1 Envionment Potection Engineeing Vol No. 3 DOI: /epe18311 NADJET DJEBBRI 1, MOUNIRA ROUAINIA 1 PREDICTION OF INDUSTRIAL POLLUTION BY RADIAL BASIS FUNCTION NETWORKS Atmospheic pollution has been eceiving a significant inteest fo seveal decades since industies cause moe and moe pollution. Thanks to the development of many pediction techniques, scientists and industies ae focusing moe on pollution pediction. The aim of this wok is to pedict the two pollutant concentations (NOx and CO) in industial sites by a modified adial basis function (RBF) based neual netwok. The modification consideed the spead paamete h of the activation function in the RBF netwok. In ode to get the best netwok, the vaiations of this paamete fo thee cases wee consideed. In the fist case, only pollutants concentations vaiables wee used, while in the second one, only the meteoological vaiables wee utilized. In the thid case, pollutants concentations wee connected with meteoological vaiables. Based on calculation eos, the best model that ensues the best monitoing of pollutants concentation could be identified. 1. INTRODUCTION A continuous incease in industial pollution and envionmental degadation has become a majo concen fo the intenational community, leading to geate attention on theats. Many counties have aleady intoduced laws to limit and epot emission fom a lage spectum of commecial and industial facilities. The pediction of ai pollutants has become an impotant task fo the contol and emegency management in the case of pollution incidents. The pediction of industial pollution is a phenomenon that eceived a special inteest fo a vey long time. This acceleated the development of the pediction methods and povided scientific data based on these techniques. The atificial neual netwoks (ANN) based methods ae widely used in ai quality monitoing which heavily elies on the local meteoological conditions and the concentations of pollutant. Radial basis netwoks can equie moe neuons than standad feed fowad back popagation netwoks (Fig. 1), but often they can be designed in a faction of the time it takes to tain standad feed fowad netwoks. They wok best when many taining 1 Univesity 2 août, 1955 Skikda, Algeia, coesponding autho N. Djebbi, addess:
2 154 N. DJEBBRI, M. ROUAINIA vectos ae available . Binet et al.  pesented a adial basis function (RBF) neual netwok method fo estimating PM 2.5 concentations based on spase obseved inputs. Liu et al.  built an emission pediction model fo compessed natual gas (CNG)/diesel dual fuel engine (DFE) based on RBF neual netwok fo analyzing the effect of the main pefomance paametes on the CO, NO x emissions of DFE. Kyiaki et al.  used a adial basis function neual netwok system, which was classifying counties based on thei emissions of cabon, sulfu and nitogen oxides, and on thei goss national income. Fig. 1. Schematic of an RBF netwok Bo et al.  poposed a method fo pedicting gas content based on the RBF neual netwok optimized by a genetic algoithm. Shouong et al.  combined the RBF neual netwok with time seies on CO 2 emissions to make a foecast of its emissions in China. Chuanbao and Fuwu  descibed an appoach fo eplacing the engine out NO x senso
3 Pediction of industial pollution by adial basis function netwoks 155 with a adial basis function neual netwok (RBFNN) based NO x peception. Zheng and Shang  selected the paametes PM 1, SO 2, NO 2, tempeatue, pessue, humidity, wind diection and wind speed as the influence factos, while the pediction models based on RBF neual netwok wee constucted. The aim of this pape is to pedict the NO x and CO pollutants concentation in industial sites by a modified adial basis function netwok (RBF). The modification we consideed concens the spead paamete h of the activation function in the RBF netwok. The vaiations of this paamete in thee cases wee consideed in ode to get the best netwok in each case, and then these thee cases wee tested until getting the best case. These thee cases ae chaacteized as follows: in the fist case (RBF1) only pollutants concentations vaiables wee used, while in the second one (RBF2), only the meteoological vaiables wee utilized. In the thid case (RBF3), pollutants concentations wee combined with the meteoological vaiables. 2. RBF NETWORK METHOD An RBF is a thee-laye netwok, with only one hidden laye (Fig. 1). The numbe of neuons in the hidden laye is equal to the numbe of histoical obsevations of pedictos (successos). In fact, each neuon in the hidden laye epesents a pai of histoical obsevations of pedictos/dependents. The output of each neuon is actually the contibution of the histoical obsevation in estimating the eal-time event . Fig. 2. RBF netwok achitectue Radial basis netwok consists of two layes (Fig. 2): a hidden adial basis laye of S 1 neuons and an output linea laye of S 2 neuons, whee R is the numbe of elements in the input vecto, a il is ith element of a 1 whee I i W 1,1 is a vecto consisting of the ith ow of IW 1,1.
4 156 N. DJEBBRI, M. ROUAINIA The dist box in Fig. 2 accepts the input vecto p and the input weight matix IW 1,1, and poduces a vecto having S 1 elements. The elements ae the distances between the input vecto and vectos I i W 1,1 fomed fom the ows of the input weight matix . Accoding to Fig. 1, the RBF uses a Gaussian pefomance function. The input to this function is the Euclidian distance between each input to the neuon and the specified vecto of the same size of the input [1, 11]. The Gaussian function uses the following elation: f( X, b) e I 2 (1).8326 X X b I (2) h whee X the netwok input with unknown output, X b obseved inputs in time o location b, and h spead. The output of the function appoaches to 1, when X X b appoaches a lage value to, espectively. The value of the output between those limits depends on h. The geneal fom of calculating a dependent vaiable ( Y ) by pedicto X is then Y LWf( X, X ) Bias (3) b whee LW and Bias weight matix of connections fom the hidden laye to the output laye and bias matix of the output laye, espectively. When an RBF netwok is developed, LW and bias matices ae calculated by solving the system of equation of T LWf( X, b) Bias (4) b whee T b is the taget associated with the bth obsevation . To detemine the best spead paamete fo intepolation of concentations using the RBF netwok to pedic NO x and CO concentations a ty-and-eo appoach was used. Vaious values of spead stating fom.1 ending to 6 with.1 incemental steps wee used. It should be noted that since the adial basis netwok acts as the exact estimato function, the application of diffeent spead values within the calibation set esults in a simila aveaged eo of appoximately zeo. Theefoe, to examine the pefomance of the netwok in a pactical manne, the appoach of coss-validation is used. In this appoach, each pai of input/output is omitted fom the n obsevation of data set once and the othe n 1 pais of data ae used to estimate the omitted one. This iteation is epeated n times, and the aveaged simulation eo fo all n pais of data is consideed as the indicato of the eal pefomance of the netwok. The algoithmic steps used to
5 Pediction of industial pollution by adial basis function netwoks 157 descibe the appoach applied to find out which spead (h) minimizes the aveage eo of concentation estimation ae shown in Fig. 3. Y Fig. 3. Algoithm of the suitable spead (h)
6 158 N. DJEBBRI, M. ROUAINIA The coefficient of detemination (R 2 ) explains how much of the vaiability in the input data can be explained by the fact that they ae elated to the obseved values o how close the points ae to the line. R 2 takes on values between and 1, with values close to 1 implying a bette fit [13 15]. It is given by R n Oi O Oi Pi i 1 i 1 n i 1 n 2 2 O i O 2 (5) The mean absolute eo (MAE) is the aveage diffeence between pedicted and actual data values. The MAE (Eq. 6) anges fom to infinity and a pefect fit is obtained when MAE =. n 1 MAE Pi Oi (6) n i 1 The mean-squaed eo (MSE) is one of the most commonly used measues of success fo numeical pediction. The smalle the MSE value, the bette the pefomance of the model is [16 18]. Its value is computed by 1 MSE n P 2 i Oi (7) n i 1 whee P i and O i ae the pedicted and obseved concentations and O epesent the obsevation mean. 3. EXPERIMENTAL PROCEDURE Site and data desciption. Gas Natual Liquefies (GNL) complex with a suface of 9 ha is located in Skikda industial aea, 6 km to the East fom Skikda city cente. It was built in 1972, evolved in 198 and enovated in 2. Ou database taken fom the industial zone (GL1K) elies on the daily measuements fom 188 goups of data containing: NO x and CO pollutant concentations in the SKIKDA aea, duing the peiod fom Octobe 215 to Apil 216, the meteoological vaiables, fo the same aea and peiod; the measued vaiables ae: the speed and diection of the wind, elative humidity and tempeatue. The inputs and outputs ae standadized in the inteval of [; 1] .
7 Pediction of industial pollution by adial basis function netwoks 159 Method. To monito the ai quality and the pediction of industial pollution, the RBF netwok based method consideing two pollutants was applied. Ou objective is to foecast the concentation of NO x and CO pollutants. In this study, the best spead paamete h of the Gaussian activation function is selected by detemining the min eo of RBF model fo the thee cases RBF1 RBF3. The best spead (h) accoding to each case was consideed to pesent the pediction of two pollutants (CO and NO x ) and thei pediction eos. To identify the best model, the mean squaed eo (MSE) and the mean absolute eo (MAE) wee calculated fo each of the thee phases. The method was implemented in Matlab (7.7 vesion). The method of RBF neual netwok was applied accoding to Figs. 1 3 and the data of industial site. The models vaiables ae given in Table 1. Vaiables of the model Table 1 Vaiable X1 X2 X3 X4 X5 X6 Desciption tempeatue humidity wind speed diection of the wind concentation of NOx concentations of CO 4. RESULTS AND DISCUSSION Figues 4 6 illustate the changes of the minimal pediction eo upon changing the spead h fo the cases RBF1 RBF3. Table 2 shows the MAE values fo these cases. The esults show that the smallest MAE is obtained in the case of RBF3 (.534), while the best spead value h best is equal to 5.8. Table 3 shows the best spead values at seveal intevals fo the same case. Theefoe, the best choice fo spead value is 5.8. Table 2 Values of hbest and MAE fo RBF1, RBF2 and RBF3 Models hbest MAE RBF RBF RBF Figues 7 9 illustate the pollutants pediction and the pediction eos at h best fo each case (RBF1, RBF2, and RBF3), while Table 4 shows the mean and the absolute pediction eos at h best.
8 16 N. DJEBBRI, M. ROUAINIA eo spead Fig. 4. Pediction eo in tems of MAE fo vaious values of the spead paamete h fo the RBF1 (using only pollutant concentations as inputs) fo h ϵ [, 6] Fig. 5. Pediction eo in tems of MAE fo vaious values of the spead paamete h fo the RBF2 (using only meteoological vaiables as inputs) fo h ϵ [, 6] Fig. 6. Pediction eo in tems of MAE fo vaious values of the spead paamete h fo the RBF3 (using pollutants concentations combined with the meteoological vaiables as inputs) fo h ϵ [, 6]
9 a) Pediction of industial pollution by adial basis function netwoks 161 Table 3 Evolution of MAE accoding to spead at RBF3 Inteval spead Spead best MAE [, 2] [, 4] [, 6] [, 8] CO concentation [ppm] NOx concentation [ppm].6.4 CO ped CO meas CO pediction NOx ped NOx meas NOx pediction a) c) CO eos [ppm] CO eos [ppm] b) d) Fig. 7. Pollutants pedictions and thei eos by RBF1: a) CO pediction at hbest, b) CO pediction eos at hbest, c) NOx pediction at hbest, d) NOx pediction eos at hbest CO pediction CO concentation [ppm].6.4 CO ped CO meas a) b).1 CO eos [ppm] NOx concentation [ppm] NOx ped NOx meas NOx pediction c) NOx eos [ppm] d) Fig. 8. Pollutants pedictions and thei eos by RBF2: a) CO pediction at hbest, b) CO pediction eos at hbest, c) NOx pediction at hbest, d) NOx pediction eos at hbest
10 162 N. DJEBBRI, M. ROUAINIA CO concentation [ppm] NOx concentation [ppm].6.4 CO ped CO meas CO pediction NOx ped NOx meas NOx pediction a) c) CO eos [ppm] NOx eos [ppm] b) d) Fig. 9. Pollutants pedictions and thei eos by RBF3: a) CO pediction at hbest, b) CO pediction eos at hbest, c) NOx pediction at hbest, d) NOx pediction eos at hbest The cuves of pedicted and measued CO and NO x concentations ae divegent in Figs. 7 and 8, while they ae convegent in Fig. 9. The pediction eos fo CO and NO x ae smalle in Fig. 9 than those in Figs. 7 and 8. We can easily conclude that the RBF3 model illustated in Fig. 9 pesents bette pefomances than RBF1 and RBF2 models fo pediction NO x and CO. Table 4 Mean squaed eos and mean absolute eos fo RBF1, RBF2 and RBF3 Model NOx concentation [ppm] CO concentation [ppm] MSE MAE R 2 MSE MAE R 2 RBF RBF RBF All these esults show the efficiency of the RBF3 based pollution pediction model and its accuacy compaing to the RBF1 and RBF2 based pediction. We can deduce fom Table 4 that the values of the MSE and MAE fo the two pollutants in the pedictive model RBF3 ae smalle than thei values in pedictive models RBF1 and RBF2 also close to. The values of coefficient of detemination (R 2 ) in (RBF3) ae bette than its values in the case of the RBF1 and RBF2 also close to 1. It can be concluded that the minimal MSE and MAE fo the two pollutants ae found in RBF3. Thus, using pollutant concentations combined with meteoological vaiables leads to a bette pediction.
11 Pediction of industial pollution by adial basis function netwoks CONCLUSION The aim of this pape was to foecast the NO x and CO pollutants concentations by the use of the fowad-fowad eto popagation ANN model with a adial basis function (RBF). This paticula netwok has a Gaussian activation function which changes with the vaiations of the spead paamete h. This change may alte the RBF netwok. The test was pefomed fo thee vaious netwoks. The modification we consideed concens the spead paamete h of the activation function in the RBF netwok. The vaiation of this paamete in thee cases was consideed in ode to get the best netwok in each case, and then these thee cases wee tested until getting the best case. The esults show that the best spead and the best pediction ae obtained in the thid case (RBF3). Thus, it can be concluded that an efficient pediction of NO x and CO concentations and foecast will be pefomed by the use of the adial basis function neual netwok with a fixed value of the spead paamete h of 5.8, and a data set containing pollutants with pevious concentations combined with meteoological vaiables. REFERENCES  CHEN S., COWAN C.F.N., GRANT P.M., Othogonal least squaes leaning algoithm fo adial basis function netwoks, IEEE Tans. Neual Netwoks, 1991, 2 (2), 32.  BIN Z., MIN W., NENG W., GAINES W.J., XIN F., YUQI T., Spatial modeling of PM2.5 concentations with a multifactoial adial basis function neual netwok, Envion. Sci. Pollut., 215, 3 (22),  LIU Z., FEI S., Study of CNG/diesel dual fuel engine s emissions by means of RBF neual netwok, J. Zhejiang Univesity Science, 24, 5 (8), 96.  KYRIAKI K., LAZAROS I., Employing a adial basis function atificial neual netwok to classify westen and tansition euopean economies based on the emissions of ai pollutants and on thei income, Intenational Fedeation fo Infomation Pocessing EANN/AIAI, 211, 2 (364), 141.  BO Z., JIANFENG S., Gas content pediction based on GA-RBF neual netwok, Chinese Contol and Decision Confeence, Xuzhou, China, 21, 978 (1), 314,  SHOURONG L., RONGXI Z., XIN M., The foecast of CO2 emissions in China based on RBF neual netwoks, 2nd Intenational Confeence on Industial and Infomation Systems, Dalian, China, 21.  CHUANBAO L., FUWU Y., Radical basis function neual netwok-based NOx soft senso technique, Intenational Confeence on Electical and Contol Engineeing, Yichang, China, 211.  Zheng H., Shang X., Study on pediction of atmospheic PM2.5 based on RBF neual netwok, Fouth Intenational Confeence on Digital Manufactuing and Automation, Qingdao, China, 213.  SHAHAB A., Data-Diven Modeling. Using MATLAB in Wate Resouces and Envionmental Engineeing, Spinge, Dodecht 214.  YIRAN S., DING L.Y., YANTAO T., YAOWU S., Ai:fuel atio pediction and NMPC fo SIengines with modified Voltea model and RBF netwok, Eng. Appl. Atif. Int., 215, 45, 313.  PIETRO Z., HAIBO C., MARGARET C.B., Pedicting eal-time oadside CO and NO2 concentations using neual netwoks, IEEE Tans. Int. Tansp. Syst., 28, 9 (3), 514.  SURAJDEEN A.I., MOUSTAFA E., MOUHAMED A.H., AHMED A.A., RBF neual netwok infeential senso fo pocess emission monitoing, Contol Eng. Pact., 213, 21, 962.  WILLMOTT C., Some comments on the evaluation of the model pefomance, Bull. Am. Meteo. Soc., 1982, 63 (11), 139.
12 164 N. DJEBBRI, M. ROUAINIA  WILLMOTT C., ACKLESON S., DAVIS R., FEDDEMA J., KLINK K., LEGATES D., O DONNELL J., ROWE C., Statistics fo the evaluation and compaison of models, J. Geophys. Res., 1985, 9 (5),  ROESON S.M., STEYN D.G., Evaluation and compaison of statistical foecast models fo daily maximum ozone concentations, Atm. Envion., 199, 24 (2), 33.  COMAN A., IONESCU A., CANDAUY., Houly ozone pediction fo a 24-h hoizon using neual netwoks, Envion. Model. Soft., 28, 23 (28), 147.  JUNNINENA H., NISKAA H., TUPPURAINENC K., RUUSKANENA J., KOLEHMAINENA M., Methods fo imputation of missing values in ai quality data sets, Atm. Envion., 24, 38,  KOLEHMAINEN M., MARTIKAINEN H., RUUSKANEN J., Neual netwoks and peiodic components used in ai quality foecasting, Atm. Envion., 21, 35, 815.  NISSES M., E-documentations techniques de complexe GL1K-Skikda, Algeia, 211.