Atmospheric Environmental Quality Assessment RBF Model Based on the MATLAB

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1 Journal of Envronmental Protecton, 01, 3, Publshed Onlne July 01 ( 689 Atmospherc Envronmental Qualty Assessment RBF Model Based on the MATLAB Zhonghua Fe 1, Dnggu Luo, Zhefe He 1, Bo L 1 1 School of Mathematcs and Physcs, Changzhou Unversty, Changzhou, Chna; School of Envronmental Scence and Engneerng, Guangzhou Unversty, Guangzhou, Chna Emal: @snacom, fzh@cczueducn Receved February 14 th, 01; revsed March 1 st, 01; accepted Aprl 6 th, 01 ABSTRACT A new method-rbf model s found to assess the atmospherc ualty by use of the PREMNMX functon n MATLAB to pretreat the orgnal data and the RAND functon to construct enough tranng samples, checkng samples and s of ther targets through lnear nterpolaton between grades of the atmospherc ualty evaluaton standard A favorable assessment result s acheved by applyng ths method to assess atmospherc envronmental ualty n a cty, whch shows ths new method s meanngful n mprovng the precson and scentfcty of atmospherc envronmental ualty assessment Keywords: Atmospherc Envronmental Qualty Assessment; The BP Network; The RBF Network; Artfcal Neural Network 1 Introducton Artfcal neural network to smulate human bran, havng the trats of self-organzed, self-learnng, adaptve, fault tolerance and other characterstcs; they can be wdely used n pattern recognton, etc Envronmental ualty assessment n essence s a knd of pattern recognton on samples accordng to standards for envronment ualty, and therefore, t s of very realstc sgnfcance to research neural network approach n the applcaton of atmospherc envronmental ualty assessment Ths paper ntroduces the prncples of the radal bass functon (RBF) network, tranng methods and the realzng functons n the Toolbox of MATLAB65 The realzng functon has advantageous propertes such as adaptaton for determnng the network constructon and ndependence of the on ntal weght values We apply ths functon to atmospherc ualty assessment n a cty, attemptng to pretreat orgnal data wth help of PREMNMX functons n MATLAB, usng the RAND functon to construct enough tranng samples, checkng samples and s of ther targets through lnear nterpolaton between grades of the atmospherc ualty assessment standard, and determnng the boundares of atmospherc ualty grades The outcome we acheved s uet satsfed So ths method s meanngful n mprovng the accuracy and objectvty of atmospherc envronment ualty assessment In addton, compared wth RBF, the BP network showed artfcalty on structure dentfcaton and random mpact on results by ntal weght value The Prncple of Radal Bass Network We wll ntroduce RBF basc prncple [1-], tranng and ts realzaton methods referenced by MATLAB65 toolbox functon The radal bass network s a three-layer feedforward network composed of nput layer, hdden and layer, see Fgure 1 (wth a sngle neurons as an example) where hdden neurons use radal bass functon as actvaton functon, usually wth Gaussan functon as radal bass functon About neural network nformaton transmsson, the nput layer s only responsble for nformaton transmsson, and the nput and are the same For hdden layer, each neuron nputs the product of the dstance between the vectors W1 and the vector X multpled by ts own offset value b1 The vector W1 s the connected weght value between neuron of hdden layer and of nput layer and also known as the th hdden layer neuron functon (RBF) center The vector X represents the th nput vector denoted by X x1, x,, xj,, xm From the Fgure, we can see that the th neuron nput for the hdden layer produced by the correspondng the th nput of the nput layer s : k

2 690 Atmospherc Envronmental Qualty Assessment RBF Model Based on the MATLAB Fgure 1 Constructon of RBF network Fgure 3 Relatonshp among W 1, X, C and r Fgure Sketch map for nput and about the hdden nerve unt n RBF network k w1j xj b 1 j By Gaussan transformaton, the th from the th neuron nput of the hdden layer s w1j xj b1 k j W1X b1 r e e e In MATLAB neural network functon t sets b C And then the hdden layer neurons s changed to: W1 X 0836 W1 X 0836 C C r e e The values of C reflects response wdth of for nput, shown n Fgure 3 For example: f C takes 4, then the response wdth wll be large, often 05 above when the dstance between the nput vector and correspondng weghts vector s less than 4, conversely, response wdth s small The bgger C takes, the better smoothness between two neurons we wll get, caused by the response range of the hdden neurons to nput vector expand wth t 05 W1 X C r 05 W1 X C 05 W1 C C The s weghted summaton of each hdden layer neurons, exctaton functon usng pure l near functon Then the neuron y produced by the correspondng the th nput of the nput layer s n y r w 1 RBF network tranng s dvded nto two steps, the frst step for the supervsed learnng tranng the weghts W1 between nput layers and hdden layer, the second step for supervsed learnng tranng the weghts W between hdden layer and the layer Network tranng needs to provde nput vector ( X ), correspondng target vector (T ) and radal bass functon expanson constants ( C ) When the number of neurons n hdden layer euals the number of nput vector, the value of C can take a smaller one The purpose of the tranng s to get the weghts W1, W, and the offset value b1, b (when the number of hdden unts euals the number of nput vector, we wll take b 0) In RBF networks tranng, one of the key problems s to decde the number of neurons n hdden layer In the past, we often make t eual wth the number of the nput vector Apparently, for many nput vector, too much hdden unts s dffcult to acceptable Therefore we wll mprove the method The basc prncple s: 0 as a neuron started tranng, by checkng the error to make the network automatcally ncrease neurons, after the tranng sample loopng once, usng the tranng sample whch make the network produce have the maxmum error as the weght vector W1 to generate a new hdden neuron, then recalculatng, checkng the error of the new network, repeatng ths process untl t reaches the reured error or maxmum number of hdden neurons Ths tranng algorthm s realzed by NEWRB functons n MAT- LAB65 It can be seen that NEWRB functon has propertes such as adaptaton for determnng the network constructon and ndependence of ntal weght value on person, whch reduce randomness of the network tranng 3 Applcaton of the Radal Bass Network The followng by ntroducng an atmospherc envron-

3 Atmospherc Envronmental Qualty Assessment RBF Model Based on the MATLAB 691 mental ualty assessment s gven to show the entre process of the applcaton of radal bass network 31 Raw Data The assessment standards of atmospherc envronmental ualty and the atmospherc montorng data of all the year round n one cty can be seen n Tables 1 and [3] Then we wll use the radal bass network to evaluate the atmospherc ualty of the cty 3 Preparatons for Neural Network 1) Tranng set, test samples and the formaton of the desred objectve Tranng set: we use RAND functon n MATLAB to generate the tranng sample by lnear nterpolaton wth the random unform dstrbuton at dfferent evaluaton levels By 500 samples generated when less than Level 1, 500 between Level 1 and Level and so on, 000 tranng samples are formed Ths method solves the problem that the tranng samples are too few to construct test samples n the past when they only used the evaluaton standard as the tranng sample Test samples: we generate the test samples n the same way of generatng the tranng sample 100 generated when less than Level 1, 100 between Level 1 and Level, by analogy, 400 test samples are formed The desred objectve (for the tranng set and test samples): adoptng an neurons, when both the tranng Table 1 Evaluaton standards for atmospherc envronmental ualty The evaluaton ndex Level 1 Level Level 3 Level 4 SO (mg/m 3 ) NO X (mg/m 3 ) TSP (mg/m 3 ) Dust fall (t/km month) Table Montorng data for atmospherc envronmental ualty and assessment results The evaluaton ndex The sample for evaluatng Sprng Summer Autumn Wnter SO (mg/m 3 ) NO X (mg/m 3 ) TSP (mg/m 3 ) Dust fall (t/km month) Network The ratng Level 4 Level 4 Level 3 Level 3 samples and test sample are less than Level 1, accordng to ther nterpolaton proporton t wll generate a number between 0 and 1 as the correspondng desred objectve; when both the tranng samples and test sample are between Level 1 and Level, accordng to ther nterpolaton proporton t wll generate a number between 1 and as the correspondng desred objectve; when between Level and Level 3, a number between and 3 as the correspondng desred objectve; and so on ) The demarcaton of atmospherc ualty evaluaton grades Accordng to the above method t can be sure that the network of Level 1, Level, Level 3 and Level 4 are respectvely less than 1, between 1 and, between and 3 and larger than 3 3) The orgnal data preprocessng There are two knds of pretreatment plans One s normalzaton, namely, by use of PRENMX functon normalzng raw data to between 1 and 1; the other s no normalzaton, that s, the orgnal data not beng preprocessed 33 Radal Bass Net Constructons, Tranng and Testng 1) Radal bass network constructon The number of nput layer neurons n RBF network depends on the number of atmospherc ualty evaluaton ndex whch s 4, and the number of the layer neurons s set to 1 The number of the hdden unts can be adaptvely determned by the use of MATLAB NEWRB functon tranng network The exctaton functon of the hdden unts s RADBAS, the weghted functon DIST, and the nput functons NETPROD The exctaton functon of the layer neurons s pure lnear functon PURELIN, the weghted functon DOTPROD, and the nput functons NETSUM [4] ) Network tranng, testng and atmospherc ualty assessment Usng the functons provded by MATLAB65, network tranng, testng and applcaton can be realzed easly by programmng Wth the method of normalzaton, network tranng 6 tmes, we can get mean suare error of the tranng sample and test sample s and respectvely Randomly choosng 1 tranng samples and 1 test samples, the relatve errors can be seen n Table 3, whch shows network has good generalzaton ablty Applyng the traned network for atmospherc ualty assessment, we get the network for the sprng, summer, autumn and wnter (see Table ), whch s 3041, 30139, 7118 and 8419 respectvely 3) Analyss of the results Accordng to the network the evaluatng samples can be ranked n the ascendng order whch s autumn, wnter, summer and sprng It reflects the ar ualty

4 69 Atmospherc Envronmental Qualty Assessment RBF Model Based on the MATLAB Table 3 Network errors of the tranng samples and checkng samples The tranng sample Test sample Seral number Target The actual The relatve error (%) Seral number Target The actual The relatve error (%) order of the four samples (see Fgure 4) The graph ntutvely shows the dstrbuton of each ndex of the four samples It s clear that: n autumn, only one ndex exceeded Level 3, n wnter, there are two ndexes exceeded Level 3, n summer, there are two ndexes exceeded Level 4 and n sprng there are three ndex exceeded Level 4 Accordng to the demarcaton of atmospherc ualty assessment grades, we know the level of the samples that s sprng and summer as Level 4, autumn and wnter as Level 3 The above analyss shows that RBF network method not only can dstngush ualty level, but also can accurately gve ther dfference at the same ualty level 3) The orgnal data normalzed problem Many experments show that f the network tranng uses the orgnal data not normalzed, no matter what we adjust the mean suare error, the network can not the rght result 34 Applcaton Effect of the BP Network Compared wth radal bass network, we construct BP Fgure 4 Order for the envronment ualty of dvdng samples network to solve the problem The process s as follows: 1) BP network constructon Takng three-layer network, the number of the nput and layer neurons s determned as 4 and 1 respectvely There has not been a unform method how to determne the number of the hdden unts Here we follow ths common emprcal formula [5]: m n n mlog n m nn o o where m s the number of the hdden unts, n s of nput layer, no s of the layer and s between 1 and 10 The numbers of two knds of hdden unts are 10 and 3 respectvely The nput and functons (exctaton functon) for hdden unts and the unts are respectvely by means of hyperbolc tangent functon and lnear functon, namely, TANSIG and PURELIN functons n MATLAB Network s traned by usng Powell-Beale conjugate gradent back propagaton algorthm, namely TRAINCGB functon n MATLAB [4] ) BP network s dependence on network structure and ntalzed weghts Normalzng raw data and controllng the mean-suare error as 00001, we make the experments for two dfferent structures (hdden unts) and twce for the same structure (reflect the nfluence of dfferent weghts) to assess the atmospherc ualty The result can be seen n Table 4 There exts large dfferences among the assessment results of the four samples and the tranng tmes

5 Atmospherc Envronmental Qualty Assessment RBF Model Based on the MATLAB 693 Table 4 The effect for the constructon of BP net and ntal weght value on atmospherc ualty assessment Number of neurons n hdden layer Tranng seral number Sprng Summer Autumn Wnter Tran number whch shows great randomness 4 Conclusons 1) NEWRB-the realzng functon of RBF network provded by MATLAB65 toolbox has propertes such as adaptaton for determnng the network constructon and ndependence of ntal weght value on person, whch can reduce the randomness of network tranng, so as to mprove the objectve scentfcty of the atmospherc ualty assessment ) Usng RAND functon n MATLAB to construct enough tranng samples, checkng samples and the correspondng target, t can avod the past problem only wth the evaluaton standard as the tranng samples whch are too few to construct test samples The method used n ths paper has remarkable effect n mprovng generalzaton of network 3) It s suggested that the orgnal data can be normalzed n the applcaton of MATLAB toolbox functons to mplement radal bass functon; otherwse, the network s hard to convergence 4) A favorable outcome appeared after we apply the radal bass network mentoned n ths paper to evaluate atmospherc envronmental ualty n a Cty The network of the four evaluatng samples s ranked n the ascendng order whch s 7118, 8419, and 3041 The correspondng samples are autumn, wnter, summer, and sprng respectvely whch perfectly reflect ther atmospherc ualty order Accordng to the demarcaton of atmospherc ualty grades, we know the level of the samples Sprng and summer are at Level 4, autumn and wnter are at Level 3 In practce, we can use many network s from the montorng statons to create regonal ar ualty soclnes for the atmospherc ualty assessment whch can reflect varaton of regonal atmospherc ualty more accurately 5) Compared wth RBF networks, the BP network has random of determnng the network constructon and ntal weght value So we suggest that RBF network s used to assess the atmospherc ualty REFERENCES [1] P D Wasserman, Advanced Methods n Neural Computtng, Van Norstrand Renhold, New York, 1993 [] S Cong, The Functon Analyss and Applcaton Study of Radal Bass Functon Network, Computer Engneerng and Applcatons, Vol 38, No 3, 00, pp [3] W D Yang and H I Cheng, The Appled Research of Neuro-Network n Evaluaton of Ar Qualty, Industral Safety and Envronmental Protecton, Vol 7, No 9, 001, pp [4] D Xu and Z Wu, The System Analyss and Desgn Based on MATLAB6X Neural Network, Xdan Unversty Press, X an, 00 [5] L Q Han, The Theory of Artfcal Neural Network, Desgn and Applcaton, Chemcal Industry Press, Bejng, 001