
采用PSO算法优化公式（3）中的参数需要构造的满足问题
的目标函数，即：
（4）
其中，m=7为污染物种类数目；k=5为大气污染分级数目；Rik为i污染物的k级污染损害率，Rke为k级标准的污染损害率目标值。在满足公式（3）的情况下对公式（4）采用PSO算法进行全局优化，但在优化的过程中发现，随着PSO参数取值范围的不同 ，a、b、c值的变化较明显，且参数a无限地趋向于PSO参数取值范围的下限。鉴于以上特点，说明大气污染损害率与污染物的相对浓度之间的函数关系基本上可由两个参数确定。
因此，采用PSO算法对（4）式优化后得到的最优解为：a =63.93, b =0.3401。
故多种大气污染物均适用的具有更强普适性的大气污染损害率计算公式可表示为：
（5）
1.3基于PSO大气质量综合污染损害率评价模型
受多种大气污染物影响的具有普适性的大气质量综合污染损害率计算公式为：
（6）
式中m为污染物的种类数目；Ri为i污染物的污染损害率；为i污染物的归一化相对权值，它由Ri所处的级别相应的k值的相对重要性确定。实际计算时，需根据各污染损害率所处的级别及污染物种类数目将权值wi`归一化为相对权值wi。
1.4 大气污染损害分指数模型
大气污染损害分指数可定义为：
（7）
1.5 基于PSO大气质量综合污染损害指数评价模型
受多种大气污染物影响的具有普适性的大气质量综合污染损
害指数计算公式为：
（8）
式中Ii为第i种污染物损害分指数，wi为i污染物的归一化相对权值，它由Ri所处的级别相应的I值的相对重要性确定。(wi的具体计算方法参见文献[12])
1.6实例评价
在实例1中，本文以某市10个监测点的SO2、NOx和TSP三种污染物的浓度监测值为例，采用基于PSO的 大气质量综合污染损害率评价模型对其进行评价，通过计算得出的综合污染损害率及综合评价结果表明，利用该种评价模型对大气质量进行综合评价，取得了令人满意的结果，具体结果详见表5。
在实例2中，本文根据长春市环境监测中心站提供的数据资料，以大气中的主要污染物：PM10（可吸入颗粒物）、SO2、NO2三种污染物的浓度值为主要监测对象，选取2002年1月1日至2002年3月31日间实际监测的三种主要污染物浓度的数据值作为数据样本，采用基于PSO的大气质量综合污染损害率评价模型对其进行评价，得到的评价结果与实际结果基本吻合。
改进的Elman神经网络在大气污染预测领域的应用
本文利用OIF Elman网络：输出－输入反馈网络（Output-Input Feedback Elman (OIF Elman)）模型对大气污染进行预测，本文的数据样本由长春市环境监测中心站提供，选取2001年12月1日至2002年11月30日连续365日的监测数据为数据样本，以大气中的主要污染物：PM10（可吸入颗粒物）、SO2、NO2三种污染物的浓度值为主要监测对象。为了较好地说明问题，文中均采用误差的平均值。网络的结构均为3-10-1式,即含有3个输入节点，10个隐层节点，1个输出节点的三层网络结构。输入层节点的输入为连续3日污染物浓度的监测值，输出为第4日该污染物浓度的预测值。
数值结果表明OIF Elman网络模型具有极佳的逼近性能，较高的拟合精度, 体现了OIF Elman在大气污染预测领域中的实用性和有效性，具有很好的应用前景。
1. An integrated PSO based model for the evaluation of air quality pollution.
Applied the PSO method with the global searching capability, this paper has optimized the parameters in the generalized formula for air pollution loss rate calculation. Therefore the formula gets more generalizations, namely the integrated PSO based model. Numerical result of examples show that the proposed model has considerable feasibility and effectiveness, and may be applicable practice.
1.1 The generalized formula for the calculation of air quality pollution.
The air pollution loss rate of the ith pollutant could be expressed as:
(1)
where ai and bi are the parameters related to the ith pollutant which are required, and ci the density of the ith pollutant measured in practice. LiZuoyong substituted ci with the relative density, namely xi=ci / ci0, ci0 is a predefined parameter of the ith pollutant, usually take as the natural basic density of the ith pollutant. So Eq. (1) may be rewrited as:
(2)
To strengthen the generalization of the model, QianLianwen introduced an universal parameter c which is required and unrelated to the ith pollutant in Eq. (2). Then Eq. (2) could be rewrited as:
(3) The optimization of parameters by PSO method
An objective function is required when optimizing the parameters of Eq. (3) using PSO method, namely that:
(4)
where m=7 is the number of the selected pollutants; k=5 the number of the air pollution levels; Rik the air pollution loss rate of the ith pollutant for level k, and Rke the objective value of the air pollution loss rate for level k, respectively. In the process of the optimizing of the parameters of Eq. (4) by PSO method, we find that the values of parameter are changed obviously when scope of the parameters of PSO are selected differently. Moreover, the value of a is approached to the lower limit of the selected scope of PSO parameter. According to the above fact, the functional relation to explain the air pollution loss rate and the relative density of pollutants may be decided by two parameters mainly. So the best solution can be achieved by PSO method for Eq. (4), that is a=63.93 and b=0.3401. Then we get the equation as follows:
(5)
1.3. The integrated PSO based model for the evaluation of air quality pollution
The generalized equation with multi-pollutants for synthetical air quality pollution loss rate can be expressed as:
(6)
where m is the number of the kinds of pollutants, Ri the air pollution loss rate of the ith pollutant, wi the normalized weight value of the pollutant defined by the relative importance of the corresponding value of k, respectively.
1.4 The air quality pollution loss index model
The air quality pollution loss index may be defined as:
(7)
1.5 The integrated PSO based loss index model for the evaluation of air quality pollution
The generalized index equation with multi-pollutants
for synthetical air quality pollution loss rate can be expressed as:
(8)
where Ii is the air quality pollution loss index of the ith pollutant, wi the normalized weight value of the pollutant.
1.6 Numerical results
Two examples are executed to test the efficiency of the proposed model in this thesis. For example 1, we take the practical density value of three pollutants, namely SO2, Nox and TSP of ten supervision spots in a city as the input data and evaluate the air quality by the proposed model. Numerical result shows that the model is quite efficient.
For example 2, we take the practical density value of three pollutants, namely PM10, SO2 and NO2 in Changchun from Jan. 1 2002 to Mar. 31 2002 as the input data and evaluate the air quality by the proposed model. Numerical result has a better precision compared with the practical values.
2. The application of OIF Elman neural network model for air pollution forecasting.
Applied the OIF Elman(Output-Input Feedback Elman (OIF Elman)) neural network to foreca
1.1计算大气污染损害率的普适公式
第种大气污染物对大气质量的污染损害率可表示为：
（1）
在公式（1）中，ai、bi为与污染物特性有关的待定参数；ci为该污染物的实测浓度。李祚泳将ci用浓度的相对值xi替换，即：xi=ci / ci0，于是公式（1）可表示为：
（2）
其中ci0为设定的i污染物的某一确定值，通常取为其天然本底浓度值，采用相对值后的大气污染损害率计算公式中的参数ai、bi可认为与该污染物的特性无关。因此公式（2）是对于多种污染物均适用的具有普适性的大气污染损害率计算公式。
为了提出一种具有更强的普适性方法，文献[18]又在文献[17]方法的基础上，在公式（2）中引入一个与污染物特性无关的待确定的普适参数c，修正为：
（3）
1.2 PSO算法对参数a、b、c的优化
采用PSO算法优化公式（3）中的参数需要构造的满足问题
的目标函数，即：
（4）
其中，m=7为污染物种类数目；k=5为大气污染分级数目；Rik为i污染物的k级污染损害率，Rke为k级标准的污染损害率目标值。在满足公式（3）的情况下对公式（4）采用PSO算法进行全局优化，但在优化的过程中发现，随着PSO参数取值范围的不同 ，a、b、c值的变化较明显，且参数a无限地趋向于PSO参数取值范围的下限。鉴于以上特点，说明大气污染损害率与污染物的相对浓度之间的函数关系基本上可由两个参数确定。
因此，采用PSO算法对（4）式优化后得到的最优解为：a =63.93, b =0.3401。
故多种大气污染物均适用的具有更强普适性的大气污染损害率计算公式可表示为：
（5）
1.3基于PSO大气质量综合污染损害率评价模型
受多种大气污染物影响的具有普适性的大气质量综合污染损害率计算公式为：
（6）
式中m为污染物的种类数目；Ri为i污染物的污染损害率；为i污染物的归一化相对权值，它由Ri所处的级别相应的k值的相对重要性确定。实际计算时，需根据各污染损害率所处的级别及污染物种类数目将权值wi`归一化为相对权值wi。
1.4 大气污染损害分指数模型
大气污染损害分指数可定义为：
（7）
1.5 基于PSO大气质量综合污染损害指数评价模型
受多种大气污染物影响的具有普适性的大气质量综合污染损
害指数计算公式为：
（8）
式中Ii为第i种污染物损害分指数，wi为i污染物的归一化相对权值，它由Ri所处的级别相应的I值的相对重要性确定。(wi的具体计算方法参见文献[12])
1.6实例评价
在实例1中，本文以某市10个监测点的SO2、NOx和TSP三种污染物的浓度监测值为例，采用基于PSO的 大气质量综合污染损害率评价模型对其进行评价，通过计算得出的综合污染损害率及综合评价结果表明，利用该种评价模型对大气质量进行综合评价，取得了令人满意的结果，具体结果详见表5。
在实例2中，本文根据长春市环境监测中心站提供的数据资料，以大气中的主要污染物：PM10（可吸入颗粒物）、SO2、NO2三种污染物的浓度值为主要监测对象，选取2002年1月1日至2002年3月31日间实际监测的三种主要污染物浓度的数据值作为数据样本，采用基于PSO的大气质量综合污染损害率评价模型对其进行评价，得到的评价结果与实际结果基本吻合。
改进的Elman神经网络在大气污染预测领域的应用
本文利用OIF Elman网络：输出－输入反馈网络（Output-Input Feedback Elman (OIF Elman)）模型对大气污染进行预测，本文的数据样本由长春市环境监测中心站提供，选取2001年12月1日至2002年11月30日连续365日的监测数据为数据样本，以大气中的主要污染物：PM10（可吸入颗粒物）、SO2、NO2三种污染物的浓度值为主要监测对象。为了较好地说明问题，文中均采用误差的平均值。网络的结构均为3-10-1式,即含有3个输入节点，10个隐层节点，1个输出节点的三层网络结构。输入层节点的输入为连续3日污染物浓度的监测值，输出为第4日该污染物浓度的预测值。
数值结果表明OIF Elman网络模型具有极佳的逼近性能，较高的拟合精度, 体现了OIF Elman在大气污染预测领域中的实用性和有效性，具有很好的应用前景。
1. An integrated PSO based model for the evaluation of air quality pollution.
Applied the PSO method with the global searching capability, this paper has optimized the parameters in the generalized formula for air pollution loss rate calculation. Therefore the formula gets more generalizations, namely the integrated PSO based model. Numerical result of examples show that the proposed model has considerable feasibility and effectiveness, and may be applicable practice.
1.1 The generalized formula for the calculation of air quality pollution.
The air pollution loss rate of the ith pollutant could be expressed as:
(1)
where ai and bi are the parameters related to the ith pollutant which are required, and ci the density of the ith pollutant measured in practice. LiZuoyong substituted ci with the relative density, namely xi=ci / ci0, ci0 is a predefined parameter of the ith pollutant, usually take as the natural basic density of the ith pollutant. So Eq. (1) may be rewrited as:
(2)
To strengthen the generalization of the model, QianLianwen introduced an universal parameter c which is required and unrelated to the ith pollutant in Eq. (2). Then Eq. (2) could be rewrited as:
(3) The optimization of parameters by PSO method
An objective function is required when optimizing the parameters of Eq. (3) using PSO method, namely that:
(4)
where m=7 is the number of the selected pollutants; k=5 the number of the air pollution levels; Rik the air pollution loss rate of the ith pollutant for level k, and Rke the objective value of the air pollution loss rate for level k, respectively. In the process of the optimizing of the parameters of Eq. (4) by PSO method, we find that the values of parameter are changed obviously when scope of the parameters of PSO are selected differently. Moreover, the value of a is approached to the lower limit of the selected scope of PSO parameter. According to the above fact, the functional relation to explain the air pollution loss rate and the relative density of pollutants may be decided by two parameters mainly. So the best solution can be achieved by PSO method for Eq. (4), that is a=63.93 and b=0.3401. Then we get the equation as follows:
(5)
1.3. The integrated PSO based model for the evaluation of air quality pollution
The generalized equation with multi-pollutants for synthetical air quality pollution loss rate can be expressed as:
(6)
where m is the number of the kinds of pollutants, Ri the air pollution loss rate of the ith pollutant, wi the normalized weight value of the pollutant defined by the relative importance of the corresponding value of k, respectively.
1.4 The air quality pollution loss index model
The air quality pollution loss index may be defined as:
(7)
1.5 The integrated PSO based loss index model for the evaluation of air quality pollution
The generalized index equation with multi-pollutants
for synthetical air quality pollution loss rate can be expressed as:
(8)
where Ii is the air quality pollution loss index of the ith pollutant, wi the normalized weight value of the pollutant.
1.6 Numerical results
Two examples are executed to test the efficiency of the proposed model in this thesis. For example 1, we take the practical density value of three pollutants, namely SO2, Nox and TSP of ten supervision spots in a city as the input data and evaluate the air quality by the proposed model. Numerical result shows that the model is quite efficient.
For example 2, we take the practical density value of three pollutants, namely PM10, SO2 and NO2 in Changchun from Jan. 1 2002 to Mar. 31 2002 as the input data and evaluate the air quality by the proposed model. Numerical result has a better precision compared with the practical values.
2. The application of OIF Elman neural network model for air pollution forecasting.
Applied the OIF Elman(Output-Input Feedback Elman (OIF Elman)) neural network to foreca
引文
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[3] 王俭,胡筱敏,郑龙熙,刘振山.BP模型的改进及其在大气污染预报中的应用.城市环境与城市生态,2002,15(5):17-19.
[4] 时小虎,梁艳春，徐旭.改进的Elman模型与递归反传控制神经网络.软件学报,2003,14(6):1110-1119.
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[2] 李祚泳,张欣莉,丁晶. 水质污染损害指数评价的普适公式.水科学进展，2001 12(2):161-163.
[3] 王俭,胡筱敏,郑龙熙,刘振山.BP模型的改进及其在大气污染预报中的应用.城市环境与城市生态,2002,15(5):17-19.
[4] 时小虎,梁艳春，徐旭.改进的Elman模型与递归反传控制神经网络.软件学报,2003,14(6):1110-1119.
[5] Kennedy J, Eberhart R. Particle swarm optimization [A].Proc IEEE Int Conf on Neural Networks[C].Perth,1995.1942-1948.
[6] Eberhart R, Kennedy J. A new optimizer using particle swarm theory [A]. Proc 6th Int Symposium on Micro Machine and Human Science[C].Nagoya,1995,39-43.
[7] 李爱国,覃征,鲍复民,贺开平. 粒子群优化算法.计算机工程与应用,2002,21:1-3.
[8] Eberhart R and Kennedy J. A new optimizer using particle swarm theory. Sixth International Symposium on Micro Machine and Human Science,1995,39-43.
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