Study on Multivariate Regression Analyzing and BP ANN Combination Method for Groundwater quality Forecasting

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1 Internatonal Forum on Energy, Envronment and Sustanable Development (IFEESD 206) Study on Multvarate Regresson Analyzng and BP ANN Combnaton Method for Groundwater qualty Forecastng Png Yang, a,laun Lu,b, Xnmn Wang,c College of Earth Scence, Jln Unversty, Changchun, 0000, Chna a 9627@qq.com, blul956@6.com, cwxm@lu.edu.cn Keywords: the quantfcaton theory, multvarate lnear regresson, data dmensonalty, BP artfcal neural network, groundwater qualty forecastng Abstract. In ths paper, the quantfcaton theory model I based on the theory of multvarate lnear regresson was used as a preprocessng tool to reduce data dmensonalty n factors nfluenced groundwater qualty. hen BP ANN groundwater qualty forecastng model was created and 8 mportant characterstc factor s used as nodes of nput layer. he smulaton results covered most of the exstng expermental data n LGuanPu area of Shenyang cty. he results showed that the method was more precse and accorded wth actual nstance. Introducton Groundwater qualty are generally affected by human actvtes, water and rock nteracton processes, sol, geologcal structure of aqufer and other natural factors. he research s related to geologcal characterstcs, geochemstry, geophyscs, remote sensng, hydrogeologcal geology and other massve geoscences data. hus reducng data dmensonalty, dscoverng the essence of the data consttute the man content of massve data analyss n hydrogeologcal geology. Many models have been proposed about dmensonalty reducton n the past few decades. For example, there are Factor Analyss model, Prncpal Component Analyss, Dscrmnant Analyss model and so on. In ths paper, the quantfcaton theory model I based on the theory of multvarate lnear regresson was used to fnd the contrbuton of each factor. As a result, the mportant factors are selected and dmenson of nput varables s reduced through quantfcaton theory I. Fnally, an BP ANN model s created by learnng and tranng wth the mass sample data of montorng wells. Overall, the combned model can be used to predct the pollutant concentraton n the groundwater for a perod of tme n the future. he effectveness of ths method has been confrmed effectve by the predctng applcaton of groundwater polluton n LGuanPu, where s a water source area n Shenyang. he background of Study Area he water source area LGuanPu s located n the southwest of Shenyang, along the north bank of Hunhe rver. Geographcal coordnates: longtude 2 5 '00 " ~ , lattude 2' 00" ~ 7 0. he study area covers an area of 26.5 square klometers. here are 62 wells n the study area and conductvty of aqufer s better. Specfc capacty can reach 0L/(s.m). he basc theory, model and calculaton Dmensonalty reduced based on the quantfcaton theory model. In ths paper,, K, C a 2, M g 2, ph values, tme t, the geologcal characterstc of aqufer, the C l, N O, S O 2 composton of aqueous meda all the nfluence factors are used as the proect and related categores n the quantfcaton theory model I. he concentraton of ammona n the groundwater s used as reference varable. As shown n able, tems (8 quanttatve tems,5 qualtatve tems) and 2 categores are lsted he authors Publshed by Atlants Press 802

2 able. Impact factors of Pollutant Concentratons n Groundwater Item Category Factor Item No Item tle Category No Category tle/unt Quanttatve Item Concentraton of C l C [mg/l] Item2 Concentraton of NO C2 mg/l 2 Item Concentraton of SO C mg/l Item Concentraton of K C mg/l Item5 2 Concentraton of Ca C5 mg/l Item6 2 Concentraton of Mg C6 mg/l Item7 Concentraton of HCO C7 mg/l Item8 Sequence Number of me t C8 N/A (998/0 as base datum lne.value=; 998/02 value=2;and so on.) Qualtatve Item9 the salnty of aqufer C9 Sand Cobble gravel(sc) C0 Sand gravel(sg) C Pebbly grt(pg) Item0 the structure of aqufer C2 Sngle Layer C Double Layer C Multlayer Item Structural faults C5 Yes C6 No Item2 Structural fold C7 Yes C8 No Item ph value of groundwater C9 Acdty C20 alkalne C2 Neutral As s descrbed n able 2, there are 8 quanttatve and 5 qualtatve varables and 9 samples s observed. able2. he sample partly data of 9 drllng wells for ItemsCategores Wells No 2# # 5# 25# 0# 8# 9# # # ItemCategory C l NO SO Sequence No of me the salnty of aqufer the structure of aqufer SC Sg pg S D M Structural faults Yes No 0 0 reference varable (ammona) For qualtatve tem, δ ( k, ) s the reacton of Category k of Item n Sample. 80

3 th th th here s response n the the type of the k tem n the sample δ ( k, ) = th th th 0 No response n the the type of the k tem n the sample For quanttatve tem, the sample data s x ( u)( u =,2,...,8;=,2,...,9),so Reacton Matrx s: x(),..., x(8), δ(,),..., δ(, r),..., δ(5, r5 ) x2(),..., x2(8), δ2(,),..., δ2(, r),..., δ2(5, r5 ) X = x9(),..., x9(8), δn(,),..., δn(, r),..., δn(5, r5 ) In quantfcaton theory I, he react data of reference varable, tem and category can be expressed by the followng lnear regresson model[,]: y = bx ( u) δ ( kbk, ) ε, =,2,...,n h m r () u u= = k= In Eq., bk s constant coeffcents or regresson coeffcent whch depends on categoryk of tem, ε s random error n the sample, y s actual observatons n the sample. As smlar as lnear regresson analyss, least squares estmaton value bu and b k calculated accordng to the prncple of least square method. It s been proved that the least squares estmaton value s mnmum varance unbased lnear estmates. From the react matrx X, t s been concluded: X Xb= X Y [,,... ] Y = y y y 2 n =, 2,..., h,,..., r, 2,..., m,..., mrm b b b b b b b b b he accuracy of the quantfcaton theory s the same as the accuracy of multple lnear regresson predcton model. It can be presented as complex correlaton, whch s a correlaton coeffcent related to predcted value and measured value. σ σ = = = σ σ y r a a yy σ y 2 yy 2 2 y y he partal correlaton coeffcent k s used to measure the contrbuton of each tem for reference varable[]. ry k = r r yy After the parameter bu and b k are calculated, the equaton of predctng groundwater qualty s presented:[5] y = 0.82 x ( u) 0.27 x ( u) 0.20 x ( u) 0.2 x ( u) x ( u) x ( u) 0.2 x ( u) 0.5 x ( u) 0.27 δ(,) δ(,2) 0. δ(,) 0.02 δ(2,) 0.2 δ(2,2) 0. δ(2,) 0.09 δ(,) 0.98 δ(,2) 0.22 δ(,) 0.00 δ(,2) 0.09 δ(5,) 0.6 δ(5,2) 0.22 δ(5,) In Eq. 2,whle regresson coeffcentbk s solved, partal correlaton coeffcent k of each tem s calculated,as s shown n able. (2) 80

4 able. ItemParameter relatonshp table Item No tle partal correlaton Varance rato range coeffcent k the concentraton of C l the concentraton of NO the concentraton of SO the concentraton of K the concentraton of Ca the concentraton of Mg the concentraton of HCO Sequence Number of me t the structure of aqufer the salnty of aqufer Structural faults Structural fold ph value of groundwater From the able,t can be seen that the values of three parameters for tems are bascally consstent. Accordng to the contrbuton on reference varables, All tems are sorted as Concentraton of NO, me t, Concentraton of C l, Concentraton of HCO 2, concentraton of SO, the structure of aqufer, the salnty of aqufer, ph value of groundwater Structural fold. From the pont of vew of varance rato, the cumulatve sum of the frst eght tems account for 95.72% of the total. It s consstent wth the current stuaton of research area where Permanganate, Ammona Ntrogen exceeded serously n recent years because of envronment polluton. In addton, t can be concluded that the factor about space(such as the structure of aqufer, the salnty of aqufer) and the factor about tme affect the transportng of groundwater contamnaton greatly[67]. It has been proved that 8dmensonal data nstead of the orgnal dmensonal data not only smplfes the nput layer of subsequent BP artfcal neural network model,but also reflects the actual state of groundwater system structure. he predcton of groundwater qualty based on BP ANN model. In the feld of system smulaton and predcton about groundwater resources, BP neural network has been more applcatons. BP neural network s smple,the speed of tranng s fast,and any functon can be ftted at arbtrary precson, especally whch s sutable for solvng problem of classfcaton and predcton. In ths paper, a BP ANN model s created to predct the pollutant concentraton. In the BP ANN structure, there are 8 nodes of nput layer: Concentraton of NO, me t, Concentraton of C l, Concentraton of HCO 2, concentraton of SO, the structure of aqufer, the salnty of aqufer, ph values, here are 6 nodes of hdden layer, because accordng to the experence, the number of hdden layer nodes s generally 75% of the number of nodes n the nput layer[8]. here s one node of out layer: concentraton of Ammona. he forward calculaton of the neural network s as follows: n o = wx θ, n=,2,...,8; =,2,...,6 () B = = f ( ) o, =,2,..., l () l L = v B γ, u = (5) u u u = C ( ), u = f2 Lu u = (6) In Eq. Eq. 6, x ( =,2,...8) s the node of nput layer. w ( =,2,...8; =,2,...6) s the connecton weght of neuron of nput layer and neuron of hdden layer. θ ( =,2,...6) s the threshold 805

5 of hdden layer. f ( ) x s the motvaton functon of hdden layer. B ( =,2,...6) s the output of hdden layer. v ( =,2,...6; u = ) s the connecton weght of neuron of hdden layer and neuron of u output layer. γ ( u = ) s the threshold of output layer. f ( ) 2 x s the motvaton functon of out layer. u Cu ( u = ) s the output of output layer. ( k) ( k) E = ( C Y ) 2 (7) 2 k= In Eq. 7, C s the actual output of output layer. Y s the expected output of output layer. C s called Mean square error, whch can gude us to correct the connecton weght value[9]. he reverse learnng process s as follows: vu = vu α E v u (8) ' vu = vu vu w = w α E w (9) ' w = w w In Eq. 8 Eq. 9, E s mean square error, α s learnng rate. In ths paper, 80 sample data of 9 wells n the dry season and the wet season of 0 years s selected from materals of borehole data n LGuanPu water sources from 998 to 2007 to be traned n the BP network.60 sample data from 2008 to 200 s selected as verfcaton sample. Verfy the result of predcton. In ths paper, the forecastng program of BP neural network for sngle well s developed by C bulder6 tools. he 8 feature factors affected the qualty of groundwater polluton concentraton of 60 sample n 2008,2009,200 s nputted to BP Neural Networks. As s shown n able. able. 60 sample data about 8 feature factors for 9 wells n Year Season No NO C l HCO SO 2 t aqufer aqufer ph structure salnty value 2008 Dry 2# S SC AC 2008 Wet 2# S SC N 2009 Dry 2# D SG AC 2009 Wet 2# D PG AC 200 Dry 2# D SG AC 200 Wet 2# M SC N 2008 Dry # M SC AL 200 Wet # S PG AL After calculated by above combned model, the values of groundwater pollutant concentraton of are obtaned. As s shown s able 5,Relatve error of result s 2.5%,5.%,2.0%...5%,the average relatve error s.75%. So t could be concluded that the accuracy of combned model for predcton s very hgh and could meet the actual requrement. 806

6 able 5.he predcton error of BP Neural Network Year Season No Actual value (Ammona) Estmate value (Ammona) Absolute error Relatve error 2008 Dry 2# % 2008 Wet 2# % 2009 Dry 2# % 2009 Wet 2# % 200 Dry 2# % 2008 Wet # % 200 Wet # % Conclusons () By the quantfcaton theory I, the feature factor s extracted whle regresson model about hydrogeologcal data s establshed and data dmensonalty s reduced. Moreover, not only qualtatve data can be processed, but also the hybrd data(qualtatve and quanttatve) can be processed. It s more consstent wth the actual stuaton n geology. (2)After reducng the data dmenson, BP neural network model s used for groundwater qualty predcton. he smulaton results of model covers most of the exstng measured data. he method demonstrated the effectveness and superorty n the feld of predcton of groundwater resources, and It provdes a new drecton about the research of groundwater contamnant mgraton and has some promotonal value. Acknowledgements hs work was fnancally supported by the Natonal Natural Scence Foundaton of Chna ( No ). References [] Na L, Webo Zhou: ANFIS Model and Its Applcaton n Groundwater Predcton n Irrgaton Dstrct Based On Prncpal Component Analyss. YELLOW RIVER,Vol.6(20),p.808 [2] ao Sun, Xanfeng Chu,Shbng Pan:Determnaton of Hydrogeologcal Pont Parameters Based on Quantfcaton heory I.Journal of Earth Scences and Envronment,Vol.29(2007),p []Suln Xang,Zhanmeng Lu,:Study on Multvarate Lnear Regresson Analyzng Model for Groundwater Dscharge Forecastng,JOURNAL OF CHINA HYDROLOGY,Vol.26(2006), p.67 []Dongan L, Junru Nng:Reservor predcton wth ntegerated nformaton based on artfcal neural network technology and geostatstcs,oil&gas GEOLOGY,Vol.(200),p.998 [5]Zhenyu Zhao,Shcheng Wang:Informaton processng of mneral resources predcton,gold GEOLOGY,Vol.9(200), p.505 [6]Qan Wang,Guange L:Applcaton of quantfcaton theory n forecastng debrs flows,he Chnese Journal Of Geologcal Hazard and Control, Vol.8(2006), p.8588 [7]Guangya Zhou,Wenquan Dong: On he Methematcal Models Of Quantfcaton heores I&II,Journal of JLn Unversty,Vol.(979),p.8. [8]Zhaota Chen,Ruzeng Gao:Prlmnary,applcaton of quantfcaton theory n SouthSchuan hydrocarbon decson,ogp,vol.28(99),p

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