Analysis of Using a Hybrid Neural Network Forecast Model to Study Annual Precipitation

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1 Aalysis of Usig a Hybrid Neural Nework Forecas Model o Sudy Aual Precipiaio Li MA, 2, 3, Xuelia LI, 2, Ji Wag, 2 Jiagsu Egieerig Ceer of Nework Moiorig, Najig Uiversiy of Iformaio Sciece & Techology, Najig School of Compuer & Sofware, Najig Uiversiy of Iformaio Sciece & Techology, Najig Key Laboraory of Meeorological Disaser of Miisry of Educaio, Najig Uiversiy of Iformaio Sciece & Techology, Najig mali775088@63.com; wagji@oslab.khu.ac.kr; lixuelia9@26.com Absrac. Whe applied o precipiaio forecasig, he mea geeraig fucio - opimal subse regressio (MGF-OSR) model is limied by is low accuracy ad high error, while he back propagaio (BP) eural ework model has difficuly i learig for marix selecio. This paper proposes a ew MGF-OSR-BP model, which uses a MGF o exed origial daa, a OSR o selec he bes series as he BP eural ework ipu ode ad learig marix, ad he resula daa for raiig. The raiig procedure deermies he umber of hidde layers ad uses a opimal umber of hidde layers for model raiig. This paper uses he MGF-OSR-BP model o aalyze precipiaio daa from Hagzhou, Chia, for 53 years, from 956 o The precipiaio daa are used as he raiig sample, ad he daa are used as he es se daa o verify he pracicaliy of he forecas sysem. A fiig verificaio is performed usig he forecased daa agais field measureme daa, ad he resuls show ha he forecas accuracy is beer ha ha of he MGF-OSR model or he MGF sepwise muliple regressio model. Key words: precipiaio forecas, eural ework (NN), mea geeraig fucio (MGF), opimal subse regressio (OSR).. Iroducio Chia is cosaly affeced by is mosoo climae, ad meeorological disasers emerge frequely. Amog hese disasers, droughs ad floods have he greaes effec o agriculure. To miigae he damage resulig from droughs ad floods as much as possible, i is impora o obai accurae precipiaio forecass []. The arificial eural ework mehod has may promie characerisics, icludig good self-adapive learig abiliy ad o-liear mappig capabiliy. Furhermore, i does o eed o kow he ieral srucure of a forecas sysem, ad isead emphasizes a o-liear mappig relaio bewee he model ipu ad oupu. Currely, eural-ework-based precipiaio forecas sysems are he subjec of much research. Ji ad Che used a eural ework iegraed forecas mehod o sudy sprig precipiaio i Najig, ad heir resuls show ha a eural ework iegraed forecas model resuls i a beer fi ad a more accurae forecas ha oher radiioal iegraed forecas formulas; however, i does o provide a good soluio for selecig a eural ework model srucure ad parameers ad deermiig hidde odes [2]. Li e al. used a back propagaio (BP) eural ework o build a flood 79

2 seaso precipiaio forecas model, ad heir resuls show ha he BP mehod has a beer fiig of hisoric samples ad beer forecas resuls ha he sepwise regressio model; however, he irisic limiaios of BP eural ework model have o bee horoughly ivesigaed [3]. Ji e al. used a eural ework combied wih he mea geeraig fucio (MGF) o build a hybrid forecas model ad coduced a forecas experime o he precipiaio i he orher, ceral, ad souher regios of he Guagxi provice i Jue, ad heir resuls show ha his forecas mehod is beer ha he MGF regressio forecas model ad forecas facor regressio forecas model. However, i ha work, he model buil upo a MGF regressio is o always he global opimum, while he advaage of opimal subse regressio (OSR) is he abiliy o selec he globally opimal subse [4]. Huag e al. coduced research o a pricipal-compoe-based eural ework model ad applied i o a waer level forecas. This model is promiely beer ha a regressio facor eural ework forecas model; however, is hisoric samples have a less accurae fi ha he radiioal eural ework model [5]. Su performed research o combiig he MGF ad OSR o build a model ad used he OSR modelig mehod o calculae he error series for a forecas formula opimizaio. The resuls show ha he MGF model has some degree of reliabiliy for a hydrological facor log-erm forecas [6]. 2. Mehods This paper uses a combiaio of MGF, OSR, ad eural eworks o build a ew hybrid MGF-OSR-BP forecas model. This ew forecas model cosiders boh he model ad he learig marix cosrucio, ses model parameers, deermies a opimal hidde ode umber ad uses OSR o selec a global opimal subse as a learig marix, which overcomes he weakess of MGF i selecig a local subse. Our experimeal resuls show ha he MGF-OSR-BP model is clearly beer a fiig hisoric samples ad forecasig idepede samples ha he MGF-OSR model ad he MGF sepwise muliple regressio model. 3 Fiig ad Forecas Resul Aalysis We used he MGF sepwise muliple regressio mehod ad he MGF-OSR mehod o process he precipiaio daa samples from Hagzhou, ad we compared ad aalyzed he respecive fied values wih hose from he origial sample daa. Similarly, we used a MGF-OSR-BP eural ework mehod o process he 5-year sample daa, ad we compared ad aalyzed he calculaed resuls ad fis of he origial daa ad he MGF-OSR model. 80

3 2400 observaio MGF-OSR model 2200 MGF Sepwise Muliple Regressio 2000 Precipiaio Year Fig.. Fiigs of he MGF Sepwise Muliple Regressio ad MGF-OSR model observaio MGF-OSR-BP NN model MGF-OSR model Precipiaio Year Fig. 2. Fiigs of he MGF-OSR model ad MGF-OSR-BP NN model. Fig. shows he variaio curves of he acual values of aual precipiaio i 8

4 Hagzhou ad he fied values from he MGF sepwise muliple regressio model ad he MGF-OSR model. This figure shows ha he wo models yield good precipiaio fiig resuls, wih he MGF-OSR model havig beer precipiaio fiig ha he MGF sepwise muliple regressio model. This resul is o surprisig because he MGF-OSR model uses OSR for modelig facor selecio ad exracs he global opimal subse variables o esablish he model. As a resul, is model fiig accuracy is beer ha ha of he regressio model. Fig. 2 shows he variaio curves of he acual precipiaio values i Hagzhou ad he fied value of he MGF-OSR model ad he MGF-OSR-BP eural ework model. I is clear ha he MGF-OSR-BP eural ework model has beer precipiaio fiig ha he MGF-OSR model. This superior fiig is exacly he advaage of eural eworks: i ca approximae a o-liear fucio wihi ay degree of accuracy. As a resul, i has a beer fiig accuracy. To compare he fiig resuls of he hree models i a quaiaive approach, he followig 4 idices are defied [7]: () Mea absolue perceage error (MAPE) y yˆ MAPE = y =. () (2) Mea squared error (MSE) MSE= ( y yˆ ) = 2. (2) (3) Mea absolue error (MAE) MAE = = y yˆ. (3) (4) Correlaio coefficie (PR) PR = ( y y )( y yˆ ) 2 2 ( y y ) ( yˆ yˆ ) = = ˆ. (4) = I formulas, y ad ŷ represe he acual ad fied values, respecively. The idex saisic resuls of he hree models are show i Table. 82

5 Table. Compariso of he fiig accuracy of he hree models model MAPE MSE MAE PR MGF-OSR-BP NN model MGF-OSR model MGF sepwise muliple regressio model Table also shows ha all hree models have good precipiaio fiig resuls, while he MGF-OSR-BP eural ework model provides a beer fi ha he oher wo models, wih a perfec resul. The MGF sepwise muliple regressio model has he lowes fiig accuracy, ad he MGF-OSR model fiig accuracy is i bewee hose of he oher wo models. Above is a compariso of he fiig resuls of he differe models. The MGF-OSR-BP eural ework model has a beer fiig accuracy ha he oher wo models; however, havig a srog forecas model fiig capabiliy does o ecessarily idicae a beer pracical forecas capabiliy. Alhough he fiig resuls are oe aspec of model evaluaio, he forecas resuls are more impora. We seleced idepede daa samples from ad used he hree models o ru forecas ess for he idepede samples, ad he resuls are show i Table 2. The resuls i Table 2 show ha, usig a MGF sepwise muliple regressio model for he 2-year idepede sample forecas, he mea absolue error is Agai, he regressio mehod is o good a aual forecasig. Whe usig he MGF-OSR model for he forecas of 2-year idepede samples, he error is moderae, ad he mea absolue error is The MGF-OSR-BP eural ework model forecas yields markedly beer resuls ha he oher wo models, ad is forecas for 2-year idepede samples has a mea absolue error of 66.5, which idicaes a beer forecas capabiliy. Furher aalysis shows ha MGF-OSR-BP eural ework model precipiaio forecas of Hagzhou i 2007 is he closes o he acual daa ad ha i has a beer forecas accuracy ha he oher wo models. Table 2. Compariso of he predicig accuracy of idepede samples of he hree models (O: observaio, P: predicio, A: absolue error, R: relaive error, AVA: average.) Year O (m m) MGF sepwise muliple regressio model MGF-OSR model MGF-OSR-BP NN model P A R/% P A R/% P A R/% AVA

6 4. Coclusios This paper uses a mea geeraig fucio (MGF) for daa exesio, based o a opimal subse regressio (OSR) o selec he opimal daa series as back propagaio (BP) eural ework ipu facors, ad esablishes a ew MGF-OSR-BP eural ework model. This model has a beer fiig accuracy ad forecas resul ha he oher wo models. I fully uilizes he advaages of MGF ad OSR i global opimal learig marix selecio, ad i modelig, i properly uilizes he excelle performace of eural eworks i self-adapive learig ad o-liear mappig. The improveme i forecas capabiliy provides a ew mehod o exed he applicaio of eural eworks i fuure forecas research areas ad provides a referece for similar middle- ad log-erm forecas research based o elemes of ime series daa. I also has promisig poeial fuure applicaios. Refereces. Ji Log. Neural ework forecasig model heory mehods ad applicaio. Chia Meeorological Press, Beijig, -208(2004) 2. Ji Log, Che Nig. Sudy ad compariso of esemble forecasig based o arificial eural ework. Aca Meeorologica Siica, 57(2):98-207(999) 3. Li Yoghua, Liu De, Ji Log. Sudy o raifall predicio model i rai seaso based o BP eural ework. Scieia Meeorological Siica, 22(4): (2002) 4. Ji Log, Luo Yig, WagYehog, e al. Sudy o mixed forecas model of eural ework of mohly precipiaio. Plaeau Meeorology, 22(6): (2003) 5. Huag Haihog, Su Chogzhi, Ji Log. Neural ework predicio model of Xiig river waer level based o pricipal compoe aalysis. Najig isiue of meeorology, 28():58-63(2005) 6. Su Yighog. Forecasig of aual precipiaio based o model of average- growig fucio i HagZhou Ciy. Waer Resources ad Power, 27(2):4-6(2009) 7. Li Yoghua, Ji Log, Miao Qilog, e al. BP Neural Nework muli-sep predicio model based o SSA-MGF. NaJig Isiue of Meeorology, 28(4): (2005) 84