Air Qualiy Index Predicion Using Error Back Propagaion Algorihm and Improved Paricle Swarm Opimizaion Jia Xu ( ) and Lang Pei College of Compuer Science, Wuhan Qinchuan Universiy, Wuhan, China 461406563@qq.com Absrac. As he laes evaluaion sandards of air qualiy released by he Sae Environmenal Proecion Deparmen, he Air Qualiy Index (AQI) is influenced by sulfur dioxide (SO 2 ), nirogen dioxide (NO 2 ), pariculae maer wih paricle size below 10 microns (PM10), pariculae maer (PM2.5), carbon monoxide (CO) and ozone (O 3 ) in he air. The variaion of AQI shows nonlineariy and complexiy. In order o improve predicion accuracy, his paper proposes an air qualiy predicion model based on Error Back Propagaion (BP) algorihm. The model is opimized by Paricle Swarm Opimizaion (PSO) algorihm using dynamic ineria weigh and experience paricles. The experimenal resuls show he improved PSO-BP model significanly reduces ieraion ime, effecively improves he predicion accuracy, and provides a new mehod for he AQI predicion. Keywords: BP PSO Dynamic ineria weigh 1 Inroducion Wih he developmen of social economy, ciies developmens have been acceleraed and he car ownership has increased. The conens of SO 2, NO 2, PM10, PM2.5 and O 3 in he amosphere have increased gradually; Environmenal polluion problems have been increasingly serious. As he Sae Environmenal Proecion Deparmen released he laes air qualiy assessmen sandards in 2012, he air qualiy has become a major issue in relaion o he fuure fae of mankind [1]. The sudy around his problem also came ino being. AQI is a single non-dimensional numerical form and is used o quaniaively describe he air qualiy. Is value looks seemingly disorderly, bu he variaion in a long ime shows a cerain rule. AQI is comprehensively influenced by SO 2, NO 2, PM10, PM2.5, CO and O 3 ; is value shows he characerisics of non-linear and abrup changes. So AQI is a complicaed nonlinear sysem. We can find he inernal relaion of influencing facors by he hisorical monioring daa, and hen esablish a predicion funcion o realize AQI predicion. Is principle is similar o he Arificial Neural Nework (ANN). A presen, he air qualiy forecasing applicaion of ANN is sill in he exploraory sage. The BP neural nework is one of he mos widely used neural nework models and has he ypical characerisics of neural neworks [2]. However, he BP algorihm has slow Springer Inernaional Publishing AG 2018 F. Qiao e al. (eds.), Recen Developmens in Mecharonics and Inelligen Roboics, Advances in Inelligen Sysems and Compuing 690, DOI 10.1007/978-3-319-65978-7_2
10 J. Xu and L. Pei convergence and is easy o fall ino a local minimum. To solve hese problems, scholars have pu forward many improved mehods. For example, Li e al. [3] inroduced a variable learning rae and an addiional momenum ino he BP algorihm o jump ou of he local minimum of he error surface. Bu he raining speed of his mehod is no very saisfacory. Zhang e al. [4] used he PSO algorihm o improve he learning sraegies of he BP neural nework. In his paper, he learning speed of BP algorihm is improved, bu for he high dimension complex problem, he PSO algorihm is faced wih he premaure convergence problem. This paper adops he dynamic ineria weigh and experience paricles [5] o improve he sandard PSO algorihm; i uses he improved algorihm o opimize he BP nework learning sraegy and hen builds he PSO-BP predicion model o realize AQI simulaion. The experimenal resuls show ha he improved PSO-BP algorihm no only could shoren he algorihm ieraion ime, bu also could improve he convergence speed and he predicion accuracy. 2 Sandard BP Neural Nework The BP neural nework is a mulilayer feed forward nework wih he one-way ransmission. I is composed of inpu layer, hidden layer and oupu layer, is main characerisic is he signal forward propagaion and he error back propagaion [6]. The sandard BP is a feed forward neural nework wih hree layers opological srucure and has only one hidden layer. The research shows if we selec he suiable connecion weighs and he ransfer funcion, a neural nework wih enough neurons and only one hidden layer could approximae any smooh, measurable funcion beween he inpu and oupu [7]. Therefore, his paper uses he sandard BP neural nework as he nework prooype. The sandard BP neural nework adops he sigmoid funcion o calculae he nework oupu of each level. The sigmoid funcion is a non-decreasing coninuous funcion; is value is a floaing poin number beween 0.5 and 1.5. The funcion represens he sae coninuous neuron model and is processed very convenienly. When he oal error of inpu samples can achieve he desired effec, he nework eners he error back propagaion sage. Using he formula (1), he BP algorihm calculaes he weighs beween he hidden layer and he oupu layer. The weighs can be used o inversely modify he weigh marix o achieve he opimizaion algorihm. The formula (1) is defined as Δw jk = ηδ y z k j = η( ) ( ) ( d k y k yk 1 yk zj m ) Δv ij = ηδ z x j i = η δ y w ( ) (1) k jk z j 1 zj xi k=1 Where Δw jk and Δv ij are he adjusing weighs. δ k and δ j are he error signals of each level. η is a proporional coefficien and is value is a random number beween 0 and 1. x i is an inpu componen. z j is an oupu componen of he hidden layer. y k is an oupu componen of he oupu layer. d k is an expeced oupu componen.
3 Improved PSO Algorihm Air Qualiy Index Predicion Using Error Back Propagaion 11 The PSO algorihm [8, 9] is a kind of ypical swarm inelligence algorihm,i can simulae he foraging behavior of birds in he naure o find an opimal soluion hrough individuals collaboraing and informaion sharing. In 1998, Shi and Eberhar in he academic paper A Modified Paricle Swarm Opimizer [10] inroduced an ineria weigh ino he evoluion equaion, hus he sandard PSO algorihm was born. The ineria weigh is a very imporan parameer in he sandard PSO algorihm. The larger he ineria weigh is, he sronger he exploraion abiliy is; he smaller he ineria weigh is, he sronger developmen abiliy is [11]. In his paper, we have sudied lieraures [12 15], compared and analyzed he advanages and disadvanages of he linear ineria weigh. A las, we linearly increase he value of he ineria weigh before 1000 ieraions, and hen linearly decrease is value, so as o balance he exploraion abiliy and developmen abiliy of he improved PSO algorihm. So we define he dynamic ineria weigh as a funcion of he ieraion ime and he funcion is defined as 1 w(k) = 1 MaxNum + 0.25, 0 + 1.25, 0.5 < MaxNum MaxNum 0.5 MaxNum 1 (2) where k is he curren ieraion. MaxMum is he maximum ieraion ime. In he algorihm learning process, he finess of each paricle has showed he weakening choice behavior, [5] inroduced experienced paricles ino he speed evoluion equaion o adjus he individual exreme and he global exreme, so as o improve he algorihm convergence speed and accuracy. The updaed formulas of he individual exreme (3) and he global exreme (4) are defined as { Pb () = Pb i (), i < 2 i r 1 Pb i () + r 2 Pb m () + r 3 Pb n (), i 2 Pgb () = r 1 Pb 1 () + r 2 Pb 2 () + r 3 Pb 3 () (4) where Pb i is he curren individual exreme value. Pb m and Pb n are he experienced individual exreme values; hey are randomly seleced from previous ones in he same generaion. Pb is he updaed individual exreme value. Pgb is he updaed global i exreme value. Pb 1, Pb 2 and Pb 3 are hree bes individual exremes from he same generaion. r 1, r 2 and r 3 are random values beween 0.5 and 1.5, and r 3 = 1 r 1 r 2. (3) 4 Simulaion Design and Analysis The simulaion experimen selecs 13 groups of Wuhan beween May 1, 2016 and May 13, 2016 as he samples; hey come from he China air qualiy on-line monioring and analysis plaform (hp://www.aqisudy.cn/). PM2.5, PM10, CO, NO 2, O 3 and SO 2 are
12 J. Xu and L. Pei he nework inpus, AQI is he arge daa. The firs 12 groups are raining samples, NO. 13 daa is a es sample. Through experimenal comparison, he nework srucure of improved PSO-BP model is 6-8-1; he populaion size is 20; he paricle dimension is 65. The iniial posiion componen is a random number beween 1 and 1. The curren velociy componen is a random number beween 0.5 and 0.5. The maximum ieraions number is 2000 and he minimum error is 0.001. Firsly, he algorihm convergence analysis and he nework oupu curve analysis are shown as Fig. 1(a) and (b). Fig. 1. (a) Convergence properies picure; (b) Oupu picure By Fig. 1(a) and (b), he convergence speed of he sandard BP algorihm and he momenum BP algorihm are slow in he lae raining; hey can reach he minimum convergence precision; he prediced values have he obvious deviaion. The improved PSO-BP algorihm keeps a good convergence rae, i can reach he minimum error a 143 ieraions; Is deviaion values only show in No. 8, No. 9, No. 10 and No. 12. So he improved algorihm has he beer effec of convergence and forecas han ohers. Secondly, he relaive error value comparison of hree algorihms is shown in Table 1. In Table 1, he deviaion value of he improved PSO-BP algorihm in No. 8, No. 9, No. 10 and No. 12 is beween 1.13 and 1.45, oher values are all smaller han 0.9. So he algorihm doesn have large deviaion value. Is Ave_Error value is only 0.64%, which is smaller han oher wo algorihms. So he improved PSO-BP algorihm in his paper is obviously beer han ohers.
Air Qualiy Index Predicion Using Error Back Propagaion 13 NO. Expeced oupu Table 1. Sandard BP Momenum BP Improved PSO-BP Prediced value Error (%) Prediced value Error (%) Prediced value Error (%) 1 68 69.801345 2.65 68.402343 0.59 68.568022 0.84 2 66 64.478980 2.30 64.435718 2.37 65.873440 0.19 3 83 82.555808 0.54 82.613787 0.47 83.318232 0.38 4 87 87.602480 0.69 87.068520 0.08 87.304945 0.35 5 55 58.106085 5.65 58.013594 5.48 55.155547 0.28 6 71 70.300322 0.99 70.347997 0.92 70.951919 0.07 7 93 95.401679 2.58 93.363184 0.39 92.745650 0.27 8 69 68.808340 0.28 69.869844 1.26 68.178084 1.19 9 63 62.557808 0.70 62.927736 0.11 63.714685 1.13 10 69 69.101081 0.15 68.885957 0.17 68.165413 1.21 11 88 89.685779 1.92 88.707819 0.80 87.670740 0.37 12 106 101.425017 4.32 103.009014 2.82 104.462997 1.45 13 75 71.917179 4.11 72.021966 3.97 75.448108 0.60 Ave_Error (%) 2.07 1.49 0.64 5 Conclusion In his paper, he dynamic ineria weigh and experience paricles are used in he improved PSO-BP algorihm o opimize nework weighs and hresholds. This inegraion mehod makes full use of he neural nework learning abiliy and he global opimizaion of PSO algorihm. I provides a new mehod for predicing AQI. In he fuure, his paper will sar from he nonlinear adjusmen mehod of ineria weigh, and furher improve he global opimizaion of PSO algorihm. References 1. Zhang, Y., Xiao, D., Zhao, Y.: A sudy of meeorological predicion wih neural nework based on ime series. J. Wuhan Univ. Technol. 27(2), 237 240 (2003) 2. Li, X.: Air qualiy forecasing based on GAB and fuzzy BP neural nework. J. Hua zhong Univ. Sci. Technol. 41(supp I), 63 65 (2013) 3. Li, Z., Zhou, B., Lin, N.: Classificaion of daily load characerisics curve and forecasing of shor-erm load based on fuzzy clusering and improved BP algorihm. Power Sys. Pro. Conrol 3, 56 60 (2012) 4. Zhang, D., Han, S., Li, J., Nie, S.: BP algorihm based on improved paricle swarm opimizaion. Compu. Simul. 2, 147 150 (2011) 5. Jia, X., Yan, Y., Rui, Z.: Graduae enrollmen predicion by an error back propagaion algorihm based on he muli-experienial paricle swarm opimizaion. In: 11h Inernaional Conference on Naural Compuaion (ICNC 2015), Zhangjiajie, China, pp. 1163 1168 (2015) 6. Lu, Y., Tang, D., Hao, X.: Produciviy maching and quaniaive predicion of coalbed mehane wells based on BP neural nework. Sci. China (Technol. Sci.) 54(5), 1281 1286 (2011)
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