Predicting CO Concentrations Levels Using Probability Distributions

Transcription

1 Iteratoal Joural of Egeerg ad Techology Volume 3 o. 9, September, 03 Predctg CO Cocetratos Levels Usg Probablty Dstrbutos. A. S. Yahaya,.A. Raml, A.Z Ul-Saufe, H. A. Hamd, H. Ahmat, Z.A Mohtar School of Cvl Egeerg, Egeerg Campus, Uverst Sas Malaysa, 4300 bog Tebal, Seberag Pera Selata, Pulau Pag Malaysa. Faculty of Computer ad Mathematcal Sceces, Uverst Tekolog MARA, Malaysa. ABSTRACT I Malaysa, ar pollutat emssos were motored all over the coutry to detect ay sgfcat chage whch may cause harm to huma health ad the evromet. Ths research s focused o carbo moode (CO) cocetrato as t s kow to cause severe health mpact to huma as well as evromet. Therefore a well developed system eed to be used order to aalyze the tredg of all of the pollutats emsso vetores. I ths research, seve theoretcal dstrbutos that are Webull, gamma, logormal, Laplace, Raylegh, log-logstc ad verse Gaussa dstrbutos were developed. It s used to verfy ad smulate the tred of the motorg data for CO emsso Kuala Lumpur, whch s the captal of Malaysa, the form of probablty desty fucto ad hece ca be used as a predcto tool. The method of mamum lkelhood estmates (MLE) was used for estmatg the parameters of the dstrbutos. The best dstrbuto was determed usg the plots for the cumulatve dstrbuto fuctos (cdf) ad performace dcators. Fve performace dcators used are the root mea square error (RMSE), de of agreemet (IA), predcto accuracy (PA) ad coeffcet of determato (R ). From the performace dcators, t was foud that the best dstrbuto to represet the CO cocetrato level Kuala Lumpur for 00 s the verse Gaussa dstrbuto. Based o the predcto usg the verse Gaussa dstrbuto, t ca be cocluded that the CO cocetrato level Kuala Lumpur does ot eceed the Malaysa Ambet Ar Qualty Gudeles of 9 parts per mllo (ppm). Keywords: Carbo moode, probablty dstrbutos, performace dcators. ITRODUCTIO Ar polluto s the presece of cotamats the ar cocetratos that prevet the ormal dspersve ablty of the ar ad terfere wth bologcal processes ad huma ecoomcs. I Malaysa, the Departmet of Evromet, Malaysa (DoE) s oe of the bodes that s resposble motorg the status of ar qualty throughout the coutry to perceve ay sgfcat chage whch may cause harm to huma health ad the evromet. There are 5 motorg locatos throughout the coutry that belog to the Departmet of Evromet- The DoE Malaysa descrbe that ar polluto occurs whe ar mpurtes the form of gaseous or partcles are emtted to the atmosphere. Peavy (985) defed ar polluto as the presece the outdoor atmosphere of oe or more ar cotamats (.e., dust, fumes, gas, mst, odor, smoke, or vapor) suffcet quattes, of such characterstcs, ad of such durato as to be or to threate to be jurous to huma, plat, or amal lfe or to property, or whch reasoably terferes wth the comfortable ejoymet of lfe or property. Based o Departmet of Evromet (DoE) report o ar qualty 998, motor vehcles remaed the major source of ar polluto the coutry (Departmet of Evromet, 998). From 8.9 mllo motor vehcles regstered 998, appromately mllo toes of carbo moode, toes of odes of troge, 000 of hydrocarbos, toes of sulphur dode ad toes of partculate matters were emtted to the atmosphere. Geerally, 00 the ar qualty was betwee good to moderate most of the tme, ecept for a umber of uhealthy days at varous locatos the states of Selagor, eger Sembla ad Sarawak. From the geographcal ad developmet pot of vew, the Klag Valley s the most proe to serous ar polluto compared to other parts of the coutry 00. Durg February to March 00, the Klag Valley epereced hot ad dry weather wth reduced rafall, codtos deal for peat swamp ad forest fres may areas of Selagor ad Kuala Lumpur. Ths has caused the ar qualty to deterorate from moderate to uhealthy level. Based o DoE data ar qualty status for the Klag Valley 00, the umber of days wth uhealthy ar qualty codtos raged from 7 to 67 days. The am of ths research was to obta the best model to predct carbo moode (CO) cocetrato level Kuala Lumpur, Malaysa. Seve theoretcal dstrbutos were used to ft the paret dstrbuto of CO. These dstrbutos were later used to uderstad the characterstc of CO cocetrato for a oe year cycle. ISS: IJET Publcatos UK. All rghts reserved. 900

2 Iteratoal Joural of Egeerg ad Techology (IJET) Volume 3 o. 9, September, 03 ISS: IJET Publcatos UK. All rghts reserved. 90. PROBABILITY DISTRIBUTIOS Seve probablty dstrbutos were used for ths research. The dstrbutos are () log-ormal dstrbuto (Kao ad Fredlader, 995) () gamma dstrbuto (Berger et al.,98) (3) Webull dstrbuto (Georgepoulus ad Sefeld,98),(4) Laplace dstrbuto (Aryal ad Rao, 005), (5) log-logstc dstrbuto (Sgh et al., 00), (6) verse Gaussa dstrbuto (Chhkara ad Folks, 989), ad (7) Raylegh dstrbuto (Celk, 003). The probablty desty fuctos ad the estmators of the parameters of the dstrbutos are gve Table. The parameters were estmated usg the method of mamum lkelhood. Table : Probablty desty fuctos ad ts parameter estmates Dstrbuto Probablty desty fucto Parameter estmates Log-ormal l ep l ; l Gamma ep g l l ; Webull ep l 0 l Laplace ep meda ; Log-logstc / l l ep e l ep l ep l ep ˆ l Iverse Gaussa 3 ep ; Raylegh ep otato: s the locato parameter, s the scale parameter, s the shape parameter

3 Iteratoal Joural of Egeerg ad Techology (IJET) Volume 3 o. 9, September, PERFORMACE IDICATORS Performace dcators were used to determe the dstrbuto that ca gve the best ft to the data. The four performace dcators are root mea square error (RMSE), de of agreemet (IA), predcto accuracy (PA) ad coeffcet of determato R Table gves the equatos for the performace dcators whch have bee used by Lu (003) ad Jue et al. (00). Idcators Table : Performace Idcators Equatos Root Mea Square Error Ide of Agreemet P O P O P O O O Predcto Accuracy O O P O Coeffcet of Determato R P P O O. S pred. S obs otato: = umber of observatos, P = Predcted values, O = Observed values, P = Mea of the predcted values, O = Mea of the observed values, S = Stadard devato of the predcted values, S obs 4. STUDY AREA pred = Stadard devato of the observed values Kuala Lumpur has bee chose as the ste for ths research as Kuala Lumpur s the captal cty of Malaysa. Kuala Lumpur s a federal terrtory stuated the mddle of Malaysa. It s a developg cty ad the most mportat cty Malaysa. Fgure shows the locato of Kuala Lumpur Malaysa. Valley s most proe to serous ar polluto compared to other parts of the coutry. I Malaysa, CO emsso s maly due to moble sources. Large ctes lke Kuala Lumpur has hgher CO cocetrato prcpally due to the umber of motor vehcles (Departmet of Evromet, 00). Accordg to the Mstry of Housg ad Local Govermet (006), the populato sze of Kuala Lumpur 998 s about, people ad 00 s about, people. From the populato sze 998 ad 00, the estmated value for populato growth Kuala Lumpur s almost.6% per year. Accordg to the data from the Mstry of Trasport (006) the vehcle umbers for Kuala Lumpur s creasg wth tme. The percetage crease of vehcle umbers per year s estmated to be about.5%. From the geographcal ad developmet pot of vew, the Klag ISS: IJET Publcatos UK. All rghts reserved. 90

4 Iteratoal Joural of Egeerg ad Techology (IJET) Volume 3 o. 9, September, 03 Fgure. Locato of the study area Accordg to the Mstry of Housg ad Local Govermet (006), the populato sze of Kuala Lumpur 998 s about, people ad 00 s about, people. From the populato sze 998 ad 00, the estmated value for populato growth Kuala Lumpur s almost.6% per year. Accordg to the data from the Mstry of Trasport (006) the vehcle umbers for Kuala Lumpur s creasg wth tme. The percetage crease of vehcle umbers per year s estmated to be about.5%. 5. DATA The CO cocetrato data was obtaed for 00 ad t was collected every hour. Table 3 gve summares of CO cocetrato for Kuala Lumpur. The ut of measuremet s parts per mllo (ppm). Table 3: Descrptve statstcs for CO cocetrato Value Total, 800 Mmum value 0.0 Mamum value 3.3 Mea 0.6 Varace 0.5 Stadard devato 0.38 Meda 0.5 Skewess.73 Kurtoss 7.64 Table 3 shows that the mmum CO cocetrato s 0.0 ppm ad ts mamum value s 3.3 ppm. There are some mssg values (about 6% of the total data). For ths research, the mssg values are ot cluded the aalyss. The coeffcet of skewess ad kurtoss are greater the zero showg that rght skewed dstrbutos are more approprate to ft the data. 5. RESULTS The parameter estmates ad performace dcators for the seve dstrbutos are gve Table 4. From Table 4, t ca be see that the verse Gaussa dstrbuto s the best dstrbuto that ca ft the data sce t gves the best results for IA, PA ad R. Thus the verse Gaussa dstrbuto ca be used for predcto purposes. To look at how well the chose dstrbuto fts the data, a plot of the observed CO cocetrato versus the predcted values usg the verse Gaussa dstrbuto was doe. Ths plot s gve Fgure. The plot shows a very good agreemet wth the value of the coeffcet of determato of However the etreme rght observatos caot be predcted that well. ISS: IJET Publcatos UK. All rghts reserved. 903

5 Iteratoal Joural of Egeerg ad Techology (IJET) Volume 3 o. 9, September, 03 Table 4: Parameter Estmates ad Performace Idcators Dstrbutos Parameter estmates RMSE IA PA R Webull = =.7 Gamma = = 0. Log-ormal = = 0.64 Laplace = 0.5 = Raylegh = Log-logstc = = Iverse Gaussa = 0.6 =.06 The verse Gaussa dstrbuto was the used to predct the probablty that the CO cocetrato eceeds the Malaysa Ambet Ar Qualty Gudeles (Departmet of Evromet, 00) whch s 9ppm. It was foud that ths value equals zero. Thus ths shows that the CO cocetrato does ot eceed the Malaysa stadards Predcted CO Cocetrato (ppm) Fgure : Plot of observed values versus predcted values 5. COCLUSIO The characterstcs of CO cocetratos Kuala Lumpur were vestgated. The results show that the mea CO cocetrato Kuala Lumpur for 00 s 0.6ppm wth a stadard devato of 0.38ppm whch s well below the Malaysa Ambet Ar Qualty Gudeles of 9ppm. The mamum value s 3.3ppm Seve dstrbutos were compared ad the verse Gaussa dstrbuto gves the best ft sce three performace dcators gves the best results for ths dstrbuto. The scatter plot of observed CO cocetratos versus the predcted values obtaed from the verse Gaussa dstrbuto shows a very good ft wth the coeffcet of determato value of However ths predcto s ot very good at the etreme rght tal of the cocetrato. ISS: IJET Publcatos UK. All rghts reserved. 904

6 Iteratoal Joural of Egeerg ad Techology (IJET) Volume 3 o. 9, September, 03 The probablty that the CO cocetrato eceeds the Malaysa Ambet Ar Qualty Gudeles was also vestgated. The value of the probablty s zero showg that there s eceedeces value. Ackowledgmet Facal supports from the Mstry of Scece, Techology ad Iovato through the Scece Fud project umber SF05 ad Uverst Sas Malaysa are hghly apprecated. REFERECES []. Aryal, G. ad Rao, A.. V. (005) Relablty model usg trucated skew Laplace dstrbuto. olear Aalyss. 63 (5 7), []. Berger, A., Melce, J. L. ad Demuth, C. L. (98) Statstcal dstrbutos of daly ad hgh atmospherc SO cocetratos. Atmospherc Evromet. 6 (5), [3]. Celk, A.. (003) A statstcal aalyss of wd power desty based o the Webull ad Raylegh models at the Souther Rego of Turkey. Joural of Reewable Eergy. 9 (7), [4]. Chhkara, R. S. ad Folks, J. L. (989) The verse Gaussa dstrbuto as a lfetme model. Thechometrcs. 9 (4), [5]. Departmet of Evromet, Malaysa (998) Malaysa evromet qualty report 998. Malaysa: Departmet of Evromet [6]. Departmet of Evromet, Malaysa (00) Malaysa evromet qualty report 00. Malaysa: Departmet of Evromet [7]. Georgepoulos, P. ad Sefeld, J. (98) Statstcal dstrbutos of ar pollutat cocetratos. Evrometal Scece ad Techology. 6 (54), 40A 45A [8]. Kao, A. S. ad Fredlader, S. K. (995) Frequecy dstrbutos of PM 0 chemcal compoets ad ther sources. Evrometal Scece ad Techology. 9(5), 9 8 [9]. Lu, H. C. (00) The statstcal character of PM 0 cocetrato Tawa Area. Atmospherc Evromet. 36 (9), [0]. Mstry of Housg ad Local Govermet (007) [Ole], [Accessed 5th Jauary 007]. Avalable from World Wde Web: []. Mstry of Trasport (007) [Ole], [Accessed 5th Jauary 007]. Avalable from World Wde Web: []. Peavy, H. S., Rowe, D. R. ad Tchobaoglous, G. (985) Evrometal egeerg. Sgapore: McGraw-Hll Co Sgh, P. (00) Smultaeous cofdece tervals for the successve ratos of scale parameters. Joural of Statstcal Plag ad Iferece. 36 (3), [3]. Jue, H., ska, H., Tuppurrae, K., Ruuskae, J., Kolehmae, M., (00) Methods for mputato of mssg values ar qualty data sets. Joural of Atmospherc Evromet, 38, ABOUT AUTHORS Ahmad Shukr Yahaya s presetly a Assocate Professor at the School of Cvl Egeerg, Uverst Sas Malysa. Hs ma research area s o statstcal data aalyses, ar polluto modelg ad smulato. or Azam Raml receved hs Ph.D. evrometal egeerg from the Uversty of Wales. He s presetly a Seor Lecturer at the School of Cvl Egeerg, Uverst Sas Malysa Hs ma research area s o ar polluto ad evrometal mpact assessmet. ISS: IJET Publcatos UK. All rghts reserved. 905