A Study of Applying Genetic Algorithm to Predict Reservoir Water Quality

Transcription

1 A Study of Applyng Genetc Algorthm to Predct Reservor Water Qualty L. Chen, M. Jamal, C. Tan, and B. Alabbad Abstract Ths paper s amed at demonstratng a genetc algorthm method and applyng t to predct the water qualty of reservor n Tawan sland usng remote sensng data. Genetc algorthms wll be combned wth operaton tree (GAOT) to fnd the relatonshps between nput and output data. A fttest functon type wll be obtaned automatcally from ths method. The advantages of GA are global optmzaton, nonlnearty, flexblty and parallelsm. In the current case study, GA s used to construct the relatonshp between algae concentraton and Landsat sensor data. The results show that the model has better performance than the tradtonal LN transform of lnear regresson method, and smlar performance compared wth back-propagaton neural network (BPNN) method. Index Terms Genetc algorthm, Landsat, LN transform lnear regresson, back-propagaton neural network, operaton tree. I. INTRODUCTION In reservor qualty assessment, tradtonal automatc methods have been used to construct the relatonshp between water qualty of a reservor and the satellte mages. Unfortunately, there are many hdden and useful relatonshps between the nput and output data, whch may not be recognzed by the analyst. Thus many knds of data mnng technques have been developed, such as statstcs, artfcal neural networks, and genetc algorthms. Evolutonary computaton technques, whch are based on a powerful prncple of evoluton: survval of the fttest, are very effcent optmzaton methods. Well-known algorthms n ths doman nclude genetc algorthms, evolutonary programmng, evoluton strateges, and genetc programmng. Among these methods genetc programmng (GP) s one of the most popular search methods. GP has been wdely used for the automatc generaton of programs or equatons between the nputs and outputs. It has an advantage over tradtonal statstcal methods because t s dstrbuton free,.e., no pror knowledge s needed about the statstcal dstrbuton of the data [1] and ts ablty to dscover the L. Chen, M. Jamal, C. Tan and B. Alabbad underlyng data relatonshps and express them mathematcally. Accordng to Chen [2], [3], constructng the data structure of a dynamc tree of the GP could be a dffcult task when GP was used to create Manuscrpt receved March 3, 2017; revsed Aprl 13, L Chen, Mohammad Jamal Mtlak Abualghanam, and Basmah Alabadd are wth the Department of Cvl Engneerng, Chung Hua Unversty, Hsnchu 707, Tawan, ROC (e-mal: lchen@chu.edu.tw, chtan@aerc.org.tw, basmaalabad@yahoo.com). Chh-Hung Tan s wth the Department of Agrcultural Engneerng Research Center, No.196-1, Zhongyuan Rd., Zhongl Dst. Taoyuan Cty 32061, Tawan. the mathematcal equatons. For example, t s hard to choose the proper sze of a tree that can express a meanngful equaton n advance. On the other hand genetc algorthm (GA) can be used to solve a dscrete optmzaton problem. GA represents a paradgm of evoluton computaton based on natural evoluton and derved from the deas of the survval of the fttest [4], such as nhertance, selecton, crossover and mutaton. The advantages of GA are global optmzaton, nonlnearty, flexblty and parallelsm [5]. In recent years, Yeh and Len [6] proposed a newly developed programmng system, genetc algorthm operaton tree (GAOT). GAOT has two parts, operaton tree (OT) and GA. OT s a tree structure whch represents a mathematcal formula and can be optmzed to generate a self-organzed regresson formula, but optmzng the tree structure s a dscrete optmzaton whch cannot be solved usng mathematcal programmng [7]. GA can be used to optmze the OT to ft expermental data n the GAOT process. Recently, some researches such as concrete researches and typhoon researches have been appled GAOT to predct accurate models [7]-[12]. Chen et al. [13] used GAOT to estmate the compressve strength of hgh-performance concrete. Substantal expermental data were used to compare the accuracy of the results obtaned usng the model-buldng technque. The results ndcated that ths model, GAOT, can be used to formulate hghly nonlnear mathematcal equatons nvolvng few estmaton errors to predct the compressve strength of hgh-performance concrete. Chen et al. [14] appled GAOT to mprove the radar-based ranfall estmaton. A case study for typhoon ranfall n shh-men rangauge staton. The 10 most torrental typhoon events between 2000 and 2010 are the nput varables. Two GAOT models, ncludng fve layers and sx layers OT, are proposed and the estmatons were compared wth the emprcal ranfall estmaton formula (Z = ar b ). The results showed that the GAOT wth sx layers s better than those of the Z-R equaton by tradtonal regressve method but smlar to those of GAOT wth fve layers. Tawan s located n a transton zone between the tropcal and subtropcal clmates. It has several reservors that provde water for drnkng, lvng and ndustral use. Eutrophcaton s one of the major water qualty problems n the reservor [15]. Phosphorus and ntrogen nutrents appled to many frut and vegetable gardens located on the upper stream of the reservor are often washed nto the reservor durng heavy rans. These nutrents are essental for algal growth and algal bloom, and they have been recognzed as lmtng nutrents n the reservor [16]. Reservor water qualty s tradtonally montored and DOI: /IJMO.2017.V

2 evaluated based on feld data. Collectng and analyzng feld data are expensve and tme consumng. To mprove tradtonal data collecton method, utlzaton of remote sensng data for water qualty assessment has been nvestgated. Therefore, objectves of ths study nclude estmaton of the water qualty for a reservor n Tawan usng Landsat 8 data and ntroducng a GAOT to compare wth the regresson method and the back-propagaton neural network (BPNN) method. Wong et al. [17] used Aqua/ MODIS data for estmatng suspended solds and salnty n marne Hong Kong, where montorng statons are few, and determned sgnfcant correlatons between MODIS data and n stu data. Danbara [18] used Landsat data to retreve of water qualty varables of Tana lake. The varable are suspended partculate matter, colored dssolved organc matter, chlorophyll-a and turbdty. The results showed that the most domnant water qualty varable whch predomnantly affects the nherent optcal propertes of the lake s suspended partculate matter. Lal et al. [19] used Landsat data to develop more accurate total suspended sold and chlorophyll-a concentraton retreval algorthms at Poteran sland water of Indonesa. The results showed that the developed algorthm for estmatng total suspended sold and chlorophyll-a concentraton produced acceptable accuracy, thus extractng water nformaton from satellte data usng these algorthms are applcable. operator exchanges parts of two sngle chromosomes and the mutaton operator changes the gene value n some randomly chosen locaton of the chromosome. After a number of successve reproductons, the less ft chromosomes become extnct, although those best ft gradually come to domnate the populaton. The reproducton process copes parent chromosomes nto a tentatve new populaton. The probablty of selected chromosomes for the next generaton s drectly proportonal to ts ftness value. A great number of selecton algorthms have been presented n the lterature [21] among them; Roulette Wheel selecton s perhaps the most common method. The crossover recombnes two parent chromosomes to produce offsprng new chromosomes for the next generaton, whch ncludes three steps. Frst, chromosomes from the matng pool are randomly pared. Then, t s determned whether these pars should go for crossover or not, based on a preset crossover probablty. Thrd, chromosome segments between matng pars are nterchanged. The operator can be one-pont crossover or mult-pont crossover as shown n Fg. 1 (a) or (b). To sustan genetc dversty nto the populaton, mutaton s also made occasonally wth small probablty. A random poston of a random strng s selected and s replaced by another character from the alphabet; e.g., n the bnary codng, ths smply means changng a 1 to a 0 and vce versa as shown n Fg. 1 (c). II. GENETIC ALGORITHM OPERATION TREE A. Genetc Algorthm The GAs are a class of stochastc algorthms that has been successfully used as optmzaton technques based on the prncples of natural selecton and genetcs for solvng a wde range of problems [20]. The GA approach dffers from other optmzaton and search procedures n four ways: (1) GAs typcally use a codng of the decson varable set rather than the decson varables themselves; (2) GAs search for optmal solutons n a populaton of decson varable set, rather than a sngle decson varable set; (3) GAs use the objectve functon tself, rather than dervatve nformaton on the objectve functon and constrants; and (4) GAs use probablstc transton rules rather than determnstc rules [5]. The dea of GAs was frst ntroduced by John Holland back n the 1970s and was later popularzed by Davd Goldberg. A GA generates a populaton of possble solutons encoded as chromosomes, evaluates ther ftness and creates a new populaton by applyng genetc operators whch are crossover and mutaton. Each chromosome conssts of "genes" (e.g., bts), each gene beng an nstance of a partcular "allele" (e.g., 0 or 1). By repeatng ths process over many generatons, the GA has fve basc components whch are: a genetc representaton of solutons to the problem; a way to create an ntal populaton of solutons; an evaluaton functon ratng solutons n terms of ther ftness; genetc operators that alter the genetc composton durng reproducton; values for the parameters of GAs. GAs use ftness values of ndvdual chromosomes to carry out reproducton. As reproducton takes place, the crossover B. Operaton Tree Fg. 1. Bnary code. The OT s a tree structure whch represents a mathematcal formula. A fve-layered OT model s shown n Fg. 2. N 1 s the root node denoted a mathematcal operaton (+,,,, ln or exp). N 2 N 15 are nteror nodes denoted a varable, a constant, or a mathematcal operaton. N 16 N 31 are leaf nodes denoted a varable or a constant [22]. Fg. 3 shows an example of operaton tree model. The model used mathematcal operatons,, and ln, varables A, and C, and constant

3 The operaton tree can express the followng equaton (1). A y C D B Establshng a regresson model usng OT needs to determne approprate mathematcal operatons, varables and constants n the root, branches, and leaves of the OT. When the tree-style structure s set up to represent a specfc mathematcal formula, operaton tree can generate predcted output value for each data by substtutng the nput values of data nto the varables on branches or leafs of the tree-style structure. OT performance can be evaluated wth root mean squared error (RMSE) between predcted and actual output values. The mnmum the RMSE of OT, the best the OT fts the dataset. The conventonal regresson analyss requres predetermned formula structure and s only allowed to adjust the regresson coeffcents n the predetermned structure. The dsadvantage can be overcome by OT. OT s a tree-style data structure whch represents a flexble mathematcal formula and optmzng the structure to ft the data best s a dscrete optmzaton problem. Therefore, the optmzaton of OT cannot be solved wth conventonal mathematcal programmng. GA, that can solve dscrete optmzaton problem, s adopted n ths study to optmze the OT to ft the data best. N2 Fg. 2. fve-layered operaton tree. Fg. 3. The parse tree of equaton 1. C. Genetc Algorthm Operaton Tree N1 N4 N5 N6 N7 N8 N9 N10 N11 N12 N13 N14 N16 N17 N18 N19 N20 N21 N22 N23 N24 N25 N26 N27 N28 N29 N30 N31 If we have a set of values for the varables on the OT, the OT (formula) can deduce a functon value [6]. How to produce an OT whose formula can ft the data best s an optmzaton problem when we own a set of data of the algae. Because t s a dscrete and contnues hybrd optmzaton problem, t s very dffcult to solve t. The GA s one of optmzaton paradgms about mmckng the natural evoluton mechansm. The framework of the GA naturally corresponds to a dscrete optmzaton problem. Therefore, ths study employed OT to express a regresson formula whch can ft the data of algae best, and GAs to optmze the N3 N15 (1) OT to ft the data set to produce a self-organzed regresson formula. OT plays the archtecture to represent an explct formula and GA plays the optmzaton mechansm to optmze the OT to ft expermental data n the GAOT process, Fg. 4. In the framework, the database s smply shuffled usng a random samplng, and dvded nto tranng and testng data. The tranng data and testng data are used to evaluate the ftness of each ndvdual (OT) n the populaton [6]. However, the ftness of tranng data s used n the reproducton process but the ftness of testng data s not. So, t s used to evaluate the generalzaton of OT. There are some parameters that may affect the performance of GA. Reference [22] suggested the followng parameters: (1) crossover rate = ; (2) mutaton rate = ; (3) populaton sze = 10 1,000. Therefore, the followng parameters as show n Table I were used n ths study. In addton, a fve-layered OT was employed n ths study as shown n Fg. 2. Table II lsts the gene codes of mathematcal operatons, varables, and constants. GAOT must comply wth the followng rules: When a node s assgned wth code 6 (natural logarthm operaton), Table II, ts code of rght branch wll be neglected. When a node (gene) s assgned wth code 8, 9 15 (varable), t wll be an end node (leaf),.e., ts offsprng nodes (rght- and left- offsprng) wll be neglected. When a node (gene) s assgned wth code 7 (constant), t would be an end node (leaf). The man steps of GAOT follows below: Intalzaton and parameters settng: Ths step sets the parameters of GAOT and randomly generates the ntal populaton. Tranng dataset: The data set s dvded nto tranng data and testng data. Operaton tree tranng model: operaton tree s a learnng tool able to buld an explct formula for use as a predcton model. Ftness evaluaton: used to evaluate each chromosome. Genetc algorthm procedure: genetc algorthm begns wth the selecton process, crossover, and mutaton. Ths procedure wll repeat untl termnaton crteron s satsfed. Optmal soluton. The correlaton coeffcent between the predcted and the actual values s adopted as the ftness functon of GAOT. GAOT s able to acheve both a hgh lnear correlaton and a small estmatng error smultaneously n most cases, so we chose the former as the objectve functon, equaton (2). y * f (2) where s the predcted value of the operaton tree; y s the modfed predcted value; α and β are the regresson coeffcents. y * f (3) 100

4 n 1 ( f f )*( y n 1 2 ( f f ) y) (4) hydroelectrc power, s used for recreaton and prevents floodng. The water qualty of the reservor has been routnely montored at a frequency of once a season snce Montorng ncludes dfferent parameters such as algae concentraton. where y the mean of actual value of dataset, f the mean of predcted value of dataset, y the actual value of data of dataset, and f the predcted value of data of dataset (=1,, n). TABLE I: SETS PARAMETERS DURING GAOT APPLICATION Set Parameters Value Populaton Sze 300 Chromosome Length 8 bt Crossover Rate 0.9 Mutaton Rate 0.01 Generatons 190 Generaton Gap 0.98 Constant Range (K) -100~100 Eltst Yes Run 7 TABLE II: GENETIC CODE OF MATHEMATICAL OPERATION, VARIABLE AND CONSTANT Code Meanng + - x y Code Meanng Ln k Band1 Band2 Band3 Code Meanng Band4 Band5 Band6 Band7 Fg. 4. Flow chart of genetc algorthm operaton tree. III. ALGAE ESTIMATION BY GENETIC ALGORITHM OPERATION TREE The purpose of ths applcaton was to utlze Landsat 8 data to evaluate algae concentratons n a reservor. Whenever the relatonshp was made, the algae concentraton n the reservor may be computed n tme. Whereas the relatonshp between algae concentraton n the reservor and correspondng mage data was constructed through the genetc algorthm operaton tree. Ths system dentfcaton problem may be vewed as a search for a functon type, whch maps nput values onto an output value. The lnear correlaton coeffcent s used as the objectves n ths study. Ths system dentfcaton problem may be vewed as a search for a functon type, whch maps nput values of Landsat 8 onto an output value of algae concentraton. The CCs value s used as the objectves n ths study. A. Study Area Dej Reservor The Dej Reservor (Fg. 5), formed by Tech Dam, s thn, hyperbola-shaped reservor. The reservor s located n the mddle of Tawan on the upstream catchment of the Daja stream. It has a total area of 60, 160 hectares wth a heght of 180 to 290 meters. In blockng the waters of the Daja Rver, t has created a reservor measurng 14 klometers n length and 592 hectares n area. It provdes muncpal water, generates B. Algae Data Set Fg. 5. Dej reservor locaton n Tawan. In ths study, the actual data of algae (Dnophyta) concentraton for 4, 6, 8, 10 /2014, are used and t s expected to have a hgh correlaton wth Landsat 8 data. These data were obtaned from Agrcultural Engneerng Research Center, Tawan R.O.C., and are used to valdate the algae dstrbutons whch derved from Landsat 8 data. Actual data are selected at same tme of Landsat Satellte data overpass. The Landsat 8 mages were acqured from the Unted States 101

5 Geologcal Survey (USGS) explorer for. Ths product s atmosphercally corrected, and contans the entre Earth every 16 days n an 8-day offset from Landsat 7. Image data was mported and processed by usng ERDAS Imagne Geometrc correctons of mages data were performed n order to compare the mages data wth algae montorng locatons. The geometrc correcton was appled, and data band for each mage was obtaned by usng ERDAS. Statstcal propertes of the seven bands are shown n Table III. Forty three entres are used as tranng data and sx as predctve data; the total number of data entres s 49. In order to compare the predctng ablty of GAOT and Lnear Regresson, Correlaton coeffcents (CCs) was used. TABLE III: STATISTICAL PROPERTIES OF SEVEN BANDS Bands Mnmum Maxmum Mean Band Band Band Band Band Band Band C. Estmaton the Algae of Reservor Usng LN (LR).To estmate the spatal varaton of algae concentraton n the reservor usng data of satellte mages, emprcal relatonshp between dgtal numbers of the pre-processed mage bands and algae concentraton was establshed usng LN transform of lnear regresson (LR) method ntally. Ths model utlzed Landsat 8 bands 1 to 7 was gven by the followng equaton (5). LN( a lg ae) 0.003X LR X X X 3 (5) X X X where X 1 = band 1, X 2 = band 2, X 3 = band 3, X 4 = band 4, X 5 = band 5, X 6 = band 6 and X 7 = band 7. In equaton (5), the weght of X 1 (0.003) s smlar wth those of X 2 (-0.001), X 3 (0.001) and X 4 (-0.003), whch are all hgher than those of X 5 (0.0001), X 6 ( ) and X 7 (0.0003). The model was appled on Landsat 8 mage and the results show on Fg Tranng Testng 7 nonlnear relatonshps may exst between the nputs and outputs, t s necessary to use a more advanced automatc programmng and optmzaton model, such as GAOT to ft the complex nonlnear transfer functon between the Landsat 8 bands and algae concentraton parameter. TABLE IV: THE CRITERIA OF LN (LR), BPNN AND GAOT ON THE TRAINING AND TESTING DATA Models LN (LR) BPNN GAOT CCs CCs CCs Tranng Testng Usng BPNN. Back propagaton neural networks (BPNNs) have quckly become the most wdely encountered artfcal neural networks. BPNNs were traned usng varous parameters, ntal condtons and numbers of hdden unts decded by testng data set to avodng over fttng at tranng stage. Then, the BPNN used one hdden layers wth four nodes and termnated after 1,000 teratons for the learnng procedure. The CC of the BPNN are 0.85 and 0.81 for the tranng set and testng set, respectvely as shown n Table IV, whch were smlar to those of the GAOT. Fg. 7 demonstrates the scatter dagram of predcted values versus actual values of algae for the BPNN. Usng GAOT. The same data were used to compare wth the LN (LR) method descrbed above. The GAOT model s mplemented n C++ Language. Fg. 8 shows the result of the parse tree of GAOT. And the fnal optmal equaton obtaned from GAOT s shown as equaton (6). Predcted Value Tranng Testng Actual Value Fg. 7. Tawan reservor algae concentraton- BPNN. 60 Predcted Value Actual Value Fg. 6. Tawan reservor algae concentraton-ln(lr). The CCs of equaton (5) are and for tranng set and testng set, respectvely as shown n Table 4. Snce Alg ae GAOT Fg. 8. The parse tree of GAOT. X 6 (6) LN X 5 X 3 X 4 102

6 The result shows that only four nput varables X3, X4, X5 and X6 were chosen automatcally from total seven nput varables by GAOT to form equaton (6) through a lot of generatons evolutons and compettons. It shows the four nput varables have most strong effects on the predcted algae concentraton. Fg. 9 shows the algae map usng GAOT model. In Table IV, the result ndcates that the CC = 0.83 for tranng set and CC = for testng set of GAOT s better than of LN (LR) and smlar to BPNN. GAOT was found better than the tradtonal model for algae concentraton estmaton for both tranng and testng sets as ndcated by the hgher CC. In order to realze the performances of LN (LR), BPNN and GAOT, ther dagrams are depcted and compared wth each other. The horzontal axs s the actual value of algae, and the vertcal axs s the predcted value of algae. Fg. 9 shows that the predcted values for GAOT are closer to deal lne (45 ) than LN (LR) model, Fg. 6. Predcted Value Tranng Testng Actual Value Fg. 9. Tawan reservor algae concentraton-gaot. IV. CONCLUSION Ths paper demonstrate the possbltes of adoptng GAOT method coupled wth the GA and OT to predct the algae concentraton of Tawan reservor by Landsat sensor data data. GAOT deals wth data to generate a fttest mathematcal equaton. Few sgnfcant varables can be chosen from all nput varables automatcally. The result shows that GAOT used real number codng as an effcent and robust model. It shows although the use of the GAOT was not smple as LN transform lnear regresson, t provded an approprate model to predct reservor algae usng the four nput varables. The response fgure demonstrates that the relatonshp between predcted algae and actual algae generated by GAOT was reasonable. The result of ths case study ndcates that the CC = 0.83 for tranng data, and CC =0. 82 for testng data of GAOT are better than those of LN (LR) (CC = 0.63 for tranng data, and CC = 0.25 for testng data), and smlar to BPNN (CC = 0.85 for tranng data, and CC = 0.81 for testng data) as shown n Table 4. The results confrms that GAOT would be the better opton than LN (LR) because t models algae concentraton wthout the lmtaton of lnear property whch LN (LR), and another method cannot conquer. The current study shows a successful applcaton of GAOT on algae montorng. Because ths method s flexble and possbly appled to other data sets, a more complex equaton ncludng more avalable varables can be acheved. Further studes can be expanded to analyze the other water qualty parameters as addtonal nput varables for lakes, rvers, seas, reservors and oceans. REFERENCES [1] J. K. Kshore, L. M. Patnak, V. Man, and V. K. 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7 parameter retreval algorthms for estmatng total suspended solds and chlorophyll-a concentraton usng landsat-8 magery at poteran sland water, n Proc Internatonal Geonformaton Conference, [20] M. Mtchell, An Introducton to Genetc Algorthms, Massachusetts: MIT Press, [21] Z. Mchalewcz, Genetc Algorthms + Data Structures = Evoluton Programs, New York: Sprnger-Verlag, [22] L. Len, I. Yeh and M. Cheng, Modelng strength of hgh performance concrete usng genetc algorthms and operaton tree, Journal of technology, vol. 21, no.1, pp.41 54, L Chen s a professor n the Department of Cvl Engneerng Department of Chung Hua Unversty n Tawan. Her current research nterests nclude envronmental mpact assessment, clmate change, water resources plannng, sol and water conservaton, remote sensng and artfcal ntellgence. Chh-Hung Tan s currently a courtesy assstant professor and a head of Department of Agrcultural Engneerng Research Center n Tawan. He has a PhD from Agrcultural and Bologcal Engneerng Department of Unversty of Florda. Hs expertse n Envronmental Scence, Waste Management, Irrgaton and Water resources. Basmah Alabbad dd her PhD n estmaton sea surface salnty by MODIS data n the Department of Cvl Engneerng at Chung Hua Unversty under the supervson of Prof. L Chen. Mohammad Jamal Mtlak Abualghanam s currently a PhD student at Cvl Engneerng Department n Chung Hua Unversty under the supervson of Prof. L Chen. Hs research algae estmaton n a reservor usng remote sensng data. 104