Estimation of Global Solar Radiation at Onitsha with Regression Analysis and Artificial Neural Network Models

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1 eserch Journl of ecent Sciences ISSN 77-5 es.j.ecent Sci. Estimtion of Globl Solr dition t Onitsh with egression Anlysis nd Artificil Neurl Network Models Abstrct Agbo G.A., Ibeh G.F. *nd Ekpe J.E. Fculty of Physicl Sciences, Industril Physics Deprtment, Ebonyi Stte University, Abkliki, Ebonyi Stte, NIGEIA Avilble online t: (eceived nd Mrch, revised st Mrch, ccepted st Mrch ) Energy plys n importnt role in determining the conditions in which living mtter cn exist nd continuous steering power for socil, economic nd technologicl prospective development. This study is imed t estimting the globl solr rdition on horizontl surfce using meteorologicl prmeters of verge temperture nd reltive humidity for period of eleven yers (99-) t Onitsh, Anmbr Stte of Nigeri. egression nlysis nd rtificil neurl network models were employed in the nlysis. Vlidtion of the results using error nlysis show tht one-vrible model of reltive humidity hs MBE., MSE.9, MPE-.75 nd one-vrible of verge temperture hs MBE.7, MSE.5, MPE-.77. Twovrible model of reltive humidity nd verge temperture hs MBE.5, MSE. nd MPE-.9. While rtificil neurl network hs MBE., MSE. nd MPE.. Bsed on the bove vlidtion results, it therefore become cler tht rtificil neurl network hs better greement with mesured globl solr rdition. Hence, should be used for estimtion of globl solr rdition of Onitsh nd other loctions with similr climtic fctors Key words: Troposphere, globl solr rdition, rtificil neurl network, regression nlysis Introduction The troposphere is the lower lyer of the erth tmosphere. Most of the wether phenomen, systems, convection, turbulence nd clouds occur in this lyer, lthough some my extend into the lower portion of the strtosphere. The troposphere contins lmost ll the tmospheric wter vpour, it contins bout 7 to percent of the totl mss of the erth tmosphere nd 99 percent of the wter vpour. The resulting solr interction on the tmosphere leds to chnges in wether s well s so clled climte chnge. This study is imed t estimting the globl solr rdition with regression nlysis nd rtificil neurl network t Onitsh, Anmbr Stte. A number of correltion with meteorologicl prmeters such s mbient temperture, the totl precipittion, reltive nd specific humidity, totl cloud cover etc hve been developed by different reserchers to estimte globl solr rdition in different loctions. Empiricl model for the estimtion of globl solr rdition with meteorologicl prmeters were first developed by nd the model ws put into convenient form by s: H n + b () Ho N Where H is the mesured globl solr rditions Ho is the monthly extrterrestril solr rdition on horizontl surfce, n is the bright sunshine hours, N is the mximum possible sunshine Hour, H is the clerness index, n is the Ho N frction of sunshine hours, nd b re regression constnts. Mteril nd Methods The dt used for this study were obtined from the Nigeri Meteorologicl Agency, Federl Ministry of Avition Oshodi, Lgos nd enewble Energy for url Industriliztion nd Development in Nigeri. The dt collected cover period of eleven yers (99 ) t Onitsh (Ltitude 5 N, Longitude nd ltitude 5 meters bove se level). The model were developed by converting solr rdition dt for Onitsh mesured in millimeters to useful form (MJ/M /dy) with conversion fctor of. proposed by 5. The two methods involves in this work re regression nlyses nd rtificil neurl network models which is discussed s follows. egression Anlysis: In regression nlysis, the first nd second order regressions of norml equtions were employed to estimte globl solr rdition s follows N N + bx + bx + cr y y () nd () Interntionl Science Congress Assocition 7

2 eserch Journl of ecent Sciences ISSN 77-5 Where, b nd c re constnts which will be determined, y is the sme s H (dependent vrible), while x were used to replce ny of the meteorologicl dt like reltive humidity, temperture ( independent) etc. To execute the regression nlysis of the first order, both sides of eqution () were multiply by nd eqution () by x, the summtion of both sides of the equtions gve N + b x y ( + N x b x xy (5 ) ) Applying our vribles (T v nd ) s the independent vrible in eqution for first order we obtined., N + b Tv H ( ) N + b H ( 7 ) Second order regression nlysis: To obtin second order regression eqution, we multiple eqution () by, x nd x successively nd summing we obtined the following equtions. N + b x + C x y ( ) N x + b x + C x xy (9 ) N x + b x + C x x y ( ) Applying these equtions by using our independent vribles, such s verge temperture nd reltive humidity we hve. H + b Tv + C Tv () H + b + C () Theory of rtificil neurl network: The neurons ct like prllel processing units. An rtificil neuron is unit tht performs simple mthemticl opertion on its inputs nd imittes the functions of biologicl neurons nd their unique process of lerning 7. The weighed sum of the inputs, v k X W + b is clculted t kth hidden node. () wkj is the weight on connection from the jth to the kth node; xj is n input dt from input node; N is the totl number of input (N7); nd bk denotes bis on the kth hidden node. Ech hidden node then uses sigmoid trnsfer function to generte n output Z k [ + ( ) ] - () between - nd. We then set the output from ech of the hidden nodes, long with the bis b on the output node, to the output node nd gin clculted weighted sum, y k V + b (5) Where N is the totl number of hidden nodes; nd vk is the weight from the kth hidden node to the sigmoid trnsfer function of the output node. esults nd Discussion Tble- shows the mesured tmospheric prmeters nd solr rdition. Where, T v monthly verge dily temperture, H mesured vlues of verge dily solr rdition on the horizontl surfce, eltive Humidity. Eqution nd 7 were used to estimte solr rdition of first order, while eqution nd were used to estimte globl solr rdition with second order. The grphs compring the results between results from the regression nlysis, (first nd second order), rtificil neurl network nd the mesured vlues of globl solr rdition is shown in tble -. In the tble below, H mesured vlue of globl solr rdition, H nd H estimtion from first order, H nd H estimtion from second order, while H 5 estimtion from rtificil neurl network. Figure- to shows the grph compring the results from the regression nlysis, rtificil neurl network nd mesured vlues of globl solr rdition. From the grph it is cler tht results from rtificil neurl network estimtion hs closer greement with mesured vlues compred with results from regression nlysis. Tble- shows the differences between estimtion from regression nlysis both first nd second order nd mesured vlues of globl solr rdition, nd the differences between estimtion from rtificil neurl network nd mesured. The results of the differences between rtificil neurl network rtificil neurl network for Februry, July, October nd November is zero, this indictes tht the estimtion of ANN nd mesured vlues re of the sme vlues, while the other months ANN lso hve smll vlues indicting close rnge with the mesured vlues compre to the vlues from regression nlysis. The totl vlue of the differences between rtificil neurl network is smll thn the totl vlues of regression nlysis both first nd second order. Vlidtion of the results using error nlysis show tht one vrible model of reltive humidity hs MBE., MSE.9, MPE -.75 nd one vrible model of verge temperture hs MBE.7, MSE.5, MPE Two vrible model of reltive humidity nd verge temperture hs MBE.5, while rtificil neurl network hs MEE.5, rtificil neurl network hs MBE. respectively. Interntionl Science Congress Assocition

3 eserch Journl of ecent Sciences ISSN 77-5 Conclusion Solr energy hs n importnt role in economic development of our country, since energy plys n importnt role in determining the conditions in which living mtter cn exist. From the results, this study hs show tht tmospheric prmeters cn be used to estimte globl solr rdition. Bsed on the vlidtion results, it therefore becomes cler tht rtificil neurl network hs better greement with mesured globl solr rdition, but both hve estimting cpcity. Hence, rtificil neurl network model should be used for estimtion of globl solr rdition t Onitsh nd other loctions with similr climtic conditions. Acknowledgment The uthors wish to express their profound grtitude to the mngement nd stff of the Nigerin Meteorologicl Agency, Oshodi, nd Lgos for supplying the dt for tmospheric prmeters for this work nd the enewble Energy for url Industriliztion nd Development in Nigeri for mking the solr rdition dt vilble. eferences. Aysegul Y., Atmosphere physics lecture notes, Cnkkle Onsekiz Mrt University (). Attiili P. nd Abdll A., Sttisticl comprison of globl nd diffuse solr rdition correltion. Met. Soc. J., 5, (99). Angstrom A.S., Solr nd terrestril rdition, Met. Soc. J., 5, -7 (97). Prescott J.A., Evportion from wter surfce in reltion to solr rdition, Trn.. Soc. S. Austr.,, - (9) 5. Ambo A.S., Solr rdition with Meteorologicl dt Nig., J. Sol. E.,, 59- (95). Ekpe J.E., Estimtion of globl solr rdition in Onitsh nd Clbr using empiricl models, M.Sc thesis submitted to Ebonyi Stte University, Abkliki-Nigeri (9) 7. Ibeh G.F., Agbo G.A., bi S. nd Chikwenze A.., Comprison of empiricl nd rtificil neurl network models for the correltion of monthly verge globl solr rdition with sunshine hours in Minn, Niger Stte, Nigeri, Int. J. of Phy. Sci., 7(), -5 () Tble - Monthly men vlues of climtic prmeters for Onitsh (99 ) S/N Month T v ( C) (%) H (MJ/M/dy) Jnury Februry Mrch April My..7.5 June July August... 9 September. 5. October.. 5. November December Interntionl Science Congress Assocition 9

4 eserch Journl of ecent Sciences ISSN 77-5 Tble - Difference between Clculted, Artificil neurl network nd Mesured Globl solr rdition S/N Month H H H H H H H H H 5 -H Jn Feb Mrch April My June July Aug Sept Oct Nov Dec Totl Globl solr rdition (MJ/M/DAY) Jn Feb Mr Apr My Jun July Aug Sept Oct Nov Dec H Figure Mesured, estimtion of first order (Tv) nd rtificil neurl network Globl solr rdition (MJ/M/DAY) Jn Feb Mr Apr My Jun July Aug Sept Oct Nov Dec Figure- Mesured, estimtion of first order nd rtificil neurl network H Interntionl Science Congress Assocition

5 eserch Journl of ecent Sciences ISSN 77-5 Globl solr rdition (MJ/M/DAY) H Jn Feb Mr Apr My Jun July Aug Sept Oct Nov Dec Figure- Mesured, estimtion of second (Tv) nd rtificil neurl network Globl silr rdition (MJ/M/DAY) H Jn Feb Mr Apr My Jun July Aug Sept Oct Nov Dec Figure- Mesured, estimtion of second order () nd rtificil neurl network Interntionl Science Congress Assocition

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