Using support vector regression to predict PM 10 and PM 2.5

Transcription

1 IOP Conference Seres: Earth and Envronmental Scence OPEN ACCESS Usng support vector regresson to predct PM 10 and PM.5 o cte ths artcle: Hou Wezhen et al 014 IOP Conf. Ser.: Earth Envron. Sc Vew the artcle onlne for updates and enhancements. Related content - Study on the medcal meteorologcal forecast of the number of hypertenson npatent based on SVR Guangyu Zha, Guorong Cha and Hafeng Zhang - Applcaton of support vector regresson for optmzaton of vbraton flow feld of hghdensty polyethylene melts characterzed by small angle lght scatterng Guangmng Xan - dal Current Short-erm Predcton Based on Support Vector Regresson Yang Guozhen, Wang Hafeng, Qan Hu et al. hs content was downloaded from IP address on 06/04/019 at 14:47

2 Usng support vector regresson to predct PM 10 and PM.5 Hou Wezhen 1, L Zhengqang 1, Zhang Yuhuan 1,,, Xu Hua 1,, Zhang Yng 1,, L Katao 1,, L Donghu 1,, We Peng 1,, Ma Yan 3 1 Insttute of Remote Sensng and Dgtal Earth, Chnese Academy of Scences, Bejng, Chna. Unversty of Chnese Academy of Scences, Bejng, Chna. 3 School of earth scences and engneerng, Hoha Unversty, Nanjng, Chna. houwz@rsa.ac.n Abstract: Support vector machne (SVM), as a novel and powerful machne learnng tool, can be used for the predcton of PM 10 and PM.5 (partculate matter less or equal than 10 and.5 mcrometer) n the atmosphere. hs paper descrbes the development of a successve over relaxaton support vector regress (SOR-SVR) model for the PM 10 and PM.5 predcton, based on the daly average aerosol optcal depth (AOD) and meteorologcal parameters (atmospherc pressure, relatve humdty, ar temperature, wnd speed), whch were all measured n Bejng durng the year of he Gaussan kernel functon, as well as the k-fold crosses valdaton and grd search method, are used n SVR model to obtan the optmal parameters to get a better generalzaton capablty. he result shows that predcted values by the SOR-SVR model agree well wth the actual data and have a good generalzaton ablty to predct PM 10 and PM.5. In addton, AOD plays an mportant role n predctng partculate matter wth SVR model, whch should be ncluded n the predcton model. If only consderng the meteorologcal parameters and elmnatng AOD from the SVR model, the predcton results of predct partculate matter wll be not satsfyng. Keywords: support vector regresson, PM 10, PM.5, AOD, meteorologcal parameters 1. Introducton In recent years, wth the rapd development of ndustralzaton and urbanzaton n Chna, urban ar polluton has been a grow problem, especally for urban communtes. Health effects dffer upon the sze of arborne partculates. In ths contrbuton, PM 10 and PM.5 (partculate matter less or equal than 10 and.5 mcrometers respectvely) are consdered due to ts effect on human health. Epdemologc studes ndcate strong lnks between the concentraton of PM 10 or PM.5 wth publc morbdty, mortalty of respratory and cardovascular dseases. Recently, PM has become the prmary ar pollutant n most major ctes n Chna, whch not only threatens people's health, but also causes the decrease of atmospherc vsblty and the degradaton of the cty scenery [1-3]. Support vector machnes (SVM) are a new statstcal learnng technque, based on machne learnng and generalzaton theores, t mples an dea and could be consdered as a method to mnmze the rsk. Besdes, a generalzaton capablty makes possble ther applcaton to modelng dynamcal and Correspondng author: Zhang Yuhuan, E-mal: zhangyh@rsa.ac.cn. Content from ths work may be used under the terms of the Creatve Commons Attrbuton 3.0 lcence. Any further dstrbuton of ths work must mantan attrbuton to the author(s) and the ttle of the work, journal ctaton and DOI. Publshed under lcence by Ltd 1

3 non-lnear data sets. hs study s motvated by a growng popularty of support vector regresson (SVR) problems, whch leads to better generalzaton than conventonal methods such as artfcal neural networks (ANN) [, 4-8]. hs paper presents a study of usng the SVR model to nvestgate of PM 10 and PM.5, whch were measured n Bejng durng he successve over relaxaton support vector regressons (SOR-SVR) are traned by performed on the data of PM.5 (or PM 10 ), the aerosol optcal depth (AOD) and meteorologcal parameters (atmospherc pressure, relatve humdty, ar temperature, wnd speed), whch were also measured at Bejng at the same perod. Wth the SVR model, based on AOD and meteorologcal parameters, we can predct the regonal partculate matter (PM) n Bejng n Chna.. Support vector regresson {(x 1,y 1),,(x m,y m)} x R n, y R Kernel selecton (lnear,polynomal, Gaussan,Splne,etc.) Dataset Data processng K-fold cross valdaton Parameter selecton (ε,c, kernel parameter) SVR equaton (A convex quadratc programmng problem) Usng SOR method to solve the problem Model ranng Model estng Fnshed Y Grd search N Dfferent parameters Support vector α and α Regresson model of SVM Optmal parameters (ε,σ,c) Fnal SVR model Predcton External data Fgure 1. (a) Flow dagram for SOR-SVR model, (b) predcton wth SVR model..1. tandard support vector regresson In recent years, Support Vector Regresson (SVR) problem s a new nterest feld n support vector n machne. In regresson problems, we are gven a tranng data set S {( x1, y1),,( xm, ym)} R R, n where x R s the nput data and y R s the target output. he man goal s to fnd a functon f( x ) that can correctly predct the observaton values y, of the new nput ponts x, by learnng from the gven tranng data set S. A standard regresson problem of a lner SVR s m 1 ( mn C ) 1 s. t. x b y y x b 0, 0, 1,,..., m where s the normal vector, b s the threshold, C s a regularzaton constant determnng the trade-off between the tranng error and the generalzaton performance, and are the slack varables, ε s the tolerance (error acceptance). hen the functon as f ( x)= x b () (1)

4 hs problem s called ε-support vector regresson (ε-svr) and a data pont vector f f ( x ) y [4,5]. x n R s called a support.. SOR-SVR model For the standard model of SVR, f we append the term b to, that s to say, maxmze the margn between the parallel separatng planes by optmzng wth respect to both and b, meanwhle, we change the expresson form wth matrx and vector, ths leads to the followng reformulaton of the SVR problem as 1 ( ) ( mn b C ) s. t. A be y e (3) A be y e where A s the m n matrx wth x as a row, 1,,... m, e s an arbtrarly vector wth the component as 1, and y ( y1, y,... y m ). Its dual problem s mn 1 1 ( ) ( ) ( ) ( ) ( AA ee y e ) C (4) st.., 0 and A e I ˆ, H, l ( y e), ( y e), Q K( H, H ) L E L A e C (5) where K s the kernel functon for nonlnear case and L s the strctly lower trangular of the symmetrc matrx Q. hus, dual problem can be smplfed as mn 1 ˆ ˆ Q l ˆ (6) st.. ˆ 0 Usng the successve over relaxaton (SOR) method to solve Eq.(6), we get the teratve formula of SOR algorthm as followng[4]: ( E ( Q e L( ))) (7) where ( ) denotes the nonnegatve gradent projecton: 0, 0 (( ) ) (8), 0 hen the regresson functon can be wrtten as f ( x) ( ) K( A, x) e ( ) (9) hs SVR problem s called SOR-SVR model and Fgure 1(a) further llustrate the dagram of ths model. 3. Methodology and results 3.1. Collect and analyze dataset he data collected to be used n the study refer to ar qualty n Bejng and contans the partculate matters (PM.5 ) montored by U.S. Embassy (Unted State Embassy n Bejng, Chna), aerosol optcal depth (AOD) measured by the sun photometer Ce318 at RADI (Insttute of Remote Sensng and Dgtal Earth, CAS), and the meteorologcal data, ncludng ar pressure, temperature, relatve humdty, and wnd speed, whch are measured by Chna Meteorologcal Admnstraton. he three observaton stes are not far away from each other, and those data were measured from 010 to 01. 3

5 In addton, the PM 10 data are provded from the Mnstry of Envronmental Protecton of PRC, whch were measured n the whole year of 010. (a) (b) (c) Fgure. me seres of daly average data results. (a) pressure and temperature; (b) relatve humdty (RH) and wnd speed; (c) AOD and PM.5. able 1. Varables of dataset No. Varable name Unt 1 PM.5 (PM 10 ) μm/m 3 AOD -- 3 Ar pressure bpa 4 temperature 5 Relatve humdty (RH) % 6 Wnd speed m/s ake the PM.5 predcton as an example, after deletng the outler from the dataset, we can get the daly average results of PM.5, AOD and meteorologcal varable respectvely, then 300 data are selected for the smulaton and dscusson, he varable of dataset are presented n table 1, and the tme seres data are shown n fgure. For the AOD results, we have already used the Angstrom formula to transform the AOD result at 550nm. 3.. Desgn and test SOR-SVR model here are several ssues that we need to consder n the SOR-SVR applcaton. Frst of all, some 4

6 parameters must be determned before runnng the partcular algorthm. hese parameters are error acceptance (ε), constant (C) and kernel specfc parameters. In ths work, gauss kernel functon K( x, x ) exp( x x / ) (10) j j was used, where s the parameter that determnes performance n the learnng of the kernel functon. As we tran and test the SVR model, k-fold cross valdaton and grd search method are also used, consequently the optmal parameter ε, C and can be obtaned. Whle the k-fold cross valdaton method s employed, wth the defned value of ε, C and, the dataset s dvded nto k parts, the k-1 parts among whch can be selected as the tranng dataset and the remanng part as the testng dataset, then the average relatve testng error can be ganed. In ths way, we can tran and test the model k tmes, and then get the average value of the each testng error as fnal error. Wth dfferent values of ε, C and, we can search and select the parameter (ε, C, ) whch correspondng to the mnmum fnal error as the optmal parameters n the SOR-SVR model. he dagram of the predcton wth SVR model can see fgure 1 (b). 3.3 Results (a) (b) Fgure 3. Usng the tranng dataset as the testng dataset, the comparson results of actual PM.5 data and predcted result. (a) ε=1, C=100, =0.1; (b) ε=10, C=100, =0. (a) Fgure 4. Predcton of PM.5. (a) me seres dagram; (b) scatter dagram. Fgure 3 shows the comparson results of actual PM.5 and predcted result whle we use the tranng dataset as the testng dataset for dfferent parameter (ε, C, ). As we can see n fgure 3 (a), though the regresson results match wth the actual PM.5 n an extremely good condton, the generalzaton ablty of ths model s not very good, due to the over-fttng. Wth the k-fold cross valdaton, the over-fttng condton can be prevented, meanwhle, combned wth grd search method, the optmal parameter (ε=0.1, C=100, =0.3) for the good generalzaton ablty can be obtaned. Wth the optmal parameter, we select 50 days data as the tranng dataset and 50 days data as the testng dataset, the predcted result of PM.5 can be found n the fgure 4. From the fgure, we can see that the predcted result by the SOR-SVM model agree well wth the actual data, the correlaton coeffcent R =0.87 and the average error s 1.66 μm/m 3, whch can prove that the SOR-SVR model has a good generalzaton ablty to predct PM.5. 5

7 Besdes, n order to nvestgate the mportant role whch AOD played n the predcton of PM.5 wth SVR model, we also consder usng the meteorologcal parameters (atmospherc pressure, relatve humdty, ar temperature and wnd speed) drectly to predct the PM 10 and PM.5 n the same as above. However, compared wth the condton combned wth AOD varable, the predcted results are satsfyng, the correlaton coeffcent R s about 0.7 and the average error s sgnfcantly larger. Due to the reason of space lmtatons, the detaled results are not shown here. Wth the SOR-SVR model, we can further use the AOD retreval result from the satellte remote sensng, combnng wth the correspondng meteorologcal data, to predct the partculate matter n a regonal dstrbuton n our next study. 4. Dscusson and Conclusons he potental of applyng support vector machne (SVM) n PM 10 and PM.5 predcton s studed and presented n ths paper, based on the daly average aerosol optcal depth (AOD) and meteorologcal parameters such as atmospherc pressure, relatve humdty, ar temperature and wnd speed. he predctng model s developed by usng the successve over relaxaton support vector regresson (SOR- SVR). he Gaussan kernel functon, as well as the k-fold crosses valdaton and grd search method, s used to obtan the optmal parameters (ε, C, ) to get a better generalzaton capablty. For the fnal model, 50 days daly average data are selected as the tranng dataset and 50 days data as the testng dataset, the predcted results agree well wth the actual data, and show that the SOR-SVR model has a good potental and generalzaton ablty to predct PM n the atmosphere. In addton, AOD plays an mportant role n predctng partculate matter wth SVR model, whch should be ncluded n the model. If only consderng the meteorologcal parameters and elmnatng AOD, the predcton results of predct partculate matter wll be not satsfyng. Wth the SOR-SVR model, we can further use the AOD retreval result from the satellte remote sensng, as well wth the correspondng meteorologcal data, to predct the PM 10 and PM.5 n a regonal dstrbuton n bg cty such as Bejng n Chna Acknowledgement hs research s supported by Natonal Basc Research Program of Chna (973 Program) under grant 010CB (010CB950801). Besdes, authors wsh to acknowledge Chna Meteorologcal Admnstraton, Mnstry of Envronmental Protecton of PRC and U.S. Embassy n Bejng for provdng the meteorologcal data, PM 10 and PM.5 data respectvely n our research. References [1] Wang Z, et al, 010 Satellte-based estmaton of regonal partculate matter (PM) n Bejng usng vertcal-and-rh correctng method Remote sens. Envron [] Arampongsanuwat S, Meesad P, 011 Predcton of PM10 usng Support Vector Regresson IPCSI [3] a A, Mckley L, Jacob D, 010 Correlatons between fne partculate matter (PM.5) and meteorologcal varables n the Unted States: Implcatons for the senstvty of PM.5 to clmate change Atmos. Envro [4] Pan M, Hou W, He G, 006 Improved Support Vector Regresson Algorthm based on Successve Over Relaxaton JCIS [5] Duan H, Hou W, He G, et al, 007 Predctng me Seres Usng Incremental Langrangan Support Vector Regresson ISNN [6] Pan M, He G, Hou W, et al, 006 Improved Support Vector Machne based on Successve Over Relaxaton CJE 4A [7] Duan H, Shao X, Hou W, et al, 009 An ncremental learnng algorthm for Lagrangan support vector machnes Pattern Recogn. Lett [8] Artmo S, et al, 011 Modelng PMx trends contamants by usng support vector machnes ACSES Res. n Comput. Sc